Which method should be used to solve for x? 2.5 x = 5.7 distributive property addition property of equality combining like terms division property of equality

Answer:

Children = 150

Students = 98

Adults = 75

Step-by-step explanation:

C + S + A = 323

5C + 7S + 12A = 2336

A = 1/2C

C = 150

S = 98

A = 75

Answer:

(3x-5)(4x+7) / 4x + 17

Step-by-step explanation:

Rewrite the division as a fraction

12 x ^2 + x-35 / 4x+17

Factor by grouping

(3x-5)(4x+7) / 4x + 17

Hope this was the answer you were looking for

Answer:

$6284.4≤μ≤$6313.6

Step-by-step explanation:

Using the formula for calculating confidence interval as shown:

CI = xbar ± Z×S/√n

xbar is the average premium

Z is the z-score at 95% confidence

S is the standard deviation

n is the sample size

Given parameters

xbar = $6600

Z score at 95% CI = 1.96

S = $800

n = 25

Substituting this parameters in the formula we have;

CI = 6600±1.96×800/√25

CI = 6600±(1.96×800/5)

CI = 6600±(1.96×160)

CI = 6600±313.6

CI = (6600-313.6, 6600+313.6)

CI = (6284.4, 6913.6)

Hence the 95% confidence interval for the mean premium amount paid by all workers who have employer provided health insurance is $6284.4≤μ≤$6313.6

Answer: a. $40,800 b. 36

Step-by-step explanation:

Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].

[tex]\sigma= \$14,900[/tex]

a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.

Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]

= 40,800

hence, the point estimate of the mean salary for all college graduates in this town = $40,800

b.  Since  lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.

Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]

Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.

z-value for 99% confidence level  = 2.576

So,

[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]

The sample size used for the analysis =36

Answer:

(2+7) root 3 equals 9 root 3

Correct question is;

Find the surface area of that part of the plane 10x + 7y + z = 4 that lies inside the elliptic cylinder x²/25 + y²/9 = 1

Answer:

A(S) = 15π√150

Step-by-step explanation:

We are given;

10x + 7y + z = 4

Making z the subject, we have;

z = 4 - 10x - 7y

Now, area of the surface as part of z = f(x, y) is;

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA

From z = 4 - 10x - 7y,

∂f/∂x = -10

∂f/∂y = -7

Thus;

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

x²/a² + y²/b² = 1 and comparing with

x²/25 + y²/9 = 1, we have;

a = 5 and b = 3

So, area of elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder [tex]\dfrac{x^2}{25}+\dfrac{y^2}{9}=1[/tex] is [tex]15\pi\sqrt{150}[/tex] and this can be determined by using the given data.

Given :

Equation (1) can also be written as:

z = 4 - 10x - 7y      ---- (3)

The surface area is given by the equation:

[tex]\rm A(s) = \int \int \sqrt{(\dfrac{\delta f}{\delta x})^2+(\dfrac{\delta f}{\delta y})^2+1}\;dA[/tex]     --- (4)

[tex]\dfrac{\delta f}{\delta x} = -10[/tex]

[tex]\dfrac{\delta f}{\delta y} = -7[/tex]

Now, substitute the known values in the equation (4).

[tex]\rm A(s) = \int \int \sqrt{(10)^2+(7)^2+1}\;dA[/tex]  

[tex]\rm A(s) = \sqrt{150} \int \int\;dA[/tex]  

Now the area enclosed by an ellipse is given by:

[tex]\dfrac{x^2}{25}+\dfrac{y^2}{9}=1[/tex]

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

By comparing the above equation:

a = 5

b = 3

The area is given by:

[tex]\rm A(s)=\sqrt{150}\times \pi(5\times 3)[/tex]

[tex]\rm A(s) = 15\pi \sqrt{150}[/tex]

For more information, refer to the link given below:

https://brainly.com/question/11952845

Answer:

  28) -1

  29) 9

  30) x^2+4x+7

  31) x-2

Step-by-step explanation:

Given:

  f(x) = x + 2

  g(x) = x^2 +3

Find:

  28) f(-3)

  29) f(g(2))

  30) g(f(x))

  31) f-1(x)

Solution:

Put the function argument values into the expression and do the arithmetic.

28) f(-3) = (-3) +2 = -1

__

29) f(g(2)) = f((2)^2 +3) = f(7) = (7) +2 = 9

__

30) g(f(x)) = g(x+2) = (x+2)^2 +3 = x^2 +4x +7

__

31) The meaning of y = f^-1(x) is x = f(y).

  x = f(y) = y+2

  y = x -2

  f^-1(x) = x -2

Answer :

[tex] \frac{2 {x}^{3} + 7 {x}^{2} + 3x - 4}{ {x}^{3} + 3 {x}^{2} + x - 1} [/tex]

Step-by-step-explanation :

I did the explanation in the picture.

Answer:  19.2222

Step-by-step explanation:

given data;

no of tornadoes = 2,1,0 because it’s fewer than 3.

period = 14 years

probability of a tornado in a calendar year = 0.12

solution:

probability of exactly 2 tornadoes

= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )

= 0.0144 * 0.2451 * 1092

= 3.8541

probability of exac one tornado

= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )

= 0.12 * 0.2157 * 182

= 12.7109

probability of exactly 0 tornado

= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )

= 1 * 0.1898 * 14

= 2.6572

probability if fewer than 3 tornadoes

= 3.8541 + 12.7109 +2.6572

= 19.2222

Answer:

[tex]\frac{}{d}[/tex] = −0.26

[tex]s_{d}[/tex] = 0.4219

Step-by-step explanation:

Given:

Sample1:  98.1  98.8  97.3  97.5  97.9

Sample2: 98.7  99.4  97.7  97.1  98.0

Sample 1           Sample 2              Difference d

98.1                        98.7                       -0.6  

98.8                       99.4                       -0.6

97.3                        97.7                       -0.4

97.5                        97.1                         0.4

97.9                        98.0                       -0.1

To find:

Find the values of [tex]\frac{}{d}[/tex] and [tex]s_{d}[/tex]

d overbar ( [tex]\frac{}{d}[/tex])  is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5

[tex]\frac{}{d}[/tex] = ∑d/n

 = (−0.6 −0.6 −0.4 +0.4 −0.1) / 5

 = −1.3 / 5

[tex]\frac{}{d}[/tex] = −0.26

s Subscript d is the sample standard deviation of the difference which is calculated as following:

[tex]s_{d}[/tex] = √∑([tex]d_{i}[/tex] - [tex]\frac{}{d}[/tex])²/ n-1

[tex]s_{d}[/tex] =

√ [tex](-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1[/tex]

    =  √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −  

                                                                     (−0.26))² + (−0.1 − (−0.26))² / 5−1

=  [tex]\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }[/tex]

= [tex]\sqrt{\frac{0.712}{4} }[/tex]

= [tex]\sqrt{0.178}[/tex]

= 0.4219

[tex]s_{d}[/tex] = 0.4219

Subscript d ​represent

μ[tex]_{d}[/tex] represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.

Answer:

Step-by-step explanation:

Given vector the following vector equations OA = 13x+7y , OB = 5x+12y and CO = -15x+12y, the following expression is true about vector OA, OB and OC;

OA+OB = CO (CO is the resultant since its is moving in the opposite direction compare to OA and OB)

Also BO+OA = BA and AO+OC = AC

If OB = 5x+12y, then BO = -(5x+12y)

BO = -5x-12y (BO = -OB)

Since BO+OA = BA

BA = -5x-12y + 13x+7y

BA = -5x+13x-12y+7y

BA = 8x-5y

Similarly AO+OC = AC

Since AO = -OA and OC = -CO

-OA-CO  = AC

AC = -(13x+7y)-(-15x+12y)

AC = -13x-7y+15x-12y

AC = -13x+15x-7y-12y

AC = 2x-19y

Answer:

2

Step-by-step explanation:

The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.

Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.

Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).

Slope = rise/run

Slope = 2/1

Slope = 2

Hope that helps.

Answer:

slope=2

Step-by-step explanation:

take two points from graph (0,0) and (1,2)

m=y2-y1/x2-x1

m=2-0/1-0

m=2

Answer:

432 mm³

Step-by-step explanation:

Volume of a Rectangular Prism: V = lwh

Step 1: Define variables

l = 8

w = 6

h = 9

Step 2: Plug into formula

V = 8(6)(9)

Step 3: Evaluate

V = 48(9)

V = 432

And we have our answer!

The given quadrilateral (call it Q) is a trapezoid with "base" lengths of 6 and 12, and "height" 2, so its area is (6 + 12)/2*2 = 18. This means the joint density is

[tex]f_{X,Y}(x,y)=\begin{cases}\frac1{18}&\text{for }(x,y)\in Q\\0&\text{otherwise}\end{cases}[/tex]

where Q is the set of points

[tex]Q=\{(x,y)\mid0\le x\le 2\land0\le y\le12-3x\}[/tex]

(y = 12 - 3x is the equation of the line through the points (0, 12) and (2, 6))

Recall the definition of expectation:

[tex]E[g(X,Y)]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty g(x,y)f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy[/tex]

(a) Using the definition above, we have

[tex]E[X]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty xf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac x{18}\,\mathrm dy\,\mathrm dx=\frac89[/tex]

(b) Likewise,

[tex]E[Y]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\ifnty yf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac y{18}\,\mathrm dy\,\mathrm dx=\frac{14}3[/tex]

Answer:

[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]

[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]

Step-by-step explanation:

Part 1: Writing a ratio as a fraction

A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,

Therefore, 8:18 as a fraction is 8/18.

Part 2: Fraction in simplest form

To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.

8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.

Instead, if both numbers are even, divide by 2.

8/2 = 4

18/2 = 9

Check to see if the new numerator and denominator can reduce any further.

4/9 = 4/9

The fraction in simplest form is 4/9.

Answer:

25 CAN be written as a fraction.

=> 250/10 = 25

Square root of 14 is 3.74165738677

It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION,  but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION

=> 374/100

-1.25 CAN be written as a fraction.

=> -5/4 = -1.25

Square root of 16 CAN also be written as a fraction.

=> sqr root of 16 = 4.

4 can be written as a fraction.

=> 4 = 8/2

Pi = 3.14.........

It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION

=> 314/100

.6 CAN be written as a fraction.

=> 6/10 = .6

Answer: a. population = "All Students"

b. 0.22

c. 0.24

Step-by-step explanation:

a. Population is the largest group of individuals having same characteristics by the researcher's point of view.

Here , the interest is  "Students study foreign language"

So, population = "All Students"

b. Let p be the pro[portion of secondary school students study a foreign language.

In a certain state 22% of secondary school students study a foreign language.

The value of proportion [tex]p_1[/tex] =- 0.22

c. A group of 100 students were selected in random sample and 24 of them study a foreign language.

The value of proportion [tex]p_2=\dfrac{24}{100}=0.24[/tex]

Answer:

32

Step-by-step explanation:

Everyone added together = 68

Four years ago, they were 68 -16 = 52

But the question told 54 years.

So there was a girl who was 2 years.

Girl = 2

Boy = 2 +3 = 5

Husband = 3 +w

Wife =w

3 +w +w + 5 + 2 = 68

10 + 2w = 68

2w = 58

w = 29

Wife = 29

Husband = 29 +3 =32

Husband = 32 years

Answer:

[tex]\large \boxed{\sf \bf \ \ 32 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We know that "All together they are 68 years old." and "Four years ago, all together the family was 54 years old."

If all the family was alive four years ago, it means that four years ago the sum of their ages was 68 - 4 - 4 - 4 - 4 because they are four members, so it gives 68 - 16 =52 which is different from 54, right ?

It means that we have the daughter in between, 54- 52 = 2, so the daughter's age is 2, and then the son's age is 5.

The husband is 3 years older than the wife. Let's note W the wife's age, we can write W + 3 + W + 5 + 2 = 68

2 W + 10 = 68

2 W = 68 - 10 = 58 so W = 29

and then the husband's age is 29 + 3 = 32.

And we can verify that 32 + 29 + 5 + 2 = 68, and four years ago, 28 + 25 + 1 + 0 = 54.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Jargon that they both understand will be used.

Step-by-step explanation:

Jargon that they both understand will be used.

Jargon is a literary term that is defined as the use of specific phrases and words in a particular situation, profession, or trade. The use of jargon becomes important in prose or verse or some technical pieces of writing, when the writer plans to convey something only to the readers who are aware of these terms. Some of such examples are:

Due diligence: This is a business term, which refers to the research that should be done before making an important business decision.

AWOL: Short for "absent without leave," AWOL is military jargon used to describe a person whose whereabouts is unknown.

Answer:

0.0321

Step-by-step explanation:

This can be found by binomial probability distribution as the  probability of success is constant. There are a given number of trials. the successive tosses are independent.

Here n= 5

The probability of getting a four in a roll of a die = 1/6

The probability of not getting a four in a roll of a die = 5/6

The probability of getting exactly three 4s in five throws is given by

5C3 (1/6)³ (5/6)² = 10 (0.0046) (0.694)= 0.0321

Answer: Find answer in the attachment

Step-by-step explanation:

Answer:

Hey there!

We can write: -2+9=7.

Let me know if this helps :)

Answer:

[tex]\large \boxed{{-2+9=7}}[/tex]

Step-by-step explanation:

-2 is also 0-2

The arrow goes from 0 to -2.

-2 + 9 = 7

The arrow goes from -2 to 7.

Answer:

The question is not complete, below is the complete question:

What is meant by the term 90% confident? when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.

c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

Answer:

The correct answer is:

If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.  (c)

Step-by-step explanation:

a 90% confidence level means that if repeated samples were taken, 9 out of 10 times, the confidence intervals of the sample chosen will be close to the mean (true value), which is a true representation of the population parameter. when using confidence intervals, there are always margins of allowable accuracy, and this is suggested by using standard diviations snd variances.

I attached a simple document to this answer that will give you more insight into confidence intervals used in statistics.

Assuming the cup is a right circular cylinder, it's volume is [tex]V=\pi r^2 h[/tex]

$h=10$, $r=\frac 42$

So the volume is $\pi\cdot(2)^2\cdot10=125.66$

hence you can fill up to 125.66 cubic Inches of milkshake

.

Answer:

(3) y+2=2(x-8)

Step-by-step explanation:

Substitute the point into the equation and see if it is true

(8,-2)

(1) y+2=2(x+8)

    -2+2 = 2(8+8)

    0 = 2(16)

False

(2) y-2=2(x-8)

  -2-2 = 2(8-8)

  -4 =2 (0)

  False

(3) y+2=2(x-8)

  -2+2 = 2( 8-8)

  0 = 2(0)

 True

(4) y-2=2(x+8)

  -2-2 = 2(8+8)

  -4 = 2(16)

False

Answer:

[tex]\boxed{y+2=2(x-8) }[/tex]

Step-by-step explanation:

[tex]x=8[/tex]

[tex]y=-2[/tex]

[tex]\sf Check \ the \ third \ option.[/tex]

[tex]-2+2=2(8-8)[/tex]

[tex]\sf Both \ sides \ must \ be \ equal.[/tex]

[tex]0=2(0)[/tex]

[tex]0=0[/tex]

Answer:

4x

Step-by-step explanation:

Given:

√x • 4√x

Required:

Simplify in rational exponent form

SOLUTION:

Recall => [tex] \sqrt{a} = a^{\frac{1}{2}} [/tex]

Thus,

[tex] \sqrt{x}*4\sqrt{x} [/tex] can be expressed in exponent form as [tex] x^{\frac{1}{2}}*4x^{\frac{1}{2} [/tex]

When multiplying 2 bases having exponents together, their exponents should be added together, while you multiply the bases. I.e. [tex]x^m*x^n = x^{m+n }[/tex]

[tex] = x*4^{\frac{1}{2}+\frac{1}{2} [/tex]

[tex] = 4x^{1} = 4x [/tex]

The answer is 4x

Answer:

15.7% of students made above an 89.

Step-by-step explanation:

If the data is normally distributed, the standard deviation is 7, and the mean is 82, then about 68.2% of students made between 75 and 89. 13.6% made between 90 and 96, and 2.1% made over 96. 13.6+2.1=15.7%

Answer:

Step-by-step explanation:

The approximate learning percentage can be estimated by using a doubling method.

If we breakdown the repetitions into three consecutive parts, we have:

1 - 2

2 - 4

3 - 6

then

1 - 2        →         46P = 39

P =39/46

P = 0.8478

P = 84.8%

2 - 4        →       39P = 33

P = 33/39

P = 0.84615

P = 84.6%

3  -  6    →       35P = 30

P = 30/35

P = 0.8571

P = 85.7%

The average value of P = (84.8 + 84.6 + 85.7)/3 = 85.03%

[tex]\simeq[/tex] 85%

From the tables of Learning Curves coefficient

The values are likened against times derived from 85% table factors at T[tex]_1[/tex] = 46

Unit                 1                2           3                    4                5            6

Date                46            39         35                33                32          30

Computed       -              39.1       35.56          33.26        31.56       30.22

b. Using your answer from part a, estimate the average completion time per repetition assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)

The average completion time = [tex]\mathtt{\dfrac{T_1 \times \ Total \ time\ factor}{n}}[/tex]

At the total time factor 30, from the learning curves table , n(30) = 17.091

Thus:

The average completion time = [tex]\mathtt{\dfrac{46 \times \ 17.091}{30}}[/tex]

The average completion time = [tex]\mathtt{\dfrac{786.186}{30}}[/tex]

The average completion time = [tex]\mathtt{26.2062}[/tex]

Answer: 247.92 euros

Step-by-step explanation:

Given:  Varia is required pay $3,500 (in US dollars) per year to the university.

So, [tex]$3500\div 12 \approx\$291.67[/tex]

i.e. She will pay $ 291.67 per month.

Recent currency value: 1 US dollar = 0.85 euro

∴ $291.67 = ( 0.85 ×291.67) euros

= 247.92 euros  [Round to the nearest cent]

∴ She can expect 247.92 euros to pay per month to the university.

Answer:

5 and 3/32 of an inch.