A manufacturer claims that the lifetime of a certain type of battery has a population mean of μ = 40 hours with a standard deviation of a = 5 hours. Assume the manufactures claim is true and let a represent the mean lifetime of the batteries in a simple random sample of size n = 100. Find the mean of the sampling distribution of , μ = Find the standard deviation of the sampling distribution of , I What is P(40.6)? Round to the nearest thousandths (3 decimal places) The area this probability represents is (choose: right/left/two) tailed. Suppose another random sample of 100 batteries gives = 39.1 hours. Is this unusually short? (yes/no) Because P(≤39.1) = Round to the nearest thousandths (3 decimal places) The area this probability represents is

The statement "the interquartile range is least influenced by an outlying value in the data set" is true.

The range is simply the difference between the maximum and minimum values in a data set.

The variance is a measure of the spread of a data set, and is calculated by finding the average of the squared differences between each data point and the mean of the data set.

The interquartile range, on the other hand, is a measure of the spread of the middle 50% of the data set. It is calculated by finding the difference between the upper quartile and the lower quartile.

Because the interquartile range only takes into account the middle 50% of the data, it is less influenced by outliers than the range and variance. This is because outliers can greatly impact the range and variance, but have little effect on the interquartile range.

In conclusion, the interquartile range is a more robust measure of spread for a data set, as it is less influenced by outliers.

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1. I based my decision on allocating points to maximize my own score, while also considering the potential benefits of contributing to the group fund.

2. The best outcome for me would be allocating the minimum points required to the GIVE account, while putting the majority in the KEEP account. This would ensure I receive the most points for myself.

3. The best outcome for the group would be if both participants maximized their contributions to the GIVE account. This would create the largest group fund, resulting in the most redistributed points and highest average score.

4. There are parallels with risk management strategies. Individuals may act in their own self-interest, but a larger group benefit could be achieved if more participants contributed to "group" risk management strategies like vaccination, safety protocols, insurance policies, etc. However, some individuals may free ride on others' contributions while benefiting from the overall results. Incentivizing group participation can help align individual and group interests.

Answer:

Your answer will be 1.35

To find the area between the x-axis and the curve defined by y = 2x^2 - 6x on the interval [0,4], we need to integrate the absolute value of the function within that range. The graph of the given function is a parabola that opens upward.

First, we find the points of intersection between the curve and the x-axis by setting y = 0:

0 = 2x^2 - 6x

0 = x(2x - 6)

x = 0 or x = 3

Next, we integrate the absolute value of the function from x = 0 to x = 3:

Area = ∫[0,3] |2x^2 - 6x| dx

Splitting the interval at x = 3, we have:

Area = ∫[0,3] (6x - 2x^2) dx + ∫[3,4] (2x^2 - 6x) dx

Evaluating these integrals and taking their absolute values, we find the area between the curve and the x-axis on the interval [0,4].

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The yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.

To calculate the yearly deposits needed, we can use the concept of future value of an annuity. The future value formula for an annuity is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value of the annuity

P = Yearly deposit amount

r = Interest rate per period

n = Number of periods

In this case, the future value needed is $2 million, the interest rate is 8% (0.08), and the number of periods is 30 years. We need to solve for the yearly deposit amount (P).

Using the given formula:

2,000,000 = P * [(1 + 0.08)^30 - 1] / 0.08

Simplifying the equation:

2,000,000 = P * [1\(.08^3^0 -\) 1] / 0.08

2,000,000 = P * [10.063899 - 1] / 0.08

2,000,000 = P * 9.063899 / 0.08

Dividing both sides by 9.063899 / 0.08:

P = 2,000,000 / (9.063899 / 0.08)

P ≈ 2,000,000 / 113.298737

P ≈ 17,650.23

Therefore, the yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.

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The inequality that models the scenario is the first one:

$24 + $2*n ≤ $37

Solving that we conclude that Eli can buy at most 6 notebooks.

We know that Eli wants to buy a calculator that costs $24 and some notebooks, such that each notebook costs $2.

Then If Eli buys the calculator and n notebooks the total cost will be:

$24 + $2*n

We know that Eli has a total of $37 to spend, so that is the maximum amount he can spend. Thus, we can write the inequality:

$24 + $2*n ≤ $37

So the correct option is the first one.

Now also let's solve the inequality for n.

$24 + $2*n ≤ $37

$2*n  ≤ $37 - $24

$2*n ≤ $13.

n ≤ $13/$2

n ≤ 6.5

So Eli can buy at most 6 notebooks.

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Answer:

\(\frac{3}{y^{2} }\)

Step-by-step explanation:

This question is asking you to simplify using the law of indices:

Just to write out the question in fraction form:

\(\frac{12y^{7} }{4y^{9} }\)

Cancel out the 4:

\(\frac{3y^{7} }{y^{9} }\)

Cancel out y^7:

\(\frac{3}{y^{2} }\)

Hope this helped and brainliest please

Answer:

3/y^2

Step-by-step explanation:

1. Rewrite the division as a fraction.

= 12y^7/4y^9

2. Cancel the common factor of 12 and 4

= 4(3y^7)/4y^9

= 3y^7/y^9

3. Cancel the common factor of y^7 and y^9

= y^7 ⋅ 3/y^9

= 3/y^2

The output of the statement: cout << pow(2.0, pow(3.0, 1.0)) << endl; is

c. 8.0.

Given statement:

output :

The output of a computer or word processor is the information that it displays on a screen or prints on paper as a result of a particular program.

cout << pow ( 2.0 , pow ( 3.0 , 1.0 )) << endl;

= pow ( 3.0 , 1.0 )

= 3^1

= 3.0

cout << pow ( 2.0 , 3.0 ) << endl;

= pow ( 2.0 ,3.0 )

= 2.0^3.0

= 8.0

Therefore The output of the statement: cout << pow(2.0, pow(3.0, 1.0)) << endl; is  c. 8.0.

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Answer:

The value of k is 24

Step-by-step explanation:

y = 24x

The equation for a direct variation is

y = kx

The constant of proportionality is k

y = 24x

The value of k is 24

To determine the number of aardvarks that were there last year, we will have to use the formula for exponential growth. Exponential growth is a type of growth that increases in size exponentially over time.

The formula for exponential growth is given by the equation:

\(Nt = N\times(1 + r)^t,\)

where N₀ is the initial population, r is the annual growth rate, t is the time in years, and Nt is the population after t years.Let's use this formula to find the number of aardvarks last year. Given that the current population of aardvarks is 756, and the growth rate is 8%, we can write the equation as

\(:Nt = N \times (1 + r)^t756 = N \times(1 + 0.08)^1So, N = 756 / (1 + 0.08)^1\)

Now, we need to find the population of aardvarks last year, which is t = 1 year before.

Thus, plugging in t = 1, we get

:\(N = 756 / (1 + 0.08)^1N= 700\)

Hence, there were 700 aardvarks last year.

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Since Lourdes garage is in the shape of a square pyramid, the surface area of the square pyramid roof is 1440 ft²

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The surface area (SA) of a pyramid is given as:SA = B + (1/2)Ph

where B is the base area, P is the perimeter and h is the slant height

Since the roof is a square pyramid with base 40 feet and slant height of 18 ft, hence:

h = 18 ftP = 40 + 40 + 40 + 40 = 160 ft.

Surface area of only roof = (1/2)Ph

Therefore, Substituting:

SA = (1/2)(160)(18) = 1440 ft²

The surface area of the roof is 1440 ft²

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If the two triangle are overlapping , then they are congruent.

The term congruent refers the triangles that have three sets of corresponding congruent sides and three sets of corresponding congruent angles.

Here we have to prove that the two overlapping triangles are congruent.

Here we know that the two triangle are overlappling.

Now we have to do the following process to prove that the overlapping triangles are also congruent.

As per the reflexive property of congruence, here when overlapping triangles share a common side or angle because the reflexive property of congruence states that a segment or angle is congruent to itself. Therefore, according to the geometry when two triangles share a side or angle this can be used to prove one set of congruent sides/angles.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

The selling price of the bag is $22.5

Step-by-step explanation:

Buying Price = $25,

Selling Price = ?

Since they sold it at a loss of 10%,

So, they sold it for a price 10% less than the buying price,

or at 90% or 0.9 of the buying price,

so,

Selling Price = (0.9)(25) = $22.5

Answer:

p is goodvjlxhkjdgmdgjmdmthdmyj

The correct option is B) Not valid. Consider the statement “Since some shoes are sneakers, some non-sneakers are non-shoes.”

We know that all sneakers are shoes, but all shoes are not sneakers.  Hence, some shoes are sneakers. But, this statement does not imply that “some non-sneakers are non-shoes.” This inference cannot be drawn by contraposition. So, it is not valid.Inferences cannot be drawn in contraposition all the time. Contraposition is a type of logical statement that involves reversing and negating the terms of an original proposition. It is a logical relationship between a proposition and its converse. If a proposition is true, the contrapositive is always true.An example of contraposition can be shown as follows:“If a person is a human, then they are mortal.”We can write the contrapositive of this statement as:“If a person is not mortal, then they are not human.”

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Answer:

126

Step-by-step explanation:

Answer:

x = 117°

Step-by-step explanation:

the angle on the lower right of the triangle and 101° are a linear pair and sum to 180° , that is

angle + 101° = 180° ( subtract 101° from both sides )

angle = 79°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 79° + 38° = 117°

Answer:

117

Step-by-step explanation:

the second angle in triangle is 180-101=79. after that you add 79+38 and than substract this from 180to get the last angle inside the triangle. it is 63. you than substract that from 180 and you get 117

Answer:

7 green cars.

Step-by-step explanation:

Look at the totals of all of the colors at the bottom. The least of them is green (at 7 cars). That's the answer.

Answer:

\(\huge\boxed{\sf x = 12 }\)

Step-by-step explanation:

Opposite sides and angles of a parallelogram are equal.

So,

3x - 1 = 35

Add 1 to both sides

3x = 35 + 1

3x = 36

Divide 3 to both sides

x = 36 / 3

x = 12

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

Mode: 2; Median: 5; Mode: 5

Step-by-step explanation:

Answer:

QR = 15

Step-by-step explanation:

The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.

(QR+5) *5 = 10^2

(QR+5) *5 = 100

Divide each side by 5.

(QR+5) *5/5 = 100/5

(QR+5)  = 20

Subtract 5 from each side.

QR = 20-5

QR = 15

To find the radius of a circle when we're given the coordinates of its center and a point it contains, we can use the following formula for distance:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

We're given:

Plug these given points into the formula for distance:

\(d=\sqrt{(2-(-2))^2+(-1-1)^2}\\d=\sqrt{(2+2)^2+(-1-1)^2}\\d=\sqrt{(4)^2+(-2)^2}\\d=\sqrt{16+4}\\d=\sqrt{20}\\d\approx4.47\)

Therefore, the radius of the circle is \(\sqrt{20}\) units, or approximately 4.47 units.

Answer

Price after discount: $50.99

You saved: $9.00

With original price $59.99 and 15% discount,

The required equation of line is  y = -5x + 2.

The equation of a line in slop intercept form is an equation of the form

y = mx + c . Where m is the slope of the line and c is the intercept of the line on the Y-axis.

Given,

Line passes through (0,2)

Therefore, (2) = m(0) + c

  or               2 = c

Also, the line passes through (1,-3)

Therefore, (-3) = m(1) + 2

or                  m = -3 - 2

                    m = -5

Hence, the required line is y = -5x + 2.

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The measure of angle A is 20 degrees, the measure of angle B is 65 degrees, and the measure of angle C is 95 degrees.

To find the measure of the angles in triangle ABC, we first need to determine the total ratio of measures.

The total ratio is 4 + 13 + 19 = 36.

Next, we can use the ratios to find the measure of each angle.

Let x be the measure of the smallest angle in triangle ABC.

Then the measures of the angles are:

Angle A = 4x
Angle B = 13x
Angle C = 19x

We know that the sum of the angles in a triangle is 180 degrees, so we can set up the equation:

4x + 13x + 19x = 180

Simplifying, we get:

36x = 180

Dividing both sides by 36, we get:

x = 5

Therefore, the measures of the angles in triangle ABC are:

Angle A = 4x = 4(5) = 20 degrees
Angle B = 13x = 13(5) = 65 degrees
Angle C = 19x = 19(5) = 95 degrees

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The probability that student chosen at random is 16 years is 0.28.

The table shows the distribution of student by age in a high school with 1500 students. Therefore, the probability that randomly chosen student is  16 years can be found as follows:

Therefore,

probability = number of favourable outcome to age / total number of possible outcome

Hence,

probability that student chosen at random is 16 years =  420 / 150

probability that student chosen at random is 16 years = 0.28

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