18. Does the rule y = 6x² represent an exponential function?
Oyes
Ono

To cut a 14-inch pizza into three equal area pieces using two parallel cuts placed symmetrically from the center, each piece will have an area of 150.

As we need to cut a 14-inch pizza into three pieces of equal area using two parallel cuts, we have to follow the steps given below

:Step 1: Cut the pizza with a line that goes through the center of the pizza and marks its diameter. This cut separates the pizza into two equal halves.

Step 2: The second cut needs to be made parallel to the first cut and needs to be at a distance of approximately 1/3 the diameter of the pizza from the first cut.

Step 3: Then, the pizza will be separated into three equal area pieces as required. As we have to cut the pizza into three equal area pieces, the area of each piece will be 150 square inches.

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Notice that the prime factorization of \(20^{20}\) and \(10^{10}\) are \(2^{40}\cdot5^{20}\) and \(2^{10}\cdot5^{10}\), respectively. also, notice that both of their prime factorizations contain only 2 and 5.

Let the divisor of 20^20 that is a multiple of 10^10 be:

\(2^y\cdot5^x\cdot2^{10}\cdot5^{10}\\=2^{10+y}\cdot5^{10+x}\)

where y and x are positive integers.

We can have y equal to 0, 1, 2, ... 30 before the exponent of 2 exceeds 40, and we can have x equal to 0, 1, 2, ... 10 before the exponent of 5 exceeds 20.

That is 11*31= 341 numbers in total.

There are (40+1)(20+1)=861 factors in 20^20, which means that the final answer is:

\(\boxed{\frac{341}{861}}\)

also are you, by any chance, the same guest who posted the same question in web2.0?

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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The equation representing the situation is 4x = y - 1, where x is the number of households with one pet and y is the total number of households. This can be answered by the concept of Simple equation.

Let's assume that there are x households with a single pet. The number of households with no pets is given as one-fourth of the number of households with multiple pets, which means there are 4 times as many households with multiple pets as there are households with no pets. Let's represent the total number of households as y.

Therefore, we can say that the number of households with no pets is (y - x)/4, and the number of households with multiple pets is 3(y - x)/4 since there are 4 times as many households with multiple pets as there are households with no pets.

Now, we can use the given information that the number of households with no pets is one-fourth of the number of households with multiple pets to write the equation:

(y - x)/4 = x/3

Solving for y, we get:

y = 4x + 3x/4 = 16x/4 + 3x/4 = 19x/4

But we are given that the total number of households y includes the households with one pet, so we can write:

y = x + (y - x)/4 + 3(y - x)/4 = x + y/4

Substituting the value of y from the previous equation, we get:

19x/4 = x + 19x/16

Solving for x, we get:

x = 16/3

Therefore, the equation representing the situation is 4x = y - 1, where x = 16/3 and y = 19x/4, which simplifies to:

4(16/3) = y - 1

y = 21

Therefore, there are 16 households with one pet and 5 households without any pets.

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It is given that machine print 63 booklets in 6 hours.

To determine the proportion could be used to determine ask the number of booklet that the machine can print it nine hours.

Use the unitary method,

In 6 hours booklets print is 63.

In 1 hour , booklets print is

In 9 hour , the booklets print is

Hence the proportion formed is

The correct option is b.

Answer: I think the answer is 1250.

Step-by-step explanation:

I did 200 divided by 4 which is 50. I then multiplied 50 * 25 and got 1250.

Answer:

y = -2x - 14

Step-by-step explanation:

Slope-intercept form: y = mx + b

First, simplify. Distribute -2 to all terms within the parenthesis:

-2(x + 5) = -2x - 10

y + 4 = -2x - 10

Note the slope intercept form: y = mx + b. Isolate the variable, y. What you do to one side of the equation, you do to the other side.

y + 4 (-4) = -2x - 10 (-4)

y = -2x + (-10 - 4)

y = -2x - 14

y = -2x - 14 is your answer.

~

Answer:

y= -2x + 14

Step-by-step explanation:

y+4=-2(x+5)

Subtract 4 from both sides of the equation

y= -2(x+5) -4

Distribute the -2

y=-2x-10-4

Simplify

y= - 2x + 14

The slope is -2 and the y intercept is 14

The area of one of the bases of the pentagonal prism is approximately 49.8 square units.

What is pentagon?

A pentagon is a geometric shape that has five straight sides and five angles. It is a type of polygon, which is a two-dimensional shape with straight sides.

To find the area of one of the bases of the pentagonal prism, we need to use the formula for the volume of a pentagonal prism, which is:

V = (1/2) * P * h * b

where V is the volume of the prism, P is the perimeter of the base, h is the height of the prism, and b is the area of one of the bases.

We are given that the height of the prism is 8 units and the volume is 284.8 \(units^3\). We can also determine the perimeter of the base using the height and the fact that the base is a regular pentagon. Specifically, we can use the formula for the perimeter of a regular polygon, which is:

P = n * s

where P is the perimeter, n is the number of sides, and s is the length of one side.

For a regular pentagon, n = 5, so the perimeter is:

P = 5s

We do not know the length of one side, but we can use the fact that the height of the prism (8 units) is the same as the apothem (the distance from the center of the pentagon to the midpoint of one of its sides). Specifically, we can use the formula for the area of a regular polygon, which is:

A = (1/2) * P * a

where A is the area of the polygon, P is the perimeter, and a is the apothem.

Since the height of the prism is equal to the apothem, we have:

a = 8 units

We can now use the formula for the area of a regular pentagon, which is:

\(A = (5/4) * s^2 * sqrt(5 + 2 * sqrt(5))\)

where A is the area of the pentagon and s is the length of one side.

We can solve for s by substituting the known values of A and a into this formula and simplifying:

\(A = (5/4) * s^2 * sqrt(5 + 2 * sqrt(5))\\\\284.8 = (5/4) * s^2 * sqrt(5 + 2 * sqrt(5))\\\\s^2 = 284.8 / [(5/4) * sqrt(5 + 2 * sqrt(5))]\\\\\)

\(s^2\) ≈ 23.6

s ≈ 4.86

Finally, we can use the formula for the area of a regular pentagon with side length s to find the area of one of the bases:

\(A = (5/4) * s^2 * \sqrt{(5 + 2 * sqrt(5))\)

A ≈ 49.8 square units

Therefore, the area of one of the bases of the pentagonal prism is approximately 49.8 square units.

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Answer:

two tens and five ones

Step-by-step explanation:

rename the place values then put them together

Answer:

Five fives

Step-by-step explanation:

5 times 5 is 25.

Hope this helped!

Stu had quite a collection of baseball cards. One day he decided to give half of them to his brother Seth. Then he gave one-third of what he had left to a friend. Then he gave half of what was left to another friend. Stu now has 50 baseball cards. How many did he start with? It seems that I should work

let Stu have x cards

he gave half to seth

so he had x/2 cards

He had x/2 he gave 1/3 of x/2 to a friend

=x/6.

Now he had x/2 - x/6 = x/3 with him balance

1/2 of x/3 he gave to another friend =x/6

Balance he had was x/3 - x/6 = x/6

x/6 = 50

multiply by 6

x= 300

Answer:

Now he had x/2 - x/6 = x/3 with him balance

1/2 of x/3 he gave to another friend =x/6

Balance he had was x/3 - x/6 = x/6

x/6 = 50

multiply by 6

x= 300

Step-by-step explanation:

Answer:

9x^2-9x-18=0

9x+2=11x-9x-18=0

9x+2=21x-18=0

9x+2=3x-3^=0

Answer:

Step-by-step explanation:

Formula

\(\frac{-b +/- \sqrt{b^2 - 4ac} }{2a}\)

Givens

a = 9

b = - 9

c = -18

Solution

\(\frac{- (-9) +/- \sqrt{(-9)^2 - 4*9*(-18)} }{2*9}\\\\\frac{9 +/- \sqrt{81 + 4*9*18} }{18} \\\\\frac{9 +/- \sqrt{ 81 + 288} }{18}\\\\\)

9 +/- √369

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

      18

9 +/- 3*√41

==========

      18

x = 9 +/- 19.209

     =========

        18

x = 1.567

or

x = -.567

50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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Answer:

100.5

Step-by-step explanation:

divide 498.75 by 35

whatever you get from that add 2.50

then times it by 6

Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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The interval for which the balls height is increasing is 0 < x < 0.75.

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words. The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.

From the given graph we observe that the graph follows an upward curve up until the point of 0.75 and after that the graph follows a downward trajectory.

Hence, the interval for which the balls height is increasing is 0 < x < 0.75.

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Answer: 3√14 units

Step-by-step explanation:

Let the length of the other leg equal to x

Hence, according to Pythagoras' theorem

\(x^2+(9\sqrt{2} )^2=(12\sqrt{2})^2 \\\\x^2+9^2(\sqrt{2)^2}=12^2(\sqrt{2})^2\\\\x^2+81(2)=144(2)\\\\x^2+162=288\\\\x^2+162-162=288-162\\\\x^2=126\)

Extract the square root of both parts of the equation:

\(x=\sqrt{126} \\\\x=\sqrt{9(14)} \\\\x=3\sqrt{14}\ units\)

The correct option is: (i) and (iii) are correct statements but not (ii).

The correct answer is:

(i) The uniform probability distribution's shape is a rectangle.

(ii) The uniform probability distribution is symmetric about the mode.

(iii) In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.

Therefore, the correct option is: (i) and (iii) are correct statements but not (ii).

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Answer: 80% of the marbles in the bad are not red

Step-by-step explanation:

10 of 50 marbles are red = 20%

40 of 50 marbles are not red = 80%

Answer:

8,12

Step-by-step explanation:

Answer:

Solution is in attached photo.

Step-by-step explanation:

After Louis XVI's failed attempts to sabotage the Assembly and to keep the three estates separate, the Estates-General ceased to exist, becoming the National Assembly. It renamed itself the National Constituent Assembly on July 9 and began to function as a governing body and constitution-drafter.

National assembly

The National Assembly was the first revolutionary government of the French Revolution and existed from June 14th to July 9th in 1789. The National Assembly was created amidst the turmoil of the Estates-General that Louis XVI called in 1789 to deal with the looming economic crisis in France.

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GIVEN:

We are given a frequency distribution table showing different classes of hours of study and the frequency of each class of data.

Required;

To determine the relative frequency for the third class

Step-by-step solution;

For a relative frequyency, we need to find the number of times an event occurs and express it as a fraction of the total events that occured in the survey/experiment.

The events in this case are hours of study and the occurrence is the total frequency for all classes of hours of study.

The total frequency is;

The relative frequency for the third class therefore would be;

ANSWER:

The relative frequency of the third class therefore is

When sampling from a normal population, such as SAT scores, the distribution of sample means will indeed have a normal distribution with the same mean as the population mean.

However, the variability in sample means will not necessarily be less than the variability in individuals. In fact, the variability in sample means is related to the sample size and the variability of the population.

To clarify, the mean of the sampling distribution of the sample mean is indeed equal to the population mean. This property is known as the expected value or the unbiasedness of the sample mean as an estimator of the population mean.

The standard deviation of the sampling distribution of the sample mean, also called the standard error of the mean, is determined by the population standard deviation (σ) and the sample size (n). The formula for the standard error of the mean is:

Standard Error of the Mean = (Population Standard Deviation) / sqrt(Sample Size)

In the case of SAT scores, if we know the population standard deviation and we take samples of a specific size, we can use the above formula to calculate the standard error of the mean. This standard error represents the average variability or dispersion of sample means around the population mean.

It's important to note that as the sample size increases, the standard error of the mean decreases, indicating that the sample means become more precise estimators of the population mean. This reduction in variability occurs due to the effect of sample size on reducing sampling error.

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Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

The binary representation of 5,318,008 is 10100010010010101111000, whereas the binary representation of 73 is 1001001.

We notice that 73 is a binary palindrome while 5,318,008 is not, therefore we conclude that the best number is 73 and the answer is a.

The appropriate conclusion would be to "Do not reject the null hypothesis at α=0.05 level."

In hypothesis testing, the null hypothesis is assumed to be true until there is sufficient evidence to reject it. The level of significance, α, is the probability of rejecting the null hypothesis when it is true. The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

In this case, since the p-value (0.061) is greater than the level of significance (0.05), there is not enough evidence to reject the null hypothesis at the 0.05 level of significance. Therefore, the appropriate conclusion would be to "Do not reject the null hypothesis at α=0.05 level." This means that the data does not provide enough evidence to support the alternative hypothesis, and we can't say for sure that the null hypothesis is false.

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Answer:

h = 9km

Step-by-step explanation:

area of a trapezoid= ½ x (a+b) x h

117 = (2+2+11 +11) / 2 x h

h = 117 / 26÷2

h = 9km

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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