An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30o angle. To the nearest foot, how far does a person travel from the bottom to the top of the escalator?
a) 50 ft
b) 43 ft
c) 87 ft
d) 25 ft

Answer:

There are 1240 students who attended Washington Middle School.

Step-by-step explanation:

Given:

Students who attend Washington Middle School are either in seventh or eighth grade.

At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.

Seventh graders represented 60% of the students on the honor roll.

If 124 students on the honor roll were in eighth grade.

Now, to find the students attend Washington Middle School.

Let the total number of students be [tex]x.[/tex]

So, the students at Washington Middle School were on the honor roll:

25% of [tex]x[/tex]

[tex]=\frac{25}{100} \times x[/tex]

[tex]=\frac{25x}{100}[/tex]

[tex]=\frac{x}{4}[/tex]

As, given seventh graders represented 60% of the students.

So, the students on the honor roll represented as seventh graders:

[tex]60\%\ of\ \frac{x}{4}[/tex]

[tex]=\frac{60}{100} \times \frac{x}{4}[/tex]

[tex]=0.6\times \frac{x}{4}[/tex]

[tex]=\frac{0.6x}{4}[/tex]

As, 124 students on the honor roll were in eighth graders.

Thus,

According to question:

[tex]\frac{x}{4} -\frac{0.6x}{4} =124[/tex]

[tex]\frac{x-0.6x}{4} =124[/tex]

[tex]\frac{0.4x}{4} =124[/tex]

Multiplying both sides by 4 we get:

[tex]0.4x=496[/tex]

Dividing both sides by 0.4 we get:

[tex]x=1240.[/tex]

Therefore, there are 1240 students who attended Washington Middle School.

Answer:

20,158 cases

Step-by-step explanation:

Let [tex]t=0[/tex] represent year 2010.

We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.

Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.

We can represent this information in an exponential decay function as:

[tex]F(t)=102,390(1-0.15)^t[/tex]

[tex]F(t)=102,390(0.85)^t[/tex]

To find number of cases in 2020, we will substitute [tex]t=10[/tex] in our decay function as:

[tex]F(10)=102,390(0.85)^{10}[/tex]

[tex]F(10)=102,390(0.1968744043407227)[/tex]

[tex]F(10)=20,157.970260446597\approx 20,158[/tex]

Therefore, 20,158 cases  will be reported in 2020.

Answer:

P1A2= 0.001

P1A'2=0.999

Step-by-step explanation:

Probability = number of ways A occurs/ number of different simple events

P1(A2) =1/1000=0.001

P1A2 = 1-(1/1000)= 999/1000 = 0.999

Probabilities are used to determine the outcome of an event.

The probability of winning is 0.001

Given

[tex]n = 1000[/tex] --- ways

Only one of the 1000 digits is a winning digit.

So, the probability of winning, P(A) is:

[tex]P(A) = \frac{1}{n}[/tex]

So, we have:

[tex]P(A) = \frac{1}{1000}[/tex]

Express as a decimal

[tex]P(A) = 0.001[/tex]

Hence, the probability of winning is 0.001

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Answer:

c

Step-by-step explanation:

Answer:

The enlargement will be 2,250 which is 25 the times

Step-by-step explanation:

In the provided scale drawing, each unit represents 3 inches in length. Use this scale to add the real world measurements to the scale drawing as shown.

It can be seen from the figure that the total height of the scale drawing is 9 in + 3 in + 9 in = 21 in. It is given that the enlargement has a height of 105 inches. Find the scale factor between the scale drawing and the enlargement by dividing as shown.

The scale factor of 5 means that each dimension of the enlargement will be 5 times larger than the matching dimension of the scale drawing. So, the dimensions of the enlarged figure are shown below.

The logo is made up of three polygons: two triangles and one square. To find the total area of the logo, the area of each region must be found and added together.

To calculate the area of a triangle, use the formula below where b is the length of the base of the triangle and h is the height of the triangle.

To calculate the area of a square, use the formula below, where s is the length of the side of the square.

Now, calculate the areas of of the two logos.

Finally, determine how many times larger the area of the enlargement is than the scale drawing by dividing, as shown below.

Therefore, the area of the enlargement will be 2,250 inches2, which is 25 times the size of the original scale drawing.

Answer:

Conclusion: The proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.

Step-by-step explanation:

To test the claim made by the CEO of a large electric utility company the newspaper must conduct a hypothesis test for one proportion.

Assumption:

The significance level (α) of the test can be assumed to be 5%.

Hypothesis:

[tex]H_{0}:[/tex] The proportion of customers satisfied with the service they receive is 0.80, i.e. [tex]p=0.80[/tex]

[tex]H_{a}:[/tex] The proportion of customers satisfied with the service they receive is different from 0.80, i.e. [tex]p\neq 0.80[/tex]

Decision Rule:

If the p-value of the test is less than the significance level (α) then the null hypothesis may be rejected. But if the p-value  is more than the significance level (α) then we cannot reject the null hypothesis.

Test Statistics:

As the sample size is large, i.e.n = 100 > 30, then according to the central limit theorem sampling distribution of sample proportion will follow the normal distribution.

The test statistic used is:

[tex]z=\frac{\hat p-p}{\frac{\sqrt{p(1-p)}} {n} }[/tex]

Given:

The p-value of the hypothesis test is computed to be 0.894.

That is:

[tex]p-value=0.894>\alpha =0.05[/tex]

This implies that we fail to reject the null hypothesis at 5% level of significance.

Conclusion:

The null hypothesis was failed to be rejected at 5% level of significance.

Thus, concluding that the proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.

Answer:

  sin(13π/40)

Step-by-step explanation:

The given expression matches the pattern ...

  sin(a)cos(b) +cos(a)sin(b) = sin(a+b)

Then ...

  sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)

  = sin(13π/40)

_____

  π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)

The trigonometric expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 can be simplified to sin(13π/40) by using the sine addition formula.

The expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 resembles the formula for the sine of a sum, sin(a+b) = sin(a)cos(b) + cos(a)sin(b). By applying this trigonometric identity, we can rewrite the expression as the sine of a single angle. Therefore, sinπ/5 cosπ/8 + cosπ/5 sinπ/8 is equivalent to sin(π/5 + π/8). To simplify it further, we must find a common denominator for the two angles, π/5 and π/8, which is 40. Thus, we get sin((8π + 5π)/40), which simplifies to sin(13π/40).

Time required for the pendulum to swing from its position furthest to the right to its position furthest to the left: 1.25 seconds

Step-by-step explanation:

A pendulum is a system consisting of a rod/string connected to a mass which is left free to oscillate back and forth around its equilibrium position, straight vertical.

The period of a pendulum is the time the pendulum takes to complete one full oscillation, that means it is the time the pendulum takes to go from its furthest position on the left to the same position again. It is calculated as

[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]

where L is the length of the pendulum and g the acceleration of gravity.

The figure in this problem represents the position of the pendulum. We observe that the time it takes for the pendulum to do one complete oscillation is 2.5 seconds.

The time it takes for the pendulum to swing from its position furthest to the right to its position furthest to the left is half the period: therefore, it is

[tex]\frac{T}{2}=\frac{2.5}{2}=1.25 s[/tex]

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Answer:

The answer to your question is 90 dB

Step-by-step explanation:

Data

I = 10⁻³

I⁰ = 10⁻¹²

Formula

     Loudness = 10log ([tex]\frac{I}{Io}[/tex])

Process

1.- To solve this problem, just substitute the values in the equation and do the operations.

2.- Substitution

     Loudness = 10 log [tex](\frac{10^{-3}}{10^{-12}} )[/tex]

3.- Simplify

      Loudness = 10log (1 x 10⁹)

      Loudness = 10(9)

      Loudness = 90

Answer:

5.4

Step-by-step explanation:

Surface area of the large 16 in diameter pizza is

[tex]A = \pi(d/2)^2 = \pi8^2 = 64\pi[/tex]

Cost per unit surface area is

[tex]c = \frac{9.6}{64\pi} = \frac{0.15}{\pi}[/tex]

Surface area of the small 12-in diameter pizza is

[tex]a = \pi(12/2)^2 = \pi6^2 = 36\pi[/tex]

So the total cost for that much surface area of pizza is

[tex]ac = 36\pi*\frac{0.15}{\pi} = 5.4[/tex]

Answer:

Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = [tex]5\frac34 \ hrs.[/tex]

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

[tex]5\frac34 \ hrs.[/tex] can be Rewritten as [tex]\frac{23}{4}\ hrs[/tex]

Number of hours rode on first day = [tex]\frac{23}{4}\ hrs[/tex]

Also Given:

Number of hours rode on second day = [tex]6\frac45 \ hrs[/tex]

[tex]6\frac45 \ hrs[/tex] can be Rewritten as [tex]\frac{34}{5}\ hrs.[/tex]

Number of hours rode on second day = [tex]\frac{34}{5}\ hrs.[/tex]

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = [tex]20-\frac{23}{4}-\frac{34}{5}[/tex]

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = [tex]\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}[/tex]

Now denominators are common so we will solve the numerator we get;

Number of hours she need to ride on third day =[tex]\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.[/tex]

Hence Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.

Final answer:

Rebecca and Dan need to ride for 7 9/20 hours on the third day to reach their goal of biking a total of 20 hours in the national park, having already biked 5 3/4 hours on the first day and 6 4/5 hours on the second day.

Explanation:

Rebecca and Dan are biking in a national park and want to achieve a goal of biking a total of 20 hours over three days. They biked 5 3/4 hours on the first day and 6 4/5 hours on the second day. To find the time they need to bike on the third day, we first convert the hours they biked into improper fractions:

Next, we add these two amounts together:

(23/4) + (34/5) = (23×5 + 34×4) / (4×5) = (115 + 136) / 20 = 251/20 hours.

Now we convert 251/20 hours to a mixed number:

251/20 = 12 11/20 hours

They have biked a total of 12 11/20 hours over the first two days. Their total goal is 20 hours, so we need to subtract the time already biked from the total goal:

20 hours - 12 11/20 hours = (20×20 - 12×20 - 11)/20 = (400 - 240 - 11)/20 = 149/20 hours.

Finally, we convert 149/20 hours back to a mixed number to find out how long they need to ride on the third day:

149/20 hours = 7 9/20 hours.

So, Rebecca and Dan need to ride for 7 9/20 hours on the third day to meet their goal of biking a total of 20 hours in the park.

Answer:

m<BCD is equivalent to 148*

Step-by-step explanation:

We know this due to the inscribed angle always being congruent to the angle that it inscribes. Hope this helps

Answer:

106°

Step-by-step explanation:

m arc BCD=148

∠A=1/2*148=74°

∠BCD=180-74=106°

After calculating the initial velocity with which the ball was thrown upwards, the time taken for the ball to reach its peak and fall back to earth was calculated to be approximately 38 seconds.

In order to find out how long the ball will be in the air, we are essentially dealing with an example of free fall in Physics. When the ball reaches its maximum height, its velocity will be zero and it will have spent a certain amount of time t to reach there. But the total time it will be in the air is twice this amount, as it will take the same amount of time to go up and come back down.

Using the second equation of motion, v = u + gt (where v = final velocity, u = initial velocity, g = acceleration due to gravity and t = time), when the ball reaches maximum height, its final velocity (v) is zero. If we rearrange this equation, we get t = (v - u) / -g.

As the problem doesn't state the initial velocity with which the ball is thrown upward, we need to find it first. We can do this by applying the equation of motion: v² = u² + 2gs, where s = displacement. If we set v = 0 at maximum height, the equation becomes u = √(2gs). Given s = 178 m and g = 9.8 m/s², we find u ≈ 186.26 m/s. Substituting these values into our time equation, we get t ≈ 19 seconds for the time to reach maximum height. As mentioned, the ball will take the same time to fall back, hence the total time in air will be around 38 seconds.

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Quantitative in general involves number while qualitative does not involves number. For example, you can count the point scored in a football game which is considered as quantitative. While you cannot count racial composition because it involves different quality or type.  

Quantitative is further divided into two type; discrete and continuous. Discrete variable involves integers while in between two values of a continuous variable, there are an infinite number which is valid and this is not the case for discrete variables.

Qualitative is variable something that you cannot count.

Answer:

A. Points scored in a football game - Quantitative; discrete

B. Racial composition of a high school classroom - Qualitative

C. Heights of 15-year-olds - Quantitative; continuous

Points scored in a football game is a discrete quantitative variable, racial composition of a high school classroom is a qualitative variable, and heights of 15-year-olds is a continuous quantitative variable.

The variables given in this question can be classified as either qualitative or quantitative.

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Answer:

The probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].

Step-by-step explanation:

The probability of an event, say E, is the ratio of the favorable outcomes to the total number of outcomes, i.e.

[tex]P (E) = \frac{Favorable\ outcomes}{Total\ outcomes}[/tex]

The sample space of flipping two coins is:

S = {HH, HT, TH and TH}

Total number of outcomes = 4

Compute the probability of flipping Heads at least once as follows:

Let X = heads.

P (X ≥ 1) = P (X = 1) + P (X = 2)

             [tex]=\frac{2}{4}+\frac{1}{4} \\=\frac{3}{4}[/tex]

Thus, the probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].

The experiment of flipping a coin is a binomial experiment.

Since there are only two outcomes of the experiment, either a Heads or a Tails.

So if X is defined as the number of heads in n flips of a coin then the random variable X follows a binomial distribution with probability p = 0.5 of success.

Answer:

k  = 0.0916

Step-by-step explanation:

T(t) = [tex]T_{s} + ( T_{o} - T_{s} )e^{-kt}[/tex]

from question; t = 12 mins , [tex]T_{s}[/tex] = 50 C , [tex]T_{o}[/tex] = 80 C , T = 60 C

60 = 50 + (80 - 50) [tex]e^{-12k}[/tex]

60-50 = 30 [tex]e^{-12k}[/tex]

10/30 =  [tex]e^{-12k}[/tex] (Taking natural Log of both sides)

In(0.3333) = In [tex]e^{-12k}[/tex]

-1.0986 = -12k

k = 0.0916

Step-by-step explanation:

The integral is the area under the curve.  When the curve is above the x-axis, the area is positive.  When the curve is below the x-axis, the area is negative.  The integral equals 0, so we want to find the value of b such that the area of the quarter circle is canceled out by the area of the triangle.

Area of the quarter circle is:

A = π/4 r²

A = 9/4 π

Area of the triangle is:

A = ½ bh

9/4 π = ½ (b − 3) (b − 3)

9/2 π = (b − 3)²

b − 3 = 3√(π/2)

b = 3 + 3√(π/2)

b = 6.760

Answer:

12.25 ft

Step-by-step explanation:

(3/8)x + (5/8)x = √384

0.375x + 0.625x  = 19.6

x = 19.6

Since L = 5/8 * 19.6 = 12.25 ft

The length of the treehouse, we use the area (384 square feet) and the given ratio (width is 3/8 the length). After setting up the equation, we solve for the length to find that the length of the treehouse is 32 feet.

The length of the treehouse, we can set up an equation using the given area and the relationship between the width and length. Let L represent the length and W represent the width. According to the problem, W =  {3}/{8}L.

The area of the treehouse is given as 384 square feet. The formula for the area of a rectangle is Area = Length  imes Width, so we have:

L times W = 384 square feet

L times  {3}/{8}L = 384

{3}/{8}L² = 384

L² =  rac{384 times 8}{3}

L² = 128 times 8

L² = 1024

L =[tex]\sqrt{1024}[/tex]

L = 32 feet

Therefore, the length of the treehouse is 32 feet.

Answer:

Line ED

Explanation:

Opposite side is EF (because its opposite to the angle)

Hypotenuse side id FD (opposite of right angle)

Adjacent is the line leftover

Answer:

B

Step-by-step explanation:

Adjacent is the one with 90° and the angle, theta

ED in this case

Answer:

The average radius of sun is approximately 9.95 times the average radius of Jupiter.                                

Step-by-step explanation:

We are given the following in the question:

Average radius of Jupiter =

[tex]4.34\times 10^{4}\text{ miles}[/tex]

Average radius of the sun =

[tex]4.32\times 10^{5}[/tex]

Relation between average radius of sun and average radius of Jupiter =

[tex]\displaystyle\frac{\text{Average radius of Sun}}{\text{Average radius of Jupiter}}\\\\= \frac{4.32\times 10^{5}}{4.34\times 10^{4}}\\\\\displaystyle\frac{\text{Average radius of Sun}}{\text{Average radius of Jupiter}} = 9.953917\\\\\text{Average radius of Sun} \approx 9.95\times \text{(Average radius of Jupiter)}[/tex]

Thus, the average radius of sun is approximately 9.95 times the average radius of Jupiter.

To determine how many times greater the Sun's radius is compared to Jupiter, divide the Sun's radius (695,700 km) by Jupiter's radius (71,400 km), resulting in the Sun being approximately 9.75 times greater than Jupiter in size.

The question asks how many times greater the average radius of the Sun is compared to that of Jupiter. To find this, we will divide the Sun's radius by Jupiter's radius. The radius of Jupiter is given as 71,400 km, while the radius of the Sun is much larger at 695,700 km.

Calculating the ratio, we get:

Therefore, the average radius of the Sun is roughly 9.75 times greater than that of Jupiter.

Answer:

The answer to your question is the height of the lamp is 18.2 ft

Step-by-step explanation:

Data

Street lamp shadow = 31.5 ft

Street sign height = 8 ft

Street sign shadow = 14 ft

Street lamp height = x

Process

1.- To find the height of the lamp use proportions. In this kind of problem, we do not look for the length, but the shadow.

Street lamp height/street lamp shadow = street sign height/street sign

                                                                                                         shadow

Substitution

                                             x / 31.5 = 8 / 14

Solve for x

                                            x = (31.5)(8) / 14

Simplification

                                            x = 254.4 / 14

Result

                                            x = 18.2 ft              

To find the length and height of the lamp, set up proportions using the shadow lengths and given values, then solve for the lamp height and length based on the information provided.

The length of the lamp:

Answer:

The Surface in R^3

Step-by-step explanation:

Represented by the equation x+y=2

when y=0

then 0=2-x

x=2

similarly

when x=0

then 0=2-y

y=2

the sketch and description is in attached file

Answer:  The equation is a plane.

Graph is attached.

The equation [tex]x + y = 2[/tex] is an equation of a plane in [tex]R^3[/tex].

z can take any value and x and y must satisfy the equation [tex]x + y = 2[/tex].

3 such points are: [tex]A = (0, 2, 0), B = (2, 0, 0), C = (1, 1, 3)[/tex].

Then we plot the points and draw a plane through them.

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Answer:

true

Step-by-step explanation:

it is possible through thorough work out and exercises

and secondly a numbers of diets has to be avoided such starchy foods and junks

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y = 3x

Comparing with the slope intercept form, slope = 3

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line passing through (4,-2) is - 1/3

To determine the intercept, we would substitute m = - 1/3, x = 4 and

y = -2 into y = mx + c. It becomes

- 2 = - 1/3 × 4 + c = 4/3 + c

c = - 2 + 4/3 = - 2/3

The equation becomes

y = - x/3 - 2/3

Answer:

79 years old

Step-by-step explanation:

Let his age be x

400-3x=163

400-163=3x

237=3x

Divide both side by 3

237/3 =3x/3

79=x

The man's age (x) =79 years old

Answer:

The repulsive force is [tex]3.067\times10^{-4}N[/tex].

Step-by-step explanation:

Consider the provided information.

The coulomb's law to calculate the repulsive force: [tex]F=\frac{kQ_1Q_2}{r^2}[/tex]

Where the value of k is 9.00×10⁹ Nm²/C²

Substitute the respective values in the above formula.

[tex]F=\frac{9\times10^9\frac{N\cdot m^2}{c^2} \times(-24\times10^{-9}C)^2}{[(13 cm)(\frac{1m}{100cm} )]^2}[/tex]

[tex]F=\frac{9\times10^9\frac{N\cdot m^2}{c^2} \times(-24\times10^{-9}C)^2}{(0.13 m)^2}[/tex]

[tex]F\approx0.0003067N[/tex]

[tex]F=3.067\times10^{-4}N[/tex]

Hence, the repulsive force is [tex]3.067\times10^{-4}N[/tex].

Answer:

Alex can do the job in 60 days alone.

Step-by-step explanation:

Alex and Brandon working together, they can finish the job of cleaning the school in 15 hours. Brandon alone in 20 hours can finish the job.

So, Brandon can complete [tex]\frac{1}{20}[/tex] part of the job in one hour.

Let, Alex alone can finish the same job in x hours.

So, Alex can complete [tex]\frac{1}{x}[/tex] part of the job in one hour.

So, working together they do [tex](\frac{1}{20} + \frac{1}{x}) = \frac{x + 20}{20x}[/tex] part of the whole job in one hour.

Hence, from the conditions given we can write

[tex]\frac{x + 20}{20x} = \frac{1}{15}[/tex]

⇒ 15x + 300 = 20x

⇒ 5x = 300

⇒ x = 60 days.

Therefore, Alex can do the job in 60 days alone. (Answer)

Answer:

36.5 Inches

Step-by-step explanation:

The perimeter of the triangle is the sum of all three(3) sides.

let the length of one congruent side be 'a', Therefore;

a + a  + 46 = 119

2a = 119 - 46

a = 73/2

a = 36.5 inches.

6.60 would be the total cost for both 3 pounds and two pounds :D

Answer:

$6.60

Step-by-step explanation:

multiply 1.20 (red apples) by 3 (lbs) = 3.6

and 1.50 (green apples) times 2 (lbs) = 3

then add the two totals = $6.60