Answer:
$10 / hour
Step-by-step explanation:
$40 ÷ 4 hours = 10/hour
Answer: Part A: Zach is paid $10 per hour
Part B: The equation would be p = 10h
Step-by-step explanation: Part A :Zach worked 4 hours and was paid $40. The question asks How much is Zach's paid per hour? Per hour means to find the unit rate and in order to find the unit rate in this case, you have to divide the $40 by the 4 to get how much Zach got per hour.
1.$40/4=10
Therefore, Zach is paid $10 per hour.
Part B: In the question it says Which equation shows the relationship between , h, the number of hours worked. The number of hours Zach worked was 4 hours. So, h = 4. Then for the next part of the problem, and p the amount paid. We know that Zach got paid $40. So p = 40. Now that we know our numbers, we could put the equation together.
1. P = 10h is the same as $40 = 10 x 4.
There's the answer, Hope it helps! Have a nice day!
nonlinear transformation 1 point possible (graded) explore which, if any, transformations to and can improve the quality of the fit and reduce the residuals. what transformations give you the best fit?
Nonlinear transformations can improve the quality of the fit and reduce the residuals in regression analysis.
Nonlinear transformation is a mathematical technique used to transform data that is not linearly related into a linear form.
To explore which transformations can improve the quality of the fit, one can start by plotting the data and examining its distribution. Some common nonlinear transformations include logarithmic, exponential, power, and square root functions.
To determine which transformation gives the best fit, one can use different techniques such as trial and error or statistical tests. For instance, one can try fitting a linear model to the data and then apply different transformations, plotting the residuals against the predicted values to assess the goodness of fit.
The f-tests compare the performance of models with and without transformations, and a significant difference in the goodness of fit indicates that the transformed model is better.
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Height: 15 ft area: 285 ft 2
What's the missing dimension
Answer: 19
Step-by-step explanation: 15 x 19 = 285ft^2
A pool table is shown. On the table, a triangle is drawn to connect the cue ball, the eight ball, and the top right pocket. The distance between the cue ball and eight ball is 8 inches, the distance between the eight ball and the pocket is 6 inches, and the distance between the cue ball and the pocket is unknown.
Using Pythagoras' theorem we found that when the angle is greater than 90°, the distance between the cue ball and the pocket is greater than 10 inches.
What is Pythagoras' Theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean Theorem. According to this statement, the square of the side of a triangle known as hypotenuse is equal to the sum of squares of the other two sides of the triangle.
The complete question is given below in the image.
It is given that a triangle is formed by the cue ball, eight ball and pocket as shown below.
The ∠y is greater than 90°.
The two sides of the triangle are 8 in. and 6in.
Two find the minimum distance between the cue ball and the pocket, we assume that the minimum angle formed by the paths of the cue ball and eight ball is 90°.
That is ∠y = 90°.
Then the triangle becomes a right-angle triangle.
So the distance x becomes the hypotenuse.
Using the Pythagoras theorem, we can find the hypotenuse of the triangle.
x² = 8² + 6²
x² = 100
x = 10 inches.
This is the minimum distance between the cue ball and pocket when y = 90°.
Therefore using Pythagoras' theorem we found that when the angle is greater than 90°, the distance between the cue ball and the pocket is greater than 10 inches.
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Translate the following sentence into an equation then solve the equation. the sum of r and 18 is 73
Answer:
r = 55
Step-by-step explanation:
Sum means addition
r + 18 = 73 Subtract 18 from both sides
r = 55
Answer:
The equation is:
r + 18 = 73
and the result is:
r = 55
Step-by-step explanation:
The sum of r and 18 is 73, in equation is:
r + 18 = 73
Solve:
r + 18 - 18 = 73 - 18
r + 0 = 55
r = 55
Check:
55 + 18 = 73
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis.
y = x^3/2
y = 27
x = 0
Volume of solid generated by revolving the plane region about the y-axis is [tex]\pi \left(\frac{1392}{7}\right)[/tex]
What do you understand by Shell method?The shell method formula is used to find the volume of a solid of revolution, formed by rotating a region about a line that is parallel to one of its sides.
The formula for the shell method is V = 2π* ∫r(x)h(x) dx where V is the volume of the solid, r(x) is the distance between the axis of revolution and the curve being rotated and h(x) is the height of the shell at x.
The shell method can be used when the region is more easily described by an equation in one variable. In contrast, the disk/washer method is used when the region is more easily described by an equation in two variables.
It is a powerful tool for solving many types of problems in calculus, physics and engineering. The shell method formula helps to determine the volume of a solid of revolution, which is an important concept in various fields of study.
Given:
y = [tex]x^\frac{3}{2}[/tex]
y = 27
x = 0
Shell method:
V = [tex]2\pi \int\limits_c^d p(y)h(y) dy[/tex]
Then the volume of a solid is
V = [tex]2\pi \int\limits_0^4x(27 - x^\frac{3}{2})dx[/tex]
= [tex]2\pi \left[ \int\limits_0^4 27x dx - \int\limits_0^4 x^\frac{5}{2}dx\right][/tex]
[tex]= 34\pi \left[\frac{x^2}{2} \right]_0^4 - \frac{4}{7} \pi \left[ x^\frac{7}{2} \right]_0^4[/tex]
[tex]= 34\pi \left(\frac{4^2}{2} \right) - \frac{4\pi}{7}(4)^\frac{7}{2}[/tex]
[tex]= 4\pi \left( \frac{68}{7} - \frac{2^7}{7} \right)[/tex]
[tex]= 4\pi \left( \frac{476 - 128}{7} \right)[/tex]
[tex]4\pi \left( \frac{348}{7} \right)[/tex]
[tex]= \pi \left( \frac{1392}{7} \right)[/tex]
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John Napier developed logarithms and Henry Briggs helped him to improve on the concept.
True
False
The given statement is True.
What is developing logarithms?
The emergence of logarithms was predicted by comparing arithmetic and geometric series.
True. John Napier is credited with developing logarithms and Henry Briggs is known for working with Napier to advance the concept and promote its use.
Together, they created the logarithmic tables that became a powerful tool in mathematics and science.
Therefore, The given statement is True.
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x f 20-24 2 15-19 5 10-14 4 5-9 1 for the distribution in table 2-3, what was the highest score obtained in this group of 12 scores? group of answer choices
The highest score obtained in this group of 12 scores is 19
What is the distribution in statistics?
In statistics, a distribution refers to the way in which a variable is spread out or distributed across different values. A distribution describes the probability of different outcomes for a variable, and can be visualized using graphs such as histograms, box plots, and probability density functions.
The distribution in Table 2-3 shows frequency (f) for different score ranges (x). Without knowing the exact scoring system, we can't say for certain what the highest score obtained in this group of 12 scores is. However, we can determine the upper limit of the highest score range by multiplying the upper limit of the range by its frequency:
Upper limit of 20-24 range = 24
Frequency of 20-24 range = 2
Upper limit of 15-19 range = 19
Frequency of 15-19 range = 5
Upper limit of 10-14 range = 14
Frequency of 10-14 range = 4
Upper limit of 5-9 range = 9
Frequency of 5-9 range = 1
To find the highest score, we need to determine the upper limit of the score range that has the highest frequency. In this case, the highest frequency is 5, which corresponds to the range 15-19.
Hence, the highest score range is 15-19, and the highest score within that range is the upper limit of that range, which is 19. So, the highest score obtained in this group of 12 scores is 19 (assuming the scoring system is such that higher scores correspond to higher ranges).
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translate the following sentence into an equation. the difference of 29 and x is equal to 17
Answer:
x - 29 = 17Step-by-step explanation:
Difference means subtract or minus (-)
So we always switch 29 and x into x and 29
Can't really explain that much more but it's the correct answer though, trust me! :)
What is the area of this compound figure?
The area of the composite figure is equal to 99 mm² square milimetresmetres.
How to calculate for the area of the figureThe composite figure can be observed to be made up of two horizontal rectangle, and a vertical rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:
area of the bigger horizontal rectangle = 11 mm × 3 mm
area of the bigger horizontal rectangle = 33 mm²
area of the smaller horizontal rectangle = 5 mm × 2 mm
area of the smaller horizontal rectangle = 10 mm
area of the vertical rectangle = 14 mm × 4 mm
area of the vertical rectangle = 56 mm²
total area of the composite figure = 33 mm² + 10 mm² + 56 mm²
total area of the composite figure = 99 mm²
Therefore, the area of the composite figure is equal to 99 mm² square milimetres.
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Help me quick pls help fast
Answer: 46ft
Step-by-step explanation:
Alright so for this you must reference the pythagorean theorem which is:
a^2+b^2=c^2. c^2 is always the diagonal side and a^2 and b^2 the other two sides.
You can therefore set this up like this:
a^2+20^2=50^2 (where a is the side you are looking for- listed as x)
Solve:
a^2=50^2-20^2
a^2=2500-400
a^2=2100
sqrt(a^2)=sqrt(2100)
a= 45.8257569496
Round: a (or x)=46
At 10:00 am, two boys start out on their bikes to meet each other from towns located 68 miles apart. They meet at 1 pm. If one boy travels 3 miles per hour faster than the other, what was the speed of each boy?
The speed of each boy is given as follows:
Faster: 12.83 miles per hour.Slower: 9.83 miles per hour.How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.For this problem, the parameters are given as follows:
Slope: velocity.Intercept: initial position.Hence the functions are given as follows:
vt.68 - (v - 3)t.They meet at 1 pm, which is three hours after 10 am, hence the velocity of the faster boy is obtained as follows:
3v = 68 - 3(v - 3)
3v = 68 - 3v + 9
6v = 77
v = 77/6
v = 12.83 miles per hour.
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what is the approximate side length of the largest square envelope that can be placed into the mailbox without bending it? you must round your answer to two decimal places.
The approximate side length of the largest square envelope that can be placed into the mailbox without bending it is 0.71x.
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles of 90 degrees each. It is a two-dimensional shape that can be represented by a closed polygon with four straight sides and four right angles.
First, we need to measure the size of the mailbox. Let's say that the length of each side of the mailbox opening is "x" inches. We can then set up an inequality to find the maximum size of the side of the square envelope that can fit into the mailbox. The inequality is:
side length of square envelope ≤ x
This inequality tells us that the side length of the square envelope must be less than or equal to the size of the mailbox opening. We want to find the largest possible side length of the square envelope, so we'll use the "less than or equal to" symbol.
To find the largest possible side length of the square envelope, we'll use the value of "x" to set up an equation. We know that the diagonal of the square envelope will be equal to the length of the side of the square envelope multiplied by the square root of 2. Therefore, we can set up the following equation:
diagonal of square envelope = side length of square envelope × √2
We want to find the maximum side length of the square envelope, so we'll use the maximum value of the diagonal of the envelope. We know that the diagonal of the envelope must be less than or equal to the length of the mailbox opening (which is "x"), so we can set up the inequality:
side length of square envelope × √2 ≤ x
We can solve for the side length of the square envelope by dividing both sides of the inequality by the square root of 2:
side length of square envelope ≤ x/√2
To get the largest possible side length of the square envelope, we'll use the maximum value of "x". Therefore, the largest possible side length of the square envelope that can fit into the mailbox without bending is:
side length of square envelope ≤ x/√2 ≈ 0.71x
We can round this value to two decimal places, which gives us:
side length of square envelope ≈ 0.71x
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What is the radius of a circle whose circumference measures 154 inches?
Answer: 77
Step-by-step explanation: to find the radius divide the circumference by 2.
Reece works at fries and more and the relationship between x the number of hours and y reece's total earnings can be represented by y=8. 25x who earns more per hour
Another person named Sarah earns $7.50 per hour, then Reece earns more per hour than Sarah.
If the relationship between the number of hours worked and total earnings for Reece at Fries n More is given by y = 8.25x, where y is total earnings and x is the number of hours worked, then Reece earns $8.25 per hour worked.
To compare Reece's earnings per hour to another person, we would need to know the hourly wage of the other person. For example, if another person named John earns $9.00 per hour, then John earns more per hour than Reece. Conversely, if another person named Sarah earns $7.50 per hour, then Reece earns more per hour than Sarah.
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show that the following function are continuos and discontinuos
A.(f×)={×+1 ,for×less than or equai to 2
{ 2×–1 ,for 1<×<2
{×–1 ×<1
The function f(x) = [tex]\left \{ {{x+1} ,for x \leq 2 \atop {2x-1}, for 1 < x < 2} \atop {x-1} , for x < 1 \right.[/tex] is continuous to all the values.
In mathematics, a function is a rule that assigns each element from one set (called the domain) to exactly one element of another set (called the range). The continuity of a function describes how smoothly it behaves as its input values change. In this context, we will analyze the continuity of the given function.
The given function is a piecewise function, which means it has different rules for different intervals of its domain. Let's analyze each interval separately to determine if the function is continuous or discontinuous.
For x less than or equal to 2, the function is f(x) = x + 1. This is a linear function, and we know that all linear functions are continuous everywhere. Therefore, the function is continuous for x less than or equal to 2.
For 1 < x < 2, the function is f(x) = 2x - 1. This is also a linear function, and as we said before, all linear functions are continuous. Therefore, the function is continuous for 1 < x < 2.
For x less than 1, the function is f(x) = x - 1. This is also a linear function and is continuous for all values of x less than 1.
Therefore, we can conclude that the given function is continuous for all values of x.
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A publishing industry report predicts that magazine
subscriptions will drop by 10% each year. If this prediction
is correct, then how many subscribers will a magazine with
98,000 subscribers have in 10 years? (Round to the near
whole number if necessary).
A76,023
C 7690
B34,170
D 16,348
The magazine will have 33320 subscribers at the end of 10 years.
What is exponential function?A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Given that, a publishing industry report predicts that magazine
subscriptions will drop by 10% each year.
The problem thus represents an exponential decay problem.
The exponential decay is given as:
[tex]F = P (1 - r)^t[/tex]
Here, F is the future value.
P is the present amount = 98000.
r is the rate of decrease = 10% = 0.1
t is the time = 10 years.
Substituting the values we have:
[tex]F = 98000(1 - 0.1)^{10}\\[/tex]
F = 33320
Hence, the magazine will have 33320 subscribers at the end of 10 years.
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En los mitos y leyendas latinoamericanas, los personajes femeninos suelen representar males que infligen daño a los hombres.¿por que sucede esto?
A possible explanation for why female characters in Latin American myths and legends often represent evils that inflict harm on men is the patriarchal nature of those societies.
Why are women seen as inflicting evil on men in Latin American myths ?In such societies, women were often seen as weaker and more vulnerable than men, and their perceived subservience reinforced the idea that they were not to be trusted. In addition, women were often seen as a threat to male power and authority, and as a result, they were often depicted as malevolent figures who used their cunning and sexuality to manipulate men.
Another explanation is that the portrayal of female characters as evils in these myths and legends was a way of maintaining social order and control. By demonizing women, men were able to justify their own actions and maintain their position of power and control over women.
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1. Students in Mrs. Henderson's third grade class are working on times tables, and they demonstrate mastery by
passing tests. Sofia has passed 4 tests so far. Her classmate, Jacob, has passed 8 of them. From now on, Sofia plans
to take and pass 3 tests per week. Meanwhile, Jacob plans to do 1 per week. At some point, Sofia will catch up to
Jacob. How long will it take?
The number of weeks when Sofia will catch up to Jacob will be 2 weeks.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
Let 'x' be the number of weeks and 'y' be the total test. Then the equations are given as,
y = 4 + 3x ...1
y = 8 + x ...2
From equations 1 and 2, then we have
4 + 3x = 8 + x
3x - x = 8 - 4
2x = 4
x = 2
The number of weeks when Sofia will catch up to Jacob will be 2 weeks.
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4. Fill in the following equivalents:
1 Tbsp. =
1/4 c. =
1 c. =
1 c. =
1/3 c. =
Based on the conversion factors, the equivalent values are as follows:
1 Tbsp. = 1/16 c
1/4 c. = 4 Tbsp
1 c. = 16 Tbsp
1 c. = 1/2 pint
1/3 c. = 80 mL
What are conversion factors?A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet.
The conversion factor for Tbsp to c is 1/4, which means that 1 Tbsp. is equal to 1/4 c.
The conversion factor for c to mL is 236.6, which means that 1 c. is equal to 236.6 mL (rounded to one decimal place).
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A mathematics teacher wanted to see the correlation between test scores and
homework. The homework grade (x) and test grade (y) are given in the
accompanying table. Write the linear regression equation that represents this
set of data, rounding all coefficients to the nearest tenth. Using this equation,
estimate the homework grade, to the nearest integer, for a student with a test
grade of 31.
Homework Grade (x) Test Grade (y)
The regression equation is y = x - 10.4
Homework grade (x) = 41
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
From the table,
We have ∑X = 488, ∑Y =439, ∑XY = 31458, ∑X² = 34834, n=7
Standard linear equation is y= a+bx
a= [ ∑Y × ∑X² - ∑X × ∑XY ]/ [ n × ∑X² - ( ∑X)² ]
On substituting and simplifying , we get a= -10.4
b= [ n × ∑XY - ∑X × ∑Y ] / [ n × ∑X² - ( ∑X)² ]
On substituting and simplifying , we get b ≈ 1
The regression equation is y = x - 10.4
Given test grade y=31
We have 31=x-10.4 => x= 41.4
Nearest integer is 41
Homework grade (x) = 41
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What is the slope of the line that passes
through the points (10, 3) and (7,0)?
Write your answer in simplest form.
Answer:
slope = 1
Step-by-step explanation:
[tex]m=\frac{0-3}{7-10} =\frac{-3}{-3} =1[/tex]
Hope this helps.
You and your brother go to the same store to buy fruit. You purchase a large watermelon for $7.71 and 2.4 pounds of red grapes. Your brother buys a platter of pre-cut fruit for $9.95 and 1.6 pounds of red grapes. The two of you spend the same amount of money. How much do the grapes cost per pound
The cost of red grapes per pound is $2.8.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, cost of a large watermelon and 2.4 pounds of red grapes is $7.71.
Let the cost of red grapes be x.
So, the total cost = 7.71+2.4x
Cost of a platter of pre-cut fruit and 1.6 pounds of red grapes is $9.95.
The total cost = 9.95+1.6x
Person and his brother spent same amount of money.
So, 7.71+2.4x=9.95+1.6x
2.4x-1.6x=9.95-7.71
0.8x=2.24
x=2.24/0.8
x=$2.8
Therefore, the grapes cost per pound is $2.8.
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Complete the function for this graph.
1 y=|x-[?]|+[]
-Hint: y = |x - h| + v
The absolute value function on the graph is:
f(x) = |x + 2| + 3
How to write the function for the graph?We know that for an absolute value function with a vertex at (a, b), then the absolute value function is:
f(x) = |x - a| + b
Here we can see that the vertex is at the point (-2, 3)
Then:
a = 2
b = 3
The function will be:
f(x) = |x + 2| + 3
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Intermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval
A. True
B. False
Option A. TRUE. The theorem is important because it guarantees the existence of solutions to certain types of equations, and it is widely used in calculus, engineering, physics, and many other fields.
The Intermediate Value Theorem is a fundamental theorem in mathematics that states that, for any given continuous function on an interval, every value between the minimum and maximum values of the function on the interval must be taken by the function at some point within the interval. This theorem states that, given a function f defined on an interval [a, b], if f(a) and f(b) have different signs (i.e. one is positive and the other is negative), then there exists at least one c in the interval (a, b) such that f(c) = 0. The theorem is important because it guarantees the existence of solutions to certain types of equations, and it is widely used in calculus, engineering, physics, and many other fields.
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Consider solving the equation below for x.
2(4x + 1)3= ax + b
Which statements are true about the solution to the equation when substituting the
given values for a and b?
Choose all that apply.
"Hint: There are two.
If a 8 and b= -1, then there is exactly one solution to the equation.
□ If a= 2 and b= 4, then there are infinitely many solutions to the equation.
□
If a 4 and b= -2, then there is no solution to the equation.
If a= 2 and b= -1, then there is exactly one solution to the equation.
If a 8 and b= 1, then there is no solution to the equation.
=
Answer:
If a = -8 and b = -1 there is exactly one solution to the equation
Step-by-step explanation:
I was unable to find the other one...
Are you sure there are two possible solutions, or did you forget to include one of the options...?
You take an SRS of size 500 from the 37,000 students at Purdue University and measure individual’s heights. You then take an SRS of size 250 from the 4,400,000 adults in the state of Indiana and measure their heights. Assuming the standard deviation of individual heights in the two populations is the same, the standard
deviation of the sampling distribution of mean heights for the Indiana sample is
(a) larger than for the Purdue sample because the sample size is smaller.
(b) larger than for the Purdue sample because it uses a smaller fraction of the population.
(c) smaller than for the Purdue sample because the sample size is smaller.
(d) smaller than for the Purdue sample because it uses a smaller fraction of the population.
(e) impossible to determine because of sampling variability.
Larger than for the Purdue sample because the sample size is smaller. Therefore, the option A is the correct answer.
What is margin of error?Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.
Given sample size = 500
Total outcomes = 37,000
The margin of error in a 95% confidence
The margin of error is given by
Margin of error (statistic) = Critical value x Standard error of the sample.
So, according to the given condition margin of error in a 95% confidence is same as for the Purdue sample because both are samples of size 500, because it depends on sample size.
Therefore, the option A is the correct answer.
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Which is an equivalent expression for 18c+144
?
Responses
An equivalent expression for 18c+144 is 18(c+8), by factoring out the greatest common factor of the terms 18 and 144.
In the original expression 18c + 144, we have two terms that do not have any common factors other than 1. However, we can see that both terms are multiples of 18, with 18 as the greatest common factor. So, we can factor out the 18 to simplify the expression.
To factor out 18, we divide each term by 18, which gives us:
18c/18 + 144/18
The first term simplifies to c, and the second term simplifies to 8, so we have:
c + 8
This expression represents the sum of c and 8, and it is equivalent to 18c + 144. However, we can still simplify this expression further by factoring out the common factor of c + 8, which gives us:
c + 8 = 18(c + 8)
So, we have the equivalent expression 18(c + 8), which is the original expression 18c + 144 after factoring out the greatest common factor of 18.
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a school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. how many ways are there to sit the committee in a row at a meeting if the students must sit together by grade?
There are 6,720 possible ways to arrange the committee in a row, with students grouped by grade.
2 seniors * 5 sophomores * 3 freshman * 2 juniors = 60
60 possible arrangements for the 4 grade levels
60 * 6 (the number of ways to arrange 6 people) = 360
360 * 6 (the number of ways to arrange 6 people) = 2160
2160 * 6 (the number of ways to arrange 6 people) = 12,960
12,960 / 2 (because the order of the two grade levels can be reversed) = 6,720
6,720 possible arrangements for the school dance committee.
The school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. To find out how many ways there are to sit the committee in a row at a meeting if the students must sit together by grade, we first need to calculate the number of possible arrangements for each grade level. Since there are 2 seniors, 5 sophomores, 3 freshman, and 2 juniors, there are 60 possible arrangements for the 4 grade levels. We then multiply this by 6, since there are 6 ways to arrange 6 people. This gives us 360 possible arrangements for the first two grade levels. We then multiply this number by 6 again, since there are 6 ways to arrange 6 people. This gives us 2160 possible arrangements for the first three grade levels. We multiply this number by 6 one more time, since there are 6 ways to arrange 6 people. This gives us 12,960 possible arrangements for all four grade levels. However, since the order of the two grade levels can be reversed, we must divide this number by 2. This gives us a total of 6,720 possible arrangements for the school dance committee.
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Choose ALL answers that describe the quadrilateral
T
U
V
W
TUVW if
T
U
‾
∥
V
W
‾
TU
∥
VW
,
T
U
‾
≅
V
W
‾
TU
≅
VW
, diagonal
T
V
‾
TV
bisects
∠
T
∠T and
∠
V
∠V, and diagonal
U
W
‾
UW
bisects
∠
U
∠U and
∠
W
∠W
The mentioned characteristics of quadrilateral are the properties of the Rhombus. So option C is correct.
What are the properties of a rhombus ?The lengths of the four sides are equal.Congruent opposite angles (i.e., they have the same measure).Adjacent angles are helpful (i.e., they add up to 180 degrees).The diagonals form a right angle split across one another.The diagonals are each other's perpendicular bisectors.Given that,
A quadrilateral TUVW,
UV || WT,
TU || VW
TV = UW (Diagonals )
TV ⊥ UW (Diagonals are perpendicular)
Hence, the given characteristics are of the rhombus.
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Use the figure. If the length of the diameter of the circle is 15 inches, what is the length of the radius of the circle?
The length of the radius of the circle is 7.5 inches.
What is diameter and radius of circle?The radius formula is easily obtained by halving the circle's diameter. The line segment created when we join a point on a circle's circumference to its exact center is referred to as the ring's radius. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.
Given that the diameter of the circle is 15 inches.
The radius of the circle is half the measure of the diameter.
That is,
R = d/2
R = 15/2
R = 7.5 inches
Hence, the length of the radius of the circle is 7.5 inches.
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