Use the standard normal distribution or the​ t-distribution to construct a 99​% confidence interval for the population mean. Justify your decision. If neither distribution can be​ used, explain why. Interpret the results. In a random sample of 42 ​people, the mean body mass index​ (BMI) was 28.3 and the standard deviation was 6.09.

Answer:

  see the attachment

Step-by-step explanation:

The graph attached shows the secant function in red. The restriction to the interval [0, π/2] is highlighted by green dots, and the corresponding inverse function is shown by a green curve.

The restriction to the interval [π/2, π] is highlighted by purple dots, and the corresponding inverse function is shown in purple.

The dashed orange line at y=x is the line over which a function and its inverse are mirror images of each other.

This is similar to the other question you posted. Follow the same steps as before.

First find g(41).

g(41) = sqrt{x - 5}

g(41) = sqrt{41 - 5}

g(41) = sqrt{36}

g(41) = 6

We now find f(6).

f(6) = -7(6) + 1

f(6) = -42 + 1

f(6) = -41

Answer:

(fºg)(41) = -41

Did you follow?

Answer:

65.8 in²

Step-by-step explanation:

Given a triangle with 2 sides and the included angle then the area (A) is

A = 0.5 × a × b × sinΘ

where a, b are the 2 sides and Θ the included angle

here a = 18, b = 12 and Θ = 147°, hence

A = 0. 5 × 18 × 12 × sin147°

   = 108 × sin147° ≈ 65.8 ( to the nearest tenth )

Answer:

The area of triangle is 59.2 in².

Step-by-step explanation:

If a, b and c are three sides of a triangle then the area of triangle by heron's formula is

[tex]A=\sqrt{s(s-a)(s-b)(s-c)[/tex]          .... (1)

where,

[tex]s=\frac{a+b+c}{2}[/tex]

From the given figure it is clear that the length of sides are 12 in, 18 in and 28.8 in. The value of s is

[tex]s=\frac{12+18+28.8}{2}=29.4[/tex]

Substitute s=29.4, a=12, b=18 and c=28.8 in equation (1).

[tex]A=\sqrt{29.4(29.4-12)(29.4-18)(29.4-28.8)}[/tex]

[tex]A=\sqrt{3499.0704}[/tex]

[tex]A=59.15294[/tex]

[tex]A\approx 59.2[/tex]

Therefore the area of triangle is 59.2 in².

Answer:

an=27(one third) - 1

thanks

The correct answer is:

                Option: B

   [tex]B.\ a_n=27(\dfrac{1}{3})^{n-1}[/tex]

We are given that the graph passes through (2,9) , (3,3) and (4,1)

Now, the function which models the graph is given by:

[tex]a_n=27(\dfrac{1}{3})^{n-1}[/tex]

when n=2 we have:

[tex]a_2=27(\dfrac{1}{3})^{2-1}\\\\i.e.\\\\a_2=27(\dfrac{1}{3})^1\\\\i.e.\\\\a_2=9[/tex]

when n=3 we have:

[tex]a_3=27(\dfrac{1}{3})^{3-1}\\\\i.e.\\\\a_3=27(\dfrac{1}{3})^2\\\\i.e.\\\\a_3=3[/tex]

when n=4 we have:

[tex]a_3=27(\dfrac{1}{3})^{4-1}\\\\i.e.\\\\a_3=27(\dfrac{1}{3})^3\\\\i.e.\\\\a_4=1[/tex]

Answer:

x=8a

Step-by-step explanation:

3/a x-4=20

We need to solve for x

Add 4 to each side

3/a x-4+4=20+4

3/a x = 24

Multiply each side by a/3 so we can get x alone

a/3 *3/a x = 24 * a/3

x = 8a

Answer:

x=8a

Step-by-step explanation:

We have to solve for x.

Add 4 to each side

Multiply each side by a/3 so we can get x

Answer:

Step-by-step explanation:

There is an infinite number of lines that pass through the point (2, 11). Therefore, there is an infinite number of equations. To define a single line, you must have at least two points. One point is not enough.

Answer:

Step-by-step explanation:

The number of packets is the greatest common divisor of the given numbers of pencils, erasers, and sharpeners.

It can be helpful to look at the differences between these numbers:

  748 -646 = 102

  646 -527 = 119

The difference of these differences is 17, suggesting that will be the number of packets possible.

  527 = 17 × 31

  646 = 17 × 38

  748 = 17 × 44

The numbers 31, 38, and 44 are relatively prime (31 is actually prime), so there can be no greater number of packets than 17.

There will be 31 pencils, 38 erasers, and 44 sharpeners in each of the 17 packets.

_____

We may have worked the wrong problem. The way it is worded, the maximum number of items in each packet will be 527 pencils, 646 erasers, and 748 sharpeners in one (1) packet. The minimum number of items in each packet will be the number that corresponds to the maximum number of packets. Since 17 is the maximum number of packets, each packet's contents are as described above.

17 is the only common factor of the given numbers, so will be the number of groups (plural) into which the items can be arranged.

Answer:

see explanation

Step-by-step explanation:

Consider the reflection in the y- axis

A point (x, y ) → (- x, y )

Consider the reflection of point A

A(- 5, 2 ) → A'(5, 2 )

Now A → E after the transformations

E = (4, 3 ), thus

A'(5, 2 ) → E(4, 3 )

(x, y ) → (x + (- 1), y + 1 ) = (x - 1, y + 1 )

Answer:

The area of rectangle EFGH is [tex]242\ in^{2}[/tex]

Step-by-step explanation:

For this problem I assume that rectangle ABCD and rectangle EFGH are similar

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

Let

z ------> the scale factor

The scale factor is the ratio between the diagonals of rectangles

so

[tex]z=\frac{22}{12}=\frac{11}{6}[/tex]

step 2

Find the area of rectangle EFGH

we know that

If two figures are similar, then the ratio of its areas is the scale factor squared

Let

z------> the scale factor

x -----> area of rectangle EFGH

y ----> area of rectangle ABCD

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{11}{6}[/tex]

[tex]y=72\ in^{2}[/tex]

substitute and solve for x

[tex](\frac{11}{6})^{2}=\frac{x}{72}[/tex]

[tex]\frac{121}{36}=\frac{x}{72}[/tex]

[tex]x=\frac{121}{36}(72)[/tex]

[tex]x=242\ in^{2}[/tex]

The area of rectangle EFGH is approximately 242 square inches.

To find the area of rectangle EFGH given the diagonal lengths of both rectangles and the area of rectangle ABCD, we need to use the properties of rectangles and their diagonals.

Step 1: Analyze Rectangle ABCD

For rectangle ABCD:

- Area [tex]\(A_{ABCD} = 72\)[/tex] square inches

- Diagonal [tex]\(d_{ABCD} = 12\)[/tex] inches

We know the area of a rectangle is given by:

[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]

Let the length be l and the width be w. So,

[tex]\[ l \times w = 72 \][/tex]

Also, for the diagonal of a rectangle, we use the Pythagorean theorem:

[tex]\[ d = \sqrt{l^2 + w^2} \]\\Given \(d_{ABCD} = 12\),\[ 12 = \sqrt{l^2 + w^2} \]\[ 144 = l^2 + w^2 \][/tex]

Step 2: Solve for l and w

We have two equations:

[tex]1. \( l \times w = 72 \)\\2. \( l^2 + w^2 = 144 \)[/tex]

We can solve these equations simultaneously. First, express \(w\) in terms of \(l\):

[tex]\[ w = \frac{72}{l} \]\\Substitute this into the second equation:\[ l^2 + \left(\frac{72}{l}\right)^2 = 144 \]\[ l^2 + \frac{5184}{l^2} = 144 \][/tex]

Multiply every term by [tex]\(l^2\)[/tex] to clear the fraction:

[tex]\[ l^4 + 5184 = 144l^2 \]\[ l^4 - 144l^2 + 5184 = 0 \]Let \(x = l^2\). Then the equation becomes:\[ x^2 - 144x + 5184 = 0 \][/tex]

Solve this quadratic equation using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\[ x = \frac{144 \pm \sqrt{144^2 - 4 \cdot 1 \cdot 5184}}{2 \cdot 1} \]\[ x = \frac{144 \pm \sqrt{20736 - 20736}}{2} \]\[ x = \frac{144 \pm 0}{2} \]\[ x = 72 \][/tex]

So, [tex]\( l^2 = 72 \) and \( w^2 = 72 \)[/tex]. Therefore:

[tex]\[ l = \sqrt{72} = 6\sqrt{2} \]\[ w = \sqrt{72} = 6\sqrt{2} \][/tex]

Step 3: Analyze Rectangle EFGH

For rectangle EFGH:

- Diagonal [tex]\(d_{EFGH} = 22\)[/tex] inches

Let the length be L and the width be W. The relationship for the diagonal is:

[tex]\[ d_{EFGH} = \sqrt{L^2 + W^2} \]Given \(d_{EFGH} = 22\),\[ 22 = \sqrt{L^2 + W^2} \]\[ 484 = L^2 + W^2 \][/tex]

Step 4: Determine Area of Rectangle EFGH

Since the diagonals scale, we assume the rectangles are similar. Thus, the ratios of the corresponding sides (lengths and widths) are the same, and their areas scale with the square of the ratio of the diagonals:

[tex]\[ \text{Area ratio} = \left(\frac{d_{EFGH}}{d_{ABCD}}\right)^2 = \left(\frac{22}{12}\right)^2 = \left(\frac{11}{6}\right)^2 = \frac{121}{36} \][/tex]

So, the area of EFGH is:

[tex]\[ A_{EFGH} = A_{ABCD} \times \frac{121}{36} = 72 \times \frac{121}{36} = 72 \times 3.3611 \approx 242 \text{ square inches} \][/tex]

Thus, the area of rectangle EFGH is approximately 242 square inches.

Answer:

Step-by-step explanation:

2 x w x l + 2 x l x h + 2 x h x w

* is times  2*5*7+2*7*4+2*4*5 =

= 70+56+40=166 cm

Hope it helps

Answer:

m<AED = 92°

Step-by-step explanation:

It is given that,

measure of arc BC = 38° therefore m<BDC = 38/2 = 19°

measure of arc AD = 146° therefore m<ACD = 146/2 = 73°

To find the measure of <CED

Consider the ΔCDE

m<D = m<BDC = 19° and

m<C = m<ACD = 73°

By using angle sum property  m<CED can be written as,

m<CED = 180 -( m<D + m<C )

 = 180 - (19 + 73)

 = 180 - 92

= 88°

To find the measure of <AED

<AED  and <CED are linear pair

m<AED + m<CED = 180

m<AED = 180 - m<CED

 = 180 - 88

 = 92°

Therefore m<AED = 92°

Answer:

  see below

Step-by-step explanation:

To find miles per hour, divide miles by hours:

  (5 2/3 mi)/(2 2/3 h) = (17/3 mi)/(8/3 h) = (17/8) mi/h = 2 1/8 mi/h

Hours per mile is the reciprocal of that:

  1/(17/8 mi/h) = 8/17 h/mi

Answer:89

Step-by-step explanation:

Given scott had an average of 83 on his first three exams

i.e. the sum of first three exams [tex]\sum S_1=83\times 3[/tex]

later he scored an average on the next six exams

i.e. the sum of later 6 exams is [tex]\sum S_2=92\times 6[/tex]

[tex]\sum S_1+\sum S_2=83\times 3+92\times 6=801[/tex]

therefore his average score is =[tex]\frac{801}{9}=89[/tex]

Thus his average score is 89

To find Scott's average for all nine exams, add up the scores from the first three and next six exams, then divide by the total number of exams.

To find Scott's average for all nine exams, we need to calculate the overall average using the given averages for the first three and next six exams.

The average of the first three exams is 83, and the average of the next six exams is 92. To find the average for all nine exams, we can use the formula:Total sum of scores / Number of exams

So, Scott's average for all nine exams is:(83*3 + 92*6) / 9 = 89.1111...

Rounding to the nearest tenth, Scott's average for all nine exams is 89.1.

Learn more about Calculating averages here:

https://brainly.com/question/18554478

#SPJ3

Answer:

see below

Step-by-step explanation:

sqrt(2) * sqrt(2) = sqrt(4) = 2

sqrt(5) * sqrt(7) = sqrt(35)

sqrt(2) * sqrt(18) = sqrt(36) = 6

sqrt(2)*sqrt (6) = sqrt(12) = sqrt(4 *3) = sqrt(4) sqrt(3) = 2 sqrt(3)

4/3 * 12/3 = 48/9  This is rational because it is written as a fraction with no square roots

32/4 * 15/4 = 480/16 =30  This can be rewritten as 30/1.  This is rational because it is written as a fraction with no square roots

sqrt(3)/2 * 22/7 = 11 sqrt(3)/7  This is not rational because there is a square root in the numerator

sqrt(11) *2/3 = 2sqrt(11)/3 This is not rational because there is a square root in the numerator

Check the picture below.

[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2\qquad \implies SA=\pi (8)\sqrt{164}+ \pi (8)^2 \\\\\\ SA=8\pi \sqrt{164}+ 64\pi \implies \stackrel{\pi =3.14~\hfill }{SA\approx 522.65296}\implies \stackrel{\textit{rounded up}}{SA=522.65}[/tex]

Answer:

522.75 yards2 is correct.

Step-by-step explanation:

Answer:

horizontal stretch

Step-by-step explanation:

yeye

Parent functions are the simplest form of a given function. Parent function have x as the term with the highest degree and a general form,

[tex]Y=ax+b[/tex]

Transformation of the function takes basic and changes it slightly with predetermined methods. This change will cause the graph of the function to be shifted or moved from the original position.

Given-

We have given the graphs and we have to identify the transformation of the parent function which is shown in the graph. For this we have an idea about the parent function and transformation of the function.

Parent functions are the simplest form of a given function. Parent function have x as the term with the highest degree and a general form,

[tex]Y=ax+b[/tex]

Transformation of the function takes basic and changes it slightly with predetermined methods. This change will cause the graph of the function to be shifted or moved from the original position.

Transformation of function is of different types.

In the given graph the graph is shifted right and hence the transformation of the parent function is horizontal stretch.

Learn more about the transformation of the function here;

https://brainly.com/question/4135838

Answer:

Step-by-step explanation:

x is a "corresponding" angle for the one marked 63°. Here, corresponding angles are congruent, so x = 63°.

__

x and z are "same-side interior angles," so are supplementary. Their sum is 180°. x + z = 180°.

__

Because x and z are supplementary and z and 63° are supplementary, you know that ...

  z = 180° -63°

  z = 117°

_____

Comments on the other answer choices

The value of y can be computed using the fact that the sum of angles interior to the triangle is 180°. The unmarked triangle interior angle is a vertical angle to the one labeled 63°, so it is 63°. Then the value of y is ...

  y° = 180° -47° -63° = 70° . . . . . . . not 47°

__

We already know that 63° + y + 47° = 180° and x = 63°. That means ...

  x + y + 47° = 180°

so it cannot be true that x+y = 180.

Answers are 1,3, and 5

Answer:

Answer C

Step-by-step explanation:

Logs work that way. When you subtract one log from another, you can rewrite it as a fraction.

f and h, because the log of a quotient is the difference of the log.

The answer is option C.

Logs work that way. When you subtract one log from another, you can rewrite it as a fraction.

A logarithm is a power to which a range of should be raised for you to get a few different wide varieties (see segment 3 of this Math evaluate for extra approximately exponents). As an example, the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.

Learn more about logarithm here: https://brainly.com/question/25710806

#SP2

Answer:

  15/17

Step-by-step explanation:

You can use what is called the Pythagorean identity:

  sin(θ)² + cos(θ)² = 1

  (-8/17)² + cos(θ)² = 1

  cos(θ)² = 1 - 64/289 = 225/289

  cos(θ) = √(225/289)

  cos(θ) = 15/17 . . . . . . . cosine is positive in the 4th quadrant

Answer:

  9 rolls

Step-by-step explanation:

The perimeter of the room measures 2(19' +12') = 62', so the area of the walls is ...

  (62 ft)(8.5 ft) = 527 ft²

We know that 8 rolls will cover 8×60 ft² = 480 ft², and 9 rolls will cover 540 ft², so we will need 9 rolls to cover the walls.

Answer:

1 hour and 40 minutes

Step-by-step explanation:

Levi's dad takes time to wash the car by himself is 1.667 hours which is 1 hour and 40 minutes.

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour.

Levi's dad take time to wash the car by himself will be

We know that the time is inversely proportional to the work.

Let t₁ is the time taken by Levi and t₂ is the time taken by Levi's dad.

We know that the formula

[tex]\begin{aligned} \dfrac{1}{t_1} + \dfrac{1}{t_2} &= 1\\\\\dfrac{1}{2.5} +\dfrac{1}{t_2} &= 1\\\\\dfrac{1}{t_2} &= 1 - \dfrac{1}{2.5}\\\\\dfrac{1}{t_2} &= \dfrac{3}{5}\\\\t_2 &= \dfrac{5}{3}\\\\t_2 &= 1.667 \end{aligned}[/tex]

Levi's dad takes time to wash the car by himself is 1.667 hours which is 1 hour and 40 minutes.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

The ratio of the lengths of EF and BC is 2:1. The correct answer is (EF, BC), where the length of EF is twice the length of BC.

The ratio of the lengths of two segments is given as 2:1. We can set up a proportion and find that the length of one segment is twice the length of the other.

In this question, the ratio of the lengths of two segments is given as 2:1. We are asked to find the lengths of the two segments, which are represented by two choices: (EF, BC) and (AD, IH). To solve this problem, we can set up a proportion. Let's assume that EF and BC represent the lengths of the segments, and we can write the proportion as:

[tex]\frac {EF}{BC} =\frac {2}{1}[/tex]

To solve for the lengths, we can cross multiply:

[tex]EF \times 1 = BC \times 2[/tex]

[tex]EF = 2 \times BC[/tex]

So, the length of EF is twice the length of BC. Therefore, the correct answer is (EF, BC), where the length of EF is twice the length of BC.

Final answer:

The student's question deals with the concept of ratios and similar triangles in High School level Mathematics. Without additional context to the specific figures and points mentioned, a precise answer cannot be given. Typically, in similar triangles, corresponding side lengths are proportional, allowing calculation of unknown lengths when a ratio is provided.

Explanation:

The question refers to finding a ratio of lengths related to geometrical figures. Since ratios and proportions frequently deal with lengths and geometry, and the provided examples reference triangles, circles, and other geometric shapes, this question is most closely related to the subject of Mathematics. The use of similar triangles to find unknown lengths is a typical high school-level geometry problem.

Based on the information given in the question, it seems we are required to use the property that states the ratios of corresponding sides of similar triangles are equal. To answer the student's question specifically, we'd need more context to the figures in question, such as circle C with center F and point F', or the configuration of the triangles abc and a'b'c'.

For instance, if we have two similar triangles, with corresponding side lengths in a ratio of 2:1, this means that if one triangle has a side length of 'x', the similar triangle's corresponding side length would be '2x'. To answer the student's query correctly, however, additional information on which particular sides of the named points are being inquired about is necessary.

Check the picture below.

Answer:

  1231 km/h

Step-by-step explanation:

The average speed is given by ...

  average speed = (total distance)/(total time)

The total time will be the sum of times down and back, each of which is given by ...

  time = distance/speed

Going to Mexico, the time required was ...

  time down = (2000 km)/(1600 km/h) = 1.25 h

Coming back, the time required was ...

  time back = (2000 km)/(1000 km/h) = 2.00 h

Then the average speed is ...

  average speed = (2000 km + 2000 km)/(1.25 h +2.00 h) = 4000/3.25 km/h

  ≈ 1231 km/h

_____

Comment on average speed

The value we computed was ...

  2/(1/s1 + 1/s2) . . . . where s1 and s2 are the speeds over the same distance

This is the harmonic mean of two numbers (the two speeds). The harmonic mean of n numbers is ...

  harmonic mean = n/(1/a1 +1/a2 +1/a3 + ... + 1/an)

This mean generally finds less use than the typical arithmetic mean or geometric mean.

  arithmetic mean = (a1 + a2 + a3 + ... + an)/n

  geometric mean = (a1·a2·a3·...·an)^(1/n)

Chris would need to drive 650 miles for the two plans to cost the same.

Further Explanation:

Let d = distance traveled in miles

Plan 1 will have an initial fee of $65 and a cost of $0.80 per mile driven. Therefore, the total cost to drive a distance of d will be:

total cost = $65 + ($ 0.80 × d)

Plan 2 will have no initial fee but has a cost of $0.90 per mile drive. The total cost, then, to drive a distance of d will be:

total cost = $0.90 × d

If the two costs are the same, then:

$65 + ($ 0.80 × d) = $0.90 × d

The distance driven, d, can then be solved algebraically.

Combining like terms:

$65 = $0.90d - $0.80d

$65 = $0.10d

Solving for d:

d = $65/$0.10

d = 650 miles

To check the answer, solve for the total cost of Plan 1 and Plan 2 and see if they are equal.

Plan 1:

total cost = $65 + ($0.80 x 650)

total cost = $65 + $520

total cost = $585

Plan 2:

total cost = $0.90 x 650

total cost = $585

Since both plans cost the same, then the distance 650 mi is correct.

Learn More

Keywords: word problem, total cost

Answer:

true

Step-by-step explanation:

false because it would just be 2y+4y -1y*2=6

5y*2=6

divide 2

5y+1=6

5y=5

divide 5 to each

then then the answer is 1

Answer:

True

Step-by-step explanation:

Solve the equation for Y by finding a, b, and of the quadratic then applying the quadratic formula.

Answer:

[tex]\large\boxed{\text{Nine over eighteen}}[/tex]

Step-by-step explanation:

In this question, we're trying to find the probability of picking a person that is a male or a doctor.

We know that there are:

With the information above, we can find the probability.

Lets first find how many male nurses there are. To find this, we would get our total amount of nurses (15) and subtract it by 9, due to the fact that 9 of the nurses are female.

[tex]15-9=6[/tex]

This means that there are 6 male nurses.

6 would be added to our probability.

We're not done yet, we also need to add the chance of getting a doctor in our probability.

Since there's 3 doctors, we would just add 3 to our probability.

[tex]6+3=9[/tex]

Now, we need to find the total. When we add all together, we would get 18. This means that 18 would go on our denominator and 9 will go on our numerator.

This means that the chance of getting a male or a doctor would be [tex]\frac{9}{18}[/tex], or nine over eighteen.

Answer:

Point-slope form:

[tex]y-0=\frac{1}{3} (x-1)\\f(x)-0=\frac{1}{3}(x-1)[/tex]

Slope-intercept form:

[tex]y=\frac{1}{3}x-\frac{1}{3} \\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]

Step-by-step explanation:

You have points on that line at (-2, -1) and (1, 0). To find your slope using those points, use the slope formula.

[tex]\frac{y2-y1}{x2-x1} \\\\\frac{0-(-1)}{1-(-2)} \\\\\frac{0+1}{1+2} \\\\\frac{1}{3}[/tex]

Now that we have your slope, you can use your slope and one of your points to write an equation in point-slope form.

[tex]y-y1=m(x-x1)\\y-0=\frac{1}{3} (x-1)\\y=\frac{1}{3} x-\frac{1}{3}[/tex]

To put it in function notation, substitute y for f(x).

[tex]f(x)-0=\frac{1}{3} (x-1)\\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]

First answer is y+1=(1/3) (x+2)

Second answer is f(x) =(1/3) x-(1/3)

Answer:

3lbs of Cashews

Step-by-step explanation:

lbs of Cashews, and 7 lbs of Peanuts

$4.00P + 6.50C = ($4.75/lbs)(10lbs)

$4.00(7) + $6.50(3) = $47.50

$28.00 + $19.50 = $47.50

$47.50 = $47.50

Therefore it's 3lbs of Cashews

Answer:

3lbs of Cashews

hope it helps! x