Step-by-step explanation:
We can use the formula for exponential growth to find the rate at which the sunfish gains mass:
M(t) = M(0) * e^(kt)
where:
M(0) = the initial mass of the sunfish (which we don't know)
k = the growth rate constant (which we also don't know yet)
t = the elapsed time since the sunfish was born (in days)
e = the mathematical constant approximately equal to 2.71828...
We are given the formula for M(t), which is:
M(t) = 4 * (81/49)^t
This means that M(0) = 4 * (81/49)^0 = 4.
To find the growth rate constant k, we can use the fact that the sunfish gains 2/7 of its mass every day. This means that the daily growth rate is 2/7 of the current mass. In other words, the daily growth rate is:
(2/7) * M(t)
We can relate this to the exponential growth formula by taking the derivative of M(t) with respect to t:
dM/dt = k * M(t)
Taking the derivative of M(t), we get:
dM/dt = ln(81/49) * 4 * (81/49)^t
Setting this equal to the daily growth rate, we get:
(2/7) * M(t) = ln(81/49) * 4 * (81/49)^t
Simplifying this expression, we get:
k = ln(81/49) * 4/7
Using a calculator, we can evaluate this expression to get:
k ≈ 0.0919
Therefore, the rate at which the sunfish gains mass is given by:
dM/dt = 0.0919 * M(t)
To find out how much mass the sunfish gains in one day, we can substitute M(t) = 4 * (81/49)^t into this formula and evaluate it at t = 1 (since we want to know the daily rate of change):
dM/dt = 0.0919 * 4 * (81/49)^1
dM/dt ≈ 0.54
This means that the sunfish gains 0.54 milligrams every day. To express this as a fraction of its mass, we can divide by the current mass:
(0.54/4) ≈ 0.1375
So the sunfish gains approximately 2/7 (or 0.2857) of its mass every 2.08 (or 7/2.54) days. Rounded to two decimal places, this is 0.14 or approximately 2/7 of its mass every 2.08 days.
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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HELP AGAIN LOL
Subtract.
(8h + 7) - (7h + 6)
The simplified form of the expression (8h + 7) - (7h + 6) is h + 1. We subtract this by using the distributive law.
What is an expression?An expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, etc.) that represents a mathematical quantity or value. Expressions can be simple, consisting of just a single number or variable, or they can be complex, involving multiple numbers, variables, and operations.
What is distributive law?The distributive law, also known as the distributive property or distributive property of multiplication over addition, is a fundamental property of arithmetic and algebra that allows the distribution of a multiplication operation over an addition or subtraction operation.
The distributive law states that for any three numbers a, b, and c:
a × (b + c) = (a × b) + (a × c)
According to the given information:
To subtract (8h + 7) - (7h + 6), we can use the distributive property of multiplication over addition to simplify the expression.
(8h + 7) - (7h + 6)
= 8h + 7 - 7h - 6 (Applying the distributive property)
Now, we can combine like terms by adding or subtracting coefficients of the same variable:
= (8h - 7h) + (7 - 6) (Grouping-like terms)
= h + 1 (Simplifying)
So, the simplified form of the expression (8h + 7) - (7h + 6) is h + 1.
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Carrington had a checking account balance of $800 at the
beginning of the month. She deposited $2,800 and used her debit
card for purchases of $310, $88, and $35.50. She also wrote
checks for $150 and $375.
What is her balance now?
Her current checking account balance is $2,641.50.
Account balance calculation.
To find Carrington's current checking account balance, we need to add up all the deposits and subtract all the withdrawals from her starting balance.
Starting balance = $800
Deposits = $2,800
Withdrawals = $310 + $88 + $35.50 + $150 + $375 = $958.50
Therefore, Carrington's current checking account balance is:
$800 + $2,800 - $958.50 = $2,641.50
Her current checking account balance is $2,641.50.
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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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How do you calculate the distance traveled by an object by first calculating when it is stopped?
To calculate the distance traveled by an object by first calculating when it is stopped, you need to follow these steps:
1. Identify the terms
2. Use the given information
3. Determine when the object is stopped
4. Calculate the distance traveled
Identify the terms:
For this question, we are focusing on distance, velocity, time, and acceleration. The object is stopped when its velocity is zero.
Use the given information:
Collect any given values such as initial velocity, final velocity, time, and acceleration.
Determine when the object is stopped:
To find out when the object is stopped, you'll need to use the equation v = u + at, where v is final velocity (0 m/s when stopped), u is initial velocity, a is acceleration, and t is time.
Solve for t (time) when the object is stopped: t = (v - u) / a.
Calculate the distance traveled:
Now that you have the time when the object is stopped, use one of the equations of motion to find the distance traveled.
We can use the equation s = ut + 0.5at²,
where s is the distance, u is initial velocity, t is the time when the object is stopped, and a is acceleration.
By following these steps and using the provided terms, you'll be able to calculate the distance traveled by an object by first calculating when it is stopped.
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PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
it's the first one. I
n my thinking
Solve the equation. Round to the nearest tenth if necessary. 196=n^2
Answer:
10
Step-by-step explanation:
It cost Chile 17. 70$ to send 177 text messages. How much would it cost to send 97 text message
The total cost of sending 97 text messages is $9.70
How to find the unit cost?A unit cost is defined as the total expenditure incurred by a specific company to produce, store, and sell one unit of a specific product or service. Unit costs are also synonymous with cost of goods sold (COGS). This accounting measure also involves all of the fixed and variable costs associated with the production of a good or service.
Now, we are told that It cost Chile 17.70$ to send 177 text messages. Thus:
Unit cost of message = 17.70/177 = $0.1 per message
Thus:
Cost of 97 text messages = 97 * 0.1 = $9.7
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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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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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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:
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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What is the area of this figure?
Enter your answer in the box.
The area of the irregular polygon is equal to 30.5 square units.
How to determine the area of a polygon
In this problem we find the representation of an irregular pentagon, that is, a polygon of five sides of different length. Whose area can be found by adding the areas of rectangles and triangles:
Rectangle
A = b · h
Triangle
A = 0.5 · b · h
Where:
A - Areab - Baseh - HeightNow we proceed to determine the area of the irregular polygon:
A = 0.5 · 1 · 4 + 0.5 · 3 · 2 + 2 · 4 + 0.5 · 3 · 2 + 3 · 4 + 0.5 · 5 · 1
A = 2 + 3 + 8 + 3 + 12 + 2.5
A = 30.5
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what is ordinary least squares (ols) method? in order for the ols method to produce best linear unbiased estimators (blue), what assumptions must be satisfied?
Ordinary Least Squares (OLS) is a method used to estimate the parameters of a linear regression model.
In OLS, the objective is to find the line that best fits the observed data by minimizing the sum of squared residuals between the predicted values of the dependent variable and the actual values.
To produce the Best Linear Unbiased Estimators (BLUE) in OLS, the following assumptions must be satisfied:
Linearity: The relationship between the dependent variable and the independent variables must be linear.
Independence: The observations must be independent of each other.
Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variables.
Normality: The residuals should be normally distributed.
No multicollinearity: The independent variables should not be highly correlated with each other.
If these assumptions are met, then OLS produces the BLUE, which means that the estimated coefficients are the best unbiased estimates of the true population parameters, and they have the smallest variance among all unbiased linear estimators.
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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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In 2011, the total number of cars produced in the world was 59.9 million.
In 2016, the total number of cars produced in the world was 21% greater than the total
number produced in 2011
In 2016, the total number of cars produced in the world was N million.
(b) Work out the value of N.
Give your answer correct to the nearest whole number.
In 2016, the total number of cars produced in the world was 72 million (rounded to the nearest whole number) by forming linear equation.
In 2011, the total number of cars produced in the world was 59.9 million.
In 2016, the total number of cars produced in the world was 21% greater than the total number produced in 2011.
Let us say in 2016 the total number of cars produced in the world was N million.
Therefore, by expressing the given problem in a linear equation we get,
Total number produced in 2016, N = 59.9 + (21% of 59.9 ) in millions
⇒ N = 59.9 + [tex][ \frac{21}{100} ] 59.9[/tex] ( in millions )
= 59.9 + 12.579 ( in millions )
= 72.479 ( in millions )
= 72 millions ( rounded to the nearest whole number)
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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 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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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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How do I rewrite the equation y=-2x^2+8x-5
Answer:
Y= (x+4)(x+4)-21
Step-by-step explanation:
If you are factoring It out:
Y=-2x^2+8x-5 is the same as Y= (x+4)(x+4)-21
Let me know if it is incorrect!
-a friendly 8th grader
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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Write the transformation matrix and the resultant matrix that will translate the triangle, (-2, 4), given the triangles vertices are at A(-1, 3), B(0, -4) and C(3, 3).
The new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:
|-3 -2 1 |
| 7 0 7 |
| 1 1 1 |
Define translationIn mathematics, a translation refers to a geometric transformation that moves every point in a figure or a space by the same distance in a given direction. In other words, it involves sliding a figure or a point to a new location without changing its size, shape, or orientation.
To translate the triangle by a vector (x, y), we use the following transformation matrix:
|1 0 x|
|0 1 y|
|0 0 1|
For the given triangle with vertices at A(-1, 3), B(0, -4), and C(3, 3), let's assume we want to translate it by a vector (−2, 4). Then the transformation matrix for translation is:
|1 0 -2|
|0 1 4 |
|0 0 1 |
To apply this transformation matrix to each vertex of the triangle, we represent the vertices as column vectors and multiply them by the matrix:
| -1 | | 1 0 -2 | | -3 |
| 3 | -> | 0 1 4 | = | 7 |
| 1 | | 0 0 1 | | 1 |
| 0 | | 1 0 -2 | | -2 |
| -4 | -> | 0 1 4 | = | 0 |
| 1 | | 0 0 1 | | 1 |
| 3 | | 1 0 -2 | | 1 |
| 3 | -> | 0 1 4 | = | 7 |
| 1 | | 0 0 1 | | 1 |
So, the new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:
|-3 -2 1 |
| 7 0 7 |
| 1 1 1 |
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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.
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?
7. The formula for the volume of
a cone is given by V=1/3 pi r²h,
where r is the radius of the base
and h is the height of the cone.
Solve the formula for h. Then find
the height of a cone with a volume
of 48 cm³ and a base with a radius
of 4 cm.
The height of the cone is approximately 1.5 cm.
What is a cone?Both a cone and a cylinder have circular bottoms and are three-dimensional shapes. The lateral surfaces of the two shapes differ most noticeably from one another. A cone has a lateral surface that tapers from a point at the apex to a circular base, whereas a cylinder has a curved lateral surface that is parallel to its base. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height, whereas the volume of a cone is calculated using V = (1/3)πr²h.
The volume of the cone is given as:
V = (1/3)πr²h
Rearranging the equation to isolate h we get:
3V = πr²h
h = (3V)/(πr²)
Now, for volume
of 48 cm³ and a base with a radius of 4 cm we have:
h = (3(48))/(π(4)²)
h ≈ 1.5 cm
Hence, the height of the cone is approximately 1.5 cm.
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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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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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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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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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