The exercise involving data in this and subsequent sections were designed to be solved using Excel.
The following estimated regression equation was developed for a model involving two independent variables.
y=40.7+ 8.63x1+ 2.71x2
After x2 was dropped from the model, the least-squares method was used to obtain an estimated regression equation involving only x1 as an independent variable. y=42.0+9.01x1
a. In the two independent variable cases, the coefficient x1 represents the expected change in (Select your answer: y, x1, x2) corresponding to a one-unit increase in (Select your answer: y, x1, x2) when (Select your answer: y, x1, x2) is held constant.
In the single independent variable case, the coefficient x1 represents the expected change in (Select your answer: y, x1, x2) corresponding to a one-unit increase in (Select your answer: y, x1, x2).
b. Could multicollinearity explain why the coefficient of x1 differs in the two models? Assume that x1 and x2 are correlated.

Find the solution in the attachments

In this exercise we have to use the knowledge of finance and thus plot a graph, this way we have that it corresponds to:

A)[tex]q= 0 \ or \ q=1[/tex]

B) The graph bellow.

C) The points of the grapg bellow.

Knowing that:

[tex]total \ cost = (variable \ cost \ per \ unit + final \ cost \ per \ unit * produced)[/tex]

The data that was informed is;

A) The result is:

[tex]T= (3+2)*9\\T= 59[/tex]

Break even points one the points at which total cost are equal to :

[tex]T(q)= Y_T(9)\\5q= 5\sqrt{9}\\q=\sqrt{9}\\ q= 0 or q=1[/tex]

B) One plot of total cost are total revenue are ploted below. The blue curve is of total revenue and real graph is of total cost.

C) With the graph, it's closes that from q=0 ot q=1. Total revenue dominantes total cost and beyond a=1 the total cost dominands total revenue.

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Answer:

At Maximum point;

x(max) = 50

p(max) = $100

Maximum revenue = $5,000

Step-by-step explanation:

The price function is;

p(x) = 200 − 2x

where

p is the price (in dollars) at which exactly x trucks will be rented per day.

The revenue function R(x) can be written as;

R(x) = p(x) × x

Substituting p(x) equation;

R(x) = (200-2x)x

R(x) = 200x-2x^2 ........1

To maximize R(x), at maximum point dR/dx = 0

differentiating equation 1;

dR/dx = 200 - 4x = 0

4x = 200

x = 200/4

x = 50

Substituting x = 50 into p(x)

p(50) = 200 - 2(50) = $100

p = $100

Maximum revenue is;

R = p × x = $100×50

R = $5,000

At the level of the maximum point, the value of x(max) should be 50 and the value of p(max) should be $100, Also, Maximum revenue = $5,000.

Since

The price function is;

p(x) = 200 − 2x

Here,

p refer to the price (in dollars) at which exactly x trucks should be rented per day.

Now

The revenue function R(x) should be

R(x) = p(x) × x

Now

R(x) = (200-2x)x

R(x) = 200x-2x^2 ........1

Now

To maximize R(x), at maximum point dR/dx = 0

So,

dR/dx = 200 - 4x = 0

4x = 200

x = 200/4

x = 50

Now

Substituting x = 50 into p(x)p(50) = 200 - 2(50) = $100

p = $100

Now

Maximum revenue is;

R = p × x = $100×50

R = $5,000

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Answer:

330 degrees.

Step-by-step explanation:

 π radians / 180 degrees = 1

(11 π)/6  radians  *  180  / π  =   11 * 180 / 6  =  11 * 30 = 330 degrees.

After converting into degree we get;

⇒ 11 pi /6 radians = 330 degree

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

The expression is,

⇒ 11 pi /6 radians

Now, To change into degree we can multiply by 180 / π in the given expression as;

⇒ 11 pi /6 radians

⇒ 11 π /6 × 180 / π degree

⇒ 330 degree

Thus, After converting into degree we get;

⇒ 11 pi /6 radians = 330 degree

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Answer:

We can be 95% sure that the true population mean zinc concentration is between 8.8 mg/g and 9.5 mg/g.

Step-by-step explanation:

Given that

N = Sample = 56

Confidence Interval = 95%

Mean Interval = 8.8 mg/g to 9.5 mg/g

UB = Upper Bound = 9.5mg/g

LB = Lower Bound = 8.8mg/g

The sample mean was 9.15mg/g

The sample mean is gotten from ½(UB + LB)

Sample Mean = ½(8.8 + 9.5)

Sample Mean = ½ * 18.3

Sample Mean = 9.15mg/g

From the definition of confidence Interval;

"Confidence Interval is a range of values so defined that there is a specified probability that the value of a parameter lies within it"

This means that the best interpretation of the data given is "the mean value of the 56 sample of fishes is between 8.8mg/g and 9.5mg/g;"

With 8.8mg/g as the lower bound and 9.9mg/g as the upper bound.

Answer:

To check that V is a vector space it suffice to show

1. Associativity of vector addition.

2. Additive identity

3. Existence of additive identity

4. Associativity of scalar multiplication

5. Distributivity of scalar sums

6.  Distributivity of vector sums

7. Existence of scalar multiplication identity.

Step-by-step explanation:

To see that V is a vector space we have to see that.

1. Associativity of vector addition.

This property is inherited from associativity of the sum on the real numbers.

2. Additive identity.

The additive identity in this case, would be the null function f(x)=0 . for every real x.   It is inherited from the real numbers that the null function will be the additive identity.

3. Existence of additive inverse for any function f(x).

For any function f(x), the function -f(x) will be the additive inverse. It is in inherited from the real numbers that f(x)-f(x) = 0.

4. Associativity of scalar multiplication.

Associativity of scalar multiplication  is inherited from associativity of the real numbers

5. Distributivity of scalar sums:

Given any two scalars r,s and a function f, it will be inherited from the distributivity of the real numbers that

(r+s)f(x) = rf(x) + sf(x)

Therefore, distributivity of scalar sums is valid.

5. Distributivity of vector sums:

Given scalars r  and two functions f,g, it will be inherited from the distributivity of the real numbers that

r (f(x)+g(x)) = r f(x) + r g(x)

Therefore, distributivity of vector sums is valid.

6. Scalar multiplication identity.

The scalar 1 is the scalar multiplication identity.

Answer:

z = 1.83<1.96

null hypothesis is accepted

The sample is came from a population mean

Step-by-step explanation:

Step :-1

The sample of 40 measured voltage amounts from a unit have a mean of 123.59 volts and a standard deviation of 0.31 volts

given sample size n =40

mean of the sample ×⁻ = 123.59 volts

standard deviation of sample σ = 0.31 volts

Step2:-

Null hypothesis :-

the sample is from a population with a mean equal to 120 volts.

H₀ : μ =120

Alternative hypothesis:-

H₁ : μ ≠120

level of significance:- α =0.05

Step 3:-

The test statistic

[tex]z = \frac{x_{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

substitute values and simplification

[tex]z = \frac{123.59-120}{\frac{0.31}{\sqrt{40} } }[/tex]

on simplification we get the calculated value

z = 1.83

The tabulated value z =1.96 at 0.05 % level of significance

Conclusion:-

Calculated Z < The tabulated value z =1.96 at 0.05 % level of significance

so the null hypothesis is accepted

The sample is came from a population mean

Answer: REJECT the null hypothesis; there IS sufficient evidence to warrant a rejection of the claim that the mean voltage is 120 volts.

t-calculated = 73.242

t-critical = 2.023

Answer:

The correct answer is 0.1714 .

Step-by-step explanation:

There are 6 men and 4 women to be interviewed for jobs.

Total number of arrangements in which they can be called for the interview process is 10!.

Number of ways any two women are interviewed before any man is 4 × 3 × 8!. = 12 × 8!.

Number of ways any three women are interviewed before any man is 4 × 3 × 2 × 7!. = 24 × 7!.

Number of ways all the women are interviewed before any man is 4! × 6!.

Required number of ways in which at least two women being interviewed before any man is given by 12 × 8! + 24 × 7! + 4! × 6! = 864 × 6!.

Required probability is 864 × 6! ÷ 10! = 0.1714

The probability that no man will be interviewed until at least two women have been interviewed is [tex]\( \bxed{\frac{2}{15}} \).[/tex]

Step 1

We may utilise the concept of permutations to estimate the likelihood that no man will be interviewed until at least two women have been interviewed.

Let us examine the case where a minimum of two women are interviewed before a guy is examined. This implies that women must have the first two places in the interview process. Men and women may be appointed to the other positions in any order, following these two positions.

Let's figure out how many options there are to choose the first two slots for women, given that there are four women and six men:

Step 2

Number of ways to select the first woman: [tex]\(4\)[/tex]

Number of ways to select the second woman: [tex]\(3\)[/tex] (since one woman has already been selected for the first position)

The total number of ways to select the first two positions for women is [tex]\(4 \times 3 = 12\).[/tex]

Step 3

After these two positions have been filled with women, the remaining 8 positions (6 men + 2 women) can be filled with the remaining people (4 men + 2 women) in any order. This can be calculated using the permutation formula:

[tex]\[ nPr = \frac{{n!}}{{(n-r)!}} \][/tex]

Where n is the total number of people and r is the number of positions to be filled.

For our scenario, [tex]\( n = 6 + 4 = 10 \)[/tex] and [tex]\( r = 8 \)[/tex]. So, the number of ways to fill the remaining 8 positions is:

[tex]\[ 10P8 = \frac{{10!}}{{(10-8)!}} = \frac{{10!}}{{2!}} = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \][/tex]

Step 4

Now, let's calculate the total number of ways to select the positions for all 10 people:

[tex]\[ 10! \][/tex]

Consequently, the ratio of the number of favourable results to the total number of outcomes represents the likelihood that no guy will be interviewed until at least two women have been interviewed:

[tex]\[ \text{Probability} = \frac{{12 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}}{{10!}} \]\[ \text{Probability} = \frac{{12}}{{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}} \]\[ \text{Probability} = \frac{{12}}{{10!/(10-8)!}} \]\[ \text{Probability} = \frac{{12}}{{10P8}} \]\[ \text{Probability} = \frac{{12}}{{10 \times 9}} \]\[ \text{Probability} = \frac{2}{15} \][/tex]

So, the probability that no man will be interviewed until at least two women have been interviewed is [tex]\( \bxed{\frac{2}{15}} \).[/tex]

Step-by-step explanation:

Given points

( x1 , y1 ) = ( 0, 4)

And

( x2 , y2 ) = ( - 4 , - 3 )

Now

Slope(m)

= ( y2 - y1 ) / ( x2 - x1 )

= ( - 3 - 4) / ( -4 - 0)

= - 7 / - 4

= 7/4

Answer:

m=7/4

Step-by-step explanation:

.24 is equivalent to

24%

24/100

6/25

12/50, and more!

Hope this helped

Answer:

Probability that the 44 randomly selected laptops will have a mean replacement time of 3.6 years or less is 0.0092.

Yes. The probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.

Step-by-step explanation:

We are given that the replacement times for the model laptop of concern are normally distributed with a mean of 3.8 years and a standard deviation of 0.4 years.

He then randomly selects records on 44 laptops sold in the past and finds that the mean replacement time is 3.6 years.

Let [tex]\bar X[/tex] = sample mean replacement time

The z-score probability distribution for sample mean is given by;

            Z = [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean replacement time = 3.8 years

            [tex]\sigma[/tex] = standard deviation = 0.4 years

            n = sample of laptops = 44

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the 44 randomly selected laptops will have a mean replacement time of 3.6 years or less is given by = P([tex]\bar X[/tex] [tex]\leq[/tex] 3.6 years)

 P([tex]\bar X[/tex] [tex]\leq[/tex] 3.6 years) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] [tex]\leq[/tex] [tex]\frac{3.6-3.8}{\frac{0.4}{\sqrt{44} } }} }[/tex] ) = P(Z [tex]\leq[/tex] -3.32) = 1 - P(Z < 3.32)

                                                            = 1 - 0.99955 = 0.0005 or 0.05%          

So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.32 in the z table which has an area of 0.99955.

Hence, the required probability is 0.0005 or 0.05%.

Now, based on the result above; Yes, the computer store has been given laptops of lower than average quality because the probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.

Answer:

16.1 my friend

Step-by-step explanation:

Answer:

16.1

Step-by-step explanation:

Remember to always follow PEMDAS. In this case, we need to multiply before we divide.

10 x .89 + 7.2

8.9 + 7.2 = 16.1

The answer is 16.1

Answer:

a. [tex]f(x)= 1.25\ \ \ \ , \ for \ 31.8\leq x\leq 32.6[/tex]

[tex]b. \ P(X=32)=0\\P(X>32.3)=0.375\\P(X<31.8)=0[/tex]

c. No.  Delicious Candy isn't violating any government regulations

Step-by-step explanation:

a.

-A uniform distribution is given by the formula:

[tex]f(x)=\frac{1}{b-a} \ \ \ for \ \ \ a\leq x\leq b[/tex]

#we substitute our values in the formula above to determine the distribution:

[tex]f(x)=\frac{1}{b-a}\\\\=\frac{1}{32.6-31.8}\\\\=1.25\\\\\therefore f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6[/tex]

Hence, the probability density function for the box's weight is given as: [tex]f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6[/tex]

b. The probability of the box's weight being exactly 32 ounces is obtained by integrating f(x) over a=b=32:

[tex]f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32}_{32} {1.25} \, dx \\\\\\=[1.25x]\limits^{32}_{32}\\\\\\=1.25[32.0-32.0]\\\\\\=0[/tex]

Hence,  the probability that a box weighs exactly 32 ounces is 0.000

ii.The probability that a box weighs more than 32.3 is obtained by integrating f(x) over the limits 32.3 to 32.6 :

[tex]f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32.6}_{32.3} {1.25} \, dx \\\\\\=[1.25x]\limits^{32.6}_{32.3}\\\\\\=1.25[32.6-32.3]\\\\\\=0.375[/tex]

Hence, the probability that a box weighs more than 32.3 ounces is 0.3750

iii. The probability that a box weighs less than 31.8 is 0.000 since the weight limits are [tex]31.8\leq x\leq 32.6[/tex].

-Any value above or below these limits have a probability of 0.000

c. Let 32 ounces be the government's stated weight.

[tex]1.25(32.6-32)=0.75\\\\0.75>0.60[/tex]

Hence, Delicious Candy isn't violating any government's regulations.

(a): The required probability density function for the weight of the box of chocolate is 1.25

(b):  The probability that a box weighs (1) exactly 32 ounces is 0

and  (2) more than 32.3 ounces is 0.375

(c): Therefore, Delicious Candy does not violate government regulation.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. Probability can range in from 0 to 1.

Given that,

The uniform distribution between [tex]a = 31.8[/tex] ounce and [tex]b = 32.6[/tex] ounce

Part(a):

The probability density function for the weight of the box of chocolate is,

[tex]\frac{1}{b-a}=\frac{1}{32.6-31.8} \\=1.25[/tex]

Part(b):

(1) P(exactly 32 ounces) = 0, because this is a continuous distribution.

(2) P(more than 32.3 ounces) =[tex]1.25\times (32.6-32.3)=0.375[/tex]

Part(c):

The stated weight of Delicious Candy =  2 pounds

That is, [tex]2\times 16=32[/tex] ounces

P(a candy weigh at least as much as stated) = P(at least 32)

[tex]1.25\times (32.6-32)=0.75[/tex]

So, 75% of candies weigh at least as much as stated.

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Answer:

The prorated monthly cost for tuition and fees and textbooks is ​$707

Step-by-step explanation:

Each semester costs $4000 + $240 = $4240.

A year has 12 months. A semester is 6 months. 12/6 = 2. So an year has two semesters.

The yearly cost is 2*$4240 = $8480

Monthly cost

12 months cost $8480

$8480/12 = $706.67

So the answer is:

Rounded to the nearest dollar

The prorated monthly cost for tuition and fees and textbooks is ​$707

The prorated monthly cost for tuition and fees and textbooks is $707

Total cost per semester = Fees for each semester + Cost of textbook per semester

= $4000 + $240

= $4,240

= 2 × $4,240

= $8480

= $8480 / 12

= $706.666666666666

Approximately,

$707

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Answer:

The correct equation in terms of s is: 4s=260

Step-by-step explanation:

Let the number of containers of strawberry ice cream produced per day=s

Let the number of containers of vanilla ice cream produced per day=v

Let the number of containers of chocolate ice cream produced per day=c

Total Number of Ice Cream Containers=280

Given:

The factory produces twice as much chocolate ice cream as strawberry ice cream. This is written as:

The factory produces 20 more containers of vanilla ice cream than strawberry ice cream. This is written as:

Therefore substituting c=2s and v=s+20 into the first equation: s+v+c=280

s+s+20+2s=280

4s=280-20

4s=260

Divide both sides by 4

s=65

The number of strawberry ice cream produced per day is 65.

The number of chocolate ice cream produced per day =2s=2(65)=130.

The number of vanilla ice cream produced per day =s+20=65+20=85.

Final answer:

The number of containers of strawberry ice cream produced per day is 65.

Explanation:

The question is asking us to find the correct equation and solution for the number of containers of strawberry ice cream produced per day by a factory, while taking into account that chocolate is produced at twice the rate and vanilla at 20 more containers than strawberry.

Given the total production is 280 containers, the equation can be set up as follows:

s + 2s + (s + 20) = 280,

where s represents the number of strawberry ice cream containers produced per day.

Step-by-step, we can solve this equation:

Therefore, the factory produces 65 containers of strawberry ice cream per day.

Answer:

[tex]A=7 \: Square\: Units[/tex]

Step-by-step explanation:

From your work here, if the diagram corresponds with what was tiled, then:

Length of the Rectangle=[tex]3\frac{1}{2} \:Units[/tex]

Width of the Rectangle =2 Units

We know that:

Area of a Rectangle = Length X Width

[tex]=3\frac{1}{2} X 2\\A=7 \: Square\: Units[/tex]

The only thing wrong is the unit of the area given. The unit of area is supposed to be in Square Units.

The Taylor polynomial approximation to f(x) = 1/x up to degree 2 about x=a was calculated. It was mentioned that Taylor's inequality could be used to estimate the accuracy of this approximation. However, due to the lack of necessary information, an exact error bound or graphical check couldn't be determined.

To begin the solution, we'll need to find the first couple of derivatives for the function f(x) = 1/x. The first derivative is f'(x) = -1/x² and the second derivative is f''(x) = 2/x³. These derivatives will be used to form the Taylor series approximation.

The Taylor series polynomial of degree 2 is given by the formula T₂(x) = f(a) + f'(a)*(x-a) + f''(a)*(x-a)²/2!, where a is the point we are approximating about and n is the degree of the Taylor polynomial. Substituting the given values, we get: T₂(x) = 1/1 - 1/1² * (x-1) + 2/1³ * (x-1)²/2!.

To estimate the accuracy of this approximation, we use Taylor's Inequality which provides an upper bound for the absolute error. The remainder term in Taylor's series is given by |R₂(x)| ≤ M * |x - a|³ / (3!*n), where M is the maximum value of the absolute third derivative on the interval [a, x]. After applying Taylor's inequality, we can get an accuracy estimate but unfortunately, the information provided doesn't give enough specifics for an exact calculation.

Finally, to verify the result graphically, you would plot |R₂(x)|, but without the explicit remainder term, this cannot be done.

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Answer:

i dont see no angle

Step-by-step explanation:

Angles can be named according to their measure in degrees or position on a plane. Angles are always counted to be positive in the counter-clockwise direction and negative in the clockwise direction.

The name of an angle in Mathematics can vary based on its measure and location. Angles are generally named according to their measure in degrees, and they can be categorized as acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (180 degrees), reflex (greater than 180 degrees), or full (360 degrees).

Angles can also be referred to in terms of their position on a Cartesian plane: angles in the first quadrant are positive and less than 90; in the second quadrant, they are more than 90 but less than 180; in the third quadrant, they exceed 180 but are less than 270; and in the fourth quadrant, they are greater than 270 but less than 360 degrees.

This consistently maintains the rule that angles are defined as positive in the counter-clockwise direction, and negative in the clockwise direction. For example, an angle of 30° south of west is the same as the global angle 210°, or it can also be expressed as −150° relative to the positive x-axis.

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Answer:

The population will be 64 times larger after 96 hours.

Leave a comment if you'd like a more in-depth explanation.

Answer:

64  times as large as the original population.

Step-by-step explanation:

Given:

The given expression is [tex]18^{x^{2}+4 x+4}=18^{9 x+18}[/tex]

We need to determine the solution of the given expression.

Solution:

Let us solve the exponential equations with common base.

Applying the rule, if [tex]a^{f(x)}=a^{g(x)}[/tex] then [tex]f(x)=g(x)[/tex]

Thus, we have;

[tex]x^{2}+4 x+4=9 x+18[/tex]

Subtracting both sides of the equation by 9x, we get;

[tex]x^{2}-5 x+4=18[/tex]

Subtracting both sides of the equation by 18, we have;

[tex]x^{2}-5 x-14=0[/tex]

Factoring the equation, we get;

[tex]x^2-7x+2x-14=0[/tex]

Grouping the terms, we have;

[tex](x^2-7x)+(2x-14)=0[/tex]

Taking out the common term from both the groups, we get;

[tex]x(x-7)+2(x-7)=0[/tex]

Factoring out the common term (x - 7), we get;

[tex](x+2)(x-7)=0[/tex]

[tex]x+2=0 \ and \ x-7=0[/tex]

   [tex]x=-2 \ and \ x=7[/tex]

Thus, the solution of the exponential equations is x = -2 and x = 7.

Hence, Option C is the correct answer.

Answer:

[tex]x + 1[/tex]

Step-by-step explanation:

log(x) is the inverse function of an exponent. "log base 8 of xyz" means "what number do I have to raise 8 to, to get xyz". In this case, it means, "what number do I have to raise 8 to, to get x + 1". That's simple, it's just x + 1!

Answer:

A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 50 months and a standard deviation of 9 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries?

The company should guarantee the batteries for 38 months.

Step-by-step explanation:

Using standard normal table,

P(Z < z) = 10%

=(Z < z) = 0.10

= P(Z <- 1.28 ) = 0.10

z = -1.28

Using z-score formula  

x = zσ  + μ

x = -1.28 *9+50

x = 38

Therefore, the company should guarantee the batteries for 38 months.

Answer:

The company should guarantee the batteries (to the nearest month) for 38 months.

Step-by-step explanation:

We have here a normally distributed data. The random variable is the average life of the batteries.

From question, we can say that this random variable has a population mean of 50 months and population standard deviation of 9 months. We can express this mathematically as follows:

[tex] \\ \mu = 50[/tex] months.

[tex] \\ \sigma = 9[/tex] months.

The distribution of the random variable (the average life of the batteries) is the normal distribution, and it is determined by two parameters, namely, the mean [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex], as we already know.

For the statement: "The company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy", we can say that it means that we have determine, first, how many months last less of 10% of the batteries that its average life follows a normal distribution or are normally distributed?

To find this probability, we can use the standard normal distribution, which has some advantages: one of the most important is that we can obtain the probability of any normally distributed data using standardized values given by a z-score, since this distribution (the normal standard) has a mean that equals 0 and standard distribution of 1.

Well, the z-score is given by the formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where, x is a raw score coming from a normally distributed data. This is the value that we have to transform into a z-score, that is, in a standardized value.

However, from the question, we want to know what value of z represents a cumulative probability of 10% in the cumulative standard normal distribution. We can find it using the standard normal table, available in Statistics books or on the Internet (of course, we can use also Statistics packages or even spreadsheets to find it).

Then, the value of z is, approximately, -1.28, using a cumulative standard normal table for negative values for z. If the cumulative standard normal only has positive values for z, we can obtain it, using the following:

[tex] \\ P(z<-a) = 1 - P(z<a) =P(z>a)[/tex]

That is, P(z<-1.28) = P(z>1.28). The probability for P(z<1.28) is approximately, 90%.

Therefore, using the formula [1]:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ -1.28 = \frac{x - 50}{9}[/tex]

 [tex] \\ -1.28 * 9 = x - 50[/tex]

 [tex] \\ -11.52 = x - 50[/tex]

[tex] \\ -11.52 + 50 = x[/tex]

[tex] \\ 38.48 = x[/tex]

[tex] \\ x = 38.48[/tex] months.

That is, less than 10% of the batteries have a average life of 38.48 months. Thus, the company should guarantee the batteries (to the nearest month) for 38 months.

The question discusses a survey of US teens and their online interaction. It's emphasizing on the statistical data that shows approximately 57% of surveyed teens reported making new friends online. Other data are also relevant to highlight various aspects of teens internet usage.

The question is about a survey conducted on US teens, where 1060 were randomly selected and it was found that 605 of them have made a new friend online. This is relevant to statistics, a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

To calculate the percentage of teens making friends online, it is calculated as follows: (Number of teens reporting making new friends online / Total number of teens surveyed) * 100 = (605/1060) * 100 = 57.08%. This implies that approximately 57% of the surveyed teens reported making new friends online.

The other data provided discuss various aspects of teen internet usage, including use of social media, smartphone adoption, and experiences with digital relationships. The given data can be used to set up and test various statistical hypotheses about teen behavior relating to internet use.

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Answer:

1 and 7/10 pounds

Step-by-step explanation:

add.

Answer:

1 and 7/10 pounds

Step-by-step explanation:

Answer:

No, H is not a subspace of the vector space V.

Step-by-step explanation:

A matrix is a rectangular array in which elements are arranged in rows and columns.

A matrix in which number of columns is equal to number of rows is known as a square matrix.

Let H denote set of all 2×2  idempotent matrices.

H is a subspace of a vector space V if [tex]u+v \in H[/tex] for [tex]u,v \in V[/tex] and   [tex]cu \in H[/tex].

Let [tex]A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}[/tex]

As [tex]A^2=A\times A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}\begin {pmatrix}1&0\\0&1 \end{pmatrix}=\begin {pmatrix}1&0\\0&1 \end{pmatrix}=A[/tex], A is idempotent.

So, [tex]A \in H[/tex]

[tex]A+A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}+\begin {pmatrix}1&0\\0&1 \end{pmatrix}=\begin {pmatrix}2&0\\0&2\end{pmatrix} \\ \left ( A+A \right )^2=\begin {pmatrix}2&0\\0&2\end{pmatrix}\begin {pmatrix}2&0\\0&2\end{pmatrix}=\begin {pmatrix}4&0\\0&4\end{pmatrix}\neq A[/tex]So, A+A is not idempotent and hence, does not belong to H.

So, H is not a subspace of the vector space V.

Yes, H is a subspace of the vector space V. It satisfies the conditions of closure under addition, closure under scalar multiplication, and contains the zero vector.

Yes, H is a subspace of the vector space V. In order for a set to be considered a subspace, it must satisfy three conditions: it must be closed under addition, closed under scalar multiplication, and contain the zero vector. Let's check if H satisfies these conditions:

Since H satisfies all three conditions, it is a subspace of the vector space V.

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Answer:A+b

by-step explanation:

Answer:

you have the correct answer!

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Data provided as per the question below:-

Number of students = 4025

Lockers = 805

The calculation of  the largest number of students who must necessarily share a locker is shown below:-

Largest number of students = ((Number of students - 1) ÷ Lockers) + 1

= ((4026 - 1) ÷ 805) + 1

= (4025 ÷ 805) + 1

= 5 + 1

= 6

Final answer:

The height of the tree is approximately 113.85 feet, which is determined by using the tangent of the given angle of elevation (68°) and the distance from the tree (46 feet) in a trigonometric calculation.

Explanation:

To find the height of the tree, we can use trigonometry. The student is 46 feet from the tree, and the angle of elevation to the top of the tree is 68°. The height of the tree can be found using the tangent function in a right triangle, where the opposite side is the tree height (h), and the adjacent side is the distance from the tree (46 feet). The tangent of the angle of elevation (θ) is the ratio of the opposite side to the adjacent side.

So, tan(68°) = h / 46 feet. To find the height (h), multiply both sides by 46 feet:

h = 46 feet × tan(68°)

We can use a calculator to find that tan(68°) is approximately 2.475. Now, multiply 46 feet by this tangent value to get the height:

h = 46 feet × 2.475h = 113.85 feet (rounded to two decimal places)

Therefore, the height of the tree is approximately 113.85 feet.

Answer:

The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is (0.4894, 0.5706)..

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1004, \pi = 0.53[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.53 - 2.575\sqrt{\frac{0.53*0.47}{1004}} = 0.4894[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.53 - 2.575\sqrt{\frac{0.53*0.47}{1004}} = 0.5706[/tex]

The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is (0.4894, 0.5706)..

The 99% confidence interval for the proportion of American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is approximately 0.502 to 0.558.

To calculate the 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems, we can use the formula:

CI = p ± Z * sqrt((p * (1-p)) / n)

Where:

CI = Confidence interval

p = Proportion of respondents who blamed Barack Obama a great deal or a moderate amount

Z = Z-score corresponding to the desired confidence level

n = Sample size

Given that 53% of respondents blamed Barack Obama a great deal or a moderate amount and the sample size is 1,004, we can calculate the confidence interval as follows:

CI = 0.53 ± Z * sqrt((0.53 * (1-0.53)) / 1004)

Since we want a 99% confidence interval, the corresponding Z-score is 2.58 (obtained from a standard normal distribution table).

Plugging in the values:

CI = 0.53 ± 2.58 * sqrt((0.53 * (1-0.53)) / 1004)

Calculating the standard deviation and rounding to 2 decimal places:

CI = 0.53 ± 2.58 * sqrt(0.53 * 0.47 / 1004)

CI = 0.53 ± 2.58 * sqrt(0.2491 / 1004)

CI = 0.53 ± 2.58 * 0.0157

The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is approximately 0.502 to 0.558.

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