A round ball has a diameter of 10 inches. What is the approximate volume of the ball?

Answer:

A = 11,600

P = 6,000

Total return = 11600-6000/6000 X 100%= 93.3%= (11600/6000) (1/17)– 1= 0.03954 * 100%= 3.954= 4.0%.

Step-by-step explanation:

The total return after 18 years in a mutual fund of $6300 is $4,900 and the annual return percentage is 77.78%.

Total Return:

Calculate the total return: $11,200 (selling price) - $6,300 (purchase price) = $4,900

Annual Return Percentage:

Annual Return Percentage = [(Final Value - Initial Value) / Initial Value]  * 100

Find the percentage return: ($4,900 / $6,300) x 100%

Annual return percentage = 77.78%

b.

If it's a (+,+) it's the 1st quadrant. If it's a (-,+) it's the 2nd quadrant. If its a (-,-) it's the 3rd quadrant. And if it's a (+,-) it's the 4th quadrant

Answer:

B

Step-by-step explanation:

Answer: The alternative hypothesis represents the claim

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 0.38

For the alternative hypothesis,

µ > 0.38

Considering the population proportion, probability of success, p = 0.38

q = probability of failure = 1 - p

q = 1 - 0.38 = 0.6

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 176

n = number of samples = 400

P = 176/400 = 0.44

We would the test statistic which is the z score

z = (p - P)/√pq/n

z = (0.44 - 0.38)/√(0.38 × 0.62)/400 = 2.47

Recall, population proportion, P = 0.38

The difference between sample proportion and population proportion(P - p) is 0.44 - 0.38 = 0.06

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.38 - 0.06 = 0.32

the p for the right tail is 0.38 + 0.06 = 0.44

These proportions are higher and lower than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above z is 1 - 0.9932 = 0.0068

We would double this area to include the area in the left tail of z = - 2.47. Thus

p = 0.0068 × 2 = 0.014

Since alpha, 0.01 < than the p value, 0.014, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the​ null hypothesis

To determine the scale of a drawing, you need the dimensions on the drawing or map as well as the actual dimensions of the object. The scale is then calculated as the ratio of these two sets of dimensions. However, without the dimensions of the drawing in this case, it is not possible to determine the exact scale.

The scale of a drawing is a ratio that compares the dimensions of the physical object to the dimensions on the drawing or map. In this case, the physical object is a pool that measures 30 feet by 66 feet. To find the scale, you would need additional information such as the dimensions of the pool in the drawing.

For example, if the pool is drawn as 2 inches by 4.4 inches on the paper, then the scale of the drawing would be 1 inch = 15 feet (for length) and 1 inch = 15 feet (for width), as 30 feet / 2 inches = 15 feet per inch and 66 feet / 4.4 inches = 15 feet per inch respectively.

Without this additional information, it is not possible to provide the exact scale of the drawing.

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The scale for the drawing shown is 1 in = 6 feets

Using the parameters given ;

Actual dimension :

Drawing dimension :

To calculate the scale of the drawing : Take the ratio of equivalent sides of the two drawings ;

Now we have ;

Hence the scale drawing is :

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Answer:

170

Step-by-step explanation:

Hello!

Let's represent a decimal as a fraction. That will help.

Since division is multiplication by the reciprocal, we can represent 0.01 as 1/100 which will be 100 when we divide.

1.7 * 100 = 170.0 (when we move one spot over.)

Thus, we see that [tex]\boxed{170}[/tex] is the answer.

Hope this helps!

Answer: The sine of ∠I is represented by the ratio 63:65

Step-by-step explanation:

First, let's draw the triangle (see the picture below.)

Remember SOHCAHTOA? We need to use it here.

-sin = opposite/hypotenuse

-cos = adjacent/hypotenuse

-tan = opposite/adjacent.

Assuming that ∠I is Ф, we can see that its opposite side is equal to 63 and the hypotenuse is 65. Therefore,

[tex]sin = \frac{63}{65}[/tex]

The sine ratio is 63: 65.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations.

Given:

∠K=90°, KJ = 63, IK = 16, and JI = 65.

Using Sine Ratio

sin [tex]\theta[/tex] = opposite/hypotenuse

sin [tex]\theta[/tex] = 63/65

Hence, the sine ratio is 63: 65.

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Answer:

Step-by-step explanation:

The sample proportion is the point estimate for the population proportion.

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

a) From the information given,

n = 1160

x = 387

p = 387/1160 = 0.33

q = 1 - 0.33 = 0.67

the point estimate of the proportion of the population who would answer yes = 0.33

b) To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.5 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96

Therefore,

Margin of error = 1.96√(0.33)(0.67)/1160 = 0.027

c) the​ 95% confidence interval for the population proportion is

0.33 ± 0.027

The numbers represent the sample proportion and the margin of error

d) The assumptions are

1) the sampling must be random

2) the sample size shouldn't be more than 10% of the population

10/100 × 1160 = 116

387 > 116

3) the sample size should be sufficiently large. That is, greater than 30

387 > 30

The point estimate is 33.4%. The margin of error for a 95% confidence interval is ±2.8%. That makes the 95% confidence interval (0.306, 0.362), and we can say with 95% confidence that the true population proportion lies within this interval. For the confidence interval to be valid, the survey must be randomized, and have at least 10 yeses and noes.

The subject here is statistics, and it involves estimating a population proportion and calculating a margin of error and a confidence interval. The proportion of subjects who said yes is 387/1160=0.334 or 33.4%. This represents the point estimate of the proportion of the entire population who would answer yes.

For the margin of error (ME) formula for a confidence interval, we use the formula ME=Z*(sqrt[(p(1-p))/n]). For a 95% confidence interval, our Z-score is approximately 1.96. Inserting our values gives us ME=1.96*(sqrt[0.334(1-0.334)/1160])≈0.028, or 2.8%.

To calculate the 95% confidence interval, subtract and add the margin of error from the point estimate: (0.334 - 0.028, 0.334 + 0.028) or (0.306, 0.362). These numbers mean that we're 95% confident that the true population proportion who would say yes lies within this interval.

To form a valid confidence interval, we need two assumptions: a random sample and at least 10 successes and failures. The survey presumably uses a random sample. With 387 yeses and 773 noes, we satisfy the success-failure condition.

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Answer:

the correct answer is B

Step-by-step explanation:

i got it correct choosing B on the assignment ;D

The triangle formed by Lin's walking path is an acute triangle.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Lin initially walked west 651 feet from his house to the lecture hall.

After class, he walked northeast 910 feet to the gym.

Finally, he walked 615 feet back to his house.

If we draw a diagram, placing Lin's house to the left, the lecture hall to the right, and the gym above, we can see that Lin walked in a diagonal path from the gym to his house.

Since Lin initially walked west and then northeast, the resulting direction would be southeast.

Regarding the type of triangle formed by Lin's walking path, we can consider the sides and angles.

Lin walked 910 feet northeast and 615 feet back to his house.

These sides are not equal in length, indicating that it is not an equilateral triangle.

Additionally, since Lin walked southeast, the angle at the gym is acute (less than 90 degrees).

Therefore, the triangle formed by Lin's walking path is an acute triangle.

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Answer:

a) [tex]\vec v_{B} - \vec v_{C} = 3\, i - 17\,j[/tex], b) [tex]\theta = 79.992^{\textdegree}[/tex] (clockwise)

Step-by-step explanation:

The resultant velocity of the boat must be:

[tex]\vec v_{B} = 15\,i[/tex]

Likewise, the velocity of the current is:

[tex]\vec v_{C} = 2\,i + 17\,j[/tex]

a) The intended velocity of the boat is:

[tex]\vec v_{B} - \vec v_{C} = (15-2)\,i + (0-17)\,j[/tex]

[tex]\vec v_{B} - \vec v_{C} = 3\, i - 17\,j[/tex]

b) The direction of the boat is:

[tex]\theta = \tan^{-1}\left(\frac{17}{3} \right)[/tex] (clockwise)

[tex]\theta = 79.992^{\textdegree}[/tex] (clockwise)

Answer:

A.) 2 x minus 4 y = 8. x + y = 7.

Step-by-step explanation:

A.) 2 x minus 4 y = 8. x + y = 7.

2x-4y = 8

x+y=7

This has one solution

B.) 3 x + y = negative 1. 6 x + 2 y = negative 2.

3x+y = -1

Multiply by 2

6x +2y = -2

This is the second equation  so it has infinite solutions

C.) 3 x + 3 y = 3. Negative 6 x minus 6 y = 3.

3x+3y =3

Multiply by -2

-6x-6y = -6

The equation is the same but the constant, which means they are parallel lines, they have zero solutions

D.) 3 x minus 2 y = 4. Negative 3 x + 2 y = 4.

3x -2y = 4

Multiply by -1

-3x +2y = -4

The equation is the same but the constant, which means they are parallel lines, they have zero solutions

Answer:

A.) 2 x minus 4 y = 8. x + y = 7.

Step-by-step explanation:

A.) 2 x minus 4 y = 8. x + y = 7.

2x - 4y = 8

x - 2y = 4

x = 4 + 2y

x + y = 7

4 + 2y + y = 7

3y = 3

y = 1

x = 4 + 2

x = 6

Only solution: (6,1)

Answer:

[tex] ME = 1.653 *\frac{7.9}{\sqrt{300}}= \pm 0.75[/tex]

±0.75 ounce

Step-by-step explanation:

Assuming this complete question: The Wisconsin Dairy Association is interested in estimating the mean weekly consumption of milk for adults over the age of 18 in that state. To do this, they have selected a random sample of 300 people from the designated population. The following results were recorded: xbar=34.5 ounces, s=7.9 ounces Given this information, if the leaders wish to estimate the mean milk consumption with 90 percent confidence, what is the approximate margin of error in the estimate?

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

[tex]\bar X=34.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=7.9 represent the sample standard deviation

n=300 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=300-1=299[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,199)".And we see that [tex]t_{\alpha/2}=1.653[/tex]

And the margin of error is given by:

[tex] ME = 1.653 *\frac{7.9}{\sqrt{300}}= \pm 0.75[/tex]

±0.75 ounce

Answer:

The approximate margin of error in the estimate is ±0.75 ounces.

Step-by-step explanation:

The question is incomplete:

The following results were recorded: xbar=34.5 ounces, s=7.9 ounces.

The sample size is n=300.

We will use the sample standard deviation to estimate the population standard deviation, so we will use the t-statistic.

To develop a confidence interval, we first have to calculate the degrees of freedom, and then look up in a t-students distribution table the critical value for a 90% confidence interval.

The degrees of freedom are:

[tex]df=n-1=300-1=299[/tex]

The critical value for a 90% CI is t=1.65.

Now, we can calculate the margin of error of the confidence interval as:

[tex]E=t\cdot s/\sqrt{n}=1.65*7.9/\sqrt{300}=13.035/17.32=0.75[/tex]

The lower and upper bounds of the confidence interval will be:

[tex]LL=\bar x-t\cdot s/\sqrt{n}=34.5-0.75=33.75\\\\UL=\bar x+t\cdot s/\sqrt{n}=34.5+0.75=35.25[/tex]

The confidence interval is (33.75, 35.25)

Final answer:

To find the equivalent inequality to 5x + 2(3x + 1) < 3, distribute the 2 and combine like terms, yielding 11x + 2 < 3. Thus, the answer is b. 11x + 2 < 3.

Explanation:

The question asks which inequality is equivalent to 5x + 2(3x + 1) < 3. To find the equivalent inequality, we distribute the 2 into the parentheses and combine like terms:

Therefore, the correct answer is b. 11x + 2 < 3.

Answer:

y = -14 in simplest form hope this helped

Step-by-step explanation:

Answer:

0.75

Step-by-step explanation:

Autosomal dominant: A pattern of inheritance in which an affected individual has one copy of a mutant gene and one normal gene on a pair of autosomal chromosomes

Heterozygous just means that a person has two different versions of the gene (one inherited from one parent, and the other from the other parent).

Being homozygous for a particular gene means you inherited two identical versions.

The trait is autosomal dominant so the characters pass into the next generation in a large ratio. the person who is heterozygous for the character have two type of allele which represents the trait for long earlobes and also for short earlobe.So a person is paired with homozygous individuals who have pure character for short earlobes.The percentage of their first child with long earlobes would be 75 percent. This is due to the dominance of the character in a generation.

Answer:

By the Central Limit Theorem, the mean of the average scores you get will be close to 1012.5.

Step-by-step explanation:

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.

Mean score of the population:

1012.5

If you do this many times, the mean of the average scores you get will be close to

By the Central Limit Theorem, the mean of the average scores you get will be close to 1012.5.

Answer:

We conclude that the calibration point is set too low.

Step-by-step explanation:

We are given that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams. The standard deviation for scale reading is known to be σ = 2.3. They weigh this weight on the scale 49 times and read the result each time. The 49 scale readings have a sample mean of x = 999.0 grams.

The calibration point is set too low if the mean scale reading is less than 1000 grams.

Let [tex]\mu[/tex] = mean scale reading

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 1000 grams     {means that the calibration point is not set too low}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 1000 grams     {means that the calibration point is set too low}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                         T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean = 999 grams

            [tex]\sigma[/tex] = population standard deviation = 2.3 grams

            n = sample of scale readings = 49

So, test statistics  =  [tex]\frac{999-1000}{\frac{2.3}{\sqrt{49} } }[/tex]  

                              =  -3.04

The value of z test statistics is -3.04.

Now, P-value of the test statistics is given by the following formula;

         P-value = P(Z < -3.04) = 1 - P(Z [tex]\leq[/tex] 3.04)

                                              = 1 - 0.99882 = 0.00118

Since, the P-value is less than the level of significance as 0.01 > 0.00118, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the calibration point is set too low.

Answer:

152

Step-by-step explanation:

[tex]m \angle {WYZ}=104[/tex] is given, and the angle next to it is a supplement. (Unfortunately, that angle can't be named in the usual way because there is no labeled point "southeast" of point Y.)

That angle has measure 180 - 104 = 76.

Now arc WXY's measure is twice the measure of this angle, so mWXY = 2(76) = 152.

Answer:

152

Step-by-step explanation:

Answer:

64k^2 - 16k +1

Step-by-step explanation:

We can rewrite this as

(-8k+1) ^2

We know that (a+b)^2 = a^2 +2ab +b^2

Let a = -8k  and b = 1

(-8k+1) = (-8k)^2 +2*(-8k)(1) + 1^2

           =64k^2 - 16k +1

Answer:

64k² - 16k + 1

Step-by-step explanation:

(−8k+1)(−8k+1)

64k² - 8k - 8k + 1

64k² - 16k + 1

Answer:

481

Step-by-step explanation:

Given:

Variance = 1.44

S.d = √1.44 = 1.2

C.I = 80%

Margin of error, E = 0.07

Mean = 3.6

Using Z table, the Z score for 80% confidence interval, Zc = 1.28

To find the sample size, n, we have:

[tex] n= [\frac{Z_c * s.d}{E}]^2 [/tex]

Substituting figures in the formula, we have:

[tex] n = [\frac{1.28 * 1.2}{0.07}]^2 [/tex]

n = 21.94286²

n = 481.49

Approximately, n = 481

Answer:

41

Step-by-step explanation:

PEMDAS parentheses equation multiplication division adding subtraction

Answer:

iii. 2.00

Step-by-step explanation:

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the population mean(the mean we are testing), [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

We are testing a mean of 3 times.

This means that [tex]\mu = 3[/tex]

The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. Sample of 100.

So [tex]X = 3.1, \sigma = 0.5, n = 100[/tex]

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}}[/tex]

[tex]t = 2[/tex]

So the correct answer is:

iii. 2.00

Answer:

a.

The random variable has binomial distribution with parameters p = 0.25, n=5.

b.

[tex]P(Y=2) = {5 \choose 2} (0.25)^2(0.75)^3 = 0.264\\P(Y<1 ) = P(Y = 0 ) = (0.75)^5 = 0.237[/tex]

Step-by-step explanation:

a.

Remember what a random variable with binomial distribution is. It is a random variable that counts the number of successes and in n trials of an experiment.

In this case, if you have  0,1,2,3,4,5  bottles of water, your success is that  the bottle has tap water, and the probability of that success is p = 0.25. and the number of trials is n = 5.

b.

Using the formula for the binomial distribution you get that

[tex]P(Y=2) = {5 \choose 2} (0.25)^2(0.75)^3 = 0.264\\P(Y<1 ) = P(Y = 0 ) = (0.75)^5 = 0.237[/tex]

Answer:180cm^2

Step-by-step explanation:

A1=25×20=500

A2=16×20=320

A1-A2

500-320=180

Answer:

4  to 5

Step-by-step explanation:

20 footballs to 25 footballs

Divide each term by 5

20/5  to 25/5

4  to 5

Answer:

36 inches

Step-by-step explanation:

1 foot is equal to 12 inches so if the kite is 3 feet you would multiply 12 times 3 and get 36 hope this helps (Brainliest???)

The kite is 36 inches long. This is because 1 foot is equivalent to 12 inches, and the kite is 3 feet long.

The question asks how many inches long is a kite that is 3 feet long. We know that 1 foot is equal to 12 inches. Therefore, to get the length of the kite in inches, we need to multiply 3 feet by 12. So, 3 feet is equal to 36 inches.

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Final answer:

The events A and B are mutually exclusive. The events A and C are not mutually exclusive. Two events A and B are independent events.

Explanation:

The events A and B are mutually exclusive because they cannot happen at the same time. P(A AND B) = 0.

No, A and C are not mutually exclusive because they can occur at the same time. In fact, C includes all of the outcomes of A; if the card chosen is blue it is also (red or blue). P(A AND C) = P(A) = 20.

Two events A and B are independent events if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of two roles of a fair die are independent events. The outcome of the first roll does not change the probability for the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are not independent, then we say that they are dependent events. Sampling may be done with replacement or without replacement. With replacement: If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once. When sampling is done with replacement, then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick.

Answer:

 x < 3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    4*x-7-(5)<0

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  4x - 12  =   4 • (x - 3)

Equation at the end of step  1  :

Step  2  :

2.1    Divide both sides by  4

Solve Basic Inequality :

2.2      Add  3  to both sides

            x < 3

By solving the given inequality "[tex]4x-7<5[/tex]", we get the answer "[tex]x <3[/tex]". A complete solution is below.

The given equation of inequality is:

Now,

By adding "7" both sides of the equation, we get

→ [tex]4x-7+7<5+7[/tex]

→              [tex]4x< 12[/tex]

→                [tex]x < \frac{12}{4}[/tex]

→                [tex]x < 3[/tex]

Thus the above solution is correct.

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Simplfied Answer: [tex]6b-4[/tex]

Combine Like Terms

[tex]8b+-2b+-4\\(8b+-2b)+(-4)\\6b+-4[/tex]

Answer:

[tex]8b - 2b - 4 \\ 6b - 4 \\ = 2(3b - 2)[/tex]