At the end of the year, a library reported 32 books lost or stolen and 24 books were sent out for repair. If the library originally had 1,219 books, how many were left on the shelves or in circulation?

A. 1,219
B. 1,187
C. 1,163
D. 1,275

To find the length of the radius, use the formula for the circumference of a circle. Divide the circumference by 2π to get the radius. In this case, the radius is approximately 59 cm.

In order to find the length of the radius, we can use the formula for the circumference of a circle: C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 367 cm, so we can plug in the values to solve for r.

367 = 2πr

To isolate r, divide both sides of the equation by 2π: r = 367 / (2π)

Using a calculator to approximate π as 3.14, we can calculate the radius: r ≈ 367 / (2 * 3.14) ≈ 58.598

Therefore, the length of the radius, rounded to the nearest centimeter, is approximately 59 cm.

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Answer:

b. 4+7x-2

Explanation:

when you add like terms for the first equation it becomes 7x-6

the second one becomes 7x+2

the third one becomes 7x-6

and the last one is also 7x-6

which means the second one is not equivalent

Answer:

B. 4 + 7x – 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]-37+n=-56\qquad\text{add 37 to both sides}\\\\-37+37+n=-56+37\\\\n=-19[/tex]

Answer:

n=-93

A. -93 *(first option)*

Step-by-step explanation:

First, you subtract by 37 from both sides of equation.

-37+n-37=-56-37

Then, simplify to find the answer.

-56-37=-93

n=-93 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

a=9

Step-by-step explanation:

1/a + 1/(2a) = 1/(a-3)

Get a common denominator for the left hand side

2/(2a) + 1/(2a) = 1/(a-3)

3/(2a) = 1/ (a-3)

Using cross products

3 * (a-3) = 1 * 2a

Distribute

3a -9 = 2a

Subtract 3a from each side

3a-3a-9 = 2a-3a

-9 = -a

Multiply by -1

-1*-9 = -1 *-a

9 = a

Aloha~! My name is Zalgo and I am here to provide a bit more knowledge to you today. The following Improper Fractions have been changed into Mixed Numbers (and also into decimals because I like Math :3):

I hope that this info helps! :D

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Mahalo~! XP)

Answer:

In order; 2 1/4, 2 2/3, 3 5/6, 5 1/2, 3 2/5, 1 7/8, 3 3/10, 2 5/12

Step-by-step explanation:

The way mixed numbers work is how many times (improper fraction) the denominator can go into the numerator.

For example, in the improper fraction 9/4, 4 can go into 9 twice making the whole number a 2, then you get whatever is left and leave it as the fraction; there is 1/4 left making making the mixed number 2 1/4. Use this rule to apply to all the improper fractions.

Answer:

Part 1) The volume of the prism is 3 times greater than the volume of the pyramid

Part 2) The prism would fill only one-third

Part 3) The cylinder and the cone

Step-by-step explanation:

Part 1) How do their volumes compare?

we know that

The volume of a rectangular prism is equal to

[tex]Vprism=BH[/tex]

where

B is the area of the base of rectangular prism

H is the height of the prism

The volume of a rectangular pyramid is equal to

[tex]Vpyramid=\frac{1}{3}BH[/tex]

where

B is the area of the base of rectangular pyramid

H is the height of the pyramid

Compare the volumes

[tex]Vprism=BH[/tex] -----> equation A

[tex]Vpyramid=\frac{1}{3}BH[/tex] -----> equation B

substitute equation A in equation B

[tex]Vpyramid=\frac{1}{3}Vprism[/tex]

[tex]Vprism=(3)Vpyramid[/tex]

The volume of the prism is 3 times greater than the volume of the pyramid

Part 2) If the pyramid was full of water, how much of the prism would it fill up?

Remember that

[tex]Vpyramid=\frac{1}{3}Vprism[/tex]

therefore

The prism would fill only one-third

Part 3) Name another pair of three-dimensional objects that have a relationship similar to this

we have the cylinder and the cone

The volume of the cylinder is equal to

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

The volume of the cone is equal to

[tex]Vcone=\frac{1}{3}\pi r^{2}h[/tex]

Compare the volumes

[tex]Vcylinder=(3)Vcone[/tex]

The volume of the cylinder is 3 times greater than the volume of the cone

The volume of the pyramid is one-third of the volume of the rectangular prism with the same base and height. Therefore, if the pyramid was full of water, it would fill one-third of the prism. Cones and cylinders with the same base and height have a similar volume relationship.

When comparing the volumes of a rectangular pyramid and a rectangular prism that have the same base and the same height, the volume of the pyramid is exactly one-third the volume of the prism. This is because the volume of the prism is calculated by length × width × height, while the volume of the pyramid is ⅓ x (base area) x height, which is ⅓ x (length × width) x height.

If the pyramid was full of water, it would fill up exactly one-third of the prism. This corresponds to the geometric rule that says the volume of a pyramid is one-third the volume of a prism with the same base and height.

Another pair of three-dimensional objects with a similar relationship is a cone and a cylinder. Like the pyramid and prism, if the cone and cylinder have the same base and height, the cone's volume is one-third of the cylinder's volume.

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Answer:

Distance = 3r

Step-by-step explanation:

We are to write an algebraic expression and then simplify it for the given situation:

The distance traveled by a train in three hours with a constant speed of r miles per hour.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

Answer: 0.4521 - 0.4879

Step-by-step explanation:

1) Find the standard deviation with the given information:

n=3000

p=47% ⇒ 0.47

1-p= 1 - 0.47 = 0.53

[tex]\sigma =\sqrt{\dfrac{p(1-p)}{n}}\\\\\\.\ =\sqrt{\dfrac{0.47(0.53)}{3000}}\\\\\\.\ =\sqrt{\dfrac{0.2491}{3000}}\\\\\\.\ =\sqrt{0.00008303}\\\\\\.\ =0.009112[/tex]

2) Find the margin of error (ME) with the given information:

C=95% ⇒ Z = 1.960

σ=0.009112

ME = Z × σ

= 1.96 (0.009112)

= 0.01786

3) Find the confidence interval with the given information:

p = 0.47

ME = 0.01786

CI = p ± ME

= 0.47 ± 0.01786

= (0.4521, 0.4879)

Answer:

145

step by step explanation:

perimeter definition:

perimeter definition:the continuous line forming the boundary of a closed geometrical figure.

add up the length of the sides:

80+20+45=145

Answer:

A

Step-by-step explanation:

Answer:

staight angle and supplementary angle

Step-by-step explanation:

Answer:

C) angle 2 and angle 8

Step-by-step explanation:

Check the picture below.

Answer:

x=6.9 inches

Step-by-step explanation:

If a tangent and a secant are draw to a circle from the same exterior point, the square of the length of the tangent is equal to the product of the total length of the secant and the length of the external segment of the secant.

From the given diagram,

(8+4)×4=x²

12×4=x²

x²=48

x=6.9 inches

Answer:

13 students

Step-by-step explanation:

We have a list of four numbers: 1, 2, 3, 4. If 50 persons were to pick a number randomly, it means that the probability of picking any of the numbers is 0.25.

Therefore, from 50 students, 0.25*50 = 12.5 ≈ 13 students aproximately would choose the same number as I did.

Answer:

2

Step-by-step explanation:

2:1  win / loss ratio

1 = 4 loses

4 x 2 = 8

the team has 6 wins it would need to win a total of 8 to have a 2:1 ratio

The baseball team must win 2 more games to achieve a win:loss ratio of 2:1, assuming they have no additional losses.

The student's baseball team currently has a record of 6 wins to 4 losses. The question asks how many more games the team must win to achieve a win:loss ratio of 2:1, assuming no more losses occur. To achieve a 2:1 win:loss ratio, the number of wins must be twice the number of losses. Since the losses are fixed at 4, the team needs 2 times 4 (which equals 8) wins to attain this ratio. The team has already won 6 games, so they need 8 - 6, which equals 2 more wins to reach a 2:1 ratio.

Answer:

Options B and D

Step-by-step explanation:

we have

[tex]y=\frac{1}{x-3}[/tex] -----> equation A

[tex]y=3-x^{3}[/tex] -----> equation B

Solve the system of equations by graphing

The solution of the system of equations is the intersection point both graphs

The solutions are the points (1.545,-0.687) and (2.956,-22.835)

see the attached figure

The approximate solutions are

(1.5,-0.7) and (2.9,-22.8)

Answer:

Options B and D

Step-by-step explanation:

Answer:

Each quart is 1.31 to the customer.

Step-by-step explanation:

Cost of 1 quart to  Wong = 0.75

Cost to you or I = 0.75 * 175/100 = 1.31

He sells each quart for 1.31 dollars.

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-7}{2-(-1)}\implies \cfrac{3}{2+1}\implies \cfrac{3}{3}\implies 1[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=1[x-(-1)]\implies y-7=x+1 \\\\\\ y=x+8\implies \boxed{-x+y=8}\implies \stackrel{\textit{standard form}}{x-y=-8}[/tex]

just to point something out, is none of the options, however -x + y = 8, is one, though improper.

Answer:

128/15 min or 8.5 min

Step-by-step explanation:

By using unitary method,

Time required to paint 5/8 of wall = 16 min.

Time required to paint 1/1 of wall = 16×8/5

Hence, Time required to paint 1/3 of wall = 16×8/5×1/3

Answer:

8 8/15

Step-by-step explanation:

simplify the two fractions you have to make them have the same denominater

enthen you can determine the answer.

Use the law of sines:

Sin(angle) = Opposite Leg / Hypotenuse

Sin(30) = 14 / x

x = 14/sin(30)

x = 28

Answer:

Step-by-step explanation:

Rewrite 2x-5y< 15 as follows:  Add 5y to both sides.  Then 2x < 15 + 5y.

Next, subtract 15 from both sides:  2x - 15 < 5y.

Finally, divide all terms by 5:           (2/5)x - 3 < y

Now find the y-intercept of this line.  Let x = 0.  Then y = -3.  Plot (0, -3) on graph paper.  Now, starting at (0, -3), move your pencil point 5 spaces to the right and 2 spaces up.  Plot this new point, (5, -1).  Now draw a dashed line through both (0, -3) and (5, -1).  Shade the area ABOVE this dashed line.

Answer:

is op 4 (-3,7)

Step-by-step explanation:

Answer:

6%

Step-by-step explanation:

To solve this you need to subtract 607000 by 572000 to see how many people in the population decreased.

607,000- 572,000= 35,000

Then you put 35,000 over 607,000

also you need x over 100

35000/607,000 x/100

Then do cross product property

35,000*100=3,500,000

607,000* x= 607,000x

3,500,000= 607,000x

Then do 3,500,000 divided by 607,000

You get 5.76%

Round to the nearest percent and get 6%

Final answer:

The rate of decrease of the population from the 2000 census to the 2010 census is 6% when rounded to the nearest percent.

Explanation:

To calculate the rate of decrease of the city's population, we use the population values from the 2000 and 2010 censuses. The population in 2000 was 607,000, and in 2010 it was 572,000. To find the population decrease, subtract the 2010 population from the 2000 population:

Population decrease = Population in 2000 - Population in 2010

Population decrease = 607,000 - 572,000

Population decrease = 35,000

Next, to find the rate of decrease as a percent, we divide the population decrease by the original population (in 2000) and then multiply by 100:

Rate of decrease (%) = (Population decrease / Population in 2000) × 100

Rate of decrease (%) = (35,000 / 607,000) × 100

Rate of decrease (%) = 0.0577 × 100

Rate of decrease (%) = 5.77%

Round this to the nearest percent, and you get a 6% decrease.

Answer:

5/4 hope this helps

Step-by-step explanation:

ANSWER

The correct answer is D.

EXPLANATION

The given exponentiial expression is

[tex] {5}^{ \frac{7}{3} } [/tex]

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

We put a=5, n=3 and m=7

This implies that,

[tex]{5}^{ \frac{7}{3} } = \sqrt[3]{ {5}^{7} } [/tex]

The correct answer is D.

The last option is correct.

Answer:

A

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, - 4) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0+4}{4+4}[/tex] = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]

Using (a, b) = (- 4, - 4), then

y - (- 4) = [tex]\frac{1}{2}[/tex] (x - (- 4)), that is

y + 4 = [tex]\frac{1}{2}[/tex] (x + 4) → A

Answer:

[ - 5, 3 ]

Step-by-step explanation:

Solve (x - 3)(x + 5) = 0

The zeros are x = - 5 and x = 3

These divide the domain into 3 intervals

(- ∞, - 5 ], [- 5, 3 ], [ 3, + ∞ )

Choose a test point in each interval and consider the sign of the result.

x = - 10 : (- 10 - 3)(- 10 + 5) = (- 13)(- 5) = 65 > 0

x = 0 : (0 - 3)(0 + 5) = (- 3)(5) = - 15 < 0 ← required result

x = 5 : (5 - 3)(5 + 5) = (2)(10) = 20 > 0

The solution is [ - 5, 3 ] or - 5 ≤ x ≤ 3

Answer:

B

Step-by-step explanation:

Right on edge 2021

Answer:

One

Step-by-step explanation:

It is one because each spoke has one space in the middle. However some people think it's 64 because they read the question wrong.

Answer:

6^8=6*6*6*6*6*6*6*6

=1679616

Step-by-step explanation:

In this expression the exponent shows that how many times 6 will be multiplied.

6^8=6*6*6*6*6*6*6*6

=1679616

Final answer:

To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, divide the weight of the 5 pound bag by the weight of each 3/4 pound bag.Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.

Explanation:

To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, we need to divide the weight of the 5 pound bag by the weight of each 3/4 pound bag. We can use the division operation to solve this.

5 pounds ÷ 3/4 pounds = 5 ÷ 3/4

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3.

5 ÷ 3/4 = 5 × 4/3 = 20/3

Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.

Answer:

The sum is a binomial with a degree of 6

Step-by-step explanation:

we have

[tex](3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)[/tex]

Group terms that contain the same variable

[tex](3x^{2}y^{2}-3x^{2}y^{2})-2xy^{5}+3x^{4}y[/tex]

[tex]0-2xy^{5}+3x^{4}y[/tex]

[tex]-2xy^{5}+3x^{4}y[/tex]

The sum is a binomial ( two terms) with a degree of 6  

[tex]-2xy^{5}[/tex] has a degree of 6 (x has an exponent of 1, y has 5, and 1+5=6)

The sum of the polynomial is a binomial with a degree of 6. The correct option is D) and this can be determined by using arithmetic operations.

Given :

Polynomials --   [tex]3x^2y^2-2xy^5[/tex] and [tex]-3x^2y^2+3x^4y[/tex]

The following steps can be used to determine the sum of the given polynomials:

Step 1 - Write the sum of the given polynomials.

[tex]3x^2y^2-2xy^5-3x^2y^2+3x^4y[/tex]

Step 2 - Subtract [tex]3x^2y^2[/tex] from [tex]3x^2y^2[/tex] in the above expression.

[tex]-2xy^5+3x^4y[/tex]

The above expression cannot be further simplified. Therefore, this is the final expression of the sum of the given polynomials.

The sum of the polynomial is a binomial with a degree of 6. Therefore, the correct option is D).

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Check the picture below.

Also check your Unit Circle for the cosine of 30°, if you don't have a Unit Circle yet, this is a good time to get one, you'll need it, you can find many online.

Answer:

36

Step-by-step explanation:

The 10 part of the ratio represents 120 chickens. Divide 120 by 10 to find the value of one part of the ratio.

120 ÷ 10 = 12 ← value of 1 part of the ratio, hence

3 parts = 3 × 12 = 36 ← number of horses

The number of horses on the farm is​ 36.

Given that, the ratio of chicken to pigs to horses on a farm is 10:2:3 and the number of chickens on the farm is 120.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

We can write the given ratio 10:2:3 as 10x: 2x: 3x.

So, 10x=120

⇒x=12

Then, the number of horses=3x=36

Therefore, the number of horses on the farm is​ 36.

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