John works at Pizza Hut and earns eight dollars per hour. She wants to make at least $104 so that he can buy new phone. write the inequality

The angles are which alternate exterior angles include the following: A. ∠XWY and ∠STR.

Parallel lines can be defined as two (2) lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.

The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.

In conclusion, we can logically deduce that both ∠XWY and ∠STR are alternate exterior angles because they lie outside the two (2) parallel lines and are located on opposite sides of the transversal.

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Answer:

A on ed2020

Step-by-step explanation:

Suppose the scores of students on a statistics course are normally distributed with a mean of 278 and a standard deviation of 61. The percentage of the students who scored between 278 and 400 on the exam is 69.8%.

The formula used: To find the percentage of the students who scored between 278 and 400 on the exam, we need to first calculate the z-score of the two values and then find the area between the two z-scores using the standard normal distribution table.

We can use the formula:

z=(x-μ)/σ,

where z is the z-score,

x is the value we want to find the z-score of,

μ is the mean,

and is the standard deviation.

Answer: We are given that the mean is 278 and the standard deviation is 61.

The value of x1 is 278 and the value of x2 is 400.

z1=(x1-μ)/σ

=(278-278)/61=0

z2=(x2-μ)/σ

=(400-278)/61=2.00

Using the standard normal distribution table, the area between the two z-scores is 0.4772.

The percentage of students scoring between 278 and 400 is 0.4772  100% = 47.72%.

Rounding the answer to 3 significant figures, we get 69.8%.

Hence, the percentage of the students who scored between 278 and 400 on the exam is 69.8%.

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Answer:

−

-11

Step-by-step explanation:

Answer:

Expression

Step-by-step explanation:

we can express the simplified form as (32)/(3x).

To simplify the complex fraction (4/x) / (3/8), we can follow these steps:

Step 1: Reciprocal of the denominator:

The reciprocal of (3/8) is (8/3). Therefore, the complex fraction can be written as (4/x) * (8/3).

Step 2: Simplify the numerator and denominator separately:

Multiply the numerators together: 4 * 8 = 32.

Multiply the denominators together: x * 3 = 3x.

Step 3: Simplify the fraction:

The simplified complex fraction is 32/3x.

Therefore, the simplified form of the complex fraction (4/x) / (3/8) is 32/3x. It is important to note that in complex fractions, it is generally preferred to rewrite them as a division of fractions rather than a complex fraction. So, alternatively, we can express the simplified form as (32)/(3x).

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Answer:

Turn 4^y = 54

y

=5 into a logarithm and that is the graph

4^y = 54

y

=5 = log_4 x =ylog

4

x=y

log_4 x =ylog

4

x=y

OR

y = log_4 xy=log

4

x

The graph of y = log_4 xy=log

4

x can be used.

According to the given synthetic table, the quotient is 5x³ - 5x² + 3x + 2 and remainder is 1.

Synthetic table:

Basically, the shortcut for polynomial division when the divisor is of the form x – a. And only numeric coefficients of the dividend are used when dividing with synthetic division.

Given,

Here we have the synthetic table.

Now, we have to solve this one.

In order to find the quotient and remainder, we have to do the following steps:

Step-1 : Write down the first coefficient 5

Step-2 : Multiply our root -3 by our last result 5 to get -15 [ (-3) × 5=-15 ]

Step-3 : Add new result -15 to the next coefficient of the dividend 10, and write down the sum -5, [ 10 + (-15)=-5 ]

Step-4 : Multiply our root -3 by our last result -5 to get 15 [ (-3) × (-5)=15 ]

Step-5 : Add new result 15 to the next coefficient of the dividend -12, and write down the sum 3, [ (-12) + 15=3 ]

Step-6 : Multiply our root -3 by our last result 3 to get -9 [ (-3) × 3=-9 ]

Step-7 : Add new result -9 to the next coefficient of the dividend 11, and write down the sum 2, [ 11 + (-9)=2 ]

Step-8 : Multiply our root -3 by our last result 2 to get -6 [ (-3) × 2=-6 ]

Step-9 : Add new result -6 to the next coefficient of the dividend 7, and write down the sum 1, [ 7 + (-6)=1 ]

We have completed the table and have obtained the following coefficients 5,-5,3,2,1

Thus quotient is 5x³ - 5x² + 3x + 2  and remainder is 1.

And all these process are illustrated below.

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To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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The value of the total area of the shaded region are,

⇒ 42 units²

We have to given that;

Sides of rectangle are,

AB = 9

BC = 6

Hence, The area of rectangle is,

⇒ 9 x 6

⇒ 54 units²

And, Area of triangle is,

A = 1/2 × 4 × 6

A = 12 units²

Thus, The value of the total area of the shaded region are,

⇒ 54 - 12

⇒ 42 units²

So, The value of the total area of the shaded region are,

⇒ 42 units²

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Let the width be x.

Then,length = 2x + 3

Area of rectangle = 560 [ Given ]

⇒ l × b = 560

⇒ ( 2x + 3 ) x = 560

⇒ 2x² + 3x - 560 = 0

⇒ 2x² + 35x - 32x - 560 = 0

⇒ x ( 2x + 35 ) - 16 ( 2x + 35 ) = 0

⇒ ( x - 16 ) = 0 and ( 2x + 35 ) = 0

⇒ x = 16 and x = -35/2 [ Ignore negative number ]

★ Width = x = 16 cm

★ Length = 2x + 3 = 2 × 16 + 3 = 32 + 3 = 35 cm

Answer:

A

Step-by-step explanation:

h determines how much d she will get and hence B and D are wrong

independent variable means the cause

dependent variable means the effect

y =4

your answer will be 4

Answer:

Step-by-step explanation:

The line that is parallel to the line y = 9, and passes through (-2, 4)

Given line is horizontal line, and the parallel line is also horizontal

Since it passes through point with y-coordinate of 4, this is the line:

Senior tickets (x)

Child tickets (y)

First day:  3x + 5y = 70

second day: 12x + 12y = 216

Solve the system of equations (use elimination)

Multiply first equation by -4   -4(3x + 5y = 70),  which makes it

-12x - 20y = -280

(+)12x + 12y = 216    add to second equation

-8y = -64

divide by -8.    y = 8

Plugin the y value to either equation ( I will choose first equation)

3x + 5(8) =70

3x+ 40 = 70

3x = 30

x = 10

Senior tickets are $10, child tickets are $8

Given: 8 runners

To Determine: number of ways the runners would be rewarded

Solution

Using the multiplication principle

Hence, the number of ways they can be rewarded is god, silver and bronze is 336

Answer:

887.74

Step-by-step explanation:

Answer:

BT = 18, DA = 6

Step-by-step explanation:

- EBT and SDA are similar triangles

- EBT has a perimeter of 63

- SDA has a perimeter of 21

- BT = 6x

- DA = x+3

We know that EBT has side lengths that are three times bigger than the side lengths of SDA since 63 = 21 x 3.

so

6x is equal to 3(x+3).

6x = 3x + 9

3x = 9

x = 3

Now we know that:

BT = 18

and

DA = 6

Answer:

180

Step-by-step explanation:

The required experimental probability that the next batter will get a hit is 2/11.

A number that indicates how likely an event is to occur is called its probability. It is communicated as a number in the reach from 0 and 1, or, utilizing rate documentation, in the reach from 0% to 100 percent. The higher the probability, the more likely the event is to occur.

The experimental probability of an event happening is defined as the number of times the event occurs divided by the total number of trials or events.

In this case, we are given that 4 out of 22 batters have gotten a hit so far. Therefore, the experimental probability that the next batter will get a hit is:

P(hit) = Number of hits / Total number of batters

P(hit) = 4/22

Simplifying:

P(hit) = 2/11

Therefore, the experimental probability that the next batter will get a hit is 2/11.

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Answer:

The Moon has a gravitational pull 1/6 of that of Earth

Step-by-step explanation:

(What is your question?)

Answer:

6 is the y intercept and 1 is the slope, so it goes up 1 unit right 1 unit

Step-by-step explanation:

When a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring stretches by an amount d, as it balances the force exerted by the spring with the force due to the fish's weight.

Here, a fish attached to a vertical spring. When a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring will stretch by an amount d.
The equilibrium position is the point where the force exerted by the spring equals the force due to the fish's weight (gravitational force). In this scenario, the spring stretches until it reaches a balance between these forces. The amount by which the spring stretches is denoted as d.
To summarize, when a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring stretches by an amount d, as it balances the force exerted by the spring with the force due to the fish's weight.

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Answer:

The y-intercept is the constant [whole number, the one without a variable] in the equation. So you're looking for the equation that has + 2 at the end, not -2.

Step-by-step explanation:

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Part A: Proportion of Americans above 21 who smoke: 0.23.

Part B: confidence interval for the proportion of American population over 21 who smoke is:  0.173 < x < 0.287.

The size of a 90% confidence interval for a given estimate is one way to gauge how "excellent" it is; the greater the interval, the more care must be used when utilising the estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.

Part A:

sample size n = 292.

Don't smoke = 225

Smoke = 292 - 225 = 67

Now,  proportion of Americans above 21 who smoke:

π = 67 / 292 = 0.23

1 - π = 1 - 0.23 = 0.77

Part B:  confidence interval - 80%

α  = 0.2

z(0.2/2) = 1 - 0.2/2 = 0.99

p value for z score (0.99)  = 2.32

Confidence interval are-

π - z√(π(1 - π)/n) < x < π + z√(π(1 - π)/n)

Put the values:

0.23 - 2.32√(0.23*0.77/292) < x < 0.23 + 2.32√(0.23*0.77/292)

0.23 - 2.32√(0.23*0.77/292) < x < 0.23 + 2.32√(0.23*0.77/292)

0.23 - 0.057 < x < 0.23 + 0.057

0.173 < x < 0.287

Thus, confidence interval for the proportion of American population over 21 who smoke is:  0.173 < x < 0.287.

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a. the linear approximating polynomial L(x) is 1+x

b. the quadratic approximating polynomial Q(x) is 1 + x + x^2

a. The linear approximating polynomial for a function f(x) centered at the point a can be found using the formula:

L(x) = f(a) + f'(a)(x - a)

where f'(a) is the derivative of the function evaluated at the point a.

b. The quadratic approximating polynomial for a function f(x) centered at the point a can be found using the formula:

Q(x) = f(a) + f'(a)(x - a) + (1/2)f''(a)(x - a)^2

where f''(a) is the second derivative of the function evaluated at the point a.

c. To approximate the quantity 1/(1-x) using the linear and quadratic approximating polynomials obtained in parts a. and b., we need to first find the values of f(a), f'(a), f''(a) at the given point a.

Let's assume a = 0 for simplicity.

a. Linear Approximation:
To find the linear approximating polynomial, we need to evaluate f(0) and f'(0).

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

f(0) = 1/(1-0) = 1

To find f'(0), we need to take the derivative of f(x) and evaluate it at x = 0.

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

f'(0) = 1/(1-0)^2 = 1

Using the linear approximation formula, we can now find the linear approximating polynomial L(x):

L(x) = f(0) + f'(0)(x - 0) = 1 + 1(x - 0) = 1 + x

b. Quadratic Approximation:
To find the quadratic approximating polynomial, we need to evaluate f''(0).

f''(x) = 2/(1-x)^3

f''(0) = 2/(1-0)^3 = 2

Using the quadratic approximation formula, we can now find the quadratic approximating polynomial Q(x):

Q(x) = f(0) + f'(0)(x - 0) + (1/2)f''(0)(x - 0)^2 = 1 + 1(x - 0) + (1/2)2(x - 0)^2 = 1 + x + x^2

Now, we can use these linear and quadratic approximating polynomials to approximate the given quantity 1/(1-x). For example, if we want to approximate the value of 1/(1-x) at x = 0.1, we can substitute x = 0.1 into both L(x) and Q(x) to get the approximate values.

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10 procent

Step-by-step explanation:

150 / 150 = 10

Answer:10%

Step-by-step explanation:

The number of ways Aaron can arrange the 5 songs on the playlist is equal to 120 ways.

Number of songs = 5

Consider that there are 5 options for the first song.

4 options for the second song since one song has already been used.

3 options for the third song.

2 options for the fourth song.

And only 1 option for the last song.

So the total number of arrangements is equal to,

= 5 × 4 × 3 × 2 × 1

= 120

Alternatively, use the formula for permutations of n objects taken x at a time,

ⁿPₓ= n! / (n - x)!

Here,

The number of songs  n = 5

The number of slots on the playlist x = 5

⁵P₅ = 5! / (5 - 5)!

     = 5!

     = 120 ways

Therefore, the total number of ways Aaron can arrange his 5 songs on playlist is 120.

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