Find the volume of the prism.

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]

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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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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Answer:

Below in bold.

Step-by-step explanation:

If the width is x feet then the length  is 10x feet, so:

2(x + 10x) = 1650

22x = 1650

x = 75 feet.

So the width is 75 feet and the length is 750 feet,

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:

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]

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

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:

(4, 3)

Step-by-step explanation:

#1. Isolate x:

3x + y = 15

y = 15 - 3x

Substitute and solve for x:

5x - 3y = 11

5x - 3(15 - 3x) = 11

5x - 45 + 9x = 11

5x + 9x = 11 + 45

14x = 56

x = 4

Substitute and solve for y:

y = 15 - 3x

y = 15 - 3(4)

y = 15 - 12

y = 3

Answer:

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

If we are looking for substitution, then should solve one of the equations for one of the variables. This will allow us to substitute same into other equation and solve for the other variable.

Let's see what would be easy solution.

Solving for x is not straight away (we isolate x and divide all terms by its coefficient) as it has coefficient of 3.

Solving for y is easy, we just need to isolate it:

Both of the variables have coefficients that are not factors of the constant term, so the easiest option is to solve the first equation for y.

This gives us the answer choice C.

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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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.

Notice how Pattern 2 is Pattern 1 with 4 balls added in the bottom row.

Pattern 3 is Pattern 2 with 5 more balls.

Pattern 4 is Pattern 3 with 6 more balls.

Generalizing the trend, we expect Pattern [tex]n[/tex] to be identical to Pattern [tex]n-1[/tex] with [tex]n+2[/tex] more balls.

If [tex]b_n[/tex] is the number of balls in the [tex]n[/tex]-th pattern, then we have the recursive relation

[tex]\begin{cases} b_1 = 6 \\ b_n = b_{n-1} + n + 2 & \text{for } n>1 \end{cases}[/tex]

We can solve this recurrence by substitution. Using the definition of [tex]b_n[/tex], we have

[tex]b_{n-1} = b_{n-2} + (n-1) + 2 \\\\ \implies b_n = (b_{n-2} + (n-1) + 2) + n + 2 \\\\ \implies b_n = b_{n-2} + 2\times2 + \bigg(n + (n-1)\bigg)[/tex]

[tex]b_{n-2} = b_{n-3} + (n-2) + 2 \\\\ \implies b_n = (b_{n-3} + (n-2) + 2) + 2\times 2 + \bigg(n + (n-1)\bigg) \\\\ \implies b_n = b_{n-3} + 3\times2 + \bigg(n + (n-1) + (n-2)\bigg)[/tex]

and so on, down to

[tex]b_n = b_1 + (n-1)\times2 + \bigg(n + (n-1) + (n-2) + \cdots + 2\bigg)[/tex]

Recall that

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

Then we find

[tex]\displaystyle b_n = 6 + 2(n-1) + \sum_{i=2}^n i[/tex]

[tex]\displaystyle b_n = 2n + 4 + \left(\sum_{i=1}^n i - 1\right)[/tex]

[tex]\displaystyle b_n = 2n + 3 + \frac{n(n+1)}2[/tex]

[tex]\displaystyle \boxed{b_n = \frac{n^2+5n+6}2}[/tex]

Answer:

28balls

Step-by-step explanation:

according to me:

from pattern 1 to 2 four balls were added

from 2 to 3 five balls were added

from 3 to 4 6 balls were added

so you can see that there is a certain sequence that is coming up

that is 4,5,6 so just added 7.

so 21 plus other 7 balls will give us 28 balls

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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In a research of investigating the effects of working in crowded versus uncrowded conditions on the job satisfaction of employees in a variety of work setting , working is a depending variable and crowding is an independent variable.

Given aim of the research is to investigate the effects of working in crowded conditions and uncrowded conditions.

We know that depending variable is a variable whose value is dependent on the other variable. Independent variable is a variable whose value does not dependent on the other variables.

In the given question working may be affected negatively in crowded environment means there will be less work in crowded environment and more work in uncrowded environment.

Hence the depending variable in research is working.

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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:

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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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

The statements that justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor include:

A. The triangle pre-image is closer to the point of dilation than the image.

D. The value of the scale factor, 6, is greater than1.

It should be noted that dilation refers to the transformation of an object.

In this case, the triangle pre-image is closer to the point of dilation than the image and the value of the scale factor, 6, is greater than1.

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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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Answer:

0.291×0.34=0.09894

Answer:  0.09894

We are going to use long division:

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.

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:

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:

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.

5) Transitive property of equality

6) Addition property of equality

7) Subtraction property of equality

8) Division property of equality

9) Multiplication property of equality

10) Transitive property of congruence

11) Substitution property of equality

12) Addition property of equality [add XY to both sides then use segment addition postulate]

13) Subtraction property of equality [subtract XY from both sides then use segment subtraction postulate]

14) Angle addition postulate

15) Addition property of equality [add angle 2 to both sides then use angle addition postulate]

16) Transitive property of equality