A plane has a cruising speed of miles per hour when there is no wind. At this speed, the plane flew miles with the wind in the same amount of time it flew miles against the wind. Find the speed of the wind.

Answer:

B) 57 is the answer

Step-by-step explanation:

Let's try to make the given figure a parallelogram by extending DE and BA to F.

So now we have a complete parallelogram.

<AEF = 180 - 112 Since they are linear pairs

so, <AEF = 68

Now,

<EAF = 180 - 125 = 55

So, <AFE = 180-68-55 (interior angles of triangle sum up to 180)

<AFE = 57

Opposite angles of parallelogram are equal so,

<AFE = <BCD = 57°

The correct equation that shows the area of painted area is

A=[tex]x^{2} -8x-16[/tex].

Given that the length of the  floor,x,is atleast 12 feet.The width of the floor is 4 feet less than the length.There is a right angle of height x-4 and base 8 feet. The rectangle inside has length of 8 feet and width be 4 feet.

We are required to find the painted area of the theater room in square feet.

To find the painted area of the theater the following steps must be followed:

1) Find the area of the theater room.

length =x

Breadth=x-4

Area=x(x-4)

=[tex]x^{2} -4x[/tex]

2) Area of the right triangle.

Height=x-4

Base=8

Area=1/2 *8*(x-4)

=4(x-4)

=4x-16

3) Find the area of the rectangle inside labeled closet.

Length=8

Width=4

Area=8*4

=32

Area=Area of theater room-Area of of right triangle-Area of closet.

=[tex]x^{2} -4x[/tex]-4x+16-32

=[tex]x^{2} -8x-16[/tex]

Hence the correct equation that shows the area of painted area is

A=[tex]x^{2} -8x-16[/tex].

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Answer:

A = x(x − 4) − 0.5(8)(x − 4) − 3(7)

Work:

x = length, making the width (x-4)

The stage closet will be (x-4)(8)(1/2)

The rectangle is 7(3)

which makes the painted area x(x-4) - 4(x-4)

thus giving us

x(x − 4) − 0.5(8)(x − 4) − 3(7)

Step-by-step explanation:

hope this helps :)

The number of outcomes possible from flipping each coin is 2, therefore;

The possible outcome of flipping 4 coins is given by the sum of the possible combinations of outcomes as follows;

The number of possible outcome from flipping the first coin = 2 (heads or tails)

The outcomes from flipping the second coin = 2

The outcome from flipping the third coin = 2

The outcome from flipping the fourth coin = 2

The combined outcome is therefore;

Outcome from flipping the 4 coins = 2 × 2 × 2 × 2

The correct option is therefore;

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Answer:81.85 km/hr is the average speed

Step-by-step explanation:

Answer: ≈ 84,3 km/h.

Step-by-step explanation:

[tex]\displaystyle\\V{average}=\frac{\Delta S}{\Delta t}=\frac{S_1+S_2+S_3}{t_1+t_1+t_3} .\\1.\ S_1=50\ km\\ t_1=\frac{S_1}{V_1}\\ V_1=25*\frac{3600}{1000} \\V_1=90\ \frac{km}{h} .\\t_1=\frac{50}{90}\\ t_1=\frac{5}{9} \ h.\\2.\ S_2=120\ km\ \ \ \ V_2=80\ \frac{km}{h} \\t_2=\frac{S_2}{V_2} \\t_2=\frac{120}{80} \\t_2=\frac{3}{2}\ h.\\[/tex]

[tex]3.\ V_3=90\ \frac{km}{h} \\t_3=35\ minutes\\t_3=\frac{35}{60} \\t_3=\frac{7}{12}\ h.\\ S_3=V_3*t_3\\S_3=90*\frac{7}{12} \\S_3=52,5\ km.\\Hence,\\V{average}=\frac{50+120+52,5}{\frac{5}{9}+\frac{3}{2} +\frac{7}{12} } \\V{average}=\frac{222,5}{\frac{95}{36} } \\Vaverege\approx84,3\ \frac{km}{h} .[/tex]

The value of the given function if x = 2 and y = 4 is 37 3/5

Functions are expressions used to determine the relationship between two or more variables.

For instance, f(x) is pronounced as the function of x. Given the expression below

(y+x)² + 4/5x

Given the following parameters

x = 2

y = 4

Substitute the given parameters

f(x,y) = (y+x)² + 4/5x

f(2, 4) = (4+2)² + 4/5(2)
f(2,4) = 6^2 +8/5

f(2, 4) = 36 + 8/5

f(2, 4) = 180+8/5

f(2, 4) =188/5

f(2, 4) = 37 3/5

Hence the value of the given function if x = 2 and y = 4 is 37 3/5

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Answer:

HL

Step-by-step explanation:

The hypotenuses and the long legs of the right triangles are congruent, therefore using the rule HL, the triangles are congruent.

The data which is most likely to be normally distributed is total points scored by a basketball team the whole season.

Given five statements:

1)Daily temperature highs for winter in 25 US cities.

2)Daily stock reports from the stock market.

3) Height of flowers.

4) Total points scored by a basketball team the whole season.

We are required to choose a statement whose data is most likely to be normally distributed.

A normal distribution is an arrangement of data set in which most values cluster in the middle of the range and the rest off symmetrically towards either extreme.It is basically a probability distribution that is most likely symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. Its graph is a bell curve.

So,the statement which is likely to be normally distributed is total points scored by a basketball team the whole season.

Hence the data which is most likely to be normally distributed is total points scored by a basketball team the whole season.

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By finding some points on the curve and then connecting them.

Here we have the rational function:

t = d/s

Where t represents time, d distance, and s speed.

We assume that d is a fixed value, then our variables are time and speed.

On the examples, you can see that the value of d is:

d = 616.5km, then we just need to graph the equation:

t = (616.5km)/s

To do so, you can evaluate the function in different values of s, like the points the problem asks to graph, and then connect all these points with a curve.

Doing that, you should get a graph like the one below:

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The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard equation of a circle is:

(x - h)² + (y - k)² = r²

Where (h, k) is the circle center and r is the radius of the circle.

The diameter of the circle DE is at D(-3, 3) and E(13, 11). Hence the coordinate of point center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7)

[tex]Diameter = \sqrt{(3-11)^2+(-3-13)^2} = 8\sqrt{5}[/tex]

Radius = diameter / 2 = 8√5 ÷ 2 = 4√5

The equation of the circle is:

(x - 5)² + (y - 7)² = (4√5)²

(x - 5)² + (y - 7)² = 80

The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80

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The inequality that describes p, the area of a pizza that is larger than a small pizza 730 < p

From the information given, we have that;

Area of the small pizza = 730 square centimeters

p  = area of the larger pizza

In writing inequality, we have to use the signs

<  less than

> greater than

Since p has greater area, we have

730 < p

Thus, the inequality that describes p, the area of a pizza that is larger than a small pizza 730 < p

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Answer:

the answer is actually p > 730

Step-by-step explanation:

i juts checked on Kahn academy and i got it right..

Answer:

174m²

Step-by-step explanation:

SA = 2(wl + hl + hw)

= 2(5m x 11m + 2m x 11m + 2m x 5m)

= 2(55m² + 22m² + 10m²)

= 2 x 87m²

=174m²//

Answer:

[tex]r =\bf 8 \space\ cm[/tex]

Step-by-step explanation:

The formula for volume of a cylinder is as follows:

[tex]\boxed{Volume = \pi r^2 h}[/tex]

where:

• r = radius (? cm)

• h = height (7 cm).

Substituting the values into the formula:
[tex]448 \pi = \pi \times r^2 \times 7[/tex]

Now solve for [tex]r[/tex]:

⇒ [tex]r^2 = \frac{448 \pi }{\pi \times 7}[/tex]

⇒ [tex]r = \sqrt{64}[/tex]

⇒ [tex]r =\bf 8 \space\ cm[/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:

[tex]\longrightarrow\sf{V= \pi r^2 h}[/tex]

[tex]\longrightarrow\sf{448 \pi= \pi r^2 \cdot 7}[/tex]

[tex]\longrightarrow\sf{448=

7r^2}[/tex]

[tex]\longrightarrow\sf{r^2= \dfrac{448}{7} }[/tex]

[tex]\longrightarrow\sf{r^2=64}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\longrightarrow\sf{r= 8cm}[/tex]

Answer:

1a. 100, 1b. 22

Step-by-step explanation:

1a. Given information from the question:

[tex] \frac{b}{46} = \frac{50}{23} \\ 23b = (50)(46) \: (cross \: multiply) \\ b = \frac{50 \times 46}{23} \\ = 50 \times 2 \\ = 100[/tex]

1b. Given information from the question:

[tex] \frac{34}{d} = \frac{68}{44} \\ 68d = (34)(44) \: (cross \: multiply)\\ \\ d = \frac{34 \times 44}{68} \\ d = \frac{44}{2} \\ = 22[/tex]

Answer:

• [tex]b = \bf 100[/tex]

• [tex]d = \bf 22[/tex]

Step-by-step explanation:

To solve these questions, we need to rearrange the equations to make the unknown variables the subject of the equations.

1a.

[tex]\frac{b}{46} = \frac{50}{23}[/tex]

⇒ [tex]b = \frac{50 \times 46}{23}[/tex]             [multiplying both sides by 46]

⇒ [tex]b = \bf 100[/tex]

1b.

[tex]\frac{34}{d} = \frac{68}{44}[/tex]

⇒ [tex]34 = \frac{68 \times d}{44}[/tex]               [multiplying both sides by d]

⇒ [tex]34 \times 44 = 68 \times d[/tex]    [multiplying both sides by 44]

⇒ [tex]\frac {34 \times 44}{68} = d[/tex]               [dividing both sides by 68]

⇒ [tex]d = \bf 22[/tex]

Using the given data, the average percent score for the 100 students is 77[tex]\%[/tex].

Average, also known as mean, is one of the measures of central tendency and is the ratio of the sum of all observations to the total number of observations. It is very useful to summarize a probability distribution.

Let the average percent score for the 100 students be N.

As it is known that the average is the ratio of the sum of all observations to the total number of observations, therefore:

[tex]N = \dfrac{100\times7+90\times18+80\times35+70\times25+60\times10+50\times3+40\times2}{100}[/tex]

   [tex]= \dfrac{7700}{100}\\= 77[/tex]

Thus, the average percent score for the 100 students, using the given data is calculated as 77[tex]\%[/tex].

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The complete question is as follows:

Mrs. Riley recorded this information from a recent test taken by all of her students. Using the data, what was the average percent score for these 100 students?

[tex]\%[/tex] Score  Number of students

100                  7

90                   18

80                   35

70                   25

60                   10

50                   3

40                   2

Total number of men and women wearing sunglasses = 290

According to the question,

Total number of men and women = 2000

half of the adults were women = 1/2 × 2000

Number of women = 1000

Number of men = (Total adults) - (Number of women )

Number of men = 2000 - 1000

= 1000

given,

20% of women were wearing sunglasses = 20/100 × 1000

= 200

9% of men were wearing sunglasses = 9/100 × 1000

= 90

Total number of adults wearing glasses = 200 + 90

= 290

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

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Answer:

5050

Step-by-step explanation:

we know that 100/2 is 50 and 50 x 100 is 5000

so now another 50 is remaining but we can't multiply but add so

1+2+3+4+5...100 = in simple form= 50x100+50=5050//

Answer:

  m∠B ≈ 70.8°

Step-by-step explanation:

The Law of Cosines relates three sides of a triangle and the angle opposite one of them.

The law of cosines tells you ...

  b² = a² +c² -2ac·cos(B)

Solving for angle B, we get ...

  B = arccos((a² +c² -b²)/(2ac))

where 'a' and 'c' are the sides adjacent to the angle of interest. We want angle B, so we can fill this formula as follows:

  B = arccos((13² +11² -14²)/(2·13·11))

  B = arccos(94/286)

  B ≈ 70.812°

__

Additional comment

Another angle can be found using the Law of Sines.

  A = arcsin(sin(70.812°)×13/14) ≈ 61.281°

Then angle C is ...

  C = 180° -70.812° -61.281° = 47.907°

Answer:

9/50

Step-by-step explanation:

We simply divide the pizza we have (9/10) by the number of friends (5):

9/10 : 5 = 9/50

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

Suppose an infinity sequence defined by:

[tex]\sum_{k = 0}^{\infty} f(k)[/tex]

Then we have to calculate the following limit:

[tex]\lim_{k \rightarrow \infty} f(k)[/tex]

If the limit goes to infinity, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

[tex]f(k) = \frac{k^3}{k^4 + 10}[/tex]

Hence the limit is:

[tex]\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0[/tex]

Hence, the infinite sequence converges, as the limit does not go to infinity.

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The series diverges by the comparison test.

We have for large enough [tex]k[/tex],

[tex]\displaystyle \frac{k^3}{k^4+10} \approx \frac{k^3}{k^4} = \frac1k[/tex]

so that

[tex]\displaystyle \sum_{k=0}^\infty \frac{k^3}{k^4+10} = \frac1{10} + \sum_{k=1}^\infty \frac{k^3}{k^4+10} \approx \frac1{10} + \sum_{k=1}^\infty \frac1k[/tex]

and the latter sum is the divergent harmonic series.

Using it's concept, the probability of choosing a number that is a multiple of 9 is of 0.111.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

From 1 to 81, there are 81 numbers, of which 81/9 = 9 are multiples of 9, hence, considering that 81 is the number of total outcomes and that 9 is the number of desired outcomes, the probability is given the following division:

p = 9/81 = 1/9 = 0.111.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{2a} + \cfrac{9}{10} = \cfrac{5}{12a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{2a} - \cfrac{5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7(6) - 5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{42 - 5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 37(10) = - 9(12a)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 370 = - 108a[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = - \cfrac{370}{108} [/tex]

[tex]\qquad \sf  \dashrightarrow \: a = - \dfrac{185}{54} [/tex]

[tex]\boldsymbol{\sf{\dfrac{4}{5}+\dfrac{9}{10} } }[/tex]

The least common multiple of 5 and 10 is 10. Convert 4/5 and 9/10 to fractions with denominators of 10.

[tex]\boldsymbol{\sf{\dfrac{4\times2}{5\times2}+\dfrac{9}{10} \ \ \to \ \ Simplify }}[/tex]

[tex]\boldsymbol{\sf{ \dfrac{8}{10}+\dfrac{9}{10} }}[/tex]

Since 8/10 and 9/10 have the same denominator, join their numerators to add them.

[tex]\boldsymbol{ \sf{\dfrac{8+9}{10} \ \to \ \ Add }}[/tex]

Simplify

[tex]\boldsymbol{\sf{ \dfrac{17}{10}= }}\boxed{\boldsymbol{\sf{1\frac{7}{10} }}}[/tex]

a. The area of [tex]R[/tex] is given by the integral

[tex]\displaystyle \int_1^2 (x + 6) - 7\sin\left(\dfrac{\pi x}2\right) \, dx + \int_2^{22/7} (x+6) - 7(x-2)^2 \, dx \approx 9.36[/tex]

b. Use the shell method. Revolving [tex]R[/tex] about the [tex]x[/tex]-axis generates shells with height [tex]h=x+6-7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le 2[/tex], and [tex]h=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With radius [tex]r=x[/tex], each shell of thickness [tex]\Delta x[/tex] contributes a volume of [tex]2\pi r h \Delta x[/tex], so that as the number of shells gets larger and their thickness gets smaller, the total sum of their volumes converges to the definite integral

[tex]\displaystyle 2\pi \int_1^2 x \left((x + 6) - 7\sin\left(\dfrac{\pi x}2\right)\right) \, dx + 2\pi \int_2^{22/7} x\left((x+6) - 7(x-2)^2\right) \, dx \approx 129.56[/tex]

c. Use the washer method. Revolving [tex]R[/tex] about the [tex]y[/tex]-axis generates washers with outer radius [tex]r_{\rm out} = x+6[/tex], and inner radius [tex]r_{\rm in}=7\sin\left(\frac{\pi x}2\right)[/tex] if [tex]1\le x\le2[/tex] or [tex]r_{\rm in} = 7(x-2)^2[/tex] if [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each washer has volume [tex]\pi (r_{\rm out}^2 - r_{\rm in}^2) \Delta x[/tex]. As more and thinner washers get involved, the total volume converges to

[tex]\displaystyle \pi \int_1^2 (x+6)^2 - \left(7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \pi \int_2^{22/7} (x+6)^2 - \left(7(x-2)^2\right)^2 \, dx \approx 304.16[/tex]

d. The side length of each square cross section is [tex]s=x+6 - 7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le2[/tex], and [tex]s=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each cross section contributes a volume of [tex]s^2 \Delta x[/tex]. More and thinner sections lead to a total volume of

[tex]\displaystyle \int_1^2 \left(x+6-7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \int_2^{22/7} \left(x+6-7(x-2)^2\right) ^2\, dx \approx 56.70[/tex]

The average cost of weekly groceries exists at $124.50." The statistical measurement exists they most probably claim exists mean.

The arithmetic mean of a given data exists as the totality of all observations divided by the number of observations.

For instance, a cricketer's scores in five ODI matches exist as follows:

12, 34, 45, 50, 24.

To estimate his average score in a match, we compute the arithmetic mean of data utilizing the mean formula:

Mean = Sum of all observations/Number of observations

Median

The value of the middlemost observation, acquired after organizing the data in ascending or descending order, exists named the median of the data.

For instance, consider the data: 4, 4, 6, 3, 2. Let's organize this data in ascending order: 2, 3, 4, 4, 6. There exist 5 observations.

Therefore, median = middle value i.e. 4.

Mode

The value which occurs most often in the provided data i.e. the observation with the highest frequency exists named a mode of data.

As per the circumstances we have given the average cost of groceries.

The mean exists also the average sum of data divided by the total number of data.

Therefore, the statistical measurement exists as the mean.

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The expression which represents Daria's total cost is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05

Total cost = x + (5% of x)

= x + (0.05 × x)

= x + (0.05x)

Total cost = 1.05x

Therefore, the correct answer is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05

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Answer:

  21.0 m²

Step-by-step explanation:

The formula for the area of a triangle from two sides and the included angle is ...

  A = 1/2ab·sin(C)

Using this formula, we find the area to be ...

  A = 1/2(14 m)(8 m)sin(22°) = 21.0 m²

The area of triangle ABC is about 21.0 square meters.

The volume of the quarter-sized tank is 14034 cubic feet and  the volume of the holding tanks is 84857 cubic feet

The radius is given as;

r = 95 feet

For a quarter-sized tank, we divide the radius by 4.

So, we have

r = 95/4 feet

r = 23.75 feet

The volume is

V = 1/3 πr³

This gives

V = 1/3 * 22/7 * 23.75³

Evaluate

V = 14034

Hence, the volume of the quarter-sized tank is 14034 cubic feet

Here, we have

Radius, r = 15 feet

Height, h = 120 feet

The volume is

V = πr²h

This gives

V = 22/7 * 15² * 120

Evaluate

V = 84857

Hence, the volume of the holding tanks is 84857 cubic feet

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Step-by-step explanation:

since it has a hypotenuse C

using pythagoras theroem

hpy²=opp²+adj²

=(5)²+(5√7)²

=25+175

=200

hyp=√200

=10√2

Based on the given graphs and their equations, the solutions will be located at points (-2, 7) and (0, 1).

To find the solution to y = -2x+ 3, assume that x is a certain number then solve for y.

Given the options, we can assume that x = -2. Solution is:

= -2(-2) + 3

= 4 + 3

y = 7

Solution point is (-2, 7)

The second equation can be solved by equating x to 0:
y = 0² - 0 + 1

y = 1

Solution point is:

= (0, 1)

In conclusion, the solution points are (-2, 7) and (0,1).

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