The key of a basketball court is made up of a rectangle and on semicircle. the length of the rectangle is 15 feet and the width is 10 feet. find the area of the key

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

To solve this problem, we can use the Chinese Remainder Theorem. We need to find the remainder when 2202 202 is divided by both 2101 and 251.

First, note that 2101 and 251 are relatively prime. Therefore, by the Chinese Remainder Theorem, there exists a unique remainder between 0 and 2101 * 251 - 1 (inclusive) that satisfies the two conditions.

To find this remainder, we can use the remainders when 2202 202 is divided by 2101 and 251.

Note that 2202 is congruent to 101 (mod 2101) and 0 (mod 251). Therefore, we can use the Chinese Remainder Theorem to find that the remainder when 2202 202 is divided by 2101 * 251 is congruent to:

101 * (251^2) * (251^(-1)) + 0 * (2101^2) * (2101^(-1)) (mod 2101 * 251)

Using the fact that 251^(-1) is congruent to 201 (mod 2101) and 2101^(-1) is congruent to 1922 (mod 251), we can simplify this expression to:

101 * (251^2) * (201) + 0 * (2101^2) * (1922) (mod 2101 * 251)

Simplifying further, we get:

101 * 251 * 201 (mod 2101 * 251)

This is congruent to 101 * 201 (mod 251), which is congruent to 101 (mod 251).

Therefore, the remainder when 2202 202 is divided by 2101 251 1 is 101, which is option (b).

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The most accurate estimate of the distance on the ground between the wall and the bottom of the ladder is 2 meters.

One approach to tackle this problem is to apply trigonometry to establish the connection between the angle, height, and distance. Specifically, we can utilize the cosine function, which relates the adjacent side and the hypotenuse of a right triangle. In this case, the adjacent side represents the distance between the wall and the ladder, and the hypotenuse corresponds to the ladder's length. The given angle is 72 degrees.

By employing the formula cos(angle) = adjacent/hypotenuse, we can input the known values and determine the unknown distance:

cos(72) = distance/6

distance = 6 * cos(72)

distance is approximately 1.9 m

Thus, the most accurate estimation for the ground distance from the ladder's bottom to the wall is 2 m.

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Answer:2m

Step-by-step explanation:

i took the test

Answer:

A. 3x+6= 0

Step-by-step explanation:

When you divide - 3 with -x, you will get a positive value and same goes for - 3 and - 2

So that is how you get the answer 3x+6= 0

Answer:

∅=30°

Step-by-step explanation:

\(sin\)∅\(=\frac{1}{\sqrt{3} }sin60^{0}\)

sin∅=\(\frac{\frac{\sqrt{3} }{2} }{\sqrt{3} } =\frac{\sqrt{3} }{2\sqrt{3} }=\frac{1}{2}\)

∅=\(sin^{-1}(\frac{1}{2})= 30^{0}\)

I hope this help you

Answer:

A-B= (a,b,c,d)-(p,q,r,s)

=( )

B-A =(p,q,r,s)-(a,b,c,d)

( )

Answer:

Step-by-step explanation:

Given,

A = { a , b , c , d }

B = { p , q , r , s }

Let's find the difference of two set A and B :

A - B = { a , b , c , d } - { p , q , r , s }

The difference of two sets A and B is denoted by A - B and defined as the set of all the elements of A only which are not in B.

⇒A - B = { a , b , c , d }

Now, let's find the difference of two sets B and A

B - A = { p , q , r , s } - { a , b , c , d }

Similarly, The difference of two sets B and A is denoted by B - A and defined as the set of the all elements of set B only which are not in A.

⇒ B - A = { p , q , r , s }

Hope I helped!

Best regards!!

Answer:

the picture is blurry on my screen can u pls insert another picture

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

Equation: (1/3)x + 4 + 12 = x

Equation: (1/3)x + 16 = x

MULTIPLY EVERYTHING WITH 3

1/3 times 3 = x   16 times 3 = 48    x times 3 = 3x

Equation: x + 48 = 3x   MINUS THE "X" BY 3X = 2X

Equation: 2x = 48   OR   x = 24

CHECK THE EQUATION:

Sister: 8   Brother: 4   Herself: 12

8 + 4 + 12 = 24

Answer:

27/64

(Decimal: 0.421875)

Answer:

24 =w

Step-by-step explanation:

1000 ^8 = 10 ^w

Rewriting 1000 as 10 ^3

10^3 ^8 = 10 ^w

We know a^b^c = a ^(b*c)

10 ^24 = 10^w

24 =w

Answer: she should use 5/8 cups i think

Step-by-step explanation:

Answer:

1/22

Step-by-step explanation:

Its 1/22 because that is the total probability of your name being drawn for the prize

Answer:

159

Step-by-step explanation:

5×7×3+ 9×6÷2×2

=105+54

=159 cm²

Step-by-step explanation:

Price of 3 kg carrots = 1.80

Price of 1 kg carrots = 1.80 ÷ 3 = 0.6

Price of 2 kg carrots = 0.6 x 2 = 1.2

Remaining amount = 3.45 - 1.2 = 2.25

Price of 5 kg potatoes = 2.25

Price of 1kg potatoes = 2.25 ÷ 5 = 0.45

Now

Cost of 4 kg of carrots = 0.6 x 4 = €2.4

Cost of 2 kg of potatoes = 0.45 x 2 = €0.9

The total cost of 4kg of carrots and 2 kg of potatoes is £3.30

Total cost is the product of the cost of each unit and the number of units purchased.

As it is given that the cost of 3 kg carrot is £1.80, therefore, the cost of 1 kg of carrot can be written as,

\(\text{Cost of 1 kg carrot}=\dfrac{\text{Total cost of carrot}}{\text{Total amount of carrot}}\)

                              \(=\dfrac{\£1.80}{3}\\\\= \£0.60\)

Thus, the cost of 1 kg carrot is £0.60.

Now., as it is given that the cost of 2 kg carrot and 5 kg potatoes is £3.45, therefore, the cost of 5 kg potatoes can be written as,

\(\text{Total cost}=\text{Cost of 2 kg carrot}+\text{Cost of 5 kg potatoes}\)

\(3.45= (0.60 \times 2) + \text{Cost of 5 kg Potatoes}\\\\\text{Cost of 5 kg Potatoes} = 2.25\)

Further, the cost of each kg of potatoes can be written as,

\(\text{Cost of 1kg of potatoes}=\dfrac{\text{Cost of 5 kg Potatoes}}{\text{Total amount of potatoes}}\)

                                      \(=\dfrac{2.25}{5}\\\\=0.45\)

Thus, the cost of each kg of potatoes is £0.45.

Further,  the total cost of 4kg of carrots and 2 kg of potatoes can be written as,

\(\text{Total cost }=\text{Cost of 4kg of carrots} +\text{Cost of 2 kg of potatoes} \\\\\text{Total cost }=(4 \times 0.60)+(2\times 0.45)\\\\\text{Total cost }= 2.24+0.90=\£3.3\)

Hence, the total cost of 4kg of carrots and 2 kg of potatoes is £3.30

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\( {x}^{2} - 16x + 64 = \)

\( ({x - 8})^{2} \)

Thus :

\(C = 64\)

To find the equilibrium price and quantity, we need to set the quantity supplied equal to the quantity demanded and solve for the price.

Given:
Q = 200 + 3P (quantity supplied)
Qd = 400 - P (quantity demanded)

Step 1: Set Q = Qd
200 + 3P = 400 - P

Step 2: Solve for P
4P = 200
P = 50

Step 3: Substitute P = 50 back into the equations to find the equilibrium quantity.
Q = 200 + 3(50)
Q = 350

Therefore, the equilibrium price is $50 and the equilibrium quantity is 350.

Now, let's consider the case with a tax on buyers.

Given:
Q° = 400 - (2P + T) (quantity demanded after tax)

Step 1: Set Q° = Q (quantity demanded after tax = quantity supplied)
400 - (2P + T) = 200 + 3P

Step 2: Solve for P
5P + T = 200

Step 3: Substitute T = 20 into the equation and solve for P
5P + 20 = 200
5P = 180
P = 36

Step 4: Substitute P = 36 back into the equations to find the new equilibrium quantity.
Q = 200 + 3(36)
Q = 308

Therefore, the new equilibrium price is $36 and the new equilibrium quantity is 308.

The original equilibrium price and quantity are $50 and 350 respectively. After the tax is placed on buyers, the new equilibrium price and quantity become $36 and 308 respectively.

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Each guest receive 352 gm veal roast.

The pound is a unit of measurement used in the U. S. customary system and the British imperial system to measure weight. One familiar use of pounds is measuring how much a person weights.

We know that,

1 pound = 453.592 gm

12.4 pound = ? gm

12.4 pound = 12.4×453.592

                   = 5624.541 gm

Total number of guest = 16

Then,

Each guest receive veal roast = \(\frac{5624.541 gm}{16}\)

                                                 = 352 gm

Hence, Each guest receive veal roast is 352 gm.

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Allura, this is the solution:

As you can see we have two right triangles in the figure:

Therefore,

Step 1: Let's calculate the hypotenuse of the left triangle, as follows:

c² = a² + b²

c² = 12² + 18²

c²= 144 + 324

c² = 468

c = 21.63

Step 2: Let's calculate the sides of the right triangle on the right, this way:

Leg 1 = 21.63

Leg 2 = x

Hypotenuse = 12 + y

Height of the right triangle = 18

In consequence, to find the value of the hypotenuse and y, we have:

c = 21.63²/√21.63² - 18²

c = 468/√468 - 324

c = 468/12

c = 39

Step 3: Now, we can solve for y, this way:

39 = 12 + y

y = 39 - 12

y = 27

The correct answer is D. 27

Answer:

12\(x^{4}\)y\(z^{7}\)√3x

Step-by-step explanation:

2√108\(x^{9}\)y²\(z^{14}\)

so you will need two of something to take one out from under the squareroot

we can rewrite \(z^{14} = z^{7} *z^{7}\) so we can take a \(z^{7}\) out

we can rewrite y² as y*y so we can take a y out

we can rewrite \(x^{9}\) as \(x^{4} *x^{4} *x\) so we can take a \(x^{4}\)out

for 108 think what is the smallest prime number that divides 108 and is 2

108= 2*54

same algorithm, smallest prime number that divides 54 is 2 so

108=2*2*27

same algorithm, smallest prime number that divides 27 is 3 so

108=2*2*3*9

we know 9 is 3*3 so

108=2*2*3*3*3 we can take out one 2 and one 3

put them all toghether now

2*2*3*\(x^{4}\)*y*\(z^{7}\)√3x = 12\(x^{4}\)y\(z^{7}\)√3x

The P-value in each of the given situations for testing the null hypothesis H₀: p = 0.6 using a z-test can be determined as follows:

A. Hₐ: p > 0.6, z = 1.47: The P-value is the probability of observing a z-score greater than 1.47, which can be found by calculating the area under the standard normal curve to the right of 1.47.

B. Hₐ: p < 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70, which can be found by calculating the area under the standard normal curve to the left of -2.70.

C. Hₐ: p ≠ 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70 or greater than 2.70, which can be found by calculating the sum of the areas under the standard normal curve to the left of -2.70 and to the right of 2.70.

D. Hₐ: p < 0.6, z = 0.25: The P-value is the probability of observing a z-score less than 0.25, which can be found by calculating the area under the standard normal curve to the left of 0.25.

To determine the P-value, we need to calculate the corresponding areas under the standard normal curve based on the given z-scores. The P-value represents the probability of observing a z-score as extreme or more extreme than the given value, assuming the null hypothesis is true.

By using standard normal distribution tables or statistical software, we can find the probabilities associated with the given z-scores. These probabilities represent the P-values for each scenario, providing a measure of evidence against the null hypothesis.


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Answer:

175m²

Step-by-step explanation:

Total area (of pool):

50 × 21 = 1050

Area of each lane:

1050 ÷ 6 = 175

7+(-1) = -3

Steps of adding 7+(-10) using number line are as following:

1) Draw a number line by ranging from -10 to +10.

2) Point out 7 on the number line.

3) Because -10 is added to 7 on the number line, please move 10 numbers left to 7 on the number line. We always go left in addition of a negative number on the number line.

4) The number we reach -3 on left side would be our final sum.

5) From the number we can clearly see that moving 10 number on left to 7, we get -3.

Note: We are moving left because of negative sign in front of 10.

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Answer:

10 percent

Step-by-step explanation:

7.5 times 10 = 75.

plez give me brainiest

Answer:

D) 100% Positve

Step-by-step explanation:

You would choose the second option (y=1/3x) because the slope would be 1/3. Think of the slope as your directions, you go up 1 over to the right 3 times. Since the y-intercept is 0, you don't have to add anything at the end.

Hope this answer makes sense.

Answer:

2(z+3)

Step-by-step explanation:

Answer:

C Multiply the numerator and the denominator of the fraction by 2.

Step-by-step explanation:

C

Answer:

C is the best method

Step-by-step explanation:

Usually what I would do whenever I have this type of problem is match the denominator (bottom value) with 100.

I try and do this because all percentages are out of 100. For example you would say I got 90 percent. And this is equivalent to 90 over 100.

So, to make the denominator which is 50 into 100 I would need to multiply by 2.

Since whatever you do to the bottom you have to do to the top to keep the fraction equivalent, you would have to multiply the top by 2 as well.

45 * 2 = 90

50 * 2 = 100

So your answer would be C because he changes the bottom into an easy fraction to calculate percentage.

Sorry If my explanation is a little unclear. Hope you have your question solved. Ask me if you have any further questions.

Answer:

y=4x-1

Step-by-step explanation:

I plugged the table into Desmos and I determined the slope and intercept from that.