The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.2 years and a standard deviation of 0.6 years. He then randomly selects records on 28 laptops sold in the past and finds that the mean replacement time is 3 years.

Assuming that the laptop replacement times have a mean of 3.2 years and a standard deviation of 0.6 years, find the probability that 28 randomly selected laptops will have a mean replacement time of 3 years or less.

P(M ≤ 3 years) =
Enter your answer as a number accurate to 4 decimal places.


Based on the result above, does it appear that the computer store has been given laptops of lower-than-average quality? Yes or no question.

Yes- The probability of this data is unlikely to have occurred by chance alone.
No- The probability of obtaining this data is high enough to have been a chance occurrence.

8 pants wil cost 192 u.m.

10 pants ----> 240u.m

8 pants  ----> x

In a rule of 3, whenever the x is located at the bottom right corner, you always have to multiply upwards and to the right, and then divide the resulting number by the number on the top left. This is the operation you need to make:

x= (8 x 240) / 10

x= 192

Check the attached image to get a better understanding of this process.

8 pants wil cost 192 u.m.

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Proportional quantities are divided into directly and inversely proportional.

Two magnitudes are said to be directly proportional

when we multiply one of them by a number, the other is multiplied by the same number, and when we divide one of them by a number, the other is divided by the same number.

Problem :

If 10 pants cost 240u.m, how much will 8 pants cost?

We have:

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \\ \bold{ Assumption \: { \rightarrow} 10 \: pants \: \rightarrow 240 \: u.m\\\sf \: \: \: \: \: \: \: \: \: Question \rightarrow8 \: pants \rightarrow \: x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

As can be seen, the number of pants and the cost are magnitudes directly proportional, and therefore, we put the + sign below the pants and the - sign above.

Therefore we will have:

[tex]\boxed{ \bold{ \: x = \dfrac{240 * 8}{10} = 192 \: u.m} }[/tex]

So the 8 pants cost 192.

To find the set of numbers with a given mean we can assume them as consecutive terms, Zina did the same thing.

Mean or Arithmetic mean is the average of the given set of numbers. It is also denoted as the equal distribution of values for a given data. To calculate the mean of data, we can use the following formula  

Mean/Average = Sum of observations ÷ Number of observations

Here we have

The average of 5 numbers is 85

Let's assume that the 5 numbers are 5 consecutive numbers and the five numbers are x, x+1, x+2, x+3, x+4, and x+5  [ for simple calculations ]  

Average of 5 numbers = Sum of numbers / 5

⇒ 85 = (x+ x+ 1 + x+2 + x+3 + x+4 ) /5

⇒ 425 = 5x + 10  

⇒ 5x = 415

⇒ x = 83

Then the 5 numbers are 83, 84, 85, 86, and 87

Therefore,

To find the set of numbers with a given mean we can assume them as consecutive terms and we can calculate the mean, Zina did the same thing.  

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Answer: 12

Step-by-step explanation: When multiplying (in this case finding a product,) by one, the number you are multiplying will always be the answer.

The percent represented by the shaded area as in the task content is; 40%.

It follows from the task content that the percent of the whole that is shaded as in the task content be determined.

By observation, the whole is partitioned into 5 parts with 2 parts shaded.

Consequently, when expressed as a fraction; the shaded region is; 2 / 5 of the whole.

Ultimately, when expressed as a percentage, the shaded region is;

( 2 / 5 ) × 100% = 0.4 × 100%

= 40%.

Ultimately, the percent of the whole that is shaded is; 40%.

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Based on the perimeter of this isosceles triangle, the possible x-coordinate for point L is either -16.85 or 10.85.

In Mathematics, the perimeter of an isosceles triangle can be determined by summing up all of its side lengths that encloses. Mathematically, the perimeter of isosceles triangle JKL is given by this mathematical expression:

Perimeter, P = JK + JL+ KL

36 = JK + JL+ KL

Next, we would determine the distance between each vertices by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance JK = √[(-3 - (-3))² + (-9 - 7)²]

Distance JK = √0 + 256

Distance JK = √256

Distance JK = 16

Distance JL = √[(-9 - (-1))² + (-3 - x)²]

Distance JL = √8² + (-3 - x)²

Distance JL = √64 + (-3 - x)²

Distance KL = √[(7 - (-1))² + (-3 - x)²]

Distance KL = √8² + (-3 - x)²

Distance KL = √64 + (-3 - x)²

Note: Side JK is equal to side KL as an isosceles triangle.

From the perimeter of this isosceles triangle, we have:

36 = JK + JL+ KL

36 = 16 + JL+ JL

2JL = 20

JL = 10 units.

Now, we can determine the possible x-coordinate for point L:

256 = 64 + (-3 - x)²

256 - 64 = (-3 - x)²

192 = (-3 - x)²

13.85 = -3 - x

x = -3 ± 13.85

x = (-3 -  13.85) or (-3 + 13.85)

x = -16.85 or 10.85

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Answer:(-7, infinite down)

Step-by-step explanation: -7,-8,-9...

Answer: there are 4 ways the committee can be formed

Step-by-step explanation:

The statement that are correct from the graph is:

Some input values are negative.

some output values are negative.

Some input values are integers.

Some output values are integers.

From the graph:

The x value is -2,-4 that is negative.

so the some inputs are negative.

Y has values -2 ,-4 which are negative.

So the some outputs are negative.

The point values from the graph is -4,-2,0,2,4 which belong to integers.

So some input values and output values are integers.

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The equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6

The coordinates of the point = (-7, -4)

The slope of the line = 10/7

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Where [tex](x_1,y_1)[/tex] is the coordinates of the point

Substitute the values in the equation

y -(-4) = 10/7(x - (-7))

y + 4 = (10/7)(x + 7)

Convert to slope intercept form

y +4 = (10/7)x + 10

y = (10/7)x + 10 - 4

y = (10/7)x + 6

Hence, the equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6

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Answer: 1 3\5

explanation :  since the denominator of both fractions are same we can go ahead and the numerators which will make the fraction 16\10 or 8/5 (simplified) and  to make this a mixed numeral 5 fits into 8 once with 3 leftover thus making 1 3/5.

hope this helps .

A 270° counterclockwise rotation about the origin is the different one

Rotation simply means turning

In order to answer this question, you need to know some rules about rotation. They are as follows:

1. If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x)

2. If a point P, whose position vector is (x,y), is rotated  270° clockwise rotation about the origin, the position of the image P' is (-y, x). This is the same number 1

3. A 90° leftward rotation about the origin is the same as a 90° counterclockwise rotation about the origin. This is the same with number 1

4.  If a point P, whose position vector is (x,y), is rotated  270° counterclockwise rotation about the origin, the position of the image P' is (y, -x). This is different from the other three.

From the graph: A(1, 2), B(2, 4), C(4, 2)

Answer for the different question: A'(2, -1), B'(4, -2), C'(2, -4)

Answer for the same three question: A'(-2, 1), B'(-4, 2), C'(-2, 4)

Therefore, a 270° counterclockwise rotation about the origin is the different one. The 4th option is the answer

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The solution of the trigonometry function is  2√3/3.

What is the trigonometric function?

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given trigonometric function is

sec^(-1) x = csc^(-1) 2

Assume that,

csc^(-1) 2 = z

→ 2 = csc z

→ 1/2 =1/ (csc z)

→ 1/2 =sin z

The trigonometry identity is [tex]\cos x =\sqrt{1-\sin^2x}[/tex].

[tex]\sqrt{1-(\frac{1}{2})^2 } =\cos z[/tex]

→ cos z = √3/2

→ sec z = 2/√3

→ sec z = 2√3/(√3×√3)

→ sec z = 2√3/3

→  z =sec^(-1) ( 2√3/3) = csc^(-1) 2

Putting csc^(-1) 2 = sec^(-1) ( 2√3/3):

sec^(-1) x = sec^(-1) ( 2√3/3)

→ x = 2√3/3

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1. The hypothesis are given as follows:

2. The critical value is of: t = 2.3974.

3. The test statistic is of: t = 2.35.

4. The decision is: Reject the null hypothesis.

5. The conclusion is: There is enough evidence to conclude that the mean is greater.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean in Los Angeles is greater, that is:

[tex]H_0: \mu \leq 178258[/tex]

At the alternative hypothesis, it is tested if there is enough evidence, hence:

[tex]H_1: \mu > 178258[/tex]

The t-distribution is used, as we have the standard deviation for the sample but not for the population. Using a t-distribution calculator, with 55 - 1 = 54 df, a right-tailed test, as we are testing if the mean is greater than a value and a significance level of 0.01, the critical value is:

t = 2.3974.

Hence the decision rule is defined as follows:

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

[tex]\overline{x} = 191790, \mu = 178258, s = 42627, n = 55[/tex]

Hence the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{191790 - 178258}{\frac{42627}{\sqrt{55}}}[/tex]

t = 2.35.

The test statistic is greater than the critical value, hence:

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The average rate of change of the function f(x) on the interval −9≤x≤1 is of:

r = -0.2.

The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the equation presented as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Over the interval −9≤x≤1, the bounds of the interval are given as follows:

a = -9, b = 1.

From the graph shown by the image presented at the end of the answer, the numeric value of the function at each of these bounds is given as follows:

Hence the average rate of change of the function on the interval is calculated as follows:

r = (1 - 3)/(1 - (-9)) = -2/10 = -0.2.

The graph is shown by the image at the end of the answer.

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g(x) is a vertical dilation of f(x), then the x-value of the vertex does not change, using that we will see that the vertex of g(x) is (-4, 24)

We know that there is a parabola graphed called f(x), such that the vertex of f(x) is at (-4, 6).

We also have a vertical dilation of this function defined as:

g(x) = 4*f(x)

Notice that because this is a vertical dilation, the x-value of the vertex does not change, then the vertex is at x = -4, like on f(x).

Evaluating there we get:

g(-4) = 4*f(-4)

And because the vertex of f(x)  is (-4, 6), then we know that:

f(-4) =6

Replacing that we get:

g(-4) = 4*f(-4) = 4*6 = 24

Then the vertex of g(x) is at (-4, 24)

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Answer:

[tex]250\pi[/tex] cm³

Step-by-step explanation:

If the radius is 20 cm, the diameter is 10 cm.

Thus, the volume is [tex]\pi(10^2)(25)=250\pi[/tex] cm³.

The percentage of pediatricians that work more than 70 h per week is; 2.275%

The formula for z-score of a normal distribution is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

sample mean; x' = 70 hours

population mean; μ = 40 hours

standard deviation; σ = 15 hours

Thus;

z = (70 - 40)/15

z = 2

From online p-value from z-score calculator, we have;

p-value =  0.02275 = 2.275%

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Answer:

[ D ] 140

Step-by-step explanation

4 x 265 = 1060

1060 - 1200 = -140

the answer is 140  i hope this helped <3

Answer:

Slope = -3/4, y-intercept = -4

Step-by-step explanation:

[tex]6x+8y=-32 \\ \\ 3x+4y=-16 \\ \\ 4y=-3x-16 \\ \\ y=-\frac{3}{4}x-4[/tex]

So, the slope is -3/4 and the y-intercept is -4.

Answer:

[tex]10\sqrt{6}[/tex] feet by [tex]\frac{20}{3}\sqrt{6}[/tex] ft

Step-by-step explanation:

If the length is [tex]l[/tex], then the width is [tex]\frac{2}{3}l[/tex].

Using the formula for the area of a rectangle,

[tex]l \cdot \frac{2}{3}l=400 \\ \\ \frac{2}{3}l^2=400 \\ \\ l^2=600 \\ \\ l=10\sqrt{6}[ \\ \\ \implies w=\frac{20}{3}\sqrt{6}[/tex]

Answer:

Step-by-step explanation:

they are expecting you to know a few things.

first,  that ∠x   is asking for the interior angle of the labeled angle, here they call it  1 , so find that angle and look at the inside of the triangle,  it's also referred to as the minor angle.

second, they are expecting you to know how many degrees it is around the interior or a triangle... do you know?

then , just take that number and subtract the two given numbers to find the final number ,  or the  ∠1

got it?

Step-by-step explanation:

a polynomial of degree n (that means the highest exponent of x is n) must have n zeroes.

in our case that means 3 zeroes.

the best way to find them is to have the factorial form of the polynomial : to see how several terms are multiplied to give us the polynomial.

the first f(x) gives us exactly that (the second f(x) is just the form with all the multiplications done) :

f(x) = x(x + 6)(x - 2)

when is the product of factors 0 ?

only when at least one factor is 0.

so, let's see,

when is x 0 ? well, x = 0.

when is (x + 6) = 0 ? x = -6.

when is (x - 2) = 0 ? x = 2.

so, the 3 zeroes are

x = -6

x = 0

x = 2

The matrix AB = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]

Given,

In the question:

The matrix is given as:

A = [tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex]   & B = [tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex]

To find the AB :

Now, According to the question:

AB =  [tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]

The basic Addition and Multiplication:

= -4 x 3 + (-3)x (-5) + 5 x (-1) = -12 +15 -5 = -2

= (-4) x (-4) + (-3)x (-5) + 5x (-3) = 16 + 15 -15 = 16

=(-4)x (-1) + (-3) x 1 + 5x 2 = 4 - 3 +10 = 11

= (-5) x 3 +(-4) x(-5) + (-2) x (-1) = -15 + 20 +2 = 7

= (-5) x(-4) + (-4)x (-5) + (-2) x (-3) = 20 + 20 + 6 = 46

= (-5) x (-1) + (-4) x 1 + (-2) x 2 = 5 - 4 - 4 = -3

= (-1) x 3 + (-2) x (-5) + (-4) x(-1) = -3 + 10 +4 =  11

=(-1) x(-4)+ (-2)x (-5) + (-4) x (-3) = 4 + 10 + 12 = 26

= (-1) x(-1) + (-2) x 1 + (-4) x 2 = 1 - 2 +(-8) = -9

Hence, The matrix AB = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]

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Answer:

Tan a =1

Step-by-step explanation:

TRIG identity:

Tan ( a+b) =  (tan a + tan b )/ (1 - tan a  tan b)     Sub in the given values

      -2       = ( tan a + 3) / ( 1 - 3 tan a)

-2 + 6 tan a = tan a + 3

5 tan a = 5

  tan a = 1

Answer:

-x^5+2x³-x²-1x-1

Step-by-step explanation:

First order the terms based on highest degree or exponent.

-x^5+2x³-x²-3x¹+2x-1

Next combine like terms.

-3x¹ is simply -3x so -3x+2x = -1x

-x^5+2x³-x²-1x-1

Answer:

The answer would be the first one because when you factor -3 out, inside of the parentheses should be all positive because negative times negative is positive.