Circle A has a radius of 16 inches. What is the circumference?

(a) The probability that X is less than 3, P(X < 3), is 0.

(b) The mean of X, denoted as E(X), is 71/24, which is approximately 2.9583 when rounded off to four decimal places.

(c) Given Y = e^X, the mean of Y, denoted as E(Y), is approximately 15.75 when rounded off to two decimal places.

(a) It is required to compute P(X<3). Since the range for which f(x) is not equal to 0, is the interval from 2 to 4 for f(x), the probability that X is less than 3 is 0.

Similarly, for X > 4, P(X > 4) = 0.

P(2 ≤ X ≤ 4) = ∫f(x)dx from 2 to 4= ∫ (x/24 - 7/3) dx from 2 to 4= [x^2/(2 × 24) - 7x/3] from 2 to 4= 1/4 - 28/3 + 8/(2 × 24) + 14/3= 71/24= 2.9583(rounded off to four decimal places)

(b) The mean of X can be computed as follows:

E(X) = ∫xf(x)dx from -∞ to ∞= ∫ (x/24 - 7/3) dx from 2 to 4= [x^2/(2 × 24) - 7x/3] from 2 to 4= 1/4 - 28/3 + 8/(2 × 24) + 14/3= 71/24= 2.9583(rounded off to four decimal places)

(c) Y = e^X

The mean of Y can be computed as follows:

E(Y) = E(e^X)= ∫ e^x f(x) dx from -∞ to ∞= ∫ e^x (x/24 - 7/3) dx from 2 to 4= [e^x (x - 31)/(24)] from 2 to 4= (e^4/6 - 31e^4/24 - e^2/6 + 31e^2/24) ≈ 15.75(rounded off to two decimal places).

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Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

3

5

(

−

2

)

Step-by-step explanation:

Simplify then multiple the numbers

Answer:

B

Step-by-step explanation:

A will equal the sine inverse (arc sine or sin^-1 ) of 0.3571. Using a calculator, sin^-1(0.3751) = 22.03 degrees (B)

a. In the picture we can see that the scatterplot is given for the data in the given table.

b. It is not linear as we can see from scatterplot.

c. The correlation between y and x is 0.

d. when r = 0 there is no relationship between x and y.

Given that,

The data is given in the table.

We know that,

a. We have to make a scatterplot of y versus x.

In the picture we can see that the scatterplot is given for the data in the given table.

b. We have to describe the relationship between y and x.

When x increases y increases upto certain point after that y start to decrease but x is increases only

Therefore, it is not linear as we can see from scatterplot.

c. We have to find the correlation between y and x.

The formula for the correlation coefficient is

r = [tex]\frac{n\times \sum XY-\sum X \times\sum Y}{\sqrt{[n\sum X^2 - (\sum X)^2][n\sum Y^2 - (\sum Y)^2]} }[/tex]

Now we find summation of all X, Y and XY, [tex]X^2[/tex] and [tex]Y^2[/tex]

X          Y           XY            [tex]X^2[/tex]            [tex]Y^2[/tex]

25        10         250         625          100

35        30        1050        1225         900

45        50        2250       2025        2500

55        30        1650        3025        900

65        10          650        4225        100

Now, ∑X = 225

∑Y = 130

∑XY = 5850

∑[tex]X^2[/tex] = 11125

∑[tex]Y^2[/tex] = 4500

Now, Substitute the values in the formula

r = [tex]\frac{5\times 5850-225 \times130}{\sqrt{[5\times 11125 - (225)^2][5\times 4500 - (130)^2]} }[/tex]

r = 0

Therefore, The correlation between y and x is 0.

d. We have to find what important point about correlation does this exercise illustrate.

Therefore, when r = 0 there is no relationship between x and y.

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There are 30 of the cupcakes are vanilla.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

Joanne is making 48 cupcakes for a bake sale.

And, 1/4 of the cupcakes are chocolate.

1/8 of the cupcakes are strawberry.

The remainder of the cupcakes are vanilla.

Hence, We get;

Amount of the cupcakes are vanilla is,

⇒ 48 - (1/4 of 48 + 1/8 of 48)

⇒ 48- (12 + 6)

⇒ 48 - 18

⇒ 30

Thus, There are 30 the cupcakes are vanilla.

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Answer: 17.29 cm

Step-by-step explanation:

Given

The dimension of a rectangular prism is [tex]13\ cm\times 9\times \ cm\times 7\ cm[/tex]

The longest line which can be drawn in the rectangular prism is diagonal across the body which is shown in the figure

Length of rectangular is given by

[tex]\Rightarrow L=\sqrt{l^2+b^2+h^2}[/tex]

Putting values

[tex]\Rightarrow L=\sqrt{13^2+9^2+7^2}\\\Rightarrow L\sqrt{169+81+49}=\sqrt{299}\\\Rightarrow L=17.29\ cm[/tex]

Answer:

17.3

Step-by-step explanation:

The dimension of a rectangular prism is 13x9x7

you would normally get 17.29 but  you have to round

which gives us the answer= 17.3

Answer:

34.55556%

Step-by-step explanation:

Answer:

a) The floor of the room, each edge and the top of the table.

b) The edge of one side and one leg of the table.

c) The angle formed between the sides of the table and the angle between the legs of the table and its edges.

d)  The vertices of the top of the table.

e) These are same lines.

Step-by-step explanation:

An angle is the amplitude between the two lines. Plane is an object which consists of two dimensions and infinite points. The segment is a fragmented line. A ray is a line which a starting point and a direction.

A) Tres planos que surgen a partir de la mesa de mi casa son la superficie de la mesa, la superficie del suelo sobre el cual se apoya la mesa, y la superficie de la pared sobre la cual reposa la mesa.

B) Dos rectas de planos distintos pueden ser el borde de la mesa, por una parte, y la pared, por el otro.

C) Dos ángulos de un plano y dos de otro son el vértice de la mesa y el ángulo formado entre el borde de la misma y un vaso, por un lado, y el ángulo formado por una baldosa y la pata de la mesa y el ángulo recto formado por las líneas de una baldosa, por la otra.

D) Dos rayas pueden ser la línea a ras del suelo y la línea a ras de la mesa.

E) Dos semirrectas pueden ser ambas patas de la mesa.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(\dfrac{4}{9})^2}[/tex]

[tex]\mathsf{= \dfrac{4}{9}\times\dfrac{4}{9}}[/tex]

[tex]\mathsf{= \dfrac{4^2}{9^2}}[/tex]

[tex]\mathsf{\dfrac{4\times4}{9\times9}}[/tex]

[tex]\mathsf{4 \times 4 = \bold{16}\leftarrow \underline{Numerator}}[/tex]

[tex]\mathsf{9\times9 = \bf 81}\leftarrow\mathsf{\underline{Denominator}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \boxed{{\bf \dfrac{16}{81}}}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

slope is 3

y-intercept is 0,-5

The error of rejecting the null hypothesis when it is actually true is known as a Type I error or alpha error. It represents the incorrect rejection of a null hypothesis that is true in reality.

Type I errors are associated with the significance level (alpha) chosen for a statistical test and occur when the test incorrectly concludes that there is a significant effect or relationship when there isn't one.

In hypothesis testing, the null hypothesis represents the assumption of no effect or no relationship between variables. The alternative hypothesis, on the other hand, suggests the presence of an effect or relationship. The significance level (alpha) is the threshold set by the researcher to determine the probability of rejecting the null hypothesis.

A Type I error occurs when the null hypothesis is true, but the statistical test incorrectly rejects it, leading to a false conclusion of a significant effect or relationship. This error is also known as a false positive. The probability of making a Type I error is denoted by alpha.

Type I errors are considered undesirable because they lead to incorrect conclusions and may result in wasted resources or inappropriate actions based on flawed evidence.

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Answer:

D). irrational numbers between 10 and 30

Answer:

12 mph

Step-by-step explanation:

Given that:

Total distance traveled = 78 miles

Time taken, t = 6 hours

Average speed for first 30 miles = 15 mph

Time taken = distance / speed

Time taken = 30 / 15

Time taken = 2 hours

Average speed for last 48 miles = x

Time taken to travel last 48 miles = (6 - 2) = 4 hours

Average speed for last 48 miles :

Distance traveled / time taken

48 miles / 4 hours

= 12 mph

To solve the equation y - 4.5 = 12.2 we have to add 4.5 on both sides of the equation.

Two or more expressions with an Equal sign is called as Equation.

The given equation is y - 4.5 = 12.2

y minus four point five equal to twelve point two.

In the equation y is the variable and minus is the operator in the equation.

To solve the equation we have to isolate the variable y.

To isolate the variable y we have to add 4.5 on both sides of the equation

y-4.5+4.5=12.2+4.5

y=16.7

Hence, to solve the equation y - 4.5 = 12.2 we have to add 4.5 on both sides of the equation.

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Answer:

[tex]2x^{3} +10[/tex]

Step-by-step explanation:

[tex]x*2x*x+10=2x^{3} +10[/tex]

Answer:

52 cubic units

Step-by-step explanation:

got it right on edg

Answer:

37h 900

Step-by-step explanation:

Answer: No solutions

Step-by-step explanation: If you solve the problem all the way, you get 0 = 4 which is not valid so there is simply no solution

The given equation 3(2x−1)+5=6(x+1) has no solution. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given equation ⇒

⇒= 3(2x−1)+5=6(x+1)

Simplify the above expression,
⇒ 6x - 3 + 5 = 6x + 1
⇒    2 ≠ 1

Thus, the given equation has no solution.

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Answer:

72

Step-by-step explanation:

Multiply all the numbers, and you get the answer

The quotient of (2x^2 + 5x + 8) divided by (x + 2) is 2x + 1, and the remainder is 12.

To divide the polynomial[tex](2x^2 + 5x + 8) by (x + 2)[/tex] using synthetic division, we follow these steps:

1. Set up the synthetic division table by placing the divisor (x + 2) on the left side of the table and writing down the coefficients of the dividend (2x^2 + 5x + 8) in descending order on the top row of the table.

  | 2   5   8

-2 |

2. Bring down the first coefficient, which is 2, from the top row and write it underneath the horizontal line.

 | 2   5   8

-2 | 2

3. Multiply the divisor (-2) by the number beneath the line (2) and write the result in the next column.

  | 2   5   8

-2 | 2  -4

4. Add the result to the next coefficient in the top row and write the sum in the next column.

  | 2   5   8

-2 | 2  -4   4

5. Repeat steps 3 and 4 until all coefficients have been processed.

  | 2   5   8

-2 | 2  -4   4

    ___________

     2   1  12

The last number in the bottom row, 12, is the remainder. The other numbers in the bottom row represent the coefficients of the quotient.

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The probability of getting exactly seven fours in ten rolls of a fair die is approximately 0.0574.

To determine the probability of exactly seven fours in 10 rolls of a fair die, we can use the binomial distribution formula:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting exactly k successes (in this case, rolling a four) in n trials (in this case, rolling a die 10 times),

nCk is the number of combinations of n items taken k at a time,

p is the probability of success on a single trial (rolling a four), and

(1-p) is the probability of failure on a single trial (not rolling a four).

In this case, n = 10, k = 7, p = 1/6 (since there is a 1/6 chance of rolling a four on a fair die), and (1-p) = 5/6.

Plugging these values into the formula:

P(X = 7) = (10C7) * (1/6)^7 * (5/6)^(10-7)

Calculating the combinations:

(10C7) = 10! / (7! * (10-7)!) = 10! / (7! * 3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

Substituting the values:

P(X = 7) = 120 * (1/6)^7 * (5/6)^(10-7)

Calculating the probability:

P(X = 7) = 120 * (1/6)^7 * (5/6)^3 ≈ 0.0595

Therefore, the probability that exactly seven fours will appear in 10 rolls of a fair die is approximately 0.0595 (rounded to 4 decimal places).

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Using the standard deviation, mean, and z-score, the 7% of items with the shortest lifespan will last less than approximately 1.59 years.

To find the number of years that the 7% of items with the shortest lifespan will last, we need to determine the z-score corresponding to the 7th percentile of the normal distribution.

Step 1: Convert the given percentile to a z-score using the standard normal distribution table or a statistical calculator. The 7th percentile corresponds to a z-score of approximately -1.405.

Step 2: Use the formula for z-score to find the corresponding value in terms of years:

x = μ + z * σ

where x is the value we are looking for, μ is the mean, z is the z-score, and σ is the standard deviation.

Plugging in the values:

x = 4.4 + (-1.405) * 1.2

x = 1.59 years

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Answer:

A

Step-by-step explanation:

the y intercept (where x is 0) should be -3 because of y<3x-3

Answer:

A=2, B=10, C=-18

The answer is the first one.

Step-by-step explanation:

[tex]5x^{2} -3x^{2} +x+9x-18=0[/tex]

[tex]2x^{2} +10x-18=0[/tex]

Formula: [tex]f(x)=ax^{2} +bx+c[/tex]

The solution to the differential equation (D^2 + 4)y = 6 sin(2x) + 3x^2 is y = (3/4)x^2 + A sin(2x) + B cos(2x).

To solve the given differential equation (D^2 + 4)y = 6 sin(2x) + 3x^2, where D represents the derivative operator, we can use the method of undetermined coefficients.

y = y_h + y_p

y = A sin(2x) + B cos(2x) + (3/4)x^2

Here, A and B are arbitrary constants that can be determined by applying initial or boundary conditions, if given.

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The function described by the points in this table is nonlinear.

Based on the given points in the table, we can determine whether the function is linear or nonlinear by examining the relationship between the x and y values.

Let's look at the x and y values:

x y

-3 9

-1 1

0 0

1 1

3 9

If we observe that for every change in x, the corresponding change in y remains constant, then the function is linear. In other words, if the ratio of the change in y to the change in x is constant, the function is linear.

Let's calculate the ratios:

For x = -3 to x = -1:

Change in y = 1 - 9 = -8

Change in x = -1 - (-3) = 2

Ratio = -8/2 = -4

For x = -1 to x = 0:

Change in y = 0 - 1 = -1

Change in x = 0 - (-1) = 1

Ratio = -1/1 = -1

For x = 0 to x = 1:

Change in y = 1 - 0 = 1

Change in x = 1 - 0 = 1

Ratio = 1/1 = 1

For x = 1 to x = 3:

Change in y = 9 - 1 = 8

Change in x = 3 - 1 = 2

Ratio = 8/2 = 4

As we can see, the ratios are not constant. The ratio changes from -4 to -1, then to 1, and finally to 4. Therefore, the function described by the points in this table is nonlinear.

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Answer:

33.94 cms of ribbon

Step-by-step explanation:

Because you need two diagonals to form the x, therefore the amount  of ribbon needed is the sum of the distance of both diagonals.

When crossing the diagonal, a rectangular angle is formed, where the diagonal would be the hypotenuse, we know that the distance of the hypotenuse can be calculated by means of the legs, which we know its value (12):

d ^ 2 = a ^ 2 + b ^ 2

a = b = 12

d ^ 2 = 12 ^ 2 + 12 ^ 2

d ^ 2 = 288

d = 288 ^ (1/2)

d = 16.97

16.97 cm is what it measures, a diagonal, therefore tape is needed:

16.97 * 2 = 33.94

A total of 33.94 cms of ribbon is needed

Answer from jmonterrozar

General solution of the second order differential equation:

-6Ae^(-3x) / x + 9Bxe^(-3x) * ln(x) - Be^(-3x) / x^2

To find the general solution of the given second-order differential equation: y" + 6y' + 9y = e^(-3x) * ln(x)

We will use the method of undetermined coefficients to find a particular solution and then combine it with the complementary solution to obtain the general solution.

Step 1: Finding the particular solution

Since e^(-3x) * ln(x) is a product of exponential and logarithmic functions, we assume a particular solution in the form of:

yp = (A + Bx) * e^(-3x) * ln(x)

where A and B are constants to be determined.

Step 2: Find the first and second derivatives of yp.

yp' = (Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x

yp" = (Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x)'

yp" = (-9(A + Bx)e^(-3x) * ln(x) + 3(A + Bx)e^(-3x) * ln(x) - 3(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x))

Simplifying, we have:

yp" = -9(A + Bx)e^(-3x) * ln(x) - 6(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x)

Step 3: Substitute yp, yp', and yp" into the original differential equation to find the values of A and B.

yp" + 6yp' + 9yp = e^(-3x) * ln(x)

Substituting the expressions we found for yp and its derivatives:

(-9(A + Bx)e^(-3x) * ln(x) - 6(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x))

6((Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x))

9((A + Bx) * e^(-3x) * ln(x))

= e^(-3x) * ln(x)

Expanding and simplifying, we get:

-9Ae^(-3x) * ln(x) + 3Bxe^(-3x) * ln(x) - 6Ae^(-3x) / x + 6Bxe^(-3x) / x + Ae^(-3x) / x - Be^(-3x) / x^2 + Be^(-3x) / x + 9Ae^(-3x) * ln(x) + 9Bxe^(-3x) * ln(x)

= e^(-3x) * ln(x)

Combining like terms, we have:

-6Ae^(-3x) / x + 9Bxe^(-3x) * ln(x) - Be^(-3x) / x^2

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