Algebra 1, Section 7.10

Answer:

Therefore,

[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]

Step-by-step explanation:

Given:

Spherical Shape Ball

[tex]Radius =15\ inches[/tex]

pi = 3.14

To Find:

Volume of Ball= ?

Solution:

Formula for Volume of Sphere is given by

[tex]\textrm{Volume of Sphere}=\dfrac{4}{3}\pi (Radius)^{3}[/tex]

Substituting the given values we get

[tex]\textrm{Volume of Ball}=\dfrac{4}{3}\times 3.14\times 15^{3}=14130\ inches^{3}[/tex]

Therefore,

[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]

Answer:

i think ainsley completed 45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Hello, remember you need to write complete questions in order to get good and exact answers. Here you haven't provided any fractions, so I'll give you my own fractions.

The first fraction is:

[tex]\frac{1}{2}[/tex]

The second fraction is:

[tex]\frac{1}{4}[/tex]

So let's say that difference is:

[tex]\frac{1}{2}-\frac{1}{4}[/tex]

Therefore, the result is:

[tex]\frac{1}{2}-\frac{1}{4}=\frac{1}{4}[/tex]

The representation of this problem is shown using the number line below. As you can see, we have written both 1/2 and 1/4 and the difference is also indicated giving the result 1/4. That is, if we walk from 1/4 to 1/2 we'll walk 1/4 units.

Answer:

-7/10

Step-by-step explanation:

Bruh trust me

Answer:

4 and -3

Step-by-step explanation:

4-3=1

4(-3)=-12

The two numbers that have a sum of 1 and a product of -12 is -4 & 3

From the question, we are determine the two unknown numbers by solving the quadratic equation

The given quadratic equation is

n² + n -12 = 0

The quadratic equation can be solved as follows

n² + n -12 = 0

By factorizing

n² +4n -3n -12 = 0

n(n+4) -3(n+4) = 0  

(n+4)(n-3) = 0

Then,

n+4 = 0 OR n -3 = 0

∴ n = -4 OR n = 3

Hence, the two numbers that have a sum of 1 and a product of -12 are -4 & 3

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Answer:

D) 50ft

Step-by-step explanation:

(18×x) + (32×18) + [(48-18-18)×(32-11)]

= 1728

18x + 576 + (12×21) = 1728

18x = 1728 - 828

18x = 900

x = 50

Answer:

3.5 alligators

Step-by-step explanation:

i did khan academy

Answer:

3.5

Step-by-step explanation:

I just answered it :) it was correct btw

Answer:

11+(2×4)

11+8

$19....

Answer:

Cost for 2 hours=19, Cost for 2 hours=11+4t

To find the percentage of the shaded area inside the square, we need to determine the area of the shaded region and calculate the percentage relative to the total area of the square. Without more information or measurements, we can't determine the exact size of the shaded area or the percentage.

To find the percentage of the area inside the square that is shaded, we need to determine the area of the shaded region and then calculate the percentage. Given the perimeter of the square is 40cm, we can find the length of each side by dividing the perimeter by 4, which gives us 10cm. The area of the square is found by squaring the length of one side, so the area is 10cm x 10cm = 100cm². To find the shaded area, we need to subtract the area of the square from the total area. Assuming the shaded region is a smaller square with side length x, the area of the shaded region is x². So the shaded area is 100cm² - x².

To calculate the percentage, we divide the shaded area by the total area of the square and multiply by 100. So the percentage of the area inside the square that is shaded is (100cm² - x²) / 100cm² * 100.

It's important to note that we don't have enough information to determine the exact size of the shaded area or calculate the percentage without more details or measurements of the shaded region.

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Answer: Area is 168ft^2

Step-by-step explanation:

Answer: Amount of change : $30

percent increase : 200%

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

To obtain the amount of change we have to subtract the wholesale price to the retail price:

Mathematically speaking:

45 -15 = $30

For the percent increase, the amount of change (30) is some percent of the original price (15). So:

30 / 15 =2 (decimal form)

If we multiply it by 100, the percentage is:

200%

Height of the trapezoid is 14.4 meter.

Solution:

Given data:

One base [tex](b_1)[/tex] = 12 meter

Other base [tex](b_2)[/tex] = 8 meter

Area = 144 square meter

Area of the trapezoid = [tex]\frac{1}{2} \times(b_1+ b_2)\times h[/tex]

[tex]$144=\frac{1}{2} \times(12+8)\times h[/tex]

[tex]$144=\frac{1}{2} \times 20 \times h[/tex]

[tex]$144= 10 \times h[/tex]

Divide by 10 on both sides, we get

14.4  =  h

Switch the sides of the equation.

h = 14.4

Height of the trapezoid is 14.4 meter.

Answer:

Step-by-step explanation:

[tex]15a\geq 75\\15(5)\geq75\\75\geq75\\True[/tex]

If we substituted 1 for a then:

[tex]15a\geq75\\15(1)\geq75\\15\geq75\\False[/tex]

Answer:

54π in³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V= πr²h ( r is the radius and h the height )

Here r = 3 and h = 6, thus

V = π × 3² × 6 = π × 9 × 6 = 54π in³

Answer:

p = - 3

Step-by-step explanation:

Given

x² - 6x = 12

To obtain the required form use the method of completing the square

add ( half the coefficient of the x- term )² to both sides, thus

x² + 2(- 3)x + 9 = 12 + 9

(x - 3)² = 21

Thus p = - 3

Given the quadratic functions expressed as;

x² - 6x = 12

The value of p given the quadratic expression is -3

Complete the square at the left hand side of the equation.

Add the square of the half of coefficient of x to both sides.

coefficient of x = -6

Half of coefficient of x = -6/2 = -3

Square of the result = (-3)² = 9

Add 9 to both sides of the equation

x² - 6x + 9 = 12 + 9

Factoring the left hand side

(x-3)² = 21

Comparing the result with (x+p)² = q

The value of p wil be -3

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Answer:

The penny has a circuferance of  2.356194

Step-by-step explanation:

To get this I used the formula for circumference c = πd or c = 2π x r²

And you just plug in 0.75 for d and multiply it by 5 to get you answer

The circumference of the penny is approximately 2.36 inches.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The circumference of a circle is expressed mathematically as;

Circumference = 2πr or dπ

Where r is the radius, d is the diameter, and π is constant pi.

Given the parameter:

Diameter of the penny d = 0.75 inches

Circumference =?

To find the circumference of the penny, we can use the formula for the circumference of a circle.

Circumference = dπ

Plug in the diameter values:

Circumference = 0.75 × π

Circumference = 0.75π in or 2.36 in.

Therefore, the circumference is approximately 2.36 inches.

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Answer:

144 pounds

Step-by-step explanation:

Weight of object Earth: Weight of Object Planet B

100:3 = 4800:b

100/3=4800/b

100b=14400

b=144

Therefore, 144 pounds

The weight of an elephant on planet B can be calculated using the weight ratio of 100 (on Earth) to 3 (on planet B). By setting up a proportion and solving for the unknown weight, we find that the elephant weighs 144 pounds on planet B.

Since the ratio is 100 to 3, we can set up a proportion to find the elephant's weight on planet B.

First, represent the known weight ratio between Earth and planet B: 100 (earth weight) to 3 (planet B weight).

Then, set up the proportion using the weight of the elephant on Earth (4,800 pounds) and let x represent the unknown weight on planet B:

100/3 = 4800/x

To solve for x, cross-multiply and divide:

100x = 4800 * 3

Finally, divide both sides by 100 to find x:

x = (4800 * 3) / 100

x = 144 pounds

Therefore, the elephant would weigh 144 pounds on planet B.

Answer:

[tex]486\ in^2[/tex]

Step-by-step explanation:

we know that

The surface area of the cube is equal to the area of its six square faces

so

[tex]SA=6b^2[/tex]

where

b is the length side of the cube

we have

[tex]b=9\ in[/tex]

substitute

[tex]SA=6(9)^2=486\ in^2[/tex]

Answer:

486

Step-by-step explanation:

Answer: I believe that the answer is either C or A

Step-by-step explanation:

Typically, 7% of babies born in the River Creek hospital have birth defects, which means 93% of babies do not. In a group of 500 babies, about 35 are expected to have birth defects.

A. The typical percentage of babies having birth defects is 7%, because 7 out of every 100 is the equivalent of 7% when expressed as a percentage.

B. To find the percentage of babies that do not have birth defects is therefore 100%-7% = 93%, because the percentage of babies that have defects and those that do not should add up to 100%.

C. If you were to expect about 7% of babies to have a birth defect in a group of 500 babies, you would calculate it as: 500 x 0.07 = 35 babies. So, you would typically expect to find about 35 babies with birth defects in a group of 500 babies.

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Answer:

4/7

Step-by-step explanation:

you just flip the numbers across the division/fraction sign

Heya.

First, let us learn about reciprocals.

Basically, it's the fraction flipped. Easy as 1, 2, 3!

Let's do an example:

We have an equation that says Find the reciprocal of 5/2.

1. Flip the fraction.

2. We then have 2/5 as a final answer.

Now onto the question:

1. We need to flip the equation.

2. This results as 4/7.

Therefore, our answer is "4/7".

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Answer:

The scale factor of the dilation is 3

Step-by-step explanation:

we know that

A dilation is a non rigid transformation that produce similar figures

so

Rectangle ABCD and rectangle A'B'C'D' are similar

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

[tex]z=\frac{D'C'}{DC}[/tex]

we have

[tex]D'C'=12-3=9\ units[/tex] ----> difference of x-coordinates

[tex]DC=4-1=3\ units[/tex]  ---> difference of x-coordinates

substitute

[tex]z=\frac{9}{3}=3[/tex]

The scale factor is greater than 1

so

The dilation is a enlargement

Started with 54 cookies, considering fractions, removals, and distributions, ending with 15 cookies.

let's break it down:

1. **Initial Batch**: They started with an unknown number of cookies, denoted as  [tex]\( x \).[/tex]

2. **Cookies for Teachers**: They took [tex]\( \frac{1}{4} \) of the cookies for their teachers, leaving \( \frac{3}{4}x \)[/tex]  cookies.

3. **Burnt Cookie**: They discarded one burnt cookie, resulting in [tex]\( \frac{3}{4}x - 1 \) cookies.[/tex]

4. **Cookies for Nursing Home**: They gave  [tex]\( \frac{2}{3} \) of the remaining cookies to the nursing home, keeping \( \frac{1}{3} \) of \( \frac{3}{4}x - 1 \) cookies.[/tex]

5. **Cookies for Neighborhood Kids**: They gave 3 cookies to the neighborhood kids, resulting in  [tex]\( \frac{1}{3}x - 3 \) cookies.[/tex]

6. **Cookies for Friends**: They wrapped up [tex]\( \frac{2}{3} \) of the remaining cookies for their friends, keeping \( \frac{1}{3} \) of \( \frac{1}{3}x - 3 \) cookies.[/tex]

7. **Final Count**: They were left with 15 cookies, so [tex]\( \frac{1}{3}x - 3 = 15 \).[/tex]

[tex]\[ \frac{1}{3}x - 3 = 15 \]\[ \frac{1}{3}x = 15 + 3 \]\[ \frac{1}{3}x = 18 \]\[ x = 18 \times 3 \]\[ x = 54 \][/tex]

So, they initially had 54 cookies.

yes is an equilateral triangle also a rhombus

Answer:

ues it is   a equilateral triangle

Step-by-step explanation:

from the meaning of equilateral, equilateral means all sides are equal in length.

a rrhombus has all its side equal.and therefore it s an  equilateral triangle

Answer:

n = 3

Step-by-step explanation:

Equation:  17.1 = 5.7 * n

Divide both sides by 5.7 to get n by itself.

Step 1:  Divide both sides by 5.7

17.1 = 5.7 * n

17.1 / 5.7 = 5.7 * n / 5.7

    divide            divide

3 = n

Answer:  n = 3

We are given the following equation and want to solve for the unknown variable, n:

[tex]17.1=5.7 \times n[/tex]

To solve for an unknown variable, we want to isolate the variable by doing operations to both sides of the equation:

For this equation, we'll divide both sides by 5.7 to isolate the unknown variable n

[tex]17.1 \boxed{\div 5.7} = 5.7 \times n \boxed{\div 5.7}[/tex]

After dividing both sides by 5.7 and simplifying, we get:

[tex]3=n[/tex]

The next step is a bit tedious, but in math, you usually want to have the variable on the LEFT side of the equation after isolation.

After reversing the equation accordingly, we have:

[tex]\boxed{n=3}[/tex]

We have a value for n, which is 3.

Let me know if you need any clarifications, thanks!

~ Padoru

Answer:



Step-by-step explanation:

A=[tex]\pi r^{2}[/tex]

A=3.14*26*26

A=2122.64

A=2122.6[tex]m^{2}[/tex]

The calculated area is 530.66 [tex]m^2[/tex], which rounds to 530.7 [tex]m^2[/tex].

To find the area of a circle with a given diameter, you first need to find the radius, which is half of the diameter. Since the diameter provided in the question is 26 meters, the radius would be 13 meters. The formula to calculate the area (A) is A = π[tex]r^2[/tex], where (pi) is approximately 3.14 and r is the radius of the circle.

Using the aforementioned radius of 13 meters, the area can be calculated as follows:

A = 3.14 x [tex](13 m)^2[/tex]= 3.14 x 169 = 530.66 [tex]m^2[/tex]

When rounded to the nearest tenth, the area of the circle is 530.7 [tex]m^2[/tex].

Answer:

D

Step-by-step explanation:

Answer: 11 more cups of flour is needed.

Step-by-step explanation: 234 - 223 = 11

We find that the cook needs 11 more cups of flour to meet the recipe's requirement of 234 cups, as they only have 223 cups.

To determine whether the cook has enough flour to follow a recipe requiring 234 cups, a simple subtraction operation is performed. The cook starts with 223 cups of flour. The amount needed subtracts the amount available: 234 cups (needed) - 223 cups (available) = 11 cups. So, the cook requires 11 more cups of flour to have enough for the recipe.

Solution:

Distance between two points is given by:

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

We have to find the distance in the standard (x, y) coordinate  plane between the points (2,3) and (5,5)

From given,

[tex](x_1, y_1) = (2, 3)\\\\(x_2, y_2) = (5, 5)[/tex]

Substituting the values we get,

[tex]d = \sqrt{(5-2)^2 + (5-3)^2}\\\\Simplify\\\\d = \sqrt{3^2 + 2^2}\\\\d = \sqrt{9+4}\\\\d = \sqrt{13}\\\\In\ decimal\ form\\\\d = 3.605 \approx 3.6[/tex]

Thus distance between the points (2,3) and (5,5) is 3.6 units

The distance between the points (2,3) and (5,5) on the standard (x, y) coordinate plane is determined using the distance formula. After substituting the given coordinate points into the formula, we find that the distance is √13 units.

In Mathematics, the distance between two points in the (x, y) coordinate plane is given by the distance formula, which is √[(x₂-x₁)² + (y₂-y₁)²]. This formula is acquired from the Pythagorean theorem. Here, the points are (2,3) and (5,5). So, substituting these values in the distance formula, we get:

Distance = √[(5-2)² + (5-3)²] = √[3² + 2²] = √[9+4] = √13.

Therefore, the distance between the two points (2,3) and (5,5) on the standard (x, y) coordinate plane is √13 units.

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Answer:

I think it's B.

Step-by-step explanation:

Answer:

I believe that the answer is A but it could be B