A six-sided die is rolled, and the number N on the uppermost face is recorded. Then a fair coin is tossed N times, and the total number Z of heads to appear is observed. Determine the mean and variance of Z by viewing Z as a random sum of N Bernoulli random variables. Determine the probability mass function of Z, and use it to find the mean and variance of Z.

Answer:

n=2/3, -1/4

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

Let's solve your equation step-by-step.

6(x − 5) = 54

Step 1: Simplify both sides of the equation.

6(x − 5) = 54

(6)(x) + (6)(−5) = 54(Distribute)

6x + − 30 = 54

6x − 30 = 54

Step 2: Add 30 to both sides.

6x − 30 + 30 = 54 + 30

6x = 84

Step 3: Divide both sides by 6.

6x/6 = 84/6

x = 14

Answer:

1) Null hypothesis:[tex]\mu = 120[/tex]  

Alternative hypothesis:[tex]\mu \neq 120[/tex]  

2) [tex]t=\frac{118.3-120}{\frac{3.7}{\sqrt{22}}}=-2.155[/tex]  

3) [tex] t_{cric}=\pm 2.08[/tex]

And the rejection zone of the null hypothesis would be [tex] |t_{calc}|>2.08[/tex]

4) Since our statistic calculated is higher than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

5) Since we reject the null hypothesis of accuracy we have enough evidence to conclude at 5% of significance that the procedure is not accurate

6) Since we reject the null hypothesi we need to expect that the p value would be lower than the significance level provided and that means:

[tex] p_v <\alpha[/tex]

Step-by-step explanation:

Data given and notation  

[tex]\bar X=118.3[/tex] represent the sample mean

[tex]s=3.7[/tex] represent the sample standard deviation

[tex]n=22[/tex] sample size  

[tex]\mu_o =120[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

Part 1: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is equal to 120 because that means accurate, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 120[/tex]  

Alternative hypothesis:[tex]\mu \neq 120[/tex]  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Part 2: Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{118.3-120}{\frac{3.7}{\sqrt{22}}}=-2.155[/tex]    

Part 3: Rejection region

We calculate the degrees of freedom given by:

[tex] df = n-1= 22-1 =21[/tex]

We need to find a critical value who accumulates [tex]\alpha/2 = 0.025[/tex] of the area in the tails of the t distribution with 21 degrees of freedom and we got:

[tex] t_{cric}=\pm 2.08[/tex]

And the rejection zone of the null hypothesis would be [tex] |t_{calc}|>2.08[/tex]

Part 4

Since our statistic calculated is higher than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

Part 5

Since we reject the null hypothesis of accuracy we have enough evidence to conclude at 5% of significance that the procedure is not accurate

Part 6

Since we reject the null hypothesi we need to expect that the p value would be lower than the significance level provided and that means:

[tex] p_v <\alpha[/tex]

Answer:

(a) Proportion of Defectives = 0.01

Expected Number Defective = 0.5

Probability of Rejecting the Shipment = 0.0138

(b) Proportion of Defectives = 0.05

Expected Number Defective = 2.5

Probability of Rejecting the Shipment = 0.459

(c) Proportion of Defectives = 0.1

Expected Number Defective = 5

Probability of Rejecting the Shipment = 0.888

Step-by-step explanation:

This is a binomial distribution problem due to the unchanging probability of getting a defective board, no matter the number of trials ran.

The expected number for binomial distribution is given as E(X) = np

The probability mass funaction for binomial distribution is given as

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 50

x = Number of successes required = ≥3

p = probability of success = changing from question to question

q = probability of failure = 1 - p

Total number of boards tested = 50

Note that probability of rejecting the shipment for each of the sub-question is the probability that 3 or more boards are defective. That is, P(X ≥ 3)

P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]

a) Proportion of Defectives=0.01

Expected Number Defective = np = 0.01 × 50 = 0.5

Probability of Rejecting the Shipment = P(X ≥ 3)

n = total number of sample spaces = 50

p = probability of success = probability of a detective board = 0.01

q = probability of failure = 1 - 0.01 = 0.99

P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)] = 0.01381727083 = 0.0138

b) Proportion of Defectives = 0.05

Expected Number Defective = np = 0.05 × 50 = 2.5

Probability of Rejecting the Shipment = P(X ≥ 3)

n = total number of sample spaces = 50

p = probability of success = probability of a detective board = 0.05

q = probability of failure = 1 - 0.05 = 0.95

P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)] = 0.45946687728 = 0.459

c) Proportion of Defectives = 0.1

Expected Number Defective = np = 0.1 × 50 = 5

Probability of Rejecting the Shipment = P(X ≥ 3)

n = total number of sample spaces = 50

p = probability of success = probability of a detective board = 0.1

q = probability of failure = 1 - 0.1 = 0.90

P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)] = 0.88827124366 = 0.888

Hope this Helps!!!

80% of the times we are confident that the mean number of oocytes retrieved will fall in interval  ( 8.8 , 10.6 ).

A confidence interval is the probability that an estimate will fall in a particular range for a certain number of times.

From the given scenario, women are selected from the age group 36-40.

The mean number of oocytes retrieved from the 98 participants was 9.7 with an 80 % confidence level z ‑interval of ( 8.8 , 10.6 )

From the given condition we can conclude that if we repeat the experiment 80% of the times we are confident that the mean number of oocytes retrieved will fall in interval  ( 8.8 , 10.6 ).

Thus, the mean number of oocytes retrieved from the 98 participants in Group A was 9.7 with an 80 % confidence level has z ‑interval of ( 8.8 , 10.6 )

Learn more about Confidence interval, here:

https://brainly.com/question/34299305

#SPJ4

The question discusses a study in reproductive endocrinology involving hormone-assisted retrieval of oocytes for assisted reproduction, like IVF. Two hormones, likely follicle-stimulating hormone and luteinizing hormone, are used from day one to boost ovulation. The reported average number of oocytes and the confidence interval indicate the effectiveness of this treatment strategy.

The study described touches upon a field within biology known as reproductive endocrinology with a focus on hormone-assisted techniques in assisted reproduction like IVF (In Vitro Fertilization). The two hormones administered from day one are likely gonadotropins, consisting of follicle-stimulating hormone (FSH) and luteinizing hormone (LH), as per the common methods in IVF procedures. FSH supports the development of multiple follicles while LH triggers ovulation. Their administration significantly boosts the usual number of oocytes (eggs) produced in a woman's ovulation cycle.

Moreover, the mean number of oocytes (9.7) retrieved from the participants in Group A gives an indication of the effectiveness of the treatment strategy. The 80% confidence level z-interval of (8.8, 10.6) suggests that the actual mean number of oocytes retrieved for the overall population of women, aged 36-40 years, following this treatment strategy, is likely to lie within this range with an 80% probability.

https://brainly.com/question/554326

#SPJ11

Answer:

Benny's mom's age is 400% of Benny's age.

Step-by-step explanation:

Let p represent the percent of his mom's age to Benny's age.

48=P(12)

p=4=400%

Answer:

  all real numbers: -∞ < x < ∞

Step-by-step explanation:

Any polynomial function is defined for all real numbers. This one is, too.

The domain is ...

  -∞ < x < ∞

_____

Additional comment

Polynomial functions are often used to model things in the real world. One common application is the use of a quadratic function to model ballistic motion (height versus time). Such functions are defined for all values of the independent variable (time), but only have practical application over a smaller domain (time and height ≥ 0). Any question of domain might need to consider the practical domain, where the function is useful.

Answer:

Six more than half of a number is 20

Step-by-step explanation:

The given expression in word problem can be translated as:

Six more than half of a number is 20

Answer:

Given:

Mean, x' = 94.32

s.d = 1.20

n = 16

a) For null hypothesis:

H0 : u= 95

For alternative hypothesis:

Ha : u≠95

Level of significance, a = 0.01

(Two tailed test)

We reject null hypothesis, h0, if P<0.01 level of significance.

Calculating the test statistic, we have:

[tex] Z = \frac{x' - u_0}{s.d / \sqrt{n}} = \frac{94.32-95}{1.20/ \sqrt{16}}[/tex]

= -2.266

= -2.27

Calculating the P value:

P value = 2P(Z < -2.27)

Using the standard normal table,

NORMSDIST(-2.27)

= 0.0116

P value= 2(0.0116)

= 0.0232

Since P value(0.0232) is greater than level of significance (0.01), we fail to reject the null hypothesis H0.

We can say that there is enough evidence to conclude the data does not support that average melting point differs from the level of 95 at the level of 0.01 significance level.

b) B(u = 94)

= P(when u=94, do not reject H0)

Using the standard nkrmal table, the z-score corresponding to

Z(0.01/2)= 0.005 will be

[tex]Z_a_/_2 = 2.58[/tex]

[tex]B(94) = ∅[Z_a_/_2+ \frac{u_0-u}{s.d- \sqrt{n}}] - ∅[-Z_a_/_2+ \frac{u_0-u}{s.d/ \frac{n}}] [/tex]

[tex]B(94) = ∅[2.58+ \frac{95-94}{1.20- \sqrt{16}}] - ∅[-2.58+ \frac{95-94}{1.2/ \frac{16}}] [/tex]

= ∅(5.91)-∅(0.75)

P(Z≤5.91)-P(Z≤0.75)

From standard normal table, we have:

P(Z≤0.75)=0.7734, P(Z≤5.91)=1

= 1 - 0.7734

= 0.2266

Probability of making type II error when u=94 is 0.2266

c) Probability of committing type II error when u= 94 at a significance level of 0.01 will be =0.10.

B(94) = 0.10

Finding sample size, n for a two tailed test:

[tex] n = [\frac{s.d(Z_a_/_2+Z_B)}{u_0-u}]^2 [/tex]

Using standard normal table, Z score corresponding to a/2 = 0.005 cummulative area(1-0.005 = 0.995) is Z= 2.58

Z score corresponding to 0.10 cummulative area(1-0.10 = 0.90) is Z = 1.28

Our sample size n, wil be=

[tex] n = [\frac{1.2(2.58+1.28)}{95-94}]^2 [/tex]

[tex] = [\frac{4.632}{1}]^2 [/tex]

= 21.46

= 22

Sample size = 22

The z-score for the hypothesis test can be calculated and compared with the critical values for a two-tailed level of .01. The probability of a Type II error can be calculated using the standard normal table, and the required sample size to ensure β(94)=0.1 when α=0.01 can be calculated using the appropriate formula. Remember, in the calculations, to use the values provided in the question.

The null hypothesis will be H0: μ = 95 and the alternative hypothesis Ha: μ ≠ 95. Since we are given σ = 1.20 and the sample mean ¯x = 94.32, we can perform a z-test.

The z-score is calculated as: z = (¯x - μ) / (σ / √n), here n is the number of samples i.e., 16. Plug in the given values to calculate the z-score.

If the obtained z-score lies within the critical values of a two-tailed level of .01 (which for a normal distribution is approximately -2.576 and 2.576), we can't reject the null hypothesis.

Beta error, β(94), is the probability of a Type II error when actual mean (µ) is 94. To calculate this, you first need to find the z value for the α level .01, and then use the standard normal table to find the corresponding values for β(94).

To ensure that β(94)=0.1 when α=0.01, use the formula for sample size in hypothesis testing. You would need to find the z-scores associated with α and β, and then use these in the formula: n = [(Zα √2π + Zβ)^2 σ^2]/ (μ - μ0)^2.

https://brainly.com/question/34171008

#SPJ11

Final answer:

By creating equations representing the cost relationship between the washer and dryer, and solving for the unknown, we find that the cost of the dryer is $325.

Explanation:

To calculate the cost of the dryer when the combined cost of a washer and dryer is $584 and the washer costs $66 less than the dryer, we can set up an equation. Let's denote the cost of the dryer as D and the cost of the washer as W.

1. The first step is to express the washer's cost in terms of the dryer's cost:

W = D - 66

2. Then, use the combined cost to create an equation:

W + D = 584

3. Substitute the expression for W into the second equation:

(D - 66) + D = 584

4. Solve for D:

2D - 66 = 584

2D = 584 + 66

2D = 650

D = 650 / 2

D = 325

Therefore, the cost of the dryer is $325.

a. Chocolate need to cover a rectangle with a length of 9 in. and a perimeter of 22 inches is 18 pieces of 1 inch square piece chocolates

b.Chocolate need to cover a rectangle with a length of 5 in. and a perimeter of 20 inches is 20 pieces of 1 inch square piece chocolates

Step-by-step explanation

a. To cover a rectangle with a length of 9 in. and a perimeter of 22 in.

perimeter = 2(length+breadth)

Breadth = 22 -9×2  = 22-18 = 4 ÷ 2 = 2 inches

Area of rectangle = 9 × 2 = 18 inches

18 pieces of  1 inch square piece  Chocolate is needed to cover the rectangle

b. To cover a rectangle with a length of 5 in. and a perimeter of     20 in.

perimeter = 2(length+breadth)

Breadth = 20 - 5 ×2  = 10 = 10 ÷ 2 = 5 inches

Area of rectangle = 5 × 5 = 20 inches

20 pieces of  1 inch square piece  Chocolate is needed to cover the rectangle

Step-by-step explanation:

O!¿

L

??k l!

?

I?I

!I

??I

llp!??OP

L??

?pl?!..).!!)

>.

∆∆¿.

¿{∆}

.¿

¿∆

∆

Answer:

You can get it by doing this

Step-by-step explanation:

The Probability

Answer:

0.08 percent chance or 1/12

To cover a rectangle gift box with dimensions of 8 inches by 10 inches by 7 inches, you need to calculate the surface area by adding the area of all six faces. After calculation, you would need 412 square inches of wrapping paper.

To calculate how much wrapping paper is needed to cover a rectangle gift box exactly, we need to find the surface area of the box. The box dimensions are 8 inches wide, 10 inches long, and 7 inches tall.

Surface area of a rectangle box is calculated by adding the areas of all six faces. The areas of the faces are:

Calculating each area:

Adding all of these areas together gives us:

160 in² + 112 in² + 140 in² = 412 in².

Therefore, you would need 412 square inches of wrapping paper to cover the box exactly.

Final answer:

To find the number of kilometers in a 95-mile drive, multiply 95 by the conversion factor of 1.61 kilometers per mile, giving you 152.95 kilometers, which rounds to 153.0 kilometers when rounded to the nearest tenth.

Explanation:

To calculate how many kilometers are in a 95-mile drive when there are approximately 0.62 miles in a kilometer, we need to use the conversion factor between miles and kilometers. The conversion factor is 1 mile equals to 1.61 kilometers. Therefore, to convert 95 miles to kilometers, you multiply 95 miles by 1.61 kilometers per mile.

The calculation will be:

95 miles × 1.61 km/mile = 152.95 kilometers

After calculating, we round the answer to the nearest tenth, resulting in:

153.0 kilometers.

The ratio of the number of women to the total number of participants in the triathlon is 4:13.

The question is asking for the ratio of the number of women to the total number of participants in a triathlon. We know that there are 13 total participants and 9 of them are men. We can determine that there are 4 ladies by taking 9 out of 13. Therefore, the ratio of the number of women to the total number of participants is 4:13. This indicates that 4 women make up each of the 13 participants, according to our calculations.

https://brainly.com/question/32531170

#SPJ2

Answer:

a) X = N(1955,556)

b) 1955 is the population mean

c) P(X <1911) = 0.4685

d) P(1868 < X <2105) = 0.1685

e) 95th percentile = 2870 (nearest whole number)

Step-by-step explanation:

a) Average number of votes per district, μ = 1955

The standard deviation, [tex]\sigma = 556[/tex]

The distribution of X will take the form [tex]N(\mu, \sigma)[/tex]

Therefore the distribution of X is N(1955,556)

b)1955 is the average of all the votes president Clinton had per district(i.e. the mean of all the values of the population) and not the mean of collected samples.

1955 is the population mean

c) Probability that a randomly selected district had fewer than 1911 votes for president Clinton

[tex]P(X < 1911) = P ( z < \frac{x - \mu}{\sigma} )[/tex]

z=(1911-1955)/556

z=-0.079

From the probability distribution table

P(z<-0.079)=0.4685

Therefore, P(X <1911) = 0.4685

d)probability that a randomly selected district had between 1868 and 2105 votes for President Clinton

[tex]P(x_{1} < X <x_{2}) = P(z_{2} < \frac{x_{2} - \mu }{\sigma} )- P(z_{1} < \frac{x_{1} - \mu }{\sigma} )[/tex]

[tex]P(1868 < X <2105) = P(z_{2} < \frac{2105 - 1955 }{556} )- P(z_{1} < \frac{1868 - 1955 }{556} )\\P(1868 < X <2105) = P(z_{2} < 0.27)- P(z_{1} < -0.16 )[/tex]

P(1868 < X <2105) = 0.6063 - 0.4378

P(1868 < X <2105) = 0.1685

e)  Find the 95th percentile for votes for President Clinton

[tex]P_{95} = \mu + 1.645 \sigma\\P_{95} = 1955 + 1.645(556)\\P_{95} = 2869.62\\P_{95} = 2970[/tex]

P95=1955+1.645*556=2870

The distribution of X is a normal distribution with a sample mean of 1,956.8. The probability of a randomly selected district having fewer than 1,600 votes is approximately 0.267. The probability of a randomly selected district having between 1,800 and 2,000 votes is approximately 0.161. The 95th percentile for votes is approximately 2,885.

b. 1,956.8 is a sample mean because it is calculated from the data of the 40 election districts in Alaska.

c. To find the probability that a randomly selected district had fewer than 1,600 votes for the candidate, you need to standardize the value and use the standard normal distribution table. First, calculate the z-score using the formula z = (x - mean) / standard deviation. Plugging in the values, we get z = (1600 - 1956.8) / 572.3 = -0.621. Then, we can use the standard normal distribution table to find the probability associated with a z-score of -0.621, which is approximately 0.267.

d. To find the probability that a randomly selected district had between 1,800 and 2,000 votes for the candidate, you need to calculate the z-scores for both values and find the area between them on the standard normal distribution. Use the same formula as before to get z1 = (1800 - 1956.8) / 572.3 = -0.275 and z2 = (2000 - 1956.8) / 572.3 = 0.075. Then, use the standard normal distribution table to find the area between z1 and z2, which is approximately 0.161.

e. The 95th percentile represents the value below which 95% of the data falls. To find the 95th percentile for votes for the candidate, you can use the z-score associated with a cumulative probability of 0.95 on the standard normal distribution table. The z-score is approximately 1.645. Then, use the formula x = z * standard deviation + mean to calculate the value. Plugging in the values, we get x = 1.645 * 572.3 + 1956.8 ≈ 2,885 votes.

https://brainly.com/question/34741155

#SPJ3

Answer:

0.3222 = 32.22% probability that the mean weight of the sample babies would differ from the population mean by more than 45 grams.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 3366, \sigma = \sqrt{244036} = 494, n = 118, s = \frac{494}{\sqrt{118}} = 45.48[/tex]

Probability if differs by more than 45 grams?

Less than 3366-45 = 3321 or more than 3366+45 = 3411. Since the normal distribution is symmetric, these probabilities are equal. So we find one of them, and multiply by them.

Less than 3321.

pvalue of Z when X = 3321. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{3321 - 3366}{45.48}[/tex]

[tex]Z = -0.99[/tex]

[tex]Z = -0.99[/tex] has a pvalue of 0.1611

2*0.1611 = 0.3222

0.3222 = 32.22% probability that the mean weight of the sample babies would differ from the population mean by more than 45 grams.

Answer:

Option D is the correct answer.

Step-by-step explanation:

The possibility that a relationship between two or more variables is caused by something other than chance is known as statistical significance. Statistical hypothesis testing is used to ascertain whether the result of a data set is statistically significant. This test provides a P-value, which represents the probability that random chance could explain the result.

Generally, a P-value of 5% or lower is regarded to be statistically significant.

Statistical significance relates to whether an effect exists, whereas practical significance indicates the magnitude of the effect.

Thus, by the definitions of Statistical significance and practical significance provided, only option  D is correct, the other options are wrong.

The correct option is D- “Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis. Practical significance refers to whether the difference between the sample statistic and the parameter stated in the null hypothesis is large enough to be considered important in an application”.

The difference between statistical and practical significance involves whether findings are unlikely due to chance (statistical significance) or if the differences observed are large enough to matter in real applications (practical significance), correctly identified as option D.

The question asks to explain the difference between statistical significance and practical significance. The correct answer is option D. Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis. This involves probability estimates and is often indicated by p-values like p < 0.05, which means the data is very unlikely to have been caused by chance factors alone, and therefore, there might be a real relationship. On the other hand, practical significance refers to whether the difference between the sample statistic and the parameter stated in the null hypothesis is large enough to be considered important in an application. This considers if the findings have a real-world impact or importance beyond just being statistically unlikely due to chance.

Answer:

Solution (x, y, λ) = (2, 2, - 6)

Step-by-step explanation:

From the above information given:

3x + λ = 0............ eqn (1)

3y + λ = 0 ........... eqn (2)

x + y − 4 = 0 ......... eqn (3)

Now, from equation 1 and 2:

x= - λ / 3

y= - λ / 3

Substitute the values of X and y into equation 3

-λ/ 3 - λ/ 3 - 4 =0

-λ - λ - 12= 0

-2λ - 12= 0

-2λ = 12

λ = - 6

x= - λ/ 3

x = - (- 6) / 3

x= 2

y= - λ/3

y= - (-6)/3

y= 2

Solution (x, y, λ) = (2, 2, - 6)

Therefore,

x = 2

y= 2

λ = - 6

Given:

Given that the quadrilateral ABCD is inscribed in the circle.

The measure of ∠A is (14z - 7)°

The measure of ∠C is (8z)°

The measure of ∠D is (10z)°

We need to determine the measures of ∠A, ∠B, ∠C and ∠D

Value of z:

We know the property that the opposite angles of a quadrilateral inscribed in a circle are supplementary.

Thus, we have;

[tex]\angle A+ \angle C=180^{\circ}[/tex]

Substituting the values, we have;

[tex]14z-7+8z=180[/tex]

       [tex]22z-7=180[/tex]

             [tex]22z=187[/tex]

                 [tex]z=8.5[/tex]

Thus, the value of z is 8.5

Measure of ∠A:

The measure of ∠A can be determined by substituting the value of z.

Thus, we have;

[tex]\angle A=14(8.5)-7[/tex]

[tex]\angle A=119-7[/tex]

[tex]\angle A=112^{\circ}[/tex]

Thus, the measure of ∠A is 112°

Measure of ∠C:

The measure of ∠C can be determined by substituting the value of z.

Thus, we have;

[tex]\angle C=8(8.5)[/tex]

[tex]\angle C =68^{\circ}[/tex]

Thus, the measure of ∠C is 68°

Measure of ∠D:

The measure of ∠D can be determined by substituting the value of z.

Thus, we have;

[tex]\angle D=10(8.5)[/tex]

[tex]\angle D=85^{\circ}[/tex]

Thus, the measure of ∠D is 85°

Measure of ∠B:

The angles B and D are supplementary.

Thus, we have;

[tex]\angle B+ \angle D=180^{\circ}[/tex]

Substituting the values, we get;

[tex]\angle B+ 85^{\circ}=180^{\circ}[/tex]

        [tex]\angle B=95^{\circ}[/tex]

Thus, the measure of ∠B is 95°

Answer:

A: 112°

B: 95°

C: 68°

D: 85°

Step-by-step explanation:

Opposite angles add up to 180

8z + 14z - 7 = 180

22z = 187

z = 8.5

A = 14(8.5) - 7

A = 112

C = 8(8.5)

C = 68

D = 10(8.5)

D = 85

B = 180 - 85

B = 95

Answer:

The rectangle divided in 2 equal parts

Step-by-step explanation:

Answer:

The middle one is correct because, if you look at the question, you need to find the 1 with more than 1/3. so just think of them as fractions. It will make it easier.

Step-by-step explanation:

A rectangle divided into six equal parts. One of the parts is shaded. = 1/6

A rectangle divided into four equal parts. One of the parts is shaded. = 1/4

A rectangle divided into two equal parts. One of the parts is shaded. = 1/2

A rectangle divided into three equal parts. One of the parts is shaded. = 1/3

So 1/2 is more than 1/3.

Answer:

180

Step-by-step explanation:

The 3 interior angles of any triangle will always add to 180 degrees.

Answer:

a)   32.57%

b)   0.9967

c)   5.3285 times.

Step-by-step explanation:

a. Return on sales is a simple ratio that is calculated by dividing the operating profit/income  by the net sales revenue.

-Given net sales revenue is $20,941 and the operating income is $6,821:

[tex]Return \ on \ sales(ROS)=\frac{Operating \ Income}{Net \ Sales \ Revenue}\\\\=\frac{6821}{20941}\\\\=0.3257\\\\=32.57\%[/tex]

Hence, the return on sales is 32.57%

b. Current ratio is a simple ratio that compares the current assets to the current liabilities.

-Given that current assets=$7,296 and current liabilities=$7,320, the current ratio is calculated as below:

[tex]Current \ Ratio=\frac{Current \ Assets}{Current \ Liabilities}\\\\=\frac{7296}{7320}\\\\=0.9967[/tex]

Hence, the current ratio is 0.9967

c. Inventory turnover is a measure of the frequency with which a company's goods is used or sold and subsequently restocked in given period.

-It's calculated by dividing the cost of goods sold by the average invenory as below:

[tex]Inventory \ Turnover=\frac{Cost \ of \ goods \ sold}{mean \ Invenory}\\\\\\=\frac{7055}{1324}\\\\=5.3285\ times[/tex]

Hence, the inventory turnover is 5.3285 times.

The calculated ratios for ABC Inc. are: Return on Sales of 19.3%, a Current Ratio of 0.997, and an Inventory Turnover of 5.33.

To calculate the ratios requested, we'll be using the financial data from ABC Inc.'s income statement and balance sheet.

https://brainly.com/question/31531442

#SPJ3

Answer:

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(60,13.5)[/tex]  

Where [tex]\mu=60[/tex] and [tex]\sigma=13.5[/tex]

And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And the standard error of the mean would be:

[tex]\sigma_{\bar X} =\frac{13.5}{\sqrt{81}}= 1.5[/tex]

4.1.5

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(60,13.5)[/tex]  

Where [tex]\mu=60[/tex] and [tex]\sigma=13.5[/tex]

And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And the standard error of the mean would be:

[tex]\sigma_{\bar X} =\frac{13.5}{\sqrt{81}}= 1.5[/tex]

4.1.5

The standard error of the mean for the sample of automobiles is 1.5 mph ,i.e, option 4, which is found by dividing the standard deviation, 13.5 mph, by the square root of the sample size, 9, because the sample size is 81 vehicles.

The standard error of the mean (SEM) is the standard deviation ()divided by the square root of the sample size (n). For the given data, with a sample size of 81 automobiles and a standard deviation of 13.5 mph, the standard error of the mean can be calculated as follows:

SEM = 13.5 /  81 = 13.5 / 9 = 1.5 mph

Therefore, the value for the standard error of the mean is 1.5.

Final Answer:

The balance of the loan after the 5-year grace period, with no payments made and interest compounding weekly at an annual rate of 4.8%, would be approximately $2884.50.

Explanation:

To solve this problem, we want to calculate the future value of the loan after 5 years of weekly compounding interest. The formula for the future value of an investment compounded more frequently than once a year is

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt}, \][/tex]

where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.

Given:
- P = $2250 (the initial loan amount)
- r = 4.8\% = 0.048 (the annual interest rate converted to a decimal)
- n = 52 (the loan is compounded weekly)
- t = 5 (the loan is for a period of 5 years)

Now we will plug these values into the formula to calculate the future value of the loan.

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \\\\\\\[ A = 2250 \left(1 + \frac{0.048}{52}\right)^{52 \times 5} \][/tex]

Calculating the term inside the parentheses first:

[tex]\[ \frac{0.048}{52} = 0.00092307692 \] (approximately)[/tex]

Adding 1 to this result:

[tex]\[ 1 + 0.00092307692 = 1.00092307692 \] (approximately)[/tex]

Now we need to raise this to the power of 260 (which is [tex]\( 52 \times 5 \)[/tex]):

[tex]\[ \left(1.00092307692\right)^{260} \] (use a calculator for this step)[/tex]

After doing this calculation, you should get a value of approximately 1.282002. (Remember, the exact result might vary slightly depending on the precision of your calculator.)

Finally, we can calculate the future value A:

[tex]\[ A = 2250 \times 1.282002 \\\\\[ A \approx 2884.505 \][/tex]

Therefore, the balance of the loan after the 5-year grace period, with no payments made and interest compounding weekly at an annual rate of 4.8%, would be approximately $2884.50.

Answer:

x + 3y = 18  is the equation in standard form.

In  slope-intercept form it is  y = -1/3 x + 6.

Step-by-step explanation:

The given line y = 3x + 2 has a slope of  3 so the line perpendicular to it has slope -1/3.

y - y1 = m(x - x1)  where m = slope and (x1, y1) is a point on the line.

Using the point (3, 5) our equation is:

y - 5 = -1/3(x - 3)     Multiply through by -3:

-3y + 15  = x - 3

x  + 3y =  15 + 3

x + 3y = 18 is the required equation.

Answer:

36.88% probability that her pulse rate is between 69 beats per minute and 81 beats per minute.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 75, \sigma = 12.5[/tex]

Find the probability that her pulse rate is between 69 beats per minute and 81 beats per minute.

This is the pvalue of Z when X = 81 subtracted by the pvalue of Z when X = 69.

X = 81

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{81 - 75}{12.5}[/tex]

[tex]Z = 0.48[/tex]

[tex]Z = 0.48[/tex] has a pvalue of 0.6844

X = 69

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{69 - 75}{12.5}[/tex]

[tex]Z = -0.48[/tex]

[tex]Z = -0.48[/tex] has a pvalue of 0.3156

0.6844 - 0.3156 = 0.3688

36.88% probability that her pulse rate is between 69 beats per minute and 81 beats per minute.

Answer:

[tex]P(69<X<81)=P(\frac{69-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{81-\mu}{\sigma})=P(\frac{69-75}{12.5}<Z<\frac{81-75}{12.5})=P(-0.48<z<0.48)[/tex]

And we can find this probability with this difference:

[tex]P(-0.48<z<0.48)=P(z<0.48)-P(z<-0.48)=0.684-0.316= 0.368 [/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the pulse rates of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(75,12.5)[/tex]  

Where [tex]\mu=75[/tex] and [tex]\sigma=12.5[/tex]

We are interested on this probability

[tex]P(69<X<81)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(69<X<81)=P(\frac{69-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{81-\mu}{\sigma})=P(\frac{69-75}{12.5}<Z<\frac{81-75}{12.5})=P(-0.48<z<0.48)[/tex]

And we can find this probability with this difference:

[tex]P(-0.48<z<0.48)=P(z<0.48)-P(z<-0.48)=0.684-0.316= 0.368 [/tex]

Answer:

BURRITOS

Step-by-step explanation:

Answer:

9.66666666 yards  repeating

Step-by-step explanation:

The formula is to divide feet by 3,so 29/3=9.666666 repeating.

Mark me brainliest if I helped:D

Answer:

3'2+3'2

Step-by-step explanation:

Answer:

3'2+3'2 is your answer

Answer:

  x = 10

Step-by-step explanation:

After your second step, simplify the result:

  [tex]x=\dfrac{6}{3}\cdot\dfrac{5}{1}=2\cdot 5\\\\x=10[/tex]

Answer:

10

Step-by-step explanation: