A college surveys 300 graduates and finds 98 graduated with honors and 207 had one or both parents graduate from college. Of the 98 students with honors, 79 had one or both parents graduate from college. Find the probability that a randomly chosen graduate from these 300 graduated with honors given that neither parent graduated from college.

Answer:

Step-by-step explanation:

The absolute change in game length is ...

  (180 min) -(150 min) = 30 min . . . . change in game length

__

The relative change is expressed as a fraction of the original game length:

  (30 min)/(150 min) × 100% = 20% . . . . relative change in game length

Answer:

a) v(t)=-32t+300

b) s(t)=-16t^{2}+300t

\(s_{max} =\frac{5625}{4}ft=1406.25 ft\)

Step-by-step explanation:

A good way to start solving this problem out is to draw a diagram of the situation (see attached picture).

a)

For part a, we need to find an equation for the velocity of the cannon ball. We have an equation of its acceleration:

\(a=\frac{dv}{dt}=\frac{d^{2}s}{dt^{2}}=-g\)

we know that:

\(g=32 ft/s^{2}\)

so we got the following differential equation:

\(\frac{dv}{dt} =-32\)

we can find the function for velocity by integrating, so we get:

\(v =\int\limits {-32} \, dt\)

which yields:

v(t)=-32t+C

we need to find the value of C. The problem tells us that v(0)=300 ft/s so we can use this to find c:

300=-32(0)+C

so

C=300

therefore the equation for velocity is:

v(t)=-32t+300

b)

For part b) we need to find an equation for the height of the cannonball. We know that:

\(v=\frac{ds}{dt}\)

so:

\(\frac{ds}{dt}=-32t+300\)

so we can integrate this equation to find the function for height of the ball, so we get:

\(s=\int\limits {-32t+300} \, dt\)

which yields:

\(s(t)=-\frac{32t^{2}}{2}+300t+C\)

which can be simplified to:

\(s(t) =-16t^{2}+300t+C\)

We know the height is measured from the ground level, this means that s(0)=0 so we can find C with this information:

\(0=-16(0)^{2}+300(0)+C\)

so C=0, therefore our equation is:

\(s(t)=-16t^{2}+300t\)

in order to find the maximum height attained by the cannonball, we can set the velocity function equal to zero and solve for t, so we get:

0=-32t+300

-32t=-300

\(t=\frac{300}{32}\)

\(t=\frac{75}{8} s\)

and substitute it into our position function so we get:

\(s(\frac{75}{8})=-16(\frac{75}{8})^{2}+300(\frac{75}{8})\)

which yields:

\(s_{max} =\frac{5625}{4}ft=1406.25 ft\)

Answer:3x+y=-8

Step-by-step explanation: If you were to solve each equation by graph the slope would be negative 3

Since 1 cubic feet = 62 pounds, the weight of the water that Jerry put in the aquarium is 558 pounds

We have to find the volume of water in the aquarium.

Recall the shape of the aquarium is a rectangular prism. Therefore,

volume = lwh

where

Therefore,

l = 3 ft

w = 2 ft

h = 1.5 ft

volume =  3 × 2 × 1.5

volume of water = 9 ft³

Therefore,

1 ft³= 62 pounds

9 ft³ = ?

cross multiply

weight of water = 9 × 62

weight of water = 558 pounds

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The value of the standard deviation does not change and remains the same.

Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.

The mean μ = 82.4

The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]

we have to find the variance,

We now add a constant k to each data value and calculate the new mean μ'.

μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k

We now calculate the new mean standard deviation σ'.

σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]

Note that x + k - μ' = x + k - μ - k = x - μ

also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ

Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ

If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.

Hence, the standard deviation does not change.

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The correct calculation of the standard deviation of the sampling distribution of p_hat subscript s - p_hat subscript p is 0.0934.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We are given that;

Percentage of students with laptop=68%

Percentage of professors with laptop=43%

p_s = 0.68 and p_p = 0.43.

Now,

The formula for the standard deviation of the sampling distribution of the difference between two sample proportions is:

sqrt[(p_s * (1 - p_s) / n_s) + (p_p * (1 - p_p) / n_p)]

where p_s and p_p are the population proportions of students and professors who have a laptop, respectively, n_s and n_p are the sample sizes of students and professors, respectively.

We are also given that 56 students and 31 professors were selected at random and asked if they have a laptop. Therefore, n_s = 56 and n_p = 31.

Substituting these values into the formula, we get:

sqrt[(0.68 * (1 - 0.68) / 56) + (0.43 * (1 - 0.43) / 31)]

sqrt[0.00367143 + 0.00505484]

= sqrt(0.00872627)

= 0.0934 (rounded to four decimal places)

Therefore, by standard deviation the answer will be 0.0934.

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Answer:

291

Step-by-step explanation:

2*2*2=8*2=16

16+(11*5*5)=291

Answer:

291cm^3

Step-by-step explanation:

11×5×5=275cm^3

2×2×2=8cm^3

8cm^3 + 8cm^3= 16cm^3

275+16=291cm^3

Answer:

8.33cm

Step-by-step explanation:

1m=100cm

Since the wire is to be cut into twelve pieces

100/12=8.33

8.33cm

if we are asked to leave in metre divide answer by 100

Answer:

calculator gave me 6.5732

Step-by-step explanation:

Answer:

the answer is c) 80

all angles of the Triangle will have a sum of 180. 80+20=100 ... 180-100= 80

The x-intercept of the function is (-1/3, 0) and (5, 0)

Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,

So to find the x-intercept put y = 0,

Therefore,

-3x²+14x+5 = 0

-3x²+15x-x+5 = 0

-3x(x-5)-1(x-5) = 0

(-3x-1)(x-5) = 0

Therefore,

x = -1/3 and x = 5

Hence the x-intercept of the function is (-1/3, 0) and (5, 0)

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Answer:

Equiangular triangle

Step-by-step explanation:

"equiangular triangle" means a triangle that has equal sides

knowing that the sum of the angles of a triangle is 180° each angle must be 60° because \(\frac{180}{3}=60\)

Answer:

is it 4 and 12 ?

Step-by-step explanation:

please let me know if it is correct! but i am 96% sure for me answer!

Answer:

There are infinite rational numbers between any two numbers

PLS MARK ME AS THE BRAINLIEST

Answer:

Large candle) $6.25

Small candle) $3.5

Step-by-step explanation:

Let x be the cost of a large candle and y be the cost of a small candle.

Because Lexi bought two large candles and five small candles for $30, the first equation is 2x+5y=30.

Because Carl bought one large candle and three small candles for $16.75, the second equation is x+3y=16.75

We have two equations:

2x+5y=30 and x+3y=16.75

   1) Multiply both sides of x+3y=16.75 by 2 to get 2x+6y=33.5

   2) Subract the two equations

       2x+6y=33.5

      - 2x+5y=30

      =        y=3.5

   3) Plug y=3.5 into one of the equations.

       2x+5(3.5)=30

       2x+17.5=30

       2x=12.5

         x=6.25

   4) Check the work by plugging both variable in the other equation

        6.25+3(3.5)=16.75

        6.25+10.5=16.75

        6.75=16.75

The problem can be translated into an equation as follows: 8x = (1/3)(x+2)

the answer that represents this situation is: 8x = (1/3)(x+2)

Simplifying the right side of the equation:

8x = (1/3)x + (2/3)

Multiplying both sides of the equation by 3 to eliminate the fraction:

24x = x + 2

Subtracting x from both sides of the equation:

23x = 2

Dividing both sides of the equation by 23:

x = 2/23

Therefore, the answer that represents this situation is:

8x = (1/3)(x+2)

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Answer:

x=2

Step-by-step explanation:

-5=-3x+1

-1         -1

-6=-3x

divide both sides by -3

x=2

The value of x when f(x) = - 5, In the function f(x) = - 3x + 1 is 2.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = - 3x + 1.

Now, when f(x) = - 5 the equation would be,

- 5 = - 3x + 1.

- 5 - 1 = - 3x.

- 6 = - 3x.

3x = 6.

x = 2.

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Answer :1,760 1,760 1,760 1,760 1,760

Answer:

The distance between Kevin's school and his house is 9,152 yards

Step-by-step explanation:

Units Conversion

Some common length units are meters, centimeters, inches, feet, miles, kilometers, and yards.

There are fixed numbers to convert one into another. For example:

1 mile = 1,760 yards

Since Kevin's school is 5.2 miles away from his house, that distance converted to yards is:

5.2 * 1,760 = 9,152

The distance between Kevin's school and his house is 9,152 yards

Answer:

I think it is d

Step-by-step explanation:

so sorry if it wrong i tried my best

Answer:

b for sure im not sure if there are any more

ugh i have this question and im not sure if there are any other answers

Step-by-step explanation:

Answer: B / (6/3)(x^4-7)

Step-by-step explanation: When Dividing an equation with variables that have exponents, the numbers divide normally and the power of the exponents will subtract *as long as it is the same variable* in this case, it will be 4-7.
Hope this helped :)

Answer:

6 miles in 66 mins

Step-by-step explanation:

4 miles = 44 mins

simplify to the lowest point

1 mile = 11 mins

? = 66 mins

? = 1 x 6

you can run 6 miles in 66 mins

Answer:

Step-by-step explanation:

4/44= 0.0909090909...*66=6

find the propotunate value by dividing each initial value and multiply it by the listed secondary value

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

The explicit formula that represents the nth term of the sequence will be aₙ = 18 - 7n.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The arithmetic sequence is given below.

11, 4, -3, .....

The first term is 11. And the common difference is given as,

d = 4 - 11

d = - 7

The explicit formula that represents the nth term of the sequence is given as,

aₙ = a₁ + (n - 1)d

aₙ = 11 + (n - 1)(-7)

aₙ = 11 - 7n + 7

aₙ = 18 - 7n

The explicit formula that represents the nth term of the sequence will be aₙ = 18 - 7n.

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Answer:

93

Step-by-step explanation:

Answer:

C = 87.92 mm

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Circumference Formula: C = πd

Step-by-step explanation:

Step 1: Define

Diameter d = 28 mm

Step 2: Solve

The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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Answer:

The range of values from one job is between $50 and $650.

Step-by-step explanation:

An electrician charges y amount to work x hours on a job. The electrician charges a $50 service fee and $30 per hour.

This means that his earnings in a job can be modeled by the following function:

\(y = 30x + 50\)

The electrician works maximum of 20 hours on any job. What is the range of values for one job?

Minimum, he works 0 hours, and earns:

\(y(0) = 30(0) + 50 = 50\)

Maximum, he works 20 hours, and earns:

\(y(20) = 30(20) + 50 = 650\)

The range of values from one job is between $50 and $650.