A scale model of a building has a height of 1/5 meter. The scale of the model is 1cm=0.5m. What is the height of the building?

Answer:

D

Step-by-step explanation:

This is because if u subsitute x with 17, 17x5 is 85 and 85+95= 180

\(\color{plum}\tt\bold{(D) \: 17}\)

Given :

▪︎Angle (5x)° and angle 95° are supplementary angles.

Which means :

\( = \tt5x + 95 = 180\)

\( = \tt5x = 180 - 95\)

\( = \tt5x = 85\)

\( \hookrightarrow\tt \color{plum}x = 17\)

Thus, the value of x = 17

Let us check whether or not we have found out the correct value of x by placing 17 in the place of x:

\( =\tt5 \times 17 + 95 = 180\)

\( =\tt 85 + 95 = 180\)

\( =\tt 180 = 180\)

Since the sum of both angles is equivalent to 180[85+95=180], we can conclude that we have found out the correct value of x.

Therefore, the correct option is (D) 17

Answer:

The area of the shape is 693 m^2

Step-by-step explanation:

Here, we want to calculate the area of the given shape

Mathematically, what we have to do here is to multiply the base of the shape with the height

We have this as;

21 * 33 = 693 m^2

Answer: 3a

Step-by-step explanation: 4a - 1a = 3a

(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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Part A: percent of 70 is 10.

x% of 70 = 10

70x / 100 = 10

x = 1000 / 70

x = 14.28 %.

Part B: percent of 2.8 is 20.

x% of 2.8 = 20

2.8x/ 100 = 20

x = 2000/ 2.8

x = 714.28%

Part C: percent of 90 is 18.

x% of 90 = 18

90x/100 = 18

x = 1800 / 90

x = 2 %

Part D: percent of 10 is 55.

x% of 10 = 55

10x / 100 = 55

x = 5500/ 10

x = 550%.

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Answer and Step-by-step explanation:

Theoretically, we should expect the coin to flip 250, or very close to 250 times, and land on heads.

This is because the probability of getting heads is \(\frac{1}{2}\), or 50%.

There is a 50% chance of landing heads or tails, so that means it would land 250 times on heads out of 500 flips of the coin.

#teamtrees #PAW (Plant And Water)

Answer:

250 times

Step-by-step explanation:

The coins has the heads or tails, with two options there is a 50% probability of landing on heads or tails.

500 x 50% = 250 times

In triangle ABC, AB = 12, BD = 4, BC  = 8 Then the length of AC  = 14.42 units.

In triangle ABC, angle ABC = 90º, which means it's a right triangle. Point D lies on segment BC, with AD as an angle bisector. Given AB = 12 and BD = 4, we need to find AC.

Since AD is an angle bisector, it divides angle BAC into two congruent angles. In right triangles, angle bisectors also divide the opposite side (BC) proportionally to the adjacent sides (AB and AC). Let CD = x. Thus:

BD/AB = CD/AC
4/12 = x/AC
x = (4 * AC)/12

Now, apply the Pythagorean theorem for right triangle ABC:

AB² + BC² = AC²
12² + (4 + x)² = AC²

Substitute x from the proportion:

12² + (4 + (4 × AC)/12)² = AC²
144 + (4 + (4 × AC)/12)² = AC²

Solve for AC:
12² + 8²  = AC²
144 + 64  = AC²

208  = AC²

Taking square root on both the sides

√208  = AC

14.42 units  = AC

So, the length of side AC in triangle ABC is approximately 14.42 units.

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The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.

This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.

It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.

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Applying SOHCAHTOA, the value of the missing side in the right triangle is calculated as: x ≈ 11.2.

SOHCAHTOA is an acronym for the basic trigonometric ratios that can be used to find the missing side of a right triangle. It means:

SOH implies sin ∅ = opposite / hypotenuse

CAH implies cos ∅ = adjacent / hypotenuse

TOA implies tan ∅ = opposite / adjacent.

To find the missing side, x, we will apply SOH:

sin 36 = x/19

19 * sin 36 = x

x ≈ 11.2

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Answer:

86, 65

Step-by-step explanation:

Quotient is 86

Remainder is 65

Answer:

dilation of 2 is may be the answer

Answer:

-32.4

Step-by-step explanation:

What you do is the -4 x the 8. after that you should get 32. Then you do 4 x the 1. Hence, you should get 4. Because of that you put the 32 and 4 together. your final answer is -32.4

Answer:

The answer is A. -32.4

Step-by-step explanation:

What you do is the -4 x the 8. after that you should get 32. Then you do 4 x the 1. Hence, you should get 4. Because of that you put the 32 and 4 together. your final answer is -32.4

Hope this helps  :)

Answer:

79,210,000

Step-by-step explanation:

:)

Answer:

∠Q = 35.5°

Step-by-step explanation:

We are given;

q = 6.5 inches

o = 8.6 inches

∠P = 55°

Let's first use cosine rule to find p.

p² = q² + o² - 2qo cos P

Plugging in the relevant values;

p² = 6.5² + 8.6² - (2 × 6.5 × 8.6 × cos 55)

p² = 42.25 + 73.96 - 32.0629

p² = 84.1471

p = √84.1471

p = 9.17 inches

Using sine rule, we can find ∠Q;

p/sin P = q/sin Q

sin Q = (q•sinP)/p

sin Q = (6.5 × sin 55)/9.17

sin Q = 0.5806

Q = sin^(-1) 0.5806

Q ≈ 35.5°

Answer:

47.5  

Step-by-step explanation:

From delta math

Answer:

y = 4.75x + 4

Step-by-step explanation:

it would be $4.75 for each game and you would only pay for shows once

The equation that represents the amount, in dollars, y,

for x games bowled is y = 4.00 + 4.75x

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The cost for bowling includes a fixed cost of $4.00 for shoes, and an additional cost of $4.75 for each game bowled.

y = 4.00 + 4.75x

This equation can be interpreted as follows: the fixed cost of $4.00 is added to the variable cost of $4.75 per game, multiplied by the number of games bowled (x).

The result is the total cost, represented by y

Therefore,

The total cost for x games bowled can be represented by the equation:

y = 4.00 + 4.75x

where y is the total cost in dollars, and x is the number of games bowled.

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Answer: 105 square units

Step-by-step explanation: To find the surface area of a triangular prism, you need to find the area of each face and add them together.

In this case, the triangular bases have the same area, which is:

(1/2) x 7 x 5 = 17.5 square units

The rectangular faces have an area of:

7 x 10 = 70 square units

Adding the areas of all the faces, we get:

17.5 + 17.5 + 70 = 105 square units

Therefore, the surface area of the triangular prism is 105 square units.

Answer:

4a^2

Step-by-step explanation:

GCF of 12 and 32 is 4.

GCF of a^3 and a^2 is a^2.

Therefore, the answer is 4a^2.

Answer:

Step-by-step explanation:

2x+1       - the first odd integer

2 x+1 + 2 = 2x+3   - the next odd integer consecutive to 2x+1

2x+3+2 = 2x+5 - the odd integer consecutive to 2x+3 (the third consecutive odd integer)

2x+1 + 2x+3 + 2x+5  - the sum of three consecutive odd integers

therefore the equation:

                                     2x+1 + 2x+3 + 2x+5 = -3

6x + 9 = -3

6x = -12

x = -2

2x+1=2(-2)+1=-3

2x+3=2(-2)+3=-1

2x+5=2(-2)+5=1

the three consecutive odd integers whose sum is -3 are: -3,-1,1

The values of c_0 =  0 ,c_1 =  0 ,c_2 =  10 ,c_3 =  20

The Maclaurin series of the function f(x) = 10x^2 sin(6x) can be written as f(x) = ∑[n=0 to infinity] c_n x^n, where the coefficients c_n are given by:

c_n = (f^n(0))/n!

In this case, the first few derivatives of f(x) are:

f(x) = 10x^2 sin(6x)
f'(x) = 20x sin(6x) + 60x^2 cos(6x)
f''(x) = 20 sin(6x) + 120x cos(6x) - 360x^2 sin(6x)
f'''(x) = 120 cos(6x) - 720x sin(6x) - 720x cos(6x) + 2160x^2 sin(6x)

Evaluating these derivatives at x=0 gives:

f(0) = 0
f'(0) = 0
f''(0) = 20
f'''(0) = 120

Therefore, the first few coefficients of the Maclaurin series are:

c_0 = f(0)/0! = 0
c_1 = f'(0)/1! = 0
c_2 = f''(0)/2! = 20/2 = 10
c_3 = f'''(0)/3! = 120/6 = 20

The rest of the coefficients can be found by taking higher order derivatives of f(x) and evaluating them at x=0.

So, the Maclaurin series of the function f(x) = 10x^2 sin(6x) can be written as:

f(x) = 0 + 0x + 10x^2 + 20x^3 + ...

or

f(x) = ∑[n=0 to infinity] c_n x^n

where c_0 = 0, c_1 = 0, c_2 = 10, c_3 = 20, and so on.

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a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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Answer:

A

Step-by-step explanation:

x. y = 28

check attachment

There are 160 numbers between 1 and 500 that are multiples of one or more of 5, 6, or 7.

To solve this problem, we need to use the inclusion-exclusion principle.

First, we find the number of multiples of 5 between 1 and 500:

⌊500/5⌋ = 100

Similarly, the number of multiples of 6 and 7 between 1 and 500 are:

⌊500/6⌋ = 83

⌊500/7⌋ = 71

Next, we find the number of multiples of both 5 and 6, both 5 and 7, and both 6 and 7 between 1 and 500:

Multiples of both 5 and 6: ⌊500/lcm(5,6)⌋ = 41

Multiples of both 5 and 7: ⌊500/lcm(5,7)⌋ = 35

Multiples of both 6 and 7: ⌊500/lcm(6,7)⌋ = 29

Finally, we find the number of multiples of all three 5, 6, and 7:

Multiples of 5, 6, and 7: ⌊500/lcm(5,6,7)⌋ = 11

By the inclusion-exclusion principle, the total number of numbers that are multiples of one or more of 5, 6, or 7 is:

n(5) + n(6) + n(7) - n(5,6) - n(5,7) - n(6,7) + n(5,6,7)

= 100 + 83 + 71 - 41 - 35 - 29 + 11

= 160

Therefore, there are 160 numbers between 1 and 500 that are multiples of one or more of 5, 6, or 7.

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If I wanted to measure my backyard to see if there was enough room for a basketball court, the math function which I would use is B)Geometry. So, correct option is B)

Basket ball court is either in the shape of rectangle or Square, and the Rod is in the shape of Cylinder and the net is  in the shape of Hemispherical Bowl.

Along with the geometrical knowledge, we need knowledge of line and segment as backyard contains large number of straight lines.

Hence, option B)Geometry is correct.

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(Complete question) is:

If you wanted to measure your backyard to see if there was enough room for a basketball court, which math function would you use from among?

A)Arithmetic,

B)Geometry,

C)Calculus

D)Algebra

Answer:

option c

Step-by-step explanation:

- Span{v1, v2, v3, 0} is equal to the span of {v1, v2, v3}.
- Span{v1, v1-v2, v3} is equal to the span of {v1, v2, v3}.
- Span{v1, v2} is NOT equal to the span of {v1, v2, v3}.

Let's analyze each of the sets of vectors to determine if they are equal to the span of {v1, v2, v3}:
1. Span{v1, v2, v3, 0}:
This set is equal to the span of {v1, v2, v3} because adding the zero vector (0) does not affect the linear independence or the span of the other vectors.

A span is the set of all possible linear combinations of the vectors, and since the zero vector does not change the linear combinations, the span remains the same.
2. Span{v1, v1-v2, v3}:
This set is also equal to the span of {v1, v2, v3}.

The reason is that the vector (v1-v2) can be written as a linear combination of v1 and v2: (v1-v2) = 1*v1 + (-1)*v2.

Since all vectors in this set can be expressed as linear combinations of {v1, v2, v3}, the span remains the same.
3. Span{v1, v2}:
This set is NOT equal to the span of {v1, v2, v3} because it is missing the vector v3.

Since v1, v2, and v3 are linearly independent, removing one of them (v3 in this case) means that the set cannot span the same space as {v1, v2, v3}.

It has a lower dimension, and therefore, the span is different.

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Answer: b=−a2−2ax+2x−7

When you said, “Find the values of a and b” I can do B and that all...

Step-by-step explanation: hope this help

The sum of x + y is always equal to 14.

What is positive integers?

Positive integers are the numbers that we use to count: 1, 2, 3, 4, and so on. A collection of positive integers excludes numbers with a fractional element that is not equal to zero and negative numbers.

Since x and y are positive integers, we can find the possible values of x and y by finding the factors of 13. The positive integer factors of 13 are 1 and 13. Therefore, the possible pairs of x and y are (1, 13) and (13, 1).

The sum of the two values for x and y in each pair is 14.

So, The sum of x + y is always equal to 14.

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Answer:

$835 (Answer c)

Step-by-step explanation:

Write out the Cost function:  C(n) = $65 + ($11/person)n

Then the total cost for 70 people would be C(70) = $65 + ($11/person)(70 people)

C(70) = $65 + $770 = $835 (Answer c)

The solution is v = \(e^{\frac{-1}{8}\)(c+\(8e^{\frac{1}{8} }\)).

What is the velocity?

The velocity of an object is its speed and direction of motion. The idea of velocity is crucial in kinematics, the part of classical mechanics that explains the motion of bodies. Velocity is a physical vector quantity that requires both magnitude and direction to define.

Here, we have

Given: A model for the velocity v at time t of a certain object falling under the influence of gravity in a viscous medium is given by the equation: (dv/dt)= 1 - (v/8).

We have the differential equation:

(dv/dt)= 1 - (v/8)

dy/dt + v/8 = 1

v' + v/8 = 1

This is a linear differential equation. We conclude that is

p(t) = 1/8

q(t) = 1

We have the formula

v = \(e^{-\int\limits {p(t)} \, dt }\)(c+∫q(t).\(e^{\int\limits {p(t)} \, dt }\))

Now, we calculate the solution of the given differential equation:

v = \(e^{\int\limits\frac{-1}{8} \, dt\)(c+∫1.\(e^{\int\limits {\frac{1}{8} } \, dt }\))

v = \(e^{\frac{-1}{8}\)(c+\(8e^{\frac{1}{8} }\))

Hence, the solution is v = \(e^{\frac{-1}{8}\)(c+\(8e^{\frac{1}{8} }\)).

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