In the triangle, not drawn to scale, angle
BAC = 30° and AB = 40 m. The length. BC,
in metres, is​

Answer:

a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

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 question, we have that:

[tex]\mu = 18, \sigma = 5.2, n = 35, s = \frac{5.2}{\sqrt{35}} = 0.879[/tex]

95% of the sample means:

From the: 50 - (95/2) = 2.5th percentile.

To the: 50 + (95/2) = 97.5th percentile.

2.5th percentile:

X when Z has a pvalue of 0.025. So X when Z = -1.96.

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

By the Central Limit Theorem

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

[tex]-1.96 = \frac{X - 18}{0.879}[/tex]

[tex]X - 18 = -1.96*0.879[/tex]

[tex]X = 16.3[/tex]

97.5th percentile:

X when Z has a pvalue of 0.975. So X when Z = 1.96.

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

[tex]1.96 = \frac{X - 18}{0.879}[/tex]

[tex]X - 18 = 1.96*0.879[/tex]

[tex]X = 19.7[/tex]

95% of the sample means are between 16.3 and 19.7 hours. This interval contains the sample mean of 16.8 hours, which supports the study.

So the correct answer is:

a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.

Answer:

(f + g)(x) = 5x² + 2x - 5

Domain: All real numbers

(f - g)(x) = -5x² + 2x - 5

Domain: All real numbers

(fg)(x) = 10x³ - 25x²

Domain: All real numbers

(f/g)(x) = [tex]\frac{2x-5}{5x^2}[/tex]

Domain: (negative infinity, 0)U(0, positive infinity)

Step-by-step explanation:

For f + g, we are simply adding the 2 together

Domain: All values of x work, as any value x outputs any value y

For f - g, we are simply subtracting the 2 together

Domain: All values of x work, as any value x outputs any value y

For f times g, we are simply multiplying (distributing) the 2 together

Domain: All values of x work, as any value x outputs any value y

For f divided by g, we are simply dividing (fraction) the 2 together

Domain: All values except for 0 work (undefined error), so asymptote at x = 0

Answer:

0.346

Step-by-step explanation:

Given:

Number of machines, n = 10

Average run time before servicing, R= 44 minutes

Service time, T= 6 minutes per machine

Required:

Find the probability that a machine will have to wait for service with two operators.

First find the service factor using the formula below:

[tex] X = \frac{T}{R + T} [/tex]

[tex]= \frac{6}{44 + 6}[/tex]

[tex]= \frac{6}{50}[/tex]

[tex]= 0.12[/tex]

X = 0.12

Given number of service operators,S = 2.

Using the finite queuing table, efficiency factor at S=2 & X=0.12 is 0.346.

Therefore, the probability that a machine will have to wait for service with two operators is 0.346

The probability that a machine will have to wait for service with two operators is 0.3455

The given parameters are:

[tex]\mathbf{n = 10}[/tex] --- number of machines

[tex]\mathbf{T = 6}[/tex] --- service time

[tex]\mathbf{R = 44}[/tex] --- average run time

[tex]\mathbf{S = 2}[/tex] --- number of service operator

Start by calculating the service factor (X)

[tex]\mathbf{X = \frac{T}{R + T}}[/tex]

So, we have:

[tex]\mathbf{X = \frac{6}{44 + 6}}[/tex]

[tex]\mathbf{X = \frac{6}{50}}[/tex]

[tex]\mathbf{X = 0.12}[/tex]

Next, we determine the efficiency factor from the finite queuing table, a

The efficiency factor at [tex]\mathbf{X = 0.12}[/tex] and [tex]\mathbf{S = 2}[/tex], is 0.3455

Hence, the probability is 0.3455

Read more about queue models at:

https://brainly.com/question/18681322

Answer:

13 inches

Step-by-step explanation:

To find the greatest number of inches possible in the length of each piece, we need to find the greatest common divisor of 39, 52 and 65.

So, the divisors of 39 are: 1, 3 and 13

The divisors of 52 are: 1, 2, 4, 13 and 26

The divisors of 65 are: 1, 5 and 13

Therefore, the common divisors are 1 and 13. Finally the greatest common divisor is 13. It means that the greatest number of inches possible in the length of each piece is 13 inches.

Answer:

[tex]10[/tex]

Step-by-step explanation:

[tex]\frac{2(10)^2(10-5)}{10(10)}[/tex]

Square the 10.

[tex]\frac{2(100)(10-5)}{10(10)}[/tex]

Subtract 10 with 5.

[tex]\frac{2(100)(5)}{10(10)}[/tex]

Multiply the numbers in the numerator.

[tex]\frac{2(500)}{100}[/tex]

[tex]\frac{1000}{100}[/tex]

Divide 1000 with 100.

[tex]=10[/tex]

Answer:

[tex]solution \\ \frac{ {2x}^{2}(x - 5) }{10x} \\ = \frac{2 \times {10}^{2}( 10 - 5) }{10 \times 10} \\ = \frac{2 \times 100 \times 5}{100} \\ = \frac{1000}{100} \\ = 10[/tex]

hope this helps...

Good luck on your assignment..

Answer:

N(L) = 20

The expected number of left handed people is 20.

Step-by-step explanation:

Given;

Percentage of left handed people P(L) = 10%

Total number of selected people N(T) = 200

The Expected number of left handed people N(L) is;

N(L) = Total number of selected people × Percentage of left handed people/100%

N(L) = N(T) × P(L)/100%

Substituting the given values;

N(L) = 200 × 10%/100%

N(L) = 200 × 0.1

N(L) = 20

The expected number of left handed people is 20.

Answer:

Option D is correct

Step-by-step explanation:

Applying the cosine theorem for triangle ABC, you would have:

cos (angle BAC) = (BA^2 + CA^2 - BC^2)/(2*BA*CA)

                           = (10^2 + 18^2 - 20^2)/(2*10*18)

                           = 24/360

=> angle BAC = ~86 deg

Hope this helps!

Answer:

The length of the short side is 14.5 units, the length of the other short side is 18.5 units, and the length of the longest side is 23.5 units.

Step-by-step explanation:

The Pythagorean Theorem

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

                                                     [tex]a^2+b^2=c^2[/tex]

Applying the Pythagorean Theorem  to find the lengths of the three sides we get:

[tex](x)^2+(x+4)^2=(x+9)^2\\\\2x^2+8x+16=x^2+18x+81\\\\2x^2+8x-65=x^2+18x\\\\2x^2-10x-65=x^2\\\\x^2-10x-65=0[/tex]

Solve with the quadratic formula

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\mathrm{For\:}\quad a=1,\:b=-10,\:c=-65:\quad x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}\\\\x_{1}=\frac{-\left(-10\right)+ \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5+3\sqrt{10}\\\\x_{2}=\frac{-\left(-10\right)- \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5-3\sqrt{10}[/tex]

Because a length can only be positive, the only solution is

[tex]x=5+3\sqrt{10}\approx 14.5[/tex]

The length of the short side is 14.5, the length of the other short side is [tex]14.5+4=18.5[/tex], and the length of the longest side is [tex]14.5+9=23.5[/tex].

Answer:

1 - 31 + 191 does not represent the distance of the 2 given points.

The distance between the 2 points is 12

Step-by-step explanation:

Remember distance formula: [tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

When we plug in our values into the distance formula into a calc,

d = [tex]\sqrt{(9-(-3))^2 + (-5-(-5))^2}[/tex]

We get d = 12. This does not equal 1 - 31 + 191 (which equals 161).

Answer:

Sample Response: The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).

Step-by-step explanation:

Answer:

21 times.

Step-by-step explanation:

There are 3 out of 10 spaces that are yellow or green so there is a 3/10 chance spinning on either of them. If we spin 70 times, then there will be a 21/70 chance of spinning either so you can expect it to be spun on 21 times.

Answer:

+2

Step-by-step explanation:

=> [tex](2-3x)(x^2-5)[/tex]

=> [tex](2x^2-10-3x^3+15x)[/tex]

Arranging it in descending order

=> [tex]-3x^2+2x^2+15x-10[/tex]

So, the coefficient of x² in this expression is +2

This depends if you are supposed to simplify the binomials first:

If you leave it in the form provided then the coefficient would be 1

However, you can multiply the binomials together in order to simplify the expression:

[tex](2 - 3x)( {x}^{2} - 5)[/tex]

[tex](2 \times {x}^{2} ) + (2 \times - 5) + ( - 3x \times {x}^{2} ) + ( - 3x \times - 5)[/tex]

[tex] { - 3x}^{3} + {2x}^{2} + 15x - 10[/tex]

Which then shows the coefficient would be 2

So it all depends on the directions provided, I would assume the correct answer is 2 if the directions are the exact same as provided on Brainly.

Answer:

Option D is correct.

90%: (0.981, 0.1337); 95%: (0.0953, 0.1362); 99%: (0.0878, 0.1402)

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

The standard error of the mean should be the same for all these given confidence intervals

But, with the sample result that should have been provided to solve this not provided, we can use mathematical methods and the right assumptions to obtain the right interval.

We first assume the sample size is large enough to make the use of z-distribution for the critical value.

90% critical value = 1.645

95% critical value = 1.960

99% critical value = 2.330

We can obtain the margin of error for each of the intervals given and since the standard error is the same for all three intervals, we can use the value of the critical value to check which intervals are the most correct.

a. 90%: (0.0962, 0.1358); 95%: (0.0919, 0.1397); 99%: (0.0899, 0.1411)

Margin of error is half the total width of the confidence interval

Margin of error of 90%: (0.0962, 0.1358) = (0.1358-0.0962)/2 = 0.0198

With critical value = 1.645

0.0198 = 1.645 × (standard error)

Standard error = 0.01204

Check if this works for the 95%: (0.0919, 0.1397)

Margin of error = 1.96 × 0.01204 = 0.02359

Margin of error calculated from the interval = (0.1397-0.0919)/2 = 0.0239

Trying the 99%: (0.0899, 0.1411)

Margin of error = 2.33 × 0.01204 = 0.02805

Margin of error calculated from the interval = (0.1411-0.0899)/2 = 0.0256

b. 90%: (0.0993, 0.1327); 95%: (0.0962, 0.1358); 99%: (0.0899, 0.1421)

Margin of error calculated from interval given = (0.1327-0.0993)/2 = 0.0167

standard error = (0.0167/1.645) = 0.010152

95%: (0.0962, 0.1358)

Margin of error = 1.96 × 0.010152 = 0.0199

Margin of error calculated from the interval = (0.1358-0.0962)/2 = 0.0198

99%: (0.0899, 0.1421)

Margin of error = 2.33 × 0.010152 = 0.02365

Margin of error calculated from the interval = (0.1421-0.0899)/2 = 0.0261

c. 90%: (0.0893, 0.1350); 95%: (0.0851, 0.1358); 99%: (0.0799, 0.1390)

90%: (0.0893, 0.1350)

Margin of Error = (0.1350-0.0893)/2 = 0.02285

Standard error = (0.02285/1.645) = 0.01389

95%: (0.0851, 0.1358);

Margin of error = 1.96 × 0.01389 = 0.02723

Margin of error calculated from the interval = (0.1358-0.0851)/2 = 0.02535

99%: (0.0799, 0.1390)

Margin of error = 2.33 × 0.01389 = 0.03236

Margin of error calculated from the interval = (0.1390-0.0799)/2 = 0.02955

d. 90%: (0.0981, 0.1337); 95%: (0.0953, 0.1362); 99%: (0.0878, 0.1402)

90%: (0.0981, 0.1337)

Margin of Error = (0.1337-0.0981)/2 = 0.0178

Standard error = (0.0178/1.645) = 0.010821

95%: (0.0953, 0.1362);

Margin of error = 1.96 × 0.010821 = 0.02045

Margin of error calculated from the interval = (0.1362-0.0953)/2 = 0.02045

99%: (0.0878, 0.1402)

Margin of error = 2.33 × 0.010821 = 0.02521

Margin of error calculated from the interval = (0.1402-0.0878)/2 = 0.0252

From this, it is evident that it is the option D that suits the mathematical answers for the co.fidemce interval.

Hope this Helps!!!

Answer:

Probability that exactly one person says he or she enjoys the beach = 80%

Check Explanation for how to get this and which error the studemt that made the 100% claim must have made.

Step-by-step explanation:

The simulation presented is that for a series of two people sample.

Numbers 0 to 6 represents that the beach-goer enjoys going to the beach and numbers 7 to 9 represents that the beach-goer doesn't enjoy going to the beach.

So, the simulation is then obtained to be

(5,8) (2,7) (0,9) (0,2) (9,0) (1,9) (4,7) (0,3) (6,7) (7,5)

Using the simulation, estimate the probability that exactly one person says he or she enjoys the beach

From the simulation, the ones with exactly one of the two numbers ranging from 0 to 6 to indicate enjoying going to the beach include

(5,8) (2,7) (0,9) (9,0) (1,9) (4,7) (6,7) (7,5)

The probability of an event is defined and expressed as the number of elements in that event divided by the total number of elements in the sample space.

Probabilty that exactly one person says he or she enjoys the beach = (8/10) = 0.80 = 80%

The student claims that this probability is 100%, but the other two simulations that did not satisfy the condition of exactly one person saying that he or she enjoys the beach include

(0,2) and (0,3), which show that in the two cases, the two participants both expressed enjoying going to the beach.

The student's error must have been in counting these two simulations as part of 'exactly one person saying he or she enjoys the beach' which is indeed an error.

Hope this Helps!!!

Answer:

The part-to-part relationship between homework help and sports

Step-by-step explanation:

Assume the table is like the one below.

[tex]\begin{array}{lcl}\textbf{Activity}& \textbf{Students} \\\text{Spanish} & 19 \\\text{Basketball} & 24 \\\text{Drama} & 15\\\text{Homework help} & 17 \\\text{Soccer} & 20 \\\end{array}[/tex]

17 students participated in homework help.  

44 students participated in basketball (24) and soccer (20), i.e. sports

Both sports and homework help are parts of the whole group of all activities.

Thus, 17:44 represents the part-to-part relationship between homework help and sports.

Explanation: Please show table.

Note: Check the file attached below for the complete question

Answer:

Betty's monthly take home is $20 less

Step-by-step explanation:

Betty's monthly income = $2300

Betty's monthly savings = $200

Amount left after savings = $2300 - $200

Amount left after savings = $2100

Federal and State Income tax rate = 20% = 0.2

Tax amount paid = $420

Monthly take home = $2100 - $420

Monthly take home = $1680

Compared to $150 per month savings, Betty's monthly take home is $20 less

Answer:

The x intercepts are (7,0) and (-4,0)

Step-by-step explanation:

y = x^2 – 3x - 28

Set y=0

0 = x^2 – 3x - 28

Factor.  What 2 numbers multiply to -28 and add to -3

-7*4 = -28

-7+4 = -3

0 = (x-7)(x+4)

Using the zero product property

0 = (x-7)      0 = x+4

x=7              x = -4

The x intercepts are (7,0) and (-4,0)

Answer:

Exponents are simply repeated multiplication so the answer is 7 * 7 * 7 * 7.

Answer:

67 cookies

Step-by-step explanation:

When packaging in groups of 4, the possible number of cookies is x = (4n+3). The possible values are:

7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71...

When packaging in groups of 5, the possible number of cookies is x = (5n+2). The possible values are:

7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77...

When packaging in groups of 7, the possible number of cookies is x = (7n+4). The possible values are:

11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, 95...

The least value that appears on all three possibilities is 67, therefore the least number of cookies that Mohan could have is 67.

Answer:

b. divide them into groups based on similarities

Step-by-step explanation:

Blocking is a method in statistics used to reduce the effect of nuisance variables in an experiment. Nuisance variables are those factors that could result in variations during the experiment. During blocking, subjects with similar features are grouped in the same block, and treatment is then administered to each of these subjects. In order to form blocks, blocking factors are used.

Blocking factors can affect the results of an experiment but they are of no importance to the experimenter. An example of a blocking factor is age.  So, for Isamu who seeks to use blocking to deal with an extraneous factor in his experiment, blocking would enable him to divide his subjects into groups based on similarities.

Answer:

Divide them into groups based on similarities!

Answer:

25/88

Step-by-step explanation:

25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles

P(red) = number of red/total

          = 25/88

Answer:

Dear user,

Answer to your query is provided below

Probability of choosing a red marble is 0.28 or (25/88)

Step-by-step explanation:

Total number of marbles = 88

Number of red marbles = 25

Probability = 25/88

Answer: A

Step-by-step explanation:

The first thing we need to do is to make sure our equation is in standard form. The given equation is not in standard form.

3x²-2x=0

Now that the equation is in standard form, we can find our A, B, C to see which quadratic equation is correct.

A=3

B=-2

C=0

We can automatically eliminate D because the first value is -3 when it is supposed to be -(-2). Also, the denominator is supposed to be 2a. We know that A=3. The denominator should be 2(3), not 2(-2).

Next, we can eliminate B and C. For the 4ac, we know it has to be 4(3)(0) because A=3 and C=0. B and C have given 4(3)(2) and 4(3)(1), respectively. This does not match A=3 and C=0.

Therefore, A is the correct answer.

Answer:

   (-6, 7)

Step-by-step explanation:

In order to make (x+4) = -2, we must have x = -6. Then the point (-6, 7) will be on the graph of f(x+4).

__

Another way to think about this is that replacing x with x-h causes the graph to be shifted right by h units. Here, we have h=-4, so the graph is shifted left 4 units. Shifting the point (-2, 7) by 4 units to the left moves it to (-2-4, 7) = (-6, 7).

Answer:

PLATO: -6,7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Y intercept is 18

For qn 2 y intercept is -8

Answer:

1) Y intercept: 0, 18

x intercept: (-6, 0)

2) Y intercept (0, -8)

x intercept (-4, 0)

Step-by-step explanation:

y=3x+18

y intercept is when x=0

y=3(0)+18

y=18

So y intercept is 18, 0

X intercept is when y=0

0=3x+18

-18=3x

x=-6

So the x intercept is (-6, 0)

HELPFUL HINT: the equations are already in y=mx+b form, so b is the y intercept!

y=-2x-8

Y intercept (0, -8)

x intercept

0=-2x-8

8=-2x

-4=x

x=(-4, 0)

Answer:

________________________

Answer:

Dear user,

Answer to your query is provided below

Water left in the tank is 158 m^3

Step-by-step explanation:

Volume of Rectangular tank = 4.5 x 6 x 8 = 216m^3

Water used = 58m^3

Water left = 216 - 58 = 158m^3

9514 1404 393

Answer:

  70%

Step-by-step explanation:

Each discount d multiplies the price by (1 -d). The total multiplier is ...

  (1 -15%)(1 -38%)(1 -44%) = (0.85)(0.62)(0.56) = 0.29512 ≈ 1 -70.49%

The total markdown is about 70%.

Answer:

r≈4.44

Step-by-step explanation:

Formula: r=(3V /4π)^⅓

Answer:

16,8,4,2,1,1/2,1/4

Step-by-step explanation: this is very straightforward, everytime the sequence is getting lower, its dividing by half! understand?

Answer:

The correct answer to the following question will be Option d (181 degrees of freedom).

Step-by-step explanation:

The given values are:

Regression model,

n = 200

Observations,

p = 18

Now,

⇒  [tex]n-p-1[/tex]

On putting the estimated values, we get

⇒  [tex]200-18-1[/tex]

⇒  [tex]181[/tex]

So that the correct choice will be "181 degrees of freedom".