A local university accepted 2,300 students out of 4,500 applicants for admission. What was the acceptance rate, expressed as a percent? (Show Work Please)

Answer:

Step-by-step explanation:

According to law of gravitation, the gravitational force between two bodies of masses M and m is expressed as F = GMm/d² ... 1 where;

G is the gravitational constant

d is the distance between the masses

If the distance between two bodies is tripled and the mass of each is doubled, then the gravitational force will become:

F2 = G(2M)(2m)/(3d)²

F1 = 4GMm/9d² ... 2

Taking the ratio of the original gravitational force to the new one we have;

F1/F = 4GMm/9d²/GMm/d²

F1/F =  4GMm/9d² * d²/GMm

F1/F = 4/9

F1 = 4/9F

This shows that if the distance between two bodies is tripled and the mass of each is doubled, the force of gravitation between them will four - ninth the original force

Answer:

x = 3 ; y = 2

Step-by-step explanation

3x - y = 7

= 3x - y - 7 = 0

= 3x - 7 = y — (equation i)

Substitute (equation i) into the second equation:

3x + (3x - 7) = 11

Expand the brackets by applying the Distributive Law and bring all the like terms together:

3x + 3x - 7 = 11

= 6x - 7 = 11

= 6x = 11 + 7

= 6x = 18

= x = \(\frac{18}{6}\)

= x = 3

Substitute the calculated value of x into (equation i) to determine the value of y:

3 x - 7 = y

= 3(3) - 7 = y

= 9 - 7 = y

= y = 2

Answer:The answer is B

Step-by-step explanation:

because i did the same test and got 100 A+

The inequality that represents p, the number of people the theater can seat is p ≤ 25

From the question, we have the following parameters that can be used in our computation:

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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The weight of a basket containing 60 apples was 3 1/5 kg. An identical basket containing 40 apples weighed 2 and a half kilograms. It weighs 150 pounds.

The typical weight of an apple ranges from 150 g to 250 g. A 10 g error was discovered in the weight of each apple. The average weight of apples is calculated by dividing the total number of apples by the actual weight of the apples. Consequently, 10 apples actually weigh 62 g on average. As an apple is rather little, the measurement should be in grams.

Apples have a high fiber content. About 4 grams, or 17% of the Daily Value, of this vitamin may be found in a single medium-sized apple (100 grams) (DV). We divide the mass of the element in 1 mole of the compound by the compound's molar mass and multiply the result by 100 to determine the mass percent of the element in the compound.

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Answer:

C. 30

Step-by-step explanation:

Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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Answer:

about 50 degrees

Step-by-step explanation:

To find the angle you would first subtract 180 - 90 (Since a triangle always equals 180) and that would be 90 and then divide by 2 to equal 45. I believe they wanted to round to nearest tenth so then the answer would change to 50. (Tell me if this is wrong; its been a while since I have done this)

I hope this helps :)

Step-by-step explanation:

you have to use this

u/v=u'×v-v'×u/v²

0×(1+cosy)-(-1×-siny)/(1+cosy)²

-siny/(1+cosy)²

hopefully its correct

Answer:

=> P(X <= 62500) = P((X-mean)/sd < (62500-65000)/3000)

= P(Z < -0.8333)

= 1 - P(Z < 0.8333)

= 1 - 0.7967

= 0.2033

=> P(X > 68500) = P(Z > (68500-65000)/3000)

= P(Z > 1.1667)

= 0.1210

=> P(60500 < X < 69500) = P((60500-65000)/3000 < Z < (69500-65000)/3000 )

= P(-1.5 < Z < 1.5)

= 0.8664

=> for P(X < x) = 0.03, for Z = -1.88

X = mean + Z*Sd = 65000 - (1.88*3000) = 59360

Step-by-step explanation:

I'm not sure if that correct , I really try my best to help

The required percent of tires last at least 60,000 kilometers is about 91%.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation,

To solve this problem, we need to use the standard normal distribution. This is a special type of normal distribution where the mean is 0 and the standard deviation is 1. We can use this to standardize the tire life spans by subtracting the mean (65,000 km) and dividing by the standard deviation (5,200 km).

This gives us a standard normal distribution with a mean of 0 and a standard deviation of 1, and we can use a table or calculator to find the probability of a tire lasting at least 60,000 kilometers.

To do this, we need to find the probability that a tire lasts less than 60,000 kilometers and subtract this from 1. This probability is:

P(tire life < 60,000 km) = P(z < (60,000 - 65,000) / 5,200)

Where z is the standardized tire life span, and the probability is calculated using the standard normal distribution.

Calculating this, we find that P(tire life < 60,000 km) = P(z < -1.346) = 0.0913

Therefore, the probability that a tire lasts at least 60,000 kilometers is 1 - 0.0913 = 0.9087 or about 91%.

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The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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Answer:

It is A

Step-by-step explanation:

The answer is A. The missing term is A-2. The sample size would be 6.

a. To answer the question, we need to know what sample space is.

A sample space is the total number of possible outcomes of an event.

Now, since there are Doors 1, 2 and 3 and Keys A, B and C. The sample space is

Key A: A-1, A-2, A-3

Key B: B-1, B-2, B-3

Key C: C-1, C-2, C-3

So, the missing item is A-2.

b.

The sample size would be 6.

To answer the question, we need to know what sample size is.

The sample size is the size of the sample space.

If there were two doors instead of 3, the sample size would be since we have 2 doors and 3 keys. The sample size is 2 × 3 = 6.

So, the sample size would be 6.

So, the answer is A. The missing term is A-2. The sample size would be 6.

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Answer:

im pretty sure its A

Step-by-step explanation:

Answer:

the answer would be A. 3,150 / 75 x h

Step-by-step explanation:

Answer:

Smaller number is 16 and larger number is 25

Step-by-step explanation:

\(x+y=41\\x=y-9\\\\(y-9)+y=41\\2y-9=41\\2y=50\\y=25\\\\x=25-9=16\)

The smaller number is 16 and the larger number is 25

The value of the product of the number as given in the task content is; Choice B; 1.

It follows from the task content that the numbers whose product are to be determined are; ¾ and 1⅓.

To effectively multiply, we must convert the mixed number to a fraction as follows;

1⅓ = 4/3.

Hence, the product is; 4/3 × 3/4 = 12/12 = 1.

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Answer:

It costs 19 cents or 0.19 dollars per fluid ounce.

Step-by-step explanation:

4.75 divided by 25 is 0.19. 0.19 is 19 cents.

Answer:

19

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

A: 2x3=6 6+4=10 so correct

B: 9-9=0 so correct

Answer:

2x+4=10

Step-by-step explanation:

2x=10-4=

2x=6

x=6÷2=

3

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Step-by-step explanation:

similar by AA

that is the answer

The surface area of the solid is 281 ft².

Given that, a solid figure made of a rectangular prism and a square pyramid,

We need to find its surface area,

To find the same, we will find the lateral surface area of square pyramid, and total surface area of rectangular prism,

So,

Surface area = 2×side×slant height + 2(length·width+width·height+height·length)-base area of the square pyramid,

= 2×5×5 + 2(4·12+12·5+4·5)-5²

= 50+256-25

= 281 ft²

Hence the surface area of the solid is 281 ft².

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Answer:

16 feet per second

Step-by-step explanation:

Divide 480 feet by 30 seconds.

Answer:

Below

Step-by-step explanation:

It is an isosceles right triangle ( the two legs are equal length).

Use Pythagorean Theorem

(7 sqrt2)^2  = L^2 + L^2

98 = 2 L^2

49 = L^2

L = 7

a. Constant speed, C =  0. 19 miles/minutes

b. The fraction representing her constant speed is  1/x miles/minutes

c. The time it takes her to drive exactly 1 mile is 5. 38 minutes

The formula for calculating constant speed is expressed as;

Constant speed = total distance covered/ total time taken

From the information given, we have that;

Now, substitute the values into the formula

Constant speed = 1. 3 / 7

Divide the values

Constant speed = 0. 19 miles/minutes

When distance 1 mile, time taken = x minutes

Constant speed = 1/x miles/minutes

If 1. 3 miles = 7 minutes

Then, 1 mile = x

cross multiply

x = 7/1. 3

x = 5. 38 minutes

Hence, the constant speed is 0. 19 miles/minutes

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The matrix operation needed to transform the original matrix (pre-image) is represented by option C. ( \(T' = \left[\begin{array}{cc}-1&0\\0&-1\end{array}\right]\cdot \left[\begin{array}{cccc}-5&-8&-5&-3\\-9&-7&-3&-6\end{array}\right]\). )

The operation used to obtain the image in dash lines is a rotation around the origin, which is defined by following vectorial expression:

\(T' = R\cdot T\) (1)

Where:

Where the original matrix is defined by the following matrix:

\(T = \left[\begin{array}{cccc}x_{1}&x_{2}&...&x_{n}\\y_{1}&y_{2}&...&y_{n}\end{array}\right]\) (2)

And the rotation matrix is:

\(R = \left[\begin{array}{cc}\cos \theta&-\sin \theta\\\sin \theta&\cos \theta\end{array}\right]\) (3)

Where \(\theta\) is the rotation angle, in sexagesimal degrees.

If we know that \(\theta = 180^{\circ}\), \((x_{1}, y_{1}) = (-5, -9)\), \((x_{2},y_{2}) = (-8,-7)\), \((x_{3},y_{3}) = (-5, -3)\) and \((x_{4}, y_{4}) = (-3, -6)\), then the resulting matrix is represented by this entity:

\(T' = \left[\begin{array}{cc}-1&0\\0&-1\end{array}\right]\cdot \left[\begin{array}{cccc}-5&-8&-5&-3\\-9&-7&-3&-6\end{array}\right]\)

The matrix operation \(T' = \left[\begin{array}{cc}-1&0\\0&-1\end{array}\right]\cdot \left[\begin{array}{cccc}-5&-8&-5&-3\\-9&-7&-3&-6\end{array}\right]\) is represented in the graph.

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Answer:

A

Step-by-step explanation:

y=f(x)

when x=3

f(3)=y=0

so A

Answer:

2/15

Step-by-step explanation:

A percent is a number given out of 100

13 1/3% basically is 13 1/3 | 100

You divide and you get 40/3 x 1/100

Simplify by 20 = 40/300 simplify again and you get 2/15.

Answer:

The answer would be

2. y= x + 6

Answer: The answer would be

2. y= x + 6

Step-by-step explanation: