What are rational numbers

Answer:

34 feet

Step-by-step explanation:

From the question, we are told that:

If the room is 30 feet high at the center and 90 feet wide at the floor,

Entire width of the room = 90 feet = 2a

a = 90/2 = 45

Height of the room = b = 30 feet

Foci (c)² = a² - b²

c = √a² - b²

c = √45² - 30²

c = √1125

c = 33.541019662 feet

Approximately to the nearest whole number = 34 feet

Denise and Donna should each stand 34 ft from the outer wall so that they will be positioned at the foci of the ellipse

Answer:

1000 milliliters in a liter, so 325 mL = 0.325 L

Step-by-step explanation:

Answer:

E: 625

F: 155

G: 625

Step-by-step explanation:

Hi!

E.

A number, reduced by 20% is 500.

Originally, that number was at 100%.

Reduced = subtraction, so that number = 100%-20%, or 80%.

80% of a number = 500.

80% = .8

.8x = 500

Divide both sides by .8

x = 625

F.

A number that is increased by 100% is a number that is doubled (multiplied by 2).

2x=310

x=155

G.

Originally, the money was at 100%. After being reduced by 20%, the money is at 80% (.8).

.8x = 500

Once again, the answer is 625.

H (?)

To change a decimal to a percent, we multiply by a 100.

1.40 * 100 = 140%

As a fraction: 140/100

Answer:

A 95% confidence interval for the mean credit card debt of all college students in Illinois is [$316.06, $375.94] .

Step-by-step explanation:

We are given that in a sample of 50 college students in Illinois, the mean credit card debt was $346. Suppose that we also have reason to believe that the population standard deviation of credit card debts for this group is $108.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

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

where, [tex]\bar X[/tex] = sample mean credit card debt = $346

            [tex]\sigma[/tex] = population standard deviation = $108

            n = sample of college students = 50

            [tex]\mu[/tex] = population mean credit card debt

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.

So, a 95% confidence interval for the population mean, [tex]\mu[/tex] is;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                                 level of significance are -1.96 & 1.96}    P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}} }[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                       = [ [tex]\$346-1.96 \times {\frac{\$108}{\sqrt{50} } }[/tex] , [tex]\$346+1.96 \times {\frac{\$108}{\sqrt{50} } }[/tex] ]

                                       = [$316.06, $375.94]

Therefore, a 95% confidence interval for the mean credit card debt of all college students in Illinois is [$316.06, $375.94] .

Answer:

W=-3 because negative divided by a negative equals a positive

Step-by-step explanation:

Hope this helps!!!

Respuesta: [tex]\frac{7}{8}[/tex] de taza o 0.875 tazas

Explicación:

Repartir un número total de objetos entre personas implica dividir el total entre el número de personas. Es decir que en este caso las 7 tazas deben dividirse entre los 8 bebes. Esta división o partición puede representarse por medio de una fracción o por medio de una división:

Fracción: Esta situación puede ser representada como una fracción si se incluye el número total de bebés o partes a repartir como denominador (número de abajo) y el número de tazas o cantidad total como numerador.

[tex]\frac{7}{8}[/tex]  de taza

División: Divida el total en la cantidad de partes a repartir

7 tazas ÷ 8 bebes = 0.875 tazas por bebé

Answer:

[tex]PS=13\text{ units}[/tex]

Step-by-step explanation:

So, we know that PR is 20, SR is 11, and QS is 5.

We also know that PQ is perpendicular to QR, forming the right angle at ∠Q.

We know all the side lengths except for PQ and PS (the one we want to find). Notice that if we find PQ first, we can then use the Pythagorean Theorem to find PS since we already know QS.

So, let's find PQ.

We can see that we can also use the Pythagorean Theorem on PQ. PQ, QR, and PR (the hypotenuse) will be our sides. So:

[tex](PQ)^2+(QR)^2=(PR)^2[/tex]

We know that PR is 20.

QR is the combined length of QS+SR, so QR is 5+11 or 16.

So, substitute:

[tex](PQ)^2+(16)^2=(20)^2[/tex]

Solve for PQ. Square:

[tex](PQ)^2+256=400[/tex]

Subtract 256 from both sides:

[tex](PQ)^2=144[/tex]

Take the square root of both sides:

[tex]PQ=12[/tex]

So, the side length of PQ is 12.

Now, we can use the Pythagorean Theorem again to find PS. Notice that PQ, QS, and PS also form a right triangle, with PS being the hypotenuse. So:

[tex](PQ)^2+(QS)^2=(PS)^2[/tex]

We already know that QS is 5. We also just determined that PQ is 12. Substitute:

[tex](12)^2+(5)^2=(PS)^2[/tex]

Square:

[tex]144+25=(PS)^2[/tex]

Add:

[tex]169=(PS)^2[/tex]

Take the square root of both sides:

[tex]PS=13[/tex]

Therefore, the length of PS is 13 units.

And we're done!

The answer to this is PS=13.

Answer: A, BAC, CAB

Step-by-step explanation: A already says it’s an angle . BAC & CAB are congruent meaning they are equal . Hope this helped !

Answer:

gehsjskkskskkskdhdhjs

Answer:

-3/5

Step-by-step explanation:

-4/5 * 3/4

Rewriting

-4/4 * 3/5

-1 * 3/5

-3/5

Answer:

-20+1 every minute

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

5x2 is 10 subtract that and add it to 6 which gives you -4 then you do -4/-4 which is 1

Answer:

799 light bulbs

Step-by-step explanation:

9+8=17

47 times 17 = 799

Answer:

Between 7 and 8

Step-by-step explanation:

7^2 = 7 × 7 = 49

8^2 = 8 × 8 = 91

57 is between 49 and 91

Answer:

$28.44

Step-by-step explanation:

Time and a half is the normal rate of pay when working overtime at any job and is calculated as 1.5 times the regularly hourly wage of the employee. Therefore we can calculate how much she earns per hour of overtime by doing the following...

$9.48 * 1.5 = $14.22 per hour

Now we can see that Odette earns $14.22 per hour of overtime, since she worked two hours we simply multiply this amount by 2.

$14.22 * 2 = $28.44

Odette Alvarez earned $28.44 for the two hours of overtime.

Answer:

s = -2

Step-by-step explanation:

2(s+2)=4(s+2)

2s + 4 = 4s + 8

2s - 4s = 8 - 4

-2s + 4

s = -2

Answer:

  a) no

  b) 143 rectangular containers

  c) 157 cylindrical containers

  d) both (preferring rectangular for the bulk of an order)

Step-by-step explanation:

a) If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs?

  No.*

For packaging 41 candles or fewer, the cylindrical container costs less than the rectangular one.

For packaging 6400 candles, there will be 10 candles left over if rectangular containers are used for most of the packaging needs. A dollar can be saved by packaging these remaining candles in a cylindrical container.

__

b) How many rectangular containers will be necessary to package 6,400 candles?

  6400/45 = 142 10/45

If rectangular containers are used for all, then 143 are needed.

__

c) How many cylindrical containers will be necessary to package 6,400 candles?

  6400/41 = 156 4/41

If cylindrical containers are used for all, the 157 are needed.

__

d) Which container should the company use to minimize costs?

  The cost of 143 rectangular containers is 143×$16 = $2288

  The cost of 157 cylindrical containers is 157×$15 = $2355

  The cost of 142 rectangular and 1 cylindrical container is $2287

If only one shape container is used, the company should use rectangular containers to minimize cost. If either shape can be used, cost will be minimized by using one cylindrical container for the remnant of the order.

_____

* This question is directed solely at the cost of materials required for packaging. We have advocated that both rectangular and cylindrical containers be made available. As a practical matter, the cost to the company of maintaining inventory of both sizes of containers may exceed the savings associated with using a cheaper container for smaller orders.

Answer:

7.34

Step-by-step explanation:

this is the extended number 7.34846922835

The standard form of  [tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}[/tex] is 3.204

Explanation :

Given : [tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}[/tex]

Lets convert fractions into decimals

[tex]\frac{1}{10} =0.1\\\frac{1}{1000}=0.001[/tex]

Now 2 times 0.1 becomes 0.2

Also 4 times 0.001 becomes 0.004

So the given expression becomes

[tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}\\3+2 \cdot 0.1+4 \cdot 0.001\\3+0.2+0.004\\3.204[/tex]

Learn more : brainly.com/question/14426774

Answer:

a = 14

Step-by-step explanation:

Step 1: Write out your problem

f (a) = 5a + 14 | f (a) = 0

Step 2: Solve

f (a) = 5 (0) + 14 , Input a.

f (a) = 0 + 14 , 5 x 0 = 0

(a) = 14 , 0 + 14

a = 14

Answer:

C. 1/6

Step-by-step explanation:

negative times a negative is a positive

4 times 3 is 12

9 x 8 is 72

12/72 can be reduced to 1/6 because the top and bottom are both divisible by 12

Answer: 1/6 C

Step-by-step explanation:

Here, we have the expression [tex]\frac{x^2 + 4}{2}[/tex] and we're asked

to evaluate the expression when x = -2.

To evaluate an expression, we simply plug

the value of the variable into the expression and solve.

So here, since x = -2, we have [tex]\frac{(-2)^2 + 4}{2}[/tex].

Notice that I used parentheses around the -2.

This is a good idea when substituting numbers in for variables.

Next, the order of operations tell us that exponent comes first.

So we have (-2)² which is 4.

So we have [tex]\frac{4 + 4}{2}[/tex].

Now when we have a division bar, it's important to understand

that it has the same effect on a problem as a set of parentheses

in that it groups terms together.

So this 4 + 4 can be thought of as being inside a set of parentheses.

So we can also write this as [tex]\frac{(4 + 4)}{2}[/tex].

Now simplify the top to get 8 and we have 8/2 which is 4.

Answer:

Increasing

Step-by-step explanation:

Remember that f(x) is the same as y in slope intercept form y = mx + b.

We don’t have a number for “b” which means the line goes across the origin.

Since 5 replaces m, that is the slope and since it’s positive, it is increasing.

Best of Luck!

Answer:

2,144.7

Step-by-step explanation:

The formula for the volume of a sphere is V=4pi r^3/3. Lets apply this formula for your sphere. The radius is 8, so lets plug in 8 in our formula. 4pi 8^3/3. Now, lets solve. 4 times pi. What is pi? We usually think of pi as 3.14. 4x3.14 is 12.56. Now, lets do 8^3/3. 8 times 3 is 512, and divided by 3 is 170.67. Alright, now we have 12.56 times 170.67. That is 2144.7 rounded to the nearest tenth.

Answer:

I believe the awnser is 539 total.

Step-by-step explanation:

If you take the 4 and times it by 1 you get 4.

Same with the nine.

But if you times 49 by 11 you get 539.

Hope this helps!

Answer: The answer is 263

Step-by-step explanation: 116 + 8 = 124 * 2 = 258 + 15 = 263

Answer: 116 + 8 = 124 * 2 = 258 + 15 = 263

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{\frac{1}{9} } = \sqrt{\frac{1}{3} } {^{2} } \\\\=\frac{1}{3}[/tex]

The square root of the fraction 1/9, would be  ± 1/3.

A perfect square number when taken the square root of it results in an integer.

Numbers that are not perfect squares when taken the square root of it are irrational numbers.

One method of obtaining square roots for perfect squares is prime factorization.

A fraction 1/9 is given,

Now, The square root of this fraction would be √(1/9).

= √1/√9.

= 1/√9.

= 1/3, But it can be both ± 1/3 as both results to 1/9.

learn more about square roots here :

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Answer:

louis age is 26

Step by step explanation:

their difference = 20

and Louis is 6 times

then 20 + 6 = 26

Louis is [tex]6[/tex] times Mary's age. If the difference in their ages is 20 then Louis is [tex]24[/tex] years old.

Age is defined as the length of time that somebody has lived or that something has existed.

Let,

Mary's age  [tex]=x[/tex] years

So, Louis' age  [tex]= 6x[/tex] years

According to question,

[tex]6x-x=20[/tex]

[tex]5x=20[/tex]

[tex]x=4[/tex]

So, Louis' age  [tex]= 24[/tex] years

Hence, we can say that Louis is [tex]24[/tex] years old.

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Answer:

2000

Step-by-step explanation: