2. based on data from ac nielsen, among households in the united states, the mean number of tv sets is 2.24, with a standard deviation of 1.38. a random sample of 40 households is selected. a. describe the sampling distribution of the sample mean number of tv sets in a sample of 40 households. state the shape of the distribution and check any necessary conditions for that. state the mean and compute the standard deviation (round to 4 decimal places). (6 pts.) b. in a random sample of 40 households, what is the probability that the sample mean is 2.55 or higher? include a sketch. show all work. (8 pts.)

Answers

Answer 1

Therefore the mean number of sample of 40 households results in 102 television sets is 2.55 & the probability of that the sample mean is 2.55 or higher is 0.412

What is probability?

The likelihood of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these situations, we state that there is a likelihood that the event will occur or not.

Here,

Given:

mean number of tv sets (n)= 2.24

standard deviation ([tex]{S_d} }[/tex]) = 1.38

sample of 40 households results in 102 television sets so ,

mean number (n') = 102/40 =2.55

its mean number =2.55

the probability that the sample mean is 2.55 or higher

=> Z = [tex]\frac{n^{'}-n }{S_d} }[/tex]

=> Z =(2.55-2.24)/1.38

=>Z = 0.2246

the normal distribution of probability =

P=[tex]\frac{1 *e^{\frac{-1}{2}Z^{2} } }{\alpha \sqrt{2\pi } }[/tex]

P=0.588

therefore P(x<2.55)=0.588

=>P(2.55< x)= 1-0.588=0.412

Therefore the probability of that the sample mean is 2.55 or higher is 0.412

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Related Questions

I need help with this someone please explain it to me

Answers

The length of the Antenna will be;

⇒ h = 18 meters

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Tyler is 1.8 meters and his shadow is 6 meters.

And, Tyler is standing 54 meters from the antenna.

Now,

Since, Tyler is 1.8 meters and his shadow is 6 meters.

And, Tyler is standing 54 meters from the antenna.

Let the length of the Antenna = x

Hence, We get by definition of proportional, we get;

⇒ 1.8 / 6 = h / (54 + 6)

⇒ 0.3 = h / 60

⇒ h = 0.3 × 60

⇒ h = 18 meters

Thus, The length of the Antenna will be;

⇒ h = 18 meters

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Write an explicit
formula for an, the nth term of the sequence 2, 4, 8, ..

Answers

Answer:

formula: Tn=a+(n-1)d

Step-by-step explanation:

Tn=2+(n-1)2

Which of the following pairs of linear equations are consistent or inconsistent XY 8 3x -- 3y 16?

Answers

The equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.

What are linear equations?

Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

The definition of linear equations, the standard form for linear equations involving one variable, two variables, or three variables, and examples of each will all be covered in detail in this article.

Find the value of the variable that causes the equation to be true in order to solve linear equations.

Utilize the inverse of the variable's multiplier and divide or multiply both sides by it.

To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.

So, we have the pair of linear equations:

x – y = 8 and 3x – 3y = 16

(a1/a2) = 1/3

(b1/b2) = -1/-3 = 1/3

(c1/c2) = 8/16 = 1/2

Since, we know that (a1/a2) = (b1/b2) ≠ (c1/c2).

The equations have no solutions and run parallel to one another. The pair of linear equations is hence incoherent.

Therefore, the equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.

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Complete question:

Find out whether the following pairs of linear equations x – y = 8 and 3x – 3y = 16 are consistent/inconsistent.

What is the range of the function?
f(x)=3^x-1 -6
Enter your answer, in interval notation, in the box.
range:

Answers

The range of the function is (-6 , ∞)

What is function ?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.

Functions can be roughly categorized into four sorts. based on the element Numerous to one function, onto function, one to one and onto function, into function.

[tex]3^{x - 1} > 0[/tex]   for x ∈ R

Subtracting both sides by 6

[tex]3^{x - 1} - 6 > 0 - 6[/tex]

[tex]3^{x - 1} - 6 > - 6[/tex]

f (x) > -6

Range = (-6 , ∞)

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What is the area of a rectangle 3 meters long and 7 meters high

Answers

Answer:

21 sq. meters

Step-by-step explanation:

you just need to multiply the width and the height, so 3x7.

3x7=21

Answer: 21m^2

Step-by-step explanation:

The equation finds the area of a rectangle is

Area= Width times Height

So take 7 times 3 = 21 m^2

Each minute, a faucet allows 4/7 gallons of water to enter a large tub, and the drain allows 5/7 gallons to leave the tub.
What is the change in the amount of liquid in the tub after 1/4 minute?
Enter your answer as a fraction in lowest terms in the box.
gal.

Answers

Answer: -1/28 gallon

Step-by-step explanation:

divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)

Answer: -1/28 gallon

Step-by-step explanation:

Just number 4 pleaseee

Answers

Answer:

blip

Step-by-step explanation:

blipgg

I can't decide in any way :')

Answers

Step-by-step explanation:

first thing that seems to be a given (and not mentioned in the description) : QM is a diameter (straight line) through the circle. otherwise this cannot be solved without further information.

remember, a half-circle has 180°.

so, arc angle MAP = 180 - 33 = 147°.

arc angle RMP = RM + MAP = 46 + 147 = 193°.

arc angle RSQ = 180 - 46 = 134°.

arc angle MRQ is the full half-circle = 180°.

arc angle MAP (as above) = 147°.

5(2x-3) < 35, the solution set is {x|x <(blank) }

Answers

Answer:

x<5

Step-by-step explanation:

5(2x-3) < 35

_____ ___

5 5

2x-3<7

2x<10

_ _

2x 2x

x < 5

Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V=P(1-r)^t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after 4 1/2 years

Answers

According to the equation model V=P(1-r)^t, the approximate value of Doug's car after 4¹/₂ years is $9,200.

What is the equation?

The equation is a mathematical statement or model that shows that two mathematical expressions are equal.

In this situation, the mathematical expressions equal to each other are V, the car's depreciated value, and P(1-r)^t, which combines variables.

Cost of the new car = $25,000

Depreciation rate per annum = 20%

Value of the car = V

The price paid initially = P = $25,000

The annual rate of depreciation = r

Depreciation period = 4¹/₂ years

Equation model: V=P(1-r)^t

Depreciated value after 4 1/2 years, V = $25,000 (1 - 0.2)^4¹/₂

= $9,158.93

= $9,200

Thus, using the equation model, after 4¹/₂ years, the value of Doug's car has depreciated to $9,200.

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e altitude of a triangle is increasing at a rate of 1 cm!min while the area of the triangle is increasing at a rate of 2 cm !min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area i

Answers

The base of the triangle is decreasing at the rate of 1.6 cm/min.

Given

dh/dt = 1 cm/min

dA/dt = 2 cm2/min

When A = 100 cm2, h = 10 cm

We know that

A = 1/2 × b × h

b = 20 cm

Let us differentiate both sides

dA/dt = 1/2 [b dh/dt + h db/dt]

Substituting the values

2 = 1/2 [20 × 1 + 10 × db/dt]

By further simplification

4 = 20 + 10 db/dt

db/dt = -1.6 cm/min

Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.

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Lillian bought snacks for her team's practice. She bought a bag of apples for $2.36 and a 4-pack of juice bottles. The total cost before tax was $6.48. How much was each bottle of juice?

Answers

The price of each bottle of juice is $1.03

What is an equation?

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let 'x' be the price of each bottle of juice. Then,

According to the question,

2.36 + 4x = 6.48

or, 4x = 6.48 - 2.36

or, 4x = 4.12

or, x = 4.12/4

or, x = 1.03

Hence, the price of each bottle of juice is $1.03

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if abc is 1 degree and 25' what is acd? give your answer in degrees and minutes

Answers

If abc is 1 degree and 25', the angle ACD is 178° 35'.

What is angle?

An angle is a figure in Euclidean geometry formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are termed dihedral angles. An angle is generated when two straight lines or rays meet at a shared terminus. The common point of contact is called the vertex of an angle.

Here,

∠ACB and ∠ACD are supplementary, so they add up to 180°.

First, convert to degrees (there are 60 minutes in a degree).

∠ACB = 1°25' = 1° + (25/60)° = 1.4167°

Now find the supplementary:

∠ACD = 180° − 1.4167°

∠ACD = 178.5833°

∠ACD = 178° 35'

The value of angle ACD is 178° 35' if abc is 1 degree and 25' .

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Select the values that make the inequalityt > -1 true.
(Numbers written in order from least to greatest going across.)

Answers

The values that make v ≥ 1 inequality true are 2, 3, 4, 5....

What is inequality in mathematics?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The inequality is given as:

v ≥ -1

The values of c for which the given inequality → v ≥ -1 is true will belong to the set (say A) -

A = [-1, - ∞)

Therefore, we have to select all numbers which fall in this set. The numbers are

-1, 0, 1, 2, 3,....

Rewrite properly as:

v ≥ 1

The above means that the true values of v are values greater than 1.

Hence, the values that make v  ≥ 1 inequality true are -1, 0, 1 , 2, 3, 4, 5....

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Determine if the table shows a proportional relationship.

IT'S DUE TOMORROW
x 18.6 54.3 58.8
y 6.2 18.1 19.6
Yes, it is proportional because all y over x ratios are equivalent to one third.
Yes, it is proportional because all y over x ratios are equivalent to one fourth.
No, it is not proportional because 18.6 over 6.2 does not equal 18.1 over 54.3.
No, it is not proportional because 18.1 over 54.3 does not equal 58.8 over 19.6.

Answers

It is proportional because all y over x ratios are equivalent to one-third. I.e., the proportionality constant of the given table is k = 1/3.

How to determine the proportionality relationship?

The proportionality relationship between two variables is determined by its proportionality constant. The proportionality constant is the ratio of y over x.

I.e., k = y1/x1 = y2/x2 = y3/x3 = ... = yn/xn

Calculation:

The given data table is as follows:

x - 18.6, 54.3, 58.8

y - 6.2, 18.1, 19.6

So, the proportionality constant is calculated as

y1/x1 = 6.2/18.6 = 1/3

y2/x2 = 18.1/54.3 = 1/3

y3/x3 = 19.6/58.8 = 1/3

Since all three ratios are the same, then the data in the table are proportional to each other.

Therefore, option A is correct.

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Help me on this problem!

Answers

Answer:

B. Since [tex]\triangle ABC \cong \triangle DEF[/tex] by SSS and [tex]\triangle DEF \cong \triangle GHJ[/tex] by SAS, [tex]\triangle ABC \cong \triangle GHJ[/tex] by the Transitive Property of Congruence.

The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS

How to determine the congruent statement and the reason?

From the question, we have the following parameters that can be used in our computation:

Triangles = ABC, DEF and GHJ

There are several theorems that make any two triangles to be congruent

One of these theorems is the SSS congruent theorem

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark

AC and GJ

CB and JH

This implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following angles must also be congruent

AB must be congruent to GH

Hence, the congruent statement on the congruency of the triangles is (d)

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Which of the following values is not an irrational number?

1.73 repeating where the 3 is repeating, pi, the cube root of 90, and the square root of 60

1.73 repeating where the 3 is repeating
π
the cube root of 90
the square root of 60

Answers

All of the given numbers are irrational numbers.  

What is an Irrational number:

A real number that can't be stated as a ratio of integers is said to be an irrational number. In simple words, an Irrational number is a number that cannot be represented as p/q where q ≠ 0.  

An irrational number's decimal expansion is neither ending nor recurrent i.e the decimal expansion of an irrational number will be a Non-terminating decimal number.  

Here are some examples of Irrational Numbers

Here we have

[tex]1.7 \overline {3}[/tex] ,  π, ∛90, and √60    

If we observe the given numbers

[tex]1.7 \overline {3}[/tex] = 1.73333333..... is a Non -terminating decimal number  

π is an example of an irrational number

∛90  cannot be represented as a p/q form

√60 = √4 × 15 = 2√15  where √15 is an irrational number

From above information

The given numbers  π, √90, and √60 all are irrational numbers

                             

Therefore,

All of the given numbers are irrational numbers

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Equation for

You have c pieces of candy to share equally among 5 people. If
each person gets 32 pieces of candy, how much candy did you start
with?

Answers

Answer:

53 candy

Step-by-step explanation:

A trapezoid has an area of 35 mm2. What is the height of the trapezoid?

Answers

The height of the trapezoid is 5mm.

What is a trapezoid?

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is referred to as a trapezium in British and other varieties of English.

In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases. If the remaining two sides are parallel, the trapezoid is a parallelogram and has two pairs of bases; if not, they are referred to as the legs (or lateral sides). A scalene trapezoid is a trapezoid without equal-sized sides.

Given: Area of trapezoid = [tex]35mm^{2}[/tex]

We know, area of trapezoid = [tex]\frac{(a+b)}{2} .h[/tex]

⇒ [tex]\frac{(8+6)}{2} .h=35[/tex]

⇒ [tex]7h=35[/tex]

⇒ [tex]h=5mm[/tex]

Hence, the height of the trapezoid is 5mm.

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what is the purpose of the permutation test? group of answer choices for hypothesis testing of mean, median, and quartiles, it is used to synthesize the population distribution of the statistic of interest for hypothesis testing of mean, median, and quartiles, it is used to synthesize the sampling distribution under the null

Answers

Permutation test is used to synthesize the population distribution of the statistic of interest for hypothesis testing of mean, median, and quartiles

An estimation of the population distribution—the distribution from which our observations originated—is the goal of a permutation test. We can then calculate how uncommon our observed values are in comparison to the population.

I find the permutation test to be more natural, and it only relies on the assumption of random assignment of treatment groups.

In a permutation test, you compare the observed test statistic to the distribution of values

you get when the treatment group assignments are shuffled/randomized/permuted.

The null hypothesis that two distinct groups originate from the same distribution is tested using permutation tests, also known as exact tests, randomization tests, or re-randomization tests. A permutation test can be used for hypothesis testing or significance testing (including A/B testing) without requiring any presumptions to be made about the distribution of the samples, such as that the samples must be normally distributed.

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An investment of $500 is made at 2.8% nominal yearly interest compounded quarterly. Write an equation that models the amount A the investment is worth t years after the principal has been invested

Answers

General Formulas and ConceptsPre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I

Functions

Function Notation

Compounded Interest Rate Formula:
[tex]\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^t[/tex]

A is final amountP is principle amountr is raten is compounded ratet is time

ApplicationStep 1: Define

Let's compile what we know (what we are given).

An investment of $500 means that our principle amount P equals 500.

2.8% nominal yearly interest means that our rate r equals 0.028.

Compounded quarterly means that our compounded rate n equals 4.

So, we have:

[tex]\displaystyle\begin{aligned}P & = 500 \\r & = 0.028 \\n & = 4 \\\end{aligned}[/tex]

Step 2: Work

In order to find an equation that models the final amount A in terms of t years, we can simply substitute in our known variables:

[Compounded Interest Rate Formula] Substitute in variables:
[tex]\displaystyle A = 500 \bigg( 1 + \frac{0.028}{4} \bigg) ^t[/tex][Equation] Simplify:
[tex]\displaystyle\begin{aligned}A & = 500 \bigg( 1 + \frac{0.028}{4} \bigg) ^t \\A & = 500 (1 + 0.007)^t \\& \boxed{ A = 500(1.007)^t }\end{aligned}[/tex]

Answer

∴ our equation that models the amount A the investment is worth t years after the principle has been invested is:

[tex]\displaystyle \boxed{ A = 500(1.007)^t }[/tex]

___

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___

Topic: Algebra I

Unit: Interest Rate Formulas

How many solutions can be found for the linear equation 4(2x+3)=2(4x+6)

Answers

Answer:

All real numbers  are solutions

Step-by-step explanation:

Open the bracket

4(2x+3)=2(4x+6)

8x +12=8x +12

8X-8X=12- 12

=0

The equation is an identity hence, all real numbers are solutions(1,2,3,4 etc)

Martha loves to wear socks with crazy patterns. She finds a great deal for these kinds of socks at her favorite store, Rock Those Socks. There is a proportional relationship between the number of pairs of socks that Martha buys, x, and the total cost (in dollars), y.
Martha can buy 2 pairs of socks for $6. Write the equation for the relationship between x and y.

Answers

The equation which represent the proportional relationship between the number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx

How to write equation?

Number of pairs of socks that Martha buys = xTotal cost (in dollars) = y

y = bx

Where,

b = constant

If y = $6 and x = 2 pairs

y = bx

6 = b × 2

6 = 2b

divide both sides by 2

b = 6/2

b = 3

In conclusion, the proportional relationship between number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx

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How do you convert 15 nm into km?

Answers

15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.

A process involving numerous stages, multiplication or division, especially a conversion factor, can be referred to as Unit Conversion. Additionally, rounding and determining the number of significant digits may be necessary steps in the procedure.

For measuring various properties, including length, weight, capacity, and temperature, many units of conversion are employed. We can change the units of measurement in mathematics to better understand.

Unit conversions are used to represent an amount in a different unit.

We have to convert 15 nm into km.

1 nm = [tex]10^{-12}[/tex] km

15 nm = 15 × [tex]10^{-12}[/tex] km

          = 1·5 × [tex]10^{-11}[/tex] km

Thus, 15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.

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what is the principal of a 10-month, 8% note that will earn $800 of interest?

Answers

Principal will be $1000

Given values

Simple interest, SI= $800

Interest rate, R=8%

Time, T=10 months

Principle, P= Y

As we know;

[tex]Simple Interest, SI=P×R×T[/tex]

By substituting the values, we get

$800= Y ×8% ×10

$800=0.8Y

$800÷0.8= Y

$1000=Y

Thus the above response is correct.  

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please help me slove these problems!! offering 30 points for good answers and explanation on it

Answers

here's two, I used mathday but day with a w

Step-by-step explanation:

good website for it and it gives good explanation! Gl

If m∠ XYZ=68 and m∠ WXZ=71, find m∠ WZX

Answers

The measure of angle WZX is given as follows:

m < WZX = 41º.

How to obtain the angle measure?

The measure of angle XYZ is of 68º, hence, due to the bisection, we have that:

m < WYZ = 34º.m < ZYX = 34º.

The measure of angle WXZ is of 71º, hence the measure of angle WXY is found as follows:

m < 2 x 71 = 142º.

(as the bisection of angle X means that it is divided into two parts of equal measure).

As the figure is a parallelogram, the opposite angles have the same measure, thus the measure of angle WZY is given as follows:

m < WZY = 142º.

Then, applying the bisection, the measure of angle WZX is given as follows:

m < WZX = 0.5 x 142º = 41º.

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Microsoft Excel Assessment Which chart type can display two different data series as different series types within the same chart? 60% 50% 4096 30% 20% 11 10% 0% France Austria Spain Germany Portugal Forested area (%) Agricultural land (%) bubble chart

Answers

An Excel Combo Chart can display two different data series as different series type. A single Excel chart with two Y-axis that allows users to compare data is known as a combo chart.

How do you arrange data in a combo chart?

Step 1: Arrange the data in the worksheet's columns and rows.

Step 2: Choose the information.

Step 3: Click the Combo chart icon on the Ribbon under the Charts group on the INSERT tab.

Step 4: Click each icon with your mouse.

step 5 Double-click the chart type that suits your data.

What is a combo chart?

A combo chart combines two column charts, two line graphs, or a column chart and a line graph into one visual representation.

An Excel Combo Chart can display two different data series as different series type. A single Excel chart with two Y-axis that allows users to compare data is known as a combo chart.

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what is the quadratic equation in standard form with rational coefficents that has a root of 5+4i?

Answers

Answer:

x^2 -10x + 41 = 0

Step-by-step explanation:

They gave you a root. A root is a solution, is a zero, is an x-intercept(if real).

This is a working backwards problem. They gave you an answer and want the equation back again.

x = 5 + 4i

working backwards:

x - (5 + 4i) = 0

x - 5 - 4i = 0

This left side is a factor of your equation.

If 5+4i is a root then 5-4i is also a root. So do the same thing:

x = 5 - 4i

x - (5 - 4i) = 0

x - 5 + 4i = 0

x - 5 + 4i and

x - 5 - 4i are the factors. Multiply them together to find the quadratic equation. Use distributive property or difference of squares or an area model to model. See image.

Answer:

x² - 10x + 41 = 0

Step-by-step explanation:

complex roots occur as a conjugate pair.

given x = 5 + 4i , then x = 5 - 4i is also a root

the corresponding factors are

(x - (5 + 4i) ) , (x - (5 - 4i) ) , that is

(x - 5 - 4i) and (x -5 + 4i)

the quadratic equation is then the product of the factors, that is

(x - 5 - 4i)(x - 5 + 4i) = 0

multiply each term in the second factor by each term in the first factor.

x² - 5x + 4ix - 5x + 25 - 20i - 4ix + 20i - 16i² = 0 ← collect like terms

x² - 10x + 25 - 16i² = 0 [ note i² = - 1 ]

x² - 10x + 25 + 16 = 0

x² - 10x + 41 = 0 ← in standard form

q. jenny can walk 4 miles in (m 3) minutes. at that pace, how many miles can she walk in 15 minutes?

Answers

If she moves at a speed of 1.33 miles per minute while walking 4 miles in 3 minutes, she can cover 20 miles in 15 minutes.

What is division?

A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

In 3 minutes, she walk 4 miles,

speed=distance/time

=4/3 miles/minute

distance=speed*time

=4/3*15

=20 miles

She can walk 20 miles in 15 minutes if she walks 4 miles in 3 minutes with a speed of 1.33 miles/minute.

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