Simplify
8(x + 6) - 10.

The equation of the volume of the sphere is 4/3 × 27π

The volume of a cylinder is expressed as

V = πr²h

Since the cylinder has thesame height and radius, therefore, the volume of the cylinder will now be

V = πr² × r

V = πr³

The volume of a sphere is expressed as

V = 4/3(πr³)

Therefore we can say

the volume of sphere = 4/3 × volume of the cylinder

Volume of cylinder = 27π

volume of sphere = 4/3 × 27π

= 4 × 9

= 36πft³

To minimize the cost of the diet while meeting the vitamin requirements, we can use a system of linear equations to solve a linear programming problem. The optimal solution will provide the pounds of each type of food to be purchased.

To solve this problem, we can use a system of linear equations. Let's assume that we buy x pounds of type X food and y pounds of type Y food. The requirements for Vitamin A and Vitamin B can be expressed as the following inequalities: 10x + 30y ≥ 140 (for Vitamin A) and 20x + 15y ≥ 145 (for Vitamin B). We also need to minimize the cost, which can be expressed as the objective function: Cost = 12x + 8y. So, we have a linear programming problem.

To find the minimum cost, we can graph the feasible region defined by the inequalities and find the corner point with the lowest cost. Alternatively, we can use a method like the Simplex algorithm to solve the system of equations and find the optimal solution. The solution will give us the values of x and y that satisfy the requirements and minimize the cost.

Once we find the optimal solution, we can round the values of x and y to the nearest hundredths and provide the student with the pounds of each type of food to be purchased.

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Without a specific equation or context, we can't find a specific value for x. If the equation were a+c=x, with a=13 and c=47, then x would equal 60.

This question appears to be missing some information to find a specific value for x. If this were an algebraic equation such as a+c=x where a and c are declared as 13 and 47 respectively, you would simply add these two numbers together. So if a=13 and c=47, then x (your answer in this case) would be 60. However, without a given equation or context, it's impossible to determine the exact value for x.

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Answer:

Step-by-step explanation:

[tex]f(x)=ln(x)\\f(3)=ln(3) = 1.099[/tex]

Using the Pythagorean theorem:

a = √(c^2 - b^2)

a = √(8^2 - 5^2)

a = √(64 - 25)

a = √39 ( Exact answer )

Or √39 =  6.244997 as a decimal and you round the decimal answer as needed.

Answer:

3x^2 - 8x + 4.

Step-by-step explanation:

Dividing each term by 9x we get:

3x^2 - 8x + 4.

As per cubic equation, the result is [tex](3x^{2}-8x+4)[/tex].

A cubic equation is an equation where the highest power of the variable is 3.

The given linear equation is:

[tex]\frac{27x^{3}- 72x^{2}+ 36x}{9x} \\= \frac{27x^{3}}{9x} -\frac{72x^{2}}{9x}+\frac{36x}{9x}\\ = 3x^{2}-8x+4[/tex]

The result is [tex](3x^{2}-8x+4)[/tex].

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Answer:

g(x)=5x+7

Step-by-step explanation:

f(x)+g(x)=9x+4

We are given f(x)=4x-3.

So we insert 4x-3 for f:

4x-3+g(x)=9x+4

Subtract 4x on both sides:

  -3+g(x)=5x+4

Add 3 on both sides:

       g(x)=5x+7

Check:

  f(x)+g(x)

=(4x-3)+(5x+7)

=(4x+5x)+(-3+7)

=(9x)     +(4)

=9x+4

Bingo. We did it! :)

The function g(x) can be found by rearranging the equation f(X) + g(X) = 9x + 4 and substituting f(x) = 4x - 3 into it. This leads to g(x) = 5x + 7.

The given combined function is f(X) + g(X) = 9x + 4 and we know that f(x) = 4x - 3. To find g(x), we need to rearrange the combined function to make g(x) the subject. So step 1: subtract f(x) from both sides of the equation, giving: g(x) = 9x + 4 - f(x).

Then, we substitute f(x) into the equation, resulting in: g(x) = 9x + 4 - (4x - 3). Simplifying this gives us g(x) = 9x + 4 - 4x + 3, which further simplifies to g(x) = 5x + 7. This is the function g(x).

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Answer:

y=2

Step-by-step explanation:

8 - y = 9 - 3

Combine like terms

8 - y = 6

Subtract 8 from each side

8-8 - y = 6-8

-y = -2

Multiply each side by -1

-1 * -y = -2 *-1

y =2

Answer:

4(x - 5)^2 - 18.

Step-by-step explanation:

For a move 5 to the right f(x) ----> f(x - 5).

For a move of 2 down  f(x - 5) ----> f(x - 5) - 2.

For this case we have that by definition of function transformation is fulfilled:

Let h> 0:

To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.

To graph[tex]y = f (x + h),[/tex] the graph moves h units to the left.

Let k> 0:

To graph [tex]y = f (x) + k[/tex], the graph k units is moved up.

To graph [tex]y = f (x) -k[/tex], the graph moves k units down.

So, we have the following function:

[tex]h (x) = 4x ^ 2-16[/tex]

5 units on the right:

[tex]h (x) = 4 (x-5) ^ 2-16[/tex]

2 units down

[tex]h (x) = 4 (x-5) ^ 2-16-2\\h (x) = 4 (x-5) ^ 2-18[/tex]

Answer:

[tex]h (x) = 4 (x-5) ^ 2-18[/tex]

Answer:

8.4

Step-by-step explanation:

the equation 4x+8y -40 can be written as 4x-8y-40=0, this represents a line in a space of two dimensions.

solving for x when y=0.8 we have the equation below>

[tex]4x+8*0,8-40=0[/tex]

Which gives that x=42/5, or in more simpler terms, 8.4

Answer:

B

Step-by-step explanation:

Factor the numerator, that is

x² + 6x + 8 = (x + 4)(x + 2), now

f(x) = [tex]\frac{(x+4)(x+2)}{x+4}[/tex]

Cancel the factor (x + 4) on the numerator/ denominator, leaving

f(x) = x + 2 ← simplified version

Cancelling the factor x + 4 leaves a discontinuity ( a hole ) at

x + 4 = 0 ⇒ x = - 4 and f(- 4) = x + 2 = - 4 + 2 = - 2

There is a discontinuity at (- 4, - 2 )

To find the zero let f(x) = 0, that is

x + 2 = 0 ⇒ x = - 2

The zero is (- 2, 0 )

Answer:

c) 5,160

Step-by-step explanation:

If from a jar of pennies, 1290 are drawn, marked, and returned to the jar and after mixing,  a sample of 200 pennies is drawn and it was noticed that 50 were marked. Based on the given information there are  5,160 pennies in the jar.

1290 pennies are drawn and returned to the jar.

200 pennies were drawn.

50 pennies were marked.

1,490 is not enough.

258,000 is way too much.

5,160 makes sense.

Final answer:

Using the proportion of marked to sampled pennies, the total number of pennies in the jar is estimated to be 5160.

Explanation:

The task is to use the information given about the marked and sampled pennies to estimate the total number of pennies in the jar.

This is a classic example of using proportions in mathematics. If out of 200 sampled pennies, 50 are marked, this represents 25% of the sample.

Since 1290 pennies were marked to begin with, we assume that the sampled 25% represents a similar proportion of the total jar.

Thus, the equation to solve is 1290 / total number of pennies = 50 / 200. Simplifying the right side of the equation gives 1290 / total number of pennies = 1 / 4.

By cross-multiplication, the total number of pennies is 4 × 1290, which equals 5160.

The y-intercept would elevate up the y-axis by 3

This is because the y-intercept in y= -4x+2 is 2 and when you change it to y= -4x+5 you are moving the intercept to a y of 5.

Answer:

(-0.75, 0.5)

or in fractions:

(-3/4, 1/2)

Step-by-step explanation:

Answer:

The correct ans would be B, 25%+10%+10%+10%+10%

Step-by-step explanation:

When percentages are found, the best way to calculate them is to break them down to the simplest percentage form, and 10% is the simplest percentage that a person can calculate of whatever digit. So if someone wishes to find out the friendly percents, then the easiest would be to calculate the 10% of the figure, add them four times, then add them 2 times plus the half of 10%, which will become 25%, and then add them all to get the 65% of that figure.

Answer:

B.

Step-by-step explanation:

i took the test

Answer:

B.

I ignored the extra y= part in each equation.

Step-by-step explanation:

The line given is in slope-intercept form, y=mx+b where m is slope and b is y-intercept.

Parallel lines have the same slope.

So the slope of y=(2/5)x+9 is m=2/5.

So we are looking for a line with that same slope.

In slope-intercept form the line would by y=(2/5)x+b where we do not know b since we weren't given a point.

So all of the choices are written in standard form ax+by=c where a,b, and c are integers.

We want integers so we want to get rid of that fraction there.  To do that we need to multiply both sides of y=(2/5)x+b for 5.  This gives us:

5y=2x+5b

Subtract 2x on both sides:

-2x+5y=5b

Now of the coefficients of x in your choices is negative like ours is. So I'm going to multiply both sides by -1 giving us:

2x-5y=-5b

Compare

2x-5y=-5b to your equations.

A doesn't fit because it's left hand side is 5x+2y.

B fits because it's left hand side is 2x-5y.

C doesn't fit because it's left hand side is 5x-2y.

D doesn't fit because it's left hand side is 2x+5y.

I ignored all the extra y= parts in your equations.

Answer:

.01 lbs

Step-by-step explanation:

If the weight of 1000 things are 1 pound that means 1 thing has a weight of 1/1000 lbs. So ten things have a weight of 10/1000 lbs or 1/100 lbs or .01 lbs.

Answer:

d =12

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

Substituting what we know

36 pi = pi r^2

Divide each side by pi

36 pi/pi = pi r^2/pi

36 = r^2

Taking the square root of each side

sqrt(35) = sqrt(r^2)

6 =r

We want the diameter

d = 2r

d = 2(6)

d = 12

According to the question the values of a and b are 17 and 6 respectively

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

According to the Definition:

Sides FJ = HJ ( from the diagram)

Hence (3b + 6) = 24cm

            3b = 24 - 6

            3b = 18

             b = 6

Sides FG = GH (from the diagram)

         (2a - 4) = 30

          2a = 30 + 4

           a = 34/2

           a = 17

Hence the value of a and b are 17 and 6 respectively.

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Answer: C

Step-by-step explanation:

Answer:

The answer is 52

Step-by-step explanation:

We need figure out the dilated by doing OB’/OB. 5+15= OB’. OB’ = 20. We already know that OB is 5. We used the substitution property. 20/5 = 4. Now, we got 4 as dilation. 13 cm x 4 = 52 cm. Therefore, our answer is 52

Perimeter of ΔA'B'C' is 52 cm.

The perimeter of ΔABC is =13 cm

Length of OB = 5 cm

Length of OB' = 15 + 5 = 20 cm

The Dilation factor can be found out b

ΔOCB and ΔOC'B' are similar as BC|| B'C'

From triangles ΔOCB & ΔOC'B' the dilation factor can be found out

by the formula below

[tex]\frac{BC}{B'C'} = \frac{5}{20}[/tex]

B'C'= 4[tex]\times[/tex]BC

so the dilation factor = 4

hence the new perimeter of the triangle = 13 [tex]\times[/tex] 4 = 52 cm

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Answer:

Option A) Bethany is correct because consecutive odd integers will each have a difference of two

Step-by-step explanation:

The sum of 3 consecutive odd integers is 91. Let the first odd integer is x. The next odd integer will be obtained by adding 2 in x i.e. (x + 2). The third odd integer will be obtained by adding 2 in the second odd integer i.e. (x + 2) + 2 = x + 4

So, the 3 odd integers will be:

x  , (x+2) and (x+4)

Their sum is given to be 91. So we can write:

x + (x+2) + (x+4) = 91

Hence, we can conclude that: Bethany is correct because consecutive odd integers will each have a difference of two.

Other options are not correct because consecutive odd integers always increase by 2. For example, the next odd integer after 1 is 3, which is obtained by adding two, similarly the next odd will be 5 and so on.

Answer:

a

Step-by-step explanation:

Answer:

-7/2 ±1/2sqrt(13) = x

Step-by-step explanation:

f(x) =x^2 + 7x + 9

To find the zeros, set this equal to zero

0 = x^2 + 7x + 9

I will complete the square

Subtract 9 from each side

0-9 = x^2 + 7x + 9-9

-9 =x^2 + 7x

Take the coefficient of the x term, 7

divide by 2, 7/2

Then square it, (7/2)^2 = 49/4

Add this to both sides

-9 +49/4=x^2 + 7x + 49/4

-36/4 +49/4 = (x+7/2)^2

13/4 =  (x+7/2)^2

Take the square root of each side

±sqrt(13/4) = sqrt( (x+7/2)^2)

± sqrt(13) /sqrt(4)= (x+7/2)

± 1/2 sqrt(13) = (x+7/2)

Subtract 7/2 from each side

-7/2 ±1/2sqrt(13) = x+7/2-7/2

-7/2 ±1/2sqrt(13) = x

The function f(x) = x^2 + 7x + 9 has no real-number zeros as the discriminant is negative, indicating that the quadratic formula solution involves an imaginary number.

The student is asking to find the zeros of the quadratic function f(x) = x^2 + 7x + 9. To solve for the zeros, we need to find the values of x that make the function equal to zero. We can use the quadratic formula, which is [tex]x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}[/tex], where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, our equation is already in the correct form with a = 1, b = 7, and c = 9. Plugging these into the quadratic formula, we get:

[tex]x = \frac{{-7 \pm \sqrt{{7^2 - 4(1)(9)}}}}{{2 \cdot 1}}[/tex]

Upon further calculation, we find that the equation has no real-number solutions as the discriminant (b^2 - 4ac) is negative (49 - 36 = 13), leading to an imaginary number in the square root. Therefore, we conclude that the function does not cross the x-axis and has no zeros on the real number line.

Answer:

17.009 in

Step-by-step explanation:

For a normal distribution with mean of 15.2 in and standard deviation of 1.1 inches, we finnd that 5% are excluded when the width of the seats are greater than 17.009 inches.

Therefore, the seat should have a width of 17.009 in.

To accommodate 95% of women based on hip breadth, airline seats should be designed at least 17.015 inches wide, calculated using the given mean of 15.2 inches, a standard deviation of 1.1 inches, and the z-score for the 95th percentile.

To determine the width of airline seats that would accommodate 95% of women, the airline needs to calculate the 95th percentile of women's hip breadths, modeled by a normal distribution.

Using the provided mean of 15.2 inches and a standard deviation of 1.1 inches, we find the z-score that corresponds to the 95th percentile. In normal distribution, the z-score for the 95th percentile is approximately 1.65.

Using the z-score formula Z =(X - μ / Σ, where Z is the z-score, X is the value we seek, μ is the mean, and Σ is the standard deviation, we can set Z to 1.65 and solve for X:

1.65 = (X - 15.2) / 1.1

X = 1.65 * 1.1 + 15.2

X = approx. 1.815 + 15.2

X = approx. 17.015 inches

Therefore, to exclude only the 5% of women with the widest hips, the airline should design seats that are at least 17.015 inches wide.

Answer:

I only used two steps: 3) then 6) then 1).

Step-by-step explanation:

Ok, if x-5 is a factor of p(x), then p(5)=0 by factor theorem.

This also goes the other way around:

If p(5)=0 then x-5 is a factor of p(x) by factor theorem.

Let's check. I'm going to evaluate p(x) for x=5.

[tex]p(5)=5^3-5(5)^2-5+5[/tex]

[tex]p(5)=125-5(25)-5+5[/tex]

[tex]p(5)=125-125-5+5[/tex]

[tex]p(5)=0+0[/tex]

[tex]p(5)=0[/tex]

This implies x-5 is a factor since we have p(5)=0.

The first step I did was 3) evaluate p(x) for x=5.

The second step I did 6) simplify and find the remainder. I did this when I was evaluating p(5); that was a lot of simplification and then I found the remainder to be 0 after that simplification. The last step was 1) apply the factor theorem, the remainder is 0 so x-5 is a factor of p(x).

To determine if x-5 is a factor of the polynomial, evaluate p(x) when x=5. If the result is 0, then the Factor Theorem implies that x-5 is a factor. If not, x-5 is not a factor.

To determine if x-5 is a factor of p(x)=x^3-5x^2-x+5, you can follow these steps:

When you evaluate p(x) for x=5, if you get 0, it demonstrates, according to the factor theorem, that x-5 is a factor of p(x) because it results in the polynomial function equaling zero. If you don't get zero, then it's not a factor.

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Answer:

153 units squared

Step-by-step explanation:

To solve, multiply your length by your width.

[tex]A=lw\\A=9(17)\\A=153[/tex]

Answer:

A=153

Step-by-step explanation:

The area of a rectangle with a length of 9 and a width of 17 is 153.

Formula: A=wl

A=wl=17·9=153

[tex]\dfrac{7}{8}=\dfrac{875}{1000}=0.875[/tex]

Answer:

[tex]\large\boxed{\dfrac{7}{8}=0.875}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\dfrac{7}{8}=\dfrac{7\cdot125}{8\cdot125}=\dfrac{875}{1,000}=0.875\\\\\bold{METHOD\ 2:}\\\\\dfrac{7}{8}=7:8\qquad\text{divide 7 by 8 (look at the picture)}\\\\7:8=0.875[/tex]

Answer:

12 Containers

Step-by-step explanation:

given it takes 1/2 a pound to make one container, we can deduce:

1 pound makes 2 containers

2 pounds makes 4 containers

thus the amount of containers is equal to 2x (x being pounds of apples picked)

so

2(6)=12

Elise can make 12 containers of applesauce. Here's how to calculate it:
Step 1: Determine the total amount of apples Elise has:
Elise has picked 6 pounds of apples.
Step 2: Identify how many pounds of apples are needed for one container of applesauce:
According to the information provided, 1/2 pound of apples is needed to make 1 container of applesauce.
Step 3: Calculate how many containers Elise can make:
To find out how many containers of applesauce Elise can make, divide the total pounds of apples by the pounds of apples per container.
The calculation is as follows:
6 pounds of apples ÷ (1/2) pound per container = 12 containers
Therefore, with 6 pounds of apples, Elise can make 12 containers of applesauce.

Answer:

red: 9/20, 0.45, 45%

White: 15%, 0.15, 3/20

Blue: 0.4, 2/5, 40%

Step-by-step explanation:

For red: you start with 9/20. It’s best to get to a denominator of 10. So divide each number by 2. You would get 4.5/10. Then change to a percent by moving the decimal of the numerator one to the right and changing it to percent. 4.5 -> 45. -> 45%. Then for the decimal, divide 45 by 100. 45/100 = 0.45.

For white: you start with 15%. Divide by 100. 15/100=0.15. Put into a fraction with a denominator of 100. It would be 15/100. Simplify. Each number can be divided by 5, so your fraction would be 3/20.

For blue: you start with 0.4. Turn this into a fraction. Since there is one decimal place, it can have a denominator of 10. The fraction is 4/10, simplified to 2/5. Using the fraction 4/10, the percent would be 40%.

I hope this helps!

Answer:

=14

Step-by-step explanation:

In a rhombus, opposite angles are equal.

In the one provided in the question, 5x° is opposite the angle 70°

Let us equate the two.

5x=70

x=70/5

=14°

The value of x in the figure is 14°

Here,

(s-3)²=0

→s-3=0

→s=3

Substituting s=3 in,

(s+3)(s+5)

=(3+3)(3+5)

=(6)(8)

=48

The solution to the equation (s-3)²=0 is s=3. Subsequently, the value of (s+3)(s+5) can be calculated by substituting s with 3, giving us the answer 48.

To solve the given equation, (s-3)²=0, we need to find the value of s. This equation means that the value inside the parenthesis, s - 3, when squared equals zero. The only way for a real number squared to equal zero is for that number itself to be zero. Therefore, s - 3 must equal zero. Solving for s, we find that:

s - 3 = 0
s = 3

Now that we know s is 3, we can find the value of (s + 3)(s + 5) by substituting the value of s:

(3 + 3)(3 + 5) = 6 x 8 = 48

Therefore, the value of (s + 3)(s + 5) when (s - 3)² = 0 is 48.