Match the following.

Solution

The volume of a sphere is given by:

And replacing the info given we got:

Then the final answer would be 33.49 ft3

We know that there are tomato juice, orange juice, and cherry juice bottles in a ratio of 4:3:4, respectively.

As you can observe in the given ratio, to get 30 orange juice, we have to multiply it by 10. So, if we multiply the whole ratio, we obtain the following

This means that 30 orange juice bottles are in the same ratio as 40 tomato juice bottles and 40 cherry juice bottles.

The resulting exponent form is, 1/9¹⁰

Exponent:

Exponent is used to show repeated multiplication of a number by itself. For example,

7 × 7 × 7 can be represented as 7³

Here, the exponent is ‘3’ which stands for the number of times the number 7 is multiplied.

Given,

Here we have the exponent form is,

9⁻⁸x9⁻²

Here we have to use the product property and then we have to get rid of negative exponents.

First step is to use the product property,

We know that, the product property states that,

for any non-zero term a,

yᵃ x yᵇ = yᵃ⁺ᵇ

where a and b are real numbers.

So, the given expression is written as,

=> 9⁻⁸⁺⁽⁻²⁾

=> 9⁻⁸⁻²

=> 9⁻¹⁰

Now the second step is to get rid of the negative components,

As per the rule, the exponent is negative, we can change the exponent into positive by writing the same value in the denominator and the numerator holds the value 1.

So, the value is,

=>  9⁻¹⁰ = 1/ 9¹⁰

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{8^3}{2^4}}[/tex]

[tex]\mathsf{= \dfrac{8\times8\times8}{2\times2\times2\times2}}[/tex]

[tex]\mathsf{= \dfrac{64\times8}{4\times4}}[/tex]

[tex]\mathsf{= \dfrac{512}{16}}[/tex]

[tex]\mathsf{= 512\div16}[/tex]

[tex]\mathsf{= 32}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{32}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Power of fractions, with numerator and denominator.

The power is composed of a base and an exponent, so the exponent indicates how many times the base is multiplied, then,

[tex]\boldsymbol{\dfrac{8^{3} }{3^{4} }=\dfrac{8\times8\times8}{2\times2\times2\times2} =\cfrac{512}{16}=32 }[/tex]

17Given:

The smaller triangle is,

Find the length of the hypotenuse,

The larger traingle is,

Now, find all the trigonometric functions for a smaller triangle.

For the larger triangle,

Therefore, the value of the function is the same because the triangles are similar so, corresponding sides are proportional.

The Standard form is y = [tex]x^{2}[/tex] + 6x - 16

Given,

A quadratic function n standard form whose graph has the given characteristics.

and, passes through (-8, 0), (-6, -16), (2,0).

To find the y =?

Now, According to the question:

Because the graph of a quadratic goes through point (-8 ,0) and point   (2, 0)

So, supposing the equation of the quadratic function is  

y = a [x - (-8)] (x - 2) = a (x + 8)(x - 2)

The graph passes through the point (-6, 16)

So, -16 = a(-6 + 8)(-6 -2)

=> -16 = a x 2 x (-8)

=> a = 1

So, y = (x + 18)(x - 2)

y = [tex]x^{2}[/tex] + 8x - 2x - 16

y = [tex]x^{2}[/tex] + 6x - 16

Hence, The Standard form of  y = [tex]x^{2}[/tex] + 6x - 16

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The original price of the pants is $28.23

Let the original price of the pants be 100x

Then, the discount given will be 15x

and the sale price would be 85x

According to the question, the sale price given is 24

So,

85x = 24

x = 24÷85

x= 0.2823

Therefore,

100x = 100*0.2823

= 28.23

Hence, the original price of the pants is $28.23

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The $7,000 worth of purchase and payment of $5,000 before the three months deadline gives the amount owed at 2.49% monthly compound interest rate as $2,153.15

Owed: $2,153.15

Compound interest accounts for the interest that is earned on an interest, such that the interest rate is compounded on an initial amount.

The given parameters are;

The amount of the items purchased from the store = $7,000

The amount of down payment required = 10%

The amount paid in three months = $5,000

Monthly interest on amount owed after three months = 2.49%

Required;

The amount owed after payment of $5,000 before three months

Solution;

Using the compound interest formula, we have;

[tex] \displaystyle{A = P \cdot \left(1 + r \right)^{n} }[/tex]

Where;

A = The amount owed

P = The amount loaned = $7,000 - $5,000 = $2,000

r = Monthly interest rate = 2.49%

n = The number of months = 3 months

Which gives;

[tex] \displaystyle{A = 2000 \times \left(1 + 0.0249 \right)^{3} \approx 2153.1509}[/tex]

The amount owed (for the 3 months period) is approximately $2,153.15

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To make a profit with the revenue of R=113.95x and cost of C =93x + 750 the value of x is 36units.

As given in the question,

The revenue for selling x units of a product is R = 113.95 x.

The cost of producing x units is C = 93 x + 750

To make a profit, the revenue must be greater than the cost.

R > C

113.95x > 93x +750

Subtract 93x from both the sides

113.95x -93x +93x-93x +750

⇒20.95x > 750

⇒x > 750/20.75

⇒x>35.799

Value of x to produce a profit is 36units

Therefore, to make a profit with the revenue of R=113.95x and cost of C =93x + 750 the value of x is 36units.

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SOLUTION:

Step 1:

In this question, we are given the following:

Use geometry to evaluate:

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is:

Answer:

119

Step-by-step explanation:

substitute x = - 4 into the expression

8x² - 9

= 8(- 4)² - 9

= 8(16) - 9

= 128 - 9

= 119

rather its multiplication,division,adding, and subtraction I will give four answers

Answers: I think its 718320000

The volume that the shipping box which measure 36 inches by 24 inches by 18 inches can hold is 9 cubic feet.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Given the data in the question;

Plug the given values into the formula above and solve for the volume V.

V = w × h × l

V = 2ft × 1.5ft × 3ft

V = 3ft² × 3ft

Volume V = 9ft³

Therefore, the volume of the rectangular prism is 9 cubic feet.

Option B is the correct answer.

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This is a Permutations of 4 people in a line

The answer is 24

Congruent polygons are those that have equal measurements. Since we are given their graphs, we simply inspect each pair of polygons to determine which among them are congruent.

I have made an example using the first pair. I rotated the first polygon (the red one) to show that they are indeed congruent.

Following the same process, we can see that pairs 3 and 4 are also congruent.

Pair 2 are not congruent because the green rectangleis longer.

So the answer is pairs 1, 3, and 4.

Answer:

Gradient = 1.

Step-by-step explanation:

Note that it passes through the points (6, 6) and (0, 0)

So, the gradient is (6-0)/(6-0)

= 1.

Variable x would be easier to solve for.

Step - by - Step Explanation

What to find?

• The value of x.

• The value of y.

• The variable that was easier to solve.

Given:

5x+3y=22

4x-2y=16

Using elimination method,

First solve for x.

To solve for x, multiply through the first equation by 2 and then multiply through the second equation by 3.

10x + 6y = 44 _____________(3)

12x - 6y = 48 ______________(4)

Add (3) and (4)

22x = 92

Divide both-side of the equation by 22

x = 92/22

Reduce the fraction by 2.

x =46 / 11

To solve for y,

Multiply through the first equation by 4 and through the second equation by 5.

20x + 12y = 88 _________________ (5)

20x - 10y = 80 __________________(6)

Subtract equation 6 from 5.

22y= 8

Divide both-side of the equation by 22.

y = 8/22

We can reduce the fraction by 2.

y = 4 / 11

Judging from the steps above, we can deduce that the variable that was easier to solve is x.

Answer: x  of first equation

Step-by-step explanation:

Answer:

1. 3

2. -5

3. -7

4. 4

Step-by-step explanation:

prove me wrong

Uniformly Varied Rectilinear Motion.

When we start to solve a physics exercise, we get the exercise data:

Initial Speed = 3.8m/s

Acceleration (a)= 3.7 m/s²

Time (t) = 3 sec.

He tells us that Carter treats at a speed of 3.8 m/s, this is the speed, since he asks us, at what speed does he treat now. Then we must calculate the final speed.

The formula to calculate the final velocity is:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=V_{o}+a*t} \end{gathered}$} }[/tex]

We substitute the data in the formula used and solve:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=3.8 \ \frac{m}{s}+3.7 \ \frac{m}{\not{s^{2}} }*3 \ s } \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=3.8 \ \frac{m}{s}+11.1 \ \frac{m}{s} } \end{gathered}$} }[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=14.9 \ m/s} \end{gathered}$} }}[/tex]

The value of x is 52.5981

The given equation is:

In(x + 2) = 4

Taking log on the right hand side of the equation, we get

x + 2 = [tex]e^{4}[/tex]

The value of [tex]e^{4}[/tex] is 54.59815

⇒ x + 2 = 54.59815

Subtract 2 on both the sides of the equation

⇒ x = 54.59815 - 2

⇒ x = 52.59815

Rounding 52.59815 to 4 places, we get

⇒ x = 52.5981

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By solving both equations we get x =:

1. x = 12

2. x = 28/3

1. |x - 3| = 2x - 15

|x - 3| - 2x = 2x - 15 - 2x

by simplifying,

- 2x + |x - 3| = -15

- 2x + x -3 = -15  and -2x - (x - 3) = -15

by solving equation ,

= -x -3 = - 15

= -x = -12

x = 12

2. 8 - 2|6 - x|= 20

6 |6 - x| = 20

6 |-x + 6| = 20

dividing both side with 6,

(6 |-x + 6|)/6 = 20/6

| -x + 6| = 10/3

add 6 on both sides,

x - 6 + 6 = 10/3 +6

x = 28/3

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Car B travelled with the rate of speed of 40mph .

In the question ,

it is given that ,

Car B travelled 5mph slower than Car A .

let the rate of speed at which Car B travelled be x mph.

So , the rate of speed of Car A is = (x+5) mph

Car A travelled the distance in 4 h , with the speed of (x+5) mph ,

the value of T = 4 h and R = (x+5) mph

So, by the formula R*T=D ,

we get ,the distance travelled by Car A = 4(x+5) miles .

Car B travelled the distance in 4.5 h , with the speed of x mph .

the value of T= 4.5h  and R = x mph

So, by the formula R*T=D,

we get , the distance travelled by Car B = 4.5*x = (4.5x) miles .

Since , both the cars travelled the equal distance ,

we get ,

4(x+5) = 4.5x

4x+20=4.5x

4.5x-4x = 20

0.5x= 20

x = 40

Therefore , the rate of speed of Car B is 40 mph.

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Explanation:

Think of -8.8 as -8.80

We're comparing -8.85 to -8.80, which means we're comparing the stuff after the decimal 85 and 80

Since 85 > 80, this places -8.85 to the left of -8.80

It's like saying how -85 is to the left of -80

I recommend drawing out a number line to see what's going on.

Answer

is ur question right

The binomial formula with the given parameters has a value of 0.0272

The given parameters are

N = 65

p = 0.5

X = 39

The interpretation of the above parameters are

Sample size, N = 65

Probability of success, p = 0.5

Number of success, X = 39

The binomial probability states that

P(x) = ⁿCₓ * pˣ * (1 - p)ⁿ⁻ˣ

Where n, p and x are the same as the parameters described above

When the values are substituted in the binomial probability formula, we have

P(39) = ⁶⁵C₃₉ * (0.5)³⁹ * (1 - 0.5)⁶⁵⁻³⁹

Evaluate the difference

P(39) = ⁶⁵C₃₉ * (0.5)³⁹ * (0.5)²⁶

Evaluate the products

P(39) = ⁶⁵C₃₉ * (0.5)⁶⁵

This gives

P(39) = 0.0272

Hence, the value of the binomial formula is 0.0272

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The mixture has two components, this means that we can calculate the percentages if we divide the portion of water or alcohol by the total amount of the mixture.

For alcohol:

For water:

Answer:

The mixture is 20% alcohol and 80% water

The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.

The area of the face is 17 in²/17 inches2.

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area.

Draw a square on a piece of paper using a pencil. A 2-D figure, that is.

The term "Area" refers to the area that a shape occupies on paper.

By squaring the side's length, the area of each face may be calculated.

To determine the overall surface area of the cube, multiply the area of each face by the number of faces.

For big square,

a = 4 in

a*a = 4 * 4 inches

[tex]a^{2}[/tex] = 16 in²

For another small square,

a = 1 in

[tex]a^{2}[/tex] = 1*1 = 1 in²

In total,

[tex]a^{2}[/tex] = 16 + 1 = 17 in²

Therefore, the area of the face is 17 in²

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The measure of angle p is 213 degrees

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following angles

Also, from the attached figure:

We can see that the three angles named above are formed by lines that meet at a point (say the point of origin)

When multiple lines meet at a point, the sum of the angles formed at this point is 360 degrees

This means that

Angle 1 + Angle 2 + Angle 3 = 360

Substitute the known values in the above equation

So, we have

p + 57 + 90 = 360

Evaluate the sum in the above equation

So, we have

p + 147 = 360

Evaluate the like terms in the above equation

So, we have

p = 213

Hence, the value of the angle with the name p is 213 degrees

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Possible question

Diagram not drawn accurately

Work out the size of the angle marked p.

See attachment