Eighty-five mall customers were randomly surveyed across the state to determine if the live entertainment provided had increased the amount of money they spent. Can the probability be found by using the binomial probability formula?

Answer:

The probability is 1/7 or 14.29%

Step-by-step explanation:

In order to find this, divide the number of marbles that are green by the total number.

8/56 = 1/7 = 14.29%

Answer:

I'm not sure if those are the answer choices but your answer should be 5/2

Hope this helps

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let b represent the number of boxes of cookies sold the first week. Then b+5 boxes were sold the second week, and 2(b+5) boxes were sold the third week. The total sold was ...

  b +(b+5) +2(b+5) = 431

  4b +15 = 431 . . . . . . simplify

  b = (431 -15)/4 = 104 . . . . . subtract 15, divide by the coefficient of b

First week: b = 104

Second week: b+5 = 109

Third week: 2(b+5) = 218

Answer:

$400,000

Step-by-step explanation:

We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other.

[tex]\frac{60}{100}=\frac{240000}{x}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

60x=100(240,000)

60x=24,000,000

y=400,000

Answer:

$400,000

Step-by-step explanation:

Answer:

t = 6 4/25 hours

Step-by-step explanation:

The formula to find out how long it takes them to do the job is

1/m  + 1/ a  = 1 /t

where m is the time for Matthew to do the job

a is the time for Arianna to do the job

and t is the time for them to do the job together

m = 14 hours

a = 11 hours

Substituting what we know

1/14 + 1/11 = 1/t

Multiplying by 154t (14*11*t) so we can clear the fractions

154t*(1/14 + 1/11) = 1/t* 154t

 11t + 14t = 154

Combine like terms

25t = 154

Divide by 25

t = 154/25

t = 6 4/25 hours

so, if you checked the link above, you know what we'll be doing, lemme run through it without much fuss.

[tex]\bf \stackrel{\textit{firstly some grouping}}{(x^2-4x)+(y^2+4y)=0}\implies (x^2-4x+\boxed{a}^2)+(y^2+4y+\boxed{b}^2)=0 \\\\[-0.35em] ~\dotfill\\\\ 2\cdot x\cdot \boxed{a}=4x\implies \boxed{a}=\cfrac{4x}{2x}\implies \boxed{a}=2 \\\\\\ 2\cdot y\cdot \boxed{b}=4y\implies \boxed{b}=\cfrac{4y}{2y}\implies \boxed{b}=2[/tex]

now, let's recall, we're simply borrowing from our very good friend Mr Zero, 0, so if we add whatever, we also have to subtract whatever.

[tex]\bf (x^2-4x+2^2-2^2)+(y^2+4y+2^2-2^2)=0 \\\\\\ (x^2-4x+2^2)+(y^2+4y+2^2)-4-4=0 \\\\\\ (x-2)^2+(y+2)^2-8=0\implies (x-2)^2+(y+2)^2=8 \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-2)^2+(y+2)^2=(\sqrt{8})^2\qquad \impliedby radius=\sqrt{8}[/tex]

Answer:

144%

Step-by-step explanation:

We are told that Linnea's company's revenue in 2017 is 36/25 of its revenue in 2016..

To find the Linnea's company's revenue in 2017 as a percent of its revenue in 2016, we will have to figure out 36 is what percent of 25.    

[tex]\text{Percent}=\frac{36}{25}\times 100[/tex]  

[tex]\text{Percent}=36\times 4[/tex]      

[tex]\text{Percent}=144[/tex]  

Therefore, Linnea's company's revenue in 2017 is 144% of its revenue in 2017.

Answer:

Perimeter of the square MATH = 100.

Step-by-step explanation:

Given that MATH is a square, it means all sides would be equal to each other.

Given MA = 2x - 5 and AT = x + 10.

we know all sides are equal, so MA = AT.

2x - 5 = x + 10

2x = x + 10 + 5

2x = x + 15

2x - x = 15

x = 15

So, AT = x + 10 = 15 + 10 = 25.

Now the perimeter would be (MA + AT + TH + HM) = 4*AT = 4*25 = 100.

Hence, option D is the correct answer i.e. 100.

Answer:

100

Step-by-step explanation:

Sides of a square are congruent.

2x – 5 = x + 10

x = 15

Sides = 2(15) – 5 = 25

Perimeter = 25 + 25 + 25 + 25 = 100

Answer:

161

Step-by-step explanation:

We will use the math operation addition to find last year's number of floats. We know this year was 127 and was fewer than 34. So 127+34=last year's floats.

127+34=161

Answer: g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96 which is choice C

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

Explanation:

Given roots: -2, 4, 4, 3

Based on that, we know that x = -2, x = 4, x = 4, and x = 3. The repeat x value of 4 is needed to help deal with a double root (multiplicity 2)

x = -2 leads to x+2 = 0, so (x+2) is one factor

x = 4 leads to x-4 = 0, making (x-4) another factor. We have two copies of (x-4) as a factor

x = 3 leads to x-3 = 0 so (x-3) is the last factor

Overall, the four factors are: (x+2) and (x-4) and (x-4) and (x-3)

Use the distributive property to expand everything out

g(x) = (x+2)(x-4)(x-4)(x-3)

g(x) = ( (x+2)(x-4) ) * ( (x-4)(x-3) )

g(x) = ( x^2 - 2x - 8 ) * ( x^2 - 7x + 12 )

g(x) = x^2( x^2 - 7x + 12 ) - 2x( x^2 - 7x + 12 ) - 8( x^2 - 7x + 12 )

g(x) = x^4 - 7x^3 + 12x^2 -2x^3 + 14x^2 - 24x - 8x^2 + 56x - 96

g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96

which shows how I got choice C as the answer

Answer:

g(-1) = -1

g(1) =5

Step-by-step explanation:

g(x) = x^3 + (x + 1)^2

If x=-1  substitute this into the equation

g(-1) = (-1) ^3 + (-1+1)^2

g(-1) = 1+0  =-1

If x=1  substitute this into the equation

g(1) = (1)^3 + (1+1)^2 = 1+2^2 = 1+4 =5

Hi There!

--------------------------------------

Function: g(x) = x³ + (x + 1)²

Substitute: -1

Substitute: g(-1) = -1³ + (-1 + 1)²

Remember to follow PEMDAS.

Parenthese's: g(-1) = -1³ + (0)²

Exponents: g(-1) = -1 + 0

Simplify: g(-1) = -1

--------------------------------------

Function: g(x) = x³ + (x + 1)²

Substitute: 1

Substitute: g(1) = 1³ + (1 + 1)²

Remember to follow PEMDAS.

Parenthese's: g(1) = 1³ + (2)²

Exponents: g(1) = 1 + 4

Simplify: g(1) = 5

--------------------------------------

Hope This Helps :)

Answer:

c

Step-by-step explanation:

Answer:

770 high-quality songs were downloaded

Step-by-step explanation:

A web music store offerst two versions:

There were 1290 for a total download size of 4403MB.

According to the information above, we have the following system of equations:

A + B =1290

2.1A + 4.3B = 4403

Where 'A' referst to the number of Standard songs and 'B' refers to the number of High Quality songs.

Solving the sistem of equations we get that:

A + B =1290 ⇒ A = 1290 - B

2.1A + 4.3B = 4403 ⇒ 2.1(1290 - B) + 4.3B = 4403

⇒ 2709 - 2.1B + 4.3B = 4403 ⇒ 2.2B = 1694 ⇒ B=770

Now, let's find the value of 'A':

A + B =1290 ⇒ A = 1290 - 770 ⇒ A = 520.

Therefore, 770 high-quality songs were downloaded.

Answer:

I think that there is a part of your question that is missing maybe? What is the method shown?

Step-by-step explanation:

Answer:

35 mi^2

Step-by-step explanation:

Area of parallelogram = base x height

7 x 5 = 35

Answer:

Area = 35 mi^2

Step-by-step explanation:

Area = b*h

The base is 7 mi

The height is 5 mi

Area = 7*5

Area = 35 mi^2

Answer:

114

Step-by-step explanation:

The first term (a1) = 1 + 3 = 4   (substituting 1 for i)

The last term (L) = 12 + 3 = 15

So the sum of the 12 terms = (n/2)(a1 + L)

= (12/2) (4 + 15)

= 6 * 19

= 114   (answer)

The value of the summation of arithmetic progression is 114

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the number of terms n = 12

Let the first term a = i + 3

when i = 1

a = 4

So , the first term of the arithmetic progression is a = 4

The second term a₁ = i + 3

when i = 2

a = 5

Now , the common difference d = second term - first term

Common difference d of the arithmetic progression = 5 - 4 =1

So , d = 1

Now , the sum of n terms of an AP is given by

Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Substituting the values in the formula , we get

Sₙ = ( 12/2 ) [ ( 2 x 4 ) + ( 12 - 1 ) x 1 )

Sₙ = 6 [ 8 + 11 ]

Sₙ = 6 x 19

Sₙ = 114

Therefore , the value of Sₙ is 114

Hence , The value of the summation of arithmetic progression is 114

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Answer:

She spend $30

A flan cost $22.5

Step-by-step explanation:

Let's call x her initial money

After she bought the flan and two chicken pies she has $24.

She spend (5/9)*x in the flan and two chicken, then

x - (5/9)*x = 24

(4/9)*x =  24

x = 24*(9/4)

x = $54

She spend (5/9)*54 = $30

Let's call f the flan cost

Each chicken pie cost 1/6 as much as the flan, then:

30 = f + (1/6)*f + (1/6)*f

30 = (4/3)*f

f = 30*(3/4)

f = $22.5

Victoria had $54 in total. She spent $30 on the flan and two chicken pies altogether. The cost of the flan is $22.50.

The problem presents a situation where Victoria spends a fraction of her money on a flan and two chicken pies. Victoria has $24 left after these purchases. To solve this, we must first calculate the total amount of money Victoria had before making her purchases. Given that 5/9 of her money was spent on the flan and two chicken pies, and she has $24 remaining, we can set up the following equation where x represents the total amount of money:

x - (5/9)x = $24

This simplifies to:

(4/9)x = $24

By multiplying both sides of the equation by (9/4), we find the total amount of money Victoria had:

x = $24 \times (9/4)

x = $54

Victoria spent 5/9 of $54 on the flan and two chicken pies, which is:

(5/9) \times $54 = $30

If each chicken pie costs 1/6 the cost of the flan, we can let f represent the cost of the flan and (1/6)f the cost of each chicken pie. We have 2 chicken pies, so the equation would be:

f + 2 \times (1/6)f = $30

This simplifies to:

f + (1/3)f = $30

Combining like terms, we get (4/3)f = $30 which leads to:

f = $30 \times (3/4)

f = $22.50

So the cost of the flan is $22.50.

2x² = 28 - x

2x²+x-28=0

2x²+8x-7x-28=0

2x(x+4)-7(x+4)=0

(x+4)(2x-7)=0

(2x-7)(x+4)=0

B.) (2x - 7)(x + 4) = 0

Answer: 70%

Step-by-step explanation:

w - width

2w + 5 - length

w + w + (2w + 5) + (2w + 5) = 6w + 10 - perimeter

34 cm - perimeter

The equation:

6w + 10 = 34    subtract 10 from both sides

6w = 24    divide both sides by 6

w = 4 cm

2w + 5 = 2(4) + 5 = 8 + 5 = 13 cm

Answer:

3/4

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−5, −4), B(−7, 3) and C(3, −2) to the image triangle A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25) and C' (2.25, −1.5).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A(−5, −4) ---> A' (−3.75, −3) = [tex]\frac{-3.75}{-5} , \frac{-3}{-4}=(\frac{3}{4} , \frac{3}{4})[/tex]

B(−7, 3) ---> B' (−5.25, 2.25) = [tex]\frac{-5.25}{-7} , \frac{2.25}{3}=(\frac{3}{4} , \frac{3}{4})[/tex]

C(3, −2) ---> C' (2.25, −1.5) = [tex]\frac{2.25}{3} , \frac{-1.5}{-2}=(\frac{3}{4} , \frac{3}{4})[/tex]

Therefore, the scale factor of the dilation is 3/4.

Answer:

16

D is correct.

Step-by-step explanation:

Coefficient: The coefficient is a number front of variable.

[tex]Expression: x^2+16y[/tex]

In the given expression there are two terms

x² and 16y

First term: x²

The coefficient of x² is 1

Second term: 16y

The coefficient of 16y is 16

Hence, The coefficient of 16 of the given expression.

Answer:

P = 8x+4

Step-by-step explanation:

The perimeter of a rectangle is found by using the formula

P = 2(l+w)

We know l = 3x+3 and

w = x-1

Substitute these values in

P =2(3x+3 + x-1)

Combine like terms

P = 2(4x+2)

Distribute the 2

P = 8x+4

Answer:

1. [tex]\Delta ADC\sim \Delta RTS[/tex] because [tex]\angle A\cong \angle R[/tex], [tex]\angle C\cong \angle S[/tex] and [tex]\angle D\cong \angle T[/tex]

Step-by-step explanation:

We have been given two triangles [tex]\Delta ADC[/tex] and [tex]\Delta RTS[/tex]. We are asked to find the relationship between these triangles.

By angle sum property let us find measure of angle C of triangle ADC.

[tex]m\angle C+m\angle D+m\angle A=180^{o}[/tex]

[tex]m\angle C+51.2^{o}+96.5^{o}=180^{o}[/tex]

[tex]m\angle C+147.7^{o}=180^{o}[/tex]

[tex]m\angle C=180^{o}-147.7^{o}[/tex]

[tex]m\angle C=32.3^{o}[/tex]

Let us find measure of angle T of triangle RTS.

[tex]m\angle T+m\angle R+m\angle S=180^{o}[/tex]

[tex]m\angle T+96.5^{o}+32.3^{o}=180^{o}[/tex]

[tex]m\angle T+128.8^{o}=180^{o}[/tex]

[tex]m\angle T=180^{o}-128.8^{o}[/tex]

[tex]m\angle T=51.2^{o}[/tex]

We can see that [tex]m\angle C=m\angle S[/tex], [tex]m\angle A=m\angle R[/tex] and [tex]m\angle D=m\angle T[/tex]. Therefore, [tex]\Delta ADC\sim \Delta RTS[/tex] and 1st option is the correct choice.

Answer:

Width of rectangular storage room= 5 feet.

Step-by-step explanation:

Let x be the width of storage room.

We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.

We are also given that the area of the room is 40 square feet.

Since the area of a rectangle is length times width.

[tex]\text{Area of rectangle}=\text{Length* Width}[/tex]

Let us substitute our given values in area formula.

[tex]40=x*(x+3)[/tex]

Upon distributing x we will get,

[tex]40=x^2+3x[/tex]

[tex]x^2+3x-40=0[/tex]

Now let us factor out our quadratic equation using splitting the middle term.

[tex]x^2+8x-5x-40=0[/tex]

[tex]x(x+8)-5(x+8)=0[/tex]

[tex](x+8)(x-5)=0[/tex]

[tex]x+8=0[/tex] or [tex]x-5=0[/tex]

[tex]x=-8[/tex] or [tex]x=5[/tex]

Since width can not be negative, therefore, the width of rectangle will be 5 feet.

Let us verify our answer.

Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.

Given: Area=40 square feet.

5*8=40.

Hence, width of rectangular storage room is 5 feet.

The width of the rectangular storage room, considering it is 3 feet shorter than the length and the area is 40 square feet, is 5 feet.

The subject of this question is Mathematics and it is typically taught in Middle School. The problem describes a rectangle where the length is 3 feet longer than the width and the area is 40 square feet. The width is x and the length is x + 3 (since it is 3 feet longer). The area of a rectangle is defined as length times width, which can be expressed as 40 = x(x + 3), or x² + 3x - 40 = 0. This can be solved as a quadratic equation. The solutions of this equation are x = 5 and x = -8. But, since dimensions cannot be negative, the width of the room is 5 feet.

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Answer:  12.0 %

Step-by-step explanation:

Since according to the question,

The initial price of the chair ( Marked price) = 36.50

And, After the discount the price of the chair = 32.12

Thus, the discount on the price = 36.50 - 32.12 = 4.38

Therefore the discount percentage = [tex]\frac{discount}{marked price} \times 100[/tex]

=  [tex]\frac{4.38}{36.50} \times 100[/tex]

= [tex]\frac{438}{36.50}[/tex]

= 12 %

Thus, the percentage of discount = 12.0 %

Step-by-step explanation:

To find whether the rates are equivalent or not, we will use proportions.

[tex]\frac{126\text{ points}}{3\text{ games}}=\frac{210\text{ points}}{5\text{ games}}[/tex]

Let us simplify our fractions.

[tex]42\frac{\text{ points}}{\text{game}}=42\frac{\text{ points}}{\text{game}}[/tex]

We can see that both unit rates are same, therefore, the rates are equivalent and equal to 42 points per game.