the number of thunderstorms in indiana in a calendar month is normally distributed with a mean of 75, and a standard deviation is 20 . single month is randomly selected. find the probability that the number of thunderstorms in that month is greater than 85. sample of ten months is selected. find the probability that the mean number of thunderstorms per month in this sample is greater than 85.

The unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).

To find a unit vector that is oppositely directed to v = (3, -4) and half its length, we can follow these steps:

Find the length of vector v:

|v| = sqrt(3^2 + (-4)^2) = 5

Divide vector v by 2 to get a vector with half its length:

v/2 = (3/2, -2)

To get a vector that is oppositely directed to v, we can reverse the direction of v/2:

-(3/2, -2) = (-3/2, 2)

Finally, we can find the unit vector in the direction of (-3/2, 2) by dividing it by its length:

|(-3/2, 2)| = sqrt((-3/2)^2 + 2^2) = sqrt(13/4)

u = (-3/2, 2) / sqrt(13/4) = (-3/2) * (2/sqrt(13))/2 + (2/sqrt(13)) * (1/2)

Therefore, the unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).

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If kawan paints the visible outside faces of her shed, she paints two rectangle faces and two triangle faces then the total surface area that she paints is 88ft².

The area of a triangle of altitude h and base b is given by;

A = 0.5bh

Therefore the area of one triangle face ;

At = 0.5 × 8 × 5

At = 20ft²

Area of a rectangle of length l and breadth b is;

A = lb

Therefore the area of a rectangle face;

Ar = 8 × 3

Ar = 24ft²

We have 2 triangle faces and 2 rectangle face, therefore total surface area as;

A = 2At + 2Ar

A  = 2×20 + 2×24

A = 40 + 48

A = 88ft²

Therefore the answer is; 88ft².

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The histogram for the frequency table is illustrated below.

To create the frequency table, we need to count how many times each time appears in the data set. The time 9:23 appears twice, so we would put a frequency of 2 in the row corresponding to 9:23. We do this for each time in the data set.

Here is the completed frequency table:

Time Frequency

6:10 1

6:21 1

6:55 1

7:12 1

7:20 1

7:34 1

8:15 1

9:01 1

9:14 1

9:15 1

9:18 1

9:23 2

As you can see, each time appears only once or twice in the data set. This tells us that there is no dominant time that most students ran the mile in.

To create the histogram, we'll draw a bar above each time on the x-axis with a height equal to the frequency of that time. For example, there are two times of 9:23, so we'll draw a bar above 9:23 with a height of 2.

As you can see, the histogram shows a relatively even distribution of times. The most common times are around 9 minutes, but there are also several times below 8 minutes and one time below 7 minutes.

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To find dy/dx, we need to take the derivative of y with respect to x. On evaluating the value of dy/dx is [tex]-9t^{8/9}[/tex]

However, we are given x in terms of t. So first, we need to use the chain rule to find dx/dt:
x = [tex]t^{1/9}[/tex]
dx/dt = (1/9) * [tex]t^{-8/9}[/tex]

Now, we can use the chain rule again to find dy/dt:

y = 9 - t
dy/dt = -1

Finally, we can use the formula for the chain rule to find dy/dx:

dy/dx = (dy/dt) / (dx/dt)
dy/dx = (-1) / ((1/9) * [tex]t^{-8/9}[/tex]
dy/dx = [tex]-9t^{8/9}[/tex]

So, the final answer is dy/dx = [tex]-9t^{8/9}[/tex]
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The measure of arc a must be 2 times measure of inscribed angle, which is 90 degrees.

What is arc?

In geometry, an arc is a segment of a circle's circumference. It is defined by two endpoints and all the points on the circle's circumference between them.

What is inscribed angle?

An inscribed angle is an angle formed by two chords in a circle that have a common endpoint.

For any inscribed angle in a circle, the measure of the angle is always half the measure of the arc that it intercepts. This is known as the inscribed angle theorem.

So, if we have an inscribed angle with a measure of 45 degrees, then the measure of its corresponding arc would be 2 times that, which is 90 degrees.

Therefore, if the inscribed angle is associated with arc a, and the measure of the corresponding angle is 45 degrees, then we know that the measure of arc a must be 2 times that, which is 90 degrees.

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Answer:

It's ASA, AAS,

Step-by-step explanation:

AAS- If two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in another triangle, then the triangles are congruent.

ASA-The ASA criterion for triangle congruence states that if two triangles have two pairs of congruent angles and the common side of the angles in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent.

The number of cans that can be packed in a certain carton has correct statement as, Statements (1) and (2) together are not sufficient, option E.

Data sufficiency refers to evaluating and analysing a collection of data to see if it is sufficient to respond to a certain query. They are intended to assess the candidate's capacity to connect the dots between each question and arrive at a conclusion.

The size of each can is not revealed in statement 1 at all.

The size of the container is not disclosed in statement 2 at all.

We obtain two situations when we take into account both assertions. Case A: If the box is 1 x 1 x 2304 (inches) in size, then there are no cans that will fit within the carton.

Case B: If the box is 10 x 10 x 23.04 (inches) in size, then the carton can hold more than 0 cans.

The combined statements are insufficient because we lack clarity in our ability to respond to the target inquiry.

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Complete question:

What is the number of cans that can be packed in a certain carton?

(1) The interior volume of this carton is 2, 304 cubic inches.

(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

C. Both statements together are sufficient, but neither statement alone is sufficient.

D. Each statement alone is sufficient.

E. Statements (1) and (2) together are not sufficient.

Using inductive reasoning, we can observe a pattern in the given data: the number of stereos sold decreases by 45 each month.

We can apply this pattern to make conjectures about the number of stereos sold in June, July, and August.

June: 235 (May's sales) - 45 = 190 stereos
July: 190 (June's sales) - 45 = 145 stereos
August: 145 (July's sales) - 45 = 100 stereos

So, the conjectures for the number of stereos sold are:
June: 190
July: 145
August: 100

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Answer:

2.25

Step-by-step explanation:

45 nickels

45*5=225

225 cents

2.25

The value of 45 nickels in decimal number can be 2.25.

In the decimal system, each digit's value depends on its position or place value within the number.

A nickel is worth 0.05 dollars.

To find the value of 45 nickels, multiply the number of nickels by the value of each nickel:

So, Value = Number of nickels × Value of each nickel

                = 45 × 0.05

                = 2.25

Therefore, the value of 45 nickels is $2.25 as a decimal number.

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The rate of change after 5 years is 14.4%, indicating that the percentage of US adults using the internet is increasing at a rate of 14.4% per year.

Based on the provided information, the rate of US adults who use the internet can be modeled by the equation dI/dt = -0.5t + 16.9, where t represents the time in years and I represents the percentage of adults using the internet.

To determine the rate of change at a specific time, we need to substitute the value of t into the equation.

For example, to find the rate of change after 5 years, we would substitute t = 5:

dI/dt = -0.5(5) + 16.9
dI/dt = -2.5 + 16.9
dI/dt = 14.4

Therefore, the rate of change after 5 years is 14.4%, indicating that the percentage of US adults using the internet is increasing at a rate of 14.4% per year.

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The potential factor that may have an impact on the confidence interval, but is not accounted for by the margin of error, is nonresponse bias.

The dean of students received a large number of responses from first-year students but very few from sophomores, juniors, and seniors. Nonresponse bias occurs when some individuals chosen for a sample do not respond to a survey or study. In this case, the dean of students may not have received a representative sample of the opinions of all students, which could lead to an overestimation or underestimation of the true proportion of students who believe first-year students should be given parking privileges in the main lot.

The margin of error is the amount of random sampling error in a survey's results. It reflects the level of precision in the survey's results and decreases as the sample size increases. However, nonresponse bias is a systematic error that is not accounted for by the margin of error, as it may lead to a biased sample and inaccurate results. To minimize nonresponse bias, the dean of students could have used techniques such as follow-up emails or incentives to encourage a higher response rate from all student groups.

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Answer: 2√5, -2√5

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

You take each given side and multiply them all together

18.4 x 8.8 x 11 = approx 1782

1) Bona can drive 108 miles if she drove for 3 hour at the same speed as Claire.

2) Janet would take 1.5 hour to complete the journey and Andrew spend half hour more driving than Janet.

1) Bona speed is 44mph

Time taken by Bona is 3 hour

distance travelled by Claire is 144 miles

Time taken by Claire is 4 hour

Claire's speed = distance / time

Claire's speed = 144/4

Claire's speed = 36 mph

Distance travelled by Bona = speed × time

Distance travelled by Bona = 36 × 3

Distance travelled by Bona = 108 miles

2) Janet distance = 60 miles

Janet speed = 40 mph

Time taken by Janet = distance / speed

Time taken by Janet = 60/40

Time taken by Janet = 1.5 hour

Janet would take 1.5 hour to complete the journey

Andrew distance = 80 miles

Andrew speed = 40 mph

Time taken by Andrew = distance / speed

Time taken by Andrew = 80/40

Time taken by Andrew= 2 hour

Andrew spend half hour more driving than Janet.

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L < M, as 1 < 1.25.  

a_2 = 1/4 > 1/8 = b_2, which shows that a_k < b_k is not guaranteed for all k > 1.

(a) Given two convergent series Σa_k (with sum L) and Σb_k (with sum M) where k=1 to ∞, and L < M, we are asked if a_k < b_k for all k > 1. The answer is no, this is not guaranteed.

Counter example:
Consider the following two convergent series:

Series A: Σa_k, where a_1 = 1/2, a_2 = 1/4, a_3 = 1/8, ... (a geometric series with a common ratio of 1/2)

Series B: Σb_k, where b_1 = 1, b_2 = 1/8, b_3 = 1/16, ... (a geometric series with a common ratio of 1/2 starting from the second term)

Sum L for Series A:
L = a_1 / (1 - (1/2)) = 1

Sum M for Series B:
M = b_1 + (b_2 / (1 - (1/2))) = 1 + 1/4 = 1.25

In this case, L < M, as 1 < 1.25. However, a_2 = 1/4 > 1/8 = b_2, which shows that a_k < b_k is not guaranteed for all k > 1.

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The equation which represents the volume of each cone is as follows:

V = (1/3)πr²h

Explanation :

In this equation, "V" represents the volume of the cone, "r" represents the radius of the base, and "h" represents the height of the cone.

V represents the volume of the cone. Volume is a measure of the space occupied by an object, and in this case, it refers to the space inside the cone.

π (pi) is a mathematical constant approximately equal to 3.14159. It is used in calculations involving circles and spheres.

r represents the radius of the base of the cone. The radius is the distance from the center of the base to any point on its circumference. Squaring the radius, r², gives us the area of the base.

h represents the height of the cone. It is the perpendicular distance from the base to the vertex (top) of the cone.

When we multiply the area of the base (πr²) by the height (h) and divide the result by 3, we get the volume of the cone. The division by 3 is necessary because the volume of a cone is one-third the volume of a cylinder with the same base and height.

So, the equation V = (1/3)πr²h provides a way to calculate the volume of a cone based on its radius and height.

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Answer:

Step-by-step explanation:

Let's start by finding the total weight of all five people:

Total weight = Average weight x Number of people

Total weight = 107.6 x 5

Total weight = 538

We know that Cathy weighs 115 lb, so we can subtract her weight from the total weight to find the total weight of the other four people:

Total weight of other four = Total weight - Cathy's weight

Total weight of other four = 538 - 115

Total weight of other four = 423

To find the average weight of the other four, we can divide the total weight of the other four by the number of people:

Average weight of other four = Total weight of other four / Number of people

Average weight of other four = 423 / 4

Average weight of other four = 105.75 lb

Therefore, the average weight of the other four is 105.75 lb.

Answer: 2100 square feet

Step-by-step explanation:

To solve this question we must add the areas of the two rectangles.

area = length x width

Rect 1:

a = lw

  = 80 x 15 = 1200 square feet

Rect 2:

a = lw

  = 30 x 30 = 900 square feet

so in total, the driveway is 1200 + 900 = 2100 square feet

Answer:

To find the area of the driveway, we need to find the area of both rectangles and add them together.

The area of the first rectangle is:

80 ft x 15 ft = 1200 sq ft

The area of the second rectangle is:

30 ft x 30 ft = 900 sq ft

To find the total area of the driveway, we add the two areas together:

1200 sq ft + 900 sq ft = 2100 sq ft

Therefore, the area of the driveway is 2100 square feet.

Answer:

16 seconds

Step-by-step explanation:

The value of the integral [tex]\int -1^1 (13 - 12) dt[/tex] is 26.

To evaluate the integral [tex]\int-1^1 (13 - 12) dt[/tex] , we need to find an antiderivative of the integrand, which is simply:

∫ (13 - 12) dt = 13t - 12

Using this antiderivative, we can evaluate the definite integral by applying the theorem:

[tex]\int-1^1 (13 - 12) dt = [13t - 12]_{(-1)^1[/tex]

Evaluating this expression at the limits of integration (-1 and 1), we get:

[13(1) - 12] - [13(-1) - 12]

Simplifying, we get:

= 13 - 12 + 13 + 12

= 26

Therefore, the value of the integral [tex]\int-1^1 (13 - 12) dt[/tex] is 26.

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There are 4,096,000,000 possible passwords of length 6 using special characters, digits, and letters, with characters allowed to be repeated.

To compute the number of passwords possible with a length of 6 using digits, letters, and special characters, with characters allowed to be repeated, follow these steps:

1. Count the number of options for each character type:
  - Digits: 10 (0-9)
  - Letters: 26 (a-z)
  - Special characters: 4 (*, &, $, #)

2. Combine the options for all character types:
  Total options per character = 10 digits + 26 letters + 4 special characters = 40

3. Calculate the number of possible passwords:
  Since characters may be repeated and the password has a length of 6, the number of possible passwords = 40^6 (40 options for each of the 6 character positions)

4. Calculate the result:
  Number of possible passwords = 40^6 = 4,096,000,000

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Answer: 9.33

Step-by-step explanation: if you add them up, it's 9.33

If each of the 3 friends orders a veggie mushroom cheddar burger for 11%, the cost of each burger would be:

11% of $1.00 = $0.11

Since the prices are listed in fractions of a dollar, we can express the cost of each burger as 11/100 of a dollar.

So, the total cost of 3 veggie mushroom cheddar burgers would be:

3 x 11/100 = 33/100 = $0.33

Assuming that the glass of water is free, the total bill before taxes would be $0.33 for the 3 burgers. However, it's important to note that this calculation is based on the assumption that the prices are listed in fractions of a dollar, which may not be the case. If the prices are listed in a different unit, the calculation would need to be adjusted accordingly.

The coordinates of the point are (7,0).

distance from (-3,-5) to (x,y) = 2 * distance from (x,y) to (9,-8)

Using the distance formula, we can write this equation as:

√[(x - (-3))^2 + (y - (-5))^2] = 2 * √[(9 - x)^2 + (-8 - y)^2]

Simplifying this equation, we get:

[tex](x + 3)^2 + (y + 5)^2 = 4[(9 - x)^2 + (-8 - y)^2][/tex]

Expanding and simplifying further, we get:

[tex]17x + 16y = 119[/tex]

So the coordinates of the point on the directed line segment from (-3,-5) to (9,-8) that partitions the segment into a ratio of 2 to 1 are:

x = (119 - 16y)/17

y = any value (since we can choose any value of y and then calculate x using the equation above)

For example, if we choose y = 0, then we get:

x = (119 - 16(0))/17 = 7

So the coordinates of the point are (7,0).

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The volume of the solid is A. [tex]\pi/3[/tex]

The volume of a solid in geometry signifies the space it occupies inside a three-dimensional area. It denotes how much content can fill up its inner region, and as usual, measured in units like cubic feet, meters, or centimeters.

Finding the measurement formula varies from shape to shape but commonly involves multiplying width, height, and length. Given that many sectors rely on this term, such as engineering, architecture, and physics, understanding the concept of the volume of a solid weighs significantly.

If we take a cross-section of (x,y)perpendicular to the x-axis, with width dx, now the cross-section is a quarter circle with radius y.

Thus, the volume of the cross-section, since y = 2x becomes: [tex]\pi x^2 dx[/tex]

Now, the volume of the solid when integrated becomes: [tex]\frac{\pi }{3}[/tex]

Option A is correct.

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No, this linear relationship is not proportional, because the ratio between Chandler's hourly wage and tips changes because the number of hours worked changes

Proportional relationships are those wherein the ratio between the two portions being as compared stays constant, no matter the values of those quantities.

In this case, we're evaluating Chandler's earnings primarily based on her hourly wage and her hints from take-out orders.

But, the ratio between Chandler's hourly wage of $15.25 and her tips of $25 per night varies relying on the number of hours she works.

For example, if Chandler works for 2 hours, her total income could be $30.50 (2 x $15.25) + $25 = $55.50.

If she works for four hours, her total earnings would be $61 (4 x $15.25) + $25 = $86. In this example, the ratio among her hourly salary and tips adjustments as her income increase with more hours worked.

Therefore, because the ratio between Chandler's hourly wage and tips changes because the number of hours worked changes, this linear relationship is not proportional.

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Answer: d

Step-by-step explanation:

Answer:

pls mrk me brainliest

Step-by-step explanation:

(⁠￣⁠(⁠ｴ⁠)⁠￣⁠)⁠ﾉ

A. To obtain the position of EFGH, Johnny translated ABCD by 3 units to the right and 4 units up. To draw and label EFGH, simply shift each vertex of ABCD by this translation vector (3, 4).

B. Tom rotated ABCD by 90º clockwise about the origin, O, to get the position of IJKL. To draw and label IJKL, rotate each vertex of ABCD 90º clockwise around the origin. This can be achieved by switching the x and y coordinates of each vertex and negating the new x value.

C. Tony placed a smaller car, MNOP, on the coordinate plane. MNOP is a dilation of ABCD with its center at the origin and a scale factor of -0.5. To draw and label MNOP, multiply the coordinates of each vertex of ABCD by the scale factor -0.5, keeping the origin as the center.

The surface area of the similar cone is 415.8 in²

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex.

The surface area of a cone is expressed as;

SA = πr( r+l) where r is the radius and l is the slant height.

The slant height of the original cone =

l= √h²+r²

l = √12²+3²

l = √144+9

l = √153

l = 12.4 in

SA= 3π( 3+12.4)

SA = 3 × 15.4

SA = 46.2 in²

The surface area of similar cone with radius 9 inches is calculated by;

(3/9)² = 46.2/x

= 9/81 = 46.2/x

x = 46.2 × 81/9

x = 415.8in²

Therefore the surface area of the similar cone is 415.8 in³

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