In a class of 100 students, 24 take Chorus, 33 take Band, and 10 take both Chorus and Band. How many students in the class are not enrolled in either Chorus or Band? (3 - 4 points) SHOW WORK!

[tex]\bf (\stackrel{x}{1}~~,~~\stackrel{y}{7.5})\implies 7.5=ab^1\implies \boxed{7.5=ab} \\\\\\ (\stackrel{x}{3}~~,~~\stackrel{y}{16.875})\implies 16.875=ab^3\implies 16.875=ab^{1+2}\implies 16.875=abb^2 \\\\\\ 16.875=\boxed{7.5}b^2\implies \cfrac{16.875}{7.5}=b^2\implies 2.25=b^2 \\\\\\ \sqrt{2.25}=b\implies \blacktriangleright 1.5=b \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf 7.5=ab\implies \cfrac{7.5}{b}=a\implies \cfrac{7.5}{1.5}=a\implies \blacktriangleright 5=a \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=5(1.5)^x~\hfill[/tex]

The ratio of the room's length to its area is 1:12, derived from length (22 feet) divided by area (264 square feet).

let's break it down step by step.

Step 1: Calculate the area of the room.

To find the area of a rectangle, you multiply its length by its width.

So, Area = Length × Width

Area = 22 feet × 12 feet

Area = 264 square feet

Step 2: Calculate the ratio of the length of the room to its area.

The ratio of length to area is:

[tex]\[ \text{Ratio} = \frac{\text{Length}}{\text{Area}} \][/tex]

Substituting the values:

[tex]\[ \text{Ratio} = \frac{22 \, \text{feet}}{264 \, \text{square feet}} \][/tex]

Step 3: Simplify the ratio.

[tex]\[ \text{Ratio} = \frac{22}{264} \][/tex]

Step 4: Simplify the fraction.

[tex]\[ \text{Ratio} = \frac{1}{12} \][/tex]

So, the ratio of the length of the room to its area is [tex]\( \frac{1}{12} \)[/tex].

Answer:

11.2

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = B(4, 7) and (x₂, y₂ ) = C(2, - 4)

d = [tex]\sqrt{(2-4)^2+(-4-7)^2}[/tex]

   = [tex]\sqrt{(-2)^2+(-11)^2}[/tex]

   = [tex]\sqrt{4+121}[/tex]

   = [tex]\sqrt{125}[/tex] ≈ 11.2

Answer:

Not a factor

Step-by-step explanation:

If (x - 3) is a factor then f(3) = 0

f(x) = x² - 4x + 30

f(3) = 2(3)² - 4(3) + 30 = 18 - 12 + 30 = 36 ≠ 0

Since f(3) ≠ 0 then (x - 3) is not a factor of f(x)

( x - 3 ) is not a factor of the polynomial 2x² - 4x + 30

What is Factor Theorem?

The Factor Theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then ( x - a ) is a factor of f ( x ) if f ( a ) = 0

Given data ,

f ( x ) = 2x² - 4x + 30

If ( x - 3 ) is a factor of f ( x ) , then by factor theorem f ( x ) = f ( 3 ) = 0

And , f ( 3 ) = 2 x 3 x 3 - 4 x 3 + 30

                            = 18 - 12 + 30

                            = 36

Therefore , f ( 3 ) ≠ 0 , so ( x - 3 ) is not a factor of 2x² - 4x + 30

Hence , ( x - 3 ) is not a factor of the polynomial 2x² - 4x + 30

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Answer:

not geometric

Step-by-step explanation:

If the sequence is geometric then the common ratio r between consecutive terms should be equal

[tex]\frac{42}{21}[/tex] = 2

[tex]\frac{126}{42}[/tex] = 3

[tex]\frac{504}{126}[/tex] = 4

There is no common ratio between consecutive terms

Hence the sequence is not geometric

Answer:

The interior angles are 70°,65°,80°,155° and 170°

Step-by-step explanation:

step 1

Find the sum of the interior angles of the pentagon

The sum is equal to

S=(n-2)*180°

where

n is the number of sides of polygon

n=5 (pentagon)

substitute

S=(5-2)*180°=540°

step 2

Find the value of x

Sum the given angles and equate to 540

x+(x-5)+(x+10)+(2x+15)+(2x+30)=540°

7x+50=540°

7x=490°

x=70°

step 3

Find all the angles

x=70°

(x-5)=(70-5)=65°

(x+10)=(70+10)=80°

(2x+15)=(2*70+15)=155°

(2x+30)=(2*70+30)=170°

Answer:

[tex]5y^{6}\sqrt{2}[/tex]

Step-by-step explanation:

We want to  simplify:

[tex]\sqrt{50y^{12}}[/tex]

We rewrite as:

[tex]\sqrt{2\times25 \times (y^{6})^2}[/tex]

We split the radical sign to obtain:

[tex]\sqrt{25} \times \sqrt{(y^{6})^2} \times \sqrt{2}[/tex]

Simplify the square root for the perfect squares to get:

[tex]5y^{6}\sqrt{2}[/tex]

Therefore the simplified form is: [tex]5y^{6}\sqrt{2}[/tex]

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

We need two points through which the line passes.

[tex](x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 3,2)[/tex]

Substituting:

[tex]m = \frac {2-4} {3-1} = \frac {-2} {2} = - 1[/tex]

Answer:

[tex]m = -1[/tex]

Answer:

volume  =  (1/3)(area of base)(height)

area of base  =  pi * radius2  =  pi * (10/2)2  =  pi * 52  =  25pi   cm2

volume  =  (1/3)( 25pi )( 9 )   cm3

volume  =  75pi   cm3

volume  ≈  236  cm3  

ANSWER

[tex]Volume = 235.6 {cm}^{3} [/tex]

EXPLANATION

The volume of a cone is calculated the using the formula:

[tex]Volume = \frac{1}{3} \pi {r}^{2} h[/tex]

From the given information the height of the cylinder is, h=9cm.

The diameter of the base is 10cm.

The radius is half of the diameter of the base, r=5cm.

We plug in the values into the formula to get:

[tex]Volume = \frac{1}{3} \times \pi \times {5}^{2} \times 9[/tex]

[tex]Volume = 75\pi {cm}^{3} [/tex]

[tex]Volume = 235.6 {cm}^{3} [/tex]

Answer:

I'm guessing you need this now, So I'm just going to give the answer without the explanation

Step-by-step explanation:

52.5

C. 5 and seventy-six hundredths sorry If I'm wrong, but I'm pretty sure I'm right

please rate my answer

Answer:

Five and seventy six hundredths

Your Welcome :3

Answer:

1st pic: 4

2nd pic: 70

3rd pic: 5

Step-by-step explanation:

Answer:

Point Q is (3 , 4)

Step-by-step explanation:

* Lets revise the rule of the point which divides of a line segment in

 a ratio

- If point (x , y) divides the line segment AB, where A is (x1 , y1) and

 B is (x2 , y2) in the ratio m1 : m2

∴ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ y = [m2(y1) + m1(y2)]/(m1 + m2)

* Now lets solve the problem

- Point Q divides ST in the ratio 5 : 2 where S (-2 , -6) and T (5 , 8)

- To find the coordinates of point Q use the same rule above

# Q is (x , y)

# S is (x1 , y1) and T is (x2 , y2)

# m1 : m2 is 5 : 2

∵ x1 = -2 and y1 = -6

∵ x2 = 5 and y2 = 8

∵ m1 = 5 and m2 = 2

- Substitute these values in the rule

∵ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ x = [2(-2) + 5(5)]/(5 + 2) ⇒ multiply the numbers

∴ x = [-4 + 25]/7 ⇒ add

∴ x = [21]/7 ⇒ Divide

∴ x = 3

* The x-coordinate of Q is 3

∵ y = [m2(y1) + m1(y2)]/(m1 + m2)

∴ y = [2(-6) + 5(8)]/(5 + 2) ⇒ multiply the numbers

∴ y = [-12 + 40]/7 ⇒ add

∴ y = [28]/7 ⇒ Divide

∴ y = 4

* The y-coordinate of point Q is 4

∴ Point Q is (3 , 4)

Answer:

0.98x24=23.52+35.95=59.47     hope im right

Step-by-step explanation:

The total cost of renting the truck for one day if you drive 24 miles is $58.47.

The function notation for the total cost of renting the truck for one day if you drive 24 miles is C(24). The total rental cost can be calculated by multiplying the cost per mile ($0.98) by the number of miles driven (24) and adding the base cost ($35.95). So, the total rental cost would be $35.95 + ($0.98 x 24) = $58.47.

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Answer:

What you have to do is add all of the sums up and put 2 over it. it is 2/20 which is 1/10.

Step-by-step explanation:

in a percent it is 0.1

Can I get brainiest

The probability that Alina selects 2 cans of lemonade is

How to calculate probability?

The given question has concept of conditional probability.

Conditional probability is applied when we have to find the possibility of an event given the another event already occurred.

Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

Here, the first event is selecting the lemonade can and second event is also selecting lemonade can given one lemonade is already selected.

The probability to select 1st lemonade= 7/20

The probability to select 2nd lemonade=6/19

Multiplying them we get:

Probability:7*6/20*19=21/190

Therefore, the probability to select two lemonades is 21/190.

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Answer:

84 ft²

Step-by-step explanation:

Solve for Volume. Volume of a box is:

V = Length (base) x Width (base) x Height (of rectangular prism/square)

Change each measurement to have the same measurement (ft -> in, or vice versa).

Note that 1 ft = 12 in.

6 in = 1/2 ft, because 6/12 = 1/2

Length = 12 ft

Width = 14 ft

Height = 1/2 ft

Solve. Plug in the corresponding number to the corresponding words.

V = 12 x 14 x 1/2

Simplify. Solve.

V = 12 x (14 x 1/2)

V = 12 x (14/2)

V = 12 x 7

V = 84

84 ft² is your answer.

~

Answer:

1,008

Step-by-step explanation:

You multiply all three numbers to get your answer.

Answer:

No

Step-by-step explanation:

0.26*16 + 12.25 = 16.41

16.41 < 16.50

Answer:

No, Vicky should not switch.

Step-by-step explanation:

Vicky's checking account charges a monthly service fee = $12.25

Account also charges per-check fee = $0.26

Vicky writes checks per month = 16

His total monthly charges = 12.25+( 16 ×0.26 )

                                           = 12.25 + 4.16

                                           = $16.41

Another account that charges a $16.50 monthly service fee and no per-check fee.

Comparison between account = 16.50 > 16.41

So Vicky should not switch to another account because it charges more than her current account.

Answer:

Step-by-step explanation:

I think its 823 ppm?

I'm not sure

Final answer:

Jordan spent $14.85 in total, of which $2.85 was spent on snacks. After subtracting the cost of snacks, it's found that she spent $12.00 on bus fares.

Explanation:

The student asked how much Jordan spent on bus fares to and from the zoo if she spent a total of $14.85, including $2.85 on snacks. To find out the amount spent on bus fares, one needs to subtract the cost of the snacks from the total amount spent. Therefore, the calculation would be $14.85 (total spent) - $2.85 (snacks) = $12.00.

Hence, Jordan spent $12.00 on bus fares.

Answer:

2 gallons per mile

Answer:

A) f(x) = -3x+7

Step-by-step explanation:

f(x) is interchangeable with y when writing a function, so the functions are the same.

The function that corresponds to the equation -3x + 7 = y is f(x) = -3x + 7, which maintains the same relationship between x and y as the given equation.

The equation -3x + 7 = y can be rewritten in function notation, which typically uses the format f(x) = some expression involving x. The correct corresponding function is one that maintains the relationship between x and y as displayed in the original equation. Therefore, among the options provided:

The correct answer indicates that the function of x (f(x)) is given by the linear equation -3x + 7.

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Answer:

y = 179x +1999

y = 249x

Step-by-step explanation:

Given:

down payment of cool cars= $1999

monthly lease rate of cool cars= $179

down payment of awesome autos= $0

monthly lease rate of awesome autos= $249

Number of months=x

total amount paid towards the lease after x months=y

Now creating a system of linear equations that describes the total amount, y, paid towards the lease after x months:

the slope intercept form of any linear function is given as y=mx +b

where m= slope  of function and b=y-intercept

In given case, slope m gives the monthly lease rate and y-intercept b gives the down payment.

So the equations for the two linear functions will be:

cool cars:

Putting the values of m=179 and b=1999, we get

y = 179x +1999

awesome autos:

Putting the values of m=249 and b=0, we get

y = 249x !

Answer:

the answer is 1. the trick here is to divide the exponent to 4.

Step-by-step explanation:

i^32 32÷4=8

i

-1

-i

1

Answer:  The required value of the given power of i is 1.

Step-by-step explanation:  We are given to simplify the following power of i :

[tex]P=i^{32}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the value of the imaginary number i(iota) is given by

[tex]i=\sqrt{-1}~~~~~\Rightarrow i^2=-1.[/tex]

From expression (i), we get

[tex]P\\\\=i^{32}\\\\=(i^2)^{16}\\\\=(-1)^{16}\\\\=(1)^8\\\\=1.[/tex]

Thus, the required value of the given power of i is 1.

The lenght of each side is 24cm, 24cm, and 8cm.

In order to solve this problem, we know that the perimeter of a triangle equation is P = a + b + c, where a, b, and c are the sides of the triangle.

The perimeter is 56cm, we can write the equation as follow:

a + b + c = 56cm (1)

If each of the two longer sides of the triangles is three times as long as the shortest side, we can assume:

c = shortest side = x

a = b = longer sides = 3x

Substituting the values in the equation (1):

3x + 3x + x = 56cm

7x = 56cm

x = 56cm/7 = 8cm

c = shortest side = 8cm

a = b = longer sides = 3(8cm) = 24cm

The solution of quadratic equation  [tex]3x^2 + 15x=0[/tex] is x =0 or -5.

Given Equation: [tex]3x^2 + 15x=0[/tex]

Now, factories each term as

3x² = 3 × x × x

15x = 3 × 5 × x

Now, taking the common term 3x as

[tex]3x^2 + 15x=0[/tex]

3 × x × x+ 3 × 5 × x =0

3x (x + 5)=  0

Now, equate each factor to 0 as

3x =0

x= 0/3

x= 0

or, x + 5= 0

x = -5

Thus, the value of x is -5 or 0.

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Answer:

5√2

Step-by-step explanation:

The question is on geometry

The formula for distance between two points is;

[tex]d= \sqrt{(X2-X1)^2 + (Y2-Y1)^2}[/tex]

where d is distance.

Given points;

(0,5)    and   (-5,0) ;

X1=0 ,X2= -5 , Y1= 5, Y2= 0

X2-X1 = -5 - 0= -5

Y2-Y1= 0-5= -5

[tex]d= \sqrt{(-5)^2 + (-5)^2}[/tex]

[tex]d=\sqrt{25+25}[/tex]

[tex]d=\sqrt{50}[/tex]

[tex]d=\sqrt{2*25} =\sqrt{2} *\sqrt{25} =\sqrt{2} *5\\\\\\\\d=5\sqrt{2}[/tex]

Answer:

[tex]d=5\sqrt{2}[/tex]

Step-by-step explanation:

Given : (0, 5) and (-5, 0)

To Find : Distance between the given points

Solution:

We will use distance formula :

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(0,5)[/tex]

[tex](x_2,y_2)=(-5,0)[/tex]

Substitute the values in the formula .

[tex]d=\sqrt{(-5-0)^2+(0-5)^2}[/tex]

[tex]d=\sqrt{(-5)^2+(-5)^2}[/tex]

[tex]d=\sqrt{25+25}[/tex]

[tex]d=\sqrt{50}[/tex]

[tex]d=5\sqrt{2}[/tex]

Hence the distance between the given points is 5√2 units

Answer:

8 in

Step-by-step explanation:

Area of a square is given by

A = s^2 where s is the side length

64 in^2 = s^2

Taking the square root of each side

sqrt(64 in^2) = sqrt(s^2)

8 in =s

Answer:

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side length

We have the area

[tex]A=64\ in^2[/tex]

Substitute:

[tex]s^2=64\to s=\sqrt{64}\\\\s=8\ in[/tex]

[tex]\sqrt{64}=8[/tex] because [tex]8^2=64[/tex]

Answer:

Step-by-step explanation:

C.35%

If you divide the number of hearts drawn by the number of total draws you get your answer.

14/20=0.35

Answer:

x = 30.

Step-by-step explanation:

The angle next to the 60 degree angle = 180 - 60 = 120 degrees (adjacent angles are supplementary).

Let the angle  just above 3x be y.  The sum of 3x and y = 120 degrees (as opposite angles of a parallelogram are equal).

We have the following equations.

3x + y = 120............(1)

2x + 90 + y = 180

2x + y = 90.............(2)

Subtracting, (1) - (2):

x = 30.

You start with the equation V = IR, plug the value 0.5 for I and you have

V = 0.5*R

So, the first three options are equivalent and correct.

V=IR

And current, Ampere is given as 0.5 so substituting it back in the main equation gives V = 0.5R