What is the solution of this inequality?

r−10>−7

Drag and drop the choices to correctly complete the inequality.

Hello there for this problem we can make a proportion

\(\frac{8\:drinks}{12\:cost}=\frac{12\:drinks}{x}\), we are trying to find how much x is

cross multiply and we get that \(8x=144\)

divide both sides by 8 and we get \(x=18\), 12 drinks would've cost 18 dollars

Answer:

1 drink = 12 ÷ 8

= 1.5

So 12 drink = 12 × 1.5

= 8 dollars

Answer:

C. :)

Hope it helps

Step-by-step explanation:

Multiplying a function by a positive constant yields a function whose graph expands and contracts vertically with respect to the graph of the original function. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done.

Vertical stretching occurs when the base chart is multiplied by a certain factor greater than 1. This will pull the chart outwards but keep the input value (or x). When a function is stretched vertically, you would expect the y-values ​​of that plot to be farther from the x-axis.

Multiplying f(x) by factors of 3 and 6 will stretch the plot by the same factors. We can also see that their input values ​​(x in this case) remain the same. When f(x) was stretched vertically, only the y values ​​were affected.

If we |a| have > 1, a f(x) stretches the basis functions by a factor of a. The input values ​​remain the same, so the graph coordinates point is (x, ay).

This means that if f(x) = 5x + 1 is stretched vertically by a factor of 5, the new function corresponds to 5 f(x). So the resulting function is 5(5x + 1) = 25x + 5.

Once you have the graph of the function, you can stretch it vertically by pulling the curve outward based on the specified scaling factor. Note the following when stretching functions vertically:

Make sure the x values ​​are the same so the base of the curve doesn't change.

This means that when a vertical stretch is applied to the base graph, its x-intercept remains the same.

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1) Since we need to find the inflection points, we need to take the second derivative of this function, and check whether f(x) is equal to zero or undefined.

2) Now, we need to find the solutions for cos(x) within the given interval:

3) The next step is to find the y-coordinate, so let's plug each value of x we have just found into the original function:

So the point of inflections are:

4) The Concavity can be found by combining the Domain with the inflection points, or we can also check them geometrically:

So, we can tell that:

Each girl on the basketball team averages 136/12 = 11.33 points.The average number of points each girl scores, we first need to calculate the total number of points scored by the team.

Since the team average is 136 points, the total points scored by the team would be 136 x 12 = 1632 points.There are 8 boys on the team, and each boy averages 12 points. Therefore, the total points scored by the boys would be 8 x 12 = 96 points. To find the total points scored by the girls, we subtract the total points scored by the boys from the total team points: 1632 - 96 = 1536 points.

Since there are 4 girls on the team, we divide the total points scored by the girls (1536) by the number of girls (4) to find the average points scored by each girl: 1536/4 = 384 points. Therefore, each girl on the team averages 384/12 = 11.33 points.

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Answer:

975 lbs.

Step-by-step explanation:

9 3/4 = 9.75

9.75 × 100 = 975

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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The OLS estimator b in the presence of measurement error will be unbiased if certain conditions are met. The variance of b|X is larger than the variance of b*|X due to the additional measurement error.

i) The least squares problem for equation (3) is formulated as follows: minimize the sum of squared residuals, SSR(b) = (y - Xb)'(y - Xb). The first-order conditions give ∂SSR(b)/∂b = -2X'y + 2X'Xb = 0. Solving for b, we get b = (X'X)^(-1)X'y, which is the OLS estimator.

ii) The OLS estimator b will be unbiased if E(ν|X) = 0 and X is of full rank. Additionally, the error term ε should satisfy the classical linear model assumptions, including E(ε|X) = 0, var(ε|X) = σε^2In, and ε being uncorrelated with X.

iii) The variance of b|X is given by var(b|X) = σε^2(X'X)^(-1). Comparing it to var(b*|X), we find that var(b|X) is larger due to the presence of measurement error. The additional error term η introduces more variability into the estimated coefficients, leading to a larger variance compared to the scenario where y* is observed directly.

Therefore, The OLS estimator b in the presence of measurement error will be unbiased if certain conditions are met. The variance of b|X is larger than the variance of b*|X due to the additional measurement error.

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Answer:

I need the answer tooo

Answer:

\(\begin{aligned} \textsf{(a)} \quad f(g(x))&=\boxed{x}\\g(f(x))&=\boxed{x}\end{aligned}\\\\\textsf{\;\;\;\;\;\;\;\;$f$ and $g$ are inverses of each other.}\)

\(\begin{aligned} \textsf{(b)} \quad f(g(x))&=\boxed{x}\\g(f(x))&=\boxed{x}\end{aligned}\\\\\textsf{\;\;\;\;\;\;\;\;$f$ and $g$ are inverses of each other.}\)

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x)=-\dfrac{x}{2}\\\\g(x)=-2x\end{cases}\)

Evaluate the composite function f(g(x)):

\(\begin{aligned}f(g(x))&=f(-2x)\\\\&=-\dfrac{-2x}{2}\\\\&=x\end{aligned}\)

Evaluate the composite function g(f(x)):

\(\begin{aligned}g(f(x))&=g\left(-\dfrac{x}{2}\right)\\\\&=-2\left(-\dfrac{x}{2}\right)\\\\&=x\end{aligned}\)

The definition of inverse functions states that two functions, f and g, are inverses of each other if and only if their compositions yield the identity function, i.e. f(g(x)) = g(f(x)) = x.

Therefore, as f(g(x)) = g(f(x)) = x, then f and g are inverses of each other.

\(\hrulefill\)

Given functions:

\(\begin{cases}f(x)=2x+1\\\\g(x)=\dfrac{x-1}{2}\end{cases}\)

Evaluate the composite function f(g(x)):

\(\begin{aligned}f(g(x))&=f\left(\dfrac{x-1}{2}\right)\\\\&=2\left(\dfrac{x-1}{2}\right)+1\\\\&=(x-1)+1\\\\&=x\end{aligned}\)

Evaluate the composite function g(f(x)):

\(\begin{aligned}g(f(x))&=g(2x+1)\\\\&=\dfrac{(2x+1)-1}{2}\\\\&=\dfrac{2x}{2}\\\\&=x\end{aligned}\)

The definition of inverse functions states that two functions, f and g, are inverses of each other if and only if their compositions yield the identity function, i.e. f(g(x)) = g(f(x)) = x.

Therefore, as f(g(x)) = g(f(x)) = x, then f and g are inverses of each other.

Answer:

see explanation

Step-by-step explanation:

given f(x) and g(x)

if f(g(x)) = g(f(x)) = x

then f(x) and g(x) are inverses of each other

(a)

f(g(x))

= f(- 2x)

= - \(\frac{-2x}{2}\) ( cancel 2 on numerator/ denominator )

= x

g(f(x))

= g(- \(\frac{x}{2}\) )

= - 2 × - \(\frac{x}{2}\) ( cancel 2 on numerator/ denominator )

= x

since f(g(x)) = g(f(x)) = x

then f(x) and g(x) are inverses of each other

(b)

f(g(x))

= f(\(\frac{x-1}{2}\) )

= 2(\(\frac{x-1}{2}\) ) + 1

= x - 1 + 1

= x

g(f(x))

= g(2x + 1)

= \(\frac{2x+1-1}{2}\)

= \(\frac{2x}{2}\)

= x

since f(g(x)) = g(f(x)) = x

then f(x) and g(x) are inverses of each other

Answer:

5(x + 3)

Step-by-step explanation:

6(2x + 4) - 2(x + 7) + 5

12x + 24 - 2x - 14 +5

10x  + 24 - 9

10x  + 15

5(x + 3)

Inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process.

Inverse distance weighting is a method used in geostatistics to estimate values at unsampled locations based on values at surrounding sample locations. It works by assigning weights to the sample points based on their proximity to the unsampled point. The closer a sample point is to the unsampled point, the higher its weight. The weights are then used to calculate a weighted average of the sample values, which is used as the estimate for the unsampled location.
The benefit of inverse distance weighting over a simple average is that it takes into account the spatial variability of the data. A simple average treats all sample points equally, regardless of their distance from the unsampled point. This can lead to inaccurate estimates if there is a high degree of spatial variability in the data. In contrast, inverse distance weighting gives more weight to sample points that are closer to the unsampled point, which is likely to provide a more accurate estimate.
Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process. For example, if there are two variables of interest (e.g., temperature and precipitation), inverse distance weighting can be used to estimate values for both variables simultaneously. This is not possible with a simple average.
Overall, inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Its ability to account for spatial variability and incorporate multiple variables makes it a powerful technique for analyzing spatial data.

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Answer: The slope is 1.

Step-by-step explanation:

The equation of the line is y = mx+b where m represents the slope.

Since x has no coefficent, m must equal to 1.

Population growth represents the rate at which the population changes

Given that:

\(r_1 = 2\) ----- i.e. when the population doubles

\(r_2 = \frac{1}{2}\) ----- i.e. when the population cut in halves

Population growth is represented as: \(A_n = ar^{n}\)

Organism A

For the first 5 days (when it doubles) is:

\(A_5 = ar_1^{5\)

Substitute \(r_1 = 2\)

\(A_5 = a\times 2^{5\)

For the next 3 days (when it cut in halves) is:

\(A = A_5 \times r_2^3\)

Substitute \(A_5 = a\times 2^{5\) and \(r_2 = \frac{1}{2}\)

\(A= a \times 2^5 \times (\frac{1}{2})^3\)

Apply law of indices

\(A = a \times 2^5 \times 2^{-3\)

\(A = a \times 2^{5-3\)

\(A = a \times 2^{2\)

So, the growth factor of organism A is:

\(A = a \times 2^{2\)

Organism B

For the 8 days, we have:

\(B=ar_1^8\)

\(B=a\times 2^8\)

The expression (n) for the number of times the population of B is greater than A is:

\(n = \frac BA\)

This gives:

\(n = \frac{a \times 2^8}{a \times 2^2}\)

\(n = \frac{2^8}{2^2}\)

Apply law of indices

\(n = 2^{8-2}\)

\(n = 2^{6}\)

The expression that is not in exponential form is:

\(n = 2 \times 2\times 2\times 2 \times 2\times 2\)

\(n = 64\)

Hence:

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The given values into the equation of the least squares regression line: 0.6 * 520 + 10.0 = 322 hot dogs were sold that day. 357 hot dogs were sold on the day when 520 people attended the fair.

In this problem, we have data collected on the number of hot dogs sold (h) and the number of people attending a fair (p) over a two-week period. The least squares regression line is a line that best fits the data points and represents the relationship between the variables.

The equation of the least squares regression line is given as 0.6p + 10.0. This equation indicates that the number of hot dogs sold (h) can be estimated by multiplying the number of people attending (p) by 0.6 and adding 10.0.

We are given that the residual for the day when 520 people attended the fair is 35. A residual is the difference between the actual observed value and the predicted value on the regression line. In this case, the predicted value is 0.6 * 520 + 10.0 = 322 hot dogs. The actual value is the number of hot dogs sold on that day. The residual is calculated as the actual value minus the predicted value, which gives us 35.

To find the number of hot dogs sold on that day, we can set up an equation using the residual: h - 322 = 35. Solving this equation, we find that h = 322 + 35 = 357. Therefore, 357 hot dogs were sold on the day when 520 people attended the fair.

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QUESTION:

Data was collected on h, the number of hot dogs sold, and p, the number of people attending a fair over a two week period. The least squares regression line has equation y = 0.6p + 100. The residual for the day when 520 people attended was 35. How many hot dogs were sold that day? OA. 322 OB. 287 OC. 220 OD. 555 O E. 357 The salaries of a random sample of a company's employees are summarized in the frequency distribution below. Approximate the sample mean using the grouped data formulas O A. $17,500.00 OB. $19,663.05 O C. $16,087.95 OD. $17,875.50 Employees Salary (5) 5.001 - 10,000 10,001 - 15,000 15,001 - 20,000 20,001 - 25,000 25,001 - 30,000

The risk factor is 1.8 and the Confidence level is (0.60, 2.85).

To calculate the relative risk (RR) and its 95% confidence interval for the participants reporting a reduction of symptoms in the experimental condition compared to the placebo condition, we can use the following formula:

RR = (a / b) / (c / d)

where a is the number of participants in the experimental group who reported a reduction of symptoms, b is the number of participants in the experimental group who did not report a reduction of symptoms, and c is the number of participants in the placebo group who reported a reduction of symptoms, and d is the number of participants in the placebo group who did not report a reduction of symptoms.

In this case, a = 38, b = 62, c = 21, and d = 79. So we have:

RR = (38 / 62) / (21 / 79) = 1.8

To calculate the 95% confidence interval for RR, we can use the following formula:

log(RR) ± 1.96 * √(1/a + 1/b + 1/c + 1/d)

Taking the antilogarithm of both sides of the inequality, we have:

RR- = exp(log(RR) - 1.96 * √(1/a + 1/b + 1/c + 1/d))

RR+ = exp(log(RR) + 1.96 * √(1/a + 1/b + 1/c + 1/d))

Substituting the values, we get:

RR- = exp(log(1.8) - 1.96 *√(1/38 + 1/62 + 1/21 + 1/79)) = 0.60

RR+ = exp(log(1.8) + 1.96 * √(1/38 + 1/62 + 1/21 + 1/79)) = 2.85

Therefore, the 95% confidence interval for RR is (0.60, 2.85).

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The required, there are 8998912 possible license plates that can be generated using this format.

Here, we have,

There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used.

Therefore, there are 8 choices for each of the three digits,

giving us 8 x 8 x 8 = 512 possible combinations for the digits.

Similarly, there are 26 letters that can be used for each of the three letters on the license plate.

Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.

Total number of license plates = number of choices for the digits x number of choices for the letters

= 512 x 17576

= 8998912

Therefore, there are 8998912 possible license plates that can be generated using this format.

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Christo and Jeanne-Claude worked for over 26 years on "The Gates," a large-scale public art installation in Central Park consisting of thousands of saffron-colored fabric panels along 23 miles of walkways, which was on display for 16 days in February 2005.

Christo and Jeanne-Claude were artists known for their large-scale public art installations. "The Gates" was a project they worked on for over 26 years, from its conception in 1979 to its installation in Central Park in February 2005. The installation involved placing thousands of saffron-colored fabric panels along 23 miles of walkways in the park, creating a visually stunning and immersive experience for visitors.

The project was met with both praise and criticism, but it ultimately succeeded in bringing people together to appreciate art in a public space. The installation remained in place for 16 days before it was dismantled.

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Answer:

1/2, 1/10, and 1/14 s the answer.

Step-by-step explanation:

The first set of numbers are integers, the second set is whole numbers, the fourth set is imaginary numbers, and the fifth set is irrational numbers. The third set is rational because it can be written as a fracton but not integers because they aren't whole numbers or their opposites.

Answer:

36πin

Step-by-step explanation:

Formula for the circumference of a circle=2πr

r=18

2 · 18

=36

36·π

hope this helps

The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

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Complete Question:-

To calculate the probability that the resulting product is even, we need to first determine the total number of possible outcomes. There are 90 two-digit numbers ranging from 10 to 99. If we choose two different numbers, there are a total of 90C2 (90 choose 2) possible combinations, which is equal to 4,005.

To calculate the number of even products, we need to consider the different scenarios. If one of the numbers is even, the product will also be even. There are 45 even numbers in the range from 10 to 99, so the number of even products that can be formed from an even number and an odd number is 45 x 45 = 2025.

If both numbers are odd, then the product will also be odd, and hence not even. There are 45 odd numbers in the range from 10 to 99, so the number of odd products that can be formed from an odd number and an odd number is 45 x 44 = 1980.

Therefore, the total number of even products that can be formed is 2025. The probability that the resulting product is even is then 2025/4005, which simplifies to 9/17, or approximately 0.5294. So, there is a 52.94% chance that the resulting product will be even.

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Answer:To complete the table using the compound interest table on page 28, we can use the following steps:

Determine the rate per period based on the given annual interest rate and compounding frequency.

Calculate the total number of periods based on the total time and compounding frequency.

Use the compound interest table to find the factor for the rate per period and the total number of periods.

Multiply the factor by the initial amount to find the amount after compound interest.

Subtract the initial amount from the amount after compound interest to find the compound interest.

Using these steps, we can complete the table as follows:

Annual

Interest Compounded

Rate

$900.00 5.50% Quarterly 1.375% 2 years 8

$640.00 6.00% Semiannually 3.00% 4 years 8

$1,340.00 5.00% Quarterly 1.25% 3 years 12

$6,231.40 5.75% Semiannually 2.875% 4 years 8

$3,871.67 12.00% Monthly 1.000% 4 years 48

$9,000.00 18.00% Monthly 1.500% 2 years 24

Quarterly 0.016%

Semiannually 0.033%

Monthly 0.058%

Monthly 0.058%

Monthly 1.500%

Quarterly 0.450%

Total

Time

2 years

4 years

3 years

4 years

4 years

2 years

Total

Number of

Periods

8

8

12

8

48

24

C.

$1,042.36

$812.65

$1,519.39

$7,305.10

$8,980.54

$20,790.56

Amount

Compound

Interest

d.

$42.36

$172.65

$119.39

$3,074.70

$4,109.87

$11,790.56

Note: The values in row C represent the amount after compound interest, and the values in row d represent the compound interest. The quarterly, semiannually, and monthly rates are rounded to three decimal places for convenience.

Step-by-step explanation:

Part A

If the number is n, then the expression is 7n+6.

Part B

Three times the sum of a number and 8.

Answer:

B

Step-by-step explanation:

+/- 7 is the sq root of 49

hope this helps

The probability that at least 16 of the 20 people who have a headache experience relief successfully is 0.976.

To find the probability that at least 16 of the 20 people who have a headache experience relief successfully, we can use the binomial probability formula: P(X) = (n choose X) * p^X * (1-p)^(n-X)

Where n is the number of trials, X is the number of successes, and p is the probability of success.
In this case, n = 20, p = 0.8 (since we are given that 80% of people experience relief successfully), and we want to find the probability that X is greater than or equal to 16.

We can calculate this by finding the probability that X is less than or equal to 15, and then subtracting that from 1:
P(X >= 16) = 1 - P(X <= 15)
= 1 - [(20 choose 0) * 0.8^0 * 0.2^20 + (20 choose 1) * 0.8^1 * 0.2^19 + ... + (20 choose 15) * 0.8^15 * 0.2^5]
= 1 - 0.0115
= 0.9885
Therefore, the probability that at least 16 of the 20 people who have a headache experience relief successfully is 0.9885, or 0.989 to three decimal places.

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Answer:

21

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD        AH

-----  =  ---------

AB         AH +y

3        9

---- = ------

10         9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21

Answer:

y = 21

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

\(\boxed{\sf AD : DB = AH : HC}\)

From inspection of the given triangle, the lengths of the line segments are:

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)

Therefore, the value of y is 21.

The simplified form of the given expression is 45.

The given expression is 32+(6-2)4-3.

An expression in math is a sentence that contains at least two numbers/variables and at least one math operation. The mathematics operators will be addition, subtraction, multiplication and division.

The expression is 32+(6-2)4-3.

Firstly, we will simplify the subtraction which is in the bracket, we get

32+(6-2)4-3=32+(4)4-3

Now, we will simplify the multiplication, we get

32+(6-2)4-3=32+16-3

Further, we will simplify the addition, we get

32+(6-2)4-3=48-3

Furthermore, we will simplify the subtraction, we get

32+(6-2)4-3=45

Hence, the simplified form of the given expression 32+(6-2)4-3 is 45.

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Answer:

11:18.

Step-by-step explanation:

22:36

We divide each number by their Greatest Common Factor.

The GCF of 22 and 36 is 2.

So, in simplest terms

22:36 = 11:18.