Factor out the GCF. Use the distributive property to write an equivalent
expression for 8d-16f.

The solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression will be solved as follows:-

E =  [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]

E = [tex]\sqrt{7\times 7\times 3\times xy^7\times x^5y^5[/tex]

E=[tex]\sqrt{7\times 7\times 3\times x^6y^{12}[/tex]

E = 7x³y⁶√3.

Therefore the solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.

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Answer:

0.035

Step-by-step explanation:

Since all of them find a job, the probability is

[tex]51\%\times51\%\times51\%\times51\%\times51\%\\\\=(51\%)^5\\\\=0.035[/tex]

(rounded to the nearest thousandth)

Answer:

Hence the expression [tex]$$(4z-y)(z-6)=4z^2-yz-24z+6y$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 4z & - & y \\ \times & {} & {} & {} & z & - & 6 \\ \end{matrix}$$[/tex]

________________

[tex]$$\begin{matrix}{} & {} & {} & - & 24z & + & 6y \\ 4{{z}^2} & - & yz & {} & {} & {} & {} \\ \end{matrix}$$[/tex]

______________________

[tex]$$\begin{matrix}4{{z}^2} & - & yz & - & 24z & + & 6y \\ \end{matrix}$$[/tex]

Work Shown:

i = P*r*t

i = 1250*0.045*5

i = 281.25

Answer:

28 units

Step-by-step explanation:

First, we are going to solve the equation  to find the value ^^

Let's solve the equation step by step

Step 1. Use the distributive property to destroy the parenthesis

Step 2. Subtract 196 to both sides of the equation

Step 3. Factor the expression

Step 4. Set each factor equal to zero and solve

Since we are dealing with lengths here, and lengths cannot be negative, the only valid solution is 28.

Now, we know from our problem that the missing side of the rectangle is given by the expression , so to find the actual length, we just need to replace  with 8 in the given expression and simplify!

We can conclude that the missing side length represented by x + 8 units of the rectangle is 28 units.

Answer:

1/3

Step-by-step explanation:

please mark brainliest if correct

The value is P(p'-p > 0.17) = 0.09

From the question we are told that

The population proportion is p=0.19

The sample size is n = 479

Generally given that the sample size is large enough , i.e  n > 30 then the mean of this sampling distribution is mathematically represent

[tex]u_{x} =p=0.19[/tex]

Generally the standard deviation is mathematically represented as

σ[tex]=\sqrt{ \frac{p(1-p)}{n}[/tex]

σ= [tex]\sqrt{ \frac{0.19(1-0.19)}{479}[/tex]

σ=0.017

Generally the the probability that the sample proportion will differ from the population proportion by greater than 17% is mathematically represented as

[tex]P(p'-p > 0.17) =P (z > \frac{0.17}{0.017} )[/tex]

[tex]P(p'-p > 0.17) =P (z > 10 )[/tex]

[tex]P(p'-p > 0.17) =P (z > 10 ) - P (z > -10 )[/tex]

From the z table  the area under the normal curve to the left corresponding to 10  and - 10 is

[tex]P(p'-p > 0.17) = 0.97042 - 0.87450\\P(p'-p > 0.17) = 0.09[/tex]

So, the value of probability is greater than 17% is P(p'-p > 0.17) = 0.09

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The probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.

The true proportion of the sample or the mean of the sample = 19%, that is, μ = 19% or 0.19.

The sample size (n) = 479.

The sample proportion is to be calculated at the point 17% or 0.17.

The standard error (s) = √{μ(1 - μ)/n} = √{0.19(1 - 0.19)/479} = 0.0179.

We are asked to calculate the probability that the sample proportion is greater that 17% or 0.17.

This is written as P(X > 0.17) = P(Z > {(0.17-0.19)/0.0179}) = P(Z > -1.1173) = 1 - P(Z ≤ -1.1173) = 1 - 0.1304 = 0.8696 or 86.96%.

To calculate this using the calculator, we use the calculator function:

Normalcdf(0.17,10000000,0.19,0.0179) = 0.8677 or 86.77%.

Thus, the probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.

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Answer: O253

Step-by-step explanation:

The correct expression which represents the volume of the cone is,

V = 2x³π/3

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The height of a cone is twice the radius of its base.

Let radius of cone = x

Then, The height of cone = 2x

Hence, The volume of cone is,

V = 1/3πr²h

V = 1/3 × π × x² × 2x

V = 2x³π/3

Thus, The correct expression which represents the volume of the cone is,

V = 2x³π/3

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Answer:

7

Step-by-step explanation:

105/15=7

7   ink cartridges you  can  buy with 105 dollars.

What is a linear equation in math?

One cartridge costs  = 15 dollars

No of cartridge we buy in 105 dollars = 105 /15

                                                              = 7

Therefore, 7   ink cartridges   buy can with 105 dollars.

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Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.

What is Pythagoras Theorem?

The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.

The formula for Pythagoras Theorem is given by,

[tex]h^{2}=a^{2} +b^{2}[/tex]

Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.

Each Subtraction in view of Pythagoras Theorem

It is is given that,

[tex]d =\sqrt{(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

or  [tex]d^{2} =(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2}[/tex]

Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.

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Answer:  [tex]\frac{3}{10}[/tex] or 30%

Step-by-step explanation:

       We will divide the wanted outcomes by the possible outcomes.

       [tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{number of prime number}}{\text{number of numbers 1 through 50}} =\frac{15}{50}=\frac{3}{10}\;\; \text{or 30\%}[/tex]

    The prime numbers from one through fifty are; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

    -> This is 15 numbers

Work Shown:

[tex]1.04 \cdot 10^4 + 5.6 \cdot 10^2\\\\10,400 + 560\\\\10,960\\\\1.096 \cdot 10^4\\\\[/tex]

Note: Something like [tex]5.6 \cdot 10^2[/tex] means we move the decimal point two spots to the right to get to 560. If the exponent was negative, then we move that many spaces to the left.

Using relations in a right triangle, it is found that:

tan(A) = 3/4 = 0.75.

The relations in a right triangle are given as follows:

In this triangle:

Hence the tangent of A is:

tan(A) = 30/40 = 3/4 = 0.75.

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The sample size required to estimate the fraction of people who are captured after appearing on the 10 most wanted list is 228.

Given  standard deviation of 0.26 ,margin of error of 0.04, and confidence interval of 98%.

We have to determine the sample size required to estimate the fraction of people who are captured after appearing on the 10 ost wanted list.

We can find the sample size with the help of margin of error.

Margin of error is the difference between the calculated values and real values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where σ is standard deviation,

n is sample size and z is critial z value.

We have to find the z value for 98% confidence level from z table.

z value=2.326.

Put the values in the formula of margin of error.

0.04=2.326*0.26/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=2.326*0.26/0.04

[tex]\sqrt{n}[/tex]=15.119

squaring both sides we get

n=228.58

By rounding we get

n=228.

Hence the sample size needed is 228.

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The length of the radius rounded to 2 decimal points is 3.88cm.

In geometry, the area enclosed by a circle of radius r is pie  π[tex]r^2[/tex].

How to round decimals?

Rounding decimals consists of rounding a decimal number to a certain number of decimal places, to save time and help us express really long numbers in shorter terms. There are certain rules to follow when rounding a decimal number. Put simply, if the last digit is less than 5, round the previous digit down. However, if it’s 5 or more than you should round the previous digit up. So, if the number you are about to round is followed by 5, 6, 7, 8, 9 round the number up. And if it is followed by 0, 1, 2, 3, 4 round the number down.

The area of circle is [tex]47.39cm^2[/tex].

Putting it in the formula we get

[tex]47.39cm^2[/tex] = π[tex]r^2[/tex]

[tex]r^2[/tex] = 47.39 / π

r^2 = 15.0847

r = 3.88 cm

Hence the length of the radius rounded to 2 decimal points is 3.88cm.

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Answer:

[tex]\frac{5}{6}[/tex], [tex]\frac{5}{6}[/tex], and "Yes"

Step-by-step explanation:

   We will do as the instructions say.

-> See attached.

The equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0

A polynomial is an algebraic equation with at least the power of its variable 3.

Analysis:

if -2, -6, -10i are the zeroes of the polynomial, it means x = -2, x = -6, x = -10i

if x = -2, (x+2) is a factor, (x+6) is a factor.

convert x = -10i to a real number,

i = [tex]\sqrt{-1}[/tex]

-10[tex]\sqrt{-1}[/tex] = 10[tex]\sqrt{- -1}[/tex] = 10[tex]\sqrt{1}[/tex] = 10

x = 10, so (x-10) is a factor.

Therefore equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0

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Answer:

0.291×0.34=0.09894

Answer:  0.09894

We are going to use long division:

The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

Note that:

f(t)= 50 (1/2)^ [tex]\frac{t-2}{5}[/tex]

f(t)= 50 (1/2)^ [tex]\frac{\frac{t}{5} } - {\frac{2}{5} }[/tex]

Note also that in indices,  [tex]x^{-y}[/tex] = 1/ [tex]x^{y}[/tex]

Then:  50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

([tex]50 \frac {1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

= 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

Therefore, The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

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The y-intercept of the point where the value of x is zero, hence the y-intercept are -a and a

Given the coordinate points on a line as  (p , a) and ( p , − a )

Determine the slope

Slope = -a-a/p-p

Slope = infinity

If the value p is zero, hence the coordinate points will become (0, a) and (0, -a)

Since the y-intercept of the point where the value of x is zero, hence the y-intercept are -a and a

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Answer:

-3

Step-by-step explanation:

[tex]Slope = \frac{Change in Y}{Change in X}[/tex]

Take two points

(1, -5) and (-1, 1)

Plug in their y and x coordinates

[tex]\frac{-5 - 1}{1-(-1)} =\frac{-6}{2} = -3[/tex]

Answer:

1st answer is correct.

Step-by-step explanation:

First, let us take two coordinates of the line.

( 0 , -2 ) ⇒ ( x₁ , y₁ )

( -1 , 1 ) ⇒ ( x₂ , y₂ )

We have to use the below formula to find the slope of the line.

Slope = m

[tex]m = \frac{y_1-y_2}{x_1-x_2}[/tex]

Let us find it now.

[tex]m = \frac{-2-1}{0-(-1)}\\m = \frac{-3}{1}\\m=-3[/tex]

The value for r = - 0.8535 ,  there is strong correlation between the variables.

Correlation coefficient describes the relationship between the two variables in the data .

The data given is

(1, 7), (2, 5), (3, -1), (4, 3), (5, -5)

Assuming Linear Regression ,

The data is plotted on the graphing calculator

The value for r = - 0.8535

as the value is in the range of - .85 to -1 , therefore there is strong correlation between the variables.

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Answer: 1.65

Step-by-step explanation:

     First, we must find 8/25 of 1.25. This is using multiplication.

1.25 * 8/25 = 0.4

    Now, we can increase 1.25 by 8/25 of it. This is using addition.

1.25 + 0.4 = 1.65

Answer: =2x²y³+3y.

Step-by-step explanation:

[tex]\frac{14x^5y^4+21x^3y^2}{7x^3y} =\frac{7x^3y*(2x^2y^3+3y)}{7x^3y}= 2x^2y^3+3y.[/tex]

60 × 48 = 2880 L

2880 ÷ 700 = 4

Answer:

20  1 Liter Cartons

40  700 ml Cartons

Step-by-step explanation:

Let A be the number of 700ml cartons.

Let B be the number of 1 L cartons

We are told that A + B = 60 cartons total

Rearrange to isolate A:  A = 60 - B

700ml is 0.700L

Total volume of milk is 48L

Total volume (in liters) of the 700 ml cartons is from (0.70 L)A

Total volume from the 1L cartons is (1 L)B

Total = (0.70)A + 1B = 48 L

Now use the rearranged equation for A in the above espression:

(0.70)A + 1B = 48 L

(0.70)(60-B) + 1B = 48 L

42 - 0.70B + B = 48

0.30B = 6

B = 20

A is 60 - B or 40

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

CHECK:

B:  20*(1 L)       = 20 L

A:  40*(0.70 L) =  28 L

Total =                   48 L  YES