The drama teacher decreased the length of a play from 90 minutes to 60 minutes. What was the percent decrease in the length of the play?


Please help I need this for a test asapppp and pleased include the solving for this question I need to submit the work

According to the given question we can conclude that the probability that a student who majors in science is a female is approximately 0.375 and the probability that a student is male or majors in art is 0.78.

Probability is the research of probabilities, which also are based on the ratio of favourable events to likely circumstances. One of the areas of probability theory is the estimation of the chance of experiments occurring. With a probability, we can calculate any number of things, from the probability of obtaining a head or a tail when flipping a coin towards the likelihood of generating a research error, for example.

A.) To find the probability that a student who majors in science is a female, we need to use Bayes' theorem. Let F be the event that a randomly selected student is female, and S be the event that the student majors in science. Then we have:

P(F|S) = P(S|F) * P(F) / P(S)

We know that P(F) = 0.6 (since 60% of students are female), and P(S|F) = 0.1 (since 10% of female students major in science). To find P(S), we need to use the law of total probability:

P(S) = P(S|F) * P(F) + P(S|M) * P(M)

We know that P(S|M) = 0.4 (since 40% of male students major in science), and P(M) = 0.4 (since 40% of students are male). Therefore:

P(S) = 0.1 * 0.6 + 0.4 * 0.4 = 0.16

Now we can calculate P(F|S):

P(F|S) = 0.1 * 0.6 / 0.16 ≈ 0.375

Therefore, the probability that a student who majors in science is a female is approximately 0.375.

B.) To find the probability that a student is male or majors in art, we need to use the law of total probability again:

P(Male or Art) = P(Male) + P(Art) - P(Male and Art)

We know that P(Male) = 0.4 (since 40% of students are male), and P(Art|Male) = 0.5 (since 50% of male students major in art). We also know that P(Female) = 0.6 (since 60% of students are female), and P(Art|Female) = 0.7 (since 70% of female students major in art). Therefore:

P(Art) = P(Art|Male) * P(Male) + P(Art|Female) * P(Female)

= 0.5*0.4+0.7*0.6

= 0.58

To find P(Male and Art), we can multiply the probabilities of being male and majoring in art:

P(Male and Art) = P(Male) * P(Art|Male)

= 0.4 * 0.5

= 0.2

Now we can calculate P(Male or Art):

P(Male or Art) = 0.4 + 0.58 - 0.2

= 0.78

Therefore, the probability that a student is male or majors in art is 0.78.

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Answer:

(-3/4)x^2 + 6x = 3

Step-by-step explanation:

It takes 8 seconds for the ball to reach its maximum height and then return to ground level; thus, the highest point (vertex) the ball will reach is reached after 4 seconds.  The graph showing this motion is a parabola that opens down.  Thus, the coefficient 'a' must be negative.

Returning to a * x ^ 2 + bx + c, we write out two instances of this formula, one for x = 0 and the other for x = 8.  This is because {0, 8} are the x-intercepts.

Then, for x = 0, a * x ^ 2 + bx + c   becomes  a * 0 ^ 2 + b*0 = 0,

and for x = 8,  a * x ^ 2 + bx + c  becomes  a(8)^2 + b(8) + c = 0

The first equation tells us that 'c' must be 0.  The second equation tells us that  64a + 8b = 0, which is equivalent to 8a = -b, or a = -b/8.

We then have the quadratic function  (-b/8)x^2 + bx + 0.  All we have to do now is to find the value of b.  The vertex of this parabola is (4, 12), and so the quadratic becomes

(-b/8)(4)^2 + b(4) = 12.  To solve this for b, multiply all terms by 8:

-b(16) + 32b = 96, or

16b = 96, or b = 6.  Since a = -b/8 (see above), a = -6/8 or a = -3/4.

Then the equation of motion is

height of ball = (-3/4)x^2 + 6x

We want to know when the ball is at a height of 3 m.  Thus, set this equation of motion = to 3 and solve for x (the times at which height = 3 m):

(-3/4)x^2 + 6x = 3            This is the desired quadratic equation.

(A) The expression to represent the elevation level of city D, in feet will be :  \(D = \frac{1}{4} * [C]\)    
(B) The elevation of city D will be -6 feet. The negative here shows that city D is below sea level.

In the question, it is given that city A is 96 feet below sea level, city C is 24 feet below sea level, and the elevation of city D is 1 over 4th of the elevation of C. Since, City A & C are both below sea level their elevation will be negative. So, by these we get elevations:

For City A,  A = -96

      City C,  C = -24

      City D,  \(D = \frac{1}{4} *[C]\)      ----> Equation (1)

By Equation (1) we get the representation of elevation for City D.

Now, Calculating the elevation of city D, we will put the value of city C in equation (1).

        =>   \(D = \frac{1}{4} *[-24]\)

        =>   \(D = -6\\\)

The negative sign here shows that the elevation is below sea level for city D.

Hence, the expression representing the elevation of city D will be \(D = \frac{1}{4} * [C]\) and, the elevation of city D will be -6.

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Answer:

Below

Step-by-step explanation:

Line AB is of the form y = mx + b    where m is the slope = 2

 Line BC is perpendicular to this and will have slope - 1/m = - 1/2   and includes the point C (0,6)

 The point slope form of line BC will then be

     ( y-6) = - 1/2 ( x - 0)    which can be re-arranged to

       y = - 1/2x + 6     < ==== equation for line BC

The linear function that relates y to x is given as follows:

y = -0.5x + 57.

The slope indicates that the height decays 0.5 feet per minute. The y-intercept indicates that the descent starts at a cruising altitude of 57 feet.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the table, when x = 0, y = 57, hence the intercept b is given as follows:

b = 57.

When x increases by 10, y decays by 5, hence the slope m is given as follows:

m = -5/10

m = -0.5.

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Answer:  ≈ 174.01

Thus, The Sky Scraper  ≈  174.01

Step-by-step explanation:

From his eye, which stands 1.55 meters above the ground, Tyler measures the angle of elevation to the top of a prominent skyscraper to be 57∘

∘. If he is standing at a horizontal distance of 112 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

1 - Draw Diagrams, Label Knowns:

Unknowns: X

2 - Identify: OPPOSITE, ADJACENT, HYPOTENUSE

3 -  WHAT FUNCTION USES THE OPPOSITE AND THE ADJACENT?

SOH - CAH - TOA

NOW SHOWING WORK:

tan 57 = opposite/adjacent =  x/112

tan 57 = x/112

tan 57/1  = x/112

112 tan 57 = x         ( Cross Multiply)

x = 172.464875    (Now, type into the calculator)

So, Now we ADD:

1.55, the distance from the ground to his eye.

172.464875  +   1.55  =  174.014875

≈ 174.01     (Round to The Nearest HUNDREDTH)

Thus, the Sky Scraper is ≈ 174.01 meters tall.

So, your answer would be :  

Sky Scraper  ≈  174.01

Hope I have explained it and helped you in your studies!

The height of the skyscraper is given by H = 174.01 m

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

We can start by drawing a right triangle, where the horizontal distance from Tyler to the base of the skyscraper is one leg, the height of the skyscraper is the other leg, and the line of sight from Tyler's eye to the top of the skyscraper is the hypotenuse.

Then we can use trigonometry to solve for the height of the skyscraper.

Let the height above the ground from his eye = 1.55 m

Now , the angle of elevation θ = 57°

The horizontal distance from the base of the skyscraper = 112 m

Now , from the trigonometric relations ,

tan θ = opposite / adjacent

So , tan 57° = x / 112

Multiply by 112 on both sides , we get

x = 172.46 m

Now , the total height of the skyscraper = 172.46m + 1.55 m

So , height H = 174.01 m

Hence , the skyscraper has a height of 174.01 m

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Answer:

4 lb/month

Step-by-step explanation:

loss of 144 lb in 36 months

144/36 = 4

Answer: 4 lb/month

$15,556.84

Paulanwill have approx $15,556.84 if she investb$5k that earns 4.10% apr compound quarterly..

Answer:

I’m pretty sure it’s $11,780.60

Step-by-step explanation:

We can use the formula for compound interest to determine how much money Paula will have in 25 years:

A = P(1 + r/n)^(nt)where:A = the total amount of money after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = $5,000

r = 4.10% = 0.041 (as a decimal)

n = 4 (compounded quarterly)

t = 25 years

Plugging these values into the formula, we get:

A = $5,000(1 + 0.041/4)^(4*25)

A = $5,000(1 + 0.01025)^100

A = $5,000(1.01025)^100

A = $5,000(2.356)

A = $11,780.60

Therefore, Paula will have approximately $11,780.60 in her account after 25 years.

Answer:

potential solutions- 1

extraneous solutions- 0

solution to equation- x=3

Step-by-step explanation:

Answer:

104

Step-by-step explanation:

Hey There!

So essentially what this problem is asking us to do is solve for the missing angle in a triangle

Remember all of the angles in a triangle will add up to 180

so to find the missing angle we subtract the given angles (38 and 38) from 180

180-38-38=104

so we can conclude that angle A equals 104

Hope this helps!

Answer:

104 degrees

Step-by-step explanation:

Hope this helps!

Have a great day!

The cost of the carpet will be $2,335.5.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The dimensions of the carpet are;

⇒ 15 feet by 18 feet

Now,

The area of the carpet = 15 x 18

                                   = 279 feet²

                                   = 270 / 3 yards²

                                   = 90 yards²

Since, The carpet costs = $25.95 per square yard.

Hence, The carpet cost for 90 yards² = 90 x $25.95

                                                          = $2,335.5

Thus, The cost of the carpet will be $2,335.5.

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Answer:

I think the perimeter of the diagram is 5 and if you round it like

If it's 5 or greater, add 1 to the digit in the tenths place, and then remove all the digits to the right. (In the example above, the hundredths digit is a 4 , so you would get 51.0 .) To round a number to the nearest hundredth , look at the next place value to the right (the thousandths this time).

Answer:

The answer is 2/5.

Step-by-step explanation:

First, use the stay-switch-flip method. Keep 1/5 the same, switch the division sign into a multiplication sign, and flip the numerator and the denominator of 1/2 to get 1/5 x 2/1. Multiply the numerators. 1 x 2 = 2. Now, multiply the denominators. 5 x 1 = 5. Therefore, you're answer is 2/5.

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Answer:

0.722 is the answer when converting inches to miles

Answer:

C

Step-by-step explanation:

The equation for the dotted line is y=(-1/2)x, so therefore y<(-1/2)x must be the area under the dotted line.

The equation for the solid line is y=2x+3, so therefore y≥2x+3 must be the area above the solid line.

The section that is both under the dotted line and above the solid line is C.

The total number of coins that were in Kay's bank are 137 coins.

In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Since she has 11 less dimes than nickels, an equation which models this situation is given by;

n = d + 11     ....equation 1.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Additionally, the coins are worth 10 dollars;

0.1d + 0.05n = 10 ....equation 2.

By solving both equations simultaneously, we have:

0.1d + 0.05(d + 11) = 10

0.1d + 0.05d + 0.55 = 10

0.15d = 9.45

d = 63 dimes.

For nickels, we have:

n = d + 11

n = 63 + 11

n = 74

Now, we can determine the total number of coins;

Total number of coins = n + d

Total number of coins = 74 + 63

Total number of coins = 137 coins.

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Answer:

a ≈ 2.2

Step-by-step explanation:

Using the Cosine rule in Δ ABC

a² = b² + c² - 2bc cos A

Here b = 3, c = 4 and A = 32° , thus

a² = 3² + 4² - (2 × 3 × 4 × cos32° )

    = 9 + 16 - 24cos32°

    = 25 - 24cos32° ( take the square root of both sides )

a = \(\sqrt{25-24cos32}\) ≈ 2.2

In triangle it is given that,

→ Height (h) = 38 cm

→ Base (b) = 44 cm

The formula we use,

→ Area of triangle = ½ × b × h

Now we have to,

find the area of the triangle,

→ ½ × b × h

→ ½ × 44 × 38

→ (44 × 38)/2

→ 1672/2 = 836 cm²

So, 836 cm² is area of triangle.

The volume of the metal sphere is 4π/3(R^3 - r^3)

The volume of the solid generated is 2π cubic units.

The volume of the ring can be found by subtracting the volumes of two spheres with radii R and r:

V = (4/3) * π * (R^3 - r^3)

So, the volume of the ring is given by:

V = (4/3) * π * (R^3 - r^3) cubic units.

Evaluate

V = 4π/3(R^3 - r^3)

We have the equation to be

y = 1/x

The volume of the solid is given by the definite integral:

V = 2π ∫[a,b] x * y dx

where a and b are the lower and upper limits of the interval over which we are integrating.

In this case, a = 1 and b = 2, so the volume of the solid is given by:

V = 2π ∫[1,2] x * 1/x dx = 2π ∫[1,2] dx = 2π (x)|[1,2] = 2π (2 - 1) = 2π.

So, the volume is to 2π cubic units.

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Answer:

Not a random variable

Step-by-step explanation:

The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.

Thus, the last book read by someone in City A is not a random variable.

Answer:

not random

Step-by-step explanation:

Answer:

9 + b is an expression

Step-by-step explanation:

Expressions don't have the = sign in them but equations do.

The possible price for the items if the store sells $600 is (c) $40

From the question, we have the following parameters that can be used in our computation:

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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Using L'hopital we can see that the limit is equal to 1/22

Here we want to take the limit of x tending to zero for x/sin(22x)

Notice that when x = 0, both numerator and denominator are zero, so we need to take the limit of the first derivatives, for:

y = x

y' = 1

And for:

y = sin(22x)

y' = 22*cos(22x)

Now taking the limit we will get:

\(\lim_{x \to 0} \frac{1}{22cos(22x)} = \frac{1}{22cos(0)} = 1/22\)

That is the value of the limit.

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Answer: D. The total sample size is too large to apply the chi-square test for homogeneity.

Step-by-step explanation: When sampling without replacement, the sample size should not exceed 10 percent of the population size. Here, the sample size of 85 is just over 24 percent of the population of 350 company employees.

The total sample size is too large to apply the chi-square test for homogeneity.

We have given that,

A manufacturing company with 350 employees is  changing the employee health insurance plan to either plan A or plan B.

                         Plan A        Plan B        Total

yes(group 1)       40(32.5)   20(27.5)      60

No (group 2)      6 (13.5)     (11.5) 25       25

Total                   46             39              85

We have to find which statement is true,

Each sample unit of the population has only one chance to be selected in the sample. we can select one sample only way and after selection we cannot pot this sample in the sample space again.

The sample size should not exceed 10 percent of the population size.when we use sampling  without replacement,

Here, the sample size of 85 is just over 25 percent of the population of 350 company employees.

Therefore,the total sample size is too large to apply the chi-square test for homogeneity.

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Answer:

The answer is A 21

Step-by-step explanation:

Sets of values that could be the intensities of Amber’s exercise during the fourth, fifth, and sixth visits are -

66%, 69%, 72%

63%, 65%, 67%

What is intensity?

In physics, the power transferred per unit area is known as the intensity or flux of radiant energy, where the area is measured on a plane perpendicular to the direction of the energy's propagation.

The program recommends a pattern of constant intensity for 3 visits, increasing intensity over 3 visits, and then decreasing intensity for 3 visits before restarting the pattern.

Let's call the starting intensity level "x".

Then the intensity levels for the first 3 visits are all equal to x, the intensity levels for the next 3 visits are increasing, and the intensity levels for the following 3 visits are decreasing.

To determine which sets of values could be the intensities of Amber's exercise during the fourth, fifth, and sixth visits, we need to follow the pattern.

If the intensity level for the first 3 visits is x, then the intensity levels for the next 3 visits are x plus some value y, and the intensity levels for the following 3 visits are x plus some value z, where y and z are positive.

If we assume that the initial intensity level x is some value between 60% and 70%, then we can eliminate the last option of 67%, 72%, and 77% because the initial intensity level is too high.

Now let's check the remaining options -

63%, 63%, 63%: This set of values corresponds to a pattern of constant intensity for all 9 visits, which is not consistent with the program's recommendation.

Therefore, this option is not valid.

66%, 69%, 72%: This set of values corresponds to a pattern of increasing intensity over 3 visits, which is consistent with the program's recommendation.

Therefore, this option is valid.

66%, 62%, 58%: This set of values corresponds to a pattern of decreasing intensity over 3 visits, which is not consistent with the program's recommendation.

Therefore, this option is not valid.

63%, 65%, 67%: This set of values corresponds to a pattern of increasing intensity followed by decreasing intensity, which is consistent with the program's recommendation.

Therefore, this option is valid.

Therefore, there are only two valid options -

66%, 69%, 72%

63%, 65%, 67%

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Answer:

8.7

Step-by-step explanation:

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Answer: true

Step-by-step explanation:

Simplifying the expression you end up with 4y^2 + 4y - 15 which is 3 terms.

The answer would be True.

Answer:

33.3 grams

Step-by-step explanation:

(98x34)/100 =