During each week of piano lessons, Nate learns to play 1 new piece. Is the total number of piano pieces Nate learns proportional to the number of weeks he takes lessons?

(f-g)(x) = -x - 14 (option C)

f (x) = 4x - 8

g(x) = 5x + 6

(f-g)(x) means f(x) - g(x)

f(x) - g(x) = 4x - 8 - (5x + 6)

open the parnethesis:

Note: Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

4x - 8 - (5x + 6) = 4x - 8 - 5x - 6

collect like terms:

f(x) - g(x)= 4x - 5x -8 - 6

f(x) - g(x) = -x - 14

(f-g)(x) = -x - 14 (option C)

Answer:

Negative

Step-by-step explanation:

From the scatter plot displayed, we could clearly observe the direction of the trend line as it produces a negative slope. For high values of y, the values of x are low and similarly, high values of x have low y values. Therefore, this kind of relationship between the two variables is considered negative.

The vectors AB and AC are (-2, -1, 5) and (-5, 1, 5) respectively. The parametric equation of the line passing through A and B is given, and the equation of the plane containing points A, B, and C is y = 0. The area of triangle ABC is calculated to be 7.5 square units.

(a) To find the vectors AB and AC, we subtract the coordinates of point A from the coordinates of points B and C, respectively:

Vector AB = B - A = (2 - 4, 0 - 1, 3 - (-2)) = (-2, -1, 5)

Vector AC = C - A = (-1 - 4, 2 - 1, 3 - (-2)) = (-5, 1, 5)

(b) The parametric equation of the line passing through points A and B can be expressed as:

x = 4 - 2t

y = 1 - t

z = -2 + 5t

The equation of the plane containing points A, B, and C can be determined using the cross product of vectors AB and AC. The normal vector of the plane is given by:

n = AB x AC = (-2, -1, 5) x (-5, 1, 5)

Using the cross product formula, we calculate the cross product:

n = ((-1)(5) - (1)(-5), (5)(-5) - (5)(-2), (-2)(1) - (-1)(-2))

= (-5 - (-5), -25 - (-10), -2 - 2)

= (0, -15, 0)

The equation of the plane can be written as:

0x - 15y + 0z + d = 0

Simplifying, we get:

-15y = 0

y = 0

Therefore, the equation of the plane is -15y = 0, or simply y = 0.

(c) To find the area of triangle ABC, we can use the formula:

Area = (1/2) * |AB x AC|

We already have the vectors AB and AC:

AB = (-2, -1, 5)

AC = (-5, 1, 5)

Calculating the cross product:

AB x AC = ((-1)(5) - (1)(-5), (5)(-5) - (5)(-2), (-2)(1) - (-1)(-2))

= (-5 - (-5), -25 - (-10), -2 - 2)

= (0, -15, 0)

Now we can find the magnitude of the cross product:

|AB x AC| = sqrt(0^2 + (-15)^2 + 0^2) = sqrt(225) = 15

Finally, we calculate the area:

Area = (1/2) * |AB x AC| = (1/2) * 15 = 7.5

Therefore, the area of triangle ABC is 7.5 square units.

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The Median score in the /// group falls within the 80th percentile in the s/s group, indicating that 80% of the scores.

The percentile of the median score for the Vmax rate in the /// group compared to the s/s group, we need more information such as the distribution of scores and the sample size for both groups. Percentile indicates the percentage of scores that fall below a certain value.

Assuming we have the necessary information, we can proceed with the calculation. Here's a step-by-step approach:

1. Obtain the median score for the Vmax rate in the /// group. The median represents the middle value when the scores are arranged in ascending order.

2. Determine the number of scores in the s/s group that are lower than or equal to the median score obtained in the /// group.

3. Calculate the percentile by dividing the number of scores lower than or equal to the median by the total number of scores in the s/s group, and then multiplying by 100.

For example, let's say the median score for the Vmax rate in the /// group is 75. If, in the s/s group, there are 80 scores lower than or equal to 75 out of a total of 100 scores, the percentile would be:

(80/100) x 100 = 80%.

This means that the median score in the /// group falls within the 80th percentile in the s/s group, indicating that 80% of the scores in the s/s group are lower than or equal to the median score for the Vmax rate in the /// group.

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Answer:

x12

Step-by-step explanation:

(x*x*x*x*x) *(x*x*x*x*x*x)

Harley and Rachael thus spend a total of 6 hours and 52.5 minutes, or 55/8 hours, at the shore (since 1 hour is equal to 60 minutes).

Find the greatest common factor between the fraction's divisor and numerator (HCF). Divide both the numerator and the quotient by HCF to get the smaller fraction. Write the full sum as well as the reduced part together.

We can find the amount of time Rachael spends at the beach by multiplying Harley's time by 3/8:

Rachael's time = (3/8) × Harley's time

Rachael's time = (3/8) × 5

Rachael's time = 15/8

So Rachael spends 15/8 hours at the beach.

To find the total amount of time that Harley and Rachael spend at the beach, we can add their individual times:

Total time = Harley's time + Rachael's time

Total time = 5 + 15/8

To add the two times, we need to convert 5 to a fraction with a denominator of 8:

Total time = 40/8 + 15/8

Total time = 55/8

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The vertexes of the original triangle are the points (-2,4), (-4,-2) and (-5,3). After the transformation the new vertexes will be:

Then, the new triangle is:

The smallest integer value of x in the solution of the following inequality. -2x + 10 ≤ 1 is x ≤ 4.5

It should be noted that an inequality is used to show the given expressions are not equal.

It should be noted that in this case, we want to calculate the smallest integer value of x in the solution of the following inequality. -2x + 10 ≤ 1. This will be illustrated as:

-2x + 10 ≤ 1.

Collect like terms

-2x ≤ 1 - 10

-2x ≤ - 9

Divide through by 2

-2x ≤ - 9

x ≤ - 9 / -2

x ≤ 4.5

Therefore, the smallest integer value of x in the solution of the following inequality. -2x + 10 ≤ 1 is x ≤ 4.5

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Answer:

The factors are,

x + 12 and x - 2

Step-by-step explanation:

x^2 + 10x - 24,

Here, we note that,

12 - 2 = 10,

and (12)(-2) = 24,

so, we  can re-write 10x as 10x = 12x - 2x

so,

\(x^2 + 12x - 2x - 24 = 0\)

Taking x common from the 1st two terms (x^2 and 12x),

and taking -2 common from the last two tems (-2x and -24), we get,

\(x^2 + 12x - 2x - 24 \\x(x+12)-2(x+12)\\taking \ (x+12) \ common,we \ get,\\(x+12)(x-2)\)

So, The factors are,

x + 12 and x - 2

Answer:

Thus,

\(\frac{1}{y^{-3}}\:=y^3\)

Step-by-step explanation:

Given the expression

\(\frac{1}{y^{-3}}\:\)

simplifying the expression

\(\frac{1}{y^{-3}}\:\)

\(\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\)

\(=\frac{1}{\frac{1}{y^3}}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}\)

\(=\frac{y^3}{1}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{1}=a\)

\(=y^3\)

Thus,

\(\frac{1}{y^{-3}}\:=y^3\)

We will prove by structural induction that every common divisor of m and n also divides every member of the set L.By structural induction, we have shown that every common divisor of m and n also divides every member of the set L.

• Base cases: m, n ∈ L

• Constructor cases: If j, k ∈ L, then 1. −j ∈ L 2. j + k ∈ L

Base case:

For m and n, let d be a common divisor of m and n. Since d divides both m and n, it follows that d also divides m + n and m - n (by adding and subtracting the two equations following structural induction). Therefore, d is a divisor of both m and n, as well as of j and k in the base cases of L.

Constructor case 1:

Suppose that −j ∈ L and d is a common divisor of m and n. Then, −j = −1 * j and since d is a divisor of j, it follows that d is also a divisor of −j.

Constructor case 2:

Suppose that j + k ∈ L and d is a common divisor of m and n. Then, d divides both j and k, and therefore d divides (j + k).

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Answer:

n = 20

Step-by-step explanation:

in a polygon

interior angle + exterior angle = 180°, so

162° + exterior angle = 180° ( subtract 162° from both sides )

exterior angle = 18°

the sum of the exterior angles of a polygon = 360°

since the polygon is regular then each exterior angle is congruent, then

n = 360° ÷ 18° = 20

Answer:

The quantity of oil in the tank is 12,000 liters

Step-by-step explanation:

Firstly, we find the volume of the tank.

The tank is a cuboid, so we find the volume of a cuboid.

Kindly understand that when finding the volume of the cuboid, we shall not use the height of 3m.

This is because the tank is not full but it is to a height of 1.2m

So mathematically, the volume is calculated as follows;

V = l * b * h

where b = 5m , l = 2m and h = 1.2m

Thus the volume would be ;

V = 5 * 2 * 1.2

V = 12 m^3

But that’s not the quantity of oil.

From the question, 1 cubic meters contains 1000 liters of oil

So 12 cubic meter will contain = 12 * 1000 = 12,000 liters of oil

Answer:

The quantity of oil in the tank is 12,000 liters

Step-by-step explanation:

Firstly, we find the volume of the tank.

The tank is a cuboid, so we find the volume of a cuboid.

Kindly understand that when finding the volume of the cuboid, we shall not use the height of 3m.

This is because the tank is not full but it is to a height of 1.2m

Answer:

Not 100% sure but here I go

Step-by-step explanation:

\(g(5) = - 5 - 4 = - 9 \\ g(5) = - 9\)

Answer:

given,

g(x) = -x-4

so

g(5) = -5-4

= -9

Step-by-step explanation:

it's from function.

A function in math is a like a machine that take an input from you and does something.

like here they asked x and they will return -x-4 .

g(5) means if x=5 then what is -5-4?(-9) for this function?

Answer:

six pounds of ribs will cost you $42

Step-by-step explanation:

and 10 lb will cost $70 so that's how much pounds will get you to $70 worth of ribs

Answer:

what does ^ mean?

if u tell me that then i can help u answer the question

Step-by-step explanation:

The graph of the function g(x) = −|x + 3| − 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

g(x) = −|x + 3| − 2

The above expression is an absolute value function that hs the following properties

Next, we plot the graph

See attachment for the graph of the function

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Answer:

$20

Step-by-step explanation:

total money to be spent-$18+$6+$6=$30

Money he has=$6

Money his uncle gave him=$4

Total money he has=$10

Money he needed =$30-$10=$20

Answer:

Tony needs $20 more to buy everything.

Step-by-step explanation:

1. Add the prices of what Tony wants to buy together. ($6 +$18 + $6=?)

2. Add the amount of money Tony has now together. ($6 + $4=?)

3. Subtract the second amount ($6 + $4=?) from the first amount ($6 +$18 + $6=?) and that is your answer ($20)

Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

Answer:

The Answer is D

Step-by-step explanation:

Answer:

The angle subtended by the arc is 171.8873385 degrees (3 radians)

Step-by-step explanation:

The formula of the length of an arc of a sector is L = \(\frac{x}{360}\) × 2 π r, where

∵ An arc of a sector is three times its radius

∴ L = 3r

→ Equate the formula of the length of the arc by 3r

∵ \(\frac{x}{360}\) × 2 π r = 3r

→ Divide both sides by r

∴  \(\frac{x}{360}\) × 2 π = 3

→ Simplify the left side

∵  \(\frac{\pi }{180}\) x = 3

→ Divide both sides by  \(\frac{\pi }{180}\)

∴ x = 171.8873385°

∴ The angle subtended by the arc is 171.8873385 degrees (3 radians)

b. the variable is not correlated with the regression error. if an explanatory variable is exogenous, it means that the variable is not correlated with the regression error term. This assumption is important for obtaining unbiased and consistent parameter estimates in regression analysis.

If an explanatory variable is exogenous, it implies that the variable is not correlated with the regression error term. In other words, the exogenous variable is unrelated to the factors that are not explicitly included in the regression model and captured by the error term.

Exogeneity is an important assumption in regression analysis, as violating this assumption can lead to biased and inconsistent parameter estimates. When an explanatory variable is exogenous, it means that its value is determined independently of the other variables in the model and the error term.

Let's briefly discuss the other options:

a. The variable cannot be correlated with other explanatory variables: Exogeneity does not necessarily imply that the variable cannot be correlated with other explanatory variables. Explanatory variables can be correlated with each other as long as they are not correlated with the regression error term.

c. The variable must have zero mean: Exogeneity does not require that the variable has a zero mean. Exogeneity refers to the lack of correlation between the variable and the regression error, not its mean value.

d. The value of the variable must be randomly assigned: Exogeneity does not require that the value of the variable is randomly assigned. Exogeneity implies that the variable is not affected by the regression error and is determined independently of the other variables in the model, but it does not necessarily imply a random assignment of values.

In summary, if an explanatory variable is exogenous, it means that the variable is not correlated with the regression error term. This assumption is important for obtaining unbiased and consistent parameter estimates in regression analysis.

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Answer:

A tiny cat named Tiny sits all day in the window and watches people pass by.

Step-by-step explanation:

A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.

Answer:

It is 1/45

Step-by-step explanation:

The probability of drawing two yellow marbles=4/45.

It is given that Total number of marbles=10 ,number of yellow marble is 2, number of pink marble is 3 and number of blue marble is 5.

To find the probability of drawing two yellow marbles if the first one is not placed back into the bag before the second draw.

The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

The probability of drawing first yellow marble=2/10=1/5

When first yellow marble is not placed back into the bag before the second draw.

Then, number of remaining  yellow marble=1

Total number of marbles=9

The probability of drawing second yellow marble =4/9

Now, the probability of drawing two yellow marbles =1/5*4/9=4/45

Hence, the probability of drawing two yellow marbles=4/45

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Answer:

Step-by-step explanation:

6x-3+2x-1=10x-18

8x-4=10x-18

18-4=10x-8x

14=2x

X=7

AB = (6*7)-3=39

BC=13

AC=39+13=52 or

AC=(10*7)-18=52

Answer:

3/13

Step-by-step explanation:

We put this equation into slope-intercept form by adding 13y to both sides. Then we divide both sides by 13. Lastly, the number we multiply x by equals our slope.

Answer:

It's true because its a rational number.

Step-by-step explanation:

Answer:

it is false since all integers (whole numbers and zero) are rational numbers, but not all rational numbers are integers (rational numbers can be fractional). To answer this question, you need to consult the definition of rational numbers.

The plane will reach an altitude of 21,000 feet approximately 29.2 minutes after lift off. Rounded to the nearest whole minute, the plane will be at an altitude of 21,000 feet 37 minutes after lift off.

To determine the number of minutes after lift off when the plane reaches an altitude of 21,000 feet, we need to solve the equation a = 21,000, where "a" represents the altitude in feet. By substituting the altitude value into the equation and solving for the variable, we can find the number of minutes.

The given equation represents the altitude "a" of the plane in feet, given by a = 3480 + 600t, where "t" represents the time in minutes after lift off. We need to find the number of minutes when the plane is at an altitude of 21,000 feet.

By substituting a = 21,000 into the equation, we have:

21,000 = 3480 + 600t

To isolate "t," we subtract 3480 from both sides:

21,000 - 3480 = 600t

Simplifying, we get:

17,520 = 600t

Dividing both sides by 600, we find:

t = 29.2

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According to the given information, 46% of people believe that there is life on other planets. A scientist, who disagrees with this finding, conducted a survey of 120 randomly selected individuals and found that 48 of them believed in life on other planets. To determine if there is sufficient evidence to conclude that the percentage differs from 48 at a significance level (α) of 0.10, a hypothesis test is needed.

The null hypothesis (H0) states that the percentage is equal to 48%, while the alternative hypothesis (H1) states that the percentage differs from 48%. In this case, the sample proportion (p) is 48/120 = 0.4, and the hypothesized proportion (p0) is 0.48.

To perform the hypothesis test, we need to calculate the test statistic (z) and compare it to the critical values. The test statistic can be calculated using the formula z = (p - p0) / √(p0 * (1 - p0) / n), where n is the sample size. After calculating the test statistic, we compare it to the critical values corresponding to α = 0.10.

If the test statistic falls within the critical region, we reject the null hypothesis and conclude that there is sufficient evidence to claim that the percentage differs from 48%. If it falls outside the critical region, we fail to reject the null hypothesis and cannot conclude that the percentage differs from 48% based on this sample.

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16-p

1) 7+9=16

2) It states that  "then subtract p from the result" so that means 16-p which is the final answer because we cannot further substitute p without a known result

Answer:

b = 4.5 m

Step-by-step explanation:

Since we have 2 sides of the shape and the total volume, we can easily find the measurement of the third side which is the breadth by:

volume = 160.875

v = l×h×b

160.875m=(6.5m)×(5.5m)×b

160.875m=35.75b

b = 4.5 m

Answer:

4.5m

Step-by-step explanation:

v=lbh

b=v/lh

= 160.875/(6.5×5.5)

=160.875/35.75

=4.5m