At a certain fast food restaurant, 77.5% of the customers order items from the value menu. If 14 customers are randomly selected, what is the probability that at least 9 customers ordered an item from the value menu

The expansion of the series is 16 + 64 + 256 + 1024

The series is given as:

[tex]\sum\limits^4_{n=1} 4^{n+1}[/tex]

When n = 1, we have:

[tex]4^{n+1} = 4^{1+1} = 16[/tex]

[tex]4^{n+1} = 4^{2+1} = 64[/tex]

[tex]4^{n+1} = 4^{3+1} = 256[/tex]

[tex]4^{n+1} = 4^{4+1} = 1024[/tex]

Hence, the expansion of the series is 16 + 64 + 256 + 1024

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Answer:

C). 16 + 64 + 256 + 1,024

Step-by-step explanation:

I took the test and got it right :)

The measure of n of the sector with the given area is: 100°

The area of a sector of a circle = ∅/360 × πr².

We are given that:

Area of the sector = 40π

Radius (r) = 12 units

∅ = n°

Plug in the values and solve for n

40π = n/360 × π(12²)

40π = n/360 × π144

Divide both sides by 144π

40π/144π = n/360 × 144π/144π

40/144 = n/360

40(360) = n(144)

14,400/144 = n

n = 100°

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Answer:

10 eggs

Step-by-step explanation:

We need to work out the price per unit :

12 eggs = rs 192

1 egg = rs 192÷12

1 egg = rs 16

? egg = rs 160

16×? = 160

? = 160÷16

? = 10

So our final answer will be 10 eggs

Answer:

10

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Just do it in reverse and reverse "roles" multiplying Becomes Devidng and Devidng Becomes multiplying:

80/2=40, 40x5=200

Answer:

y=-(2/3)x -9

Step-by-step explanation:

shuffle the equation so that y is alone in left hand side

The coefficient of x in the right hand side is the slope of line and the other term in right hand side is constant term

The slope-intercept form of the given equation will be y = -2x/3 - 9.

The meaning of slope-intercept form  is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Given an equation, 8x +12y = -108

Converting in  slope-intercept form,

12y = -108 - 8x

y = -2x/3 - 9

Hence, the slope-intercept form of the given equation will be

y = -2x/3 - 9.

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Answer:

One dollar

Step-by-step explanation:

So you divide 8.70 by 87 to get 0.10. So then you multiply 0.10 by 10 to get a dollar

Sending 87 text messages cost $8.70. Sending 10 text messages would cost $1.00.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that,

Cost to send 87 text messages: $8.70

Number of text messages: 87

To find out how much it would cost to send 10 text messages,

Use a proportion.

If it cost Jose $8.70 to send 87 text messages,

Set up the proportion:

$8.70 / 87 messages = x / 10 messages

To solve for x,

Cross-multiply and divide:

($8.70 x 10) / 87 = $1.00

Therefore, it would cost $1.00 to send 10 text messages.

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The distance from the base of the tree to the tallest would be 14.21 cm

X1 = 8 feet

y1 = 16 feet

x2 = 11 feet

y2 = 9 feet

To proceed with the solution we have to

We have to solve for the shorter tree

[tex]\sqrt{(y2 -y1)^2 + (x2-x1)^2} \\\\= \sqrt{9-0^2 + 11-0^2}[/tex]

= 9² + 11²

= √81 +121

= 14.21

√8² + 16²

= √64 +256

= 17.89

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Answer: On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).

Step-by-step explanation:

When x=1, f(x)=3. So, it passes through (1,3).

So, everything is eliminated except for option (4).

Answer:

D!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

Answer:

x-intercept is 6 [(6, 0) is the point]

y-intercept is 4 [(0, 4) is the point]

Step-by-step explanation:

To find the x-intercept, we can set y equal to 0 and solve for x. This works because the x-intercept is the point of the graph where the line crosses the x-axis (meaning y is equal to 0 at this point. So, if we set y=0 and solve, we get this:

[tex]2x+3(0)=12\\2x=12\\x=6[/tex]

So, the x-intercept is 6; if it is written as a point, it is (6, 0) since y is 0

To find the y-intercept, we can set x equal to 0 and solve for y. This works the same way - x is equal to 0 at the point where the line crosses the y-axis. If we set x=0 and solve, we get this:

[tex]2(0)+3y=12\\3y=12\\y=4[/tex]

So, the y-intercept is 4; if it is written as a point, it is (0, 4) since x is 0

Answer:

-7, 8.

Step-by-step explanation:

x^2 - x - 56 = 0

Let's see if we can factor this function:

We need 2 numbers whose product is -56 and whose sum is -1 ( which is the coefficient of x).

They are  -8 and 7 , so the factors are:

(x - 8)(x + 7) = 0

x - 8 = 0 giving x =  8 and

x + 7 = 0 giving x = -7.

The zeros are -7, 8

The large rectangle is 8/3 times bigger than the small rectangle.

Area of large rectangle will be:

= 4x(2x - 2)

= 8x² - 8x

Area of small rectangle will be:

= (3x - 3)x

= 3x² - 3x

The ratio will be:

= 8x² - 8x/3x² - 3x

= 8(x² - x)/3(x² - x)

= 8/3

The large rectangle is 8/3 times bigger than the small rectangle.

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Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 3, 4 )

m = [tex]\frac{4-2}{-3-3}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]

[tex]\small\mathbb\green{slope=M= \frac{y2 - y1}{x2 - x1} = \frac{4 - ( - 2)}{3 - 3} \: = \frac{6}{0} \: = ∞} [/tex]

Step-by-step explanation:

3x° + 2x° = 180° ( supplementary angle )

5x° = 180°

x = 180° / 5

x = 36°

[tex]...[/tex]

Answer:

The first choice

Step-by-step explanation:

You are setting up as you read it.  The left side has 5 x and 6 units, so you would set up 5 positive x times and 6 positive unit tiles.  On the the right you are setting up 4 positive x tiles and 3 negative unit tiles.  It is not asking you to solve with the algebra tiles, just to set it up.

E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15

Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.

P(F|E)=P(E and F)÷P(E)

It is given that P(E)=0.3,P(F|E)=0.5

Using Bayes' formula,

P(F|E)=P(E and F)÷P(E)

Rearranging the formula,

⇒P(E and F)=P(F|E)×P(E)

Substituting the given values in the formula, we get

⇒P(E and F)=0.5×0.3

⇒P(E and F)=0.15

∴The correct answer is 0.15.

If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.

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The solution of the given exponential equation is 0.688.

Given that Mike is working on solving the exponential equation 37ˣ = 12.

An exponential equation is an exponential equation where the power (or)  part of the exponent is a variable.

firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:

aˣ = y

logₐy = x

Now, we will apply this transformation to our equation and we get

log₃₇12=x

Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:

x=log12/log37

So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:

x≈1.079/1.568

x=0.688

Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.

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Answer:

2/50=1/25

Step-by-step explanation:

2 aces are removed hence 2 aces are left out of 50 cards

Answer:

n^3 + 1.

Step-by-step explanation:

Each term is 1 more than a perfect cube.

2 = 1^3 + 1

9 = 2^3 + 1

28 = 3^3 + 1

65 =  4^3 + 1

126 = 5^3 + 1

So the explicit formula is n^3 + 1.

The explicit formula that generates the given sequence is indeed aₙ = n³+1.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The nth term of the sequence can be obtained by substituting n = 1, 2, 3, ... into the expression n³+1:

a₁ = 1³+1 = 2

a₂ = 2³+1 = 9

a₃ = 3³+1 = 28

a₄ = 4³+1 = 65

a₅ = 5³+1 = 126

Hence, the explicit formula that generates the given sequence is indeed aₙ = n³+1.

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The survey shows that adding up the daily media use figures to obtain a report of weekly media use leads to the staggering number of more than 60 hours a week of media use by 11- to 14-year-olds.

It should be noted that a survey simply means a list of questions that are used to get information about a group.

In this case, the daily media use figures to obtain a report of weekly media use leads to the staggering number of more than 60 hours a week of media use by 11- to 14-year-olds.

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The expected value of the number of people selected before and including the first time a woman has a turn is 1.6667 and the standard error is 0.7454.

It should be noted that the expected value will be:

1[p(x = 1)] + 2[p(x = 2)] + 3[p(x = 3)]

= 1(0.5) + 2(0.3333) + 3(0.1667)

= 1.6667

Var(X) = E(X²) - E(X)2

= 3.3335 & (1.6667)²

= 0.555611

The standard error will be:

= ✓0.555611

= 0.7454

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The correct answer is 7.

A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that collectively make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.

I am aware that this query's equation is,

6b + 6 = 48

subtract 6 from both side in the equation.

6b + 6 - 6 = 48- 6

6b = 42

now, divide by 6 from both side in the equation.

6b/6 = 42/6

b = 7.

Therefore, the correct answer is 7.

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I understand this is the question.

Oksana wrote the equation below on the whiteboard.

6 b + 6 = 48

What is the value of b?

(a)4

(b)7

(c)8

(d)9

Answer:

8, 10, 14

Step-by-step explanation:

1. 8² + 10² = 164 and 14² = 196, so this works.

2. 9² + 12² = 15² = 225, so this is a right triangle.

3. 10² + 14² = 296 and 17² = 289, so this is an acute triangle.

4. 12² + 15² = 369 and 19² = 361, so this is an acute triangle.

Answer:

a

Step-by-step explanation:

The linear functions that match the following graph are given by:

A linear function is modeled by:

y = mx + b

In which:

The system of equations in this problem is composed by two lines.

The decaying line goes though (-2,4) and (2,-4), hence the slope is given by:

m = (-4 - 4)/(2 - (-2)) = -2

Hence:

y = -2x + b

When x = -2, y = 4, hence we find b as follows:

4 = -2(-2) + b

b = 0.

Hence:

y = -2x -> 2x + y = 0.

The increasing line goes though (1,-2) and (2,3), hence the slope is given by:

m = (3 - (-2))/(2 - 1) = 5

Hence:

y = 5x + b

When x = 1, y = -2, hence we find b as follows:

-2 = 5 + b

b = -7.

Hence:

y = 5x - 7.

-5x + y = -7.

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Answer:

Your answer should be 52!!

Step-by-step explanation:

Work included on the picture below.

Answer:

27.183, 27.2

Step-by-step explanation:

First, do the formula for the triangle:

[tex]\frac{1}{2}[/tex] x 4.1 x 2.6 = 5.33

Next, multiply that by the base side:

5.33 x 5.1 = 27.183

Answer:

1/2 x 4.1 x 2.6 = 5.33

5.33 x 5.1 = 27.183

Rounding off to nearest tenth = 27.2 m^3

The area of the patio is 192 [tex]m^{2}[/tex]

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Length of swimming pool=18 m

Width of swimming pool=8 m

Area of swimming pool= 18*8 = 144[tex]m^{2}[/tex]

Width of patio=3m

Total length of swimming pool=18+2(3)=24 m

Total width of swimming pool=8+2(3)=14 m

Total area=24*14=336 [tex]m^{2}[/tex]

Area of patio= total area - Area of swimming pool

                     =336-144

                     =192 [tex]m^{2}[/tex]

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the PERT weighted average is 9 days

PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.

The formula for finding the PERT weighted average is given as;

PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6

We have;

Substitute the values into the formula

PERT weighted average  = [tex]\frac{6 + 4(8) + 16 }{6}[/tex]

PERT weighted average  = [tex]\frac{54}{6}[/tex]

PERT weighted average  = 9 days

Thus, the PERT weighted average is 9 days

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Answer:

36

Step-by-step explanation:

Chad's original garden is 3 ft x 8 ft.

original area = 3 x 8 = 24 square feet

Chad's super Chadly new garden is 3 feet wider, and 2 feet longer.

new width = 3 + 3 = 6

new length = 8 + 2 = 10

new Area = 6 x 10 = 60 square feet

To find how much larger the new area is, subtract the original area.

60 – 24 = 36 square feet

Answer:

Step-by-step explanation:

Each intercept is found by solving for the variable after the other variable is set to zero.

Set y = 0 and solve for x:

  -3x = 66

  x = 66/(-3) = -22 . . . . . divide by the coefficient of x

The x-intercept is (-22, 0).

Set x = 0 and solve for y:

  11y = 66

  y = 66/11 = 6 . . . . . . . . divide by the coefficien tof y

The y-intercept is (0, 6).

__

Additional comment

The given equation is in standard form (almost). This form makes it easy to find the intercepts by dividing the constant by the variable's coefficient, as we did above.

(We say "almost" standard form because the leading coefficient is negative. It would be positive in standard form: 3x -11y = -66.)

Answer: (-22,0) and (0,6) in order

Step-by-step explanation:

x-intercept means point of graph that intersects the x-axis and y=0

y-intercept means point of graph that intersects the y-axis and x=0

So the x-intercept is -3x + 0 = 66 as y = 0

x = -22 so the coordinate is (-22,0)

The y-intercept is 0 + 11y = 66 as x = 0

y = 6 so the y-intercept is (0,6)

it is true that a linear expression does not have a squared variable.

The following are the forms of a linear expression

y = mx + c

Ax + By = C

x = a

Notice that none of the above expressions have a squared variable

This means that, a linear expression does not have a squared variable.

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