A publisher prints 1,512 copies of a book in each print run. If they print 305 runs, how many books will be printed?

Answer:

x - 1

Step-by-step explanation:

(f + g)(x)=f(x) + g(x)

(f + g)(x)=(3x - 7) + (-2x - 6)

(f + g)(x)= 3x - 7 - 2x + 6

(f + g)(x)= 3x - 2x - 7 + 6

(f + g)(x)= x -1

The developer would earn $50.00 if 20 apps are downloaded. Similarly, they can calculate earnings for any other number of app downloads using this equation.

To represent the proportional relationship between the total earnings (y) and the number of apps downloaded (x), we can use the formula for direct variation, which is:

[tex]\[ y = kx \][/tex]

Where:

- [tex]\( y \)[/tex] represents the total earnings,

- [tex]\( x \)[/tex] represents the number of apps downloaded, and

- [tex]\( k \)[/tex] is the constant of proportionality.

In this scenario, the app developer earns $20.00 for every 8 apps downloaded. This means that for every 8 apps downloaded, the earnings increase by $20.00. So, the constant of proportionality [tex](\( k \))[/tex] is the rate at which earnings increase per app downloaded.

To find the value of [tex]\( k \)[/tex], we can divide the total earnings by the number of apps downloaded:

[tex]\[ k = \frac{y}{x} \][/tex]

Given that the developer earns $20.00 for every 8 apps downloaded, we can substitute these values into the equation:

[tex]\[ k = \frac{20}{8} \][/tex]

[tex]\[ k = 2.5 \][/tex]

Now that we have the value of [tex]\( k \)[/tex], we can rewrite the equation with this value:

[tex]\[ y = 2.5x \][/tex]

This equation represents the proportional relationship between the total earnings [tex](\( y \))[/tex] and the number of apps downloaded [tex](\( x \))[/tex]. It shows that for every additional app downloaded, the total earnings increase by $2.50, maintaining a consistent rate of increase.

This equation allows the app developer to predict their earnings based on the number of apps downloaded. For example, if 20 apps are downloaded, the total earnings can be calculated as:

[tex]\[ y = 2.5 \times 20 = 50 \][/tex]

So, the developer would earn $50.00 if 20 apps are downloaded. Similarly, they can calculate earnings for any other number of app downloads using this equation.

Answer:

c. They are equal to each other.

d. They are the negative of each other.

Step-by-step explanation:

c. Adding c to d and d to c are the same and thus both expressions are equal. In addition, the numbers can be added in any order and will result in the same final answer. This is also known as commutative property.

d. a-b= -(b -a)

In this case, subtracting b from a is not equal to subtracting a from b. The order of terms in subtraction affects the final answer.

Answer:

36, 28, 20

Step-by-step explanation:

To find the three terms of each sequence, simply subtract 8 from each number. For an example, you can notice the pattern by subracting 52 from 60. The answer I recieved was 8. That shows that the pattern is to subtract 8 from the following number.

Hope this helped :)

Answer:68

Step-by-step explanation:each is by 8 so add 8 onto each number to find the total

Answer:

3√5 or ≈6.7082

Step-by-step explanation:

1) √45

2) Factor out the perfect square: √3²×5

3) The root of a product is equal to the product of the roots of each factor: √3²√5

4) Reduce the index of the radical and exponent with 2: 3√5

5) Solution: 3√5 or ≈ 6.7082

after removing the perfect square factor from inside the square root of 45, we are left with 3√5.

To remove all perfect squares from inside the square root of √45, we need to factorize 45 and separate the perfect square factors.

The prime factorization of 45 is 3 × 3 × 5. Since 3 is repeated twice, it represents a perfect square factor.

We can rewrite the square root of 45 as the square root of (3 × 3 × 5). Using the property of square roots (√ab = √a × √b), we can simplify it as √(3 × 3) × √5.

The square root of 3 × 3 equals 3, so the expression simplifies to 3√5.

Therefore, after removing the perfect square factor from inside the square root of 45, we are left with 3√5.

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[tex]\boxed{(x+6)^2+(y+2)^2=72}[/tex]

The center-radius form of the circle equation is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here we know that the y-intercepts are:

[tex]y=4 \ and \ y=-8[/tex]

So:

[tex]\bullet \ If \ y=4, \ x=0 \\ \\ \\ (0-h)^2+(4-k)^2=r^2 \\ \\ \therefore \mathbf{(I)} \ h^2+16-8k+k^2=r^2 \\ \\ \\ \bullet \ If \ y=-8, \ x=0 \\ \\ \\ (0-h)^2+(-8-k)^2=r^2 \\ \\ \therefore \mathbf{(II)} \ h^2+64+16k+k^2=r^2 \\ \\ \\ \bullet \ If \ x=-12, \ y=-8 \\ \\ \\ (-12-h)^2+(-8-k)^2=r^2 \\ \\ \therefore 144+24h+h^2+64+16k+k^2=r^2 \\ \\ \therefore \mathbf{(III)} \ h^2+208+16k+24h+k^2=r^2[/tex]

So we have the following system of equations:

[tex]\left\{ \begin{array}{c}(I)\:h^{2}+16-8k+k^{2}=r^{2}\\(II)\:h^{2}+64+16k+k^{2}=r^{2}\\(III)\:h^{2}+208+16k+24h+k^{2}=r^{2}\end{array}\right.[/tex]

[tex]Subtract \ II \ from \ I \\ \\ \\\left\{ \begin{array}{c}h^{2}+16-8k+k^{2}=r^{2}\\-(h^{2}+64+16k+k^{2}=r^{2})\\---------------------\\h^{2}+16-8k+k^{2}-h^{2}-64-16k-k^{2}=r^{2}-r^{2}\end{array}\right.[/tex]

[tex]Simplifying: \\ \\ h^{2}+16-8k+k^{2}-h^{2}-64-16k-k^{2}=r^{2}-r^{2}\\ \\ 16-8k-64-16k=0 \\ \\ -24k-48=0 \\ \\ k=-\frac{48}{24} \\ \\ \therefore \boxed{k=-2}[/tex]

From (I):

[tex]h^2+16-8k+k^2=r^2 \\ \\ \\ For \ k=-2 \\ \\ h^2+16-8(-2)+(-2)^2=r^2 \\ \\ \therefore r^2=h^2+36 \\ \\ \\ Substituting \ k \ and \ r^2 \ into \ (III): \\ \\ h^{2}+208+16(-2)+24h+(-2)^{2}=h^2+36 \\ \\ Simplifying: \\ \\ 180+24h=36 \\ \\ 24h=36-180 \\ \\ 24h=-144 \\ \\ h=-\frac{144}{24} \\ \\ \therefore \boxed{h=-6}[/tex]

Finding the radius:

[tex]r^2=(-6)^2+36 \\ \\ r^2=36+36 \\ \\ r^2=72 \\ \\ \therefore \boxed{r=6\sqrt{2}}[/tex]

Finally, the equation of the circle is:

[tex](x-(-6))^2+(y-(-2))^2=72 \\ \\ \boxed{(x+6)^2+(y+2)^2=72}[/tex]

Answer:

[tex](x+6)^2 + (y+2)^2 = 72[/tex]

Step-by-step explanation:

We are given the following information in the question:

y intercept = 4, -8

The circle passes through the point (-12, -8)

Equation of circle:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

where r is the radius of circle, (h,k) is the center of circle.

The circle passes through the points (0,4), (0,-8_ and (-12,-8)

Putting these points in the equation of circle we get:

[tex]1) (0-h)^2 + (4-k)^2 = r^2\\h^2 + (4-k)^2 = r^2\\2) (0-h)^2 + (-8-k)^2 = r^2\\h^2 + (-8-k)^2 = r^2\\3) (-12-h)^2 + (-8-k)^2 = r^2\\[/tex]

Now, we have three equations in three variables.

Solving the three equations, we obtain:

h = -6, k = -2, r = [tex]6\sqrt2[/tex]

Putting these values in the equation of circle:

[tex](x-(-6))^2 + (y-(-2)) = (6\sqrt{2})^2\\(x+6)^2 + (y+2)^2 = 72[/tex]

The above equation is the required equation of circle.

Answer:

x = -5

Step-by-step explanation:

Solve for x:

3 x + 1 = -14

Subtract 1 from both sides:

3 x + (1 - 1) = -14 - 1

1 - 1 = 0:

3 x = -14 - 1

-14 - 1 = -15:

3 x = -15

Divide both sides of 3 x = -15 by 3:

(3 x)/3 = (-15)/3

3/3 = 1:

x = (-15)/3

The gcd of -15 and 3 is 3, so (-15)/3 = (3 (-5))/(3×1) = 3/3×-5 = -5:

Answer:  x = -5

Answer:

Step-by-step explanation:

3x + 1 = -14;

substr 1 : 3x+1-1 = - 14 -1

3x = -15

divid by 3

x = -5

Answer:

1/5

Step-by-step explanation:

Lets start with the number 100. We know that 1/10 of 100 is 10! 1/10 can also be written as 10%.

Now lets think about it, We're looking for 20%. If 1/10 of 100 is 10%, then 2/10 of 100 is 20%!

So you've got the fraction 2/10! Now you need to simplify it :)

Both the numerator (2) and the denominator (10) can be divided by 2!

(2/2)=1

(10/2)=5

Therefore, after simplifying 2/10 your final answer should be 1/5!

Answer:

[tex]2\pi \approx 6.28\ meters[/tex]

Step-by-step explanation:

Mei's horse is 3 meters from the center of the carousel. After one rotation, Mei travelled

[tex]l_M=2\pi r=2\pi \cdot 3=6\pi\ meters[/tex]

Anju's horse is 2 meters from the center. After one rotation, Mei travelled

[tex]l_A=2\pi r=2\pi \cdot 2=4\pi\ meters[/tex]

The difference in their travelled distances is

[tex]l_M-l_A=6\pi -4\pi =2\pi \approx 6.28\ meters[/tex]

Mei travels 6.28 meters more than Anju in one rotation.

In one rotation, Mei's horse travels a distance of

2 * 3.14 * 3 = 18.84 meters.

In one rotation,

Anju's horse travels a distance of 2 * 3.14 * 2 = 12.56 meters.

Therefore, Mei travels 18.84 - 12.56 = 6.28 meters more than Anju in one rotation.

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Answer:

D = 60,000,000,000

Step-by-step explanation:

When "E" appears on a calculator , it means exponential and it is used to denote numbers that are too big or small to appear on the calculator screen in their decimal form.

Therefore 6E-10 means 6 exponential 10 , mathematically written as  6^10

which is 60,000,000,000

Answer:

(14 + x)/31 ≥ .6

14 + x ≥ 18.6

x ≥ 5

The correct answer is B.

Sam needs to win at least 5 more of his 13 remaining matches in order to achieve at least a 60% win rate and qualify for the year-end tournament.

The question: how many of Sam's 13 remaining matches must he win to qualify for the year-end tournament by winning at least 60% of his matches this year, is a mathematics question related to percentage and probability. To solve it, you need to figure out the total number of matches Sam will play in the year and calculate what number constitutes 60% of that total. Sam is set to play a total of 31 matches (18 + 13). Sixty percent of 31 is 18.6, we will round this up to 19 as you cannot win portion of a match. Given that Sam has already won 14 matches, he needs to win at least 5 more of his 13 remaining matches (19-14 = 5) in order to win at least 60 percent of his matches for the year. So, the correct answer is 5.

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Answer:

m∠y=50°

m∠x=50°

Step-by-step explanation:

we know that

The angles in matching corners are called corresponding angles. When the two lines are parallel Corresponding Angles are equal

so

m∠y=50° -----> by corresponding angles

and

The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. When the lines are parallel, the alternate interior angles are equal.

so

m∠x=m∠y -----> by alternate interior angles

so

m∠x=50°

therefore

m∠y=50°

m∠x=50°

Answer:

-x/4-3=x

Step-by-step explanation:

Answer:

-12/5

Step-by-step explanation:

-x/4-2=x+1

-x/4-x-2=1

-x/4-x=1+2

-x/4-x=3

-1/4x-4/4x=3

-5/4x=3

x=3/(-5/4)

x=(3/1)(-4/5)

x=-12/5

Answer:

4.61 g/cm3

Step-by-step explanation:

density is mass divided volumen

[tex]density \: = \frac{64.54g}{14 {cm}^{3} } = 4.61 \frac{g}{ {cm}^{3} } [/tex]

The density of the object is 4.61 g/cm³

Using the parameters given for our Calculation;

The density of an object can be calculated as the ratio of the mass to the volume of the object.

Inputting the values thus;

Hence, the density is 4.61 g/cm³

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Answer:

x = - 2, x = 4

Step-by-step explanation:

Given

f(x) = (x - 4)(x + 2)

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

(x - 4)(x + 2) = 0 ← in standard form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4 → (4, 0 )

x + 2 = 0 ⇒ x = - 2 → (- 2, 0 )

Answer:

[tex]\frac{4^{21}}{5^{6}}[/tex]

Step-by-step explanation:

[tex]\frac{4^{7*3}}{5^{2*3}}=\frac{4^{21}}{5^{6}}[/tex]

Answer:

Step-by-step explanation:

m² + 8m = -3

(m² + 8m+16) -16 = -3

(m+4)² = 13.....continue

Answer:

12

Step-by-step explanation: 282 divided by 94 = 3

4x3=12

Answer:

12 defective widgets

Step-by-step explanation:

Here we calculate the "experimental probability:" 4 defective widgets out of 94 widgets comes out to a probability of being defective of 4/94, which of course could be reduced.

But we can go ahead and calculate the expected number of defective widgets by mult. that 282 widgets by the probability 4/94:

282        4

------- * ------- = 12

   1         94

In this sample of 282 widgets, we could expect that 12 will be defective.

Answer: 3.5−2.5n

Explanation:

To find the common difference take the end term and subtract the first term:

8.5 -11 = -2.5

Take the third term and subtract the 3rd term to verify:

6-8.5 = -2.5  check

The formula for an arithmetic sequence is:

an = a1+d(n-1)

an = 11 -2.5(n-1)

Distribute:

an = 11 -2.5n+2.5

Combine terms:

answer = 13.5 - 2.5n

Explanation: Tread more on Brainly.com - https://brainly.com/question/13244259#read more find the common difference take the end term and subtract the first term:8.5 -11 = -2.5Take the third term and subtract the 3rd term to verify:6-8.5 = -2.5  check The formula for an arithmetic sequence is: an = a1+d(n-1)an = 11 -2.5(n-1)Distribute: an = 11 -2.5n+2.5Combine terms: answer = 13.5 - 2.5nAnswer:

Answer: 3.5−2.5n

Answer:

you need to show a picture of a graph for my answer to be acurate but I'll try.

Step-by-step explanation:

The x intercept is found by setting y = 0 in the above equation and solve for x. Hence, the x intercept is at (c/a , 0). The y intercept is found by setting x = 0 in the above equation and solve for x.

Answer:

[tex]\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}[/tex]

Step-by-step explanation:

Noah's running speed = 6 mph.

Use formula [tex]D=v\cdot t,[/tex] where

D is the distance,

v is the speed,

t is the time.

If [tex]t=1[/tex] hour, then [tex]D=6\cdot 1=6[/tex] miles.

If [tex]t=\dfrac{1}{2}[/tex] hour, then [tex]D=6\cdot \dfrac{1}{2}=3[/tex] miles.

If [tex]t=1\dfrac{1}{3}[/tex] hours, then [tex]D=6\cdot 1\dfrac{1}{3}=6\cdot \dfrac{4}{3}=8[/tex] miles.

If [tex]t=1\dfrac{1}{2}[/tex] hours, then [tex]D=6\cdot 1\dfrac{1}{2}=6\cdot \dfrac{3}{2}=9[/tex] miles.

If [tex]t=9[/tex] hours, then [tex]D=6\cdot 9=54[/tex] miles.

If [tex]t=4\dfrac{1}{2}[/tex] hours, then [tex]D=6\cdot 4\dfrac{1}{2}=6\cdot \dfrac{9}{2}=27[/tex] miles.

So, the table is

[tex]\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}[/tex]

Please find attached the answers in the attached diagram

Average speed is the total distance travelled per time.

Average speed = total distance / total time

Noah's average speed is 6mph

From the above formula, the formula to determine miles run is average speed x time

Total miles he ran in 1 hour = 6 x 1 = 6 miles

Total miles he ran in 1/2 hours = 6 x 1/2 = 3 miles

Total miles he ran in 1 1/3 hours = 6 x 4/3 = 8 miles

The formula to determine total time:  total distance / average speed

Time it took Noah to run 1 1/2 miles = 3/2 ÷ 6 = 1/4 miles

Time it took Noah to run 9 miles = 9 ÷ 6 = 1 1/2 miles

Time it took Noah to run 4 1/2 miles = 9/2 ÷ 6 = 3/4 miles

Please find attached an image of the table used in answering this question

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Answer:  the explanation is given below. The number is NOT an integer.

Step-by-step explanation:  We are given to check whether the number -0.5 is an integer or not.

We know that

an integer is a number where the digits after the decimal are zero, or the denominator of its fractional form is 1.

The given number is

[tex]n=-0.5.[/tex]

Here, we can see that the digits after the decimal is 5, not zero. Also,  

this number can be represented as a negative fraction with denominator not equal to 1 is as follows :

[tex]n=-\dfrac{5}{10}=-\dfrac{1}{2}.[/tex]

Therefore, this number is NOT an integer.

Answer:

The selling price is $16.43

Step-by-step explanation:

we know that

A markup percentage is the amount of the cost of an item that you add on to create the selling price

we have that

[tex]100\%+210\%=310\%=310/100=3.10[/tex]

To find out the selling price, multiply the cost of a calculator by the factor 3.10

so

[tex]\$5.30(3.10)=\$16.43[/tex]

therefore

The selling price is $16.43

Answer:

11

Step-by-step explanation:

90=79+x

-79-79

_________

11=x

Answer: 2

Step-by-step explanation:

Answer:

7614

Step-by-step explanation:

Answer: l = 7.2

Step-by-step explanation:

90/12.5 = 7.2

7.2 * 12.5 = 90

Answer:

length of the rectangle is 7.2 centimeters.

Step-by-step explanation:

Area of the rectangle has been given as 90 square centimeters.

Height of the rectangle = 12.5 centimeters

Now we have to calculate the length of the rectangle.

Since, Area of the rectangle = Length × height

90 = 12.5 × length

Length = [tex]\frac{90}{12.5}[/tex]

           = 7.2 centimeters

Therefore, length of the rectangle is 7.2 centimeters.

Answer:

1 2/3 an egg to a bird

Step-by-step explanation:

because there are 5 eggs and divide 5 by 3 you get 1 2/3 and there are 3 birds so each gets 1 2/3rds an egg

Answer:

C) 3:5

Step-by-step explanation:

The question asks for the ratio of birds to eggs. It's asking how many birds there are in comparison to the number of eggs. The key to ratios is paying attention to which is listed first.

There are 3 birds, and 5 eggs, therefore the ratio is 3:5

Answer:19

Step-by-step explanation:

Subtract then add