What is the value of x ?

Answer:

The answer choice is D.

Step-by-step explanation:

Multiply 5 and 8

= 40

Then put d to 40

=40d

And also multiply 6 with 5

which equals to 30.

Now the expression would be: 40d + 30

Answer:

To find the inverse, interchange the variables and solve for

y

.

f

−

1

(

m

)

=

m

x

−

b

x

Step-by-step explanation:

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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The boolean function f(x, y, z) = y'z x'yz xyz can be simplified to f(x, y, z) = y'z + x'yz + xyz. This simplified form represents a sum of three terms involving the negation and conjunction of the input variables.

The given boolean function f(x, y, z) = y'z x'yz xyz can be broken down into three terms: y'z, x'yz, and xyz. Each term represents the conjunction of some input variables and their negations. The "+" operator represents a logical OR operation, indicating that the function evaluates to true if any of the terms evaluate to true.

To simplify the function, we can express it as f(x, y, z) = y'z + x'yz + xyz. This form represents the logical OR of the three terms. In other words, the function will be true if any of the terms evaluate to true. This simplified representation is equivalent to the original function but is expressed in a more compact and readable form.

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Answer:

The left side would point down (quadrant 3)

Step-by-step explanation:

Since the polynomial is negative, the function would point downwards.

The area of square four is a² + b² + 2ab

The area of a square = l²

The Area so the two square = a² + b²

Area of the  triangles = 4(0.5ab) = 2ab

Add the area together

Area of the square four = area of square + area of 4 triangles

Area of the square four = a² + b² + 2ab

Hence the area of the square four is a² + b² + 2ab

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Answer:

c) 20 ounces

Step-by-step explanation:

Answer:

Step-by-step explanation:

our lengths are:

7.5a-1.5b,  3.5a+4.5b, 6.5c+2a, 8.5-6.5c

P=7.5a+3.5a+2a-1.5b+4.5b+6.5c-6.5c+8.5=16a+3b+8.5

F is the numerator of the fraction. To solve move g over to the opposite side by multiplying both sides by g:

F = h * g

Answer:

Step-by-step explanation:

Using set notation to answer the question. let:

n(U) be the total people in a sport centre =130

n(G) be number of people that use the gym.  = 76

n(P) be number of people that use the swimming pool. = 60

n(T) be number of people that use the track = 32

n(G∩P) be number of people that uses the gym and the pool = 23

n(P∩T) be number of people that uses the  pool and the track = 8

n(G∩T) be number of people that uses the gym and the track = 320

n(G∩P∩T) be number of people that uses all three facilities = 6

Using the relationship below;

n(U)= n(GUPUT)+n(GUPUT)'

where n(GUPUT)' is the number of people that doesn't use any facility.

Before we can get that, we need to know n(GUPUT) using the formula;

n(GUPUT) = n(G) + n(P)+n(T)-n(G∩P)-n(P∩T)-n(G∩T)+n(G∩P∩T)

n(GUPUT) = 76+60+32-23-8-20+6

n(GUPUT) = 123

n(GUPUT)' = n(U)- n(GUPUT)

n(GUPUT)' = 130 - 123

n(GUPUT)' = 7

This means that 7 person doesn't use any facility.

Probability that a person selected at random doesn't use any facility = n(GUPUT)' /n(U) = 7/130

Answer:

B

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

w - (-v)

-3 - (-6)

3

Hope this helps!

the mean score for a critical reading test, using Excel, the probability that a random sample of 500 students will have a mean score of more than 590 can be calculated to be approximately 0.408.

To calculate the probabilities using Excel, we can utilize the standard normal distribution. First, we need to convert the sample means to z-scores by using the formula: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). For the sample mean of more than 590, we can calculate the probability of z being greater than the corresponding z-score using the formula "=1-NORM.S.DIST(z-score,TRUE)". In this case, the z-score is (590 - 580) / (115 / sqrt(500)), which gives approximately 0.408.

Similarly, for the sample mean of less than 575, we calculate the probability of z being less than the corresponding z-score using the formula "=NORM.S.DIST(z-score,TRUE)". The z-score is (575 - 580) / (115 / sqrt(500)), which gives approximately 0.084.

Therefore, the probability that a random sample of 500 students will have a mean score of more than 590 is approximately 0.408, and the probability that the sample mean is less than 575 is approximately 0.084.

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a) The 95% confidence interval is 18.95% to 34.49%. b) The confidence interval for women (18.95% to 34.49%) does not include the value of 23.6%.

To construct a 95% confidence interval for the percentage of successful challenges made by women playing singles matches, we can use the formula for the confidence interval for a proportion. The formula is:

Confidence Interval = p ± Z * \(\sqrt{p(1-p)/n}\)

Where:

p is the sample proportion (successful challenges / total challenges)

Z is the z-score corresponding to the desired confidence level

n is the sample size

a. Let's calculate the confidence interval for the percentage of successful challenges made by women:

Sample size (n) = 135

Number of successful challenges (x) = 36

Sample proportion (p) = x/n

p = 36/135 ≈ 0.2667

To find the z-score corresponding to a 95% confidence level, we need to calculate the critical value. Since the sample size is large enough (n > 30), we can approximate the critical value using the standard normal distribution.

The z-score corresponding to a 95% confidence level (two-tailed test) is approximately 1.96.

Confidence Interval = 0.2667 ± 1.96 * \(\sqrt{0.2667(1-0.2667)/135}\)

Calculating the confidence interval:

Confidence Interval = 0.2667 ± 1.96 * \(\sqrt{0.2667*0.7333/135}\)

= 0.2667 ± 1.96 * \(\sqrt{0.19511/135}\)

= 0.2667 ± 1.96 * 0.03943

≈ 0.2667 ± 0.07723

The lower bound of the confidence interval is:

0.2667 - 0.07723 ≈ 0.1895

The upper bound of the confidence interval is:

0.2667 + 0.07723 ≈ 0.3449

Therefore, the 95% confidence interval for the percentage of successful challenges made by women is approximately 18.95% to 34.49%.

b. To compare the results with the 95% confidence interval for the percentage of successful challenges made by men (23.6%), we can observe that the confidence interval for women does not overlap with the value for men.

The confidence interval for women (18.95% to 34.49%) does not include the value of 23.6%. This suggests that there may be a significant difference in the percentage of successful challenges made by women compared to men.

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The true statements are:

b. The variability of the sampling distribution of the mean (\(\overline x\)) is less than the variability of the individual observations (x)

a. A sufficiently large sample size for the central limit theorem is greater than 30.

The CLT states that if a sample is drawn randomly from any population, the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution, as the sample size increases.

This means that for large enough sample sizes, the mean and standard deviation of the sample mean can be estimated using a normal distribution.

Let's check each option as follows  

Statement c is false because a sample size of 30 or greater is often considered sufficiently large for the central limit theorem.

Statement d is false because the variability of the sampling distribution of the mean decreases as the sample size increases, which is why the central limit theorem is useful.

Therefore,

The true statements are:

b. The variability of the sampling distribution of the mean (X-bar) is less than the variability of the individual observations (X)

a. A sufficiently large sample size for the central limit theorem is greater than 30.

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In the design of timber members, the modification factor K12 is used to account for several factors, including the effect of shrinkage, swelling, and temperature changes on the strength of the timber member.

The modification factor K12 is used to adjust the strength of timber members for shrinkage, swelling, and temperature changes. The factors accounted for by this factor are as follows:

1. Shrinkage: Shrinkage is the decrease in the dimensions of timber that occurs as the moisture content decreases. The strength of timber members decreases with decreasing moisture content. The reduction in strength due to shrinkage can be accounted for by using the modification factor K12.

2. Swelling: Swelling is the increase in the dimensions of timber that occurs as the moisture content increases. The strength of timber members decreases with increasing moisture content. The reduction in strength due to swelling can be accounted for by using the modification factor K12.

3. Temperature Changes: The strength of timber members is affected by temperature changes. As temperature increases, the strength of timber members decreases. The reduction in strength due to temperature changes can be accounted for by using the modification factor K12.

4. Duration of Load: The duration of load affects the strength of timber members. A long-duration load reduces the strength of timber members more than a short-duration load. The reduction in strength due to the duration of load can be accounted for by using the modification factor K12.

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The volume of the cylinder is option d.10 units

To solve for the volume of the cylinder, we can first cancel out the h on both sides by dividing both sides by h:

(1/3)πr² = πr²

Next, we can simplify the equation by multiplying both sides by 3:

πr² = 3(100π)

πr² = 300π

Finally, we can solve for the volume of the cylinder by plugging in the values we have:

V = πr²h = πr²(2h/2) = (πr²/3)(3h) = (100π/30)(3) = 300π/30 = 10

Therefore, the volume of the cylinder is also 10 cubic feet, which is the same as the volume of the cone.

Hence the option (d) is correct.

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tThe population in this scenario refers to the entire group of policyholders of the large automobile insurance company.

Set up the hypotheses ; Null hypothesis (H0): The mean age in the population of policyholders is 50.  Alternative hypothesis (Ha): The mean age in the population of policyholders is different from 50. Determine the significance level: The significance level is given as 5%.  Calculate the test statistic: The test statistic for a two-sample t-test is given by:
    t = (sample mean - hypothesized mean) / (standard error)

 In this case, the sample mean is 47.2, and the hypothesized mean is 50. The standard error can be calculated using the formula: standard error = sqrt(variance / sample size).  In this case, the variance is 121 and the sample size is 361. Calculate the degrees of freedom:  For a two-sample t-test, the degrees of freedom is calculated as the sum of the sample sizes minus 2.  In this case, the sample size is 361.  Determine the critical value:  Since the alternative hypothesis is two-tailed (different from 50), we divide the significance level by 2 (5% / 2) to get the critical value for each tail.

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Answer: 3/20 also known as 15%  Hope this helps Have a great night

Step-by-step explanation:

Answer:

B. (1, -5), (3, -9), (6, -2)

Step-by-step explanation:

First vertex: -2 + 3 = 1, -1 - 4 = -5, so (1, -5)

Second vertex: 0 + 3 = 3, -5 - 4 = -9, so (3, -9)

Third vertex: 3 + 3 = 6, 2 - 4 = -2, so (6, -2)

(1, -5), (3, -9), (6, -2)

I hope this helps :))

The number of students who registered for both robotics and app development is 70.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total members = 280

The number of members who registered for the robotics class.

= 75% of 280

= 3/4 x 280

= 3 x 70

= 210

The number of members who registered for the app development class

= 50% of 280

= 1/2 x 280

= 140

We see that,

210 + 140 = 350

But we have 280 members.

So,

The number of students who registered for both robotics and app development.

= 350 - 280

= 70

Thus,

The number of students who registered for both robotics and app development is 70.

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Answer:

Step-by-step explanation:

Answer:

The interpretation of that same problem is listed throughout the section below on explanation.

Step-by-step explanation:

Interpretation:

Researchers seem to be confident with 95% that the sample selection standard error seems to be + as well as - 4 percent respectively.

This same margin of sampling error would then decrease from either the mean or average value by four percentage points smaller or even larger, it describes the survey method.

So that the above is the right answer.

Answer:

6

Step-by-step explanation:

Answer:

\( \sf \: x = 8\)

Step-by-step explanation:

Given equation,

→ 11x + (-4x) = 56

Now the value of x will be,

→ 11x + (-4x) = 56

→ 11x - 4x = 56

→ 7x = 56

→ x = 56/7

→ [ x = 8 ]

Hence, the value of x is 8.

Option C is correct.  Less than 100  is closest to total deaths resulting from ladder misuse each year.

According to the Consumer Product Safety Commission (CPSC), on average, approximately 300 people die each year in the United States from falls involving ladders.

However, not all of these deaths are due to ladder misuse. In fact, the number of deaths resulting specifically from ladder misuse is likely to be lower. It is estimated that a significant portion of ladder-related fatalities are caused by factors such as overreaching, misusing the ladder, or failing to follow proper safety guidelines.

To reduce the number of deaths and injuries resulting from ladder misuse, it is important to follow safety guidelines and to choose the right ladder for the job, taking into consideration factors such as height, weight, and stability.

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Using it's concept, it is found that there is a 0.64 = 64% probability that the sum of two randomly chosen numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is no greater than 10.

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem:

For a sum no greater than 10, we have that:

Hence, the number of desired outcomes is:

\(D = 10(2) + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 = 64\)

The probability is:

\(p = \frac{D}{T} = \frac{64}{100} = 0.64\)

0.64 = 64% probability that the sum of two randomly chosen numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is no greater than 10.

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Answer:

17

Step-by-step explanation:

replace x with 5

3*5+2

next you use pemdas

you multiply before you add

3*5=15

15+2=17

Answer:

804.2

Step-by-step explanation:

Formula
\(\pi r^{2}\)

plug in

\(\pi *16^{2}\)

≈ 804.24772

round to nearest tenth

≈ 804.2

Answer:

24

Step-by-step explanation:

9+6(2+3/6)

9+6(2+1/2)

2+1/2 = 2.5

9+6(2.5)

9+15

24