Find the area of the shape below.
9 cm
11 cm
6cm
15 cm

This is a binomial probability problem with n=11 (the number of drivers selected) and p=0.07 (the probability that a driver was involved in an accident).

To find the probability of getting 3 or more drivers who were involved in an accident, we need to find the probability of getting 3, 4, 5, ..., 11 drivers who were involved in an accident and then add those probabilities together.

We can use the binomial probability formula to calculate each of these individual probabilities:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the number of drivers who were involved in an accident, k is the number of drivers we want to calculate the probability for, and (n choose k) is the binomial coefficient, which is calculated as:

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can calculate the probability of getting exactly k drivers who were involved in an accident.

For k=3, we have:

P(X=3) = (11 choose 3) * 0.07^3 * 0.93^8 = 0.1038

For k=4, we have:

P(X=4) = (11 choose 4) * 0.07^4 * 0.93^7 = 0.0286

For k=5, we have:

P(X=5) = (11 choose 5) * 0.07^5 * 0.93^6 = 0.0052

For k=6, we have:

P(X=6) = (11 choose 6) * 0.07^6 * 0.93^5 = 0.0007

For k=7, 8, 9, 10, 11, we have:

P(X=7) = (11 choose 7) * 0.07^7 * 0.93^4 = 0.0001

P(X=8) = (11 choose 8) * 0.07^8 * 0.93^3 = 0.0000

P(X=9) = (11 choose 9) * 0.07^9 * 0.93^2 = 0.0000

P(X=10) = (11 choose 10) * 0.07^10 * 0.93^1 = 0.0000

P(X=11) = (11 choose 11) * 0.07^11 * 0.93^0 = 0.0000

To get the probability of getting 3 or more drivers who were involved in an accident, we need to add up the probabilities for k=3, 4, 5, ..., 11:

P(X>=3) = P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) + P(X=11)

P(X>=3) = 0.1393

Therefore, the probability of getting 3 or more drivers who were involved in an accident out of 11 randomly selected drivers is 0.1393, or about 13.93%.

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

7+3 * 8

Step-by-step explanation:

It is 7+3*8 because if your going to check your work you can add 7 + 3 8s just to check it and you should get 31  

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(

12

,

67.45

)

Equation Form:

x

=

12

,

y

=

67.45

Answer:

Option a. 1.2 is the correct answer

Step-by-step explanation:

Given the data in the question;

sample size n = 10

sub group = 6

The average of sample means x" = 3.2

Average range value R' = 0.6

the value of UCL for the R-chart = ?

To get the value of UCL for the R-chart, we say;

\(UCL_R\) = D₄ × R'

from table of constants "Tabular values for x-bar and range charts

for size 6, the factor for control limits for range D₄ = 2.004

so we substitute  

\(UCL_R\) = 2.004 × 0.6  

\(UCL_R\) = 1.2024 ≈ 1.2  

Hence, Option a. 1.2 is the correct answer.

a. There is a 0.7643 percent probability that the website will have fewer than 5 million visitors in a single day.

b. There is a 0.0375 percent chance that the website will have 3 million or more visitors in a single day.

c. There is a 0.3186 percent chance that the website will receive between 3 million and 4 million visitors in a single day. Therefore, about 5,276,320 visits per day's worth of website traffic will necessitate Smiley's People buying more server space.

d. The amount of web traffic that will require Smiley's People to purchase additional server capacity is approximately 5,276,320 visitors per day.

In order to calculate the likelihood, we must standardise the data using the equation z = (x - mu) / sigma, where x is the value we are interested in, mu is the mean, sigma is the standard deviation, and z is the standardised value.

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When the reviewers plot the histogram, the distribution will tend to look like a normal curve because of the law of the central limit theorem.

It should be noted that a normal curve simply means a continuous probability distribution that is symmetrical on the sides of the mean.

In this case, when reviewers plot the histogram, the distribution will tend to look like a normal curve because of the law of the central limit theorem.

According to the theorem, when the sample size is at least 30, then the distribution of the sample mean will be approximately normal.

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Answer:

I'd say the second answer.

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

the ratio is 14 to 6 so if you have 14 small milkshakes you would also have 6 regular milkshakes

to find a percentage we can buff up the ratio to add up to 100

14 + 6 = 20

100 / 20 = 5

that means we must multiply each side by 5

14 * 5 = 70

6 * 5 = 30

the ratio is now 70 to 30

you would have 70% of milkshakes that are small

The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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Answer:

She bought more polka dot fabric

Step-by-step explanation:

you can cross multiply so 9x11=99 and 12x7=84. Since 99>84, 11/12>7/9

I think its D I hope you do good on your test! Good luck!

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Answer:

x = 9

Step-by-step explanation:

2x + 15 = 5x - 12 (since it is parallel)

15 + 12 = 5x - 2x

27 = 3x

x = 9

Answer:

1.1

Step-by-step explanation:

In this image, we can see that every box, we add 0.2

From 0.1 to 0.3, we add 0.2

We continue with this pattern for the rest of the boxes

When adding decimals, you can imagine it like you are adding normal numbers, and that you are carrying extra (more than 9) to the next column in the same way.

{column/place value}

At first, it might seem like adding 0.2 to 0.9 would result in 0.11, but let's think that through a little bit more. We know that 0.1 is less than 0.2, so, it doesn't make sense for that to be the sum.

Instead, we have to carry the 11 over to the other side of the decimal. (This is because each place value is equal to 10 of the value to the right. If we add digits in the ones place that add up to 10, we carry the "1" over to the right, into the tens place.)

So, we carry the "1" from 11 to the one's place. Now, we are left with

1.1

(hope this helps!! decimals can be tricky at first)

Answer:

9rs cannot be factored any further since 9 and r and s are all prime numbers.

14xy cannot be factored any further since 14, x, and y have no common factors.

5x^2 cannot be factored any further since 5 and x^2 are both prime.

32x^2 can be factored as 2^5 * x^2.

20x^2 can be factored as 2^2 * 5 * x^2.

30x^2 can be factored as 2 * 3 * 5 * x^2.

5x^3 cannot be factored any further since 5 and x^3 are both prime.

25y^3 can be factored as 5^2 * y^3.

9xy cannot be factored any further since 9, x, and y are all prime numbers.

12x^4 can be factored as 2^2 * 3 * x^4.

Step-by-step explanation:

The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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Answer:

D. 3/19

Step-by-step explanation:

12/1 = 12

12/2 = 6

12/3 = 4

These are the only ones that make the equation true.

There are also only 19 numbers because they need to be less than 20 like the question indicated. Therefore, the answer is D.

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

Step-by-step explanation:

it would be "c" because the question asks for the number that makes the inequality true

4x≤ x+3

the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example

4 x -7=-28

-28+3=-25

-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5

5 is not greater than 8 so it doesnt work

There are six sides to a die and only one side has a two, so the probability of rolling a 2 is 1/6.

There are two sides to a coin and only one side has a head, so the probability of its coming up heads is 1/2.

The two events (rolling a die and flipping a coin) are independent, so the probability of both events occurring is (1/6)(1/2) = 1/12

Answer:

y=-1/3x+7

Step-by-step explanation:

y=mx+c

m=-1/3, c=7

y=-1/3x+7

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.98}{2} = 0.01\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.01 = 0.99\), so Z = 2.327.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031\)

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.0001 = 2.327\frac{0.0003}{\sqrt{n}}\)

\(0.0001\sqrt{n} = 2.327*0.0003\)

\(\sqrt{n} = \frac{2.327*0.0003}{0.0001}\)

\((\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2\)

\(n = 48.73\)

Rounding up

49 measurements are needed.

Answer:

490000

Step-by-step explanation:

Substituting \(x=40\),

\(I=-425(40)^2 + 45500(40) - 650000=490000\)

Answer:

b

Step-by-step explanation:

Discuss measures that can be taken to develop the spirit of hard work

Answer:

January

Step-by-step explanation:

Answer:

x alpha 1/y

: Introducing a constant k

x = k/y

where x = 7, y= 6

7 = k / 6

Cross Multiply

K ( constant) = 42

Answer: k = 42

Step-by-step explanation:

Formula = \(y = \frac{k}{x}\)

plug in values:

6 = \(\frac{k}{7}\)

multiply both sides by 7

k = 42