Two cylinders have radii in the ratio 3:5 and heights in the ratio 10:9. Find the ratio of their volumes.
Please tell fast

6 students can be seated in a row of 6 chairs in 121 ways.

Given,

Number of students = 6

Number of chairs = 6

We have to find the number of ways the students can be seated in a row.

Here,

Jack insists on sitting in the first chair.

So, 1 way of sitting for jack.

Next,

5 students and 5 chairs are there.

So they can sit in;

5! = 120 ways

Therefore,

Total number of way of sitting is 120 + 1 = 121 ways.

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Answer:

7.6

Step-by-step explanation:

(i)The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. (ii)Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.

i. To sketch the signals x(t) and h(t), we can analyze their mathematical expressions. The input signal x(t) is a linear function with negative slope from t = 0 to t = 4, and it is zero for t > 4. The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. We can plot the graphs of x(t) and h(t) based on these characteristics.

ii. To determine the output signal y(t), we can use the convolution integral, which is given by the expression:

y(t) = ∫[x(τ)h(t-τ)] dτ

In this case, we substitute the expressions for x(t) and h(t) into the convolution integral. By performing the convolution integral calculation, we obtain the expression for y(t) as a function of t.

To sketch the output signal y(t), we can plot the graph of y(t) based on the obtained expression. The shape of the output signal will depend on the specific values of t and the coefficients in the expressions for x(t) and h(t).

Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.

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Answer:The end of immigration quotas in the 1960s led to

a significant decrease in safe places for refugee immigrants.

a significant increase in discrimination against immigrants.

a significant increase in the number of Asian immigrants.

a significant decrease in the number of Asian immigrants.

Step-by-step explanation:

Answer:

\(\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }\)

Step-by-step explanation:

hello,

\(2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2\)

hope this helps

Answer:  Yes

Step-by-step explanation:

I hope this makes sense!  : )

Answer:

+ 9

Step-by-step explanation:

x²+ 6x

to complete the square

add ( half the coefficient of the x- term )² to x² + 6x

x² + 2(3)x + 3²

= x² + 6x + 9

= (x + 3)² ← a perfect square

Answer:

13/3

Step-by-step explanation:

Write as a fraction first,

0.65/0.15

convert decimal to fractions,

13/20/3/20 = 13/3

Answer:

C: Nick's final score is 85 points.

Explanation:

Nick initially scores 90 points on his first turn. On the next, he lost 15 points and lost 10 more. 15 plus 10 would be 25; when subtracted from 90, the difference is 65. On his final turn, he scores 20 points. When added to the current score of 65, the sum is 85 points. Nick's final score is 85 points.

Answer:

15630

Step-by-step explanation:

Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.

Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.

Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.

Then, by binomial distribution,

P(x≤30) =r=030nCr*pr*q(n-r)

Now we can substitute given values and find the desired probability,

P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)

P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50

P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r

P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r

The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.

P(x≤30) = 0.000932

Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.

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The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius is given as,

r = 36 / 2

r = 18 inches

The area of the circle is given as,

A = π x (18)²

A = 3.14 x 324

A = 1,017.36 square inches

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

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The complete question is given below.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth is cut from the square?

(π = 3.14)

1,017.36 in2

1,489.24 in2

1,182.96 in2

1,276.00 in2

Answer: 15000

Step-by-step explanation: Step by step solution for calculating 135 is 0.9 percent of what number

We already have our first value of 135 and the second value of 0.9. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1135 = 0.9% × Y

STEP 2135 =

0.9

100

× Y

Multiplying both sides by 100 and dividing both sides of the equation by 0.9 we will arrive at:

STEP 3Y = 135 ×

100

0.9

STEP 4Y = 135 × 100 ÷ 0.9

STEP 5Y = 15000

Finally, we have found the value of Y which is 15000 and that is our answer.

You can easily calculate 135 is 0.9 percent of what number by using any regular calculator, simply enter 135 × 100 ÷ 0.9 and you will get your answer which is 15000

Answer:

8.49 units

Step-by-step explanation:

1. The distance formula is: \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

2. Let's plug in the numbers: \(\sqrt{(-1-5)^{2} +(4--2)^{2} }\)

3. \(\sqrt{(-6)^{2} +(6)^{2} }\)

4. \(\sqrt{36 + 36}\)

5. \(\sqrt{72}\) ≈ 8.485

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

total cards = 52

Step 02:

probability:

p(event) = favorable outcomes / total outcomes

total cards = 52

total queens = 4

total face cards = 12

first event (queen):

p(queen) = 4 / 52

second event (face card):

without replacement

p(face card) = 11 / 51

total probability (queen and face card):

The answer is:

p (queen and face card) = 0.0166

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given line equations are y=3x-6 and y=-2x+8.

Here, 3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = 1/2 ×2 × 12/5

Multiply and simplify.

A = 12/5

Therefore, the area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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Answer:

Step-by-step explanation:

The closure property for subtraction holds for integers, but not necessarily for whole numbers.

Closure property is an important concept in mathematics. It refers to the property of a set of numbers to produce a result within the same set when a mathematical operation is performed on any two numbers in that set.

Whole numbers are a subset of integers and include only non-negative numbers, whereas integers include both positive and negative numbers along with zero.

When we subtract two whole numbers, the result may not always be a whole number. For instance, if we subtract 3 from 2, the result is -1, which is not a whole number. This is why Karim concluded that whole numbers are not closed under subtraction.

On the other hand, when we subtract two integers, the result will always be an integer. For example, if we subtract 3 from 2, the result is -1, which is an integer. This is why Ali concluded that integers are closed under subtraction.

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Answer:

x= -12

Step-by-step explanation:

3(x+7)+6= -9

3x+21+6= -9

subtract 6 from both sides that gives you your equation that you can work with.

3x+21= -15

then subtract 21 from both sides that gives you

3x/3 = -36/3

the 3 cancels out and leaves you with -36 divided by 3

your answer is -12

\(\text {Hello! The answer to your problem is...}\)

\(\fbox {x=-12}\)

\(\text {Your 1st Step is to Simplify the Equation}\)

\(\text {(3)(x)+(3)(7)+6=-9 (Distribute)}\)

\(\text {3x+21+6=-9}\)

\(\text {(3x)+(21+6)=-9 (Combine Like Terms)}\)

\(\text {3x+27=-9}\)

\(\text {Your 2nd Step is to Subtract 27}\)

\(\text {3x+27-27=-9-27}\)

\(\text {3x=-36}\)

\(\text {Your 3rd/Final Step is to Divide 3}\)

\(\text {3x/3=-36/3}\)

\(\fbox {x=-12}\)

\(\text {Best of Luck!}\)

\(\text {-LimitedX}\)

Yes, the inverse of the matrix which is \(A^{-1}\) = \(\begin{bmatrix} 0 & \frac{1}{3} \\ -\frac{1}{2} & 0 \end{bmatrix}\)  for the 2 x 2 matrix \(\begin{bmatrix} 6 & 3 \\ 3 & 0 \end{bmatrix}\).

To find the inverse of a matrix, we need to check if it is invertible first, which means its determinant should not be equal to zero.

Let's calculate the determinant of the matrix,

A: \(\begin{bmatrix} 6 & 3 \\ 3 & 0 \end{bmatrix}\)

det(A) = (6 x 0) - (3 x 3) = -9

Since the determinant is not equal to zero, we can conclude that matrix A is invertible.

To find the inverse of matrix A, we can use the following formula:

\(A^{-1}\) = (1/det(A)) x adj(A)

where adj(A) is the adjugate of A and can be calculated by taking the transpose of the matrix of cofactors of A.

The matrix of cofactors of A is:

\(\begin{bmatrix} 0 & -3 \\ -3 & 6 \end{bmatrix}\)

Taking the transpose of the matrix of cofactors, we get:

\(\begin{bmatrix} 0 & -3 \\ 3 & 6 \end{bmatrix}\)

So, the adjugate of A is:

adj(A) = \(\begin{bmatrix} 0 & -3 \\ 3 & 6 \end{bmatrix}\)

Now, we can find the inverse of A:

\(A^{-1}\) = (1/-9) x adj(A)

= (-1/9) x \(\begin{bmatrix} 0 & -3 \\ 3 & 6 \end{bmatrix}\)

= \(\begin{bmatrix} 0 & \frac{1}{3} \\ -\frac{1}{2} & 0 \end{bmatrix}\)

Therefore, the inverse of matrix A is:

\(A^{-1}\) = \(\begin{bmatrix} 0 & \frac{1}{3} \\ -\frac{1}{2} & 0 \end{bmatrix}\)

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The given differential equation is y'' = 39x.

To determine the value of A, we can integrate the equation twice. The first integration will give us the general solution, and then we can compare it to the given form to determine the value of A.

Integrating the equation once, we get:

y' = ∫(39x) dx

y' = (39/2)x^2 + C1

Integrating again, we obtain:

y = ∫((39/2)x^2 + C1) dx

y = (39/6)x^3 + C1x + C2

Comparing this to the given general solution y = Ax^3 + C1x + C2, we can equate the coefficients:

A = 39/6

A = 6.5

Therefore, the value of A is 6.5.

Regarding the type of differential equation, the given equation y'' = 39x is a second-order linear homogeneous ordinary differential equation. It is not separable, exact, or Bernoulli because it does not meet the criteria for those specific types of differential equations.

Answer:

ithink the first one :p

Step-by-step explanation:

The measure of variability that is used when the statistic with the greatest stability is sought is the Standard Deviation.

The Standard Deviation takes into account the dispersion of data points from the mean and provides a measure of the average distance between each data point and the mean. It is widely used in statistical analysis and is considered a robust measure of variability, providing a more precise and stable measure compared to other measures such as Mean Deviation, Quartile Deviation, or Range.

The Standard Deviation is a statistical measure that quantifies the dispersion or variability of a dataset. It takes into account the differences between individual data points and the mean of the dataset. By calculating the average distance between each data point and the mean, it provides a measure of how spread out the data is.

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Answer:

y = 0, 3, 6

Step-by-step explanation:

insert x values into the equation to get y

The values of x and y the triangles to the fight congruent are x = 3 and

y = 1.

What is congruent triangles?

Triangles with the same size and shape are said to be congruent. This implies that the corresponding sides and angles are both equal. Without comparing every angle and side of the two triangles, we can determine whether two triangles are congruent.

If given these triangles are congruent then all corresponding side must be equal

As we can see that both triangle are right triangle

Therefore hypotenuse of one triangle equal to another

x+1  = 4y   ..... (A)

And lenght ( height)  of one  must equal to another triangle

x = y +2          .... (B)

therefore

Plug the value of x = y + 2 in equation A

y + 2 + 1 = 4y

        3y = 3

          y = 1

and x = y+2

x = 1 + 2

x = 3

Hence, the values of x and y the triangles to the fight congruent are

x = 3 and y = 1.

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Complete question:

Complete question is attached below.

Answer:

A. Probability of Russell = 12/37 or 32.4% (Rounding to the next tenth)

B. Probability of Peter = 5/74 or 6.8% (Rounding to the next tenth)

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

              Guard Forward Center Totals

Over 6 feet 25     30        30        85

Under 6 feet 130 120      35        285

Totals           155 150      65        370

2. Russell is 5'9". What is the probability he is a forward?

Probability = Number of forwards under 6 feet/Total number of players

Probability = 120/370

Probability = 12/37 or 32.4% (Rounding to the next tenth)

3. Peter is 6'2". What is the probability he is a guard?

Probability = Number of guards over 6 feet/Total number of players

Probability = 25/370

Probability = 5/74 or 6.8% (Rounding to the next tenth)

Hope this helps you!!!!! :D

The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.

The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

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Answer:

90°

Step-by-step explanation:

X = 90°

A right angle is 90° and they are all 90° (right-angles).

As well as that is, that there are 360° on a point

9x4=36 so it must be the same 90° (1 right angle) times 4

90x4 = 360

Answer:

D: 7c + 9t

Step-by-step explanation:

I assume c = car and t = truck

Since it costs 7 dollards PER car and 9 dollars PER truck, you would use 7c+9c as the equation.

Approximately 38% of deaths among 16 to 19 year-olds are related to motor vehicles.

According to the Centers for Disease Control and Prevention (CDC), motor vehicle crashes are the leading cause of death for teenagers in the United States.

In 2019, a total of 2,375 teenagers aged 16-19 years died in motor vehicle crashes, and an additional 258,000 were treated in emergency departments for injuries sustained in motor vehicle crashes.

These deaths accounted for 62% of all deaths among teenagers aged 16-19 years.

Therefore, around 38% of fatalities among individuals aged 16 to 19 are connected to automobiles.

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(a)The unit vector that gives the direction of the steepest ascent is (1/√2, -1/√2).

The unit vector that gives the direction of the steepest ascent at P is the gradient vector evaluated at P divided by its magnitude. The gradient of the function f(x, y) is given by (∂f/∂x, ∂f/∂y) = (2x+2, 4y+4). At P(1,-2), the gradient vector is (4,-4), and its magnitude is √(4^2 + (-4)^2) = 4√2.

Therefore, the unit vector in the direction of steepest ascent is (4/4√2, -4/4√2) = (1/√2, -1/√2).

The unit vector that gives the direction of the steepest descent at P is the negative of the unit vector that gives the direction of the steepest ascent. Therefore, the unit vector in the direction of steepest descent is (-1/√2, 1/√2).

(b) A vector that points in the direction of no change in the function at P is perpendicular to the gradient vector.

Therefore, the vector (-4, -2) is perpendicular to the gradient vector (4, -4) and points in the direction of no change in the function at P. Note that there are infinitely many vectors perpendicular to the gradient vector, but this particular vector is chosen because it has the smallest possible magnitude.

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The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.

(a) The given units can be converted as follows: 6 glints = 1 filn...

(1)12 grees = 1 zool...

(2)2 grees = 10 twibbs...

(3)5 grees = 1 bic...

(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:

7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord

(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.

1 mega = 106

Thus 1 megafiln = 106 filn

16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.

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