A school has an art club, a drama club, and a cooking club. The ratio of the number of students in these clubs is given.

Art club to drama club: 7 to 13
Cooking club to art club: 5 to 14
There are 130 students in the drama club. No students are in more than one club.

How many students are in the cooking club?

Simplify brackets

2/5(x - 4) = 2x

Simplify 2/5(x - 4) to 2(x - 4)/5

2(x - 4)/5 = 2x

Multiply both sides by 5

2(x - 4) = 10x

Divide both sides by 2

x - 4 = 5x

Subtract x from both sides

-4 = 5x - x

Simplify 5x - x to 4x

-4 = 4x

Divide both sides by 4

-1 = x

Switch sides

x = -1

Answer:

$613.35

Step-by-step explanation:

As 1.45% of employee's pay check goes to the Medicare, so

Total pay of Kasey in next year=$42300

Amount to be paid to medicare=1.45% of Kasey^' s pay

=42300*  1.45/100

=42300*  145/10000

=  6133500/10000

=613.35

Kasey will have to pay $613.35 to Medicare.  

Answer:

1. 24 in^2

2. 51 in^2

3. 286 cm^2

4. 90 m^2

5. 60 cm^2

6. 57.06 m^2

7. 185 ft^2

8. 13.5 in^2

9. 252 ft^2

10. I'm not quite sure how to do this one

11. 315 m^2

12. 322 ft^2

13. I cant see all of this one

14. 39 in^2

15. 100 in^2

16. 72.5 in^2

Some of the numbers were very blurry and did my best to make them out so If I got any of them wrong I apologize.

Answer:

im about a year and a half late but please give him brainliest

Step-by-step explanation:

Answer:

Astronomers

Step-by-step explanation:

Answer:

astronomers

Step-by-step explanation:

Hello there!

_________________________________

In this problem, it says the more it advertises, the more it sells. In this case then, C. Graph Z, would be your answer since it shows the increase of both

_________________________________

I hope I helped

Brainlyiest?

X8lue83rryX

Answer:

The correct answer option is C. Graph Z.

Step-by-step explanation:

We are given that a cereal company finds that the more it spends on advertising, the more boxes of cereal it sells.

It means that the advertising is directly proportional to the number of boxes of cereal sold.

Therefore, the sales of the cereal company can be represented by graph Z where the value of y increases as the value of x increases.

Answer:

Customer has bought too much sand

Step-by-step explanation:

Given that the dimensions (Length, Width and Height) of rectangular box are = 6,5, 1.2.

Volume of a rectangular box = Length * Width * Height

=> 6*5*1.2

=> 36 cubic feet

As mentioned, customer bought a sand box and 40 cubic feet of sand.

So,

Volume of rectangular box (R) = 36 cubic feet

Volume of Sand (S) = 40 cubic feet

From analysis

S > R

Which shows that the capacity of sandbox is 36 cubic feet and volume is 40 feet that is a little greater than desired capacity.

Therefore, customer has bought too much sand.

Answer:

1) [tex]30\ in\ by\ 12\ in[/tex] --------> [tex]120\ in^{2}[/tex]

2) [tex]30\ in\ by\ 18\ in[/tex] --------> [tex]180\ in^{2}[/tex]

3) [tex]12\ in\ by\ 15\ in[/tex] --------> [tex]60\ in^{2}[/tex]

4) [tex]18\ in\ by\ 15\ in[/tex] --------> [tex]90\ in^{2}[/tex]

Step-by-step explanation:

Verify each case

case 1) [tex]30\ in\ by\ 12\ in[/tex]

Find the area with the original dimensions

[tex]A=30(12)=360\ in^{2}[/tex]

Reduce the area of the poster by one-third

[tex]360/3=120\ in^{2}[/tex]

therefore

[tex]30\ in\ by\ 12\ in[/tex] --------> [tex]120\ in^{2}[/tex]

case 2) [tex]30\ in\ by\ 18\ in[/tex]

Find the area with the original dimensions

[tex]A=30(18)=540\ in^{2}[/tex]

Reduce the area of the poster by one-third

[tex]540/3=180\ in^{2}[/tex]

therefore

[tex]30\ in\ by\ 18\ in[/tex] --------> [tex]180\ in^{2}[/tex]

case 3) [tex]12\ in\ by\ 15\ in[/tex]

Find the area with the original dimensions

[tex]A=12(15)=180\ in^{2}[/tex]

Reduce the area of the poster by one-third

[tex]180/3=60\ in^{2}[/tex]

therefore

[tex]12\ in\ by\ 15\ in[/tex] --------> [tex]60\ in^{2}[/tex]

case 4) [tex]18\ in\ by\ 15\ in[/tex]

Find the area with the original dimensions

[tex]A=18(15)=270\ in^{2}[/tex]

Reduce the area of the poster by one-third

[tex]270/3=90\ in^{2}[/tex]

therefore

[tex]18\ in\ by\ 15\ in[/tex] --------> [tex]90\ in^{2}[/tex]

Answer:

-48x-96

Step-by-step explanation:

Split the angle using the sum and difference formulas and simplify.

Answer: 5.89 cubic inches.

Step-by-step explanation:

you use the formula v=pi radius squared h/3

Answer:

5.9

Step-by-step explanation:

Answer:~ 967

Step-by-step explanation:

Answer:

Caleb arrived first 2 hours before Alyssa

Step-by-step explanation:

To solve the situation, find the speed per hour they were driving by dividing the distance they drove by the time it took.

Alyssa drove 105 miles in 3.5 hours or 105/3.5 = 30 miles per hour.

Caleb drove 168 miles in 4 hours or 168/4 = 42 miles per hour.

Since they both left at the same time and drove the same 210 miles to the beach, Caleb arrived first since he was driving faster.

He arrived in 210/42 = 5 hours.

Alyssa arrived in 210/30 = 7 hours.

He arrived 2 hours before her.

2X - 8 is used to represent Eight less than the product of two and a number X. ​

To represent "Eight less than the product of two and a number X" as an expression, we can use the following equation:

2X - 8

In this expression, 2X represents the product of two and the number X, and subtracting 8 from it gives us "eight less than the product of two and a number X."

The product of two and the number X is obtained by multiplying 2 and X, which gives us 2X.

The expression "2X - 8" then subtracts 8 from the product 2X. This subtraction of 8 represents "eight less than" the product of two and a number X.

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[tex]3a + b = 7\Leftrightarrow 3(3a + b) = 3 \times 7\Leftrightarrow 9a + 3b = 21 \: (1)\\ 6x + 8y = 40\Leftrightarrow \frac{2(3x + 4y)}{2} = \frac{40}{2} \Leftrightarrow 3x + 4y = 20 \: (2) \\ (1),(2)\Rightarrow 9a + 3b > 3x + 4y[/tex]

[tex]\bf \begin{array}{lll|llll} 3a+b&=&7&&6x+8y&=&40\\&&&&&\\ 3(3a+b)&=&3(7)&&\frac{1}{2}(6x+8y)&=&\frac{1}{2}(40)\\&&&&&\\ 9a+3b&=&21&&\frac{6x}{2}+\frac{8y}{2}&=&\frac{40}{2}\\&&&&&\\ 9a+3b&=&21&&3x+4y&=&20 \end{array}\\\\ ~\hspace{7.5em}21>20[/tex]

Answer:

C

Step-by-step explanation:

Since it is greater than or equal to, the graph line is a solid line.

Then, since we know that it is greater than, we know that we can shade above the graph line.

To check this, all you have to do is choose a random point in the shaded region and plug it in the equation. If it checks out, it is correct.

Answer:

Graph represented by option C is the correct choice.

Step-by-step explanation:

We are asked to graph an inequality [tex]y\geq2x-3[/tex].

The boundary line of our given inequality will be a solid line as we have greater than or equal to [tex]\geq[/tex] sign.

The boundary line of our given inequality would be [tex]y=2x-3[/tex].

Now, we will test point (0,0) to shade in the correct region as:

[tex]0\geq2(0)-3[/tex]

[tex]0\geq0-3[/tex]

[tex]0\geq-3[/tex]

Since the point (0,0) is a solution for our given inequality, therefore, the shaded area of our inequality will include point (0,0).

Please find the attachment.

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ r=5\\ s=\frac{25\pi }{3} \end{cases}\implies \cfrac{25\pi }{3}=5\theta \implies \cfrac{25\pi }{15}=\theta \implies \cfrac{5\pi }{3}=\theta[/tex]

Answer:

30

Step-by-step explanation:

Really hope i'm right

1st row

the first one is length less than 10

one next to it is width greater than 5

next to that is length greater than 10

2nd row

the first one is length greater than 10

one next to that is width less than 5

next to that is width greater than 5

3rd row

first one is width less than 5

and last is length less than 10

Answer:

Step-by-step explanation:5.6 times 10.5=58.8sq miles, divide by 2 because it is half, so 29.4 is the approximate of area thing

Answer:

The answer is 29.4 miles squared.

Answer:

The area of the triangle is [tex]128.62\ cm^{2}[/tex]

Step-by-step explanation:

we know that

Applying the law of sines

The area of a triangle is equal to

[tex]A=\frac{1}{2}(a)(c)sin(B)[/tex]

substitute the values

[tex]A=\frac{1}{2}(12)(22)sin(103\°)[/tex]

[tex]A=128.62\ cm^{2}[/tex]

Answer:

The number is +1

Step-by-step explanation:

we have

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

This is the equation of a vertical parabola with vertex at point (-2,-1)

The function has no real zeros

we know that

If the number +1 is added to the equation on the right side

then

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

Is a translation one unit up

The vertex of the parabola will be the point (-2,0) and the function will have one real root

see the attached figure to better understand the problem

Answer:

1

Step-by-step explanation:

Answer:

The inverse function is a) h(x) = 1/2x - 1/2

Step-by-step explanation:

To find the inverse of any function, start by switching the x and f(x) values.

f(x) = 2x + 1

x = 2f(x) + 1

Now solve for the new f(x). The result will be your inverse function.

x = 2f(x) + 1

x - 1 = 2f(x)

(x - 1)/2 = f(x)

h(x) = 1/2x - 1/2

The inverse of the function f(x)=2x+1 is found by switching x and y in the function to create a new equation, rearranging that equation to solve for y, resulting in the inverse f^-1(x)=(x-1)/2.

To find the inverse of the function f(x)=2x+1, you first switch the roles of x and y in the function.

So, the inverse of the function is f^-1(x)=(x-1)/2.

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Answer:

The reduced paid up insurance value is $47,770 and the annual premium is $4,097

The reduced paid-up insurance value is $6,692.83.

The annual premium for the reduced paid-up insurance is the amount of money that the policyholder would

We have,

To determine the reduced paid-up insurance value and the annual premium,

We need to use the information given and the following formulae:

The cash value of a policy is the amount of money that the policyholder would receive if they surrendered the policy before it matured.

The net amount at risk is the difference between the face value of the policy and the cash value.

The present value of a policy is the sum of the net amount at risk and the present value of the future premiums.

We are given that:

The policy is a 20-Year Endowment insurance policy, purchased when the policyholder was 40 years old.

The face value of the policy is $85,000.

The policyholder is now 50 years old.

The permanent insurance amount is $48.20 per thousand.

We need to determine the reduced paid-up insurance value and the annual premium.

We can use the following steps to determine the reduced paid-up insurance value and the annual premium:

Step 1: Calculate the cash value of the policy

The cash value of the policy can be calculated using the following formula:

Cash value = (Present value of future endowment benefits) - (Present value of future premiums)

We are given that the policy is a 20-Year Endowment policy, so the endowment benefit is $85,000. We can use the following formula to calculate the present value of the future endowment benefits:

Present value of endowment benefits = Endowment benefit / (1 + i)n

where i is the interest rate and n is the number of years.

Since the policyholder is 50 years old and the policy has 10 years left, we can assume an interest rate of 4% and calculate the present value of the endowment benefits as follows:

Present value of endowment benefits = $85,000 / (1 + 0.04)^10 = $48,598.20

We can calculate the present value of future premiums using the following formula:

Present value of future premiums = Net amount at risk / (Present value of an annuity due of $1 for n years, at i%)

where n is the number of years and i is the interest rate.

Since the policyholder has paid premiums for 10 years, there are 10 years left to pay. Using the same interest rate of 4%, we can calculate the present value of an annuity due of $1 for 10 years as follows:

Present value of an annuity due of $1 for 10 years, at 4% = 7.3601

We can now calculate the net amount at risk as follows:

Net amount at risk = Face value - Cash value

Face value = $85,000

Cash value = $48,598.20 + (Annual premium x Present value of an annuity due of $1 for 10 years, at 4%)

Net amount at risk = $85,000 - $48,598.20 - (Annual premium x 7.3601)

Step 2: Calculate the reduced paid-up insurance value

The reduced paid up insurance value is the amount of insurance that the policyholder can receive without paying any more premiums. It can be calculated as follows:

Reduced paid up insurance value = Cash value / Permanent insurance amount

Using the cash value calculated in Step 1 and the permanent insurance amount of $48.20 per thousand, we can calculate the reduced paid up insurance value as follows:

Reduced paid up insurance value.

= $48,598.20 / ($48.20 x 85)

= $6,692.83

Step 3: Calculate the annual premium

The annual premium for the reduced paid-up insurance is the amount of money that the policyholder would

Thus,

The reduced paid-up insurance value is $6,692.83.

The annual premium for the reduced paid-up insurance is the amount of money that the policyholder would

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Answer:

90 cm^2

Step-by-step explanation:

The scale factor between triangle ABC and triangle PQR is 4:6 or  2:3

The scale factor is 2/3

When relating areas, we use the scale factor squared

Area of ABC = scale factor squared * Area of PQR

40 =  (2/3) ^2 Area of PQR

40  =4/9 Area of PQR

Multiply each side by 9/4

40 *9/4 = 9/4 *4/9 * Area of PQR

90 = Area of PQR

When we work with lengths of similar figures, we multiply by the scale factor.

When we work with areas of similar figures, we have a length and a width, so we are really multiplying by the scale factor two times, or the scale factor squared.

A = l*w

A = SF (l) * SF (w)

  = SF ^2 lw

So the area of the new  figure is the scale factor squared times the area of the old figure.

A new = SF^2 A old

To get from the old figure to the new figure we multiply by 6/4 or 3/2

A new =  (3/2)^2 (40)

A new = 9/4 * 40

           = 90

To evaluate the expression a • b for a = 5 and b = 8, you multiply the values of a and b. So, a • b = 5 • 8 = 40.

The question is asking to evaluate the expression a • b where a = 5 and b = 8. The dot (•) in the expression a • b signifies multiplication in mathematics. To evaluate this expression for a = 5 and b = 8, you simply multiply the given values of a and b. So, the calculation is 5 × 8.

Therefore, a • b = 5 • 8 = 40 when a = 5 and b = 8.

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The dot product of vectors a = 5 and b = 8 is calculated by multiplying the corresponding components of each vector and summing the results. Therefore, a • b = (5 * 8) = 40.

Evaluating the Dot Product of a and b

Given: a = 5 and b = 8

Objective: Determine the dot product of vectors a and b, denoted as a • b.

Steps:

Express the dot product formula: The dot product of two vectors a and b is defined as:

a • b = ∑(aᵢ * bᵢ)

where:

aᵢ and bᵢ represent the i-th components of vectors a and b, respectively

the summation sign (∑) indicates that the product of corresponding components is calculated for each dimension and then summed

Substitute the given values: Substituting the values of a and b into the formula:

a • b = (5 * 8)

Calculate the product: Performing the multiplication:

a • b = 40

Answer:

The dot product of vectors a and b, denoted as a • b, is equal to 40.

Answer: -11

Step-by-step explanation:

(n+8)* -4= 12

   -8          -8

n* -4= 12

   /-4   /-4

n= -11

Based on the calculations, the unknown number (n) is equal to -11.

In this exercise, you're required to find an unknown number (n). Thus, we would translate the word problem into an algebraic expression as follows:

The sum of a number (n) and 8:

n + 8

Multiplying by -4, we have:

(n + 8) × -4 = 12

-4n - 32 = 12

-4n = 12 + 32

-4n = 44

n = -11.

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Answer:

2929 feet away from the door

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

since the .77 is larger than .5, you automatically round it up

Answer:

36

Step-by-step explanation:

The number 35.77 is closest to 36. It's all about the destimal, if we had 35.44 that's not above 50 so it would be 34. This would apply to any whole number.

Answer : C: $125.

Hopefully that helps you ! have a good day !

The correct answer is B.

Hope this helps.

Answer:

To calculate the monthly accrued interest on a loan or investment, you first need to determine the monthly interest rate by dividing the annual interest rate by 12. Next, divide this amount by 100 to convert from a percentage to a decimal. For example, 1% becomes 0.01.

Step-by-step explanation: