The area, in square inches, of the composite figure is: 112.125 square inches.
How to obtain the areaTo obtain the area in square inches of the composite figure, we can start by calculating the area of the rectangle to be
= length x width = 14 x 2
= 28 square inches
The leg length of 25 will be divided by 2 to give 12.5. Next we find the area of the isosceles right triangle as follows:
= (leg length)^2 / 2 = (12.5)^2 / 2 = 78.125 square inches.
The combined area = Area of rectangle + Area of isosceles right triangle
= 28 + 78.125
= 106.125 square inches
So, the area of isosceles triangle = (base x height) / 2
= (4 x 3) / 2
= 6 square inches
Now we can add up the areas of the individual shapes to find the total area of the composite figure:
Total area = Combined area + Area of isosceles triangle
= 106.125 + 6
= 112.125 square inches
Complete Question:
Find the area, in square inches, of the composite figure. A composite figure consisting of an isosceles right triangle, a rectangle, and an another isosceles triangle. The combined length of the right triangle and the rectangle is 25 inches. The length of only the rectangle is 14 inches. The base of the other isosceles triangle, which is the same as the width of the rectangle, is 2 inches plus 2 inches, and the height of the isosceles triangle is 3 inches
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Question 7
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Question 8
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Question 9
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
The number of people that prefer mustard is 900 and the graphical representation of a datasets are box plots & circle graphs
Interpreting the histogramThe histogram is not given and the data represented on the histogram are not properly presented
This means that the histogram cannot be interpreted
Predicting the number of hotdogsHere, we have
Ketchup = 63
Mustard = 27
Chili = 60
So, we have
Mustard = 27/(63 + 27 + 60) * 5000
Evaluate
Mustard = 900
This means that 900 people prefer mustard
The graphical representation of a datasetGiven that
Data = Milligrams of Vitamin C from 100 different gummy vitamins sold
This data can be represented using a box plot because the five-summary data can be easily identified from the dataset
From the five-summary, the median can be derived
The graphical representation of a datasetIn this case, the graph to use is a circle graph
This is so because the circle graph would show the proportion of the student's preferences
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A clothing store has each customer spin this spinner to reveal a discount. Even numbers get 20% off and odd numbers get 15% off. The pointer lands on an even number 135 times out of 250 spins
The average discount that is obtained by spinning the spinner is 17.7%.
Let, the probability of landing on an even number is denoted by P(E) and the probability of landing on an odd number is denoted by P(O).
We have that the pointer lands on an even number 135 times out of 250 spins.
So, the probability that is of landing on an even number is:
P(E) = Number of times the pointer lands on an even number / Total number of spins
P(E) = 135 / 250
Since, we have the sum of probabilities of all possible outcomes must be 1, we can find the probability of landing on an odd number as follows:
P(O) = 1 - P(E)
P(O) = 1 - (135 / 250)
Now, we know that even numbers get 20% off, and odd numbers get 15% off.
We find the average discount considering these probabilities:
Average Discount = (P(E) * 20%) + (P(O) * 15%)
Average Discount = (135 / 250) * 20% + [1 - (135 / 250)] * 15%
Now, let's perform the calculations:
Average Discount = (135 / 250) * 0.20 + [1 - (135 / 250)] * 0.15
Average Discount = 0.108 + (1 - 0.54) * 0.15
Average Discount = 0.108 + 0.46 * 0.15
Average Discount = 0.108 + 0.069
Average Discount = 0.177
So, the average discount that is obtained by spinning the spinner is 17.7%.
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complete question:
A clothing store has each customer spin this spinner to reveal a discount. Even numbers get 20% off and odd numbers get 15% off. The pointer lands on an even number 135 times out of 250 spins. find the average discount obtained by spinning the spinner?
Ann fills her water bottle with 1 liter of water before school. She sets a goal to drink all of the water by the end of the school day. To stay on track, she drinks the same amount of water each hour for 8 hours. How many milliliters of water does Ann drink each hour?
Ann drinks 125 milliliters of water each hour to stay on track and finish her 1-liter water bottle by the end of the school day.
To solve this problem, we first need to convert the given volume of water from liters to milliliters since milliliters are a more appropriate unit of measurement for the amount of water that Ann drinks each hour.
1 liter = 1000 milliliters
Therefore, Ann drinks 1000 milliliters of water in total for the day.
To find out how many milliliters of water Ann drinks each hour, we can divide the total amount of water by the number of hours she drinks it for.
1000 milliliters / 8 hours = 125 milliliters per hour
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PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
it's the first one. I
n my thinking
linda has one square rug and two identical rectangular rugs. she arranged them in two different ways and took two measurements as shown below. what is the side length of the square rug?
Answer: Let the side length of the square rug be x, and the dimensions of the rectangular rug be l and w.
In the first arrangement, the three rugs are arranged side by side, with the rectangular rugs aligned vertically and the square rug aligned horizontally. The length of this arrangement is l + 2x, and the width is w. We know that the length is 3 times the width, so we can write:
l + 2x = 3w
In the second arrangement, the two rectangular rugs are arranged side by side, with the square rug placed on top. The length of this arrangement is l, and the width is w + x. We know that the length is twice the width, so we can write:
l = 2(w + x)
We now have two equations with two unknowns, l and w:
l + 2x = 3w
l = 2(w + x)
Substituting the second equation into the first, we get:
2(w + x) + 2x = 3w
4x = w
Substituting this value of w into the second equation, we get:
l = 2(4x) = 8x
So the dimensions of the rectangular rug are 4x by x, and the dimensions of the square rug are x by x.
To find the value of x, we use the measurements given in the diagram:
l + 2x = 60
l = 36
Substituting into the equation l = 2(w + x), we get:
36 = 2(4x + x)
36 = 10x
x = 3.6
So the side length of the square rug is 3.6 feet.
Step-by-step explanation:
Suzy is shooting basketballs at Bob’s Gym. She makes 9 field goals. After 10 minutes, her friend Joshua joins her. They shoot basketballs together for another 20 minutes.
a. Write an expression for the total number of field goals Suzy and Joshua make during the 30 minutes they spend at the gym. Be sure to define the variable used in the expression.
b. Altogether, Suzy and Joshua made 27 goals. Use the expression you created to determine the number of field goals they made in the last 20 minutes. Explain your thinking.
The second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.
what is expression ?An expression is a grouping of figures, symbols, and algebra (such as addition, reduction, multiply, and division) that expresses a value. Variables, that are symbols for unknowable values, are symbols that can be included in expressions. The statement can be evaluated to give a specific value after the contents of the variables are assigned. An expression using a variable x, for instance, is 3x + 5. When we give x a number of 2, the expression is evaluated to: 3(2) + 5 = 6 + 5 = 11 . As a result, the expression's value at x = 2 is 11.
given
a. Assume that "S" represents the number of field goals Suzy scores each minute and "J" represents the number of field goals Joshua scores each minute.
The calculation for the total number of field goals Suzy and Joshua score in their 30-minute workout is as follows:
[tex]Field goals total = (9 + 10 S) + (20 (S + J)[/tex]
The first term (9 + 10S) denotes Suzy's total number of field goals in the first 10 minutes, while the second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.
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3. The horizontal distance "d" of the tip of a pendulum from its
vertical position at rest can be represented by a sinusoidal function.
The tip of the pendulum has a maximum displacement of 7.5 inches
and completes one cycle in 3.1 sec. Assume that the pendulum is at
rest at t= 0 and swings forward first.
Determine the value of y when t = 3.1 s:_
Approximate the value of t when y = 4 for the second time:
The second time that d = 4 is approximately 2.275 seconds after the pendulum starts swinging forward from its vertical position at rest.
What is the sinusoidal function?
A sinusoidal function is a mathematical function that describes a repetitive oscillation that resembles a sine or cosine wave. It can be expressed in the general form:
f(x) = A sin (Bx + C) + D
We can use the general form of a sinusoidal function to model the horizontal distance "d" of the tip of the pendulum from its vertical position at rest:
d = A sin(ωt + φ) + C
where:
A = amplitude (maximum displacement) = 7.5 inches
ω = angular frequency = (2π)/T, where T is the period = 3.1 seconds
φ = phase shift (initial horizontal displacement) = 0 (since the pendulum is at rest at t=0)
C = vertical displacement = 0 (since the pendulum is at rest at its vertical position)
Plugging in the given values, we get:
d = 7.5 sin((2π/3.1)t)
Now we can use this equation to answer the given questions:
Determine the value of d when t = 3.1 s:
We simply plug in t = 3.1 into the equation:
d = 7.5 sin((2π/3.1)(3.1))
d = 7.5 sin(2π)
d = 0 inches
Therefore, when t = 3.1 seconds, the horizontal distance of the tip of the pendulum from its vertical position is 0 inches.
Approximate the value of t when d = 4 for the second time:
To find when d = 4 for the second time, we need to find the two values of t for which the sinusoidal function equals 4. We can use the fact that the sine function repeats itself every 2π radians to solve this problem.
First, we find the period of the sinusoidal function:
T = 2π/ω = 2π/(2π/3.1) = 3.1 seconds
Next, we find the time it takes for the function to complete half a cycle, or π radians:
t1 = (π/ω) + kT, where k is an integer
t1 = (π/(2π/3.1)) + k(3.1)
t1 = (3.1/2) + 3.1k
We want to find the second time that d = 4, so we need to find the smallest integer value of k for which t2 > t1, where t2 is the time when d = 4 for the second time.
t2 = (3π/ω) + kT
t2 = (3π/(2π/3.1)) + k(3.1)
t2 = (9.3/2) + 3.1k
We want to find the smallest integer value of k such that t2 > t1 and d = 4:
7.5 sin((2π/3.1)t1) = 4
7.5 sin((2π/3.1)t2) = 4
calculating
t1 ≈ 0.604 s
t2 ≈ 2.275 s
Therefore, the second time that d = 4 is approximately 2.275 seconds after the pendulum starts swinging forward from its vertical position at rest.
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If a line with slope 4 has one point of intersection with the quadratic function y =
x² + 2x − 8, what is the y-intercept of the line?
-
4
a. 10
b.
-10
c. 4
d. -8
The y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.
What is the y-intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis.
This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.
These points satisfy x = 0 because of this.
When the line touches the y-axis, it forms a y-intercept.
Find the y when x = 0 to find these.
When the line touches the x-axis, the position for the y-intercept will look like (0,y).
So, have the given quadratic function:
y = x² + 2x − 8
Now, plot the given quadratic function on the graph:
(Refer to the graph attached below)
As we can see that the y-intercept is -4.
Therefore, the y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.
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If a line with slope 4 has one point of intersection with the quadratic function y = x² + 2x − 8, what is the y-intercept of the line?
a. -4
b. 10
c.-10
d. 4
e. -8
3. Find the area of the shape below. Break
the larger shape into smaller pieces if needed.
8.4m
4m
11.4m
8m
ak direst
boyut ved FI
The total area of the given figure is 85.2m² respectively.
What is the area?The quantity of unit squares that cover a closed figure's surface is its area.
Square units like cm² and m² are used to measure area.
A shape's area is a two-dimensional measurement.
The space inside the perimeter or limit of a closed shape is referred to as the "area".
Area of rectangle one:
= l*b
= 4*11.4
= 45.6m²
Area of rectangle second:
= l*b
= 4*8.4
= 33.6m²
Area of the triangle:
= 1/2*b*h
= 1/2*4*(11.4-8.4)
= 1/2*4*3
= 2*3
= 6m²
Total area of the figure: 45.6 + 33.6 + 6 = 85.2m²
Therefore, the total area of the given figure is 85.2m² respectively.
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What is the area, in square centimeters, of an 8.5 inch by 11 inch sheet of paper?A) 94 cm2 B) 240 cm2 C) 420 cm2 D) 6.0 × 102 cm2 E) 1.2 × 104 cm2
The square of the centimeter of the area is calculated by the square of the centimeter. The area of the rectangle is calculated by the formula width x length. So the rectangles area is 94cm
Squares have only one side that is squared to find the area of the shape. But in rectangle there will be two sides given that width and length of the shape. So to find the area the width and the length of the rectangle is given so the numerical must be multiplied. In the given question the width of the rectangle is 8.5 and the length of the rectangle is 11.
o the area of the rectangle can be found by the formula= w x l
=8.5 x 11
=93.5
approximately can be taken as 94 cm.
A rectangle can is a four sided shape that includes the length, width and height and that opposites sides are equal in the rectangle. The adjacent sides of the rectangle is perpendicular and the angle is right angle that is it is measured as 90 degree. A rectangle can be a parallelogram but parallelogram can not be equal to the rectangle.
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The question has an area because the square because the square has only one side and the area of the square can be found by squaring one side of square. So the actual question should be What is the area, in rectangle centimeters, of an 8.5 inch by 11 inch sheet of paper?
How do I go about solving this? (Teacher got sick mid-lesson & still wanted us to finish the worksheet but he never went over how to solve this kind of equation) Any kind of help is greatly appreciated.
[tex]g(a) = 4a-2\\h(a) = 3a\\Find: g(h(8))[/tex]
The composite function g(h(8)) when evaluated is 94.
Evaluating the composite functionsFrom the question, we have the following parameters that can be used in our computation:
g(a) = 4a - 2
h(a) = 3a
To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.
h(a) is defined as 3a, so h(8) = 3(8) = 24.
Now we can plug in 24 for a in g(a) and simplify:
g(a) = 4a - 2
g(h(8)) = g(24) = 4(24) - 2 = 94
Therefore, g(h(8)) = 94.
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g A region is prone to flooding once every 20 years. If the probability of flooding in that region any one year is >o. What is the probabilit, of not flooding the next year
As the probability of flooding any given year is 0.05, the probability of not flooding in the next year is 0.95 or 95%.
The probability of flooding in a region once every 20 years means that the probability of flooding any given year is 1/20 or 0.05.
Given that the probability of flooding in any one year is greater than zero, we know that the probability of not flooding is less than 1.
To find the probability of not flooding the next year, we need to use the complement rule, which states that the probability of an event occurring plus the probability of that event not occurring equals 1. Therefore, the probability of not flooding the next year is 1 - the probability of flooding in the next year. Since the probability of flooding any given year is 0.05, the probability of not flooding in the next year is 1 - 0.05 = 0.95 or 95%. This means that there is a 95% chance that the region will not experience flooding in the next year.However, it's important to note that this probability only holds true if the assumption that the region is prone to flooding once every 20 years remains constant. If there are any changes in the weather patterns or the region's geography, the probability of flooding can change.Know more about the the probability
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Graph y+6=4/5(x+3) using the point and slope given in the equation.
Use the line tool and select two points on the line.
Answer:
Plot (-3, -6). From this point, go up 4 units, then right 5 units, to (2, -2). Plot (2, -2), and then draw a line that goes through these two points.
how many centimeters
Answer:
[tex].28(22) + 3 = 9.16[/tex]
The predicted width of a foot with a length of 22 centimeters is 9.16 centimeters.
Solve the equation. Round to the nearest tenth if necessary. 196=n^2
Answer:
10
Step-by-step explanation:
For incoming freshman at BYU, ACT scores are Normally distributed with a mean of 28 and a standard deviation of 2. How many standard deviations away from the mean is an ACT score of 31?
Answer:
To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:
z = (x - μ) / σ
Where:
x = ACT score of 31
μ = mean of ACT scores (28)
σ = standard deviation of ACT scores (2)
z = number of standard deviations away from the mean
Substituting the values, we get:
z = (31 - 28) / 2
z = 1.5
Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.
Choose ALL answers that describe the quadrilateral below.
All answers that describe the quadrilateral are parallelogram and rhombus.
How is the diagram a rhombus and parallelogram?In the diagram provided as seen from online sources, the lines, BO=OD and this equals x. Next, SO=OC which equals s. Since the diagonals bisect each other, we can refer to this as a parallelogram.
Next, angle ABO equals angle ADO and since the opposite sides are parallel and equal, we can also refer to the quadrilateral as a rhombus.
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in a two-way anova test, the sum of squares for factor a is based on the sum of the squared differences between the mean for each level of factor a and the
Grand mean of the response variable. In a two-way ANOVA (Analysis of Variance) test, the sum of squares for factor A (also called the "between-groups" sum of squares for factor A) measures the variation in the response variable that can be attributed to the levels of factor A.
Specifically, it measures the sum of the squared differences between the mean of each level of factor A and the grand mean of the response variable (which is the mean of all the observations across all levels of factor A and factor B).
Mathematically, the sum of squares for factor A can be expressed as:
SSA = ∑ni(ȳi.-ȳ..)²
where ni is the sample size of the i-th level of factor A, ȳi. is the mean of the i-th level of factor A, and ȳ.. is the grand mean of the response variable.
In other words, the sum of squares for factor A represents the variation in the response variable that is due to the differences between the means of the levels of factor A, after taking into account the overall mean of the response variable.
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In a two-way ANOVA test, the sum of squares for factor A is based on the sum of the squared differences between the mean for each level of factor A and the overall mean of the data.
This represents the variation in the data that can be attributed to the different levels of factor A.
The sum of squares for factor B is calculated in the same way, but for the levels of factor B instead.
The interaction term in the ANOVA represents the variation that cannot be explained by either factor A or factor B
alone, but is instead due to the combination of the two factors.
Overall, the ANOVA test allows us to determine if there are significant differences between the means of different
groups, and if these differences are due to the factors being tested or random chance.
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Cylinder M and cylinder N are similar. The radius of cylinder N is equal to its height, and the ratio of the height of cylinder N to the height of cylinder M is 5: 3. The surface area of cylinder N is 256m square feet greater than the surface area of cylinder M. Find the surface area of each cylinder,
The surface area of cylinder M is approximately 184.85 square feet, and the surface area of cylinder N is approximately 401.92 square feet.
How do we find the surface area of both cylinders?Let r_N and h_N be the radius and height of cylinder N, and r_M and h_M be the radius and height of cylinder M. We are given that the radius of cylinder N is equal to its height (rN = hN), and the ratio of the height of cylinder N to the height of cylinder M is 5 : 3.
So, we can write:
hN = rN
hN / hM = 5 / 3
The surface area formulas for cylinders M and N:
Surface Area (M) = 2πr_MhM + 2πr_M^2
Surface Area (N) = 2πrNhN + 2πrN^2
If Surface Area (N) = Surface Area (M) + 256
∴ 2πrNhN + 2πrN^2 = 2πrMhM + 2πrM^2 + 256
Combine like terms:
4πrN^2 = 2πrMhM + 2πrM^2 + 256
Divide both sides by 2π:
2rN^2 = rMhM + rM^2 + 128/π
Since hN = rN, we can write:
hM = (3/5)rN
Now substitute hM into equation
2rN^2 = rM((3/5)rN) + rM^2 + 128/π
2rN^2 = (3/5)rN x ((3/5)rN) + ((3/5)rN)^2 + 128/π
= 2rN^2 = (9/25)rN^2 + (9/25)rN^2 + 128/π
= 2rN^2 = (18/25)rN^2 + 128/π
rN = 5.64, hN = 5.64,
rM = 5.64 x (3/5) = 3.38
rM = 3.38.
let's calculate the surface areas:
Surface Area (M) = 2π(3.38)(3.38) + 2π(3.38)^2 ≈ 71.15 + 113.70 ≈ 184.85 square feet
Surface Area (N) = 2π(5.64)(5.64) + 2π(5.64)^2 ≈ 200.96 + 200.96 ≈ 401.92 square feet
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12. Look for Relationships In the graph of a
vertical motion model shown, how is the initial
velocity related to the vertex of the parabola?
The vertical component of the initial velocity will basically decide where the vertices will be. that is how the initial velocity is related to the vertex of the parabola.
Describe Parabola?A parabola is a symmetrical curve that is formed by the intersection of a plane and a cone, where the plane is parallel to one of the cone's generating lines. The shape of a parabola is similar to that of a U-shaped curve, but with a sharper curve near the bottom of the U.
The parabola has several important properties, including a focus and a directrix. The focus is a point on the axis of symmetry of the parabola that is equidistant from every point on the curve. The directrix is a line that is perpendicular to the axis of symmetry and is equidistant from every point on the curve.
The equation of a parabola in standard form is y = ax² + bx + c, where "a" determines the direction and shape of the parabola, "b" determines the horizontal shift of the parabola, and "c" determines the vertical shift of the parabola.
The initial velocity will have two component basically, a horizontal component and a vertical component. The vertical component will decide how high the object will go, or in other words the vertical component of the velocity will decide the position of the vertex of the parabolis path which the object is going to follow.
When the vertical component of the velocity becomes 0, the object will be at it's maximum height (i.e the object will be at the vertex of the parabola)
The vertical component of the initial velocity will basically decide where the verties will be. that is how the initial velocity is related to the vertex of the parabola.
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In each graphic, the triangle was dilated to create the image triangle. Determine which scale factor was used for each dilation by dragging the correct scale factor to each graph.
pls help me
The scale factor applied for each dilation are-
For ΔABC - scale factor = 2For ΔDEF - scale factor = 1/2For ΔGHJ - scale factor = 1/3For ΔKML - scale factor = 3Explain about the term scale factor :The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
The form will be smaller if the scaling factor is a fraction. Reduction is the term for this. Therefore, a scaling factor of 1/2 suggests that the fresh shape is equal to half of the old shape.
Part a: For ΔABC
Length AB = 2 units
Length A'B' = 4 units
A'B' = 2 *AB
Hence, For ΔABC - scale factor = 2
Part b: For ΔDEF -
Length DF = 2 units
Length D'F' = 1 units
D'F' = 1/2 DF
Hence, For ΔDEF - scale factor = 1/2
Part c: For ΔGHJ
Length GH = 3 units
Length G'H' = 1 units
G'H' = 1/3 GH
Hence, For ΔGHJ - scale factor = 1/3
Part d: For ΔKML -
Length KM = 2 units
Length K'M' = 6 units
K'M' = 3*KM
Hence, For ΔKML - scale factor = 3
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please answer correctly
The location of point P within line segment AB is (8.333, - 6.667).
How to find the coordinates of a point within a line segment
Herein we find the a line segment whose endpoints are A(x, y) = (10.2, - 6) and B(x, y) = (4.6, - 8), in which we must locate the point P. This can be done by following line segment AB:
P(x, y) = A(x, y) + (2 / 6) · [B(x, y) - A(x, y)]
P(x, y) = (10.2, - 6) + (2 / 6) · [(4.6, - 8) - (10.2, - 6)]
P(x, y) = (10.2, - 6) + (1 / 3) · (- 5.6, - 2)
P(x, y) = (10.2, - 6) + (- 1.867, - 0.667)
P(x, y) = (8.333, - 6.667)
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Plot and connect the points A (6, -7), B (1, -7), C (1, -4), D (3, -2), E (7. -2), F (7,-4), and find the length of AB.
OA. 6 units
O B.
7 units
O C.
5 units
D. 8 units
Using distance formula, the distance between AB is 5 units and the graph of the coordinates from A to F are attached below
What is the length of ABTo find the length of AB, we have to use distance formula which is given as
AB = √(x₂ - x₁)² + (y₂ - y₁)²
substituting the values into the equation;
AB = √(1 - 6)² + (-7 - (-7))²
AB = 5
The length of line AB is 5 units
To plot the points from A to F, we have to use a graphing calculator, input the points and draw all lines
Kindly find the attached graph of all the coordinates from A to F below
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units Answer:
5
Step-by-step explanation:
Phoenix Corp. reported the following information for 2013 and 2014.Interest payable, December 31, 2013 $5,700Interest payable, December 31, 2014 6,200Interest expense--2014 12,250How much cash was paid for interest during 2014?A. $11,750B. $12,250C. $12,500D. $12,750
Cash paid for interest during 2014 was $12,750. Based on the provided Phoenix Corp. information, the question requires you to calculate the cash paid for interest throughout the 2014 calendar year.
Also provided are the amounts for the year's interest expenditure and the balance of interest payable as of December 31, 2013 and 2014.
These are the formulas that can be used to determine the cash paid in interest in 2014:
Interest paid in 2014 minus any increases in interest due equals the cash paid in interest.
The difference between the balance of interest payable as of December 31, 2014, and as of December 31, 2013, can be used to compute the increase in interest payable:
Interest payable at December 31, 2014 minus interest payable at December 31, 2013 equals $6,200 minus $5,700, which equals $500 in
additional interest.
This signifies that the corporation incurred more interest expense than it paid during the year Since the balance of interest payable increased from 2013 to 2014, the corporation incurred more interest expense than it paid in that period. As a result, the money used to pay interest in 2014 is:
Interest paid in 2014 plus the increase in interest due is $12,250 plus $500.= $12,750
Thus, $12,750 is the correct response (D).
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What is the length of the hypotenuse? If necessary, round to the nearest tenth.
c=
feet
The length of the hypotenuse in the given right-angle triangle is 7.5 feet.
What is Pythagoras' theorem?According to Pythagoras' theorem, "the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides." Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case since it is opposite the angle of 90°.
It is a right-angle triangle.
[tex]c = \sqrt{6^{2} +4^{2} } \\c = \sqrt{36 + 16}\\ c = \sqrt{56}\\ c = 7.48[/tex]which is nearly equal to 7.5
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Complete question:
A(n) ______ design compares different independent variable levels by using homogeneous groups of experimental units.
A blocked design compares different independent variable levels by using homogeneous groups of experimental units.
In this type of experimental design, subjects are divided into homogeneous groups, or blocks, based on similar characteristics or traits. These blocks help to control or account for potential confounding variables that may affect the outcome of the experiment.
By grouping subjects into blocks, researchers can reduce the variability within each group and increase the accuracy of the experimental results. This allows for a more precise comparison of the effects of different levels of the independent variable on the dependent variable. Blocked designs are particularly useful when there are natural groupings within the experimental units or when the variability between units is high.
In summary, a blocked design is a powerful experimental tool that can help researchers account for potential confounding factors and reduce variability among experimental units. By doing so, it enables the accurate comparison of different levels of the independent variable, ultimately leading to more reliable and valid results.
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The rectangle below is dilated by a scale factor of 5. Find the perimeter and area of
the rectangle below, as well as the perimeter and area of the dilated rectangle. Figures
are not necessarily drawn to scale.
10
Perimeter of given rectangle
Area of given rectangle
Submit Answer
units
units²
Perimeter of dilated rectangle
Area of dilated rectangle
units
units2
Area of rectangle = 50 [tex]unit^2[/tex].
Perimeter of rectangle =30 unit.
Area of dilated rectangle = 1250 [tex]unit^2[/tex].
Perimeter of dilated rectangle = 150 unit.
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.
Here the given rectangle length l = 10 unit and width = 5 unit.
Now using formulas,
Area of rectangle = lw square unit.
=> A = 10*5 = 50 [tex]unit^2[/tex].
Perimeter of rectangle = 2(l+w) unit
=> P =2(10+5) = 2(15) = 30 unit.
Here scale factor= 5
The dilated rectangle length [tex]l_1[/tex]= 10*5 = 50 unit and
width [tex]w_1 = 5\times5 = 25[/tex] unit
Now area of dilated rectangle [tex]A_1[/tex]= [tex]l_1w_1[/tex] square unit.
=> [tex]A_1[/tex]= 50*25 = 1250 [tex]unit^2[/tex].
Perimeter of dilated rectangle [tex]P__1[/tex] = 2([tex]l_1+w_1)[/tex] unit.
=> [tex]P__1[/tex] = = 2(50+25) = 2(75) = 150 unit.
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I NEED HELP ON THIS ASAP!!
The values of the exponential function are calculated below and as x increases, the exponential function increases.
What are the values of the functionIn the table of function given, we can calculate the value of f(x) as it relates to x.
The given exponential function is ;
f(x) = 2ˣ
Substituting the values;
f(-4) = 2⁻⁴ = 1/2⁴ = 1/16
f(-3) = 2⁻³ = 1/2³ = 1/8
f(-2) = 2⁻² = 1/2² = 1/4
f(-1) = 2⁻¹ = 1/2
f(0) = 2⁻⁰ = 1/2⁰ = 1
As the value of x increases, the exponential function increases.
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The cost of 1 hat and 1 bag is £27.
The cost of 2 hats and 1 bag is £42.
(a) How much does 1 hat cost?
(b) How much does 1 bag cost?
Answer:
(a) 1 hat is $15
(b) 1 bag is $12
Step-by-step explanation:
1 hat at $15 + 1 bag at $12 is equal to $27
2 hats at $30 together + 1 bag at $12 is equal to $42
suppose that 8% of all bicycle racers use steroids, that a bicyclist who uses steroids tests positive for steroids 94% of the time, and that a bicyclist who does not use steroids tests positive for steroids 9% of the time. what is the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
The probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).
We can use Bayes' theorem to calculate the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids. Let A be the event that a randomly selected bicyclist uses steroids, and B be the event that a randomly selected bicyclist tests positive for steroids. Then, we want to find P(A|B), the probability that a bicyclist uses steroids given that they test positive for steroids:
P(A|B) = P(B|A) * P(A) / P(B)
where P(B|A) is the probability of testing positive given that the bicyclist uses steroids, P(A) is the prior probability of a bicyclist using steroids, and P(B) is the probability of testing positive for steroids.
We are given that P(A) = 0.08, P(B|A) = 0.94, and P(B|not A) = 0.09. We can calculate P(B) using the law of total probability:
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
= 0.94 * 0.08 + 0.09 * 0.92
= 0.0976
where P(not A) = 1 - P(A) = 0.92.
Substituting the values we have:
P(A|B) = 0.94 * 0.08 / 0.0976
= 0.763
Therefore, the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).
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