Ratio of the number of students in art class to the number of students in gym class was 2:7, however art class is small, and gym class is large, students changed for the second semester. Now the students in art class to the number students in gym class is 5:4. If 75 students are in art class in second semester, how many were in art class and gym class first semester?

Answers

Answer 1

semester 1:

let the number of students in the art class be 2a, and the number of the students in the gym class be 7a. (check: the ratio is 2a:7a = 2:7)

so the total number of students is 9a.

semester 2:

the 9a students are go to the art class and gym class at a a ratio of 5: 4,

so 5a students go to the art class, and 4a students go to the gym class.

75 students are in art class in second semester means that 5a=75,

so a=75/5=15.

In the 1st semester the number of students was:

art class: 2a=2*15=30

gym class: 7a=7*15=105

Related Questions

a plane flies 1440 miles at a speed of 240mph how long does it take

Answers

We will use the formula: Time = Distance/Speed.

We know that the distance is 1440 miles, and the speed is 240 mph.

We can put them in our formula: Time = 1440/240 = 6 hours or (6x60) = 360 minutes.

Speed =

240 =

Rearrange;

time =

time = 6 hours

Are all whole numbers integers? Please Explain.

Answers

intergers consists of both negative and positive numbers and whole numers starts from 0,1,2,3..... so i would say YES

based on the census state A has 11 fewer electoral votes for president then state b. If the total number of electoral votes for these two states is 87 find the number for each state.

Answers

a + b = 87
a = b - 11

b - 11 + b = 87
2b - 11 = 87
2b = 87 + 11
2b = 98
b = 98/2
b = 49 <===

a = b - 11
a = 49 - 11
a = 38 <===

A one-minute advertisement on a local television station during prime time (8-10p.m.) costs the advertiser $12,800. To the nearest cent, how much does the advertisement cost per second? Show your work using dimensional analysis.

Answers

To determine the cost per second can be calculated by converting the given unit in terms of second. The conversion factor that will be used is 1 minute is equal to 60 seconds. Also, use proper dimensional analysis as shown below.

R = ($12,800 / minute) (1 minute / 60 seconds)
R = $213.33/seconds

Therefore, one second of advertisement during prime time costs $213.33.

Order square root of three, 2pi, and 1.5 from least to greatest

Answers

Be more specific please

1.5, square root of 3, and 2pi

Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 50 miles per hour and the other train travels at 60 miles per hour. How much time passes until the trains are 660 miles apart?

Answers

Let n = the hours elapsed when the two trains are 660 miles apart.

Let the first train travel east and the second train travel west.
The distance traveled by the first train is
x = (50 mi/h)*(n h) = 50n mi

The distance traveled by the second train is
y = (60 mi/h)*(n h) = 60n h

The distance between the two trains after n hours is
x + y = 50 n + 60n = 110n mi

Because this distance is 660 miles, therefore
110n = 660
n = 6 hours

Answer: 6 hours

Select from the drop-down menu to correctly identify the property shown.

−4.8 + (3.2 + (−1.6)) = (3.2 + (−1.6)) + (−4.8)

A. Associative Property
B. Commutative Property
C. Opposite of a Sum Property

Answers

The answer is Commutative Property.

Answer:

Option B is correct.

Commutative property is used here.

Explanation:

Commutative Property states that we can add any number in any order, we will get the same result i.e, a+b = b+a.

let a = -4.8 and b = (3.2+(-1.6))

then, using commutative property we have;

a+b=b+a then,

−4.8 + (3.2 + (−1.6)) = (3.2 + (−1.6)) + (−4.8).

Given that f(x)= x2+3 and g(x)= x+4/3 solve for (f(g(x)) when x =2

Answers

[tex]\bf \begin{cases} f(x)=x^2+3\\\\ g(x)=x+\cfrac{4}{3} \end{cases} \\\\\\ \boxed{x=2}\qquad g(2)=(2)+\cfrac{4}{3}\implies \boxed{g(2)=\cfrac{10}{3}} \\\\\\ f(~~g(x)~~)=[g(x)]^2+3\implies f(~~g(2)~~)=[g(2)]^2+3 \\\\\\ f(~~g(2)~~)=\left[ \boxed{\frac{10}{3}} \right]^2+3\implies f(~~g(2)~~)=\cfrac{10^2}{3^2}+3 \\\\\\ f(~~g(2)~~)=\cfrac{100}{9}+3\implies f(~~g(2)~~)=\cfrac{100+27}{9} \\\\\\ f(~~g(2)~~)=\cfrac{127}{9}[/tex]

Solve for x. 4−(2x+4)=5
A x=6
B x=−10
C x=−52

Answers

4 - (2x + 4) = 5
4 - 2x - 4 = 5
-2x = 5
x = - 5/2 <==

The solution for x in the equation 4 - (2x + 4) = 5 is x = -5/2. So, the correct choice is x = -5/2. Option c is the correct choice.

To solve for x in the equation 4 - (2x + 4) = 5, follow these steps:

1. First, simplify the equation by combining like terms. Start by removing the parentheses by distributing the negative sign:

4 - 2x - 4 = 5

2. Now, simplify further by combining the constants on the left side of the equation:

(4 - 4) - 2x = 5

0 - 2x = 5

3. Next, isolate the variable x by getting rid of the -2 coefficient. To do this, divide both sides of the equation by -2:

(0 - 2x) / -2 = 5 / -2

0 / -2 - (2x / -2) = -5/2

0 + x = -5/2

4. Finally, simplify:

x = -5/2

So, the solution for x is:

x = -5/2

So, Option c is the correct choice.

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Que. Solve for x. 4−(2x+4)=5

A x=6

B x=−10

C x=−5/2

if five notebooks cost $5.25, how much would three notebooks cost?

Answers

$5.25/5 notebooks= $1.05 each

$1.05*3 notebooks= $3.15 for 3 notebooks

The answer will be $3.15..

What are all the positive integers that are in the solution set for
m < 3

Answers

1 and 2 because it’s not asking for negatives. 3<3 wouldn’t work because they are the same.

The graph of g(x) = (1/2)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?

Answers

reflect across y axis means that you replace x with -x

f(-x)=2(-x)=-2x
g(x)=-2x
de graph is the one that passes through (0,0) and (1,-2) and -1,2)

Answer:

The answer is option two on the quiz. The graph is asking us to reflect the given graph over the y-axis. Therefore, the only one that matches is the second option. The graph that passes through (0,1), (-1,2), and (0,5)

Jeff prepares meals in the home of his customers. His fixed cost for transportation and supplies is $14.50. The labor and groceries needed for each family meal is $8.80, so the expense function is E=5.7q+8.8. T or F

Answers

The expense function is:E ( q ) = m q + b,where b stays for Fixed costs.In this case:m = 8.8 ( the labor and groceries for each family meal ) and b = 14.5So E = 8.8 q + 14.5, not E = 5.7 q + 8.8Answer: False

Answer:

The given equation is false

Step-by-step explanation:

Given equation : E= 5.7q+8.8

To show : It is true or false

Solution : Cost of transportation and supplies is fixed = $14.50

Cost of labor and groceries for each family meal =$8.80

Let x is the number of meals

so, according to the question Expense function for x number of meals is

Expense function = x(cost of labor and groceries for 1 family meal)+ cost of transportation and supplies(fixed)

E= 8.80x+14.50 which is the required equation.

Therefore, given equation is false.

Soon after taking an aspirin, a patient has absorbed 320 mg of the drug. After 2 hours, only 80 mg remain. Find an exponential model for the amount of aspirin in the bloodstream after t hours.

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ \textit{at 0 seconds, t = 0, the patient has 320mg in its blood} \\\\\\ 320=I(1-r)^0\implies 320=I\cdot 1\implies 320=I \\\\\\ A=320(1-r)^t\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{2 hours later, t = 2, the patient has 80mg in its blood} \\\\\\ 80=320(1-r)^2\implies \cfrac{80}{320}=(1-r)^2\implies \cfrac{1}{4}=(1-r)^2 \\\\\\ \sqrt{\cfrac{1}{4}}=1-r\implies \cfrac{\sqrt{1}}{\sqrt{4}}=1-r\implies \cfrac{1}{2}=1-r\implies r=1-\cfrac{1}{2} \\\\\\ r=\cfrac{1}{2}\implies r=0.5\qquad A=320(1-0.5)^t\implies \boxed{A=320(0.5)^t}[/tex]

Tatiana wants to give friendship bracelets to her 32 classmates. She already has 5 bracelets, and she can buy more bracelets in packages of 4.

Answers

what's the answer choices?

i dont know but good luck son

I need help on and c plz

Answers

Wouldn't you just multiply 3/4 (the height) by 2 1/4 (the width) l x w = a if it's flat so 27/4 simplified to be 6 3/4 (hopefully i'm right)

Write a number sentence that demonstrates each property.
Commutative property of addition
Associative property of addition
Identity property of addition

Answers

they are usually represented like this

commutative property of addition
a+b=b+a

associative property of additon
(a+b)+c=a+(b+c)

identity property of addition
a+0=a

so number sentatnces

lets say a=1,b=2,c=3

commutative property of addition
1+2=2+1

associative property of addition
(1+2)+3=1+(2+3)

identity property of addition
1+0=1

Answer:

a + b = b + a

(a + b) + c = c + (b + a)

0 + a = a

I hope this helps, have an amazing day!

Steps to divide 125.00 by 7.75

Answers

_____
7.75 | 125

we want to get rid of that decimal....so we move it 2 spaces to the right....by doing that, we also have to move the decimal under the division sign by 2 spaces to the right....turning ur problem into :

16.1 R 225 <== ur answer
______
775 |12500.0
775
------- subtract
4750
4650
---------subtract
1000
775
-----------subtract
225

The price of gourmet coffee beans at the corner market has increased 10% per year over the past several years if the current cost is $40 per pound what did a pound of gourmet beans cost two years ago

Answers

$20 because 10% of 40 is 10 and the price now is 40 so 2 years before would have been 20

Answer: $32.4

Step-by-step explanation:

Given : The price of gourmet coffee beans at the corner market has increased 10% (0.1) per year over the past several years.

The current cost is $40 per pound .

The exponential decay equation is given by :-

[tex]y=A(1-r)^x[/tex], where r is the rate of decay and A is the initial amount and x is the time period.

Put A = 40 , r= 0.1 and t=2, we get

[tex]y=40(1-0.1)^2=\$32.4[/tex]

Hence, the cost of a pound of gourmet beans two years ago= $32.4

For a Circle of radius is 5 feet, find the arc length s subtended by a central angle of 42 degrees

Answers

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{r\theta \pi }{180}\qquad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=5\\ \theta = 42 \end{cases}\implies s=\cfrac{5\cdot 42\cdot \pi }{180}[/tex]

The arc length subtended by a central angle of 42 degrees in a circle of radius 5 feet is 3.665 feet.

What is Circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The formula for arc length is given by:

s = rθ

where s is the arc length, r is the radius of the circle, and θ is the central angle subtended by the arc in radians.

To use this formula, we first need to convert the central angle from degrees to radians:

θ = (π/180) × 42 = 0.733 radians

Now we can plug in the values of r and θ into the formula to get:

s = 5 × 0.733

= 3.665 feet

Therefore, the arc length subtended by a central angle of 42 degrees in a circle of radius 5 feet is 3.665 feet.

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HELP PLEASE,

Part a of the question was posted earlier on.

Answers

[tex]\bf \lim\limits_{x\to 6}~\cfrac{x^2+x+42}{x-6}\implies \lim\limits_{x\to 6}~\cfrac{(x+7)(x-6)}{(x-6)}\implies \lim\limits_{x\to 6}~x+7 \\\\\\ \lim\limits_{x\to 6}~(6)+7=13 \\\\\\ \textit{since the original equation holds for all, }x\ne 6,\textit{ then it approaches}\\ \textit{the same limit as }x+7[/tex]

X-3)4x^2+3x+2 what is the quotient?

Answers

Answer:

4x+15

Step-by-step explanation:

Given : Divisor = [tex]x-3[/tex]

Dividend = [tex]4x^2+3x+2[/tex]

To Find : Quotient

Solution:

[tex]Dividend = (Divisor \times Quotient) + Remainder[/tex]

[tex]4x^2+3x+2 = (x-3 \times 4x) +(15x+2)[/tex]

[tex]4x^2+3x+2 = (x-3 \times 4x+15) +(47)[/tex]

So, The quotient is 4x+15

Hence The quotient of the given expression is 4x+15

Answer: A

Step-by-step explanation:

A pair of fair dice is rolled.
a. What is the probability of rolling a sum of 9?
b. What are the odds against rolling a sum of 9?

Answers

a) 4/36, or 1/9
b) 1-1/9=8/9

Sample space={6 x 6} = 36 possible outcomes:

Favorable outcome {(3+6),(4+5),(5+4),(6+3) = 4 favorable outcome:

P(getting a sum = 9) = 4/36 = 1/9 = 0.1111

the odds AGAINST = the number of failure/number of success

the odds AGAINST = 1/9

Y + z — 2y

If y=4 and z= 2
(Simplify)

Answers

Substitute y for 4 and z for 2
4+2-2y
Then add like terms
6-2y
That is as simplified as it gets.

A certain recipe calls for 2/3 cup of flour. A chef is making an amount that is 3/7 of the recipe . How much should flour should the chef use?

Answers

2/7 cup of flour

Simply multiply 2/3 by 3/7 to get the answer. To multiply 2 fractions together, you multiply the numerators together and then multiply the denominator together.

2/3 x 3/7 = 6/21

But 6/21 can be expressed in a simpler fashion. Notice that both 6 and 21 can be evenly divided by 3. So divide both the numerator and denominator by 3

(6/3)/(21/3) = (2)/(7) = 2/7

805 tens in standard form

Answers

Hey! Hope that I can help.

Identify the triangles that are right triangles.

Answers

Right triangles have a 90 degree corner.

triangles often have a small box in the corner and are 90 degrees

Tyron is making 52 cookies fi a party. Some will be pecan cookies. Some will be honey ginger cookies . The ratio of pecan to honey ginger cookies will be 7:6 . Suppose you use systematic guess and check to find the number of each type of cookie

Answers

There will be 28 pecan cookies and 24 honey ginger cookies

The length and width of a rectangle whose length is 8 centimeters more than its width

Answers

What is the question? Please give more details.

Answer to both of these?

Answers

14a³ /a = 14a²

9b/3b = 3

hope this helps

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