Which expression is a sum of cubes?

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:

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.

Check the picture below.

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.

He drives 55 miles per hour for x hours. You want to multiply the number of hours by his speed , so you have 55x.

Then you want to subtract that from the total miles he has to drive.

The equation is Y = 385 - 55x

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:

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

Answer:

-81

Step-by-step explanation:

b=a+3

Subtract 3 from each side

b=a+3

b-3 = a+3-3

b-3 =a

Then subtract b from each side

b-b-3 = a-b

-3 = a-b

We want (a-b) ^4

We know a-b = -3

(-3) ^4

-81

Answer:

  22 ft/s

Step-by-step explanation:

15 mph is 1/4 of 60 mph. At 1/4 the speed, the car will travel 1/4 as far in a second.

  1/4×(88 ft/s) = 22 ft/s

Answer:

22 ft/s

Step-by-step explanation:

At 60 mph a car travels  88 feet per second. There are 22 feet per second that a car  travels at 15 mph.

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:

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 )

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?

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:

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: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:

the point estimate of the true proportion of employees is 0.401

Step-by-step explanation:

Given data

plan A = ( 0.241 , 0.561 )

to find out

the point estimate for estimating the true proportion of employees who prefer that plan

solution

we know that given data 98% confidence interval for the proportion of employees who prefer plan A: (0.241, 0.561) so point estimate for estimating the true proportion o employees who prefer that plan is p^E

and we can say here  

lower limit = [tex]p^{-E}[/tex] = 0.241    ..............1

upper limit = [tex]p^{+E}[/tex]  = 0.561    ...............2

now add these two equations 1 and 2

=  [tex]p^{-E}[/tex] + [tex]p^{+E}[/tex]

=  [tex]p^{-E}[/tex] + [tex]p^{+E}[/tex]  = 0.241 + 0.561

2 p = 0.802

2p = 0.806

p = 0.401

So the point estimate of the true proportion of employees is 0.401

The point estimate in this scenario is 0.401, which is the estimated proportion of employees who prefer Plan A. This is calculated by averaging the lower and upper limits of the given 98% confidence interval.

The question is asking for the point estimate which is a single value used as an estimate of the population parameter. In a confidence interval, the point estimate is the mid-point or center of the interval. Here, the confidence interval given for the proportion of employees preferring Plan A is (0.241, 0.561). To find the point estimate, you average the two end values.

The formula for finding the point estimate is: (Lower limit + Upper limit) / 2.

Applying the values from your question: (0.241 + 0.561) / 2 = 0.401.

So, the point estimate, or the estimated true proportion of employees who prefer Plan A, is 0.401.

https://brainly.com/question/32817513

#SPJ6

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:

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:

Part a) 0.63

Part b) 0.22

Part c) 0.68

Step-by-step explanation:

The individual probabilities are calculated as

1) Probability of scoring in first attempt = 70%

2) Probability of missing in first attempt = 30%

3)  Probability of scoring in second attempt provided she scores in first attempt = 90%

4)  Probability  of missing in second attempt provided she scores in first attempt = 10%

5) Probability of scoring in 2nd attempt provided she misses in ist attempt = 50%

6)  Probability of missing in 2nd attempt provided she misses in ist attempt = 50%

Part a)

probability of making the throw exactly  both the times = [tex]P(ist)\times P (2nd)[/tex]

Applying values we get

probability of making the throw exactly  both the times= [tex]0.7\times 0.9=0.63[/tex]

Part b)

She will make it exactly once if

1) She scores in first attempt and misses second

2) She misses in first attempt and scores in  the second attempt

Probability of case 1 = [tex]0.7\times 0.1=0.07[/tex]

Probability of case 2 =[tex] 0.3 \times 0.5 =0.15[/tex]

Thus probability She will make it exactly once equals [tex] 0.15+0.07=0.22[/tex]

Part c)

It is a case of conditional probability

Now by Bayes theorem we have

[tex]P(B|A)=\frac{P(B\cap A)}{P(A)}[/tex]

P(B|A) is the probability of scoring in second attempt provided that she has scored only once

P(B) is the probability of scoring exactly once

Given that she makes it exactly once [tex]\therefore P(A)=0.22[/tex]

[tex]P(B\cap A)=0.15[/tex]

using these values we have

[tex]P(B|A)=\frac{0.15}{0.22}\\\\P(B|A)=0.68[/tex]

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:

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

A reflection along parallel line l and m is the same as a translation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

A composition of reflection over two parallel lines is the same as a translation, hence:

Find out more on translation at: https://brainly.com/question/12861087

Answer: the answer would be choice A

Step-by-step explanation: it passes through the origin making it a proportional relationship

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)

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:

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:

  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.