An exam was given to a group of freshman and sophomore students. The results are below: Freshman: 106 got A’s, 130 got B’s, and 149 got C’s. Sophomore: 192 got A’s, 118 got B’s, and 168 got C’s. If one student is chosen at random from those who took the exam, find the probability that: a) the student was a sophomore. round to 4 decimal places as needed.

Answer:

Harold typed 76, Rebecca typed 62  

Step-by-step explanation:

It's Easy. For the first one, convert 1/5 and 2/3 to the like denominator of 15.  

Therefore, you have 3/15 and 10/15. Add these to get 13/15. Now, find 13/15 of 60. To do this you will have to multiply 13 and 15 by 4 to get 52/60. Since the question asks you for how many are left, you subtract 52 from 60 to get 8.  

And For the second one, first subtract 14 from 138. You have 124. Divide 124 by 2 to get 62. Then add 14 to Harold's total pages to get 76. 62 +76 = 138.

ANSWER

[tex]y + 1=2(x-6)[/tex]

EXPLANATION

The point-slope form of a line is given by;

[tex]y-y_1=m(x-x_1)[/tex]

where

[tex]m = 2[/tex]

is the slope of the line and (6,-1) is point.

We substitute the point and the slope into the formula to obtain:

[tex]y + 1=2(x-6)[/tex]

Hence the b point slope form of the line with the given properties is

Answer:

The point-slope equation for a line that goes through the point (4, 1/3) with a slope of 3/4 is:

Choice B: [tex]\displaystyle y - \frac{1}{3} = \frac{3}{4}(x - 4)[/tex].

Step-by-step explanation:

This question gives

Consider the point-slope form of the equation of a line in a cartesian plane:

[tex]y - y_0 = m (x - x_0)[/tex],

where

For this line:

The point-slope equation of this line will be:

[tex]\displaystyle y - \frac{1}{3} = \frac{3}{4}(x - 4)[/tex].

Answer:

B.

Step-by-step explanation:

Got Correct On MyPath.

The air conditioning system can circulate approximately 14.44 cubic yards of air per minute.

To convert cubic feet to cubic yards, we need to know that there are 27 cubic feet in one cubic yard. Using this conversion factor, we can find the number of cubic yards of air that the air conditioning system can circulate per minute.

1. Start with the given value of 390 cubic feet per minute.

2. Divide this value by the conversion factor of 27 cubic feet per cubic yard:

390 cubic feet ÷ 27 cubic feet per cubic yard = 14.44 cubic yards

3. Rounding to the nearest hundredth, the air conditioning system can circulate approximately 14.44 cubic yards of air per minute.

In summary, the air conditioning system can circulate approximately 14.44 cubic yards of air per minute.

Answer:

C. [tex]x=0,\ y=1,\ z=0[/tex]

Step-by-step explanation:

Consider the system of three equations:

[tex]\left\{\begin{array}{l}4x+3y+6z=3\\5x+5y+6z=5\\6x+3y+6z=3\end{array}\right.[/tex]

Multiply the first equation by 5, the second equation by 4 and subtract them:

[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\6x+3y+6z=3\end{array}\right.[/tex]

Multiply the first equation by 3, the second equation by 2 and subtract them:

[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\3y+6z=3\end{array}\right.[/tex]

Multiply the second equation by 3, the third equation by 5 and add the second and the third equations:

[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\48z=0\end{array}\right.[/tex]

Fro mthe third equation

[tex]z=0[/tex]

Substitute it into the second equation:

[tex]-5y+6\cdot 0=-5\\ \\-5y=-5\\ \\y=1[/tex]

Substitute y=1 and z=0 into the first equation:

[tex]4x+3\cdot 1+6\cdot 0=3\\ \\4x+3=3\\ \\4x=0\\ \\x=0[/tex]

The solution is

[tex]x=0,\ y=1,\ z=0[/tex]

Answer:

ageed its C

Step-by-step explanation:

238(56)+238(34)+162(90)

=238(56+34) + 162(90)

=238(90) + 162(90)

=90(238+162)

=90(400)

=36000

For this case we must resolve the following expression:

[tex]238 (56) +238 (34) +162 (90) =[/tex]

We multiply term by term:

[tex]13328 + 8092 + 14580 =[/tex]

We add the terms:

[tex]13328 + 8092 + 14580 = 36000[/tex]

Finally, the answer is 36,000.

Answer:

[tex]238 (56) +238 (34) +162 (90) = 36,000.[/tex]

Answer:

5.69034 × 1011

Step-by-step explanation:

Decimal  

1234000000

Scientific Notation  

1.234 x 10^9

×10^  

9

1st Number  

1.234

×10^  

9

Operation  

2nd Number  

5.678

×10^  

11

Answer:

x = [tex]\frac{1}{a-b}[/tex]

Step-by-step explanation:

Given

ax = bx + 1

Collect the terms in x on the left side by subtracting bx from both sides

ax - bx = 1 ← factor out x from each term on the left side

x(a - b) = 1 ← divide both sides by (a - b)

x = [tex]\frac{1}{a-b}[/tex]

Answer: Cross section

Step-by-step explanation: A cross section sounds just like what it is. It’s a plane that intersects a solid figure. A cross section can happen on any solid figure.

Answer:

False

Step-by-step explanation:

First, there is no x in your equation. I think you meant y = mx + b.

Second, m is the slope, and b is the y-intercept.

[tex]\dfrac{_nP_3}{_nC_2}=6\\\\\dfrac{\dfrac{n!}{(n-3)!}}{\dfrac{n!}{2!(n-2)!}}=6\\\\\dfrac{n!}{(n-3)!}\cdot \dfrac{2(n-2)!}{n!}=6\\\\2(n-2)=6\\\\2n-4=6\\\\2n=10\\\\n=5[/tex]

The value of n is 5

The formula to calculate permulation and combination are:

[tex]_nP_r = \frac{n!}{(n-r)!}\\\\\\_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Putting in values we get:

[tex]_nP_3 = \frac{n!}{(n-3)!}\\\\\\_nC_2 = \frac{n!}{2!(n-2)!}[/tex]

Now we know that

[tex]\frac{_nP_3}{_nC_2} = 6[/tex]

So, putting in values we get:

[tex]\frac{\frac{n!}{(n-3)!}}{\frac{n!}{2!(n-2)!}} =6\\\\ \frac{n!}{(n-3)!} \times \frac{(n-2)! \times 2!}{ n!} = 6\\\\ \frac{1}{(n-3)!} \times (n-2)! \times 2! = 6\\\\ 2(n-2) = 6\\\\ n = 5[/tex]

Thus the value of n is 5.

Answer:

[ - 6 , 6 ]

Step-by-step explanation:

This is because the value of f(t) for x values only ranges from -6 to 6.

Please mark for Brainliest!! :D Thanks!!

For more questions or more information, please comment below!

Answer:

See attached!

Step-by-step explanation:

Answer:

y = -5

Step-by-step explanation:

To find the slope , we use

m = (y2-y1)/(x2-x1)

3/2 = (-2-y)/(2-0)

3/2 = (-2-y)/2

Since the denominators are the same, the numerators have to be the same

3 = -2-y

Add 2 to each side

3+2 = -2-y+2

5 = -y

Divide each side by -1

5/-1 = -y/-1

-5 = y

Answer:

D

Step-by-step explanation:

For the segment addition postulate, two segments added together have to equal the third segment. In other words, if we added them together, the sum should be the first letter of the first line and the second letter of the second line.

BC + CD = BD

Answer: $343.96

Step-by-step explanation:

x-0.75x=85.99

0.25x=85.99

Answer:

343.96

Step-by-step explanation:

The discount it 75%.  That means we pay 25%

25% of the original price is 85.99

Let x be the original price

x*25% = 85.99

.25x = 85.99

Divide each side by .25

.25x/.25 = 85.99/.25

x =343.96

The original price is 343.96

Answer:

16 centimeters cubed

Step-by-step explanation:

Volume of cone is equal to 1/3 * pi * r^2 * h

We are using 3.14 for pi so I'm going to rewrite my formula for volume.

V=1/3 * 3.14 * r^2 * h

We are given diameter is 3 but we need the radius.  We know the radius is half of the diameter so the radius is 1.5 since that is half of 3.

We are given the height is 7.

V=1/3 * 3.14 * 1.5^2 *7

Put into calculator

V=16.485

The whole number that this is closest to is .... 16

So

The Volume of the cone is approximately 16 centimeters cubed.

Answer: [tex]16\ cm^3[/tex]

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height of the cone.

To find the radius, you need to divide the diameter by 2. Then:

[tex]r=\frac{3\ cm}{2}=1.5\ cm[/tex]

Knowing the radius and the height ([tex]h=7\ cm[/tex]), you can substitute them into the formula.

Therefore, the volume of the cone rounded  to the nearest whole number is:

 [tex]V_{(cone)}=\frac{1}{3}(3.14)(1.5\ cm)^2(7\ cm)\\\\V_{(cone})=16\ cm^3[/tex]

Answer:

The volume of the sphere is [tex]V=18\pi\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of cylinder is equal to

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

we have

[tex]V=27\pi\ ft^{3}[/tex]

substitute

[tex]27\pi=\pi r^{2}h[/tex]

simplify

[tex]27=r^{2}h[/tex]

Remember that

A sphere and a cylinder have the same radius and height

so

The height of cylinder is equal to the diameter of sphere

h=2r

substitute

[tex]27=r^{2}(2r)[/tex]

[tex]13.5=r^{3}[/tex] -----> equation A

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

substitute equation A in the formula of the volume of sphere

[tex]V=\frac{4}{3}\pi (13.5)[/tex]

[tex]V=18\pi\ ft^{3}[/tex]

Answer:

It's (A.) guys

Step-by-step explanation:

[tex]\displaystyle\\\lim_{x\to 2}\dfrac{x^2+2x-3}{x-3}=\dfrac{2^2+2\cdot2-3}{2-3}=\dfrac{5}{-1}=-5[/tex]

The right-hand limit of the function f(x) = (x^2 + 2x - 3)/(x - 3) as x approaches 2 is -5 after substitution of x = 2 into the function.

The question asks about the right-hand limit of the function f(x) = (x^2 + 2x - 3)/(x - 3) as x approaches 2. The first step in finding this limit is to simplify the function, if possible. In this case, we can factor the numerator to obtain (x - 1)(x + 3). However, since we are looking for a limit as x approaches 2, the denominator x - 3 will not be zero, and the expression does not need further simplification for this purpose. We then substitute x = 2 directly into the simplified function and find the limit.

So, the right-hand limit as x approaches 2 is simply f(2) = ((2)^2 + 2*2 - 3)/(2 - 3) = (4 + 4 - 3)/(-1) = 5/(-1) = -5.

Answer:

B. A relation that is a function

Step-by-step explanation:

Answer:

B. A relation that is a function

Step-by-step explanation:

Let's see what a function is.

A function is a relation each different input has an output.

The given situation is " The enrollment at a high school does not change for 3 years in a row"

This means the consecutive years, the number of enrollment is the same.

Here each different years mapped with only one output. This is relation is a function.

This is classified as "a constant function" because three different inputs has the same output.

Therefore, the answer is  B) A relation that is a function.

Step-by-step explanation:

80=64+P if its it's there

Answer: I think its B, p+64 > 80.

Step-by-step explanation: P is the points she needs and 64 is the points she already has. They need to be more than 80, so p+64 is greater than 80.

Answer:

total=quantity*price per item on that row

New account balance=old account balance plus total on that row

Step-by-step explanation:

I won't do all of the rows but I will do a couple and explain to you how I got the answer and how you should too:

The total for each row is equal to that row's price per item times that row's quantity.

The amount balance is going to include previous account balance into it. So once you find the total for that row you will take previous account balance and add it to the previous account balance (We are doing adding instead of subtracting because the number we are getting is negative for the total.)

So example:

Second row total is 2(-45.25)=-90.50 so that is what we are adding to 2500.68 or we are subtracting 90.50 from 2500.68 giving us 2410.18

Third row total is 75(-1.39)=-104.25.  Third row account balance is 2410.18-104.25=2305.93.

So again total=quantity*price per item on that row

New account balance=old account balance plus total on that row

If you want me to check your forth row to see if you are doing it right, I will.

We can solve this problem by using the known value (115) to solve for the angle parallel to the equation.

To find the solve for the angle to the exact right of 115, subtract 115 from 180. This works because 115 and the unknown angle form to make a straight line, which is 180 degrees.

180-115=65

Now, since it is parallel, we know that 5x+5=65 degrees.

Solve the equation.

Subtract 5 on both sides.

5x=60

Divide both sides by 5 to isolate x.

5x=13

The value of x is 13.

Hope this helps!

[tex]y=2x\\y=x^2-15\\\\x^2-15=2x\\x^2-2x-15=0\\x^2-5x+3x-15=0\\x(x-5)+3(x-5)=0\\(x+3)(x-5)=0\\x=-3 \vee x=5\\\\y=2\cdot(-3) \vee y=2\cdot5\\y=-6 \vee y=10\\\\(x,y)\in\{(-3,-6),(5,10)\}[/tex]

Answer:

the solution of linear equation 4b + 6 = 2 - 6 + 4 is b = -2

Step-by-step explanation:

We need to solve the linear equation

4b + 6 = 2 - 6 +4

Adding constants

4b + 6 = 0

Adding -6 on both sides

4b + 6 -6 = 0 -6

4b = -6

Dividing with 4 on both sides

4b/4 = -6/4

b = -2

So, the solution of linear equation 4b + 6 = 2 - 6 + 4 is b = -2

Answer:

0

Step-by-step explanation:

Answer:

4 muffins are of $2.90

1 muffin is of  2.90/4 =0.725

1 dozen(12 muffens) 0.725x12=

Step-by-step explanation:

Answer:

8.70

Step-by-step explanation:

3 * 4 = 12.

12 = 1 dozen

So you have to multiply 2.90 * 3

The answer is 8.70

=======================

That's one way to do the problem. Here's another.

4 muffins = $2.90

12 muffins = x                Cross multiply.

4x = 12*2.90

4x = 34.80                     Divide by 4

4x/4 = 34.80/4              Do the division

x = $8.70

Answer:

[tex]m = -4[/tex]

Step-by-step explanation:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

[tex]\frac{-4 - 8}{2-(-1)}[/tex]

[tex]-4 - 8 = -12\\ 2-(-1)=3[/tex]

[tex]\frac{-12}{3} = -4[/tex]

[tex]m = -4[/tex]

Answer:

M=-4

Step-by-step explanation:

The formula for the slope is:

m=[tex]\frac{y^{2} -y^{1} }{x^{2} -x^{1} }[/tex]

You have two points the first one would be: (-1,8)

So [tex]x^{1}= -1  y^{1}= 8 [/tex]

The second point is: (2,4)

So [tex]x^{2}= 2  y^{2}= 4 [/tex]

Now you just have to put the values inside the formula:

m=[tex]\frac{-4-8)}{2-(-1)}[/tex]

m=[tex]\frac{-12}{3}[/tex]

m=-4

Answer:

The decimal point move to the left

Step-by-step explanation:

Let

x ----> a number

we know that

[tex]0.01=\frac{1}{100}[/tex]

When you multiply a number by 0.01 is equal to divide the number by 100

so

[tex]x*(0.01)=\frac{x}{100}[/tex]

therefore

The decimal point move to the left

Answer:

Third option: [tex]35,669 ft^3[/tex]

Step-by-step explanation:

You need to use the formula for calculate the volume of a cylinder:

[tex]V_c=\pi r^2h[/tex]

Where r is the radius (In this case is 8 feet) and h is the height (In this case is 172 feet).

The formula for calculate the volume of a half sphere is:

[tex]V_s= \frac{2}{3} \pi  r^3[/tex]

Where r is the radius (In this case is 8 feet)

You need to add the volume of the cylinder and the volume of the half-sphere. Then the volume of grain that could completely fill this silo, rounded to the nearest whole number is (Remeber to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex]):

[tex]V=(\frac{22}{7}) (8ft)^2(172ft)+ (\frac{2}{3})(\frac{22}{7})(8ft)^3=35,669 ft^3[/tex]

Answer:

The correct answer is third option 35,669 feet³

Step-by-step explanation:

It is given that, Grain silo formed by cylinder with radius 8 feet and height 172 feet and a half sphere on the top

We have to find the volume of cylinder + volume of semi sphere

To find the volume of cylinder

Here r = 8 feet and f cylinder = πr²h

 = (22/7) * 8² * 172

 = 34596.57 ≈ 34597 feet³

To find the volume of hemisphere

here r = 8 feet

Volume of hemisphere = (2/3)πr³

 = (2/3) * (22/7) * 8³

 = 1072.76 ≈ 1073 feet³

To find the total volume

Total volume = volume of cylinder + volume of hemisphere

 = 34597 + 1073

 = 35,669 feet³

The correct answer is third option 35,669 feet³

Answer:

see explanation

Step-by-step explanation:

One way to divide is to use the denominator as a factor in the numerator

Consider the numerator

x(x - 9) + 9x - 5x + 7

= x(x - 9) + 4x - 7

= x(x - 9) + 4(x - 9) + 36 + 7

= x(x - 9) + 4(x - 9) + 43

quotient = x + 4, remainder = 43

Hence

[tex]\frac{x^2-5x+7}{x-9}[/tex] = x + 4 + [tex]\frac{43}{x-9}[/tex]

Answer:

Second option.

Step-by-step explanation:

You can use the formula for calculate the area of a trapezoid. This is:

[tex]A_{(trapezoid)}=\frac{h}{2}(B+b)[/tex]

Where "B" is the larger base, "b" is the minor base and "h" is the height.

You can identify in the figure that:

[tex]B=8units\\b=4units\\h=4units[/tex]

Then you can substitute values into the formula, getting that the area of the trapezoid is:

[tex]A_{(trapezoid)}=\frac{4units}{2}(8units+4units)[/tex]

 [tex]A_{(trapezoid)}=24units^2[/tex]

Answer: 24 units or answer b

Step-by-step explanation: