Michael fills a plastic ball with air until it is a sphere with a radius of 6 cm. What is the volume of the ball?

Answer:

7.5 years because United States has mor thne 9 years

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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The true statements about the image of the parallelogram are,

The corresponding sides have different lengths.

The parallelograms are congruent.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A parallelogram in a coordinate plane is translated, rotated, and then reflected.

In the case of translation, rotation and reflection would only change its coordinate points, and the preimage and image will be congruent.

The coordinate points of the vertices would only change if given.

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The probability that a girl will win two weeks in a row is 24%.

Probability tells how many times something will happen or be present.

The probability of a girl winning in a given week is 17/35 since there are 17 girls and 35 students total. Assuming each week's selection is independent of previous selections, the probability of a girl winning two weeks in a row is (17/35) x (17/35) = 289/1225.

Rounding this to the nearest percent gives a probability of 24%.

Therefore, the probability is 24%.

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The numbers that multiply to give 10 are -

2 x 5

5 x 2

2.5 x 4

Given is two multiply two numbers to give 10.

The numbers that multiply to give 10, we get -

2 x 5 = 10

5 x 2 = 10

2.5 x 4 = 10

Therefore, the numbers that multiply to give 10 are -

2 x 5

5 x 2

2.5 x 4

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{Question in english is given below -

Multiplied numbers that give 10}

The present value of the loan is found to be  approximately $70.28.

To find the present value of a loan, we can use the formula:

Present Value = Future Value / (1 + (interest rate * time))

Given that the future value is $1,321.17, the interest rate is 7.75%, and the time is 230 days, we can plug in these values into the formula:

Present Value = 1321.17 / (1 + (0.0775 * 230))

Calculating the expression in the parentheses first:

Present Value = 1321.17 / (1 + 17.8075)

Simplifying further:

Present Value = 1321.17 / 18.8075

Evaluating the division:

Present Value ≈ $70.28

Therefore, the present value of the loan is approximately $70.28.

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The total number of students running the club is given as follows:

45 students.

The total number of students running the club is obtained applying the proportions in the context of the problem.

The number of eight graders is given as follows:

30 - 9 = 21.

The equivalent percentage of eight graders is given as follows:

46.6%.

Hence the total number of students running the club is given as follows:

0.466n = 21

n = 21/0.466

n = 45 students.

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Answer:

\(2.\bar{81}mm\)

Step-by-step explanation:

First the formula for find the are of a trapezoid is:

\(A = \frac{h(a+b)}{2}\)

Where \(a\) is the top, \(h\) the height and \(b\) the base measures.

Then we need to know what is the base (\(b\)), for that isolate \(b\) from the equation

\(2A = h(a+b)\\\frac{2A}{h} = a+b\\\frac{2A}{h} - a = b\)

Then in the new equation replace the given values:

\(A = 65mm^2\\a = 9mm\\h = 11mm\)

\(\frac{2 \cdot 65mm^2}{11mm} -9mm = b\\\frac{130mm^2}{11mm} -9mm = b\\11.\bar{81}mm -9mm = b\\2.\bar{81}mm = b\)

So the final answer is \(2.\bar{81}mm\)

Answer:

Sharifa can pay for the DVD player first.

Step-by-step explanation:

Max:

99 - 31 = $68 remaining

68 / 8.5 = 8 weeks

Sharifa:

99 - 25.5 = $73.50 remaining

73.5 / 10.5 = 7 weeks

Answer: (13,-7)

Step-by-step explanation:

By using the formula \((x_{m},y_{m}) =(\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2} )\)

\((x_{m},y_{m})\\\) is the coordinates of the midpoint.

For finding the midpoint X variable do:

\((\frac{4+22}{2})=13\)

For finding the midpoint Y variable do:

\(\frac{-10+(-4)}{2} = -7\) (you can either keep the parenthesis or take them out. Either way, the answer is the same.

Considering coordinate numbers follow the format: (x,y), you'll simply just substitute the numbers found above into their respective places.

x: 13

y: -7

(13,-7).

Answer:

\(\large \boxed{\mathrm{(a) \ One \ solution}} \\ \\ \large \boxed{\mathrm{(b) \ One \ solution}} \\ \\ \large \boxed{\mathrm{(c) \ All \ real \ numbers}}\)

Step-by-step explanation:

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

Expand brackets.

2x+4x-4=2+4x

Combine like terms.

6x-4=2+4x

Subtract 4x from both sides.

Add 4 to both sides.

2x=6

Divide both sides by 2.

x=3 (One solution)

25-x=15-(3x+10)

Distribute negative sign.

25-x=15-3x-10

25-x=-3x+5

Add x and -5 to both sides.

20=-2x

Divide both sides by -2.

-10=x (One solution)

4x=2x+2x+5(x-x)

Solve for brackets.

4x=2x+2x+5(0)

4x=2x+2x

Combine like terms.

4x=4x

Divide both sides by 4.

x=x

All real numbers are solutions. (All real numbers)

Answer: 1$

Step-by-step explanation:

If six pieces of candy cost 2$

6=2x

x=3

Given the expression:

You can find its value by following these steps:

1. You have to solve the operation that is inside the parentheses. Then, you need to add 14 and 6:

2. Finally, you must solve the Multiplication. Then, you get this result:

Hence, the answer is:

Answer:

60

Step-by-step explanation:

1) Add 14 + 6 which gives you 20

2) Multiply 20 x 3 which gives you 3

Your welcome :)

Answer:

Answer E is correct

Step-by-step explanation:

We know that,

\((x^ay^b)^c=x^a^cy^b^c\)

Let us use the above to find the answer to this question.

Let us solve it now.

\((a^\frac{2}3} b^\frac{1}{3})^\frac{1}{2}\)

\(a^\frac{2}3}^*^ \frac{1}{2} *b^\frac{1}{3}^*^\frac{1}{2}\)

\(a^\frac{2*1}{3*2} * b^\frac{1*1}{3*2}\)

\(a^\frac{2}{6} * b^\frac{1}{6}\)

Here, we can simplify the \(a^\frac{2}{6}\) as \(a^\frac{1}{3}\) by dividing the numerator and denominator by 2.

Therefore, the answer will be,

\(a^\frac{1}{3} b^\frac{1}{6}\)

Answer:

59,09

.........................................................

The probability that a randomly chosen young adult has at least a high school education can be found using the rule of probability called the "complement rule".

To find the answer, we need to subtract the probability that a randomly chosen young adult does not have at least a high school education from 1. In other words:

Probability of having at least a high school education = 1 - Probability of not having at least a high school education.

By using this rule, we can calculate the probability.

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Answer:

C 64

Step-by-step explanation:

1. 2(2)(4)(8(2)-3(4))

2.2(8)(16-12)

3. 16(4)

4. 64

Each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.Option B,E,F.

Each chart has the following three components:

1. B. A center line representing the average: This line is drawn to show the average value or mean of the data being analyzed. It provides a reference point to compare the data points above and below it.

2. E. An upper line representing the maximum acceptable variation upwards: This line is drawn to indicate the upper limit of acceptable variation or deviation from the average. It helps identify if the data points exceed the acceptable range.

3. F. A lower line representing the maximum acceptable variation downwards: This line is drawn to indicate the lower limit of acceptable variation or deviation from the average. It helps identify if the data points fall below the acceptable range.

These three components together create a control chart, which is a graphical representation used in statistical process control. Control charts help monitor and analyze data over time, allowing organizations to identify trends, detect abnormalities, and make data-driven decisions to improve processes and quality.

In summary, each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.

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To determine the significance of each independent variable, we need to apply the decision rule at the 0.05 significance level.

In statistical hypothesis testing, the decision rule is used to determine whether to reject or fail to reject the null hypothesis based on the test statistic and the level of significance. In this case, we are interested in testing the significance of each independent variable in a regression model at the 0.05 level of significance. To do this, we can use the t-test for each independent variable by calculating the t-statistic and comparing it to the critical value of the t-distribution with n-k-1 degrees of freedom, where n is the sample size and k is the number of independent variables in the model. If the absolute value of the t-statistic is greater than the critical value, then we reject the null hypothesis and conclude that the independent variable is statistically significant at the 0.05 level. Otherwise, we fail to reject the null hypothesis and conclude that the independent variable is not statistically significant at the 0.05 level.

Alternatively, we can also use the p-value approach to determine the significance of each independent variable. We calculate the p-value for each variable and compare it to the level of significance. If the p-value is less than or equal to 0.05, then we reject the null hypothesis and conclude that the independent variable is statistically significant at the 0.05 level. Otherwise, we fail to reject the null hypothesis and conclude that the independent variable is not statistically significant at the 0.05 level.

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A total number of 4 x 10⁶ DVD's were sold in the span of next three years.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that in 1996, 1 million DVDs were sold.

Since no further information is given, assume that the increase in the sales of the DVD's took place at the same rate every year. So, initially, 1 million DVD's have been sold. So, for the next {x} years, we can write the total number of DVD's sold as -

y = mx + c

y = 10⁶x + 10⁶

y = 10⁶(x + 1)

For {x} = 3, we can write -

y = 4 x 10⁶

Therefore, a total number of 4 x 10⁶ DVD's were sold in the span of next three years.

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Answer:

60

Step-by-step explanation: you just multiply the radius by 2

Answer:

60

Step-by-step explanation:

r=d/2

30=d/2

60=d

d=60

Answer:

wildflower: $8

daffodil: $14

Step-by-step explanation:

9w + 9d = 198

2w + 5d = 86

         -18w - 18d = -396

(+)       18w + 45d = 774

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

                    27d = 378

d = 14

9w + 9(14) = 198

9w = 72

w = 8

wildflower: $8

daffodil: $14

The absolute minimum and maximum values of the function f(x,y) = 1+xy – x – y on the region D, bounded by the parabola y = x^2 and the line y = 4, we can follow these steps:

Find the critical points of f(x,y) by setting the partial derivatives of f equal to zero:

fx = y - 1 = 0

fy = x - 1 = 0

Solving these equations simultaneously gives the critical point (1,1).

Check the boundary of region D, which is composed of two curves: y = x^2 and y = 4.

2.1. Along the curve y = x^2:

Substituting y = x^2 into f(x,y), we obtain a function of one variable:

g(x) = f(x, x^2) = 1 + x^3 - 2x^2

Taking the derivative of g(x) and setting it equal to zero to find its critical points:

g'(x) = 3x^2 - 4x = 0

x(3x - 4) = 0

Solving for x, we get x = 0 and x = 4/3. Plugging these values into g(x), we find that g(0) = 1 and g(4/3) = -1/27.

Therefore, the minimum value of f(x,y) along the curve y = x^2 is g(4/3) = -1/27, and the maximum value is g(0) = 1.

2.2. Along the line y = 4:

Substituting y = 4 into f(x,y), we obtain a function of one variable:

h(x) = f(x, 4) = 1 + 4x - x - 4

Simplifying, we get h(x) = 3x - 3.

Taking the derivative of h(x) and setting it equal to zero to find its critical point:

h'(x) = 3 = 0

Since h'(x) is never zero, there are no critical points along the line y = 4. We only need to check the endpoints of the line segment that lies within D.

At the endpoint (4/2, 4), we have f(2, 4) = -2, and at the endpoint (-2, 4), we have f(-2, 4) = 9.

Therefore, the minimum value of f(x,y) along the line y = 4 is f(2,4) = -2, and the maximum value is f(-2,4) = 9.

Compare the values obtained in steps 1 and 2 to find the absolute minimum and maximum values of f(x,y) on D.

The values of f at the critical point (1,1), along the curve y = x^2, and along the line y = 4 are:

f(1,1) = -1

g(4/3) = -1/27

g(0) = 1

f(2,4) = -2

f(-2,4) = 9

Therefore, the absolute minimum value of f(x,y) on D is f(-2,4) = 9, and the absolute maximum value is f(0) = 1.

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the expression is simplifying to 11+2x

Answer:

y = x + 3.

Step-by-step explanation:

To determine the linear function, we can use the two points given to calculate the slope and then use the point-slope formula.

The slope (m) is calculated as:

m = (y2 - y1) / (x2 - x1)

m = (10 - 18) / (7 - 15)

m = -8 / -8

m = 1

Using the point-slope formula, we can write the equation of the line as:

y - y1 = m (x - x1)

y - 18 = 1 (x - 15)

y - 18 = x - 15

y = x + 3

So, the linear function is y = x + 3.

Answer: 3x + 6

Step-by-step explanation: PLEASE MARK ME AS BRAINLISTI AND HAVE A GREAT DAY!!!

Answer:

3x+6

Step-by-step explanation:

Answer:

B.6x^2

Step-by-step explanation:

\(\left(2x^2\right)\times\:3\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=2x^2\times\:3\\\\=6x^2\)

Answer:

2√97

Step-by-step explanation:

BD² = BC² + DC²

⇒ BD = √BC² + DC²

= √(18)² + (8)²

= √324 + 64

= √388

Rewrite 388 as 2² · 97.

Factor 4 out of 388.

√4(97)

Rewrite 4 as 2².

√2² · 97

Pull terms out from under the radical.

2√97

The result can be shown in multiple forms.

Exact Form:

2√97

Decimal Form:

19.69771560...

Answer:

1250 (corrected to 3 significant figures)

Step-by-step explanation:

the formula to calculate circumference is 2πr, where r is the radius.

hence, we can form the equation

2πr = 7850

r ≈ 1249.3663

= 1250 (corrected to 3 significant figures)