A________ has cross-sectional shapes, taken parallel to a base, that are similar
but not congruent to one another.
A. prism
B. polygon
C. cube
D. pyramid

17 quarters, A set of one or more equations comprising numerous variables is referred to as a system of equations.

A set of one or more equations comprising numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions of systems of equations, or the points where the components of these equations overlap.

Explanation:

q+p =47

25q + p =455

If 19 is the answer, then 25 times 19 is 475. 17 quarters and 30 pennies equal $4.55.

Not 47 q=17, 25x17 = 425 with p = 30, and 17+30 = 47 q + p = 47, but 455 q=18, 25x18 = 450 and p=5, but 18+5 =23, and multiply by 25 to get 25q + 25p = 1175 and subtract 25q+p = 455 to remove one variable.

720/24 = 30 cents, or 24p = 720.

Q = 47/30 = 17 quarters.    

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Answer:

y = 2x - 1

Step-by-step explanation:

(3, 5) (5, 9)

slope = (9-5)/(5-3) = 4/2 = 2

y = mx + b

5 = 2(3) + b

-1 = b

y = 2x -1

Answer:

f(x)=2x-1; y=2x-1

Step-by-step explanation:

First we need to find the slope and to do so you use the equation \(\frac{y_{1} -y_{2}}{x_{1}-x_{2}}\) .

Plugging in for the values we get (9-5)/(5-3)=4/2=2, which means we have a slope of 2.

Now we just have to find the y-intercept, and to do this we multiply the x-value by the slope (2) and see what we have to add to that to get the y-value.

For example, 5*2=10, 10-1=9, so -1 is our y-intercept.

This means our equation in slope-intercept form is y=2x-1 and in function form is f(x)=2x-1

Lengths of time it takes for new light bulbs to burn out are an example of continuous numerical data type.

Quantitative information that can be measured precisely and that can take on any value within a range is known as continuous numerical data. Measurements of length, time, weight, temperature, and many other quantifiable physical qualities are examples of continuous numerical data.

Continuous numerical data can have any value as long as it falls within a specified range, and using mathematical operations like addition, subtraction, multiplication, and division, it is possible to compare and analyze the numbers.

Since it alludes to a continuous range of precise numerical values. The duration of time in this scenario is expressed in hours, minutes, or seconds and can have any value within a specific range, for example, 0.5 hours, 1.25 hours, 2.75 hours, and so on.

Numerical data types like float and decimal can be used to represent continuous numerical data.

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Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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The value of x = 2√21 / 3. This can be solved using rationalization method.

When a radical or surd is rationalised, it is moved from the denominator to the numerator. We rationalise a number to convert it into a fraction's denominator. If the denominator is linear in terms of a radical, the denominator and numerator are multiplied by a number such that the result of the multiplication expands and rationalizes the denominator.

Given that,

It is a 30°-60°-90° triangle.

Thus, √7 = √(3/2) × x

or, 2√7 = √3 × x

or, x = 2√7 / √3

or, x = (2√7  × √3)/ (√3 × √3)

or, x = 2√21 / 3

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There is insufficient evidence to substantiate the publisher's claim at the 0.05 level of significance.

To determine if there is sufficient evidence to substantiate the publisher's claim, we need to conduct a hypothesis test.

Let's assume the null hypothesis is that the proportion of readers who own a personal computer is equal to 0.32.

The alternative hypothesis is that the proportion is greater than 0.32.

We can use a one-tailed z-test for proportions to test the hypothesis.

At the 0.05 level of significance, the critical z-value for a one-tailed test is 1.645.

If our calculated z-value is greater than 1.645, we reject the null hypothesis and conclude that there is sufficient evidence to support the publisher's claim.

Assuming we take a random sample of readers and find that 350 out of 1000 readers own a personal computer, the calculated z-value can be computed as:

\(z = (p - P) / \sqrt( P(1-P) / n )\)

where

p = sample proportion = 350/1000 = 0.35

P = hypothesized proportion = 0.32

n = sample size = 1000

z = (0.35 - 0.32) / sqrt( 0.32 * 0.68 / 1000 )

z = 1.42

Since the calculated z-value (1.42) is less than the critical z-value (1.645), we fail to reject the null hypothesis.

Therefore, there is insufficient evidence to substantiate the publisher's claim at the 0.05 level of significance.

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The Probability of drawing a three given that the card is not a face card is 1/9.

In summary:

- P(face card | queen) = 1/13

- P(three | not a face card) = 1/9

The probabilities, we need to consider the total number of favorable outcomes and divide it by the total number of possible outcomes.

1. P(face card | queen):

A face card is a jack, queen, or king. There are four queens in a standard deck of 52 cards. So the total number of favorable outcomes is 4 (there are four queens in the deck). The total number of possible outcomes is 52 (the total number of cards in the deck).

P(face card | queen) = Number of favorable outcomes / Total number of possible outcomes

                    = 4/52

                    = 1/13

Therefore, the probability of drawing a face card given that the card is a queen is 1/13.

2. P(three | not a face card):

A face card is a jack, queen, or king. So not a face card includes all the other cards in the deck except for jacks, queens, and kings. There are 12 cards of each suit, and there are four suits in a deck. So the total number of not face cards is (12-3) * 4 = 9 * 4 = 36.

The total number of favorable outcomes is the number of threes in the deck, which is four.

P(three | not a face card) = Number of favorable outcomes / Total number of possible outcomes

                         = 4/36

                         = 1/9

Therefore, the probability of drawing a three given that the card is not a face card is 1/9.

In summary:

- P(face card | queen) = 1/13

- P(three | not a face card) = 1/9

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Answer:

4x - 1

Step-by-step explanation:

(–7x + 3) + (11x − 4)

−7x + 3 + 11x − 4

(−7x + 11x) + (3 − 4)

4x - 1

The value of the double integral is:

∫∫R (4x^2)/(1+x^4) dA = (2/5)(2)^(-1/5) - (2/5)

To evaluate the double integral ∫∫R 4x^2/(1+x^4) da, we need to set up the limits of integration for x and y.

Since the region R is bounded by y = 0, y = x, and x = 1, we can set up the limits of integration as follows:

0 ≤ y ≤ x
0 ≤ x ≤ 1

Now we can set up the double integral as:

∫∫R 4x^2/(1+x^4) da = ∫0^1 ∫0^x 4x^2/(1+x^4) dy dx

Integrating with respect to y first, we get:

∫0^1 ∫0^x 4x^2/(1+x^4) dy dx = ∫0^1 [(4x^2/4) ln|1+x^4|]0^x dx

Simplifying, we get:

∫0^1 [(x^2/1+x^4) ln|1+x^4|] dx

This integral is not easy to evaluate directly, so we can use substitution. Let u = 1+x^4, du/dx = 4x^3. Then the integral becomes:

∫1^2 [(1/u) ln u] du/4

Integrating by parts, we get:

∫1^2 [(1/u) ln u] du/4 = [-ln u/u]1^2/4 - ∫1^2 (-1/u^2)(-ln u) du/4

= [-ln(1+x^4)/(1+x^4)]0^1 - (1/4) ∫1^2 (ln u)/u^2 du

= (-ln2/2) - (1/4) [(-1/u^2) ln u - ∫(-1/u^2) du]1^2

= (-ln2/2) + (1/4) [(1/2) ln2 + (1/2) ln17]

= (-ln2/2) + (1/8) ln(34/17)

Therefore, the value of the double integral is approximately -0.077.

The region R is bounded by y=0, y=x, and x=1. We want to evaluate the double integral of the function 4x^2/(1+x^4) over this region.

First, we set up the integral:

∫∫R (4x^2)/(1+x^4) dA

Since the region R is bounded by y=0 and y=x, we can set the limits for y from 0 to x. Similarly, as the region is also bounded by x=1, we can set the limits for x from 0 to 1:

∫(from 0 to 1) ∫(from 0 to x) (4x^2)/(1+x^4) dy dx

Now we integrate with respect to y:

∫(from 0 to 1) [(4x^2)/(1+x^4)]y |_0^x dx

Which simplifies to:

∫(from 0 to 1) (4x^3)/(1+x^4) dx

Now, we integrate with respect to x:

(2/5)(x^5 + 1)^(-1/5)|_0^1

Evaluating the integral at the limits gives us:

(2/5)(1^5 + 1)^(-1/5) - (2/5)(0^5 + 1)^(-1/5) = (2/5)(2)^(-1/5) - (2/5)

And thus, the value of the double integral is:

∫∫R (4x^2)/(1+x^4) dA = (2/5)(2)^(-1/5) - (2/5)

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The algebraic expression is: x% * 100

The statement is given as:

How much x% of sugar syrup can you make if you have 100 grams of sugar?

The amount of sugar is given as:

100 grams

So, the algebraic expression is:

x% * 100

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Using the segment addition postulate, the numerical length of TV is: 9 units.

According to the segment addition postulate, if U lies between line segment TV, therefore:

TV = TU + UV

Plug in the values:

3x + 6 = 4 + 5x

Solve for x

3x - 5x = 4 - 6

-2x = -2

x = 1

TV = 3x + 6 = 3(1) + 6

TV = 9 units

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Answer: Rs 7,280

Step-by-step explanation:

The technique to find tax is by multiplying the sales price and the percent of tax.

If you are still confused, I can provide some examples:

------------------------------------------------------------------------

Given

Price: Rs 45,500

Tax: 16%

Calculate

45,500×16%=Rs 7,280

Hope this helps!! :)

Please let me know if you have any questions

The number of students who watch between 1 - 2 hours is 9.

We have,

From the table,

Number of students who watch tv for 1 hour = 5

Number of students who watch tv for 1.5 hours = 3

Number of students who watch tv for 2 hours = 1

Now,

The number of students who watch between 1 - 2 hours.

= Number of students who watch tv for 1 hour + 1.5 hours + 2 hours

= 5 + 3 + 1

= 9

Thus,

The number of students who watch between 1 - 2 hours is 9.

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The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .

What is probability?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

A highway construction site's cycle time for trucks transporting concrete is evenly spread over the range of 50 to 70 minutes, thus a = 50 and
b = 70
f(x) = 1/[b - a] = 1/[70 - 50] = 1/20 = 0.05, thus a uniform distribution.
Let P(cycle time is less than 65 minutes if it is known that the cycle time exceeds 55 minutes) be:
P(60 < X < 65) = ₆₀∫⁶⁵ f(x) dx =  ₆₀∫⁶⁵ (0.05) dx = 0.05*[65 - 60] = 0.05*5
= 0.25
Thus, the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .

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Answer:

32, 64, 128

Step-by-step explanation:

Let us start by looking at the geometric progression. A geometric progression multiplies each number by a constant, which we can name r, to get the next term. Let us find this constant:

16÷8=2

8÷4=2

Both expressions confirm that our r, the constant, is indeed 2.

To find the next few terms, we simply multiply by r:

1. 16r=16×2=32

2. 32r=32×2= 64

3. 64r= 64×2 = 128

I hope this helps! Please let me know if you have any further questions :)

The ordered pair that could be the image point is (a) (2.5,1)

From the question, we have the following parameters that can be used in our computation:

Point C = (5, 2)

This means that

C = (5, 2)

The point is dilated using the origin as a center of the origin

So, the image point is

C = k(5, 2)

Let k = 1/2

So, we have

C = 1/2(5, 2)

Evaluate

C' = (2.5, 1)

Hence, the ordered pair that could be the image point is (a) (2.5,1)

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Question

Triangle ABC is dilated with the origin as the center of the dilation. Which ordered pair could represent the image of point C(5, 2) after the dilation?

A (2.5,1)

B (5,−2)

C (7.5,4.5)

D (−1,−4)

The probability of winning the game by flipping 4 heads in a row is 1/128.

To win the game by flipping 4 heads in a row, we must first flip 3 tails in a row. The probability of flipping tails on any given flip is 1/2. So, the probability of flipping 3 tails in a row is (1/2) x (1/2) x (1/2) = 1/8.

Once we have flipped 3 tails in a row, we then need to flip 4 heads in a row. The probability of flipping heads on any given flip is also 1/2. So, the probability of flipping 4 heads in a row is (1/2) x (1/2) x (1/2) x (1/2) = 1/16.

To find the probability of winning by flipping 4 heads in a row, we need to multiply the probabilities of flipping 3 tails in a row and then flipping 4 heads in a row: (1/8) x (1/16) = 1/128.

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Answer:

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

For the given equation, the value of x = -21.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

For the given equation,

x ≠ ±3

On taking LHS,

⇒ \(\frac{5}{x+3} - \frac{2}{x-3}\)

Taking LCM,

⇒ \(\frac{5(x-3) - 2(x+3)}{(x+3)(x-3)}\)

⇒ \(\frac{5x - 15 - 2x - 6}{x^2 - 9}\)

⇒ \(\frac{3x - 21}{x^2 - 9}\)

On Comparing both sides,

⇒ \(\frac{3x - 21}{x^2 - 9} = \frac{4x}{x^2 - 9}\)

⇒ 3x - 21 = 4x

⇒ x = -21

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The probability that an employee is sick more than two days in a three-month period is 0.1991.

Poisson distribution: Poisson distribution is a probability distribution which is used to measure the probability of a certain number of events occurring in a given time period if the events are rare and random.

The formula for calculating the Poisson distribution is: P(X=k) = (e^-λ * λ^k) / k!

Where, X = Random variable

k = Number of occurrences of the event

λ = Expected value of the event

e = Euler’s constant = 2.71828….

k! = Factorial of k

Mean of Poisson distribution: Given, Mean of the Poisson distribution is 1. Let X be the random variable which represents the number of days an employee is sick in a month.

∴ P(X=k) = (e^-λ * λ^k) / k!

The probability that an employee is sick more than two days in a three-month period is P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + .....

To calculate the probability, we need to find the value of λ for three months.

λ for three months = Mean for a month * Number of months∴ λ = 1 * 3 = 3

Now, we have λ = 3P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + .....= (e^-3 * 3^3) / 3! + (e^-3 * 3^4) / 4! + (e^-3 * 3^5) / 5! + .....= 0.1991

Hence, the probability that an employee is sick more than two days in a three-month period is 0.1991.

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Answer:

3.7001 × 10 to the power of 4 is the answer for #1

Step-by-step explanation:

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.

Given that,

Speed of first bicycle = 9 mph

Speed of second bicycle = 5 mph

Suppose the length of the circle 24 miles.

We need to find the relative velocity

Using formula of relative velocity

\(v=v_{1}-v_{2}\)

Put the value into the formula

\(v=9-5\)

\(v=4\ mph\)

We need to calculate the time

Using formula of time

\(t=\dfrac{d}{v}\)

\(t=\dfrac{24}{4}\)

\(t=6\ hr\)

We need to calculate the distance of the points where the two bicycles meet

Using formula of distance

For first bicycles,

\(d=9\times6\)

\(d=54\ miles\)

For second bicycles,

\(d'=5\times6\)

\(d'=30\ miles\)

Hence, The points where the two bicycles meet after every 6hr at 30 miles and 54 miles.

Answers:

================================================

Explanation:

The number 987 has three nonzero digits, showing that we have 3 sig figs here. But we want to round to 2 sig figs. This means we need to keep the 2 left-most digits, and drop the third one

We go from 987 to 980

But wait: we need to round to 990 instead since 987 is closer to 990 than it is to 980.

In other words, we round to the nearest tens place value in this case. A similar situation happens when we round 792 to 790

Also, 432.75 will round to 430

Notice that the zero at the end of something like 430 is not a significant digit. You can think of 430 as \(4.3 \times 10^2\) to see that the 4.3 now has 2 sig figs (meaning that 0 at the end is effectively just a placeholder more or less).

Answer:

Christianity and Islamic religion

Step-by-step explanation:

Based on the picture you provided It would be Christianity and Islamic religion.

Based on the Events of the Common Era (year 0) was the birth of Jesus of Nazareth. From Year 0 to year 29 Jesus of Nazareth expanded his faith. During the 29th year Jesus of Nazareth was crusified in Jeruselem.

Estimated around Year 570 Muhammad  (the Prophet of Islam) was born and rose his religion to great heights. In 632 Muhammad died.

Hope this helps

Answer:

Christianity and Islam

Step-by-step explanation:

At present, Tyrone is 48 years old and his daughter is 24 years old.

Let's start by using variables to represent the ages of Tyrone and his daughter.

Let T be Tyrone's current age and D be his daughter's current age.

We know that Tyrone is twice as old as his daughter, so we can write:

T = 2D

We also know that in 6 years, Tyrone's age will be three times what his daughter's age was six years ago. Six years ago, Tyrone's age was T - 6 and his daughter's age was D - 6. So we can write:

T + 6 = 3(D - 6)

Now we have two equations with two variables, so we can solve for T and D.

First, substitute T = 2D from the first equation into the second equation:

2D + 6 = 3(D - 6)

Simplifying this equation, we get:

2D + 6 = 3D - 18

Add 18 to both sides:

2D + 24 = 3D

Subtract 2D from both sides:

24 = D

So Tyrone's daughter is 24 years old now.

We can use the first equation to find Tyrone's age:

T = 2D = 2(24) = 48

Therefore, Tyrone is 48 years old now.

So at present, Tyrone is 48 years old and his daughter is 24 years old.

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Tyrone is twice as old as his daughter. in 6 years Tyrone's age will be three times what his daughters age was six years ago. how old will they be at present?

Answer:25 pear trees

Step-by-step explanation:

15/150

60/150

50/150

15+60+50=125

150-125=25

Answer:

There’s not

Step-by-step explanation:

It’s 618

The correct statement is: 98.5% of the variation in age is explained by a linear relationship with yearly income. The correlation coefficient, r, is 0.969.

The r2 value of 0.9846 means that approximately 98.5% of the variability in age can be explained by the linear relationship with yearly income. Since the r2 value is the square of the correlation coefficient, r, we can find r by taking the square root of 0.9846, which gives us approximately 0.969. Therefore, the correct statement is that the correlation coefficient, r, is 0.969.

The other options are incorrect because they either mix up the variables (e.g., stating that the variation in income is explained by age) or introduce information that is not supported by the given r2 value (e.g., stating that the relationship is nonlinear).

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Answer:

we have:

x + 4 + x + 6 + x + 2 + x + 18 + x = 180.3

<=> 5x + 30 = 540

<=> 5x = 520

<=> x = 104

we also have: m<5 + x = 180

<=> m<5 = 180 - 104

<=> m<5 = 76