Yes, it is possible for the range of a data set of positive data values to be less than the mean of that data set.
How to find range of the data?The range of a data set is the difference between the maximum and minimum values in the data set, while the mean (also known as the average) of a data set is the sum of all the values divided by the total number of values.
For example, consider the following data set of positive values: {2, 3, 5, 7, 9}. The range of this data set is 9 - 2 = 7, while the mean is (2 + 3 + 5 + 7 + 9)/5 = 26/5 = 5.2. In this case, the range (7) is less than the mean (5.2).
This can occur when the data set has a relatively small range, meaning that the difference between the maximum and minimum values is not very large compared to the mean.
the distribution of the data set and the specific values within it can affect the relationship between the range and the mean.
It's important to note that range and mean are just two measures of central tendency and variability, and other measures such as median, mode, and standard deviation can provide additional insights into the characteristics of a data set.
therefore, Yes, it is possible for the range of a data set of positive data values to be less than the mean of that data set.
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In circle E with
m
∠
D
E
F
=
4
8
∘
m∠DEF=48
∘
and
D
E
=
6
DE=6, find the area of sector DEF. Round to the nearest hundredth
The area of sector DEF is 15.09 square units
How to find the area of sector DEF?The formula for area of a sector is:
A = (θ/360) * πr²
Where θ is the angle subtended at the center and r is the radius of the circle.
In this case, DE is the radius.
Thus r = 6 cm and θ = 48°
Substituting:
A = (48/360) * π * 6²
A = (48/360) * (22/7) * 36
A = 15.09 square units
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Complete Question
Check image attached
If y=5/3+4 what’s Y and what slope would that make?
Answer: 5/3
Step-by-step explanation:
y = mx +b
m is equal to the slope
b is the y intercept
therefore, m or 5/3 is the slope.
The power of -1 to a function, or ((f^-1)(x)), means...
The power of -1 to a function, or [tex]((f^{-1})(x)),[/tex]represents the inverse function of f. In other words, if f(x) produces a certain output y, then the inverse function[tex]f^{-1}(y)[/tex]will produce the input x. It is important to note that not all functions have an inverse, and if they do, they may only be valid for certain inputs and outputs.
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f1. The inverse of f exists if and only if f is bijective.
[tex]((f^{-1})(x)),[/tex]
The inverse function of f is denoted by. For a function, its inverse admits an explicit description: it sends each element to the unique element such that f(x) = y1.
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Each statement can be represented with a fraction and a division expression. Move the correct fraction and division expression to each line.
There are 5 identical pieces cut from 3 feet of rope. The length, in feet, of each piece of rope is____ or ____
There are 2 muffins shared equally by 3 friends. The amount of muffin that each friend gets is ____ or ____
pls answer quick! I will give brainiest to whoever is right
Answer:
act back its also known as act or tactics
the graph of y=ex is transformed as showed in the graph below. Which equation represents the transformed function?
The transformed function [tex]y =e^x + 3[/tex] by shifting the graph of [tex]y =e^x[/tex] upwards with 3 units as per given graph.
What is a transformation?A transformation in a graph is a function that maps each point in the original graph to a corresponding point in a new graph.
According to the graph it shows that there is transformation to 3 unit upwards.
To transform the equation [tex]y =e^x[/tex] to [tex]y =e^x + 3[/tex] , we can add 3 to both sides of the given equation:
[tex]y+3 =e^x + 3[/tex]
So the equation [tex]y = e^x + 3[/tex] is the transformed version of [tex]y = e^x[/tex] Geometrically, this transformation shifts the graph of [tex]y = e^x[/tex] upwards by 3 units, while maintaining its shape and curvature. This means that it will intersect the y-axis at the point (0, 3) and will never touch the x-axis.
In summary, the transformed function [tex]y = e^x + 3[/tex] by shifting the graph of [tex]y = e^x[/tex] upwards with 3 units.
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URGENT - Will also give brainliest to simple answer
Answer:
The answer for the Area is 8
Step-by-step explanation:
Area of semi circle =1/2pir²
r=d/2=8/2=4
A=1/2×4²
A=1/2×4×4
A=2×4
A=8
Answer:
32 or 100.53
Step-by-step explanation:
*assuming 8 is radius and not diameter*
A = [tex]r^{2}[/tex]
r = 8
[tex]8^{2} = 64[/tex]
A = 64 or ≈201.062
divide by 2 for half of the circle
32 or 100.53
Q1: Use simple exponential smoothing with a = 0.75 to forecast the water pumps sales for February through May. Assume that the forecast for January was for 25 units. [4 marks) Month January February March April Air-condition sales 28 72 98 126
Therefore, using simple exponential smoothing with a = 0.75, the forecast for water pump sales for February through May are:- February: 26.5 units, March: 37.63 units, April: 72.66 units.
To use simple exponential smoothing with a = 0.75, we first need to calculate the forecast for January:
F1 = 25 (given)
Next, we calculate the forecast for February using the formula:
F2 = a * Y1 + (1 - a) * F1
F2 = 0.75 * 28 + 0.25 * 25
F2 = 26.5 (rounded to one decimal place)
We repeat this process for each month, using the previous month's forecast and the actual sales data for the current month. The results are as follows:
Month Actual Sales Forecast
-------------------------------------
January 28 25
February 72 26.5
March 98 37.63
April 126 72.66
- May: 101.17 units
Hi, I'd be happy to help you with your question. To use simple exponential smoothing with a smoothing constant α = 0.75 to forecast the water pump sales for February through May, given that the forecast for January was 25 units, follow these steps:
Step 1: Start with the given forecast for January, which is 25 units.
Step 2: Calculate the forecast for February using the formula:
Forecast_February = α * (Actual_January) + (1 - α) * Forecast_January
Step 3: Calculate the forecast for March using the formula:
Forecast_March = α * (Actual_February) + (1 - α) * Forecast_February
Step 4: Calculate the forecast for April using the formula:
Forecast_April = α * (Actual_March) + (1 - α) * Forecast_March
Step 5: Calculate the forecast for May using the formula:
Forecast_May = α * (Actual_April) + (1 - α) * Forecast_April
Please note that you have provided sales data for air-conditioning sales, but the question is about water pump sales. If you meant to ask about air-conditioning sales, you can use the given sales data to calculate the forecasts for February through May. If you need help with water pump sales, please provide the correct sales data for January through April, and I will gladly help you with the calculations.
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Select all the sets of transformations that result in the same image when performed in any order.
The sets of transformations that result in the same image when performed in any order are:
Translation, dilation with center (0,0)
Two translations
What is transformation?In mathematics, a transformation refers to a process that changes the size, shape, position, or orientation of a geometric figure or an object in a coordinate plane or space. There are several types of transformations, such as translation, rotation, reflection, and dilation, which are used to alter the original figure to create a new one that is similar or congruent to the original. Transformations are used in geometry, algebra, and other branches of mathematics to study and understand various properties of geometric shapes and objects.
Here,
For the first set, if we perform a translation followed by a dilation with center (0,0), the result will be the same as if we perform the dilation first followed by the translation. This is because the dilation does not change the direction of the translation, and the center of dilation is at the origin, so the translation is unaffected.
For the second set, any two translations can be combined to form a single translation, so the order in which they are performed does not matter.
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Use a linear regression algorithm to determine the equation for the line of best fit for the data in the table.
a. Identify the correlation coefficient.
b. What type of correlation exists for the data?
a. The correlation coefficient: ≈ -0.184
b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'
How to solve
To find the line of best fit using a linear regression algorithm, we need to find the slope (m) and y-intercept (b) of the equation in the form y = mx + b.
We will start by calculating some statistics from the given data.
First, let's find the means of x and y:
x_mean = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 9 = 45 / 9 = 5
y_mean = (8 + 4.037 + 7.200 + 4.180 + 4.763 + 1 + 1.047 + 2.436 + 1.844) / 9 ≈ 34.507 / 9 ≈ 3.834
Next, we need to find the sum of the product of the differences between each point and the mean for both x and y:
Σ((x - x_mean) * (y - y_mean)) = (1 - 5) * (8 - 3.834) + (2 - 5) * (4.037 - 3.834) + ... + (9 - 5) * (1.844 - 3.834) ≈ -8.311
We also need to find the sum of the squared differences between each x and the mean of x:
Σ((x - x_mean)^2) = (1 - 5)^2 + (2 - 5)^2 + ... + (9 - 5)^2 = 60
Now, we can calculate the slope (m):
m = Σ((x - x_mean) * (y - y_mean)) / Σ((x - x_mean)^2) ≈ -8.311 / 60 ≈ -0.1385
To find the y-intercept (b), use the formula:
b = y_mean - m * x_mean ≈ 3.834 - (-0.1385) * 5 ≈ 4.525
Now we have the line of best fit equation:
y = -0.1385x + 4.525
a. To find the correlation coefficient (r), we need to divide the covariance of x and y by the product of the standard deviations of x and y.
First, let's find the covariance:
cov(x, y) = Σ((x - x_mean) * (y - y_mean)) / (n - 1) ≈ -8.311 / 8 ≈ -1.039
Next, find the standard deviations of x and y:
sd_x = sqrt(Σ((x - x_mean)^2) / (n - 1)) = sqrt(60 / 8) ≈ 2.738
sd_y = sqrt(Σ((y - y_mean)^2) / (n - 1))
sd_y = sqrt((8 - 3.834)^2 + (4.037 - 3.834)^2 + ... + (1.844 - 3.834)^2) / 8 ≈ sqrt(33.904) / 8 ≈ sqrt(4.238) ≈ 2.058
Now we can calculate the correlation coefficient:
r = cov(x, y) / (sd_x * sd_y) ≈ -1.039 / (2.738 * 2.058) ≈ -0.184
b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'
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10-
9
8
7
6
654321
AJ
B
1 2 3 4 5 6 7 8 9 10
a) What are the coordinates of A?
b) What are the coordinates of B?
X
The coordinates of B when it is given that A(5,-2) and M(12,6) is (29, 14).
How to find the coordinatesIf M is the mid-point of line segment AB, and the coordinates of A = (5,-2) while the coordinates of B = (12,6), then the coordinates of M = (8.5,2), which is what you stated that you got.
You are provided with M = (12,6) so you need to identify the coordinates of B. So, just ask yourself how did I get from A to M ? The answer is move 7 right and 8 up since 5 + 7 = 12 while -2 + 8 = 6. All you have to do is add 7 more to the x-value and 8 more to the y-value to obtain the correct answer of (19,14).
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Find the coordinates of B when it is given that A(5,-2) and M(12,6),
Divide the sum of 13/5 and -12/7 by their difference
Answer to these fraction is 31/151
Describe fraction.
Any numerical value that is not a whole number is referred to as a fraction. It symbolizes a portion of something or several portions of something. The numerator and the denominator are the two components of a fraction. The denominator indicates how many equally sized pieces make up a whole, whereas the numerator indicates how many equally sized parts are picked from the whole or collection.
To divide a fraction, all you need to do is flip its numerator and denominator, multiply the outcome by the other fraction, and simplify1.
In light of this, we have:
SUM:
(13/5) + (-12/7) = (13× 7 + -12 ×5) / (5 ×7)
= (91 - 60) / 35 = 31/35
DIFFERENCE:
(13/5) - (-12/7) = (13× 7 - -12× 5) / (5× 7)
= (91 + 60) / 35 = 151/35
Dividing these two fractions:
(31/35) ÷ (151/35) = (31/35)×(35/151) = 31/151
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One cubic foot of a chemical weighs 50 pounds. How many pounds of the chemical can a container with the dimensions shown hold?
The container can contains 3,000 pounds of chemicals.
How many pounds can the container hold?One cubic foot of a chemical weighs 50 pounds which means 1 ft³ of chemical = 60 pounds
We must find how many pounds in the container whose dimension 6 ft, 4 ft and 2.5 ft. So, the l = 6 ft, b = 4 ft and h = 2.5 ft.
Volume of box = L*B*H
Volume of box = 6 x 4 x 2.5
Volume of box = 60 ft³
From 1 ft³ of chemical = 60 pounds; then, the 50 ft³ of chemical will be:
= 50 x 60
= 3,000 pounds
Full question "One cubic foot of a chemical weighs 60 pounds. How many pounds of the chemical can a container with the dimensions shown hold? The base is 6, the width is 4, and the height is 2.5"
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2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
a
AC and BD are the diagonals of the MNOP, the diagonals of the rectangle MNOP bisect each other and are congruent.
What is a rectangle and its properties?
A rectangle and a rectangle are quadrilaterals that share the following properties: Opposite sides are equal. Two diagonals are the same length. It has two class 2 reflection symmetries and a rotational symmetry (through 180°). To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following proof:
Proof:
Let MNOP be a rectangle whose diagonal MO and diagonal NP intersect at Q.
First we show that the diagonals bisect each other. Since MNOP is a rectangle, we know that opposite sides are parallel and congruent. Therefore, we can draw segment MP and segment NO which are both parallel and congruent to each other.
Now consider the triangle MON. Since segment MP is parallel to segment NO, we know that angles MNO and MON are alternate interior angles and are congruent. Similarly, the angles NMO and ONM are also congruent. Therefore, triangle MON is an isosceles triangle with legs MO and NO. This means that the height drawn from Q to the side MN (which is the perpendicular bisector of MO and NO) bisects MO and NO. Similarly, the height drawn from Q to the side OP bisects OP. Therefore we have shown that the diagonals of a rectangle bisect each other.
Next, we show that the diagonals are congruent. Since MNOP is a rectangle, we know that opposite sides are parallel and congruent. Therefore, MP is compatible with NO and MO is compatible with NP. Using the fact that the diagonals bisect each other, we can write:
MQ = QO (because the height drawn by Q to the side MN divides MO and NO)
and
NQ = QP (because the height drawn from Q to the side OP divides NP and MO)
Combining these two equations, we get:
MQ + NQ = QO + QP
But we also know that MO is NP-consistent, so we can substitute:
MQ+ NQ = MO + MO
Simplification:
MQ + NQ = 2MO
Therefore, we have shown that the diagonals of a rectangle are congruent. Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent as necessary.
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Jason is making 30 sundaes with mint, chocolate, and vanilla ice cream. 1/5 of the sundaes are mint ice cream and 1/2 of the remaining sundaes are chocolate. The rest will be vanilla. How many sundaes will be vanilla?
Hi
1/5 is mint : so 30*1/5 = 6
1/2 of what remain is chocolate : which mean (30-6) /2 = 24/2 = 12
So vanilla will be : 30-6-12 = 30-18 = 12
recap : 6 mint, 12 chocolate and 12 vanilla.
Help please!!!
It would be much appreciated! <3
Workout of the fastest person's total time is 2 minutes 34 seconds.
What about time?Time is a concept used to describe the sequence and duration of events or changes that occur in the universe. It is a measure of the interval between two events or occurrences, and it allows us to describe and understand the order and duration of events.
In physics, time is often described as a dimension, along with the three spatial dimensions, and is often measured in units such as seconds, minutes, or hours. Time is also relative, meaning that its perception and measurement can vary depending on factors such as motion and gravity.
Overall, time is a fundamental concept in many fields, including physics, philosophy, and everyday life, and its study and understanding are crucial to our understanding of the world around us.
According to the given information:
From the given table we can observe that Ben is the fastest
Total time =53.44 + 49.79+ 50.50
= 153.73 seconds.
Hence, total time = 2 minutes 34 seconds
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RIGHT ANSWER GETS BRAINLIEST POINTS AND 15 POINTS. Fill in the blanks with greater or less
Answer: The mean of data set K is greater than the mean of data set L.
The median of data set K is greater than the median of data set L
Step-by-step explanation:
we need to calculate the mean (average) of each data set and compare them.
Mean of data set K = (28 + 145 + 112 + 57 + 130) / 5 = 112.4
Mean of data set L = (141 + 171 + 68 + 124 + 43) / 5 = 109.4
'Arranging the values in data set K in ascending order, we get:
28, 57, 112, 130, 145
The median of data set K is the middle value, which is 112.
The mean of data set L is 109.4.
GIVING 50 POINTS, BRAINLYEST, 5 STARS, AND THANKS IF YOU ANSWER CORRECTLY!!!
A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads. (2 points)
Part B: Flip a coin 15 times and record the frequency of each outcome. (4 points)
Part C: Determine the experimental probability of landing on heads. (4 points)
Part D: Compare the theoretical and experimental probabilities. Explain your answer. (2 points)
Answer:
Part A: 1/2 or 0.5
Part B: heads is 8, tails is 7.
Part C: 8/15 or 0.533.
Part D: The theoretical and experimental probabilities are close but not exactly the same. This is because the theoretical probability is based on an ideal situation where the coin is fair, and the outcomes are equally likely. The experimental probability is based on actual data that may vary due to chance or other factors. The more trials we perform, the closer the experimental probability will get to the theoretical probability. It's like when you practice a skill and get better at it over time, but you still make mistakes sometimes.
Step-by-step explanation:
Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. This is because there are two possible outcomes (heads or tails) and only one favorable outcome (heads). This is also the same probability of me winning the lottery, finding a unicorn, or getting a date.
\(∘-∘)/ <-------- single pringle
Part B: I flipped a coin 15 times and got the following results:
H T H H T T H H T H T H T T H
or (in a more orderly fashion)
HHHHHHHH
TTTTTTT
The frequency of heads is 8 and the frequency of tails is 7. This means that I was slightly luckier than average, but not enough to make a difference. Maybe I should have used a different coin, or a different hand, or a different day.
Part C: The experimental probability of landing on heads is the ratio of the frequency of heads to the total number of trials. In this case, it is 8/15 or 0.533. This is slightly higher than the theoretical probability, but still within the margin of error. It's like when you order a pizza and get one extra slice, but it's the one with pineapple.
Part D: The theoretical and experimental probabilities are close but not exactly the same. This is because the theoretical probability is based on an ideal situation where the coin is fair, and the outcomes are equally likely. The experimental probability is based on actual data that may vary due to chance or other factors. The more trials we perform, the closer the experimental probability will get to the theoretical probability. It's like when you practice a skill and get better at it over time, but you still make mistakes sometimes.
✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧
a data analyst is using a function in a spreadsheet. when they input the function, they follow a predetermined structure that includes all required information for the function and its proper placement. what aspect of a function does this describe?
Analyst input the function, they follow a predetermined structure that includes all required information for the function and its proper placement. so, syntax of a function does this describe.
What is syntax?Syntax is a predetermined structure that includes all required information and its proper placement.
A formula in Excel is used to do mathematical calculations. Formulas always start with the equal sign = typed in the cell, followed by your calculation.
In the syntax of all Excel functions, an argument enclosed in [square brackets] is optional, other arguments are required. Meaning, your Sum formula should include at least 1 number, reference to a cell or a range of cells. For example: =SUM(B2:B6) - adds up values in cells B2 through B6.
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What is the area of this composite shape? Enter your answer in the box
The area of the given composite figure is 40 square inches.
What is a composite figure?
A composite figure and shape are the same thing. A composite figure is any object that may be disassembled into multiple fundamental shapes.
We are given a composite figure which can be broken into a triangle and a rectangle.
So,
⇒ Area of composite figure = Area of Rectangle + Area of triangle
⇒ Area of composite figure = (length * breadth) + ([tex]\frac{1}{2}[/tex] * base * height)
⇒ Area of composite figure = (5 * 7) + ([tex]\frac{1}{2}[/tex] * 5 * 2)
⇒ Area of composite figure = 35 + 5
⇒ Area of composite figure = 40 square inches
Hence, the area of the given composite figure is 40 square inches.
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9x9x9x9x9x9x9x9x9x9x9x9xx99x9x9x999999xx99x
Answer: 2.2197307e+25
Step-by-step explanation: I just times it
What must you prove first before you can prove something is a rectangle or a rhombus?
Before proving that a shape is a rectangle or a rhombus, you must first prove that it is a parallelogram by showing that its opposite sides are parallel and then use specific properties to prove its rectangle or rhombus nature.
Before proving that a given shape is a rectangle or a rhombus, you must first prove that it is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel to each other. To prove that a shape is a parallelogram, you can show that its opposite sides are parallel by using the slope formula or by showing that the opposite sides have the same length and are parallel to each other.
Once you have established that a shape is a parallelogram, you can then proceed to prove whether it is also a rectangle or a rhombus. To prove that a shape is a rectangle, you must show that it is a parallelogram with four right angles. To prove that a shape is a rhombus, you must show that it is a parallelogram with four sides of equal length.
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To prove that a quadrilateral is a rectangle or a rhombus, you must first establish some key properties. For a rectangle, you need to prove that it has four right angles and opposite sides are parallel. For a rhombus, you must demonstrate that all four sides are of equal length and opposite sides are parallel.
Before proving that something is a rectangle or a rhombus, you must first prove that it is a parallelogram. This means showing that opposite sides are parallel and congruent in length. Once this is established, you can then prove additional properties to determine whether the shape is a rectangle (where all angles are 90 degrees) or a rhombus (where all sides are congruent).
To prove that a quadrilateral is a rectangle or a rhombus, you must first establish some key properties. For a rectangle, you need to prove that it has four right angles and opposite sides are parallel. For a rhombus, you must demonstrate that all four sides are of equal length and that opposite sides are parallel. Once these properties are verified, you can confidently classify the shape as a rectangle or a rhombus.
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If Joanne has three hours and 45 minutes before swim practice, she wants to go to the store which will take 220 minutes. She also wants to take her brother to the park for 230 minutes which activity does Joanne have time to do before practice
WILL MARK BRAINLIEST!!
A number pattern is shown below.
Please create an equation for the pattern, and find what the difference between the last number in row 6 and the first number in row 6 is. Show or explain your work.
The last number in row 6 is 58. The difference between the last number in row 6 and the first number in row 6 is 10
How to solveTo find the equation for the pattern, let's first observe the pattern in the given rows:
Row 2: 8 10 (difference = 2)Row 3: 15 17 19 (difference = 2)Row 4: 24 26 28 30 (difference = 2)Row 5: 35 37 39 41 43 (difference = 2)We notice that the difference between the consecutive numbers in each row is 2.
Now let's observe the first number in each row:
Row 2: 8 (24)Row 3: 15 (35)Row 4: 24 (46)Row 5: 35 (57)It seems that the first number in each row can be calculated by multiplying the row number by (row number + 2). So, for row 6, the first number would be:
6 * (6 + 2) = 6 * 8 = 48
Now let's calculate the remaining numbers in row 6:
Row 6: 48 50 52 54 56 58 (difference = 2)
The last number in row 6 is 58. The difference between the last number in row 6 and the first number in row 6 is:
58 - 48 = 10
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find the equation of a line which passes through the point (0,3) and (6,0)
Answer:
y=-0.5x+3
Step-by-step explanation:
The equation of a line is
y=mx+b, with m being the slope, and b being the y-intercept
The slope is -0.5, and the y intercept is 3
so:
y=-0.5x+3
Answer:
y= -1/2x+3
Expiation:
you can find the equation between two points by using the slope formula and the slope intercept form which is y=mx+b.
A single 6-sided die is rolled which BEST describes the probability of rolling a number 4 or less
A. likely
B.impossible
C.certain
D. unlikely
Part A: Complete the square to rewrite the following equation in standard form. Show all
necessary work. (6 points)
x² - 4x + y² + 8y = -4
Part B: What are the center and radius of the circle? (4 points)
Answer:
A) (x - 2)² + (y + 4)² = 4²B) The center is (2, - 4), radius is r = 4 units-----------------------------
Standard form for the equation of a circle is:
(x − h)² + (y − k)² = r²,where the center is (h, k) and the radius is r units.
Part AComplete the square by adding missing parts of the identity:
(a ± b)² = a² ± 2ab + b²Apply this to the given equation:
x² - 4x + y² + 8x = - 4x² + 2(-2)(x) + (-2)² + y² + 2(4)(y) + 4² = - 4 + (-2)² + 4²(x - 2)² + (y + 4)² = - 4 + 4 + 4²(x - 2)² + (y + 4)² = 4²Part BAs per the standard form, the center is (h, k) = (2, - 4) and radius is r = 4 units.
One of the legs of a right triangle measures 16 cm and the other leg measures 2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer: 16.1 cm
Step-by-step explanation:
Attached below is a diagram of the triangle.
If you have two legs, you can find the hypotenuse of the right triangle by using the Pythagorean Theorem.
Pythagorean Theorem: a² + b² = c²
Let's set
a = 16 cm
b = 2 cm
So we get,
16² + 2² = c²
256 + 4 = c²
260 = c²
Take the square root of both sides to get c. Since you are taking the square root, there are two answers, positive and negative, but a side length can not be negative.
[tex]\sqrt{260}[/tex] = c
Input this into your calculator, and you get
c = 16.1245155 cm
Rounding to the nearest tenth you get c = 16.1 cm
Todd throws a ball from his tree house. The height in feet of the ball, h(t), above the ground after t seconds is modeled by the function h(t) = −3t2 + 9t + 12. Select the appropriate domain for the function.
A. 0 ≤ t ≤ 4
B. 0 ≤ t ≤ 12
C. t ≥ 0
D. 0 ≤ t ≤ 18.75
The solution of the given problem of function comes out to be Option C, t ≥ 0, which is the proper domain for the specified function
Explain function.Each subject will include a range of problems on the final exam covering both real and fictitious locations as well as the formation of numerical factors. a diagram illustrating the connections between various components that work together to produce the same outcome. A service is made up of several individual components that work together to produce unique outcomes for each input.
Here,
In order to represent the height of the ball above the ground after t seconds, the function
=> h(t) = -3t² + 9t + 12
has the correct domain of C. t ≥ 0.
Reason: Since time (t) here refers to the duration in seconds since the ball was thrown, it cannot be negative.
Therefore, t values greater than or equal to 0 should be the only values allowed in the function's domain.
Option C, t ≥ 0, is the proper domain for the specified function and accurately represents this limitation.
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what is the image of
(0,3) after a dilation by a scale factor of
2 centered at the origin? PLEASE HURRY ITS DUE TODAY :((
The image of the point (0, 3) after dilation by a scale factor of 2 centered at the origin is (0, 6).
What is the image of (0,3) after a dilation by a scale factor of 2 centered at the origin?Dilation is a transformation in which a figure is enlarged or reduced by a scale factor.
We are to find the image of (0,3) after a dilation by a scale factor of 2 centered at the origin.
The scale factor is 2, which means the figure will be enlarged.
To find the image of (0, 3) after dilation, we multiply its x-coordinate and y-coordinate by 2.
Hence;
(0, 3)
Multiply the coordinates by 2.
(0 × 2, 3 × 2)
= (0, 6)
Therefore, the image after dilation is (0, 6).
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A sphere has a radius of 2. 1 cm. What is the volume of sphere in cm3 (use 3. 14 for π? round to the nearest whole number
The volume of the sphere is approximately 39 cm³.
A sphere is a three-dimensional shape that is perfectly round, just like a ball. It is characterized by its radius, which is the distance from its center to any point on its surface. In your problem, the sphere has a radius of 2.1 cm, which means that every point on its surface is exactly 2.1 cm away from its center.
To find the volume of a sphere, we use the formula V = (4/3)πr³, where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.
Plugging in the values from your problem, we get:
V = (4/3)π(2.1)³
V = (4/3)π(9.261)
V = 39.082 cm³
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