Assume the random variable X is normally distributed with mean mu equals 50 and standard deviation sigma equals 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. Upper P (Upper X greater than 34 )

Answer:

  2x -3y = 12

Step-by-step explanation:

For some horizontal change Δx and some vertical change Δy between the two points, an equation of the line through points (x1, y1) and (x2, y2) can be written as ...

  Δy·x -Δx·y = Δy·(x1) -Δx·(y1)

Here, we have ...

  Δy = y2 -y1 = 2 -(-2) = 4

  Δx = x2 -x1 = 9 -3 = 6

So, our equation can be ...

  4x -6y = 4·3 -6·(-2) = 24

Factoring out a common factor of 2 makes the equation be ...

  2x -3y = 12 . . . . . . equation of the line in standard form

Solving for y gives the equation in slope-intercept form:

  y = 2/3x -4

_____

More conventional solution

Plotting the points and drawing the line, you see that the y-intercept is -4. You also see that there is a "rise" of 2 grid squares for each "run" of 3 grid squares. Thus the slope of the line is 2/3. With this information, you can write the equation directly in slope-intercept form:

  y = mx + b . . . . . . line with slope m and y-intercept b

  y = 2/3x -4 . . . . . . the line through the given points

Final answer:

The line passing through the points (3, -2) and (9, 2) has a slope of 2/3, and its equation is y = (2/3)x - 4, which can be graphed by plotting the given points and ensuring the slope is represented correctly.

Explanation:

To graph the line that passes through the points (3, -2) and (9, 2), we first find the slope of the line. The slope formula is (y2 - y1) / (x2 - x1). Plugging in our points, we get (2 - (-2)) / (9 - 3) which simplifies to 4 / 6, further reduced to 2 / 3. Therefore, the slope of the line is 2 / 3.

Next, we use one of the points and the slope to write the equation in point-slope form, y - y1 = m(x - x1). Using the point (3, -2), the equation becomes y + 2 = (2/3)(x - 3). After distributing the slope and moving -2 to the other side, we get the equation y = (2/3)x - 4.

Finally, we can graph the line by plotting the two given points and drawing a straight line through them, ensuring that the rise over the run matches the slope of 2 / 3. The equation of the line y = (2/3)x - 4 can be verified using various x-values to see if the resulting y-values fall on the line plotted.

Answer:

A)   2704 hands

B)   16 hands

C)   144 hands

D)   384 hands

E)   208 hands

F)   400 hands

Step-by-step explanation:

See the attached file for explanation

There are 2704 possible hands, 16 hands consist of a pair of aces, 144 hands have all face cards, 384 hands have 1 king, 208 hands consist of two of a kind, and 384 hands contain at least 1 king.

To answer these probability related questions, we must look at the combinations which we can draw. A standard deck contains 52 cards and the hand in question consists of 1 card from 2 different decks, so:

A. The total number of different hands possible is 52 * 52 = 2704.

B. There are 4 aces in each deck so there are 4 * 4 = 16 hands that consist of a pair of aces.

C. A deck has 12 face cards and since 2 cards are being drawn, the number of hands with all face cards is 12 * 12 = 144.

D. The number of hands with exactly 1 king is found by multiplying the number of kings in a deck (4) by the number of non-kings in a deck (52-4). So, 4 * 48 = 192, but we must consider this happening in both decks: so 2 * 192 = 384.

E. For two of a kind hands (2 aces, 2 kings etc.), there are 13 kinds, thus 13 * 4 * 4 = 208.

F. For at least 1 king, either the first card or second card can be a king, so we use similar mathematics as used in D, which is 2 * 192 = 384.

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Answer:

The dimensions of the rectangle that will allow for the most economical fence to be built are 30x15 feets, where two sides of 30 feets long cost $33 each one per foot, one side of 15 feets costs also $33 and the remaining side costs $99

Step-by-step explanation:

If x and y were the dimensions of the rectangle (in feets), then we have that x*y = 450. Therefore, y = 450/x.

Note that the rectangle as a result is formed by 2 sides with length x and 2 other sides with length 450/x. Lets suppose that x is the length of the 2 sides that costs both $33 and the other two sides, which have length 450/x, one costs also $33 and the other costs $99.

The cost, in $, function f,in terms of x, is given as follows

[tex] f(x) = 2 * 33 * x + 33*\frac{450}{x} + 99*\frac{450}{x} = 66x + \frac{59400}{x} [/tex]

We want to minimize f, so we will derivate it and equalize the derivate to 0:

[tex] f'(x) = 66 - \frac{59400}{x^2} [/tex]

[tex] f'(x) = 0 \leftrightarrow 66 = \frac{59400}{x^2} \leftrightarrow x^2 = \frac{59400}{66} = 900 \leftrightarrow x = \sqrt{900} = 30 [/tex]

(Note that x cant be negative, so in the equation we didnt count the opposite of the square root of 900)

We concluded that one dimension is 30 feets, and the other should be 450/30 = 15.

Answer:

−x2+3x−11

Step-by-step explanation:

−3x2+4x+2x2−x−11

(−3x2+2x2)+(4x−x)−11

−x2+3x−11

Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

(0.0657,0.0943)  is the 90% confidence interval for the population proportion of visitors that click on the advertisement.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 978

Percentage of users that clicked on advertisement = 8%

Sample proportion:

[tex]\hat{p} = 0.08[/tex]

90% Confidence interval:

[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.645[/tex]

Putting the values, we get:

[tex]0.08\pm 1.645(\sqrt{\dfrac{0.08(1-0.08)}{978}})\\\\= 0.08\pm 0.0142\\\\=(0.0658,0.0942) = (6.57\%,9.43\%)[/tex]

(0.0657,0.0943)  is the 90% confidence interval for the population proportion of visitors that click on the advertisement.

Answer:

Step-by-step explanation:

See attached file for answer pls

Answer:

Step-by-step explanation:

Considering the central limit theorem, the distribution is normal since the number of samples is large. Also, the population standard

deviation is known. We would determine the z score.

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

α = 1 - 0.90 = 0.1

α/2 = 0.1/2 = 0.05

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

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 2.05. Thus, confidence level of 90% is 1.645

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Confidence interval = mean ± z × σ/√n

Where

σ = population standard Deviation

Confidence interval = x ± z × σ/√n

x = 22.8 hours

σ = 6.4 hours

n = 175

i) Confidence interval = 22.8 ± 1.645 × 6.4/√175

= 22.8 ± 0.80

The lower end of the confidence interval is

22.8 - 0.80 = 22

The upper end of the confidence interval is

22.8 + 0.80 = 23.6

ii) error bound is the same as the margin of error

Error bound = 0.8

Answer:

[tex]25.00\geq 3.50p[/tex]

Step-by-step explanation:

since you have $25.00, you can only spend up to that much money, so it will have to be less than or equal to , and since p = slices of pizza, you multiply that by 3.50 to know how much you can buy.

hope this helps :)

Answer:

$3.5p<=$25.00

Step-by-step explanation:

If you only have $25.00 to spend on pizza it can not exceed that limit, so your total amount needs to be more than or equal to money the pizza slices cost

Answer:

x=46 4/5, x=46.8

Step-by-step explanation:

To find x-intercept/zero, substitute y=0

-222=5x-3(-7*0-4)

-222=5x-3(-7*-4) Solve

x= -234/5

x=46 4/5, x=46.8

Answer:

I think that the answer is either A or C. I'm not too sure on which one.

Step-by-step explanation

Answer:

= 10√3

Step-by-step explanation:

[tex]2 \sqrt{27} - \sqrt{48} + 4 \sqrt{12} \\ = (2 \times \sqrt{9 \times 3}) - (\sqrt{16 \times 3}) + (4 \times \sqrt{4 \times 3} )\\ = (2 \times 3 \sqrt{3}) - 4 \sqrt{3} + (4 \times 2 \sqrt{3} ) \\ = 6 \sqrt{3} - 4 \sqrt{3} + 8 \sqrt{3} \\ = 10 \sqrt{3} [/tex]

Answer:

10√3

Step-by-step explanation:

2√27 − √48 + 4√12

2√(3²×3) − √(4²×3) + 4√(2²×3)

6√3 − 4√3 + 8√3

√3(6 - 4 + 8)

10√3

Answer:

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

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

The margin of error is given by:

[tex] ME= z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

For this case since the confidence is 99% we are confident that the true proportion of interest would be on the interval calculated and the best option for this case is:

Of confidence intervals with this margin of error, 99% will contain the population proportion

Step-by-step explanation:

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".  

Solution to the problem

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

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

The margin of error is given by:

[tex] ME= z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

For this case since the confidence is 99% we are confident that the true proportion of interest would be on the interval calculated and the best option for this case is:

Of confidence intervals with this margin of error, 99% will contain the population proportion

Answer:

Loans

Step-by-step explanation:

I don´t know how to explain it,and I hope my answer is correct though.

Answer:

banks create money by issuing loans and opening checking accounts  

Step-by-step explanation:

Answer:

[tex]x\geq \$40[/tex]

The graph in the attached figure

Step-by-step explanation:

Let

x ----> represents the amount that Jennifer has

y ----> represents the amount that Matthew has

we know that

The amount that Jennifer has is greater than or equal to $34 plus three times the samount that Matthew has

The inequality that represent this situation is

[tex]x\geq 3y+34[/tex]

we have

[tex]y=\$2[/tex]

substitute

[tex]x\geq 3(2)+34[/tex]

[tex]x\geq \$40[/tex]

The solution is the interval [40,∞)

In a number line the solution is the shaded area at right of x=40 (closed point)

see the graph attached

Inequality representing amount owed by Jennifer : x > 40

Important Information : Amount owed by Mathew =  $2

Amount owed by Jennifer = at least 34 more than triple amount owed by Mathew

So, x > 3 (2) + 34

x > 34 + 6

x > 40

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Answer:

2

Step-by-step explanation:

Multiply all of the fractions together.

The solution is: 6,582,390,417 in word form is, six billon five hundred eighty two million three hundred thousand and ninety four hundred seventeen.

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

The number 42,316 is different from 61,432 because the digits are in different positions.

here, we have,

given that,

6,582,390,417

so, the values of each of the digits in 6,582,390,417 in word form is:

6: six billon

5: five hundred

8: eighty two million

3: three hundred thousand

and ninety four hundred

seventeen.

Hence, The solution is: 6,582,390,417 in word form is, six billon five hundred eighty two million three hundred thousand and ninety four hundred seventeen.

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There are 7,991 5-digit numbers that are divisible by either 45 or 60 but not divisible by 90.

To find the number of 5-digit numbers that are divisible by either 45 or 60 but not by 90, we can use the principle of inclusion-exclusion. First, let's find the number of 5-digit numbers divisible by 45 and the number divisible by 60, then subtract the number divisible by 90 to avoid overcounting.

A 5-digit number divisible by 45 must also be divisible by 9 and 5. The smallest 5-digit number divisible by 45 is 10005 (9 * 5 * 445), and the largest is 99990 (9 * 5 * 2222). We can find the number of 5-digit numbers divisible by 45 by subtracting the two numbers and adding 1 (99990 - 10005 + 1).

A 5-digit number divisible by 60 must also be divisible by 12 and 5. The smallest 5-digit number divisible by 60 is 10020 (12 * 5 * 167), and the largest is 99960 (12 * 5 * 833). We can find the number of 5-digit numbers divisible by 60 using the same method as before (99960 - 10020 + 1).

Finally, we subtract the number of 5-digit numbers divisible by 90. A 5-digit number divisible by 90 must be divisible by 45 and 2. The smallest 5-digit number divisible by 90 is 10035 (9 * 5 * 445 and 2 * 5017), and the largest is 99945 (9 * 5 * 2221 and 2 * 49973). Again, we use the same method as before to find the number of 5-digit numbers divisible by 90 (99945 - 10035 + 1).

To find the final answer, we subtract the number of 5-digit numbers divisible by 90 from the sum of the numbers divisible by 45 and 60.

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Answer:

The null hypothesis was not rejected.  

The proportion of readers who own a personal computer is 47%.

Step-by-step explanation:

The claim made by a publisher is that 47% of  their readers own a personal computer.

A single proportion z-test can be used to determine whether the claim made by the publisher is authentic or not.

The hypothesis for this test can be defined as follows:

H₀: The proportion of readers who own a personal computer is 47%, i.e. p = 0.47.

Hₐ: The proportion of readers who own a personal computer is different from 47%, i.e. p ≠ 0.47.

The information provided is:

[tex]n=280\\\hat p=0.43\\\alpha =0.01[/tex]

The test statistic is:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.43-0.47}{\sqrt{\frac{0.47(1-0.47)}{280}}}=-1.34[/tex]

The test statistic value is, z = -1.34.

Decision rule:

If the p-value of the test is less than the significance level α = 0.01 then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

[tex]p-value=2\times P (Z < z)[/tex]

               [tex]=2\times P (Z < -1.34)\\=2\times [1-P(Z<1.34)]\\=2\times [1-0.90988]\\=0.18024\\\approx0.18[/tex]

*Use a z table for the probability.

The p-value of the test is 0.18.

p-value = 0.18 > α = 0.01

The null hypothesis was failed to be rejected at 1% level of significance.

Conclusion:

There is enough evidence to support the claim made by the publisher. Hence, it can be concluded that the proportion of readers who own a personal computer is 47%.

Answer:

320

Step-by-step explanation:

2/5 = .4

800 * .4 =320

Answer:

17x +21

Step-by-step explanation:

-3(x+3)+5(4x+6)

Distribute

-3x-9+20x+30

Combine like terms

17x +21

The measure of each angle in the Summer Triangle depends on the position and alignment of the stars and cannot be determined without specific coordinates and time of observation.

The Summer Triangle is a prominent summer asterism formed by three bright stars: Vega, Deneb, and Altair. The measure of each angle in the Summer Triangle depends on the position and alignment of these stars in the sky. The angles cannot be determined without the specific coordinates and time of observation.

Astronomers use angles to measure the separation between celestial objects in the sky. A full circle has 360°, and the half-sphere of the sky from horizon to opposite horizon contains 180°. By measuring the angular separation between two stars or objects, astronomers can determine how far apart they appear in the sky. The angle is typically measured in degrees (°).

For example, if two stars are 18° apart, their separation spans about 1/10 of the dome of the sky. To give you a sense of how big a degree is, the full Moon is about half a degree across, which is similar to the width of your smallest finger (pinkie) seen at arm's length.

Answer: The value of y is 13

Step-by-step explanation: To find the value of y, we will use properties of equality.

Step 1: -7y = -91  (We want to find the value of y, or 1 y)

Step 2: (Use the division property of equality) -7y/-7 = -91/-7

Step 3: (Answer) y = 13

Answer:

y= 13

Step-by-step explanation:

-7y = -91

divide both sides by -7

y = 13

Answer:

x = 92

Step-by-step explanation:

Supplementary angles add to 180 degrees,

x+y = 180

We know y =88

x+88 = 180

Subtract 88 from each side

x+88-88=180-88

x =92

Answer:

Any number that is not a fractional value positive and negative but technically  all numbers are irrational

Step-by-step explanation:

Any number that is not a fractional value positive and negative but technically all numbers are irrational.

We have to find the numbers that are positive negative and 0 that are not irrational

Fractional values are represented using fixed-point arithmetic and are useful for DSP applications.

For a fractional division, we first scale the denominator to the range 0.5 ≤ d < 1.0.

Then we use a table lookup to provide an estimate of x0 to d−1.

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Answer:

RANDOM

Step-by-step explanation:

Answer:

it can be written in eqn form as

x-8=>17

or,x=>25

Answer:

x-8 ≥17

If you need to find x, Add 8 on both sides

x ≥25

Hope this helped

Final answer:

The sales manager should allocate approximately $341,310 for advertising to achieve the target sales volume of $200,000. This amount is determined by using the linear equation provided and solving for the advertising expenditures.

Explanation:

To find out how much the sales manager should allocate for advertising expenditures to achieve a target sales volume of $200,000, we use the given linear equation:

Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)

First, we convert the target sales volume to thousands of dollars - which would be $200 (since $200,000 is in thousands), and then plug it into the equation:

200 = 46.41 + 0.45(Advertising Expenditures)

Next, we solve for Advertising Expenditures:

200 - 46.41 = 0.45(Advertising Expenditures)
153.59 = 0.45(Advertising Expenditures)

Advertising Expenditures = 153.59 / 0.45
Advertising Expenditures = 341.31

Therefore, the sales manager should allocate approximately $341,310 for advertising in the budget to achieve the target sales volume of $200,000. This value is rounded to the nearest dollar as requested.

To achieve a target sales volume of $200,000, the company should allocate approximately $341,310 for advertising.

To determine the amount to allocate for advertising to reach a target sales volume of $200,000, we use the provided linear equation:

⇒ Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)

⇒ 200 = 46.41 + 0.45(Advertising Expenditures)

⇒ 200 - 46.41 = 0.45(Advertising Expenditures)

⇒ 153.59 = 0.45(Advertising Expenditures)

⇒ Advertising Expenditures = 153.59 ÷ 0.45

⇒ Advertising Expenditures ≈ 341.31

Therefore, the company should allocate approximately $341,310 (rounded to the nearest dollar) for advertising expenditures to achieve the target sales volume of $200,000.

Complete question:

Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.

Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)

If the company has a target sales volume of $200,000, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.

Answer:

A) Null hypothesis: H0: p = 0.398

Alternative hypothesis: H0: p < 0.398

B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.

C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.

Step-by-step explanation:

A) The null and alternative hypotheses are given below:

From the given information, the claim is that the proportion of students who enroll in her institution have a lower completion rate. This is representing the alternative hypothesis. Thus

Null hypothesis:

H0: p = 0.398

Alternative hypothesis:

H0: p < 0.398

B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.

C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.

Answer:

The boat is approaching the dock at rate of 2.14 ft/s

Step-by-step explanation:

The situation given in the question can be modeled as a triangle, please refer to the attached diagram.

A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.

The length of rope from bow to pulley is 13 feet that means y = 13 ft.

We know that Pythagorean theorem is given by

[tex]x^{2} + y^{2} = z^{2}[/tex]

Differentiating the above equation with respect to time yields,

[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}[/tex]

[tex]x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}[/tex]

dx/dt = 0  since dock height doesn't change

[tex]y\frac{dy}{dt} = z\frac{dz}{dt}[/tex]

[tex]\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}[/tex]

The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s

First we need to find z

z² = (5)² + (13)²

z² = 194

z = √194

z = 13.93 ft

So,

[tex]\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}[/tex]

[tex]\frac{dy}{dt} = \frac{13.93}{13}(2)[/tex]

[tex]\frac{dy}{dt} = 2.14[/tex] [tex]ft/s[/tex]

Therefore, the boat is approaching the dock at rate of 2.14 ft/s

So, the boat approached the dock with a speed of 2.1337 m/sec.

Pythagoras Theorem is an important topic in Maths, which explains the relation between the sides of a right-angled triangle.

So, the formula is,

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

Differentiating the above equation,

[tex]2a\frac{da}{dt} +2b\frac{db}{dt} =2c\frac{dc}{dt} ...(1)[/tex]

It is given that,

[tex]a=5m\\\frac{da}{dt}=0\\ c=13\\\frac{dc}{dt}=2 m/s[/tex]

[tex]b=\sqrt{13^2-5^2} \\b=12 m/s[/tex]

Substituting the above values in equation (1) we get,

[tex]2\times5\times0+2\times12\frac{db}{dt} =2\times13\times2\\\frac{db}{dt} =\frac{26}{12}\\ \frac{db}{dt} =2.1337 m/s[/tex]

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