Find the area of the shaded (gray) region.



Question 13 options:

24 cm squared


60 cm squared


84 cm squared


36 cm squared

The rate of change of the Distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

The rate of change of the distance between the planes, we need to determine how the distance between them changes over time.

the distance between the two planes is represented by the variable D, and time is represented by the variable t.

At noon, the southbound plane starts flying and continues for 4 hours until 4 pm. During this time, the plane covers a distance of 900 km/h * 4 hours = 3600 km due south.

Meanwhile, the eastbound plane is also traveling towards the airport. It starts from a distance of 2000 km away from the airport at 4 pm.

To find the distance between the planes at any given time, we can use the Pythagorean theorem, as the planes are moving at right angles to each other. The distance D between the planes can be calculated as:

D^2 = (2000 km)^2 + (3600 km)^2

Simplifying the equation:

D^2 = 4000000 km^2 + 12960000 km^2

D^2 = 16960000 km^2

Taking the square root of both sides:

D = sqrt(16960000) km

D = 4120 km

Now, we can find the rate of change of the distance between the planes by calculating the derivative of the distance equation with respect to time

dD/dt = 0

Since the distance between the planes is constant, the rate of change is zero.

Therefore, the rate of change of the distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

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Answer:

44

Step-by-step explanation:

11/4 gallons = 2.75 gallons there are 16 cups in a gallon that men's there's 32 cups for 2 gallons and 12 cups for .75 gallons 32+12=44 cups

Answer:

x=2/3

Step-by-step explanation:

Answer:40

Step-by-step explanatio 30 + 2 | 3x2 + 2 | =:40

Answer:

15.37 inches

Step-by-step explanation:

The difference is the bigger no. minus the smaller no. 37.8 - 22.43  = 15.37

Answer:

6.4 km

Step-by-step explanation:

4x1.6

Answer:

6.4 km

Step-by-step explanation:

1.6 * 4 = 6.4

The meaning of the composite function c(p(45)) is the number of calories burned doing push-ups in 45 seconds

The functions are given as:

So, the interpretation of the function c(p(t)) is

The number of calories burned doing push-ups in t seconds

In c(p(45)), the value of t is 45

Hence, the meaning of the composite function c(p(45)) is the number of calories burned doing push-ups in 45 seconds

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At the 5% significance level, a researcher conducts six separate hypothesis tests. the likelihood of finding two or fewer Type Errors.

Declare your null and alternate hypotheses in Step 1. Data collection is step two. Perform a statistical test in step three. In step four, you must choose whether to reject or not to reject your null hypothesis. Deliver your results in Step 5. Five steps make up the statistical process: design the study, assemble the data, Analyze the data, draw conclusions, and take action. In a planned experiment, the variables are under the researchers' control.

Utilizing sample data, hypothesis testing is a method used to determine whether a hypothesis is tenable. The test offers proof that, given the available data, the hypothesis is plausible. By measuring and reviewing a representative sample of the population under study, statistical analysts can evaluate a theory.Procedures for testing hypotheses Identifying the null hypothesis is the first step.

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Answer:

Step-by-step explanation:

33.3%

19.4%

Answer: B.A point is a location, and a line has many points located on it.

Step-by-step explanation:

Answer:

The cost price of the article was Nu 1,000

The original selling price was Nu 1,120

The second selling price was Nu 1,200

Step-by-step explanation:

System of Equations

Let's call:

x = Original selling price of the article

y = Cost of the article

The first condition implies that the difference between the selling price and the cost price (the profit) is 12%. Recall the profit % is always calculated with respect to the cost, that is, the profit at the first condition is:

0.12y = Original profit

Setting up the equation, we have:

\(x-y=0.12y\)

The second condition states the selling price is 80 Nu more than before, that is:

x+80= Second selling price of the article

y = Cost of the article (it doesn't change)

The profit of this condition is 20%, thus:

0.2y = Second profit

This produces a second equation:

\(x+80-y=0.2y\)

Let's put both equations together to form a system of equations:

\(x-y=0.12y\)

\(x+80-y=0.2y\)

Operating on both equations:

\(x=1.12y\)

\(x=1.2y-80\)

Equating both equations, we have an equation with only y's:

\(1.12y=1.2y-80\)

Subtracting 1.2y on each side:

\(1.12y-1.2y=-80\)

Operating:

\(-0.08y=-80\)

Solving:

\(\displaystyle y=\frac{-80}{-0.08}=1,000\)

a)

The cost price of the article was Nu 1,000

b) The selling price of the article will be calculated in both cases:

Original selling price: x=1.12y= 1.12*1000=1,120

The original selling price was Nu 1,120

The second selling price was x+80=1,200

The second selling price was Nu 1,200

Answer:

Think about the PEMDAS rules for order of operations.

Multiplication comes before addition or subtraction, so first we have "the product of a number and 5" - that's 5x. Then "six more" than that would be 5x + 6. "Equals" means the "=" sign, so the final answer is 5x + 6 = 8.

Answer:

x=y

Step-by-step explanation:

The Length of the rod is 3/5 meters.

The civil engineer wants to find the length of a rod that stretches for 1 meter and can be given by the function x=2y^(3/2).

To find the length of the rod, we need to integrate the function x=2y^(3/2) with respect to y. Integrating both sides of the equation,

we have:'int dx = int 2y^(3/2) evaluating the left-hand side gives x = 2/5 y^(5/2) + C, where C is the constant of integration. To find the value of C,

we use the given information that the rod stretches for 1 meter. At y = 0, x = 0 since the rod has no length when it is not stretched. At y = 1, x = 1 since the rod stretches for 1 meter.

Therefore, we have:1 = 2/5 (1)^(5/2) + C1 = 2/5 + CC = 3/5 Substituting C = 3/5 back into the equation for x,

we have:x = 2/5 y^(5/2) + 3/5

The length of the rod is given by the value of x when y = 1. Substituting y = 1,

we have:x = 2/5 (1)^(5/2) + 3/5 = 3/5

The length of the rod is 3/5 meters.

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Answer:

12

Step-by-step explanation:

divid half of line

Answer:

Perimeter = 60

Step-by-step explanation:

In order to find the perimeter of the given triangle, we must first determine the value of the missing side. We can use the Pythagorean Theorem to find the missing side of the given right triangle.

According to the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse (the side that is opposite of the right angle, 90°), and a and b represent the legs of the triangle. Use the formula to solve for the missing side. Rearrang the formula to isolate the variable, a:

a² + b²  =  c²

Subtract b² from both sides:

a² + b² - b² =  c² - b²

a² =  c² - b²

Next, substitute the given values into the formula:

c (hypotenuse) = 26

b (leg) = 24

a² =  c² - b²

a² =  (26)² - (24)²

a² = 676 - 576

a² = 100

\(\sqrt{(a)^{2}} = \sqrt{100}\)

a = 10

The value of the missing side is 10.

Now, we can solve for the perimeter of the triangle:

P = a + b + c

P = 10 + 24 + 26

P = 60

Therefore, the perimeter of the given right triangle is 60.

Let:

C1 = Possible combinations for 11th grade

C2 = Possible combintations for 12th grade

TC = Total different groupings

For C1:

For C2:

Therefore:

Answer: 9 pounds

Step-by-step explanation:

16 ounces is one pound 144/16=9

Answer:

9

Step-by-step explanation: 144 ÷ 16 = 9

(16 ounces are in a pound)

Answer:

4 and half i.e 4.5 hours

Step-by-step explanation:

Its simple

To solve this question you just need to find out what is 30% of 15

So  \(\frac{30}{100}\)*15 = 4.5

4.5 is the answer we get after we divide (30*15=450) by 100

Answer:

A

Step-by-step explanation:

Answer:

32 units

Step-by-step explanation:

The large triangle on top has an area of 20, cause 4*10 = 40

40/2 = 20.

the square on the bottom has an area of 4, well, cause 2*2 = 4.

The smaller triangle on the left has an area of 2, cause 2*2=4

4/2=2

The triangle on the right, has an area of 6, because 6*2=12

12/2=6

20+4+2+6 = 32

Answer:

32 Units =)

Step-by-step explanation:

Answer:

Yes it is.

Step-by-step explanation:

-(5/12) = -*5/12 = -5/12

5/-12 = -5/12

Best of Luck!

Answer:

n = -6

Step-by-step explanation:

2n + (n + 2) = -16

3n + 2 = -16

3n = -18

Answer:

43.5%

Step-by-step explanation:

Substitute the original price of $850 and the sale price of $480 to find

amount of discount=850−480=370

Use the amount of discount, $370, to find the discount rate. Use the equation

amount of discount=discount rate×original price.

Rearrange the equation to solve for the unknown value.

discount rate=amount of discountoriginal price

Substitute in the known values and solve to find the discount rate.

370850=0.435=43.5%

Thus, the discount rate on the patio set was 43.5%.

Answer:

Step-by-step explanation:

Solution

When, x=2

f(2)=3×2+8

=14

Again,

When, x=1

f(1)=3×1+8

=11

When, x=0

f(0)=3×0+8

=8

When, x=-1

f(-1)= 3×(-1)+8

=5

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To meet the goal of $320.00 for the playground, they need to raise a total of $400.00

We know that for each $20 raised, they get $16 for the playground. They need to get $320.00 for the playground.

Taking the quotient:

N = $320.00/$16 = 20

This means that they need to raise $20 20 times, so they get $16 20 times which is equal to $320.

Then, we can conclude that they need to raise a total of:

$20*20 = $4,000

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Answer:

Step-by-step explanation:

Use of formula: (a^b)^c = a^(bc)

Answer: 0.07

Step-by-step explanation:

To find the relative frequency of people in the sample whose place of residence is suburban and whose highest degree is a two-year degree, we need to calculate the ratio of the number of people with those characteristics to the total sample size.

Looking at the contingency table, we can see that the number of people in the suburban category with a two-year degree is 21.

The total sample size is given as 311.

Therefore, the relative frequency can be calculated as:

Relative frequency = (Number of people in suburban category with two-year degree) / (Total sample size)

= 21 / 311

≈ 0.0676

Rounded to two decimal places, the relative frequency is approximately 0.07.