A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. Find the volume of the foam.

solving simultaneously

let equation 1 be -3-3y=12x

let equation 2 be -5-y=2x

equation 2 make y subject of formula=> y=-5-2x

replace (y=-5-2x) in equation 1

-3-3(-5-2x)=12x

solve for x

x=2

replace x=2 in equation 2

y=-5-2(2)

y=-9

Therefore, x=2 y=-9

[tex]\bf \begin{array}{ccll} miles&minutes\\ \cline{1-2} \frac{1}{3}&4\\\\ 1&x \end{array}\implies \cfrac{~~\frac{1}{3}~~}{1}=\cfrac{4}{x}\implies \cfrac{1}{3}=\cfrac{4}{x}\implies x=12[/tex]

Answer:

[tex]\$11.13[/tex]

Step-by-step explanation:

step 1

Find the surface area of the cylinder

The surface area of the cylinder is equal to

[tex]SA=\pi r^{2} +2\pi rh[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter

[tex]h=5\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]SA=(3.14)(1.5)^{2} +2(3.14)(1.5)(5)=54.165\ in^{2}[/tex]

Find the cost

[tex]54.165*(0.75)=\$40.62[/tex]

step 2

Find the surface area of the square prism

The surface area of the prism is equal to

[tex]SA=b^{2} +4bh[/tex]

we have

[tex]b=3\ in[/tex]

[tex]h=5\ in[/tex]

substitute

[tex]SA=(3)^{2} +4(3)(5)=69\ in^{2}[/tex]

Find the cost

[tex]69*(0.75)=\$51.75[/tex]

step 3

Find the difference of costs

[tex]\$51.75-\$40.62=\$11.13[/tex]

Answer:

25[tex]\sqrt{x}[/tex]

Step-by-step explanation:

Using the rule of exponents

• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex], then

[tex]x^{\frac{1}{2} }[/tex] = [tex]\sqrt[2]{x^{1} }[/tex] = [tex]\sqrt{x}[/tex]

Hence

25 [tex]x^{\frac{1}{2} }[/tex] = 25[tex]\sqrt{x}[/tex]

ANSWER

[tex]\cos(y) = \frac{4}{5} [/tex]

EXPLANATION

From the mnemonics SOH-CAH-TOA.

We want to find the cosine of y

CAH means cosine ratio involves adjacent over the hypotenuse.

[tex] \cos(y) = \frac{adjacent}{hypotenuse} [/tex]

From the right by triangle, the side ajacent to angle y is 64 units and the hypotenuse is 80 units.

[tex] \cos(y) = \frac{64}{80} [/tex]

[tex]\cos(y) = \frac{4}{5} [/tex]

Answer:4/5

Step-by-step explanation:

Answer:

D) 3+x/10+x > 8/10!

Answer:

the second part is a

Step-by-step explanation:

Answer:

[tex]x = \frac{y}{2}- 5[/tex]

[tex]x = \frac{1}{2} y - 5[/tex]

Step-by-step explanation:

[tex]1. \: \frac{y}{2} = x + 5 \\ 2. \: \frac{y}{2} - 5 = x \\ 3. \: x = \frac{y}{2} - 5 \\ \\ or \\ \\ 1. \: 2x + 10 = y \\ 2. \: 2x = y - 10 \\ 3. \: \frac{2x}{2} = \frac{y - 10}{2} \\ x = \frac{1}{2} y - 5 [/tex]

Answer:

Inverse.

Step-by-step explanation:

Answer:

theyre called inverse funtions .

inverse of :

cos= cosectant

tan= cotangent

sin= secant

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h,k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 6x

y = x² + 2(- 3)x + 9 - 9 + 2 = (x - 3)² - 7 ← in vertex form

with vertex = (3, - 7)

To determine whether maximum or minimum consider the value of a

• If a > 0 then minimum

• If a < 0 then maximum

here a = 1 > 0 ⇒ minimum

Hence (3, - 7) is a minimum

Answer:

A.

Step-by-step explanation:

On the right side of the equation we are multiplying the initial amount by the growth rate that is raised to a number of years.  M is equal to this product.  The growth rate does not depend upon the initial amount.

Answer:

In interval notation it is  ( -∞, ∞).

Step-by-step explanation:

All values of x can be input to this function.

what pyramid???????

i think you forgot the pyramid

Answer:

OPTION A 755m^2;815m^2

Step-by-step explanation:

I hope it really helps I know everyone always needs help from time to time best of luck!

B

Step-by-step explanation:

half of 11 is 5.5 so counting that from either of the points leads to .5

Then continuing from there, half of 9 is 4.5 so moving the point up would get 2.5

Answer:

B

Step-by-step explanation:

Answer:

On the graph B, at 0 seconds the graph will be at [tex]y=0.[/tex]

The graph will be going down until 2 seconds, when the diver reaches her deepest point. At 2 seconds the height of the graph will be -8ft.

Step-by-step explanation:

In graph B we are measuring the distance from the surface, that is we are setting the surface to be y=0. Thus if the diver reaches her deepest point 8ft down, she will be below y=0 and at -8ft.

Thus, in shape the graph B will be similar to graph A, but it will be shifted downed by 8ft.

Answer:

On Graph B, at 0 seconds, the graph will be at 0 feet.

Then the graph will increase until 2 seconds, when the diver reaches her deepest point. At 2 seconds the height of Graph B will be at 8 feet.

Step-by-step explanation:

It just works.

Answer:

25%

Step-by-step explanation:

350/1400 as a simplified fraction is 1/4 because you can divide 350 into 1400.

And now we know that 1/4 is 25%.

Or just divide 1 by 4. And you'll get .25 and then just move the decimal to the right 2 times.

Hope this helps!

Harold gave 1,400 stamps to his brother and sister. He gave 350 stamps to his brother. What percent of stamps did Harold give to his brother.

The percent[tex]\frac{350}{1,400}[/tex] represents the number of stamps that Harold gave to his brother out of all the stamps.

To find what percent of stamps that Harold gave to his brother, we can change the fraction [tex]\frac{350}{1,400}[/tex] to a percent.

We can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 350 and 1400 using 350.

350 ÷ 350 = 1

1400 ÷ 350 = 4

Our reduced fraction is [tex]\frac{1}{4}[/tex].

1 ÷ 4 = 0.25

0.25 × 100 = 25%

Therefore, Harold gave his brother 25% of his stamps.

Answer:

  D)  (-2, -3)(-4, -3)(-2, -9); because corresponding pairs of sides and corresponding pairs of angles are congruent

Step-by-step explanation:

For triangles to be congruent, it is not enough that corresponding angles are congruent. In addition, there must be at least one pair of corresponding sides that are congruent. (Then all pairs will be congruent.)

The points listed in choices B and D are points that form a right triangle with leg lengths 2 and 6. However, choice B only refers to the angle measures, and not the sides. Choice D is the correct one.

To determine which triangle is congruent with the original triangle, we'll need specific criteria to compare. Congruent triangles have all corresponding sides and angles that are congruent, which means they will have the same size and shape but may be in different positions or orientations.
Assuming that the original (unillustrated) triangle has been given to us, we would compare it with the triangles listed in the options. However, without the original triangle's information, I can't directly compare it with the options given, so I will offer a step-by-step guide on how you could establish the congruence between triangles if the original triangle's dimensions were known.
Step 1: Determine the lengths of the sides of each of the given triangles using the distance formula, which is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Step 2: Calculate the angles between each pair of sides using the dot product formula or by using the law of cosines. Remember that for angles, you might initially find the cosine of the angle with the dot product and then use the inverse cosine function to find the angle itself.
Step 3: Compare the lengths of sides and the measures of angles of the given triangles to those of the original triangle. If all sides and angles match, the triangles are congruent.
Step 4: Choose the correct answer based on which triangle has all three sides and angles that match the original triangle.
Let's briefly analyze the given triangles in the options:
Option A and Option C describe the same triangle: (-1, 1), (-2, 1), (-1, 4). In a congruence context, the reason for congruence would be the same whether it's because of corresponding pairs of angles or both sides and angles, but usually the congruence criteria involve both sides and angles (SSS, SAS, ASA, AAS).
Option B and Option D also describe the same triangle: (-2, -3), (-4, -3), (-2, -9). The reasoning provided once again does not fundamentally alter the congruence relationship since congruence should involve both sides and angles.
However, since we can't see the original triangle, I can't confirm which one is congruent. If you have the specific characteristics of the original triangle, you could use the steps outlined above to find out which triangle from these options is congruent with it. Remember, for two triangles to be congruent, they must have exactly the same three side lengths and the same three angles.

Answer:

  A.  $22,500

Step-by-step explanation:

10% = 10/100 = 1/10

To divide a decimal number by 10, move the decimal point one place to the left (remove a zero):

  $225000./10 = $22500.0 = $22500

Answer:

A.

Statement: ∠6 ≅ ∠14

Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

Step-by-step explanation:

In the figure attached, a plot of the problem is shown.

Given p || q and r is a transversal which cut p and q, then ∠1 ≅ ∠5 and ∠2 ≅ ∠6.

Given r || s and q is a transversal which cut r and s, then ∠6 ≅ ∠14 and ∠8 ≅ ∠16.

From the picture we see that ∠1 and ∠2 are supplementary, that is, their addition is equal to 180º. ∠2 ≅ ∠6 and ∠6 ≅ ∠14, then ∠2 ≅ ∠14, in consequence ∠1 and ∠14 are supplementary.

To prove that ∠1 and ∠14 are supplementary angles, given that p || q, and r || s, the next logical step in the proof is statement: ∠6 ≅ ∠14, with the reason being: for parallel lines cut by a transversal, corresponding angles are congruent.

Considering the given scenario: p is parallel to q and r is parallel to s, and the task is to prove that ∠1 and ∠14 are supplementary angles, the most logical step in this proof would be Option A.

Statement: ∠6 ≅ ∠14

Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

This statement and reasoning holds true because when you have two parallel lines that are cut by a transversal, it produces corresponding angles that are congruent or equal in measure.

Hence, in the given scenario, since the lines p, q and r, s are parallel and are being cut by a transversal, it implies that ∠6 and ∠14 are equal in measure.

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Answer:

118.3 m²

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 13 ( or 18.2) and h = 18.2( or 13) ← sides perpendicular

A = 0.5 × 13 × 18.2 = 118.3 m²

Answer: the answer is b

Step-by-step explanation:

Answer:

the answer is letter b.

[tex]1 - 2x + {5x}^{4} [/tex]

Answer:

68

Step-by-step explanation:

We let the random variable X denote the height of students of the college. Therefore, X is normally distributed with a mean of 175 cm and a standard deviation of 5 centimeters.

We are required to determine the percent of students who are between 170 centimeters and 180 centimeters in height.

This can be expressed as;

P(170<X<180)

This can be evaluated in Stat-Crunch using the following steps;

In stat crunch, click Stat then Calculators and select Normal

In the pop-up window that appears click Between

Input the value of the mean as 175 and that of the standard deviation as 5

Then input the values 170 and 180

click compute

Stat-Crunch returns a probability of approximately 68%

Final answer:

Using the empirical rule for a normal distribution, approximately 68% of the students' heights fall within one standard deviation (170 cm to 180 cm) from the mean of 175 cm.

Explanation:

The student's question involves applying the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data, which states that:

About 68% of the data falls within one standard deviation of the mean.

About 95% falls within two standard deviations.

About 99.7% falls within three standard deviations.

In this case, the mean height is 175 cm and the standard deviation is 5 cm. The student is interested in the percentage of students with heights between 170 cm and 180 cm, which corresponds to one standard deviation below and above the mean, respectively. Therefore, using the empirical rule, we can conclude that approximately 68 percent of the students' heights will lie in this range.

ANSWER

[tex]\frac{5x - 6}{2}[/tex]

EXPLANATION

The given function is

[tex] \frac{2x + 6}{5} [/tex]

Let

[tex]y = \frac{2x + 6}{5} [/tex]

Interchange x and y.

[tex]x= \frac{2y + 6}{5} [/tex]

Solve for y.

5x=2y+6

5x-6=2y

Divide both sides by 2

[tex] \frac{5x - 6}{2} = y[/tex]

Hence the given function has inverse

[tex]\frac{5x - 6}{2}[/tex]

1. When [tex]x=-1[/tex], you know that [tex]y=f(-1)=1[/tex]. The tangent line at [tex]x=-1[/tex] has slope

[tex]\dfrac{\mathrm dy}{\mathrm dx}(-1,1)=(2(-1)+1)(1+1)=-2[/tex]

Then the tangent line has equation

[tex]y-1=-2(x+1)\implies\boxed{y=-2x-1}[/tex]

2. Plug [tex]x=-0.9[/tex] into the equation for the tangent line to get

[tex]f(-0.9)\approx-2(-0.9)-1\implies\boxed{f(-0.9)\approx0.8}[/tex]

3. Separating the variables in the ODE gives

[tex]\dfrac{\mathrm dy}{y+1}=(2x+1)\,\mathrm dx[/tex]

Integrating both sides yields

[tex]\ln|y+1|=x^2+x+C[/tex]

Given that [tex]f(-1)=1[/tex], we get

[tex]\ln|1+1|=(-1)^2+(-1)+C\implies C=\ln2[/tex]

so that the particular solution to the ODE is

[tex]\ln|y+1|=x^2+x+\ln2\implies y+1=e^{x^2+x+\ln 2}\implies\boxed{y=2e^{x^2+x}-1}[/tex]

4. As [tex]x\to\infty[/tex], the exponential terms grows without bound, so that [tex]\boxed{f(x)\to\infty}[/tex] as well.

Answer:

0.2

Step-by-step explanation:

R can be as small as -1 to display a perfect negative linear relationship or as large as 1 to display a perfect positive linear relationship. The closer the r-value is to 0 the weaker the correlation so therefore 0.2 is closest to 0 making it the answer choice with the weakest correlation.

Answer:

An extra 95

Step-by-step explanation:

80 84 86 88 88 92 94 94

IQR = 9

80 84 86 88 88 92 94 94 94

IQR = 9

The rocket exceed the height of 500 ft in 1.46 seconds or 8.43 seconds.

Standard form of the quadratic equation in the variable x is an equation of the form a[tex]x^{2}[/tex] + bx + c = 0, where a, b, c are real numbers and a ≠ 0. Any equation of the form P(x) = 0, Where P(x) is a polynomial of degree 2, is a quadratic equation.

Given equation of height is:

h(t)= -[tex]16t^{2} +160t+300[/tex]

Now, the exceeded to 500 feet.

So,

-[tex]16t^{2} +160t+300[/tex]=500

16[tex]t^{2}[/tex] -160 t +200=0

Now, solve for t: a=16, b= -160, c= 200

D= [tex]\sqrt{b^{2}-4ac }[/tex]

 = [tex]\sqrt{(-160)^{2}-4*16*200 }[/tex]

 = [tex]\sqrt{12800 }[/tex]

 = 80√2

As D>0 then,

x= [tex]\frac{-b\pm \sqrt{b^{2}-4ac }}{2a}[/tex]

x= (160 ±80√2)/32

x=  (160 +80√2)/32   or x= (160 -80√2)/32

So, x= 8.43 and x=1.46

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Answer:

8

Step-by-step explanation:

edg

Answer:

8 years

Step-by-step explanation:

An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation [tex]100e^{0.05t} = 150[/tex] represents the situation, where t is the number of years the money has been invested.

To find out how long has the money invested we need to find out 't'

[tex]100e^{0.05t} = 150[/tex] , solve for t

divide both sides by 100

[tex]e^{0.05t} = 1.5[/tex]

Now to remove 'e' we take ln on both sides

[tex]ln(e^{0.05t) = ln 1.5[/tex]

the value of [tex]ln(e)= 1[/tex]

[tex]0.05t = ln 1.5[/tex]

Now divide by 0.05 on both sides

t = 8.10930

The money is invested for 8 years

The publisher should produce and sell approximately 4480 books in order to break even on the total costs of production.

The problem requires figuring out when the revenues from selling the book will equal the total cost of production. This is a problem in algebra.

The one-time fixed costs total $45,920, and the variable costs per book are $11.25. The books will be sold for $21.50 each.

Step 1: Set up an equation

Let x be the number of books that need to be sold. The equation is then: 45920 + 11.25x = 21.50x.

Step 2: Solve for x

Subtract 11.25x from each side to isolate the variable on one side giving you: 10.25x = 45920. Then, divide both sides by 10.25 to derive x. So, the equation is x = 45920 / 10.25.

Step 3: Derive the solution

By doing the calculation, x approximately equals 4480. Thus the publisher needs to sell just about 4480 books to break even.

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The publisher must produce and sell 4,478 books to cover total production costs. They need to break even by equating total costs with total revenue, using the formula FC + (VC × N) = P × N, and solving for N after substituting the given fixed costs, variable costs per book, and price per book.

To determine how many books a publisher must produce and sell to cover production costs, the following formula is used:

To break even, TC must equal TR. This can be expressed as:

FC + (VC × N) = P × N

Now we substitute the given values:

$45,920 + ($11.25 × N) = $21.50 × N

To find N, we solve the equation for N:

Therefore, the publisher must produce and sell 4,478 books to cover total production costs.

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Answer:

true

True

False

False

Step-by-step explanation:

a. The problem tells me that for every 3 parts of red paint, I have 8 parts of yellow paint. To find the ratio of 1 part of yellow paint I can write the following statement

For 8 parts of yellow paint ------------ 3 parts of red paint

        1 part of yellow paint  -------------      x

So [tex]x=\frac{1 part of yellow paint * 3 parts of red paint }{8 parts of yellow paint}[/tex]

[tex]x= \frac{3}{8} parts of red paint[/tex]

b, I have the following relationship

3 parts of red paint ----- 8 parts of yellow paint

If I multiply the entire expression by 3 I have left

3 * 3 parts of red paint -------- 8 * 3 parts of yellow paint

So

9 parts of red paint ---------- 24 parts of yellow paint

c.I have the same relationship

3 parts of red paint ----- 8 parts of yellow paint

If I multiply the entire expression by 1/2 I have left

3/2 parts of red paint -------- 8/2 parts of yellow paint

So

3/2 parts of red paint ---------- 4 parts of yellow paint

as 3/2 is different from 10, then the approach is false

d. observing the relation of part a,

For 3 parts of red paint ------------ 8 parts of yellow paint

      1 part of red paint   -------------      x

So [tex]x=\frac{1 part of red paint * 8 parts of yellow paint }{3 parts of red paint}[/tex]

[tex]x= \frac{8}{3} parts of yellow paint[/tex]  that is different than 3/8 parts of yellow paint, then the approach is false

Answer:

true

True

False

False

Step-by-step explanation: