A survey of 541 adults aged 18-24 year olds was conducted in which they
were asked what they did last Friday night. It found:
181 watched TV
• 180 hung out with friends
• 150 ate pizza
• 46 watched TV and ate pizza, but did not hang out with friends
• 36 watched TV and hung out with friends, but did not eat pizza
• 29 hung out with friends and ate pizza, but did not watch TV
• 25 watched TV, hung out with friends, and ate pizza
How may 18-24 year olds did not do any of these three activities last Friday

Answer:

easy

Step-by-step explanation:

How to solve a system of equations by elimination.

Write both equations in standard form.

Make the coefficients of one variable opposites.

Add the equations resulting from Step 2 to eliminate one variable.

Solve for the remaining variable.

Substitute the solution from Step 4 into one of the original equations.

Answer: e² - 4

Step-by-step explanation:

Differentiate of e²x - 3e-4x is e² - 4

Answer:

[tex]\dfrac{\text{d}y}{\text{d}x} = 2e^{2x}+12e^{-4x}[/tex]

Step-by-step explanation:

Given function:

[tex]y=e^{2x}-3e^{-4x}[/tex]

[tex]\boxed{\begin{minipage}{3.7cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{\text{d}}{\text{d}x} e^{2x}-\dfrac{\text{d}}{\text{d}x}3e^{-4x}\\\\& =2 \cdot e^{2x}-(-4)\cdot 3 e^{-4x} \\\\ &= 2e^{2x}+12e^{-4x}\end{aligned}[/tex]

The required rate for ratio of the two different quantities i.e

Gabby worked 30/4 hours per day.

Option (c) is correct.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Gabby worked 30 hours in 4 days.

According to given question we have

The ratio of the two quantities of the different kind and in the different units is a fraction that shows how many times one quantity is of the other.

By the use of arithmetic we have,

Gabby worked 30 hours in 4 days means

4 days= 30 hours

1 days = 30/4 hours

Therefore, the required rate for ratio of the two different quantities i.e

Gabby worked 30/4 hours per day.

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Answer: 30/4 hours per day

Step-by-step explanation:

Solution:

B.) [tex](6-\sqrt{33}, 6+\sqrt{33})[/tex]

Hope this helps! If so, please lmk! Thanks and good luck!

The number of coffee product he sells is 38.

He makes $11.50 per hour.

He earns $0.50 for each of these items he sells.

Last week he worked 30 hours and earned $364.

Therefore, the number of coffee product he sells last week can be calculated as follows:

let

x = number of coffee product he sells.

364 = 11.50(30) + 0.50(x)

364 = 345 + 0.50x

364 - 345 = 0.50x

19 = 0.5x

divide both sides by 0.5

x = 19 / 0.5

x = 38

Therefore, the number of coffee product he sells is 38.

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(a) There are 665280 ways of selection if the order of the choices matters.

(b) There are 924 ways of selection if the order of the choices does not matters.

(a)  If the order of the choices matters, then we must use the permutation formula that is

[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]

Here n is the total no. of objects and r is chosen objects

We have n = 12

               r = 6

After we substitute the value we get

[tex]^{12}P_6 = \frac{12!}{(12 - 6)!}[/tex]

[tex]^{12}P_6 = \frac{12!}{6!}[/tex]

[tex]^{12}P_6[/tex] = 665280

Thus, there are 665280 ways of selection if the order of the choices matters

(b)  If the order of the choices does not matter, then we must use the combination formula that is

[tex]^nC_r = \frac{n!}{r!(n - r)!}[/tex]

After we substitute the value we get

[tex]^{12}C_6 = \frac{12!}{6!(12 - 6)!}[/tex]

[tex]^{12}C_6 = \frac{12!}{6! 6!}[/tex]

[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7×6! / 6!×6!

[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7/ 6!

​[tex]^{12}C_6 =[/tex] 665280/ 720

​[tex]^{12}C_6 =[/tex] 924

Thus, there are 924 ways of selection if the order of the choices does not matters.

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Answer: 3 gallons per hour

Step-by-step explanation: 14-(3x) =5 14-5=9 9/3=3

If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.

First step is to calculate the value loss

Value loss=1/3× original  value

Value loss= 1/3× $215,613

Value loss= $71,871

Second step is to calculate the new value

New value=$215,613-$71,871

New value= $143,742

Third step is to calculate the value gained

Value gained= 1/2× new value

Valued gained=1/2× $143,742

Valued gained=$71,871

Fourth step is to calculate the current value

Current value= $143,742+$71,871

Current value=$$215,613

Therefore If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.

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Answer:

I think it's because of the down payment and the positive slope because you are going to pay in installments by months.

Answer is - 2 [tex]\sqrt{3}[/tex] / 13

Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position

cosθ = cos (π + d) (d is the inner angle of the tringle)

       = - cos 2

       = - 4 / - [tex]\sqrt{(- 6^{2} + (- 4^{2} )[/tex]

       = - 4 / - [tex]\sqrt{36 + 16 }[/tex]

      = - 4 / -[tex]\sqrt{52}[/tex]

      = - 4 / 2[tex]\sqrt{13}[/tex]

      = - 2 / [tex]\sqrt{13}[/tex]

multiply by [tex]\sqrt{13}[/tex]

we get,

      = -  [tex]\frac{2 \sqrt{13} }{13}[/tex]

Formulae :

Arc cosecant      y = arcs(x) = csc-1(x). Another way to write x = csc(y).

Arccosine      y = arcos(x) = cos-1(x). Another way to write x = cos(y).

Arc cotangent    y = arcos(x) = cot-1(x). Another way to write x = cot(y).

Arc secant       y = arcsec(x) = sec-1(x). Another way to write x = sec(y).

Arcsine       y = arcsine(x) = sin-1(x). Another way to write x = sin(y).

Arctangent   y = arctan(x) = tan-1(x). Another way to write x = tan(y).

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The population of a city after 5 years would be 261698.

We know the the formula for the exponential growth of the population is,

P(t) = a(1+r)^t

where, a is the initial population

t is the time period

r is the rate of growth

In this question, we have a = 210000, %R = 4.5

So, r = 0.045

We need to find the population after 5 years.

t = 5

Using above formula,

P = 210000 × ( 1 + 0.045)^5

P =  210,000 × (1.045)^5

P = 210,000 × 1.25

P = 261698.2

P ≈ 261698

Therefore, the population of a city after 5 years would be 261698.

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Answer: please=356

Step-by-step explanation:

219 +485 = 348 + please

704=348 + please

please=356

Answer:

$5.90

Step-by-step explanation:

(7.19)(.82)  Put these numbers in your calculator and multiply them together.

5.8958 Round to the nearest cent

$5.90

valid . some trees grow flowers i belive

Answer:

4 lines

Step-by-step explanation:

We know that a parallelogram is constructed using two parallel lines intersecting other pairs of parallel lines so basically we require 4 lines to construct a parallelogram.

Answer:4

Step-by-step explanation:

Answer:

B: 3x+(4x+2)=180

Step-by-step explanation:

Supplementary angles are those angles that sum up to 180 degrees. The question gives you the two angles that compose the 180 degree angle thus you get the equation:

Angle 1 + Angle 2 = Supplementary Angle

In this case we see that these two angles are Angles B and C and a supplementary angle is 180 degrees thus:

(4x+2)+3x = 180

Furthermore this also allows you to find x.

Answer:

30

Step-by-step explanation:

Let the cat have a weight of x.

Then, the dog weighs 9x.

The hamster weighs x/20.

The mouse weighs 3x/10.

So, the dog is 9/(3/10) = 30 times as heavy.

The weight of the dog is 30 times the weight of the mouse.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Let the weight of the dog be x,
A dog is 9 times as heavy as a cat,
weight of the dog = 9x - - - - -(1)

A hamster is 20 times as light as a cat
Weight of the hamster = x /20

A mouse is 6 times as heavy as a hamster.

Weight of the mouse = 6(x /20)
m(20/6) = x

Now, put x = m(20/6) in equaiton 1,
weight of the dog = 9[m(20/6)]
weight of the dog = 30m

Thus, the weight of the dog is 30 times the weight of the mouse.

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Answer:

It's coordinates are (1,-2)

The required measure of the angle m∠B is 121°.

Given that,
Angle A and B are two vertical equal angles.
m∠B = 3x - 17
m∠A = 2x + 29

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
m∠A = m∠B
2x + 29 = 3x - 17
-x = - 46
x = 46

Now,
m∠B = 3  *46 - 17
m∠B =  138 - 17
m∠B = 121°

Thus, the required measure of the angle m∠B is 121°.

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Answer:

B. 6

Step-by-step explanation:

$10.35 × 24 = 248.4 per week

248.4 × 30% = 74.52 {30% of her earnings}

$74.52 × 6 weeks = $447.12

∴ She needs to work for 6 weeks in order to save up to $399

Answer:

r = e or 2.718282

Step-by-step explanation:

a) simplify both sides of the equation

2.718282 = r

b) flip the equation

r = 2.718282

The solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.

It follows from the task content that the solution to the given trigonometric equation is to be determined.

Given;

Cos(x) - 1 = 0

Add 1 to both sides of the equation;

Cos (x) = 1

Therefore, the value of x can be determined by evaluating the cos inverse of (-1).

Hence,

x = Cos-¹(1)

x = nπ (where n is any integer real number value).

Ultimately, the solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.

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The equation of the two-step problem is 2x = x + 19

The conditions are given as

Let the variable in the equation be x

So, a possible equation is as follows

2x = x + 19

The solution to the equation is as follows

2x = x + 19

Subtract x from both sides

x = 19

Hence, the equation of the two-step problem is 2x = x + 19

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Answer:

○ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]

Step-by-step explanation:

We are told that:

[tex]z(x)= 15x - x^2 + 3[/tex],

and told to find an expression for [tex]z(x - 1)[/tex].

In order to find [tex]z(x - 1)[/tex], we have to replace [tex]x[/tex] in the definition of [tex]z(x)[/tex] with [tex](x-1)[/tex]:

[tex]z(x - 1) = 15(x -1) - (x - 1)^2 + 3[/tex]

Now we can simplify:

⇒ [tex]z(x-1) = 15x - 15 - (x - 1)^2 + 3[/tex]      [Distributing 15 into the first brakets]

⇒ [tex]z(x-1) = 15x - 15 - (x^2 - 2x + 1) + 3[/tex]

⇒ [tex]z(x-1) = 15x - 15 - x^2 + 2x - 1 + 3[/tex]     [Distributing the minus sign]

⇒ [tex]z(x - 1) = 17x - x^2 -13[/tex]          [Combining like terms]

⇒ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]

Therefore, the first option is the correct one.

The statement that correctly compares the number of songs on Georgia and Scarlet's playlists are is  17 < 36.

Georgia has 17 songs on her playlist while Scarlet has 36 songs on her playlist.

In the number line, the number 36 comes after the number 17. This means that 36 is greater than 17.

The statement that therefore correctly compares the number of songs in the playlist is:

17 < 36

In conclusion, the statement that correctly compares the songs in the two playlists is 17 < 36.

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The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:

x = 4 - 3 · y

Second, substitute x in the first two equations:

3 · (4 - 3 · y) + 2 · y - z = 8

12 - 9 · y + 2 · y - z = 8

- 7 · y - z = - 4

2 · (4 - 3 · y) + 2 · z = - 4

8 - 6 · y + 2 · z = - 4

- 6 · y + 2 · z = - 12

Third, clear z in the first equation derived in the previous step:

z = 4 - 7 · y

Fourth, substitute z in the second equation derived in the second step:

- 6 · y + 2 · (4 - 7 · y) = - 12

- 6 · y + 8 - 14 · y = - 12

- 20 · y = - 20

y = 1

Fifth, calculate y and x:

z = 4 - 7 · 1

z = - 3

x = 4 - 3 · 1

x = 1

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

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They sold 10 bags of butter popcorn, 20 bags of kettle corn and 26 bags of cheddar cheese.

Here, we are given that two boy scouts were selling popcorn for a fundraiser.

Their total revenue = $640

Let the bags of butter popcorn be x

then, the bags of kettle corn sold = 2x

and the bags of cheddar popcorn sold = 2x + 6

Cost of kettle corn = $15/ bag

Cost of butter popcorn = $8/ bag

Cost of cheddar popcorn = $10/ bag

Thus, the total revenue from from kettle corn = $30x

total revenue from from butter popcorn = $8x

total revenue from from cheddar popcorn = $10(2x + 6)x

Thus, we will get the following equation-

30x + 8x + 10(2x + 6) = 640

38x + 20x + 60 = 640

58x + 60 = 640

58x = 580

x = 580/ 58

x = 10

Thus, 2x = 20 and 2x + 6 = 26

Hence, they sold 10 bags of butter popcorn, 20 bags of kettle corn and 26 bags of cheddar cheese.

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all that sides which can be applicable in the given side of triangle are:

F.5

A.7

C.9

Third Side of a Right Angle Triangle Pythagorean Theorem. The length of the hypotenuse in a right triangle can be determined using the Pythagorean Theorem. You can determine the length of the missing side using algebra and square roots as long as you are only given two lengths.

a,b and c are the sides of a triangle if it satisfies:

a<b+c  , b<a+c and c<b+a

Here, a=4 and b=7

We have to find c

i.e. all those c which satisfies:

4<7+c , 7<4+c and c<4+7=11

D.3   it is not true since it doesn't satisfies second inequality

F.5   it is true

A.7   it is true

C.9   it is true

E.11   This is clearly false, since it doesn't satisfies inequality third

F.5 This is clearly false, since it doesn't satisfies inequality third

Hence, correct options are:

F.5

A.7

C.9

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The value of x is 11 units and the length of side RS = 11x-4 is 117 units.

with measurement BC = 60, CD = 50.

Triangle RST : RS = 11x-4, ST = 70

Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.

Given:

BC = 60 and CD = 50

RS = 11x - 4 and ST = 70

Now, considering

BC : CD = RS : ST

60 : 50 = 11x - 4 : 70

60/50 = (11x - 4)/70

50 * (11x - 4) = 70 * 60

11x - 4 = 84

11x = 88

x = 11

So, RS = 11x - 4

RS = 11 x 11 - 4

RS = 117

Hence, the value of x is 11 and the length of side RS is 117

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