Answer:
not a function
Step-by-step explanation:
Answer:
not a function
Step-by-step explanation:
Please show your work.
According to the properties of quadrilaterals:
If a shape is a Parallelogram than it is a Square: False.
If a shape is a Square than it is a Rectangle: True.
If a shape is a Rhombus than it is a Quadrilateral: True.
If a shape is a Trapezoid than it is a Parallelogram: False.
If a shape is a Quadrilateral than it is a Rectangle: False.
Explain about quadrilaterals ?
Quadrilaterals are closed two-dimensional shapes with four straight sides and four angles. The word "quadrilateral" comes from the Latin words "quadric" which means "four" and "latus" which means "side". Some common examples of quadrilaterals include squares, rectangles, parallelograms, rhombuses, and trapezoids.
Each type of quadrilateral has its own unique set of properties and characteristics. For example, a rectangle has four right angles and opposite sides that are parallel and congruent. A parallelogram has opposite sides that are parallel and congruent, and opposite angles that are congruent. A rhombus has four congruent sides and opposite angles that are congruent.
According to the question:
Here are the answers to the true or false questions:
1. If a shape is a Parallelogram than it is a Square.
False. A parallelogram can have any angle measure as long as the opposite sides are parallel. A square is a specific type of parallelogram with four congruent sides and four right angles.
2. If a shape is a Square than it is a Rectangle.
True. A square is a special type of rectangle where all four sides are congruent.
3. If a shape is a Rhombus than it is a Quadrilateral.
True. A rhombus is a type of quadrilateral with four congruent sides.
4. If a shape is a Trapezoid than it is a Parallelogram.
False. A trapezoid has only one pair of parallel sides, while a parallelogram has two pairs of parallel sides.
5. If a shape is a Quadrilateral than it is a Rectangle.
False. A quadrilateral is a broad category of four-sided shapes that includes rectangles, but it also includes many other types of shapes, such as trapezoids, parallelograms, rhombuses, and kites.
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PLEASE ANSWER ASAPP!!!! At a carnival game, it cost Taylor $6 to toss 63 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The coordinates to plot a graph are (2,0.19), (42,4), (63,6).
Describe Graph?A graph is a visual representation of data that shows the relationship between variables. It consists of a set of points or vertices, connected by lines or curves called edges or arcs. Graphs are commonly used in mathematics, statistics, and other fields to display information in a way that is easy to understand and interpret.
There are several different types of graphs, including:
Line Graphs: Line graphs show the relationship between two variables using a continuous line. They are often used to display trends over time, such as stock prices or temperature changes.
Bar Graphs: Bar graphs use bars of different lengths to represent data. They are often used to compare different sets of data or to show the frequency of different values in a data set.
TOSS DOLLARS
2 0.19 (rounded to nearest cent)
42 4
63 6
To plot the points on a coordinate axes, you can use the TOSS values on the x-axis and the DOLLARS values on the y-axis. For example, the point (2, 0.19) would be plotted with 2 on the x-axis and 0.19 on the y-axis. Similarly, the point (42, 4) would be plotted with 42 on the x-axis and 4 on the y-axis, and the point (63, 6) would be plotted with 63 on the x-axis and 6 on the y-axis.
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Figure 1 and figure 2 are right triangles. two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long What scale factor was used to produce Figure 2 from Figure 1? 7 over 3, 3 over 7, 7 or 3
The scale factor used to produce Figure 2 from Figure 1 is given as follows:
7/3.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The side lengths are given as follows:
Figure 1: 3 units.Figure 2: 7 units.Hence the scale factor of the dilation is given as follows:
7/3.
(the scale factor is the division of the side length of the dilated figure by the equivalent side length of the original figure).
Missing InformationThe problem asks for the scale factor used from figure 1 to figure 2.
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Answer:
C 7/3 because i got it right
(c) In a test of a new package design, you drop a carton of a dozen eggs from a height of 1 foot and count the number of broken eggs
The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective. However, if there are several broken eggs, the package design may need to be improved to provide better protection.
When testing a new package design, it is important to simulate real-world conditions as much as possible. In this case, dropping a carton of a dozen eggs from a height of 1 foot is a good way to simulate the types of impacts that the package may experience during shipping and handling.
To conduct the test, you will need to follow these steps:
Obtain a carton of a dozen eggs and the new package design.Place the eggs inside the package according to the manufacturer's instructions.Find a suitable location to drop the package from a height of 1 foot. Make sure the area is clear and there is nothing that could interfere with the drop or damage the package.Drop the package from a height of 1 foot.Open the package and examine the eggs. Count the number of broken eggs.
The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective.
However, if there are several broken eggs, the package design may need to be improved to provide better protection.
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11. Measurement Write and simplify an expression to represent the area of each figure.
a) X 2 x + 3 X-2
b) x+y x-y 3 2x + y
The answer of the question based on the to represent the area of the figure the answer is given below,
What is Rectangle?A rectangle is four-sided polygon with opposite sides that are parallel and congruent (equal) in the length.
a) The figure is a rectangle with a length of 2x + 3 and a width of x - 2. The area of the rectangle is:
Area = length x width
Area = (2x + 3)(x - 2)
Using the distributive property of multiplication, we can simplify this expression:
Area = 2x² - 4x + 3x - 6
Area = 2x² - x - 6
Therefore, the expression for the area of the figure is 2x² - x - 6.
The figure is a trapezoid with a height of 3 and two parallel sides of length x + y and x - y. average of lengths of the two sides are:
(x + y + x - y)/2 = 2x/2 = x
So, the area of the trapezoid is:
Area = (1/2) x height x (sum of parallel sides)
Area = (1/2)(x)(3)(x + y + x - y)/2
Area = (3/2) x²
Now, we need to subtract the area of the triangle from the trapezoid. The triangle has a height of 3 and a base of y, so its area is:
(1/2)(y)(3) = (3/2)y
Therefore, the expression for the area of the figure is:
Area = (3/2)x² - (3/2)y.
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21, 9:55:40 PM Watch help video lve the following logarithm problem for the positive solution for x. log_(x)(1)/(256)=-(4)/(3) Answer:
The positive solution for x in the equation log_x(1)/256 = -4/3 is x = 4.57
To solve the logarithm problem for the positive solution for x, we can use the following steps:
1. First, we can rewrite the equation in exponential form:
x^(-(4)/(3)) = 1/256
2. Next, we can raise both sides of the equation to the power of -(3)/(4) to isolate x:
(x^(-(4)/(3)))^(-(3)/(4)) = (1/256)^(-(3)/(4))
3. Simplify the left side of the equation:
x = (1/256)^(-(3)/(4))
4. Simplify the right side of the equation:
x = 256^((3)/(4))
5. Take the fourth root of both sides of the equation:
x = (256^((3)/(4)))^(1/4)
6. Simplify the right side of the equation:
x = 256^((3)/(16))
7. Simplify the exponent:
x = 256^(3/16)
8. Calculate the value of x:
x ≈ 4.57
Therefore, the positive solution for x is approximately 4.57.
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Evaluate the algebraic expression when f = 6, g = 8, h = 12 and j = 2.
A. 10
B. 12
C. 20
D. 22
please hurry
Answer:
Step-by-step explanation:
There is no algebraic expression in the question????
Help me please I’m confused
The value of (f· g)(x) from the given functions is -x^4 - x^2 - x.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here,
The given functions are f(x)=x³+x+1 and g(x)=-x.
(f·g)(x)= f(x) × g(x)
= (x³+x+1) × (-x)
= -x^4 - x^2 - x
so, e get,
(g·f)(x)= g(x) × f(x)
= (-x) × (x³+x+1)
= -x^4 - x^2 - x
Therefore, the value of (f· g)(x) from the given functions is -x^4 - x^2 - x.
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7y−10=−3(5−x)
Step 2 of 2 : Find the equation of the line which passes through the point
(14,−14)(14,−14) and is parallel to the given
line. Express your answer in slope-intercept form. Si
The answer is [tex]y = (3/7)x - 20[/tex]
To find the equation of the line that passes through the point (14,-14) and is parallel to the given line, we will use the slope-intercept form of an equation, which is [tex]y = mx + b[/tex], where m is the slope and b is the y-intercept.
First, we need to find the slope of the given line. To do this, we will rearrange the equation to get it in slope-intercept form:
[tex]7y - 10 = -3(5 - x)[/tex]
[tex]7y - 10 = -15 + 3x[/tex]
[tex]7y = 3x + 5[/tex]
[tex]y = (3/7)x + (5/7)[/tex]
The slope of the given line is 3/7.
Since the new line is parallel to the given line, it will have the same slope. So, the slope of the new line is also 3/7.
Now, we will use the point-slope form of an equation to find the equation of the new line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plugging in the point (14,-14) and the slope 3/7, we get:
[tex]y - (-14) = (3/7)(x - 14)[/tex]
[tex]y + 14 = (3/7)x - 6[/tex]
[tex]y = (3/7)x - 20[/tex]
This is the equation of the new line in slope-intercept form. The slope is 3/7 and the y-intercept is -20.
So, the final answer is [tex]y = (3/7)x - 20[/tex].
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The vector ü has length 16 and points at an angle of 5° The vector ü has length 11 and points at an angle of 25°
The sum of the two vectors is a vector with length 26.56 and an angle of 12.72°.
The vector ü can be represented in Cartesian coordinates as (16cos5°, 16sin5°) and the vector ü can be represented as (11cos25°, 11sin25°).
To find the sum of these two vectors, we add their corresponding coordinates:
(16cos5° + 11cos25°, 16sin5° + 11sin25°)
Using a calculator, we can approximate these values:
(25.82, 5.81)
Therefore, the sum of the two vectors is approximately (25.82, 5.81) in Cartesian coordinates. To find the length and angle of this vector, we can use the Pythagorean theorem and the inverse tangent function:
Length = √(25.82² + 5.81²)
≈ 26.56
Angle = tan⁻¹(5.81/25.82)
≈ 12.72°
So the sum of the two vectors is a vector with length 26.56 and an angle of 12.72°.
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ins all the integers from -7 through 4 , inclusive. Set Q contains the absolute values of all the numbers in Set P. numbers are in the intersection of sets P and Q ?
The numbers in the intersection of sets P and Q are 0, 1, 2, 3, and 4.
The integers in Set P are {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}.
The absolute values of these integers are {7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4}, which make up Set Q. The intersection of Set P and Set Q are the integers that are in both sets, which are {0, 1, 2, 3, 4}.
Therefore, the numbers in the intersection of sets P and Q are 0, 1, 2, 3, and 4.
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Find the Euclidean inner product of the given vectors. u=[[5],[3],[-4]],v=[[1],[0],[-5]]
The Euclidean inner product of the given vectors is 25.
The Euclidean inner product of two vectors u and v is defined as the sum of the products of the corresponding entries of the vectors. In mathematical terms, it is given by:
Euclidean inner product = u[1]*v[1] + u[2]*v[2] + u[3]*v[3]
Given the vectors u=[[5],[3],[-4]] and v=[[1],[0],[-5]], we can find the Euclidean inner product by substituting the values into the formula:
Euclidean inner product = (5)*(1) + (3)*(0) + (-4)*(-5)
= 5 + 0 + 20
= 25
Therefore, the Euclidean inner product of the given vectors is 25.
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Please help asap i need this badly
Answer:
75 seconds
Step-by-step explanation:
You want to know how long it took Sean to drink his slushy, given a graph of amount remaining versus time.
RemainingSean will have finished his slushy when the amount remaining is zero. That point on the graph occurs when the time is 75 seconds.
It takes 75 seconds for Sean to finish the slushy.
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If f(v)=12v^(4)-40v^(3)+4v^(2)+17v+21, use synthetic division to find f(3) Submit
The value of f(3) using synthetic division is 72.
To find f(3) using synthetic division, we need to divide the polynomial f(v) by the factor (v - 3). This will give us the quotient and the remainder, which will help us find the value of f(3).
Write the coefficients of the polynomial in a row: 12 -40 4 17 21
Write the value of the factor we are dividing by to the left of the row: 3 | 12 -40 4 17 21
Bring down the first coefficient: 3 | 12 -40 4 17 21
------------------
12
Multiply the first coefficient by the factor and write the result under the second coefficient: 3 | 12 -40 4 17 21
------------------
12 36
Add the second coefficient and the result from step 4: 3 | 12 -40 4 17 21
------------------
12 -4
Repeat steps 4 and 5 for the remaining coefficients: 3 | 12 -40 4 17 21
------------------
12 -4 0 51
The last number in the bottom row is the remainder. This is the value of f(3): 3 | 12 -40 4 17 21
------------------
12 -4 0 51 72
So, f(3) = 72.
Therefore, the value of f(3) using synthetic division is 72.
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A large wooden prism will be covered with spray paint for a prop in a school play. The prop must be painted on all sides. A can of spray paint costs $4.00 and will cover 40 square feet. What is the cost to paint the box ?
Part A: how many full cans of spray paint need to be purchased?
Part B What is the cost to paint the box
(a) The number of cans of spray paint that needs to be purchased is 3.
(b) The cost to paint the wooden prism is $12.00.
What is the cost of the painting?
To determine the cost of painting the wooden prism, we need to calculate the surface area of the prism and then divide it by the coverage of each can of spray paint.
Let's assume the wooden prism has dimensions of 6 feet by 4 feet by 3 feet.
Part A:
The surface area of the prism can be calculated as follows:
The top and bottom faces have an area of 6 ft x 4 ft = 24 ft² each
The two side faces have an area of 6 ft x 3 ft = 18 ft² each
The front and back faces have an area of 4 ft x 3 ft = 12 ft² each
Therefore, the total surface area of the prism is:
2(24 ft²) + 2(18 ft²) + 2(12 ft²) = 96 ft²
Since each can of spray paint covers 40 ft², we need:
96 ft² ÷ 40 ft²/can = 2.4 cans
We can't purchase a partial can of spray paint, so we need to round up to the nearest whole can.
Therefore, we need to purchase 3 cans of spray paint.
Part B:
The cost of painting the box will be the number of cans required multiplied by the cost per can.
Since we need to purchase 3 cans, the cost will be:
3 cans x $4.00/can = $12.00
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Find the values of a and b to express this recurring decimal as a fraction.
Simplify this fraction as much as possible before entering your answer.
0.727272... = [tex]\frac{a}{b}[/tex]
a=
b=
Answer: Let x = 0.727272...
Then, 100x = 72.727272...
Subtracting x from 100x gives:
100x - x = 72.727272... - 0.727272...
99x = 72
x = 72/99
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 9. Therefore:
x = (72/9) / (99/9) = 8/11
So, a = 8 and b = 11. Therefore, the recurring decimal 0.727272... can be expressed as the fraction 8/11.
Step-by-step explanation:
The CEO of Super Electronics asked customers to fill out a survey to win a $100 gift certificate. The customers were asked to list the products they purchased that day. 88 bought laptop computers. 52 bought desktop computers. 64 bought printers. What is the probability that the winner of the gift certificate bought a printer from Super Electronics? A.
Answer:
To calculate the probability that the winner of the gift certificate bought a printer from Super Electronics, we need to use the total number of customers who participated in the survey as the denominator and the number of customers who bought printers as the numerator.
The total number of customers who participated in the survey is:
Total Customers = Number of Customers who bought Laptops + Number of Customers who bought Desktops + Number of Customers who bought Printers
Total Customers = 88 + 52 + 64
Total Customers = 204
The number of customers who bought printers is 64.
Therefore, the probability that the winner of the gift certificate bought a printer from Super Electronics is:
P(Bought a Printer) = Number of Customers who bought Printers / Total Customers
P(Bought a Printer) = 64 / 204
P(Bought a Printer) = 0.3137 (rounded to 4 decimal places)
So, the probability that the winner of the gift certificate bought a printer from Super Electronics is 0.3137 or approximately 31.37%.
Descriptive statistics and basketball wins: Here are the numbers of wins for the 30 National Basketball Association teams in the 2012–2013 season.
60
44
39
29
23
57
50
43
37
27
49
42
37
29
19
56
51
40
33
26
48
42
31
25
18
53
44
40
29
23
Create a frequency table for the number of wins using the data provided.
What is the Mean, Mode, and Median for the number of wins?
What is the standard deviation and variation?
How many teams had over 41 wins?
What percent of teams scored below 30 wins?
Create a histogram for the number of wins with a normal curve.
Does our data set for age represent a normal curve (somewhat bell-shaped)? If not, is it positively or negatively skewed?
What is the lowest and highest Z-score for wins and make sure to include that in the SPSS data file (2 points)?
What does the Z-score for the number of wins for 37 (2 points)?
The Mean, Mode, and Median for the number of wins are 37.8; 29, 42; 38 respectively. The standard deviation and variation are 11.15 and 124.26 respectively. 9 teams had over 41 wins. 16.67% of teams scored below 30 wins. Our data set for age does not represent a normal curve, it is positively skewed. The lowest and highest Z-score for wins are -1.78 and 1.99 respectively. The Z-score for the number of wins for 37 is -0.07.
To create a frequency table, we need to categorize the number of wins into intervals and count the number of teams in each interval. We can use the following intervals: 15-24, 25-34, 35-44, 45-54, 55-64.
| Interval | Frequency |
|---------|----------|
| 15-24 | 3 |
| 25-34 | 5 |
| 35-44 | 8 |
| 45-54 | 5 |
| 55-64 | 2 |
To calculate the mean, we add up all the values and divide by the number of values:
Mean = (60 + 44 + 39 + 29 + 23 + 57 + 50 + 43 + 37 + 27 + 49 + 42 + 37 + 29 + 19 + 56 + 51 + 40 + 33 + 26 + 48 + 42 + 31 + 25 + 18 + 53 + 44 + 40 + 29 + 23)/30 = 37.8
To find the mode, we look for the value that appears most often. In this case, it is 29 and 42, both appearing twice.
Mode = 29, 42
To find the median, we need to order the values from smallest to largest and find the middle value. If there is an even number of values, we take the average of the two middle values.
Ordered values: 18, 19, 23, 23, 25, 26, 27, 29, 29, 31, 33, 37, 37, 39, 40, 40, 42, 42, 43, 44, 44, 48, 49, 50, 51, 53, 56, 57, 60
Median = (37 + 39)/2 = 38
To calculate the standard deviation, we first find the variance by subtracting the mean from each value, squaring the result, and then taking the average of those squared differences. The standard deviation is the square root of the variance.
Variance = [(60-37.8)^2 + (44-37.8)^2 + ... + (23-37.8)^2]/30 = 124.26
Standard deviation = sqrt(124.26) = 11.15
To find the number of teams with over 41 wins, we can count the values that are greater than 41:
Number of teams with over 41 wins = 9
To find the percent of teams with below 30 wins, we can count the values that are less than 30 and divide by the total number of teams:
Percent of teams with below 30 wins = (5/30)*100 = 16.67%
To create a histogram, we can use the intervals and frequencies from the frequency table and plot them on a graph with the intervals on the x-axis and the frequencies on the y-axis. We can also add a normal curve by calculating the mean and standard deviation and using a normal distribution function.
The data set for the number of wins does not represent a normal curve, as it is slightly positively skewed (there are more values on the lower end of the distribution).
The lowest Z-score is for the value 18, which is (18-37.8)/11.15 = -1.78. The highest Z-score is for the value 60, which is (60-37.8)/11.15 = 1.99.
The Z-score for the value 37 is (37-37.8)/11.15 = -0.07. This means that the value 37 is 0.07 standard deviations below the mean.
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Chose one of two tables below to create your own Question (with solution).
A. If a friend's kid has no curfew, what is the probability that they don't have chores? B. the probability that a friend's kid doesn't have chores given that they have no curfew is 1/3. C. I chose this question because it involves calculating a conditional probability based on a given set of data.
Describe Probability?Probability can also be used to describe more complex events, such as the likelihood of a stock price increasing by a certain amount in a given period of time, or the probability of a medical treatment being effective for a certain disease.
My Conditional Frequency Question is:
If a friend's kid has no curfew, what is the probability that they don't have chores?
Solution:
The conditional probability of a kid not having chores given that they have no curfew can be found using the formula:
P(No Chores | No Curfew) = P(No Chores and No Curfew) / P(No Curfew)
From the table, we can see that the number of kids who have no curfew and no chores is 2, and the total number of kids who have no curfew is 6. Therefore:
P(No Chores | No Curfew) = 2/6 = 1/3
So the probability that a friend's kid doesn't have chores given that they have no curfew is 1/3.
I chose this question because it involves calculating a conditional probability based on a given set of data. This is a common type of question in statistics and probability, and it requires an understanding of the basic concepts of probability such as conditional probability and independence. The table provided gives us the data we need to calculate the conditional probability, and the solution involves applying the formula for conditional probability and simplifying the fraction.
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pls help!! Which number sentence is true?
A
B
C
D
The true number sentence is expression B: 3 + 4 = 7.
We must analyse each expression and contrast them in order to determine which number statement is correct.
Expression A: Paste the formula 5 + 8 = 12 – 1.
Taking into account the left-hand side of the equation:
The formula is 5 + 8 = 13.
Following is an evaluation of the right-hand side of the equation:
12 – 1 to get 11.
Expression A is incorrect since 13 and 11 are not equivalent.
B Expression
3 + 4 = 7
This is a straightforward addition equation, and the answer is that 3 + 4 = 7. As a result, expression B is accurate.
C expression
2 x 2 = 5 - 1
Taking into account the left-hand side of the equation:
2 x 2 = 4
Following is an evaluation of the right-hand side of the equation:
5 - 1 = 4
Expression C is accurate since 4 and 4 are equal.
D Expression
the formula 9 + 2 Equals 6 x 2.
Taking into account the left-hand side of the equation:
9 + 2 = 11 to copy
Following is an evaluation of the right-hand side of the equation:
6 x 2 =
Expression D is incorrect since 11 and 12 are not equal.
Hence, expression B—3 + 4 = 7—is the correct number expression.
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Heather runs 3 miles in 28 minutes. At the same rate, how many miles would she run in 42 minutes?
Heather runs 3 miles in 28 minutes, so at the same rate, she would run 4.494 miles in 42 minutes.
To find out how many miles Heather would run in 42 minutes at the same rate, we use the concept of unit rate. Unit rate is a comparison of two different quantities when they are combined together. In this case, we need to find the unit rate of Heather's running speed in miles per minute.
Step 1: Find the unit rate of Heather's running speed in miles per minute.
To do this, we divide the distance she ran by the time she took to run it:
3 miles ÷ 28 minutes = 0.107 miles per minute
Step 2: Use the unit rate to find out how many miles Heather would run in 42 minutes.
To do this, we multiply the unit rate by the time she runs:
0.107 miles per minute × 42 minutes = 4.494 miles
Therefore, Heather would run 4.494 miles in 42 minutes at the same rate.
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.
Ms. Smith wants to buy a home theater system. which is on sale for 35% off the original price of $2299. The sales tax is 6.25%
Answer:
$948.34
Step-by-step explanation:
35% = .35
.35 x $2299
= $804.65
That is the total before the sales tax and after the sale.
6.25% = .0625
.0625 x $2299
= $143.69, and because that is 6.25% of the total, it must be added onto that as tax.
That means the total is $804.65 + $143.69
= $948.34
Graduate Management Admission Test (GMAT) is a computer adaptive test intended to assess certain analytical, writing, quantitative, verbal and reading skills in written English for use in admission to a graduate management program such as an MBA programme. GMAT scores are normally distributed with a mean of 550 and a standard deviation of 120. Suppose a random sample of 35 students is selected randomly. (a) Describe the shape of the sampling distribution of the sample means. State the theorem used and explain briefly. (b) Find the mean and the standard deviation of the sample means. (c) What is the probability that the average score of those 35 selected students is above 600? (d) A student, Ann, is randomly selected from the population, find the probability that her score is above 600?
The probability that Ann's score is above 600 is 1 - 0.6628 = 0.3372.
(a) The shape of the sampling distribution of the sample means will be approximately normal. This is because of the Central Limit Theorem, which states that the sampling distribution of the sample means will be approximately normal if the sample size is large enough, regardless of the shape of the population distribution. In this case, the sample size of 35 is large enough for the Central Limit Theorem to apply.
(b) The mean of the sampling distribution of the sample means will be equal to the mean of the population, which is 550. The standard deviation of the sampling distribution of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is 120/√35 ≈ 20.28.
(c) To find the probability that the average score of the 35 selected students is above 600, we need to find the z-score for 600 using the mean and standard deviation of the sampling distribution of the sample means. The z-score is (600 - 550)/20.28 ≈ 2.47. Using a z-table, we can find the probability that the z-score is less than 2.47, which is 0.9932. Therefore, the probability that the average score of the 35 selected students is above 600 is 1 - 0.9932 = 0.0068.
(d) To find the probability that Ann's score is above 600, we need to find the z-score for 600 using the mean and standard deviation of the population. The z-score is (600 - 550)/120 ≈ 0.42. Using a z-table, we can find the probability that the z-score is less than 0.42, which is 0.6628.
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An open-topped box is constructed from a rectangular piece of cardboard that is twice as long as it is wide by removing a square of size 3 inches from each corner and turning up the edges.
If the box is to hold 1,620 in3, how big should the originial piece of cardboard be?
The original piece of cardboard should be approximately 32.86 inches by 16.43 inches.
To find the size of the original piece of cardboard, we can use the formula for the volume of the box, which is V = l × w × h. Since the box is open-topped, the height will be the size of the square that was removed from each corner, which is 3 inches. Also, given that the length of the original piece of cardboard is twice the width, we can substitute l = 2w in the formula. Therefore, the formula becomes:
V = (2w) × w × 3
Now, we can plug in the given volume of 1,620 in3 and solve for w:
1,620 = (2w) × w × 3
540 = 2w^2
270 = w^2
w = √270
w ≈ 16.43 inches
Now, we can use the value of w to find the length of the original piece of cardboard:
l = 2w = 2(16.43) = 32.86 inches
Therefore, the original piece of cardboard should be approximately 32.86 inches by 16.43 inches.
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3(3x+5)-8=7 give statement and give reasons and give check
Answer:
x = 0
Step-by-step explanation:
3(3x+5) - 8 =7
9x + 15 - 8 = 7
9x + 7 = 7
9x = 0
x = 0
Let's check
3(3(0) + 5) - 8 = 7
3(0 + 5) - 8 = 7
3(5) - 8 = 7
15 - 8 = 7
7 = 7
So, x = 0 is the correct answer.
Jack is w years old now his brother
is 3 years older than he is now if his brother is x years old express x in terms of w
The expression for Jack's brother's age is x = 3 + w
How to determine the valueIt is important that we know algebraic expressions are defined as expressions which are composed of variables, coefficients, constants, factors and terms.
These algebraic expressions are also identified with mathematical operations, such as;
SubtractionMultiplicationDivisionAdditionBracketParenthesesFrom the information given, we have that;
Jack is w years old
His brother is 3 years old than him
His brother's age is also x
This is represented as;
x = 3 + w
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It takes 12 bags of bird pellets to fill some bird feeders. The bird feeders need to be refilled every 2 weeks. How many bags of birdseed are needed for 14 weeks? Explain.
Answer:
Step-by-step explanation
So first do 12-6=6 then multiply 14x6 which is 84 so 84 bags in 14 weeks is 3 and a half months.
olve the compound inequality. 4u+5>13 and 2u+6>=16 raph the solution on the number line. there is no solution, click on "No solut
we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5. The solution to the compound inequality is u >= 5.
To solve the compound inequality, we need to isolate the variable on one side of the inequality.
For the first inequality, 4u + 5 > 13, we can subtract 5 from both sides to get:
4u > 8
Then, we can divide both sides by 4 to get:
u > 2
For the second inequality, 2u + 6 >= 16, we can subtract 6 from both sides to get:
2u >= 10
Then, we can divide both sides by 2 to get:
u >= 5
Now, we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5.
On the number line, we can draw a closed circle at 5 and shade to the right to indicate that the solution includes 5 and all numbers greater than 5.
The solution to the compound inequality is u >= 5.
Here is the graph of the solution on the number line:
0 1 2 3 4 5 6 7 8 9 10
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A 6-foot person standing 18 feet from a streetlight casts a 10-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the streetlight to the end of the shadow.
Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.
what is triangle ?A triangle is a polygon with three vertices and three angles that has three sides. It is one of the fundamental geometric shapes and has numerous uses in fields like engineering, physics, architecture, and more. The lengths of a triangle's sides and angles can be calculated using a variety of geometric formulas. Triangles come in a variety of shapes, including equilateral, isosceles, scalene, right-angled, acute-angled, and obtuse-angled triangles, each of which has unique attributes.
given
Let x represent the person's height.
Let x represent the streetlight's height.
Let d represent the distance between an individual and a streetlight.
Let s be the size of the shade cast by the subject.
According to the facts provided, x equals 6 feet (height of the person)
d Equals 15 feet (distance from the person to the streetlight)
The shadow's extent, s, is 15 feet.
Finding y's number, or the streetlight's height, is necessary.
The following ratios can be written using the comparable triangles property:
y / (d + s) Equals x / s
Inputting the numbers provided yields:
By condensing and figuring out x, we arrive at:
y = 12 feet
Consequently, the streetlight has a 12 foot height.
We can divide the streetlight's height by the person's height to determine how many times higher the streetlight is:
y / x = 12 / 6 = 2
Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.
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Please help me
Write 3 3/4 feet as a single fraction greater than one.
Answer: 9/4
Step-by-step explanation:
Answer:
15/4 feet
Step-by-step explanation:
When given a mixed number like [tex]3\frac{3}{4}[/tex], you multiply the denominator by the whole number and add the numerator.
In this case, multiply 3 x 4 and then add 3. After finding that value, put it over the original denominator, giving 15/4