A hollow cylinder, given some initial velocity, rolls up an incline to a height of 1. 0 m without slipping. If a hollow sphere of the same mass and radius is given the same initial velocity, how high does it roll up the incline?.

Answer:

x= 15

Step-by-step explanation:

23-8= 15

x=15

The height is increasing at the rate of (6/5π) ft/min.

It is given that Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min. Also, its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.

For this, we need to find the volume of a cone. Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

The volume of a cone is - V=1/3hπr²

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Car insurance for an 18-year-old typically ranges from $200 to $400 per month.

The cost of car insurance for an 18-year-old can vary significantly depending on various factors. Young drivers, especially those with limited driving experience, are generally considered higher risk by insurance companies, which leads to higher premiums. Insurance providers take into account factors such as the driver's age, gender, location, type of vehicle, driving record, and credit history. Additionally, factors like the level of coverage and deductibles chosen, as well as discounts available, can also impact the cost. It's important for young drivers to shop around and compare quotes from different insurance companies to find the best coverage options at the most affordable rates. Additionally, taking driver's education courses and maintaining a clean driving record can help in reducing insurance costs over time.

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What is the average monthly cost of car insurance for an 18-year-old?

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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The index forms are solved to give:

17. 5x

18. 3x^2

19. 4

20. 2

Index forms are described as mathematical forms of writing numbers that are too small or too large in more convenient ways.

From the information given, we have that;

\(\sqrt{\frac{100x^6}{4x^4} }\)

Find the square root

10x³/2x²

Divide the values

5x

\(\sqrt{\frac{81x^8}{9x^4} }\)

Find the square root

9x⁴/3x²

Divide the values

3x²

\(\sqrt{\frac{64x^9}{4x^7} }\)

Find the square root

8/2√x⁹/x⁷

4

\(\sqrt{\frac{24x^5}{6x^3} }\)

√4x²

Find the square root

2

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Answer:

5.4x10^9

Step-by-step explanation:

Answer:

Angle A is 30

Angle B is 150

Step-by-step explanation:

So we have the supplementary angles A and B. In other words:

\(A+B=180\)

We are also told that Angle B is 30 more than four times Angle A. In an equation, this is:

\(B=30+4A\)

We now have a system of equations. Solve by substitution of B into the first equation:

\(A+B=180\)

\(A+(30+4A)=180\)

Combine like terms:

\(5A+30=180\)

Subtract 30:

\(5A=150\)

Divide by 5:

\(A=30\)

So, Angle A is 30 degrees.

And since the angles are supplementary, this means that Angle B is 180 minus 30 or 150 degrees.

Answer:

I’m confused on what you want me to do but that is false

Step-by-step explanation:

Answer:

the answer is 1.309<1315

Answer:

d = A or 49

Step-by-step explanation:

25^2 =625

24^2 = 576

625-576= 49 or 7^2

Answer: 10+2t

Step-by-step explanation: I guess not sure sorry

Answer:

Point A reamains unchanged.

Step-by-step explanation:

Let

A(1, -1)

B(1, 1)

C(-4, -1)

D (-4, 1)

REFLECTED OVER Y-AXIS:

When we reflected over Y-AXIS we have to change the sign of X-Coordinates of all vertices so, above given vertices becomes

A(-1, -1)

B(-1, 1)

C(4, -1)

D (4, 1)

REFLECTED OVER X-AXIS:

When we reflected over X-AXIS we have to change the sign of Y-Coordinates of all vertices so, above given vertices becomes

A(-1, 1)

B(-1, -1)

C(4, 1)

D (4,-1)

When we rotated over 180 degree than we have to change the signs of both coordinates of all vertices

A(1, -1)

B(1, 1)

C(-4, -1)

D (-4,1)

we can see that after the opertion of all three processes i.e  reflected over the y-axis, reflected over the x-axis, and rotated 180ºrespectively vertices are same as original vertices so, Rectangle remain unchanged. and point A is also unchanged

From the amounts found using simple and compound interest formulas, we found that Carlie earns more interest than Jack by $1009.45.

What is the difference between simple and compound interests?

Simple interest is based on the principal amount, which is the main distinction between it and compound interest. Contrarily, compound interest is calculated using the principle sum and interest that has been compounded over the course of a period. Simple interest is a predetermined proportion of the principal amount borrowed or lent that is paid or received over a set period of time. Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

The complete question is given below.

Given,

  The principal amount deposited by both Jack and Carlie  P = $17,250

The rate of interest r = 6% = 0.06

The time period = 6.5

Jack's account earns annual simple interest and Carlie's account earns annual compound interest.

So the amount in each person's account after a time period of t = 6 years.

Jack:

Amount = P(1+rt) = 17250 ( 1 + 0.06*6) = $23,460

Carlie:

number of times compounded in a year n = 1

Amount = \(P(1 + \frac{r}{n})^{nt}\) = 17250 ( 1+0.06)⁶ = $24,469.45

Therefore from the amounts found using simple and compound interest formulas, we found that Carlie earns more interest than Jack by $1009.45.

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Answer:

x + 27 = - 12

x = - 39

Step-by-step explanation:

The formula for the nth partial sum of the given series \(7 - 7/6 + 7/36 + ..+ (-1)^{n-1} 7/6^{n-1} + ..\)  is \(s_n = (42/7)(1 - (-1/6)^n)\), and the sum of the series is 6.

The given series is  \(7 - 7/6 + 7/36 + ..+ (-1)^{n-1} 7/6^{n-1} + ..\)

To find the formula for the nth partial sum, we can use the formula for the sum of a geometric series:

\(S = a(1- r^n)/(1 - r),\)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 7 and r = -1/6. The formula for the nth partial sum is:

\(s_n = 7(1 - (-1/6)^n)/(1 + 1/6) = (42/7)(1 -(-1/6)^n)\).

To find the sum of the series, we can take the limit as n approaches infinity:

\(\lim_{n- \to \infty} s_n\)

\(= \lim_{n- \to \infty} a_n (42/7)(1 - (-1/6)^n)\)

= (42/7)(1 – 0) = 6.

Therefore, the sum of the given series is 6.

In summary, the formula for the nth partial sum of the given series is \(s_n = (42/7)(1 - (-1/6)^n)\), and the sum of the series is 6.

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Answer:

The age of the youngest friend is 9 years old.

Step-by-step explanation:

3a = 30 - 3

= 27 ÷ 3

= 9

= 9 + 10 + 11 = 30

= 9 is the smallest number. So, the youngest friend is 9 years old.

Answer:

9

Step-by-step explanation:

11+10+9 = 30

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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Answer:

B

Step-by-step explanation:

It made more machines per hour than the other ones

The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

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The cost to send 130 text messages is:

We know that,

The total cost of sending 80 text messages =  $8.00

So, the cost of sending 1 text message = $8/80

=$0.1 per text message

The cost of sending 130 text messages = 130*$0.1

Therefore, the cost incurred to send 130 text messages = $13

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Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

the formula for y is y(t) = Ce^(0.06t), where C is a positive constant.

What is Equation?

In mathematics, an equation is a statement that asserts the equality of two expressions that are joined by the equal sign "=".

The differential equation dy/dt = 0.06y represents the growth of a bacterial colony, where y is the number of bacteria and t is the time. To find the formula for y, we need to solve this differential equation.

The given equation is separable, meaning we can separate the variables y and t on opposite sides of the equation:

dy/y = 0.06 dt

Integrating both sides, we have:

∫(1/y) dy = ∫0.06 dt

ln|y| = 0.06t + C

Here, C is the constant of integration. We can write it as ln|C|, where C > 0.

Now, exponentiating both sides, we get:

|y| = e^(0.06t + ln|C|)

Since y represents the number of bacteria, it cannot be negative. Therefore, we can drop the absolute value signs:

y = Ce^(0.06t)

So, the formula for y is y(t) = Ce^(0.06t), where C is a positive constant.

None of the given options (A) through (E) match this form exactly. However, option (D) y(t) = 5e^(0.06) is very close. It should be y(t) = Ce^(0.06t), so option (D) is the closest representation among the given options.

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Answer:

ABCD has congruent diagonals.

ABCD is a rhombus.

ABCD has four congruent angles

Step-by-step explanation:

The following statements would be considered true

1. The quadrilateral ABCD could have the congruent diagonals as the diagonals are perpendicular

2. ABCD would be treated as the rhombus as it is a  regular quadrilateral

3. ANd, It Have the four congruent angles that means the four angles be 90 degrees

The other statements would be false.

Answer:

A,B,E

Step-by-step explanation:

Edge 2021

There are 3,628,800 different ways that 10 students can wear 10 hats, where each hat has a different color, and each student wears one hat.

The problem is related to permutation, in which order is important. In the problem, the 10 students are wearing 10 hats and each hat has a different color. So, we need to find out how many ways these students can wear these hats. For solving this type of problem, we use the permutation formula.

The formula is nPr = n!/(n-r)!.Here, n = total number of objects, r = number of objects taken at a time.In the given problem, the total number of objects is 10, and all objects are different.

The students are supposed to wear hats, and each student is wearing only one hat. So, we need to find the permutation of 10 students taken 10 at a time.

Using the permutation formula, we get,10P10=10!/0!=10×9×8×7×6×5×4×3×2×1=3,628,800.

Therefore, there are 3,628,800 different ways that 10 students can wear 10 hats, where each hat has a different color, and each student wears one hat.

Thus, we can conclude that the permutation formula can be used to find the number of ways when order is important, and the combination formula can be used to find the number of ways when order is not important. In the given problem, we found that there are 3,628,800 different ways that 10 students can wear 10 hats, where each hat has a different color, and each student wears one hat.

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Answer:

441.96

Step-by-step explanation: divide 1450 by 3.28

Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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Answer:

Probability ≈ 0.4762

Step-by-step explanation:

See explanation below;

\(Total Number of Outcomes - 10C4,\\10 ! / 4! * ( 10 - 4 ),\\10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 6 * 5 * 4 * 3 * 2 * 1,\\\\Total Outcomes = 210,\\\\Number of Outcomes - 5C2 * 5C2,\\5C2 = 5 * 4 * 3 * 2 * 1 / 2 * 1 * ( 3 * 2 * 1 ),\\\\Number of Outcomes - ( 10 )^2 = 100,\\\\Conclusion; Probability = 100 / 210 = 0.4762\)

Solution; Probability ≈ 0.4762

Answer:

D). 36

Step-by-step explanation:

98 + (x + 37) + (x + 47) = 180

182 + 2x = 180

2x = -2

x = -1

so now we plug it in.

-1 + 37 = 36

hope this helps!

Answer:

∠A = 36°

Step-by-step explanation:

Angle opposite 82° = 98°   (180° - 82° = 98°)

the sum of all angles in a triangle = 180° so:

180 = 98 + (x + 37) + (x + 47)

180 = 98 +2x +84

2x = -2

x = -1

∠A = -1 + 37 = 36°