Complete the sentence.​ Then, use the laws of exponents to write an equivalent expression for the given expression.

To divide powers that have the same base and different​ exponents, keep the​ ___ and​ ___ the exponents.

c = 11.05 ≈ 11 cm. When the diagonal length for the rectangular prism is given is to the nearest whole unit, the correct answer is B.

A quantity known as length has the ability to calculate approximate distance between two areas. In addition to height the breadth, it creates an object's length. Children will learn about length in math lessons to help them solve practical challenges both inside and outside of the classroom. the length or width that is possible to measured; a thing's greatest or longest dimension. 10 feet in length. Table of Metric units, Metric System Table: The length characteristic. The quantity or measurement between two points is the definition of length. In other words, a geometric arrangement or object's largest two or highest three dimensions.

given

Start by calculating the length of the base's diagonal using the Pythagorean theorem:

a² + b² = c²

Fill in the equation with the length and width:

8² + 3² = c²

64 + 9 = c²

73 = c²

c ≈ 8.54 cm

Using our estimated diagonals for the base and the height, we can now determine the prism's diagonal's length. Apply the same formula:

(8.54)² + 7² = c²

73 + 49 = c²

122 = c²

√122 = c

c = 11.05 ≈ 11 cm. When the diagonal length for the rectangular prism is given is to the nearest whole unit, the correct answer is B.

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The general solution to the differential equation [tex]3x^2y' + 6xy = 15y^3[/tex] is

y = ±√(c/15) where c is an arbitrary constant.

To solve this differential equation, we first divide both sides by

[tex]3x^2[/tex] to obtain [tex]y' + 2x/3y = 5y^3/3x^2[/tex]

Next, we can use the substitution

[tex]v = y/x^(2/3)[/tex] to get[tex]v' = (y'x^(2/3) - 2y/3x^(1/3))/x^(2/3) = y'x^(2/3) - 2v/3[/tex]

Substituting back into the original equation gives [tex]v' + 2v/3 = 5v^3[/tex]. This is a separable differential equation and can be solved using the separation of variables. Integrating both sides,

we get [tex](v^2)/2 = -2v/3 + c[/tex] where c is an arbitrary constant. Solving for v, we get v = ±√(c/15). Finally, substituting back for y, we get

[tex]y = ±x^(2/3)√(c/15).[/tex]

Thus, the general solution to the differential equation [tex]3x^2y' + 6xy = 15y^3 is y = ±√(c/15)[/tex] where c is an arbitrary constant.

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1.  -4, -2, 0, 2... is an arithmetic sequences with a common difference of 2.

2.1/2, 5/8, 3/4, 13/16... is not an arithmetic sequences.

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common difference, denoted by the letter d.

We use the common difference to go from one term to another.

Take the current term and add the common difference to get to the next term, and so on. That is how the terms in the sequence are generated.

The given sequence can only be an arithmetic sequences if they have same common difference

1.

2-0 = 2

0 - (-2) = 2

-2 -(-4) = 2

Thus, the given sequence is an arithmetic sequences with a common difference of 2.

2.

13/16-3/4 = 1/16

3/4 -5/8  = 1/8

5/8 - 1/2 = 1/8

Thus, the given sequence is not an arithmetic sequences.

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Complete question:

Arithmetic Sequences as Linear Functions.

Determine whether each sequence is an arithmetic sequence. Write yes or no.

1. -4, -2, 0, 2, ...

2. 1/2, 5/8, 3/4, 13/16 ...

For a polling organization that conducts a telephonic poll from 850 registered votes and ask them to whom they will vote in coming presedential election. In the context of question, population size, sample and percentage of voter preference is given below.

a. The population being studied is the population of registered voters who will vote in the upcoming presidential election.

b. The sample being studied is the group of 850 registered voters who were surveyed by telephone.

c. Based on the sample, it is estimated that 45% of the population would vote for candidate B. However, it's important to note that this is only an estimate based on a sample of registered voters, and it may not accurately reflect the views of the entire population. Additionally, since the sample size is only 850, the estimate may have a margin of error associated with it. To get a more accurate estimate of the percentage of the population that would vote for candidate B, a larger sample size or a different method of polling would be necessary.

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The required sample need if they plan to create a 99% confidence interval but still maintain their accuracy is 4160.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
The sample size is given as,
n = p × q × (Z/E)²

Assume the estimate for population proportion,
p = 0.5

Now,
q = 1 - p
q = 1 - 0.5
q = 0.5

Confidence level = 99%

Z value = 2.58
The margin of error,
E = 0.02

The sample size is given as,
Substitute the value in equation 1.
n = 0.5×0.5×(2.58/0.02)²

n = 4160

Thus, the required sample need if they plan to create a 99% confidence interval but still maintain their accuracy is 4160.

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Answer:

Hence the solution to the differential equation is Step-by-step explanation:

Answer:

D

Books Cost

10

$122.50

11

$134.75

12

$147

Step-by-step explanation:

The table format is all messed up but I was able to figure out the numbers.

Since 10 books cost $122.50, each book must cost $122.50/10 = $12.25

For 1 book => 10 x $12.25 = $122.50

For 11 books => 11 x $12.25 = $134.75

For 12 books => 12 x $12.25 = $147

Answer choice is D which perfectly fits the numbers

For the system of equations to have a unique solution the value of k must not be 6

Now, According to the question:

The given equations are,

kx + 2y = 5

3x + y = 1

The above equations can be written as,

kx + 2y – 5 = 0

3x + y – 1 = 0

We need to find the value of k.

So, we know that if the two equations are [tex]a_1x+b_1y+c_1=0[/tex], [tex]a_2x+b_2y+c_2=0[/tex] Then we will compare the coefficients such that

[tex]\frac{a_1}{a_2},\frac{b_1}{b_2} and \frac{c_1}{c_2}[/tex].

If [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]  then the equations have unique solution, if [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex]

then the equations have infinitely many solutions and if [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]

then the equations have no solutions.

Here we can clearly see that,

[tex]a_1=k,b_1=2,c_1=-5\\\\\\a_2=3,b_2=2,c_2=-1[/tex]

So, [tex]\frac{a_1}{a_2},\frac{b_1}{b_2} , \frac{c_1}{c_2}[/tex]

[tex]\frac{a_1}{a_2}=\frac{k}{3}, \frac{b_1}{b_2}=\frac{2}{1} , \frac{c_1}{c_2}=\frac{5}{1}[/tex]

We know that if the system of equation has unique solution then [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]

So, we solve on putting their values and we get,

[tex]\frac{k}{3}\neq \frac{2}{1}[/tex]

[tex]k\neq 6[/tex]

Hence, for the system of equations to have a unique solution the value of k must not be 6.

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The given question is incomplete, complete question is:

Find the value of k for which the following system of equation has the unique solution:-

kx + 2y = 5

3x + y = 1.

If monthly disability is $1000, the amount of disability per week is $250.

Based on the provided information in the question, the average monthly disability benefit (cash received) per person is $1000. The weekly benefit can be determined using division operation. The weekly benefit will be the average monthly disability benefit divided by number of weeks per month. Assuming that there are 4 weeks per month, the weekly benefit is:

Weekly monthly disability benefit = Monthly benefit/Number of weeks per month =$1000/4 = $250

Hence, if the monthly disability benefit is $1000 per person, then the weekly disability benefits is $250 per week.

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Answer:

8 slices per pizza.

Step-by-step explanation:

To find the number of slices in one pizza, we can use division.

If you order 12 pizzas, you will get 96 slices of pizza. To find the number of slices in one pizza, we can divide the total number of slices by the number of pizzas:

96 ÷ 12 = 8

Therefore, there are 8 slices in one pizza.

Answer:

8

Step-by-step explanation:

12 pizzas have 96 slices
So one pizza must have 96/12 = 8 slices of pizza

The number that is 1.5 standard deviations below the mean is 1.55 (rounded to three decimal places).

To find :  The number that is 1.5 standard deviations below the mean

We need to first calculate the mean and standard deviation of the random variable X.

First, let's find the mean. The mean, also known as the expected value, is calculated as follows:

[tex]Mean = (1 * 15 + 2 * 30 + 3 * 28 + 4 * 10) / 100 = 2.8[/tex]

Next, let's find the variance, which is calculated as:

[tex]Variance = ( ( (1 - 2.8)^2 * 15) + ( (2 - 2.8)^2 * 30) + ( (3 - 2.8)^2 * 28) + ( (4 - 2.8)^2 * 10) ) / 100 = 0.72[/tex]

Finally, the standard deviation is calculated as the square root of the variance:

[tex]SD = \sqrt{0.72} = 0.85[/tex]

Now that we have the mean and standard deviation, we can calculate the number that is 1.5 standard deviations below the mean:

[tex]Number = Mean - 1.5 * SD = 2.8 - 1.5 * 0.85 = 1.55[/tex]

So, the number that is 1.5 standard deviations below the mean is 1.55 (rounded to three decimal places).

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The complete question is :

A sample of 100 clients of an exercise facility was selected. Let X = the number of days per week that a randomly selected client uses the exercise facility.

X Frequency

0 2

1 13

2 31

3 29

4 11

5 7

6 7

Find the number that is 1.5 standard deviations BELOW the mean. (I also have to round the answer to three decimal places.)

4071.5 is the volume v of the solid .

How is volume measured?

The 3-dimensional space that is occupied by matter or surrounded by a surface is measured in volume, which is expressed in cubic units.

                            A derived measure called the cubic meter (m3) serves as the SI unit of volume.

Limits of intgration: 18 - x2 = x2;  2x2 = 9; x = ±3;

V = π∫-33[(18 - x2)2 - (x2)2]dx

       = 2π∫03(324 - 36x2)dx

      = 2π(324x - 12x3)03

        = 1296π

        = 4071.5

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The characteristics of the absolute value functions in this problem are given as follows:

The absolute value function is defined by the following rule:

f(x) = |x - h| + k.

For which:

For item a, we have that h = -3, meaning that the function was shifted 3 units left, and then:

The vertex is at (h,0), as h = -3, while there was no change to k.

The domain is all real values, as is the standard for the absolute value function.

The range is [0, ∞), as there was no vertical shift.

For item b, we have that k = 2, meaning that the function was shifted 2 units up, and then:

The vertex is at (0,2), as k = -2, while there was no change to h.

The domain is all real values, as is standard.

The range is [2, ∞), due to the vertical shift of k = 2 moving the graph 2 units up.

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The equation of the line passing through the points (1, -9), and (-3, -9) is y = -9.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Points are (1,3) and (3,2)

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

m = 2 - 3 / 3 - 1

m = -1/2

The equation of the line is given as

y - y₁ = m (x - x₁)

y - 3 = -1/2(x - 1)
y = -1/2x + 1/2 + 3
y = -1/2x + 7/2

As point (0, a) lies on the line, so
a = -1/2(0) + 7/2
a = 7/2

Thus, the required value of a is given as 7/2 and the equaiton of the line is y = -1/2x + 7/2.

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The value of b on the given linear equation is: b= 9.

Here we have a linear equation.

Remember that the general linear equation can be written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the two points (2, 3) and (3, 0), then the slope is:

a = (0 - 3)/(3 - 2) = -3

The line is like:

y = -3*x +b

To find the value of b, we can replace the values of the point (3, 0), then we will get:

0 = -3*3 + b

0 = -9 + b

9 = b

That is the value of b.

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Answer:

(-4, -8) and (0, -5)

Step-by-step explanation:

For a point to be a solution, both equations on a graph must intercept. In other words, if they cross at the same point, then they are a solution.

From what I see in the screenshot, it looks like the parabola and line at points (-4, -8) and (0, -5). Therefore, they should be the two solutions in the system of equations.

Hope this helps.

the simplest form of the given expression will be -6[tex]x^{4}[/tex]+26x²+48.

What is a quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally, the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation (8+6x²)((6-x²)

= (8*6)-8x²+36x²-6[tex]x^{4}[/tex]

= -6[tex]x^{4}[/tex]+26x²+48

Hence the simplest form of the given expression will be -6[tex]x^{4}[/tex]+26x²+48.

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If (x,y) is a solution to equations y = x²  and  2y+6 = 2(x+3) , then the value of xy is (a) 1  .

The values of x and y are solutions to two equations:

⇒ y = x²   ....equation(1)

⇒ 2y + 6 = 2(x + 3)    ....equation(2)

To find the value of xy, we first need to find the values of x and y which satisfy both equations.

We can put value of y from the equation(1) into the equation(2) :

⇒ 2y + 6 = 2(x + 3)

⇒ 2x² + 6 = 2(x + 3)

⇒ 2x² + 6 = 2x + 6

⇒ 2x² - 2x = 0

⇒ 2x(x - 1) = 0

that means either "2x=0"   or "x-1=0" ;

⇒   x = 0  or x = 1 .

when x = 1  , we have y = (1)² = 1 .

So , the product is = 1 × 1 = 1 .

Therefore , the value of xy is (a) 1  .

The given question is incomplete , the complete question is

If (x,y) is a solution to equations y = x²  and  2y+6 = 2(x+3) , what is the value of  xy ?

(a) 1

(b) 2

(c) 3

(d) 9

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On, solving the provided question, we can say that from the provided number line, the value of b is = 1

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

from the provided number line,

the value of b = 13/8 - 5/8 =

1.625 - 0.625 = 1

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Answer:

The answer is c. 30 cm, 40 cm, 50 cm. This set of measures could not be the side lengths of a right triangle, as it does not satisfy the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the square of the hypotenuse (50 cm) is not equal to the sum of the squares of the other two sides (30 cm and 40 cm).

Step-by-step explanation:

Answer:

The expression is:

5x + 2v - 5

The terms in this expression are:

5x, with a coefficient of 5

2v, with a coefficient of 2

-5, with a coefficient of -5

So the coefficients are 5, 2, and -5 respectively.

∠DEF ≅ ∠FHG as, The other two corresponding angles are equal.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, Are two triangles DEF and FGH.

DE || FG so the m∠D = m∠F.

Therefore, The sides opposite to ∠D and ∠F are equal and they are

EF and GF.

Given, m∠E = m∠G>

Therefore, The measure of angle D is equal to the measure of angle F.

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The line equation that passing through point (6,-1) and perpendicular to y = -2x + 8 is

From the case we know that:

Point = (6, -1)

Line 1: y = -2x + 8

Line 2?

If line 1 and line 2 is perpendicular, hence the slope of both lines should fulfill this rule:

m1 x m2 = -1

(-2) x m2 = -1

m2 = 1/2

Next, we will try to find the line equation using the passed through point:

y - y1 = m (x - x1)

y - (-1) = 1/2 (x - 6)

y + 1 = 1/2 (x - 6)

y + 1 = 1/2 x - 3

y = 1/2 x - 4

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Answer: $50

Step-by-step explanation:

Discrete mathematics has had a significant impact on reducing cultural distinctions by serving as a universal language that transcends cultural barriers. One way it has done this is by providing a common framework for communication and collaboration between mathematicians from different cultures.

Discrete mathematics is a branch of mathematics that deals with discrete objects, such as numbers, graphs, and algorithms. It provides a basis for computer science, information technology, and other fields that rely on computational methods and mathematical models.

These fields have become increasingly important in our interconnected world, and their growth has helped to reduce cultural distinctions by bringing mathematicians from different cultures together to work on common problems and develop a shared understanding of mathematical concepts and methods.

Another way discrete mathematics has reduced cultural distinction is by providing a common language for representing and solving problems in various fields, such as engineering, finance, and biology.

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The value of fraction in simplest form is, 1/1296.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

⇒ 1/6 with an exponent of 4.

Now, We can simplify as;

⇒ (1/6)⁴

⇒ 1 / 6⁴

⇒ 1/ 6×6×6×6

⇒ 1 / 1296

Thus, The value of fraction in simplest form is, 1/1296.

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The p-value in this example would be 1 - 0.99865 = 0.00135.

A p-value is a measure of how likely it is to observe a result from a statistical test, given that the null hypothesis is true. It is calculated by taking the probability of the observed result under the assumption of the null hypothesis, then subtracting this probability from 1.

Formula:

P-value = 1 - Probability(observed result | null hypothesis)

For example, if the observed result is that the mean of a sample is 5 and the null hypothesis states that the mean is 3, the p-value is calculated by taking the probability of observing a mean of 5 or greater under the assumption that the mean is 3. This probability can be calculated from a standard normal distribution table by looking up the z-score corresponding to the mean of 5 and subtracting it from the total area under the curve (which is equal to 1).

Therefore, the p-value in this example would be 1 - 0.99865 = 0.00135.

By interpreting the p-value, we can determine the likelihood that the observed result would occur given that the null hypothesis is true. In this example, the p-value of 0.00135 indicates that it is very unlikely that the mean of the sample would be 5 or greater if the true mean is 3. Therefore, we can reject the null hypothesis and conclude that the true mean is not 3.

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Answer:

4.5

Step-by-step explanation:

2 time 4.5 is 9

Answer: x=4.5

Step-by-step explanation:

2x=9

2*x=9, now flip the 2, and make it division.

x=9/2

x=4.5