Suppose y varies directly with x, and y = 104 when x = 8. What is the value of y when x = 18?​

The equation of the line in slope-intercept form that passes through the point (3, -2) and is parallel to the line y = 2x + 4 is, y = 2x - 8.

We know that the equation of a straight line with slope 'm' and y intercept 'c' is given by,

y = mx + c

Given the equation of a straight line is,

y = 2x + 4

comparing it with slope intercept form we get, slope = 2.

Since the slopes of parallel lines are equal.

So the slope of the required line = 2.

So let the slope intercept equation of the line will be:

y = 2x + c

Now it is given that the line passes through (3, -2), so it will satisfies the equation.

-2 = 2*3 + c

-2 = 6 + c

c = -2 - 6 = - 8

The equation of the required line is, y = 2x - 8.

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The number of seats in the front row of the theater is a = [2y/(n(n-1)) - x/(n-1)]/2

Let's call the number of seats in the first row "a". We can use the information given in the problem to set up an equation in terms of "n", "d", "x", and "y"

y = a + (a + d) + (a + 2d) + ... + (a + (n-1)d) (1)

We can simplify this equation by using the formula for the sum of an arithmetic series

y = [n/2][2a + (n-1)d] (2)

We can solve this equation for "a" in terms of "n", "d", and "x"

2a = (2y/n) - (n-1)d - 2xd

a = [(2y/n) - (n-1)d - 2xd]/2

Since we know that the number of seats in the last row is "x", we can substitute that into the equation

x = a + (n-1)d

x = [(2y/n) - (n-1)d - 2xd]/2 + (n-1)d

Simplifying this equation gives us

2x = (2y/n) + (n-1)d

2d = (2x - (2y/n))/(n-1)

Now we can substitute this value of "d" into the equation we found for "a"

a = [(2y/n) - (n-1)d - 2xd]/2

a = [(2y/n) - x - (2x - (2y/n))/(n-1)]/2

a = [2y/(n(n-1)) - x/(n-1)]/2

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i believe its 625

Step-by-step explanation:

hope its right sorry if it isn't

It represents exponentially growth function.

The given function is

y = [tex]9^{x}[/tex]

Since,

A mathematical function with the form f (x) = [tex]a^{x}[/tex] is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's basis and must be greater than 0.

Now after plotting,

It begins as a horizontal line, grows slowly at first, then picks up speed. It has an increasing slope.

Which represents exponentially growth.

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General Idea:

We need to convert the liter to milliliter to find out how much the science teach has in ml.

[tex]\text{1L}=\text{1000 mL}[/tex]

[tex]\text{0.4L}=0.4\times\text{1000 mL}=\text{400 mL}[/tex]

Capacity of a Spoon given below:

[tex]\text{1 spoonful}=\text{5 mL}[/tex]

Each student asked to fill 2 spoonful, which means 10 mL of seawater is expected to be filled in their container.

[tex]\text{Amount of seawater filled by 22 students}=[/tex]

[tex]\text{Number of students} \times\text{Amount}[/tex] [tex]\text{ of seawater filled by each student in their container}[/tex]

[tex]=22\times10 \ \text{mL}=220 \ \text{mL}[/tex]

Conclusion:

Number of milliliters of seawater that will be left after all 22 students have filled their container is given below:

[tex]400 \ \text{mL}-220 \ \text{mL}= \boxed{\bold{180 \ mL}}[/tex]

There are 11 letters in the word mathematics. The probability of selecting the letter "e" first is 1/11, which is approximately 0.091 in decimal form when rounded to the nearest thousandth.

This is because there is only one "e" in the word mathematics, and we are selecting one letter out of the 11 total letters.

To find the probability that the first letter is "e" in the word "mathematics," follow these steps:

1. Count the total number of letters in the word: There are 11 letters in "mathematics."

2. Count the occurrences of the letter "e": There is 1 "e" in "mathematics."

3. Calculate the probability: Divide the occurrences of "e" by the total number of letters.

Probability = (Occurrences of "e") / (Total number of letters) = 1 / 11

In decimal form and rounded to the nearest thousandth, the probability that the first letter is "e" in the word "mathematics" when arranged randomly is approximately 0.091.

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The required equation of function g(x) is x²- 1.

To find the function g(x), which is the translation 1 unit down of f(x) = x², we can subtract 1 from the y-coordinate of each point on the graph of f(x).

The graph of f(x) = x² is a parabola that opens upward and passes through the origin (0, 0). The y-coordinate of any point on this parabola is equal to the square of its x-coordinate.

The function g(x) can be written as:

g(x) = f(x) - 1

      = x² - 1

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After the translation 1 unit down of the function f(x)=x² is g(x) = x² - 1.

The given function is f(x)=x².

The translation of a function f(x) 1 unit down is given by g(x) = f(x) - 1.

So, for f(x) = x², the translation 1 unit down of f(x) is g(x) = x² - 1.

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Horizontal Shift: None

Vertical Shift: Down 1 Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

Therefore, after the translation 1 unit down of the function f(x)=x² is g(x) = x² - 1.

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From the picture attached, the functions are quadratic, linear and exponential respectively.

A linear function is represented by a straight line on a graph with the form y = mx + b, where m is the slope and b is the y-intercept. Plotting function 2 produces a Linear curve.

Quadratic Function

A quadratic function is a mathematical function that can be represented by a parabola on a graph. It has the form: y = ax² + bx + c

where a, b, and c are constants.

Coefficient a determines the shape of the parabola, while the coefficients b and c determine its position on the graph. By plotting function 1 on the graph, we will get a parabola which signifies a Quadratic curve.

Exponential Function

An exponential function has a curve that varies with horizontal movement on a graph, with the form y = abˣ, where a and b are constants and b > 1. Base, b, determines function growth/decay.

By plotting function 3 on the graph we will notice a steeper curve which denotes the Exponential curve.

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Answer

x = 2

multiplie the 2 on both sides

= 4+3x = 10

subtract the 4

= 3x = 6

divide by 3

= x = 2

Answer:

C = 74π feet = about 232.48 feet

Answer:

  11%

Step-by-step explanation:

You want to know the rate of inflation if the price of a haircut increased from $7 to $20 in 10 years.

The inflation of prices is modeled by an exponential function.

  p(t) = p₀·(1 +r)^t

where p₀ in the price at t=0, r is the annual inflation rate, and t is the number of years.

Solving for r, we find ...

  p(t)/p₀ = (1 +r)^t . . . . . . . . divide by p₀

  (p(t)/p₀)^(1/t) = 1 +r . . . . . . take the t-th root

  r = (p(t)/p₀)^(1/t) -1 . . . . . . . subtract 1

For the given numbers, we find the rate to be ...

  r = (20/7)^(1/10) -1 ≈ 0.11 = 11%

The rate of inflation is 11% per year.

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Due to its larger time frame and less sensitivity to transient variations in the data, the 200-day moving average is often smoother than the 50-day moving average.

The 200-day moving average is typically smoother than the 50-day moving average because it covers a longer period of time and is therefore less reactive to short-term fluctuations in the data. However, the choice between using a 50-day or a 200-day moving average ultimately depends on the specific data being analyzed and the desired level of sensitivity to changes in the data.

A 200-day moving average will be smoother than a 50-day moving average. The 200-day moving average considers a longer period of time, which reduces the impact of short-term fluctuations and provides a clearer overall trend. The 50-day moving average is more sensitive to recent price changes and will appear more volatile in comparison.

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The temperature range is the difference between the highest and lowest temperatures. To calculate it, we subtract the lowest temperature from the highest temperature. In this case, we have:

**Temperature range = 15 °C - (-18 °C) = 15 °C + 18 °C = 33 °C**

So, the temperature range is **33 °C**.️

Answer:

Step-by-step explanation:

We are given with a triangle whose Height is 7 cm and base is 10 cm.

We have to calculate the Area of triangle.

As we know that area of triangle is calculated by,

Putting the required values we get,

Area = 1/2 × 7 × 10

Area = 7 × 5

Area = 35 cm².

Hence, The area of the triangle is 35 cm².

The total number of students in the seminar is 258, with 98 boys and 160 girls given a ratio of 8:5 between boys and girls.

We can begin by using the given ratio of boys to girls, which is 8:5, and the information that there are 160 girls to find the number of boys in the seminar.

If the ratio of boys to girls is 8:5, then we can say that for every 8+5=13 students, there are 8 boys and 5 girls.

To find the number of boys, we can set up a proportion

8/13 = x/160

where x is the number of boys.

Simplifying this proportion, we get

x = 8/13 × 160

x = 98.46

Therefore, the number of boys in the seminar is approximately 98.

To find the total number of students in the seminar, we can add the number of boys and girls

Total number of students = Number of boys + Number of girls

Total number of students = 98 + 160

Total number of students = 258

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The distance further than Kia, that Jeremy had to drive can be found to be 100 kilometers.

Assuming that the picture posted is up to scale, we can use a ruler to find the distance that Jeremy drives from A to B to be 5 centimeters. This means that the actual distance is :

= 5 x 200 per cm

= 1, 000 kilometers

Using that same ruler, we can find that Kia drove 4. 5 cm from B to C which means the actual distance was :

= 4. 5 x 200

= 950 kilometers

The distance more than Kia that Jeremy drove was:

= 1, 000 - 900

= 100 kilometers

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Answer: 5024

Step-by-step explanation:

multiply 3.14 and 1600

Next year's annual lease payment is $85,800 we get it by multiplying monthly lease payment by 12

To calculate next year's annual lease payment, we need to first calculate next year's monthly sales.

Since sales are expected to increase by 6%, next year's monthly sales will be:

$150,000 + (6% x $150,000) = $159,000

Now calculate the monthly lease payment by adding up all the monthly lease expenses:

Rent: 4% x $159,000 = $6,360

Insurance: $200

Maintenance: $125

Utilities: $375

Taxes: $90

Total monthly lease payment = $6,360 + $200 + $125 + $375 + $90

= $7,150

Finally, we can calculate next year's annual lease payment by multiplying the monthly lease payment by 12:

Annual lease payment = $7,150 x 12

= $85,800

Therefore, next year's annual lease payment is $85,800.

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The correct option is C, the quadratic equation in the graph is:

y = -2x² + 4x - 2

Here we have a quadratic equation. We can see that the vertex is at (1, 0), then if we assume that the leading coefficient is a, we can write it as:

y = a*(x - 1)²2

Now we also can see that it passes through the poin (0, -2), then we can replace these values there to get:

-2 = a*(0 - 1)²

-2 = a

Then the quadratic equation is:

y = -2*(x - 1)²

y = -2*(x² - 2x + 1)

y = -2x² + 4x - 2

The correct option is C.

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If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has exactly one solution.

This is because the linear function intersects the quadratic function at its minimum point, where there is only one value of x that satisfies both equations.
If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has one unique solution.
Here's a step-by-step explanation:
1. A nonlinear system is a set of equations where at least one of the equations is not linear.
2. In this case, the nonlinear system contains one linear function and one quadratic function.
3. The quadratic function has a minimum point, which is the lowest point of its parabolic graph.
4. The linear function touches the quadratic function at its minimum, which means they intersect at exactly that point.
5. Since the two functions intersect at one point, the system has one unique solution, which corresponds to the coordinates of that intersection point.

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Answer:

Roots: 1/2 , -3/2

Vertex: (-1/2, -4)

AOS: x = - 1/2

Min/Max: (-1/2, -4)

Step-by-step explanation:

x y

-2 7

-1.5 1

-1 -1

-0.5 -3.5

0 -3

0.5 -1

1 1

The missing value is, y = 10/3

Since, The inverse variation formula is xy = k

Hence, In the first set of values you have x and y so you can solve for k:

2 x 15 = k

k = 30

Now in the second set of values you have x and we have k from the first set so we have:

9 x y = 30

y = 30/9

y = 10/3

Thus, The missing value is, y = 10/3

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True. The statement "If Ha is not equal, you have to double the probability of being beyond your test statistic to get your p-value" is true.

If the alternative hypothesis (ha) is not equal, then you have to double the probability of being beyond your test statistic in order to obtain the p-value.

Thus,  When the alternative hypothesis (Ha) is not equal (two-tailed test), you need to consider both tails of the distribution, so you double the probability of being beyond the test statistic to calculate the p-value.

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Therefore, we can say with 90% confidence that the true population mean height of female runners is between 64.874 inches and 66.726 inches.

To construct a 90% confidence interval for the mean height of female runners, we can use the formula:
CI = x ± z*(σ/√n)
where x is the sample mean (65.80 inches), σ is the population standard deviation (unknown), n is the sample size (12), and z is the z-score corresponding to the desired level of confidence (90%).
Using a z-table or calculator, we find that the z-score for a 90% confidence interval is 1.645.
We are given the sample standard deviation (s = 1.95 inches), but we need to estimate the population standard deviation using the formula:
s/√n = σ/√n
1.95/√12 ≈ 0.562
So, our 90% confidence interval is:
CI = 65.80 ± 1.645*(0.562)
a. The left boundary of the confidence interval is:
65.80 - 0.926 = 64.874 (rounded to two decimal places)
b. The right boundary of the confidence interval is:
65.80 + 0.926 = 66.726 (rounded to two decimal places)

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Scientific notation is a way of writing very large or very small numbers using powers of 10. In scientific notation, a number is expressed as the product of a coefficient and a power of 10.

1,649,000 in scientific notation is written as

1,649,000 = 1.649 x [tex]10^{6}[/tex]

Hence, the correct option is A.

To write the standard number 1,649,000 in scientific notation, we first need to move the decimal point so that there is only one non-zero digit to the left of the decimal point.

In this case, we can move the decimal point six places to the left to get 1.649. Next, we need to express the remaining digits as a power of 10, Since we moved the decimal point six places to the left, we can express this as [tex]10^{6}[/tex].

Putting this together, we get

1,649,000 = 1.649  x [tex]10^{6}[/tex]

Hence, the correct option is A.

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(a) The probability that a household views television between 4 and 12 hours a day is 0.8864. (b) A household must view at least 12.63 hours of television/day to be in the top 4% of all television viewing households. (c) The probability that a household views television more than 3 hours a day is 0.9830.

(a) To find the probability that a household views television between 4 and 12 hours a day, we need to standardize the values using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For x = 4 hours:

z = (4 - 8.35) / 2.5 = -1.74

For x = 12 hours:

z = (12 - 8.35) / 2.5 = 1.46

Using a standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores:

P(z < -1.74) = 0.0401

P(z < 1.46) = 0.9265

Therefore, the probability that a household views television between 4 and 12 hours a day is:

P(4 ≤ x ≤ 12) = P(z < 1.46) - P(z < -1.74) = 0.9265 - 0.0401 = 0.8864 (rounded to four decimal places).

(b) To find the number of hours of television viewing a household must have in order to be in the top 4% of all television viewing households, we need to find the z-score that corresponds to the top 4% of the normal distribution:

P(z > z*) = 0.04

Using a standard normal distribution table or a calculator, we can find that the z-score that corresponds to a probability of 0.04 is approximately 1.75.

Using the formula for z-score:

z = (x - μ) / σ

We can solve for x:

x = μ + zσ = 8.35 + 1.752.5 = 12.63 (rounded to two decimal places)

Therefore, a household must view at least 12.63 hours of television per day to be in the top 4% of all television viewing households.

(c) To find the probability that a household views television more than 3 hours a day, we can standardize the value of x = 3 using the formula for z-score:

z = (x - μ) / σ = (3 - 8.35) / 2.5 = -2.14

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score:

P(z > -2.14) = 0.9830 (rounded to four decimal places).

Therefore, the probability that a household views television more than 3 hours a day is 0.9830.

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Shirley is incorrect because regardless of how the expressions are grouped they would produce the same output or result.

In Mathematics and Geometry, the standard form for a difference of two (2) squares is modeled or represented by this mathematical equation:

a² - b² = (a + b)(a - b) or a² - b² = (a - b)(a + b).

Where:

a and b represent numerical values (numbers or numerals).

Based on the information provided, we have the following mathematical equation:

(x - 15)(x + 15) = x² + 15x - 15x - 225

(x - 15)(x + 15) = x² - 225

By rewriting the product, we have the following;

(x + 15)(x - 15) = x² - 15x + 15x - 225

(x + 15)(x - 15) = x² - 225

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