Which expression is equivalent to the following complex fraction?

Answer: The graph moved left 3 units.

(x, y) = (x - 3, y)

The value of the expression for the given values of x, y and z is B. -5.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is,

x²z² - y²(x + z)

We have certain values for x, y and z.

x = 2, y = -3 and z = -1.

Substituting the values,

(2²)(-1²) - (-3²) (2 + -1) = (4 × 1) - (9 × 1)

                                 = 4 - 9

                                 = -5

Hence the value of the expression is -5.

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Answer:

maybe 10000

Step-by-step explanation:

Answer:

9007.35

Step-by-step explanation:

First find the effective rate: .06/12= .005

let x= amount

[tex]x=100\frac{1-(1+.005)^{-12*10}}{.005}\\100*\frac{1-.549632733}{.005}\\9007.345333[/tex]

Answer:

1.92755 ,1.870320 i hope it will help you

Answer:

First bag's unit price=$1.92 per kg  Second bag's unit price=$1.87 per kg

Step-by-step explanation:

1.92 becomes 1.93

Answer:

4 places after the decimal.

the result is 0.0215

Step-by-step explanation:

I assume the expression is really

43 / (2⁴ × 5³)

this is the same as

(((((((43 / 2) / 2) / 2) / 2) / 5) / 5) / 5)

since the starting value is an odd number, the first division by 2 creates a first position after the decimal point, and it must be a 5, as the result is xx.5

the second division by 2 splits again the uneven end .5 in half, creating a second position after the decimal point again ending in 5, as the result is now xx.x5

the third division by 2 does the same thing with that last 5 and creates a third position after the decimal point ending again in 5, as the result is now xx.xx5

the fourth division by 2 does again the same thing, a fourth position after the decimal point is created ending in 5. now xx.xxx5

in essence, every division of the 0.5 part by 2 is the same as a multiplication by 0.5, which squares 0.5 leading to 0.5². the next division did the same thing leading to 0.5³.

and finally the fourth division to 0.5⁴.

0.5⁴ = (5/10)⁴ = 5⁴/10⁴

so, now we start to divide this result by 5. since the positions after the decimal point are divisible by 5 without remainder, as we have 5⁴ to work with.

every divisible by 5 takes one of these powers away.

so, we go from 5⁴/10⁴ to 5³/10⁴ to 5²/10⁴ to 5/10⁴.

all the time we maintain the 10⁴ in the denominator of the fraction. and that determines the positions after the decimal point.

so, after all the individual divisions we come to and end and are still limited to the 4 positions after the decimal point.

9514 1404 393

Answer:

Step-by-step explanation:

I find this approach the most straightforward of the various ways that trinomial factoring is explained or diagramed.

You want two factors of "ac" that have a total of "b". Here, that means you want factors of 2·50 = 100 that have a total of 25. It is helpful to know your times tables.

  100 = 1·100 = 2·50 = 4·25 = 5·20 = 10·10

The sums of these factor pairs are 101, 52, 29, 25, and 20. We want the pair with a sum of 25, so that's 5 and 20.

The trinomial can be rewritten using these factors as ...

  2x^2 +5x +20x +50

Then it can be factored by grouping consecutive pairs:

  (2x^2 +5x) +(20x +50) = x(2x +5) +10(2x +5) = (x +10)(2x +5)

_____

Additional comment

It doesn't matter which of the factors of the pair you write first. If our rewrite were ...

  2x^2 +20x +5x +50

Then the grouping and factoring would be (2x^2 +20x) +(5x +50)

  = 2x(x +10) +5(x +10) = (2x +5)(x +10) . . . . . same factoring

Answer:

This Question Is From The Novel Of The Fantastic Mr.Fox

Q. Boggis , Bunce and Bean are Offering a reward for Mr.Fox , They are tired of Losing Chickens Geese and Cider , Create a Description And Drawing of Mr.Fox to allow him to be captured , use the word bank....

________________________________

Swift | Slay | Ginger | Rough | Fast

Thief. | Clever | Fur | Tail | Wife | Night

Cunning | Bushy | wiry | bush | Den | trick

________________________________

Answer:

I don't really understand the question

Step-by-step explanation:

c

Answer:

Step-by-step explanation:

4x+3y=13

5x-4y=-7

Answer:

So, the initial number of apples is 7.

Step-by-step explanation:

The number of apples of An, Binh, and Chi are the same. An gave away 17 apples, Chi gave away 19 apples, so now Chi's apples are 5 times higher than the total remaining apples of An and Binh. How many apples did each of you have at first? (Solve the above problem by equation or system of equations)

Let the initial numbers of apples is a.

An gave 17 apples

Chi gave 19 apples

So,

x - 19 = 5 (x - 17 + x)

x - 19 = 5 (2x - 17)

x - 19 = 10 x - 85

9 x = 66

x = 7

Complete Question

Assisted-Living Facility Rent.Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486 (the Wall Street Journal, October 27, 2012). Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is s = $650. a. Develop a 90% confidence interval estimate of the population mean monthly rent.

Answer:

[tex]CI: 3388.39<X<3583.61[/tex]

Step-by-step explanation:

Sample Size n=120

Mean \=x =3486

Standard Deviation \sigma=650

Confidence interval CI=0.9

Therefore

Level of sig [tex]\alpha=0.1[/tex]

Therfore

The Critical Value from table is

Z_c=1.645

Generally the equation for Standard error is mathematically given by

[tex]S.E=\frac{\sigma}{\sqrt{n}}[/tex]

[tex]S.E=\frac{650}{\sqrt{120}}[/tex]

[tex]S.E=59.3366[/tex]

Generally the equation for Margin error is mathematically given by

[tex]M.E= = Z_c * SE[/tex]

[tex]M.E=1.65 * 59.34[/tex]

[tex]M.E= 97.61[/tex]

Therefore

[tex]CI= \=x \pm M.E[/tex]

[tex]CI= 3486 \pm 97.61[/tex]

Lower limit

[tex]LL= \=x-M.E=3486-97.6087[/tex]

[tex]LL= 3388.39[/tex]

Upper limit:

[tex]UL= \=x+E=3486+97.6087[/tex]

[tex]UL= 3583.61[/tex]

Therefore The  90% confidence interval estimate of the population mean monthly rent.

[tex]CI: 3388.39<X<3583.61[/tex]

9514 1404 393

Answer:

  2xy^2

Step-by-step explanation:

The terms are "like" so can be combined. It might be helpful to think of this as an application of the distributive property.

  -3xy^2 +5xy^2 = (-3 +5)xy^2 = 2xy^2

Answer:

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.

This means that [tex]n = 1000, \pi = \frac{450}{1000} = 0.45[/tex]

96% confidence level

So [tex]\alpha = 0.04[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.054[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4177[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4823[/tex]

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

Answer:

A F(x) it is the power function, make sure to take notes as well

Answer:

The answer is "840".

Step-by-step explanation:

Following are the number of ways in which selecting a team A  by 9 children:

[tex]= ^{9_{C_{3}}\\\\\\[/tex]

[tex]=\frac{9!}{3! \times 6!} \\\\=\frac{9\times 8\times 7\times 6!}{3 \times 2\times 1\times 6!}\\\\=\frac{9\times 8\times 7}{3 \times 2\times 1}\\\\=\frac{3\times 4\times 7}{1}\\\\=\frac{84}{1}\\\\=84[/tex]

Following are the number of ways in which selecting a team B  by remaining 6 children:

 [tex]= ^{6}_{C_{3}}[/tex]

[tex]= \frac{6!}{(3! \times 3!)}\\\\= \frac{6!}{(3\times 2\times 1 \times 3!)}\\\\= \frac{6\times 5 \times 4 \times 3!}{(3\times 2\times 1 \times 3!)}\\\\= \frac{ 5 \times 4 \times 3!}{3!}\\\\= 5 \times 4 \\\\=20[/tex]

Following are the number of ways in which selecting a team C  by remaining 3 children:

[tex]= ^{3}_{C_{3}}\\\\=\frac{3!}{3!}\\\\= 1[/tex]

Following are the number of ways in which making 3 teams by 9 children:

[tex]= \frac{(84 \times 20 \times 1)}{3!}\\\\= \frac{(84 \times 20 )}{6}\\\\= 14 \times 20\\\\= 280\\\\[/tex]

(Note: we've split by 3! Because it also is necessary to implement three teams between themselves)

Now 3 leagues have to be played. One is going to be run by each team.

That is the way it is

Different possible divisions

[tex]= 280 \times 3!\\\\= 280 \times (3 \times 2 \times 1)\\\\= 840[/tex]  

Answer:

their sizes vary

Step-by-step explanation:

their sizes vary

Answer:

C. -1.5 < -0.5

Step-by-step explanation:

On a number line, the farther a number is to the right away from 0, the greater the number. While the farther it is from 0 to the left, the smaller it is.

Thus, the out of the options given, the only inequality given that is true is:

-1.5 < -0.5

This is because, -1.5 on the numberline is farther away to the left from 0 than -0.5. therefore, -1.5 is lesser than -0.5.

Answer:

[tex]\sigma = 1.8[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}[/tex]

Required

The standard deviation

First, calculate the expected value E(x)

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2[/tex]

[tex]E(x) = 2.7[/tex]

Next, calculate E(x^2)

[tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2[/tex]

[tex]E(x^2) = 10.5[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{E(x^2) - (E(x))^2}[/tex]

[tex]\sigma = \sqrt{10.5 - 2.7^2}[/tex]

[tex]\sigma = \sqrt{10.5 - 7.29}[/tex]

[tex]\sigma = \sqrt{3.21}[/tex]

[tex]\sigma = 1.8[/tex] --- approximated

Answer:

$0.60

Step-by-step explanation:

To find the cost of 1 orange, divide the $6 by 10:

6/10 = 0.6

Hope it helps (●'◡'●)

Answer:

There may be 1 or 3 tricycles in the parking lot.

Step-by-step explanation:

Since at any point in time, there could be bicycles, tricycles, and cars in the school parking lot, and today, there are 53 wheels in total, if there are 15 bicycles, tricycles, and cars in total, to determine how many tricycles could be in the parking lot, the following calculation must be performed:

13 x 4 + 1 x 3 + 1 x 2 = 57

11 x 4 + 1 x 3 + 3 x 2 = 53

10 x 4 + 3 x 3 + 2 x 2 = 53

8 x 4 + 5 x 3 + 2 x 2 = 51

10 x 2 + 1 x 3 + 4 x 4 = 39

9 x 3 + 1 x 2 + 5 x 4 = 49

Therefore, there may be 1 or 3 tricycles in the parking lot.

2 kg dough = 1 hour

1 kg dough = 1 hour/2 = 1/2 hour

6 kg dough = 6 × (1/2 hour) = 6/2 hours = 3 hours

Answer: 3 hours

Step-by-step explanation: x represents the number of hours she works

2x=6

x=6/2

x=3

Answer:

Domain:  

( − ∞ , 2 ] , { x | x ≤ 2 }

Range:  

[ 0 , ∞ ) , { y | y ≥ 0 }

Answer:

x=[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Hi there!

We are given the following equation:

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

and we need to find the value of x

To do this, we need to isolate the value of x with a coefficient of 1 (1x) on one side. The value of x, or everything else is on the other side

So let's get rid of [tex]\frac{1}{10}[/tex] from the left side by adding [tex]\frac{1}{10}[/tex] to both sides (-[tex]\frac{1}{10}[/tex]+[tex]\frac{1}{10}[/tex]=0).

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

  +[tex]\frac{1}{10}[/tex]  +[tex]\frac{1}{10}[/tex]

___________

[tex]\frac{4x}{5}[/tex]=[tex]\frac{3}{10}[/tex]+[tex]\frac{1}{10}[/tex]

as the fractions on the right side both have the same denominator, we can add them together

[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]

Now we need to have the value of 1x. Currently we have [tex]\frac{4x}{5}[/tex].

In order to get x with a coefficient of 1, multiply both sides by the reciprocal of [tex]\frac{4}{5}[/tex], which is [tex]\frac{5}{4}[/tex]

[tex]\frac{5}{4}[/tex]×[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]*[tex]\frac{5}{4}[/tex]

which simplifies down to

x=[tex]\frac{20}{40}[/tex]

Now reduce the fraction by dividing the numerator and denominator both by 20

x=[tex]\frac{1}{2}[/tex]

Hope this helps!  

Answer:

9614

Step-by-step explanation:

Generic number with 4 digit

1000t + 100h + 10y + x

x = 3 + y

x = m - 5

h = 6

m = 9

if we substitute the value we have:

x = 9 - 5 = 4

4 = 3 + y

y = 1

Final number

9614

Answer: 3

Step-by-step explanation: m=2 so 7.5x2 = 15

15/5 is 15 divided by 5 so the answer is 3

Answer:

2107 marbles can be stored in the container.

Step-by-step explanation:

Since a merchant keeps marble in a cylindrical plastic container that has a diameter of 28cm and height of 35cm, and a marble has a diameter of 25mm, to determine the number of marbles that can be stored in such a container if air space accounts for 20 % between marbles, the following calculation must be performed, knowing that the volume of a cylinder is equal to height x π x radius²:

35 x 3.14 x (28/2) ² = X

109.9 x (14 x 14) = X

109.9 x 196 = X

21,540.4 = X

In turn, the volume of each 25mm diameter marble is equal to:

25mm = 2.5cm

4/3 x 3.14 x 1.25³ = X

4.18666 x 1.953125 = X

8.1770 = X

21,540.4 x 0.8 = 17,232.32

17,232.32 / 8,177 = 2,107.41

Therefore, 2107 marbles can be stored in the container.

Answer:

ಠ_ಠ

Step-by-step explanation: