If (a + 10)(b - 8) = 0 and a is a positive, what is the value of b?

The proper decision is to reject the null hypothesis.

The concept, procedures, and method of testing a hypothesis against the null hypothesis. The testing hypothesis is said to have that level of significance if the null hypothesis is only rejected if its probability is less than a preset significance level.

Given: p-value = 0.02916

Level of significance = 9%

The P-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis were true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed.

If the P-value is less than (or equal to), then the null hypothesis is rejected in favor of the alternative hypothesis. And, if the P-value is greater than, then the null hypothesis is not rejected.

Therefore, p-value is less than the level of significance.

Hence, we are rejecting the null hypothesis.

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The answers are =

a) left-skewed

b) Standard Error ≈ 3.146

c) the probability is approximately 0.7867.

d) standard deviation of = 94.094.

e) the probability is approximately 0.8669.

(a) The distribution of students' grades is left-skewed.

(b) If n = 30 students are selected at random, the distribution of the sample mean grade is approximately normal with a mean of 68 and a standard deviation of 3.146.

To calculate the standard deviation of the sample mean, also known as the standard error, you divide the population standard deviation by the square root of the sample size:

Standard Error = σ / √n = 17.2 / √30 ≈ 3.146

(c) To find the probability that the sample mean grade for these 30 students is less than 72.0, we can use the z-score formula and the standard error calculated above:

z = (x - μ) / (σ / √n)

z = (72 - 68) / (17.2 / √30) ≈ 0.7952

Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to this z-score.

From the table or calculator, the probability is approximately 0.7867.

(d) If n = 30 students are selected at random, the distribution of the sample total grade is approximately normal with a mean of 30 × 68 = 2040 and a standard deviation of √(30) × 17.2 = 94.094.

The mean of the sample total grade is the product of the population mean and the sample size (n).

The standard deviation of the sample total grade is the product of the population standard deviation and the square root of the sample size (n).

(e) To find the probability that the total grade for these 30 students is less than 2160.0, we can use the z-score formula and the standard deviation calculated above:

z = (x - μ) / (σ × √n)

z = (2160 - 2040) / (17.2 × √30) ≈ 1.105

Using the standard normal distribution table or a calculator, the probability corresponding to this z-score is approximately 0.8669.

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The number has 15 digits in its base 2 representation before tripling, and after tripling, it has 14 digits.

To determine the number of digits in a base 2 number that consists of 15 ones when tripled, we need to calculate the value of the number after tripling it and then determine the number of digits in its base 2 representation. The given number consists of 15 ones, which in base 2 represents the number 111...111, where there are 15 ones.

When we triple this number, we get 111...111 * 3. Multiplying a base 2 number by 3 is equivalent to shifting all the digits to the left by 1 and adding a 0 at the rightmost position. So, the tripled number in base 2 would be 111...1110, where there are 14 ones followed by a 0. Therefore, the number has 15 digits in its base 2 representation before tripling, and after tripling, it has 14 digits.

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Answer:c

Step-by-step explanation:

Answer:

The answer would be B.

Answer:

7. 2s^7

8. 2s^4/5s^2

9. 108s^9

10. h^7

Step-by-step explanation:

7) (2s^3)^4

= 2s^(3+4)

= 2s^7.

8) (2s^2/5s)^2

= (2s^4/5s^2)

= 2s^4/5s^2.

9) 3s^5 × 4s^-2 × 9s^6

= 12s^{5+(-2)} × 9s^6

= 12s^3 × 9s^6

= 108s^9.

10) h^5/h^-2

= h^{5-(-2)}

= h^7.

if it helps don't forget to like and mark me

The accounting equation is a fundamental principle in accounting that states that assets equal liabilities plus equity. Using this equation, missing amounts can be determined in various situations.

The accounting equation is expressed as Assets = Liabilities + Equity. It serves as the foundation for double-entry bookkeeping and ensures that the financial statements are balanced. By rearranging the equation, missing amounts can be determined.

For example, if the assets and equity are given, the missing amount of liabilities can be calculated by subtracting equity from assets. Conversely, if the liabilities and equity are known, the missing amount of assets can be calculated by adding liabilities to equity.

Similarly, if the assets and liabilities are provided, the missing amount of equity can be calculated by subtracting liabilities from assets. Alternatively, if the assets and equity are known, the missing amount of liabilities can be calculated by subtracting equity from assets.

In each situation, the missing amount can be determined by applying the accounting equation and rearranging it to solve for the missing variable. This equation provides a framework for ensuring that all financial transactions are properly recorded and that the financial statements accurately reflect the financial position of a business.

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Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

By removing the outlier, the mean increases from 78.125 to 79.1429. This adjustment reflects the impact of the outlier on the overall Average.

Part A: To determine if there is an outlier in the data set, we can calculate the measures of central tendency, such as the mean and median, and analyze the deviation of each data point from these measures.

Calculating the mean:

Mean = (78 + 82 + 73 + 59 + 79 + 80 + 83 + 81) / 8 = 78.125

Calculating the median:

First, we need to arrange the data in ascending order: 59, 73, 78, 79, 80, 81, 82, 83.

Median = (79 + 80) / 2 = 79.5

Based on the calculated mean and median, we can observe that there is a potential outlier since the value 59 is significantly smaller than the other data points. To confirm this, we can also analyze the data using a box plot or other statistical techniques.

Part B: If there is an outlier, removing it from the data set will affect the mean value. The mean is sensitive to extreme values, so removing the outlier will shift the mean towards the remaining data points. In this case, since the outlier value is significantly smaller than the other data points, removing it will result in an increase in the mean.

To illustrate this, let's calculate the mean without the outlier (59):

New Mean = (78 + 82 + 73 + 79 + 80 + 83 + 81) / 7 = 79.1429

By removing the outlier, the mean increases from 78.125 to 79.1429. This adjustment reflects the impact of the outlier on the overall average.

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Answer:

10

Step-by-step explanation:

i. The price p* at which total revenue is at its maximum is 12.5.

ii. When p > p*, dq/dp = -1.032.

Since the absolute value of dq/dp (-1.032) is greater than 1, we can conclude that the demand is elastic when p > p*.

To find the price, p*, at which total revenue is at its maximum, we need to maximize the revenue function R(p) = p * q(p), where q(p) is the demand function.

(i) To find p*, we maximize the revenue function by taking its derivative with respect to p and setting it equal to zero:

R'(p) = (dq/dp) * p + q(p) = 0.

To find dq/dp, we differentiate the demand function:

dq/dp = 130 * (-1)p^(-2) - 0.2.

Substituting this into the equation for R'(p):

(130 * (-1)p^(-2) - 0.2) * p + q(p) = 0.

Simplifying:

-130p^(-1) - 0.2p + q(p) = 0.

Now, we substitute the demand function q(p) = 130p^(-1) - 0.2p + 5:

-130p^(-1) - 0.2p + 130p^(-1) - 0.2p + 5 = 0.

Simplifying further:

-0.4p + 5 = 0.

Solving for p:

0.4p = 5.

p = 5 / 0.4.

p = 12.5.

(ii) To determine the elasticity of demand, we take the derivative of the demand function with respect to p:

dq/dp = 130 * (-1)p^(-2) - 0.2.

When p > p*, substituting p = 12.5 into dq/dp:

dq/dp = 130 * (-1)(12.5)^(-2) - 0.2.

First, let's calculate (12.5)^(-2):

(12.5)^(-2) = 1 / (12.5)^2 = 1 / 156.25 = 0.0064

Substituting this value back into dq/dp:

dq/dp = 130 * (-1) * 0.0064 - 0.2

      = -0.832 - 0.2

      = -1.032

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If the government was to impose a minimum wage of $12 then the number of unemployed workers would be 4,000.

If the government was to impose a minimum wage of $12 then a situation would arise where the demand for workers is 8,000 yet the supply for workers is 12,000.

This would lead to an unemployment rate of:

= 12,000 - 8,000

= 4,000 people

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Answer:

m=3/5

step by step example:

 1.from both sides of the equation

10+6=12

10m+6=1210m+6=12

10+6−6=12−6

2

Simplify

Subtract the numbers

Subtract the numbers

10=6

3

Divide both sides of the equation by the same term

10=6

10m=610m=6

1010=610

4

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

=35

To solve this problem, we can set up an integral to find the area of the region s. Let's assume that the line passing through the origin divides the region into two equal parts. We can express this line as y = mx, where m is the slope of the line.

To find the equation that gives the value of m, we can set up an integral that represents the area of one of the two regions. Let's call the area of one of the regions A. Since the line passes through the origin, the boundaries of the integral for this region are 0 and some value of x, which we'll call x0.

The equation for the line is y = mx, so the equation for the curve that defines the upper boundary of this region is y = mx. We can solve for x in terms of y to find the limits of integration for this region:

x = y/m

Since we want to find the area of this region, we can integrate with respect to y:

A = ∫0x0 (x/y) dy

Now we need to set up a similar integral to find the area of the other region. Let's call the area of the other region B. Since the two regions have equal areas, we know that A = B.

The boundaries of the integral for the second region are x0 and some value of x, which we'll call x1. The equation for the line is still y = mx, so the equation for the curve that defines the upper boundary of this region is y = mx. We can solve for x in terms of y again:

x = y/m

And integrate with respect to y:

B = ∫x0x1 (x/y) dy

Now we can set up an equation that equates the two regions:

A = B

∫0x0 (x/y) dy = ∫x0x1 (x/y) dy

We can solve this equation for m:

m = x1/(2x0)

So the equation involving one or more integrals whose solution gives the value of m is:

m = x1/(2x0)

where x0 and x1 are the limits of integration for the two regions. We could solve this equation by finding the value of x1 that satisfies the condition that the two regions have equal areas, given a value of x0. However, we are only asked to write the equation, not solve it.

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A)

If the order of choice is taken into consideration, we consider four possibilities for the first choice and three for the second. Then the total number of ways is given by:

B)

If the order of choices is not taken into consideration, we must divide the the previous result by 2, which is the total number of ways by which we can organize two letters (ex: AB and BA):

Answer:

0.25

Step-by-step explanation:

Answer:

\(\frac{13}{10} \:\:\:miles\)

Step-by-step explanation:

Maggie paddles her kayak  \(\frac{1}{2}\) mile to an island.

Then she paddles \(\frac{4}{5}\)  miles to a beach.

Now we have to find the total miles she travels.

Let us find now.

For that, you have to add two distances together.

\(\frac{1}{2} +\frac{4}{5}\)

\(\frac{1*5}{2*5} +\frac{4*2}{5*2}\)

\(\frac{5}{10} +\frac{8}{10}\)

\(\frac{13}{10} \:\:\:miles\)

Hope this helps you :-)

Answer:

1.3 miles total

Step-by-step explanation:

(1/2) + (4/5) miles total

Convert each fraction so that both denominators are the same:

(1/2) = (5/10)

(4/5) = (8/10)

---

Add:

(5/10) + (8/10) = (13/10) miles

Maggie paddled a total of (13/10) miles, which we could reduce and also say 1.3 miles total.

The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.

Let's denote the radius of the smallest snowball as r. According to the given information, the radius of the largest snowball is 1.5 times the radius of the smallest snowball, so its radius is 1.5r.

The volume of the smallest snowball is V_small = (4/3)πr^3.

The volume of the largest snowball is V_large = (4/3)π(1.5r)^3 = (4/3)π(3.375r^3) = (4/3)(3.375)(πr^3) = (4.5)(πr^3).

To find how many times greater the volume of the largest snowball is than the volume of the smallest snowball, we divide the volume of the largest snowball by the volume of the smallest snowball:

(V_large / V_small) = (4.5)(πr^3) / ((4/3)πr^3) = (4.5)/(4/3) = (4.5)(3/4) = 3.375.

Therefore, the volume of the largest snowball is 3.375 times greater than the volume of the smallest snowball.

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Answer:  0.1

Explanation:

Because y = rx, we can divide both sides by x to isolate r.

r = y/x

Then we'll plug in the values from the table

You only need to show your work for one row.

The  equation she will use to determine how much money she'll have after 2 years is: A = 49,000*(1+0.153/12)^(2*12).

After 2 years she'll have $70,960.36.

The formula for compound interest is: A = P * (1 + r/n)^(n*t).  In the formula, we convert the annual interest rate to a monthly rate by dividing it by 12 (the number of months in a year), and we multiply the number of years by 12 to get the number of months.

Using this formula, we can calculate how much money Lara will have after 2 years:

A = 49000 * (1 + 0.153/12)^(12*2)

A = $70,960.36

Therefore, Lara will have $70,960.36 after 2 years of compounding her investment monthly at 15.3%.

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Answer:

u + c = 6

Step-by-step explanation:

u² - c² ← is a difference of squares and factors as

u² - c² = (u - c)(u + c) = 36 , thus

6(u + c) = 36 ( divide both sides by 6 )

u + c = 6

Answer:

Train A= 249 tons

Train B= 87 tons

Step-by-step explanation:

Total weight of Train A and Train B= 336 tons

Weight of Train A > Weight of Train B

Difference of their weights= 162 tons

Let the weight of Train A be t.

Then weight of Train B= t-162

Total weight= 336 tons

         t+t-162= 336

                 2t= 336+162

                 2t= 498

                   t= \(\frac{498}{2}\)

                   t= 249

t-162= 249-162

       = 87

∴ the weights of Train A and Train B are 249 tons and 87 tons respectively.

Answer:2 gallons

Step-by-step explanation: 264 divided by 11 equals 24. 24 x 2 equals 48. so he need 2 gallons of gas to travel 48 miles

Hence, he required \(2\) gallons of gas.

What is the miles?

Mile is a unit of distance, commonly used to measure large distances.

Here given that,

Jack's car used \(11\) gallons to travel \(264\) miles.

Then,

\(\frac{264}{11}=24\)

So , we multiply it with \(2\)

\(24(2)=48\)

Hence, he required \(2\) gallons of gas.

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The solution of t(n)=2t(n/2) n² using the master theorem is O(n² logn).

The given recursion relation is t(n)=2t(n/2) + n².

We will find the solution of t(n) using the Master Theorem below:

Master Theorem: If a recursion relation is of the form t(n) = a t(n/b) + f(n), then it can be solved using the following formula:

If f(n) = O(\(n^d\)), then t(n) has the following time complexity:

1. If a < bd, then t(n) = O(\(n^d\))2.

If a = bd, then t(n) = O(\(n^d\) logn)3.

If a > bd, then t(n) = O(\(n^{(logb a)\))

Let's compare f(n) = n² with \(n^d\):

We see that f(n) = O(n²)

since d = 2 and f(n) grows at the same rate as n².

Now we will compare a with bd:a = 2,

b = 2,

d = 2

We see that a = bd

Therefore, t(n) = O

(\(n^d\) logn) = O(n² logn)

Thus, the solution to t(n) = 2t(n/2) + n² using the Master Theorem is O(n² logn).

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Answer:

5m

Step-by-step explanation:

Calculamos usando la fórmula de la proporción

Sombra / Altura

Deje que la altura de la luz de la calle = x

1,4 m / 1,75 m = 4 m / x

Multiplicar cruzada

1,4 × x = 1,75 × 4

Dividir ambos lados por 1.4

x = 1,75 × 4 / 1,4

x = 5

Por lo tanto, la altura de la farola es de 5 m.

Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and rotation.

Rigid transformations are transformation that produces an image with the same size, shape and angle as the original object. Rigid transformations are translation, rotation and reflection.

Dilation is not a rigid transformation.

All the transformations attached are rigid transformations.

Answer:

Trinomial

Step-by-step explanation:

The given polynomial is a trinomial because it has three terms.

10v4 +5v2 + 2v-5

Hope this helps.