In a random sample of ​people, the mean driving distance to work was miles and the standard deviation was miles. Assume the population is normally distributed and use the​ t-distribution to find the margin of error and construct a ​% confidence interval for the population mean . Interpret the results. Identify the margin of error. nothing ▼ square miles miles per hour miles ​(Round to one decimal place as​ needed.) Construct a ​% confidence interval for the population mean. ​(Round to one decimal place as​ needed.) Interpret the results. Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. nothing​% of all random samples of people from the population will have a mean driving distance to work​ (in miles) that is between the​ interval's endpoints. B. It can be said that nothing​% of the population has a driving distance to work​ (in miles) that is between the​ interval's endpoints. C. With nothing​% ​confidence, it can be said that most driving distances to work​ (in miles) in the population are between the​ interval's endpoints. D. With nothing​% ​confidence, it can be said that the population mean driving distance to work​ (in miles) is between the​ interval's endpoints.

Answer:

the flux of the flow field F across σ = 135

Step-by-step explanation:

Given that :

F = 2xi + 3yj

and σ is the cube with opposite corners at (0,0,0) and (3,3,3) oriented outwards.

Using divergence theorem,

[tex]\iint \ F.ds = \iiint \ div. f \ dV[/tex]

[tex]div \ f = \dfrac{\partial }{\partial x}2x + \dfrac{\partial}{\partial y }(3y)[/tex]

f = 2 +3 = 5

where ;

F = 2xi + 3yj

Thus , the triple integral can now be ;

[tex]= \iiint 5.dV[/tex]

[tex]=5 \iiint \ dV[/tex]

[tex]= 5 \ \int^{3}_{0}\int^{3}_{0}\int^{3}_{0} \ dV[/tex]

= 5(3)(3)(3)

= 135

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

36 square units

Answer:

The cookbook costs $36 per copy while the science fiction costs $11 per copy

Step-by-step explanation:

Here in this question, we are interested in calculating the price of the cookbook and the price of the science fiction novel.

Since we do not know the price of each, we start by assigning variables to stand in for these unknown prices.

Let the price of the cookbook be $x , while the price of the science fiction be $y

Now, on the first day, 4 copies of the cookbook and 5 copies of the fiction;

mathematically that would be 4 * x and 5 * y

We add both and sum to be $199

Thus we have;

4x + 5y = 199 ••••••••••(i)

On the second day;

3 copies of cookbook 3 * x = 3x with 4 copies of science fiction 4 * y

Adding both yielded 152;

Thus, we have ;

3x + 4y = 152••••••••••(ii)

So we need to solve both equations simultaneously to get the values of x and y

4x + 5y = 199

3x + 4y = 152

Multiply equation i by 3 and equation ii by 4

3 * 4x + 5y = 199

4 * 3x + 4y = 152

12x + 15y = 597

12x + 16y = 608

Now, subtract multiplied equation ii from multiplied equation i

(12x-12x) + (15y-16y) = (597-608)

-y = -11

y = 11

To get x, simply substitute in any of the equations;

let’s use equation 1

4x + 5y = 199

4x + 5(11) = 199

4x + 55 = 199

4x = 199-55

4x = 144

x = 144/4

x = 36

Answer:

m<B = m<C = 55

Step-by-step explanation:

Since those two sides are congruent, the base angles are congruent.

m<B = m<C = x

m<A + m<B + m<C = 180

70 + x + x = 180

2x + 70 = 180

2x = 110

x = 55

m<B = m<C = 55

Answer:

0.0006s2+0.0096

Step-by-step explanation:

Answer:

76/86

Step-by-step explanation:

Answer:

76/86 is the answer it is the lowest term

Answer:

$32

Step-by-step explanation:

24/3= 8

8x4= 32

Adam gets paid $32 per hour

The amount Adam paid per hour is $32.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Janet:

Paid per hour = $24

Adam:

Paid per hour = $32

This means,

3/4 = $24

Multiply 4/3 on both sides.

1 = 4/3 x 24

1 = $32

Thus,

Adam paid $32 per hour.

Learn more about fractions here:

https://brainly.com/question/24370499

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Answer:

It should be 75 cm if we're taking the same test.

Step-by-step explanation:

y=0.3x-2

20.5=0.3(75)-2

0.3*75=22.5

22.5-2=20.5

20.5=20.5

Using the line of best-fit, it is found that the approximate length of the reptile is of 75 centimetres.

-------------

The mass y, in grams, of a reptile with length of x centimetres is given by:

[tex]y = 0.3x - 2[/tex]

-------------

[tex]y = 0.3x - 2[/tex]

[tex]20.5 = 0.3x - 2[/tex]

[tex]0.3x = 22.5[/tex]

[tex]x = \frac{22.5}{0.3}[/tex]

[tex]x = 75[/tex]

The approximate length of the reptile is of 75 centimetres.

A similar problem is given at https://brainly.com/question/24141057

Answer: ps = 1012.5

Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5

Step-by-step explanation:

Given that;

p = 120 + q ; p = 165

Now to find the producer's surplus for supply equation p=f(q) at the indicated unit price; we find p

so from p = 120 + q ; p = 165, if we substitute for q

120 + q = 165

q = 165 - 120 = 45

so

ps = ⁴⁵∫₀ ( 165 - (120+q) dq

ps = ⁴⁵∫₀ ( 45 - q) dq

USING THE EXPRESSION [ xⁿdx = xⁿ⁺¹ / n+1]

ps =  [45q - q²/2]₀⁴⁵

ps = [45(45) - 45²/2] [45(0) - (0)²/2]  

ps =  [2025 - 1012.5] - [0]

ps = 1012.5

Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5

Answer:

7

Step-by-step explanation:

Because these two triangles share an angle and their corresponding sides are parallel, they are similar.

So, we can set up a proportion relating corresponding sides:

10 / (10 + 8) = (3x - 6) / (3x - 6 + 12)

10/18 = (3x - 6) / (3x + 6)

Cross-multiply:

18 * (3x - 6) = 10 * (3x + 6)

54x - 108 = 30x + 60

24x = 168

x = 168/24 = 7

The answer is 7.

~ an aesthetics lover

Answer: Mass of lamina = 4

Step-by-step explanation: A lamina is a plate in 2 dimensions, described by the plane it covers and its density function, [tex]\rho(x,y)[/tex].

To determine mass of the lamina:

mass (M) = [tex]\int {\int\limits_D \rho(x,y) \, dA[/tex]

where D is region bounded by the axis.

For the question:

M = [tex]\int\limits^2_0 {\int\limits^2_0 xy \, dy \,dx[/tex]

Calculating the double integral:

M = [tex]\int\limits^2_0 { x\frac{y^{2}}{2} \,dx[/tex]

M = [tex]\int\limits^2_0 { x(\frac{2^{2}}{2}-0)} \,dx[/tex]

M = [tex]\int\limits^2_0 { 2x} \,dx[/tex]

M = [tex]\frac{2.2^{2}}{2} - 0[/tex]

M = 4

The mass of lamina is 4 units.

Answer:

The function  is  [tex]D = 2sin ( \frac{\pi}{2} - \frac{\pi}{12} t) + 6[/tex]

Step-by-step explanation:

From the question we are told that

    The  maximum depth is [tex]d = 8 \ ft[/tex]

      The  minimum depth is  [tex]d_i = 4 \ ft[/tex]

Generally the average depth is mathematically represented as

       [tex]d_a = \frac{8 + 4}{2}[/tex]

=>   [tex]d_a = 6 \ ft[/tex]

Generally  the amplitude is mathematically represented as

      [tex]A = d - d_a[/tex]

=>    [tex]A = 8 - 6[/tex]

=>    [tex]A = 2[/tex]

Generally the period is  24 hours given that the the interval between the maximum depth and the minimum depth is half a day

Generally the period is mathematically represented as

         [tex]T = \frac{2 \pi }{w}[/tex]

here w is the angular  frequency

So

     [tex]w = \frac{2 \pi}{24}[/tex]

      [tex]w = \frac{\pi}{12}[/tex]

Generally the depth can be modeled with a sin function as follows

     [tex]D = Acos (wt) + d_a[/tex]

Now  from co-function identity we have  that [tex]for \ cos (z) = sin (\frac{\pi}{2} - z)[/tex]

So  

     [tex]D = Asin ( \frac{\pi}{2} - wt) + d_a[/tex]

     [tex]D = 2sin ( \frac{\pi}{2} - \frac{\pi}{12} t) + 6[/tex]

The function that models the depth, in feet, of the water at the pier yesterday, as a function of time t in minutes past high tide is; D = 2 sin((π/2) - (π/12)t) + 6

We are given;

Thus;

Average depth; d = (d1 + d2)/2

d = (4 + 8)/2

d = 6 ft

Now, to find the amplitude, we will just subtract the minimum depth from the maximum one to get; A = d2 - d1

A = 8 - 6

A = 2 ft

Now, the period T is a whole day which is 24 hours and so we can find the angular frequency ω from the formula;

ω = 2π/T

Thus;

ω = 2π/24

ω = π/12

Where;

d_i is average depth

Thus;

D = 2 sin((π/2) - (π/12)t) + 6

Read more about sinusoidal functions at; https://brainly.com/question/2410297

Answer:

True

Step-by-step explanation:

The given statement is true as a common approach to keeping a record of each customer's account receivable is to use a subsidiary accounts receivable ledger. An account's receivable subsidiary ledger  is an accounting ledger that shows the transaction and payment history of each customer to whom the business extends credit.

Answer:

[tex]\huge\boxed{\dfrac{9^{36}}{9^3}=9^{33}\to\mathbb{B)}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m},\ \text{for}\ a\neq0.\\\\\text{We have}\ \dfrac{9^{36}}{9^3}=9^{36-3}=9^{33}[/tex]

Answer:

[tex] \boxed{ \bold{{ \boxed{ \sf8 {x}^{7} + 3 {x}^{6} + {x}^{5} + 5 {x}^{4} - 2 {x}^{3} }}}}[/tex]

Step-by-step explanation:

Here, we have to arrange the polynomial from higher power to lower power.

So, Option C is the correct option

Hope I helped!

Best regards! :D

Answer: Option A.

Step-by-step explanation:

We have the functions f(x) and g(x), that are inverses between them.

This means that if:

f(x) = y

then:

g(y) = x.

now, remember that:

When we have a point (x, y), and we reflect it over the line y = x, our new point will be (y, x).

So before we whe had:

f(x) = y.

and now in that same place, we have:

g(y) = x.

So the old graph of f(x) now coincides with the graph of g(x). (And the old graph of g(x) now coincides with the graph of f(x) )

So A is true.

B) This depends on the function:

if we have f(x) = x  + 1.5

then f(0) = 1.5

now we want that:

g(1.5) = 0, then we can write:

g(x) = x - 1.5

Now f(x) and g(x) are inverses, and we would have that:

f(x) = g(x) + 3.

So f(x) is g(x) translated up by 3 units, but this is a particular case, not a general one, so B is not always true.

C and D) When we do rotations of 90° or 180°, we are effectively changing the quadrant of our point. so rotations will cause not only changes as the reflection over the x = y line, those will also cause changes in the sign of our variables, so, while for some functions f(x) and g(x) we can have that the rotations will map one into the other, this is not the general case.

Answer:

if ABCD is a rhombus then the diagonal of rhombus bisect it into two equal triangles.

Step-by-step explanation:

In triangles ABC and CDA,

so the triangles are congruent to each other by S.S.S. fact/ axiom

Answer:

D. He needs 6 cups of flour for 3 batches

Answer:

-15

Step-by-step explanation:

start from the inside and go out.

So first plug in -3 into g(x)

g(-3) = -3 - 7 = -10

then plug in -10 into f(x)

f(-10) = 2(-10) + 5 = -15

so f(g(x)) = -15

Answer:

Step-by-step explanation:

f(x) = 2x + 5

g(x) = x − 7

To find f(g(x)) substitute g(x) into f(x) that's replace every x in f(x) by g(x)

That's

f(g(x)) = 2(x - 7) + 5

= 2x - 14 + 5

f(g(x)) = 2x - 9

When x = - 3

Substitute - 3 into f(g(x))

That's

Hope this helps you

Answer:

27.0000

Step-by-step explanation:

27.2163 rounded to the nearest hundredth is 27.0000 or 27 because the hundredth place held a 1 and 5 or above rounds up and 4 or below rounds down. The .2163 turned into zeros because the second number (the hundredths place) was a 1 so it rounded down, and hen it rounds down, all the numbers round to 0.

Answer:

2¹+3¹ , 2³ -2¹ , 3²

Step-by-step explanation:

to know the magnitude of the value of each expression 3² =9 ,

2³ -2¹ =8-2=6

2¹ +3¹ = 5

Answer:

[tex]\Huge \boxed{\mathrm{ Rational }}[/tex]

Step-by-step explanation:

Rational numbers can be expressed as fractions with whole numbers as the numerator and the denominator.

[tex]\displaystyle \frac{0.4}{0.8}[/tex]

Multiply both the numerator and the denominator by 10.

[tex]\displaystyle \frac{4}{8} =\frac{1}{2}[/tex]

The result is a simplified fraction with both the numerator and the denominator being whole numbers. The result is rational.

Answer:  17 per week

Step-by-step explanation:

10 weeks = 70 days

105 + 65 = 170

107 / 70 = 2.42857142857

2.42857142857 x 7 days = $17

Answer:

the answer is 117/500 hop this helps:)

Step-by-step explanation:

0.234 = 117 / 500

as a fraction

To convert the decimal 0.234 to a fraction, just follow these steps:

Step 1: Write down the number as a fraction of one:

0.234 = 0.234/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 3 numbers after the decimal point, we multiply both numerator and denominator by 1000. So,

0.234/1

= (0.234 × 1000)

(1 × 1000)

= 234

1000

.

Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(234,1000) = 2. So,

(234÷2)

(1000÷2)

= 117/500

when reduced to the simplest form.

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

I would appreciate it!

Step-by-step explanation:

The slope of the tangent line of a function f(x) is the derivative, f'(x).

Here, we can use exponent rule to find the derivatives:

If y = xⁿ, then y' = nxⁿ⁻¹.

7. g(x) = x²

g'(x) = 2x

g'(2) = 4

8. g(x) = x² − 4x

g'(x) = 2x − 4

g'(1) = -2

9. g(x) = 5/(x + 3)

g(x) = 5 (x + 3)⁻¹

g'(x) = -5 (x + 3)⁻²

g'(-2) = -5

Answer:

x= 2, y= 2, and z= 6

Step-by-step explanation:

If this is a Diophantine equation, add 35 to both sides and factor the left:

(3x+1)(2y+7)(z+5) = 847 = 7 times 112

Each integer factorization of 847 into 3 factors leads to a different number/value of x, y, and z. If the first factor, (3x+1), is 1 more than a multiple of 3, and the second factor, (2y+7), is odd, then x, y, and z will be integers.

For example:

847 = 121 times -7 times -1 gives (x, y, z) = (40, -7, -6) because 121 times -7 times -1 is 847 as well, it checks out.

If x, y, and z need to be positive, then the three numbers/factors need to be greater than 1, 7, and 5. The only combination that works is 7 times 11 times 11, which gives (x, y, z) = (2, 2, 6).

:)

Answer:

x =1     x = -7

Step-by-step explanation:

|4x + 12| = 16

Absolute value equations have two solutions, one positive and one negative

4x+12 = 16          4x+12 = -16

Subtract 12 from each side

4x+12-12 = 16-12          4x+12-12 = -16-12

4x =4                               4x =-28

Divide by 4

4x/4 = 4/4                       4x/4 = -28/4

x =1                                   x = -7

Answer:

Step-by-step explanation:

f(x) = x² - 5x + 7

To find f(3) substitute the value of x that's 3 into f(x) that's replace every x in f (x) by 3

We have

We have the final answer as

Hope this helps you