In order to estimate the average electric usage per month, a sample of 196 houses was selected, and their electric usage determined. a) Assume a population standard deviation of 350 kilowatt hours. Determine the standard error of the mean. b) With a 0.95 probability, determine the margin of error. c) If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean

Answer: C

Step-by-step explanation:

We can automatically eliminate D because since both matrices are 2x2, the product exists.

[tex]\left[\begin{array}{ccc}1&5\\-3&4\end{array}\right] \left[\begin{array}{ccc}2&6\\6&-1\end{array}\right] =\left[\begin{array}{ccc}1*2+5*6&1*6+5*(-1)\\(-3)*2+4*6&(-3)*6+4*(-1)\end{array}\right]=\left[\begin{array}{ccc}32&1\\18&-22\end{array}\right][/tex]

Answer: n=2

Step-by-step explanation: 4n-2n=4

4(2)-2(2)=

8-4=4

Answer:

n=2

Step-by-step explanation:

Step by Step Solution:

More Icon

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*n-2*n-(4)=0  

Step by step solution :

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  2n - 4  =   2 • (n - 2)  

Equation at the end of step

1

:

STEP

2

:

Equations which are never true

2.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    n-2 = 0  

Add  2  to both sides of the equation :  

                     n = 2

Answer:

120,960 ways

Step-by-step explanation:

Assuming that each piece is unique, then the order of each piece matters.

There are 9 pieces in total, there are 3 options for the first piece (3 piano pieces), and the remaining 8 pieces can be permuted. The number of possible arrangements is:

[tex]n=3*\frac{8!}{(8-8)!}\\ n=3*8*7*6*5*4*3*2*1\\n=120,960\ ways[/tex]

The program can be arranged in 120,960 ways.

Answer:

Step-by-step explanation:

The spread of the height of each person in the group depends on the standard deviation. A low standard deviation means that the heights are closer to the mean than that of a high standard deviation. If an individual is picked, the probability of picking one who is more than 68 inches tall is small as this depends on the number of individuals in this category. The probability of picking a sample of four people who average more than 68 inches tall would be higher since average would be taken. Therefore, it is more likely to pick a sample of four people who average more than 68 inches tall

Answer:

It's the third Answer: It is the portion of internal energy that can be transferred from one substance to another.

Hope this helps

Answer:

c

Step-by-step explanation:

Answer:

C. HL

Step-by-step explanation:

The Hypotenuse-Leg Theorem is the only viable way to determine congruency between 2 right triangles.

Answer/Step-by-step explanation:

Let's highlight the dimensions of the bedroom and living room using the information given in the question:

==>Squared Bedroom dimensions:

Side length = w = x ft

Area = x*x = x²

==>Rectangular living room dimensions:

width = side length of the squared bedroom = x

length = (x + 9) ft

Area = L*W = x*(x+9) = x² + 9x

Now let's match each given expression with what they represent:

==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"

As we have shown in the dimensions of the squared bedroom above.

==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room

==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"

i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.

==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".

i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x

Answer:

tan =-1

Step-by-step explanation:

tan(θ)=sen(θ)/cos(θ)

so

[tex]tan(angle)=\frac{\frac{-\sqrt{2} }{2} }{\frac{\sqrt{2} }{2} } }\\\\tan(angle)=-1[/tex]

Answer:

Step-by-step explanation:

[tex]cos \: \: theta \: = \frac{ \sqrt{2} }{2} = \frac{1}{ \sqrt{2} } = cos \: \frac{\pi}{4 } [/tex]

[tex]cos \: (2\pi \: - \frac{\pi}{4} ) \: \: ( \frac{3\pi}{2} < theta < 2\pi)[/tex]

[tex] = cos \: \frac{7\pi}{4} [/tex]

Theta = 7π / 4

[tex]sin \: theta = sin \: \frac{7\pi}{4} [/tex]

[tex] = sin \: (2\pi \: - \frac{\pi}{4} )[/tex]

[tex] - sin \: \frac{\pi}{4} [/tex]

[tex] = \frac{ - 1}{ \sqrt{2} } [/tex]

[tex] = - \frac{ \sqrt{2} }{2} [/tex]

Finding tan theta:

[tex]tan \: theta = tan \: \frac{7\pi}{4} [/tex]

[tex] =tan \: (2\pi - \frac{\pi}{4} )[/tex]

[tex] = - tan \: \frac{\pi}{4} [/tex]

[tex] = - 1[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

it should be -4=x.

Answer: -4

Step-by-step explanation:

Answer:

V= 452.39cm³ (to 2 d.p. )

S.A. = 326.73cm² (to 2 d.p. )

Step-by-step explanation:

Vcylinder = π r² h = π (4)² (9) = 144 π = 452.3893421cm³ = 452.39cm³ (to 2 d.p. )

S.A. cylinder = 2π r h + 2π r² = 2π (4)(9) + 2π (4)² = 104π = 326.725636cm² = 326.73cm² (to 2 d.p. )

Answer:

Step-by-step explanation:

We know that'

GCF × LCM = Product of given number

1. Two numbers have a GCF of 2

= 2 × LCM = Product of given number

LCM = Product of given number / 2

LCM is half of given product.

2. Two numbers have an LCM of 2

= GCF × 2 = Product of given number

GCF = Product of given number / 2

GCF is half of given product.

3. Two numbers have a GCF of 3

= 3 × LCM = Product of given number

LCM = Product of given number / 3

LCM is one-third of given product.

4. Two numbers have an LCM of 10

= GCF × 10 = Product of given number

GCF = Product of given number / 10

GCF is one-tenth of given product.

Answer:

1. 1/x = 8

Answer = 8x-1

2. 8x+1=3

Answer ; x=1/4

3. 7= 14/X

Answer ; x = 2

4.1/2x^2 = 2

Answer ;x=2

Step-by-step explanation:

[tex]\frac{1}{x} =8 \\8x = 1\\\\\\8x+1=3\\Collect -like- terms \\8x =3-1\\8x = 2\\Divide -both -sides- by ;8\\\frac{8x}{8} =\frac{2}{8} \\x = 1/4\\\\\\7= \frac{14}{x} \\Cross -multiply\\7x =14\\Divide-both-sides-by-7\\x = 2\\\\\\\frac{1}{2} x^{2} =2\\\frac{x^{2} }{2} =2\\Cross-multiply\\x^{2} =4\\Squre-root -both-sides\\\sqrt{x^2}=\sqrt{4} \\x = 2\\[/tex]

Answer:

1. 1/x=8 ⇒ 8x= 1

2. 8x+1= 3⇒ x=1/4

3. 7= 14/x ⇒ x =2

4. 1/2x^2= 2 ⇒ x=2 this is a repeat of one above

None is matching x=1/2

Answer:

3x - 300

Step-by-step explanation:

Expand the brackets or use distribute law.

Answer:

solution,

[tex]3(x - 100) \\ = 3 \times x - 3 \times 100 \\ = 3x - 300[/tex]

hope this helps..

Answer:

240cm³

Step-by-step explanation:

First, let's assume the entire shape is full rectangular prism without that has the middle being cut out.

What this means is that, to get the volume of the solid made out of clay, we would calculate the solid as a full rectangular prism, then find the volume of the assumed middle cut-out portion. Then find the difference between both.

Let's solve:

Find the volume of the rectangular prism assuming the solid is full:

Volume of prism = width (w) × height (h) × length (l)

w = 4cm

h = 7cm

l = 3+6+3 = 12cm

Volume of full solid = 4*7*12 = 336cm³

Next, find the volume of the assumed cut-out portion using same formula for volume of rectangular prism:

w = 4cm

h = 7-3 = 4cm

l = 6cm

Volume of assumed cut-out portion = 4*4*6 = 96cm³

Volume of solid made from clay = 336cm³ - 96cm³ = 240cm³

Answer:

x = 7

y = 8

Step-by-step explanation:

4y-4 = 28

4y = 32

y = 8

10x+65 = 135

10x = 70

x = 7

Answer:

Step-by-step explanation:

(4y-4)=28

4y=32

y=8

(10x+65)=135

10x=70

x=7

Step-by-step explanation:

x - y = 34

x + y = 212

2x = 246

x = 123

123 + y = 212

y = 89

(123, 89)

Answer:

12

Step-by-step explanation:

The way to find the slope side of a traingle is

A^2+B^2=C^2  Next you substitute

5^2+B^2=13^2  Next simplify

25+B^2=169  Next use the subtraction property of equality

B^2=144  Next find the square root

B=12

Hope this helps :)

Answer:

height =12

Step-by-step explanation:

use Pythagorean theorem for right angle triangle:

a²+b²=c²

a²=c²-b²

a²=13²-5²

a²=144

a=√144-=12

Answer: $5,000

Step-by-step explanation: First begin with the interest formula.

Interest = Principal × Rate × Time

In this problem, we're solving for the interest.

The principal is the amount invested or $2,500.

The rate is 8% which we can write as .08.

The time is 25 years.

So we have I = (2,500)(.08)(25).

Now we multiply.

(2,500)(.08) is equal to 200.

Now, multiply 200(25) to get 5,000.

This means that the interest earned is $5,000.

Answer:

Let the number of children taken to the movies  = x

Let the number of adults taken to the movies  = y

Lets talk about Matinee tickets first:

so 4$ per child/adult

4x + 4y [tex]\leq[/tex] 80    (since the budget is 80$, we can spend 80$ , hence the less- than or equal-to)

4(x+y)[tex]\leq[/tex] 80

x + y [tex]\leq[/tex] 40

So, for the matinee show, the sum of number of children and adults should be less than or equal to 40

Lets talk about the Evening show:

so 6$/child and 8$/adult

6x + 8y [tex]\leq[/tex] 100

2(3x + 4y) [tex]\leq[/tex] 100

3x + 4y [tex]\leq[/tex] 50

So, for the Evening show, the sum of 3 times the number of children and 4 times the number of adults should not exceed 50

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

[tex]x - h = 4\cdot p \cdot (y-k)^{2}[/tex]

Where:

[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

[tex]p[/tex] - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

[tex]p = x_{D} - x_{V}[/tex]

[tex]p = \frac{1}{48}-0[/tex]

[tex]p = \frac{1}{48}[/tex]

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].

Answer:

4a^2+4ab+b^2

Step-by-step explanation:

To find the square we multiply the expression with itself

(2a+b)×(2a+b) = 4a^2+4ab+b^2

Answer:

Answer is given below with explanations.

Step-by-step explanation:

Answer is option 1) 85 : 51

[tex]given \: that \: \\ triangle \: SPT \: is \: similar \: to \: triangle \: QPR \\ corresponding \: sides \: of \: similar \: \\ triangles \: are \: in \: proportion \\ then \: \\ \frac{SP}{ QP} = \frac{PT }{ PR} \\ \frac{3x}{3x + 24} = \frac{51}{85} \\ taking \: reciprocal \: on \: both \: sides \\ \frac{3x + 24}{3x} = \frac{85}{51} [/tex]

Option 1 is correct.

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Answer:

The population under consideration in the data set are all the adults in the United States.

Step-by-step explanation:

Sampling

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

The population of interest are all the residents of New York State.

In this question:

Sample of 765 adults in the United states.

So the population under consideration in the data set are all the adults in the United States.

ith 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:

E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.i think is the answer

Answer: -150

Step-by-step explanation: The result of a multiplication problem is called the product so we know that we will be multiplying here.

When multiplying integers, if the signs

are different, the product is negative.

So a positive times a negative always equals a negative.

Therefore, (+25) · (-6) is -150.

Answer: -150

Step-by-step explanation: took the unit test on edge

Answer:

Step-by-step explanation:

Total amount of yogurts made by Stacy = 1.5 Litres

Volume of each cups to be filled with yogurts = 125mL = 125*10⁻³Litres

To get the number of cups Stacy can fill for her to exhaust 1.5Litres can be gotten using the relationship;

Number of cups = Total volume of yogurts made/Volume of each cup

Number of cups = 1.5/125*10⁻³

Number of cups = 1.5/0.125

Number of cups = 12 cups

Number of cups Stacy can fill is 12 cups

Answer:

Option D

Step-by-step explanation:

We are given the following equations -

[tex]\begin{bmatrix}-5x-12y-43z=-136\\ -4x-14y-52z=-146\\ 21x+72y+267z=756\end{bmatrix}[/tex]

It would be best to solve this equation in matrix form. Write down the coefficients of each terms, and reduce to " row echelon form " -

[tex]\begin{bmatrix}-5&-12&-43&-136\\ -4&-14&-52&-146\\ 21&72&267&756\end{bmatrix}[/tex]  First, I swapped the first and third rows.

[tex]\begin{bmatrix}21&72&267&756\\ -4&-14&-52&-146\\ -5&-12&-43&-136\end{bmatrix}[/tex]  Leading coefficient of row 2 canceled.  

[tex]\begin{bmatrix}21&72&267&756\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\\ -5&-12&-43&-136\end{bmatrix}[/tex]  The start value of row 3 was canceled.

[tex]\begin{bmatrix}21&72&267&756\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\\ 0&\frac{36}{7}&\frac{144}{7}&44\end{bmatrix}[/tex]       Matrix rows 2 and 3 were swapped.

[tex]\begin{bmatrix}21&72&267&756\\ 0&\frac{36}{7}&\frac{144}{7}&44\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\end{bmatrix}[/tex]      Leading coefficient in row 3 was canceled.

[tex]\begin{bmatrix}21&72&267&756\\ 0&\frac{36}{7}&\frac{144}{7}&44\\ 0&0&0&\frac{4}{9}\end{bmatrix}[/tex]

And at this point, I came to the conclusion that this system of equations had no solutions, considering it reduced to this -

[tex]\begin{bmatrix}1&0&-1&0\\ 0&1&4&0\\ 0&0&0&1\end{bmatrix}[/tex]

The positioning of the zeros indicated that there was no solution!

Hope that helps!

Answer:

The value of α is 0.05.

Step-by-step explanation:

A poll of 1000 adults was conducted to determine their favorite pie.

The poll result states that among the 1000 ​respondents, 14 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 3 percentage points.

[tex]\hat p=\text{Sample Proportion of adults who chose chocolate pie} = 0.14\\\hat q=\text{Sample Proportion of adults who did not chose chocolate pie}\\=1-\hat p\\=0.86\\n=\text{Sample size}=1000\\E=\text{Margin of Error}=0.03\\p=\text{Population Proportion of adults who chose chocolate pie}[/tex]

The confidence level is 95%.

Determine the value of significance level, α as follows:

[tex]\text{Confidence Level}=(1-\alpha)\%\\\\95\%=(1-\alpha)\%\\\\0.95=(1-\alpha)\\\\\alpha=1-0.95\\\\\alpha=0.05[/tex]

Thus, the value of α is 0.05.

This is the value 40 million

================================================

Explanation:

You could use a calculator, or you could do it mentally. The second approach will have us note that 4*1 = 4, and then we tack on 7 zeros since we have two zeros in 400 and five zeros in 100,000 giving a total of 2+5 = 7

So that means 400*100,000 = 40,000,000 = 40 million

-------

You could also use scientific notation

400 = 4 x 10^2

100,000 = 1 x 10^5

400*100,000 = (4x10^2)*(1x10^5)

400*100,000 = (4*1) x (10^2*10^5)

400*100,000 = 4 x 10^(2+5)

400*100,000 = 4 x 10^7

400*100,000 = 40,000,000

The exponent of 7 means we move the decimal point 7 spots to the right to go from 4.0 to 40,000,000

Answer:

A) 0.989

B) 0.875

Step-by-step explanation:

Let the X denote height measurements of ten year old children.

Thus, X follows the Normal distribution with mean = 56.2 inches and standard deviation = 3.3 inches.

A) we have to find the probability that a randomly chosen child has a height of less than 63.75 inches.

That is;

P(X < 63.75)

using z score formula, we have;

Z = (X - μ)/σ

Where, μ is mean and σ is standard deviation.

Thus;

Z = (63.75 - 56.2)/3.3

Z = 2.288

From z distribution table, we have the value as approximately 0.989

B) Similarly, using z score formula, we have;

Z = (X - μ)/σ

Where, μ is mean and σ is standard deviation.

Thus;

we have to find the probability that a randomly chosen child has a height of more than 60 inches.

Z = (60 - 56.2)/3.3

Z = 1.1515

From z-tables, the value is approximately 0.875