Correct the errors and fill in the blanks by completing the square.

Answer:

87+(4+8)=(7+4)+x

87+12=11+x

87+12-11=x

88=x

After the conversion, we get T² = 1/3 A

It is given that

T = [tex]A^{\frac{3}{2} }[/tex]

We have to convert the equation without rational exponents

T³ = A²

1/2 T = A³

T² = A³

T² = 1/3A

Therefore we get T² = 1/3 A without using the exponents.

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The confidence limits for the proportion of consumers motivated by advertising in the population, given a confidence level equal to 0.95. is; CI = (0.47, 0.77)

We are given;

Sample Size; n = 60

sample proportion; p' = 65% = 0.65

Confidence level = 0.95

Now, formula for confidence interval of proportion is;

CI = p' ± z√(p(1 - p)/n)

At CL of 95%, z = 1.96Thus;

CI = 0.65 ± 1.96√(0.65(1 - 0.65)/60)

CI = 0.65 ± 1.96√0.00379167

CI = 0.65 ± 0.12

CI = (0.65 - 0.12), (0.65 + 0.12)

CI = (0.47, 0.77)

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The range is the set of y outputs. In this case, the range is the profit.

A negative profit means the company lost money. This is when the cost is larger than the revenue. For instance, if the revenue was $100 but the cost is $150, then the profit = revenue - cost = 100-150 = -50 to signal they lost $50.

Positive profit means the company made money.

The x intercept represents the break-even point. This is where the company neither loses money, nor gains money. The profit is $0 here.

Answer/Step-by-step explanation:

In order to open a restaurant you have to rent a venue, furnish and decorate it, hire a staff and buy food and drinks. Before serving (selling) any meals you have to spend a lot of money. This is why the negative y-values.

At the point where the line crosses the x-axis (horizontal axis) you now begin to have a positive output to your operation. If you sell enough meals, you will turn a profit. That is, you make enough money to pay all those start-up expenses and still have money left over to keep!

Answer:

a. leisure

b. £189

c.£ 1610

Step-by-step explanation:

The curve intersects the vertical lines when

[tex]x=2 \implies y = \dfrac1{2+2^3} = \dfrac1{10}[/tex]

and

[tex]x=3 \implies y = \dfrac1{2+3^3} = \dfrac1{29}[/tex]

Split up the region into washers of thickness [tex]\Delta y[/tex].

For [tex]-1\le y\le\frac1{29}[/tex], the inner and outer radii of each washer will be constant, with outer radius [tex]x=3[/tex] and inner radius [tex]x=2[/tex]. Each washer in this interval will contribute a total volume of

[tex]\pi (3^2 - 2^2) \Delta y = 5\pi\,\Delta y[/tex]

For [tex]\frac1{29} \le y \le \frac1{10}[/tex], the washers will have a varying outer radius of length

[tex]y=\dfrac1{2+x^3} \implies x = \sqrt[3]{\dfrac1y - 2}[/tex]

and inner radius [tex]x=2[/tex]. Their volumes are

[tex]\pi \left(\left(\sqrt[3]{\dfrac1y - 2}\right)^2 - 2^2\right) \, \Delta y = \pi \left(\left(\dfrac1y - 2\right)^{2/3} - 4\right) \, \Delta y[/tex]

Let [tex]\Delta y\to0[/tex]. Then as the number of washers goes to infinity, the total volume of the solid converges to the definite integral

[tex]\displaystyle 5\pi \int_{-1}^{1/29} dy + \pi \int_{1/29}^{1/10} \left(\left(\dfrac1y - 2\right)^{2/3} - 4\right) \, dy[/tex]

The first integral is trivial, but the second one requires hypergeometric functions to evaluate exactly. With a calculator, we find the approximate volume to be 0.117884.

The computation shows that the tons of sugar when they'll have same price is 18 tons.

The first company charges $5500 to rent trucks plus an additional fee of $200.25. Thai will be:

= 5500 + (200.25 × s)

= 5500 + 200.25s

where s = tons of sugar

The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. This will be:

5041 + 225.75s

Then we will equate both of them. This will be:

5500 + 200.25s = 5041 + 225.75s

5500 - 5041 = 225.75d - 200.25s

459 = 25.5s

s = 459/25.5

s = 18

At 18 tons, they'll have same price.

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The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. For want mount if sugar do they charge the same price.

Mark has 18 and Don has 77 number of marble to sell.

Let’s say Mark has x number of marble and Don’s marble number is y.

According to this problem we have,

Y = 4x +5

And x + y = 95

Or, x + 4x + 5 = 95

Or, 5x = 90

Or, x = 18 and y = 77  

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The area of circle of diameter 10 inches is 25π in.² and,

area of circle of radius 8 cm is 64π cm².

How is Area of circle is calculated ?

Area of circle is calculated using formula :

A = πr²

1) It is given that diameter of circle is 10 inches then the radius will be half of it that is :

d = 10 inches

r = 5 inches

Now calculating the area of circle using the above formula :

A = πr²

A = π(5)²

A = 25π in.²

2) It is given that radius of circle is 8 cm then calculating area using above formula :

A = πr²

A = π(8)²

A = 64π cm²

Therefore, the area of circle of diameter 10 inches is 25π in.² and,

area of circle of radius 8 cm is 64π cm².

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The required number of people that are in the US labor force is 0.0086t² + 0.087t + 25.375.

To determine the total number of people available in the US labor force.

In mathematics, it deals with numbers of operations according to the statements.

Here,
As per the data available, the number of Men in the US labor force is M = 0.0016t² + 0.315t + 19.467 and the number of women are W = 0.007t² -0.228t + 5.908.
Total people available in the US labor force,
= Number of women + number of men
= 0.0016t² + 0.315t + 19.467 + 0.007t² -0.228t + 5.908
=  0.0086t² + 0.087t + 25.375.

Thus, the required number of people that are in the US labor force is 0.0086t² + 0.087t + 25.375.

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The degree of the resulting polynomial, 5x^4^y² - x^3y - 12y + 8x, after subtraction is: degree 4.

Given, (10x^4y^2 - 9x^3y - 9y) - (5x^4^y2 + 10x^3y + 12y - 8x), to subtract, open the parentheses using the distributive property.

10x^4y^2 - 9x^3y - 9y - 5x^4^y² - 10x^3y - 12y + 8x

Combine like terms together

10x^4y^2 - 5x^4^y² - 9x^3y - 10x^3y - 9y - 12y + 8x

5x^4^y² - x^3y - 12y + 8x

The highest degree is 4. This determines the degree of a polynomial.

Therefore, the degree of the resulting polynomial, 5x^4^y² - x^3y - 12y + 8x, after subtraction is: degree 4.

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From the union operation between sets, we have that the number of elements for each case will be as follows:

a) 11069.

b) 9975.

c) 11031.

The union operation between sets is the set that contains all elements that belong to at least one of the sets.

In item a, if the sets are disjoint, all the elements belong to only one set, and the number of elements in A1∪A2∪A3 is given by:

102 + 992 + 9975 = 11069.

For item b, if they are all contained into A3, the number of elements is the cardinality of A3, given by 9975.

For item c, we have that:

Hence:

n(A1∪A2∪A3) = 4 + 3 x 10 + 78 + 968 + 9951 = 11031.

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Answer:

140

Step-by-step explanation:

the square root of 16 is 4 so do that times 35

Answer: correct me if I’m wrong

Step-by-step explanation:

Partial fractions:

[tex]\displaystyle \frac1{(n^2-1)^2} = \dfrac14 \left(\frac1{n+1} - \frac1{n-1} + \frac1{(n+1)^2} + \frac1{(n-1)^2}\right)[/tex]

Now evaluate the sums. The first two terms form a telescoping sum,

[tex]\displaystyle \sum_{n=2}^\infty \left(\frac1{n+1} - \frac1{n-1}\right) = \sum_{n=1}^\infty \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \sum_{n=1}^N \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \left(\frac1{N+2} + \frac1{N+1} - 1 - \frac12\right) \\\\ ~~~~~~~~= -\frac32[/tex]

The others are flavors of [tex]\zeta(2)[/tex].

[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n+1)^2} = \sum_{n=3}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \sum_{n=1}^\infty \frac1{n^2} - 1 - \frac1{2^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6 - \frac54[/tex]

[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n-1)^2} = \sum_{n=1}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6[/tex]

It follows that

[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n^2-1)^2} = \frac14 \left(-\frac32 + \left(\frac{\pi^2}6 - \frac54\right) + \frac{\pi^2}6\right) = \boxed{\frac{\pi^2}{12} - \frac{11}{16}}[/tex]

It should be noted that the product of the fractions 5/2 and 2/3 will be 5/3.

It should be noted that this is a number that is expressed as a quotient, in which a numerator is divided by a denominator.

Therefore, it should be noted that the product of the fractions 5/2 and 2/3 will be illustrated as thus:

= 5/2 × 2/3

= 5/3.

Therefore, the product of the fractions 5/2 and 2/3 will be 5/3.

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Answer:

70 squares

Step-by-step explanation:

this is my answer to your question

Answer:

Hello,

100

Step-by-step explanation:

a square 4*4 : wide=4 , lenght=4

number of rectangles= wide*(wide+1)*lenght*(lenght+1) /4 = 4*5*4*5/4=100

Proof:

1 per 1 : 16 (rectangles )

1 per 2: 3*4=12

1 per 3: 2*4=8

1 per 4: 1*4=4 so 4*(4+3+2+1)=4*10=40

2 per 1: 4*3

2 per 2: 3*3

2 per 3: 2*3

2 per 4: 1*3 so 3*(4+3+2+1)=30

3 per 1: 4*2

3 per 2: 3*2

3 per 3: 2*2

3 per 4: 1*2 so 2*(4+3+2+1)=20

4 per 1: 4

4 per 2: 3

4 per 3: 2

4 per 4: 1 so 1*(4+3+2+1)=10

Total=40+30+20+10=(4+3+2+1)*(4+3+2+1)=100

The number of watts it will consume is 436.32

A light bulb consumes 2400 watts/hour

The number of watts it will consume in 5 days 12 hours can be calculated as follows

The first step is to change 5 days 12 hours to hours

120 hours + 12 hours

= 132 hours

The bulb consumes 2400 watts per hour

= 2400/132

= 18.18

The number of watts consumed in 5 days 12 hours is

= 24 × 18.18

= 436.32

Hence the light bulb will consume 436.32 watt-hour in 5 days 12 hours

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The probability that it will be a blue highlighters is 3 / 10.

In statistics, what does a probability mean?

the highlighters which are dried up and will not write or eight

number of red highlighters = 10

number of blue highlighters 15

number of green highlighters = 5

number of yellow highlighters = 10

therefore the total number highlighters in the box

= 10 + 10 + 15 + 5 + 10 = 50

probability of Blue = number of blue highlighters

Total number of highlighters

= 15 /50 = 3/10 = 0.3

the probability that it will be a blue highlighters is 3 / 10

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The actual height of Caleb based on the ratio in the photograph and actual is 48 inches.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

Let's say Allison and Caleb's height in the photograph is A' and C' while in actuality it is A and C.

Since the ratio of height in the photograph will same as the ratio in actual life.

Thereby,

C/A = C'/A'

C/60 = 3.2/4

C = 192/4

C = 48 inches.

Hence "The actual height of Caleb based on the ratio in the photograph and actual is 48 inches".

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Given question is incomplete complete question follows ;

In a photograph, Alison stands next to her brother Caleb. Alison is 4 cm tall in the photograph. Her actual height is 60 in. Caleb is 3.2 cm tall in the photograph.

What is his actual height?

(Show your work)

Answer:

its the first alternative

Answer:

52kg

Step-by-step explanation:

it's just sum of the kgs bought

Answer:

True sometimes when it is stressful.

Step-by-step explanation:

Answer:

Step-by-step explanation:

your very right

Answer:

7(x + 4) = 70

x = 6

Step-by-step explanation:

7(x + 4) = 70  Distribute the 7.  Multiply everything inside the parentheses by 7

7x + 28 =70  Subtract 28 from both sides of the equation

7x = 42  Divide both sides by 7

x = 6

Answer:

8 boys and 16 girls

Step-by-step explanation:

2 boys plus 4 girls is six and six goes into 24 four times so 2 times four is eight and 4 times four is 16

Answer:

Step-by-step explanation: Since there are 24 students in total and the ratio is 2:4 then divide 24 by (2+4) which is 4. So the amount of boys is 2x4 which is 8. The amount of girls is 4x4 which is 16. 8+16=24

Answer:

[tex]\frac{1}{36}[/tex]

Step-by-step explanation:

The first roll.  There are six possible answers (1,2,3,4,5,6), but of those 6 answers, there is only one that I want; 3. so, The probability of rolling a 3 is [tex]\frac{1}{6}[/tex].  There is the same probability for rolling a 4.

If I multiply these together I will find the probability that I am looking for.

[tex]\frac{1}{6}[/tex] x [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{36}[/tex]

Answer: -0.25x+y=7/8

Step-by-step explanation:

y = 0.25x + 7/8

-0.25x+y=7/8 ==>Subtract 0.25x from both sides to get the Ax+By=C format