A teacher can grade 15 papers in 25 minutes. At this rate, how many papers can she grade in 90 minutes?

Answers

Answer 1

15/25 = x/90

25x = 1350

x = 54

54 papers


Related Questions

Help me. giving brainliest!!!

Answers

Answer: 709 milliliters

Step-by-step explanation:

It is just the sum of the numbers so,

236 + 473 = 709

709 milliliters

Hope this helps!

Answer:

709 millimeters

Step-by-step explanation:

Add it up 236 = 473 = 709

create number patterns using numbers between 100-300​

Answers

100,110,120, 130, 140, 150, ….

The quotient of x and 3 plus 24 PLEASE HELP

Answers

Answer:

(24 divided by 3) + x

Step-by-step explanation:

i did it

If k is a real number, then the vectors(1,k),(k,3k+18)are linearly independent precisely whenk=a,b, wherea=,b=, anda

Answers

The vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.

If k is a real number, then the vectors (1,k), (k,3k+18) are linearly independent precisely when k≠a,b, where a=-18 and b=1/3. This is because for the vectors to be linearly independent, the equation c1(1,k) + c2(k,3k+18) = (0,0) should only have the trivial solution of c1 = c2 = 0. If k = a or k = b, then there will be nontrivial solutions for c1 and c2, making the vectors linearly dependent.

To find the values of a and b, we can set the equations for the x and y components equal to 0 and solve for k:

c1 + c2k = 0

c1k + c2(3k+18) = 0

From the first equation, we can solve for c1 in terms of c2 and k:

c1 = -c2k

Substituting this into the second equation:

-c2k^2 + c2(3k+18) = 0

c2(-k^2 + 3k + 18) = 0

Since c2 cannot be 0, we can divide both sides by c2 and solve the quadratic equation for k:

-k^2 + 3k + 18 = 0

(k-1/3)(k+18) = 0

So k = 1/3 or k = -18. Therefore, the vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.

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Ben has scored 15 points. He has 8 points more than Greg. Which equation can be used to determine

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The equation that can be used to determine Greg's score is 15 - 8 = x. This equation shows that if you subtract 8 points from Ben's score of 15 points, you will get Greg's score.

Step-by-step explanation:

Start with Ben's score: 15 pointsSubtract 8 points from Ben's score: 15 - 8Set this equation equal to x, which represents Greg's score: 15 - 8 = xSolve for x: 15 - 8 = 7Therefore, Greg's score is 7 points.

In conclusion, the equation 15 - 8 = x can be used to determine Greg's score.

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The cargo bed of a commercial truck is shaped like a rectangular prism. The dimensions are shown. Billy has 80 cubic meters of mulch to take to his house. How many trips will he have to make until all the mulch is at his house?

Answers

Answer:

We need to find out how many trips Billy needs to make to transport 80 cubic meters of mulch. Since we know the dimensions of the cargo bed, we can find its volume and then divide the total volume of mulch by the volume of the cargo bed to find the number of trips.

The volume of the cargo bed is:

V = l × w × h

where l is the length, w is the width, and h is the height. Using the dimensions given in the diagram, we get:

V = 4 m × 2.5 m × 1.5 m = 15 cubic meters

Now we can divide the total volume of mulch by the volume of the cargo bed to find the number of trips:

Number of trips = total volume of mulch / volume of cargo bed

Number of trips = 80 cubic meters / 15 cubic meters ≈ 5.33

Since Billy cannot make a fractional number of trips, he will need to make 6 trips to transport all the mulch to his house.

LetP(x)=10x5−35x4+22x3+13x2+4x+4. (a) Use the Rational Roots Theorem to find all possible rational roots ofP(x). LetP(x)=10x5−35x4+22x3+13x2+4x+4. (b) Find all roots ofP(x)

Answers

The Rational Roots Theorem states that the possible rational roots of a polynomial equation are the factors of the constant term divided by the factors of the leading coefficient. Therefore, the possible rational roots of P(x) are ±1, ±2, ±4, and ±4.

To find the exact roots of P(x), we can use synthetic division. Synthetic division is an efficient way of dividing a polynomial by a number. Using this method, we can determine that there are three roots for P(x): 1, -2, and -3. To verify this, we can evaluate P(x) for each of the three roots and confirm that the result is zero.

We can also use the quadratic formula to find the remaining two roots. Since P(x) is a 5th degree polynomial, the two remaining roots are complex and can be found using the quadratic formula. The complex roots of P(x) are -0.5 ± 0.5i.

In conclusion, the roots of P(x) are 1, -2, -3, -0.5 ± 0.5i. All of these results can be verified by evaluating P(x) and confirming that the result is zero.

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∟A= 7x + 24° , ∟B = 3x + 92° Solve for x and then find the measure of ∟A:
∟A=_____°

Answers

Measure of ∟A is 119°

To solve for x, we must use the fact that the angles have the same measure, so ∟A = ∟B.



Substitute 7x + 24° for ∟A and 3x + 92° for ∟B and set them equal to each other:

7x + 24° = 3x + 92°

Subtract 3x from both sides:

7x - 3x = 92° - 24°

4x = 68°



Divide both sides by 4 to solve for x:

x = 17°



Now that we have x, we can substitute 17° for x into the original equation for ∟A to find its measure:

∟A = 7x + 24°

∟A = 7(17°) + 24°

∟A = 119°



Therefore, the measure of ∟A is 119°.

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A blue print of a house has a scale of 1. 5 in 5 feet would a ping pong table that is 9 feet by 5 feet fit in a space that has a drawing dimensions of 3 inches and 4. 8 inches if so how much space in feet square will remain after the table is put in the room

Answers

There will be about 111.25 square feet of space remaining in the room after the ping pong table is put in.

First, we need to convert the scale of the blueprint to a real-world scale. Since the scale is 1.5 in 5 feet, we can write this as:

1.5 inches : 5 feet

To convert this to a ratio that we can use, we can divide both sides by 1.5 inches:

1 inch : 3.33 feet

Now we can use this ratio to convert the dimensions of the room from the blueprint to real-world dimensions:

3 inches x 3.33 feet/inch = 9.99 feet

4.8 inches x 3.33 feet/inch = 15.96 feet

So the room is approximately 10 feet by 16 feet.

Next, we need to see if the ping pong table will fit in the room. The table is 9 feet by 5 feet, which means it needs at least a space of 9 feet x 5 feet = 45 square feet. To convert this to the scale of the blueprint, we can use the inverse of the ratio we calculated earlier:

1 foot : 1/3.33 inches

So the table needs at least a space of 9 feet x (1/3.33 inches/foot) = 27 inches by 5 feet x (1/3.33 inches/foot) = 15 inches on the blueprint.

The space in the room is 3 inches x 4.8 inches on the blueprint, which is equivalent to 3 inches x (1/1.5 inches/foot) = 2 feet and 4.8 inches x (1/1.5 inches/foot) = 1 foot 7.8 inches in real-world dimensions.

Since the table will fit on the blueprint, we can now calculate the remaining space in the room. The total area of the room is approximately 10 feet x 16 feet = 160 square feet.

The area taken up by the ping pong table is approximately 9 feet x 5 feet = 45 square feet, or 27 inches x 15 inches on the blueprint. To convert this to square feet, we can use the ratio we calculated earlier:

27 inches x (1/12 feet/inch) x 15 inches x (1/12 feet/inch) = 3.75 square feet

So the remaining space in the room is approximately 160 square feet - 45 square feet = 115 square feet - 3.75 square feet

= 111.25 square feet.

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What is the intersection of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14-37

Answers

The intersection set, A∩ B, of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14 } is equals to the { 6, 14}.

For any two sets A and B, the intersection, A∩ B (read as A intersection B) lists all the elements that are present in both sets, and are the common elements of A and B. The intersection of sets is denoted by the symbol '∩'. It is subset of both of sets, A and B. For example, if Set A = {1,2,3,4,5} and Set B

= {3,4,6,8}, A ∩ B = {3,4}.

Here, we have two sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14 }

The common elements in sets A and B

= { 6,14 }

Therefore, the intersection of A and B,

A ∩ B = { 6, 14}.

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Complete question:

What is the intersection of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14}?

need help by tonight please help me

Answers


it is a negative correlation but you should know how to put the points on the diagram. just find out the numbers on the graph and indicate it with a point, then join it together, it would be scattered but it will give the pattern of a negative correlation.

100 POINTS!! I posted 2 math questions worth 50 points! Please help! :)

Answers

Where are the questions?

By what will the product of 2 numbers decrease if one of the numbers is decreased by 25% and the other number is decreased by 50%

Answers

Answer:

62.5%

Step-by-step explanation:

the product of the two numbers=xy

the product of the altered numbers=(0.75x)(0.5y) OR 0.375xy

finally you subtract this from one to get your decrease: 1-0.375=0.625

then simply convert that to a percent, leaving you with 62.5%. hope this helps!

The box plots display the math scores for two 7th grade math classes. which statement is best supported by the information in the box plots? A, the range for Mrs. Morales‘s class is greater than the range for Mr. Florez‘s class  B, the data for Mr. Flores’s class are more symmetrical than the data for Mrs. Morales‘s class C, the median score for Mrs. Morales’s class is equal to the median for Mr. Flores’s class  D, the interquartile range for Mr. Flores‘s class is greater than the interquartile range for Mrs. Morales‘s class 

Answers

Therefore, the best statement supported by the information in the box plots is statement B, "the data for Mr. Flores’s class are more symmetrical than the data for Mrs. Morales's class."

What is box plot?

A box plot, also known as a box-and-whisker plot, is a graphical representation of the distribution of numerical data. It displays the five-number summary of a dataset, which includes the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.

Here,

From the box plots, we can make the following observations:

A) The range for Mrs. Morales's class appears to be 100-50 = 50.

The range for Mr. Florez's class appears to be 95-55 = 40.

Therefore, statement A is not supported by the information in the box plots.

B) The box plot for Mr. Flores's class is more symmetrical than the box plot for Mrs. Morales's class, which is skewed to the left.

Therefore, statement B is supported by the information in the box plots.

C) The median score for Mrs. Morales's class appears to be between 70 and 75.

The median score for Mr. Florez's class appears to be between 75 and 80.

Therefore, statement C is not supported by the information in the box plots.

D) The interquartile range for Mrs. Morales's class appears to be between 60 and 80, which is a range of 20.

The interquartile range for Mr. Florez's class appears to be between 65 and 85, which is also a range of 20.

Therefore, statement D is supported by the information in the box plots.

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f(x)=x^4−19x^3+135x^2+2 - Fias the toe crical nambers a,b of f′ (that is. the values at which f′′′ is zero or undetined) and lat thoir euact values in the fiet colume of the tibie below (n ancendeng order, a

Answers

Local Minima is 5 and 80

The critical numbers, a and b, of f'(x)=x^4−19x^3+135x^2+2 can be found by setting the derivative f'(x) = 0 and solving for x.

The derivative is: f'(x) = 4x^3 − 57x^2 + 270x

By setting the derivative equal to 0, we get:
4x^3 − 57x^2 + 270x = 0

Solving for x, we get:
x = 0, x = 5, x = 9

The critical numbers of f'(x) are 0, 5 and 9. The second derivative f''(x) is undefined at x = 0, so this is a local maximum point, while x = 5 and 9 are local minimum points.

Table:
Critical number | Second derivative (f''(x)) |  Value
0 | Undefined | Local Maximum
5 | -80 | Local Minimum
9 | 80 | Local Minimum

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The owner of a beverage company wants to determine whether two of his machines are filling bottles with the correct amount of liquid. He randomly selects 20 bottles filled by each of the two machines and measures the number of ounces that the bottles contain. The histograms below show the data. If the machines are designed to dispense between 5 and 6 ounces into a bottle, which machine appears to be doing a better job? Explain how you determined your answer.

Answers

Based on the histograms, it appears that Machine B is doing a better job of dispensing the correct amount of liquid.

What is histogram?

The most common graph for displaying frequency distributions is a histogram.

To begin, Machine B's histogram is more symmetrically distributed around the 5.5-ounce mark, which is the target fill level.

Machine A's histogram, on the other hand, is skewed to the right, indicating that it is more likely to dispense more than 5.5 ounces.

Second, Machine B's histogram has a narrower spread, with most measurements falling between 5.4 and 5.6 ounces.

This indicates that the machine fills the bottles consistently within a narrow range of the target fill level.

Thus, the histogram for Machine A, on the other hand, has a wider range, with some measurements falling below 5.4 ounces and others exceeding 5.6 ounces, indicating a less consistent performance.

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Your question seems incomplete, the probable complete question is:

The average length of an official chess table in the International Chess Federation is 110 centimeters (cm)
with a tolerance of 16.5 cm. If c is the length of the chess table and V is the variation from 110 cm, the
function V(c) = |c-110| can be used to find the amount of variation.
Complete the statements by typing decimal values in the blank spaces.

Answers

Answer:

1. What is the maximum length of a chess table that is still within the tolerance limit?

To find the maximum length of a chess table that is still within the tolerance limit, we add the tolerance to the average length:

110 cm + 16.5 cm = 126.5 cm

Therefore, the maximum length of a chess table that is still within the tolerance limit is 126.5 cm.

2. What is the minimum length of a chess table that is still within the tolerance limit?

To find the minimum length of a chess table that is still within the tolerance limit, we subtract the tolerance from the average length:

110 cm - 16.5 cm = 93.5 cm

Therefore, the minimum length of a chess table that is still within the tolerance limit is 93.5 cm.

Step-by-step explanation:

2. Kim, Doug, and Conner all run on the cross country team. In the last race Doug finished first, Kim finished 3 minutes after Doug, and Conner finished with a time that was twice Doug’s time.

a. What is the sum of their times?
b. What property or properties did you use?
c. Evaluate the expression if Doug ran the race in 27 minutes.

Answers

a) The sum of their times is of 4x + 3.

b) The property used is the combination of like terms, which we use to add the terms with the variable x.

c) If Doug ran the race in 27 minutes, the total time for the team is of 111 minutes.

How to obtain the expression?

Doug finished first, and the times of the other two athletes are as function of Doug, hence the variable x represents the time needed for Doug to finish the race, that is:

D = x.

Kim finished 3 minutes after Doug, hence:

K = D + 3

K = x + 3.

Conner finished with a time that was twice Doug’s time, hence:

C = 2x.

Then the total time is given as follows:

T = D + K + C

T = x + x + 3 + 2x

T = 4x + 3.

If Doug ran the race in 27 minutes, the total time for the team is obtained as follows:

T = 4 x 27 + 3

T = 111 minutes.

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if tan t = 11/7 and 0≤ t≤????/2 find sin t, cost, csc t, sect, and cott. To enter the square root of a number, type "sqrt(a)". For example, type "sqrt(2)" to enter √2. sin t = cos t = csc t = sec t = cot t =

Answers

The hypotenuse is sqrt(11^2 + 7^2) = sqrt(170). Then, sin t = 11/sqrt(170), cos t = 7/sqrt(170), csc t = sqrt(170)/11, sec t = sqrt(170)/7, and cot t = 7/11.

Since we know that tan t = 11/7, we can use the Pythagorean identity (sin^2 t + cos^2 t = 1) to find the other trigonometric functions. First, we will find sin t and cos t:

tan t = 11/7 = opposite/adjacent = sin t/cos t

sin t = 11*cos t

cos t = 7*sin t

Substituting the second equation into the first equation:

sin t = 11*(7*sin t)

sin^2 t = 121*sin^2 t

121*sin^2 t - sin^2 t = 0

120*sin^2 t = 0

sin^2 t = 0/120

sin^2 t = 0

sin t = 0

Since sin t = 0, cos t = 1. Now we can find the other trigonometric functions:

csc t = 1/sin t = 1/0 = undefined

sec t = 1/cos t = 1/1 = 1

cot t = 1/tan t = 1/(11/7) = 7/11

So, the values of the trigonometric functions are:

sin t = 0

cos t = 1

csc t = undefined

sec t = 1

cot t = 7/11

Note: Another way to find the values of the trigonometric functions is to use the Pythagorean Theorem to find the hypotenuse of the right triangle with sides 11 and 7.

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Use simple interest to find the ending balance.
$36,000 at 6.3% for 4 years

Answers

Answer:

$45072

Step-by-step explanation:

I = Prt

I = 36000(6.3/100)(4)

I = 9072

ending balance = 36000 + 9072

= 45072

Martina can run 3 miles without stopping. Last year she could run 3,640 yards witho stopping. How many more feet can Martina

Answers

Martina can run 4,920 more feet this year compared to last year.

Martina can run 3 miles without stopping. Last year she could run 3,640 yards without stopping. We need to find out how many more feet Martina can run this year compared to last year.

First, we need to convert both measurements to the same unit so that we can compare them. We will convert both measurements to feet.

1 mile = 5,280 feet
1 yard = 3 feet

So, 3 miles = 3 x 5,280 feet = 15,840 feet

And, 3,640 yards = 3,640 x 3 feet = 10,920 feet

Now, we can subtract the number of feet Martina could run last year from the number of feet she can run this year to find out how many more feet she can run this year.

15,840 feet - 10,920 feet = 4,920 feet

Therefore, Martina can run 4,920 more feet this year compared to last year.

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Ms.lang borrows $2,300 for 30 months at 13% interest per year. How much interest will ms.lang pay? What is the total amount she will repay?

Answers

Answer:

The formula to calculate simple interest is:

I = Prt

Where I is the interest, P is the principal amount borrowed, r is the interest rate per period, and t is the time period.

Using this formula, we can calculate the interest Ms. Lang will pay as follows:

I = Prt

I = 2300 * 0.13 * (30/12)

I = $975

Therefore, Ms. Lang will pay $975 in interest over the 30-month period.

To calculate the total amount she will repay, we need to add the interest to the principal amount borrowed:

Total amount = Principal + Interest

Total amount = $2300 + $975

Total amount = $3275

Therefore, Ms. Lang will repay a total of $3275, which includes the $2300 principal and $975 interest.

now, we're assuming this is on a simple interest rate, so hmm say a year has 12 months, so 30 months will just be 30/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$2300\\ r=rate\to 13\%\to \frac{13}{100}\dotfill &0.13\\ t=years\to \frac{30}{12}\dotfill &\frac{5}{2} \end{cases} \\\\\\ I = (2300)(0.13)(\frac{5}{2}) \implies I = 747.5~\hfill \underset{ \textit{amount to be repaid} }{\stackrel{ 2300~~ + ~~747.5 }{\text{\LARGE 3047.5}}}[/tex]

Helpppp pleasee ill give everything please see the photo (find the missing angle. Round to the nearest degree

Answers

Answer:

64.15°

Step-by-step explanation:

here

theta = 64.15°

( solution in picture)

Darcy gave her beauty technician a $4.80 tip. The tip was 5% of the cost of the procedure. Write an equation to find b, the cost of the procedure.

Answers

Therefore , the solution of the given problem of equation comes out to be required equation is 0.05b = 4.80 .

How do equations operate?

Mathematical formulas frequently use the same variable letter to try to impose unity between two assertions. Many academic numbers are shown to be equal using mathematical equations, also known as assertions. Using y + 6 as an illustration, the normalise does not divide 12 into two parts, but instead b + 6. It is possible to determine the connection integer between each sign part and the number of lines. The significance of a symbol usually contradicts itself.

Here,

The following equation can be set up to represent the circumstance if x is the procedure's cost:

=>  5% of x = $4.80

The percentage must first be divided by 100 to become a decimal before we can answer for x:

=>  0.05x = $4.80

Then, by dividing both lines by 0.05, we can separate out x:

=>  x = $96

Consequently, the process will cost you $96. It is possible to confirm that the gratuity is 5% of $96:

=>  5% of $96 = 0.05 × $96 = $4.80

So, the solution is:

=> 0.05b = 4.80

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7. Use a half-angle identity to find each exact value. a. sin 195 b. cos 165
8. Find the following: a. cos θ/2 given sin θ = - 4/5 with 180º < θ < 270º. b. cot θ/2, given tan θ = - √5 / 2 with 90° < θ < 180°.

Answers

The exact values are sin 195 = 0.9763, cos 165 = 0.6088, cos θ/2 = 0.8944, and cot θ/2 = -0.2764.

To find the exact value of sin 195 and cos 165 using a half-angle identity, we need to use the following formulas:

sin(x/2) = √[(1-cosx)/2] and cos(x/2) = √[(1+cosx)/2]

For sin 195, we can use the half-angle identity for sine:

sin(195/2) = sin(97.5) = √[(1-cos195)/2] = √[(1+0.9063)/2] = √(0.9532) = 0.9763

For cos 165, we can use the half-angle identity for cosine:

cos(165/2) = cos(82.5) = √[(1+cos165)/2] = √[(1-0.2588)/2] = √(0.3706) = 0.6088

For question 8, we can use the given values and the half-angle identities to find the exact values of cos θ/2 and cot θ/2.

For cos θ/2 given sin θ = -4/5 with 180º < θ < 270º, we can use the half-angle identity for cosine:

cos(θ/2) = √[(1+cosθ)/2] = √[(1+√(1-sin^2θ))/2] = √[(1+√(1-(-4/5)^2))/2] = √[(1+√(1-(16/25)))/2] = √[(1+√(9/25))/2] = √[(1+(3/5))/2] = √(0.8) = 0.8944

For cot θ/2 given tan θ = -√5/2 with 90° < θ < 180°, we can use the half-angle identity for cotangent:

cot(θ/2) = (1+cosθ)/sinθ = (1+√(1-sin^2θ))/sinθ = (1+√(1-(1/tan^2θ)))/(1/tanθ) = (1+√(1-(1/(-√5/2)^2)))/(-√5/2) = (1+√(1-(4/5)))/(-√5/2) = (1+√(1/5))/(-√5/2) = (1+(1/√5))/(-√5/2) = (1-(1/√5))/(-√5/2) = -0.2764

Therefore, the exact values are sin 195 = 0.9763, cos 165 = 0.6088, cos θ/2 = 0.8944, and cot θ/2 = -0.2764.

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Hellllllllllllllllp meeeeeeeeeeeee

Answers

Answer: Option B is the correct answer

Step-by-step explanation:

Area of lateral surface = 3 x Area of rectangle

The rectangle is of  5 inches wide and 14 inches long.

Area of rectangle =  5 x 14 = 70 square inches

Area of lateral surface = 3 x Area of rectangle

Area of lateral surface = 3 x 70 = 210 square inches

Option B is the correct answer.

60 students went on a school trip to the zoo. 32 of the students bought a packed lunch

Answers

From the given information provided, the number of students who brought a packed lunch and did not visit the gift shop is 32.

The number of students who brought a packed lunch and did not visit the gift shop can be calculated by subtracting the number of students who visited the gift shop from the number of students who bought a packed lunch:

32 - 0 = 32

A frequency tree is a visual representation of data that shows how the total number of individuals or items is distributed among different categories or groups. It is commonly used in statistics and probability to organize and analyze data in a hierarchical structure.

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Keith who runs a daycare center bought 14 gallons of paint to do up the classroom how many classrooms can he get painted in all if each room requires 7/4 gallons of paint

Answers

Answer:

Keith bought 14 gallons of paint, and each classroom requires 7/4 gallons of paint.

To find how many classrooms can be painted, we can divide the total amount of paint by the amount of paint needed per classroom:

14 ÷ (7/4) = 8

Therefore, Keith can paint 8 classrooms in total.

I REALLY NEED HELP ON THESE QUESTIONS!

Answers

The surface areas of these cylinders are 75.39 cm, 835.76 cm,  1324.11 cm, and 3543.71 cm.

How to calculate the surface area of a cylinder?

The surface area of a cylinder can be calculated by using the formula  2π r h + 2π r², which means we need the radius and the height to calculate the area. Let's now use this formula to know the area of each cylinder:

Cylinder 1:

2π 2 4+ 2π 2² = 75.39 cm

Cylinder 2:

2π 7 12+ 2π 7² = 835.76 cm

Cylinder 3:

2π 8.2  17.5+ 2π 8.2² = 1324.11 cm

Cylinder 4:

2π 12 35 + 2π 12r² = 3543.71 cm

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Need help with dilation & reflection! asap would be great :)

Answers

The value of image of coordinates of triangle ABC are,

A' = (4, - 4)

B' = (5 - 1)

C' = (1, - 3)

And, After dilate DEFG by a scale factor of 3 about (- 5, 5) is,

D' = (- 15, 6)

E' = (- 12, 12)

F'  = (- 6, 12)

G' = (- 9, 6)

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Reflect the triangle ABC across the line y = x

And, Dilate DEFG by a scale factor of 3 about (- 5, 5).

Now,

We know that;

The rule of reflection across the line y = x is,

(x, y) → (y, x)

Thus, The value of coordinates of triangle ABC are,

A = (- 4, 4)

B = (- 1, 5)

C = (- 3, 1)

Hence, The image of coordinates of triangle ABC are,

A' = (4, - 4)

B' = (5 - 1)

C' = (1, - 3)

And, The coordinates of DEFG are,

D = (- 5, 2)

E = (- 4, 4)

F = (- 2, 4)

G = (- 3, 2)

Hence, After dilate DEFG by a scale factor of 3 about (- 5, 5) is,

D' = (- 5x3, 2x3) = (- 15, 6)

E' = (- 4x3, 4x3) = (- 12, 12)

F' = (- 2x3, 4x3) = (- 6, 12)

G' = (- 3x3, 2x3) = (- 9, 6)

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