What is the surface area of the cylinder with height 7 cm and radius 5 cm? Round
your answer to the nearest thousandth.

Step-by-step explanation:

Given expression

8(5s)

The expression equivalent to the given expression is

B. 5(s 8)

D . 40s

Hope it will help :)❤

The value of x for the right triangles is derived to be x = 1 or x = -2/3 using the trigonometric ratio of tangent for the angles a and b

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tan a = (x + 2)/x and tan b = 4/(3x - 1) {opposite/adjacent}

(x + 2)/x = 4/(3x - 1)

(3x - 1)(x + 2) = 4x {cross multiplication}

by expansion we have a quadratic equation;

3x² - x - 2 = 0

we can rewrite the equation and factorise as follows;

3x² + 2x - 3x - 2 =0

x(3x + 2) - 1(3x + 2) = 0

(x - 1)(3x + 2) = 0

x = 1 or x = -2/3

Therefore, the value of x for the right triangles is derived to be x = 1 or x = -2/3 using the trigonometric ratio of tangent for the angles a and b.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

Solution given:

3(5x+8)

distribute

15x+8*3

15x+24 is a required answer.

Answer:

15x + 24

Step-by-step explanation:

Apply the Distributive Property of Multiplication.  Multiply each of the two terms inside parentheses by 3:

3(5x + 8) = 15x + 24

Answer:

y=3/2x-4

This is the answer.

Given :-

A line having a slope of 3/2 passes through (2,-1) .

To Find :-

The equation of the line .

Answer :-

According to the question ,

m = 3/2

Point = (2,-1)

We know Point slope form of the line as ,

y - y¡ = m ( x - x ¡ )

Substitute ,

y - (-1) = 3/2 ( x - 2 )

y + 1 = 3/2x - 3/2*2

y +1 = 3/2x - 3

2( y +1) = 3/2x *2 - 3*2

2y + 2 = 3x - 6

3x -2y -8 = 0

Answer:

x = 8 or x = -1 is the answer

Step-by-step explanation:

3x² - 21x -24

divide with 3

x² - 7x - 8

Factorizing,

x² + x - 8x - 8

x(x + 1) -8 (x + 1)

(x - 8) (x + 1)

x = 8,-1

Answer:

False

Step-by-step explanation:

The question is asking for the absolute value of -1. The absolute value is the distance of a number from 0. Think of a number line. -1 is one place away from 0, so the absolute value of -1 is 1. Therefore, the statement is not true.

Answer:

p=3 , q=1 , r=2

Step-by-step explanation:

1176=2*2*2*3*7*7

1176=(2^3)*(3^1)*(7^2)

given that 1176 = (2^p)*(3^q)*(7^r)

Comparing Equation 1 & 2

we get p=3 , q=1, r=2

The relationship between ∠8 and ∠4 include the following: A. corresponding angles.

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem to lines l and m, we have the following:

8 ≅ ∠4

3 ≅ ∠7

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Answer:

Before I answer both this clubs are banter, and how has Manchester united won more games than Liverpool

Step-by-step explanation:

Man U has won 11 matches meaning 11/18 matches times 100= 61 1/9%

Looserpool has won 9 matches out of 18 9/18 times 100= 50 %

So obviously its Manchester useless

Given:

In an asteroid field, 75% of the asteroids are carbonaceous asteroids.

There are 375,000 carbonaceous asteroids in the asteroid field.

To find:

The number of asteroids that are not carbonaceous.

Solution:

Let the total number of asteroids be x.

According to question,

\(75\%\text{ of }x = 375000\)

\(\dfrac{75}{100}x=375000\)

\(0.75x=375000\)

Divide both sides by 0.75.

\(x=\dfrac{375000}{0.75}\)

\(x=500000\)

Asteroids not carbonaceous = Total asteroids - Carbonaceous asteroids

                                                \(=500000-375000\)

                                                \(=125000\)

Therefore, 125,000 asteroids are not carbonaceous.

Answer:

(2) The statement is true.

-1 < r < 1

The probability that someone is driving slower than 20 mph on the 405 freeway is approximately 7.08%.

We are given that the average speed on the 405 freeway is 42 mph and is normally distributed with a standard deviation of 15 mph.

To solve this problem, we need to use the standard normal distribution since we are given the mean and standard deviation of the speed on the 405 freeway.

We know that

\(Z=\frac{X-\mu}{\sigma}\)

Here, X = 20

\(\mu=42\)

\(\sigma=15\)

Z=(20-42)/15

Z=-22/15

Z=-1.47

Using a standard normal distribution table

P(Z<-1.47)=0.0708

or 7.08%

Therefore, the probability that someone is driving slower than 20 mph on the 405 freeway is approximately 0.0708 or 7.08%.

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Based on the given equation of b -4/6=b/2, the value of the variable b, can be found to be -2

The variable can be found by solving the equation through the operations of mathematics.

First, cross-multiply:

b -4/6 = b/2

b - 4 = 6b / 2

After cross-multiplying, collect like terms:

b - 4 = 3b

b - 3b = 4

-2b = 4

b = 4 / -2

b = -2

In conclusion, the variable is -2.

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The theorem that proves that the triangles are congruent is the Side-Side-Side (SSS) Congruence Theorem.

The Side-Side-Side (SSS) Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This theorem is useful for proving that two triangles are congruent without having to use angles. The SSS Congruence Theorem is a useful tool for solving geometry problems involving triangles. It can be used to find the unknown side length of a triangle given the lengths of the other two sides, or in more complicated proofs involving multiple triangles. This theorem is also helpful in determining the area of a triangle, as the area is proportional to the product of the lengths of the sides.

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The distance of the ball from the foot of the tower is : 35.18m

The ball would be moved 57.2m away from the foot of the tower for the Angle of elevation to be halved.

Angle of elevation is the angle formed between the horizontal and the  line of view from the vertical.

Analysis:

The height of the tower and the distance of the ball from the foot of the tower form a right angle triangle.

so we use trigonometry.

a) let distance of the ball from foot of tower be x.

  so that, tan 52 = 45/x

  x = 45/tan52

  x = 45/1.279 = 35.18m

b) let the distance of the ball in the new position from the foot of the tower be y.

if the angle of elevation is halved, then new angle is 52/2 = 26°

 tan 26 = 45/y

y = 45/tan26 = 45/0.487 = 92.4m

distance moved from old position to new position = 92.4 - 35.18 = 57.2m

In conclusion, the distance of the ball from the foot of the tower and the distance the ball should move to make its elevation 26° are 35.18m and 57.2m respectively.

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Answer: C or B sorry if its wrong

Step-by-step explanation:

have a lovely day

The time that the ball is in the air if the player lets the ball drop is 2.145 sec

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-16t²+32t+5

by comparing this equation to the standard form of the quadratic equation we get

a=-16 b=32 c=5

the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:

the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)

t = -32/2×-16

t=1sec

by putting h(t) to zero and determining the time (t) when the ball hits the ground:

-16t²+32t+5=0

-16(t²+2t+5/16)=0

t²-2t-5/16=0

(t)²-2×1×t+(1)²-5/16=1

(t-1)²=21/16

t-1=√21/√16

t=1+4.58/4

t=1+1.145

t=2.245sec

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Answer:

638 miles / 11 hours = 58mph

So if he is traveling at 58 miles per hour for 7 hours, multiply the two numbers. 7(58) = 406

At the same rate of speed, Eric would travel 406 miles in 7 hours.

Step-by-step explanation:

I hope you undertand it

Answer:

522

Step-by-step explanation:

638 miles.......11hours

x miles ............ 9 hours

x = 638 * 9 / 11 = 522 miles

To determine the amount of N2(g) produced from the reaction between NH3 and CuO, we need to calculate the limiting reactant first.

First, we need to balance the chemical equation:

2 NH3 + 3 CuO -> N2 + 3 Cu + 3 H2O

The molar mass of NH3 is 17.03 g/mol, and the molar mass of CuO is 79.55 g/mol.

To find the limiting reactant, we compare the number of moles of each reactant. The number of moles can be calculated by dividing the given mass by the molar mass.

For NH3: moles of NH3 = 9.05 g / 17.03 g/mol

For CuO: moles of CuO = 45.2 g / 79.55 g/mol

Next, we calculate the mole ratio of NH3 to N2 using the balanced equation, which is 2:1.

To find the moles of N2 produced, we multiply the moles of NH3 by the mole ratio (2 moles NH3 : 1 mole N2).

Finally, to find the mass of N2 produced, we multiply the moles of N2 by the molar mass of N2, which is 28.02 g/mol.

The final calculation gives us the mass of N2 produced from 9.05 g of NH3 and 45.2 g of CuO.

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461+1=462

462÷7=66

Your answer is 461

Answer:

461

Step-by-step explanation:

Work backwards.

7 X 66=462

462-1=461

So 461 is the answer

arccos(2x) + arccos(x) = π/2

Apply cos to both sides, then expand the right side using the identity I mentioned in a comment:

cos(arccos(2x) + arccos(x)) = cos(π/2)

cos(arccos(2x)) cos(arccos(x)) - sin(arccos(2x)) sin(arccos(x)) = 0

Now think of arccos(2x) and arccos(x) as angles in two right triangles. Let θ = arccos(2x) and φ = arccos(x) (and let's also assume that both have measure between 0 and π/2). These are angles such that

cos(θ) = 2x

cos(φ) = x

In these triangles, you then have

sin(θ) = sin(arccos(2x)) = √(1 - 4x ²)

sin(φ) = sin(arccos(x)) = √(1 - x ²)

while

cos(θ) = cos(arccos(2x)) = 2x

cos(φ) = cos(arccos(x)) = x

So the original equation is transformed to

2x ² - √(1 - 4x ²) √(1 - x ²) = 0

Solve for x :

2x ² = √(1 - 4x ²) √(1 - x ²)

(2x ²)² = (√(1 - 4x ²) √(1 - x ²))²

4x ⁴ = (1 - 4x ²) (1 - x ²)

4x ⁴ = 1 - 5x ² + 4x ⁴

0 = 1 - 5x ²

x ² = 1/5

x = ± 1/√5

Now bearing in mind that we assume 0 < φ < π/2, we should have cos(φ) = x > 0, so we take the positive solution,

x = 1/√5

if n decreases then the value of level of significance of each samples \(\alpha\) decreases

1. Critical Value: The value of the statistic for which the test just rejects the null hypothesis at the given significance level.

2. Power of the Test: The probability that the test correctly rejects the null hypothesis when the alternative is true.

3. Significance Level: The prescribed rejection probability of a statistical hypothesis test when the null hypothesis is true.

4. Size of the test: The probability that the test incorrectly rejects the null hypothesis when it is true.

if n decreases then the value of level of significance of each samples \(\alpha\) decreases and hence 1- \(\alpha\) increases which are called the rejection of test sample increases

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There are 128 four-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7, with 7 appearing before 3).

To determine the number of 4-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7 with 7 appearing before 3), we can break down the problem step by step.

Step 1: Choose the positions of 3 and 7.

Since 7 must appear before 3, we have two possible cases:

Case 1: 7 is in the thousands place, and 3 is in the hundreds place.

Case 2: 7 is in the hundreds place, and 3 is in the thousands place.

Step 2: Determine the digits in the remaining two positions.

In the remaining two positions (tens and units place), we have eight possible digits to choose from (0, 1, 2, 4, 5, 6, 8, 9). This is because we have used the digits 3 and 7, leaving eight options for the remaining two positions.

Step 3: Calculate the total number of valid numbers.

For each case in Step 1, we multiply the number of choices from Step 2 to get the total count.

Case 1: 7 in thousands place, 3 in hundreds place.

In this case, we have 8 choices for the tens place and 8 choices for the units place. The total count for Case 1 is 8 * 8 = 64.

Case 2: 7 in hundreds place, 3 in thousands place.

Similarly, we have 8 choices for the tens place and 8 choices for the units place. The total count for Case 2 is also 8 * 8 = 64.

Step 4: Sum up the counts from both cases.

To get the final answer, we sum up the counts from both cases:

64 (Case 1) + 64 (Case 2) = 128.

Therefore, there are 128 four-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7, with 7 appearing before 3).

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Answer:

5/6

Step-by-step explanation:

15/28 - 5/12

LCM of 28 & 12 is 336

420 - 140

--------------

336

=280

--------

336

= 280/336

=5/6

Answer: It's B

Step-by-step explanation: I cheated but it's right ;-;

The answer of the given question based on the Newton's law is , the scenario demonstrates Newton's third law of motion.

Newton's laws of motion are set of fundamental principles that describe  behavior of a objects in motion. They were formulated by Sir Isaac Newton in the 17th century and are considered to be the foundation of classical mechanics. It consists of three laws of motion they are , Newton's First Law of Motion , Newton's Second Law of Motion , Newton's Third Law of Motion. These laws explain how objects move and interact with one another, and they have numerous applications in physics, engineering, and other fields.

The scenario given describes Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

In this case, the action is the force exerted by the car on the wall, and the reaction is the force exerted by the wall on the car. According to Newton's third law, these forces are equal in magnitude but opposite in direction, which means that the car and the wall exert the same amount of force on each other in opposite directions.

Therefore, the scenario demonstrates Newton's third law of motion.

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Answer:

Change in Y over change in X. So down 8 and over 2. Simplified it would be 4/1

Answer:

42/6

Each color blocks have 6 each, and they're 7 groups of them. Simple.