Find the volume of the composite solid

The roots of the given polynomial using the rational zero theorem are;  2, -4 and 6.

We are given the polynomial;

y = x³ - 4x² - 20x + 48

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 48

Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

These are the possible values for p.

The leading coefficient (the coefficient of the term with the highest degree) is 1.

These are the possible rational roots:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0

Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.

Thus, these are the roots of the given polynomial.

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We observe, that P(V|B)>P(V|A), so the person is more likely to have virus, however is still very small probability (only 15%), so in order to confirm illness, he should make one more test.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

P(V/A)  is not 0.95. It is opposite:

P(A/V)=0.95

From the text we can also conclude, that

P(A/∼V)=0.1

P(B/V)=0.9

P(B/∼V)=0.05

P(V)=0.01

P(∼V)=0.99

P(V/A) is not 0.95. It is opposite:

P(A/V)=0.95

From the text we can also conclude, that

P(A/∼V)=0.1

P(B/V)=0.9

P(B/∼V)=0.05

P(V)=0.01

P(∼V)=0.99

What we need to calculate and compare is P(V/A) and P(V/B)

P(V∩A)=P(A)⋅P(V/A)⇒P(V/A)=P(V∩A)/P(A)

P(V∩A) means, that person has a virus and it is detected, so

P(V∩A)=P(V)⋅P(A/V)

=0.01⋅0.95

=0.0095

P(A) is sum of two options: "Person has virus and it is detected" and "Person has no virus, but it was mistakenly detected", therefore:

P(A)=P(V)⋅P(A/V)+P(∼V)⋅P(A/∼V)=0.01⋅0.95+0.99⋅0.1=0.1085

Dividing those two numbers we obtain

P(V/A)=0.0095/0.1085=0.08755760368663594

Analogically,

P(V/B)=P(V∩B)/P(B)=P(V)⋅P(B/V)/P(V)⋅P(B/V)+P(∼V)⋅P(B/∼V)

=0.01⋅0.9/0.01⋅0.9+0.99⋅0.1

=0.1538461538461539

We see that P(V|B)>P(V|A), meaning the individual is more likely to have a virus, but is still very unlikely (only 15%), therefore person should perform another test to confirm illness.

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Answer:

C)   (-3,-2)

Step-by-step explanation:

Solutions to the graphed system of inequalities are any points that are contained within the overlapping shaded region.

Plot the points on the given coordinate grid.

The only point that is contained with the overlapping shaded region is:

Answer:

Step-by-step explanation:

a) To find how much farther Jill's best friend jumped, we need to subtract Jill's distance from her best friend's distance. First, we need to convert both distances to the same unit, in this case inches. 6 7/8 feet is equal to 6 7/8 * 12 inches/foot = 82 7/8 inches. 6 15/16 feet is equal to 6 15/16 * 12 inches/foot = 83 16/16 inches. Now that both distances are in inches, we can subtract them: 83 16/16 inches - 82 7/8 inches = 1 9/16 inches. Therefore, Jill's best friend jumped 1 9/16 inches farther.

b) To determine if Jill's best friend beat the school record, we need to compare her distance to the record distance. The record distance for seventh graders is 6 feet 1 3/5 inches, which is equal to 6 1/5 * 12 inches/foot = 74 inches. Jill's best friend jumped 83 16/16 inches, which is greater than 74 inches. Therefore, Jill's best friend beat the school record and the seventh graders should be awarded 50 points.

c) To find the total distance thrown by Claire and Grace, we need to add their individual distances. First, we need to convert both distances to the same unit, in this case inches. 42 5/8 feet is equal to 42 5/8 * 12 inches/foot = 510 5/8 inches. 39 3/5 feet is equal to 39 3/5 * 12 inches/foot = 472 3/5 inches. Now that both distances are in inches, we can add them: 510 5/8 inches + 472 3/5 inches = 983 8/5 inches. Therefore, the total distance thrown by Claire and Grace is 983 8/5 inches.

d) To determine if the total distance thrown by Claire and Grace is greater than 83.7 feet, we need to compare their distance to the record distance. The record distance for seventh graders is 83.7 feet, which is equal to 83.7 * 12 inches/foot = 1004.4 inches. The total distance thrown by Claire and Grace is 983 8/5 inches, which is less than 1004.4 inches. Therefore, the total distance thrown by Claire and Grace is not greater than the record distance and the eighth graders should be awarded 50 points.

Jacob's body metabolizes caffeine at a rate of 13.5% per hour.

a)Jacob's body will takes 4.77 ~5 hours to metabolize half of the 96 mg of caffeine.

b) If Jacob consumes an energy drink with 212 mg of caffeine in it, Jacob's body will take 4.77948 ~ 5 hours to metabolize half of the 212 mg of caffeine.

c) Jacob consumes a cup of coffee with c mg of caffeine in it. Jacob's body will take 4.77948~ 5 hours to metabolize half of the c mg of caffeine.

The volume will slowly decrease at regular intervals and at a regular rate. This growth reduction is calculated using the exponential decay formula. The general form is y = a(1- r)ᵗ

We have, decay rate r = 13.5 % = 0.135

Initial value , a = 96 mg

plugging the value in formula we get,

y = 96(1 - 0.135)ᵗ --(1)

Now, Half of 96 is 48

so, 48 = 96(0.865)ᵗ --(2)

dividing equation by 96 we get

=> 48/96 = (0.865)ᵗ

taking natrual logarithm both sides,

=> ln(1/2) = ln ((0.865))

=> ln(1/2) = t In (0.865)

=> t = ln(1/2)/In (0.865)

=> t = 4.77948

Since, decay rate is constant so, half never changes for any .

a) 4.779~5 hours, long will it take for Jacob's body to metabolize half of the 96 mg of caffeine.

b) Jacob's body to metabolize half of the 212 mg of caffeine is 4.779~ 5 hours.

c) for Jacob's body to metabolize half of the cmg of caffeine is 4.77948.. So, we have 4.77948 ~ 5 hours is decay constant rate.

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Answer:

You've got it right

Step-by-step explanation:

If you want to get stellar communication on the question then maybe include a number line to visually represent why, but otherwise you have the answer right.

The length of James's rectangular yard, given a fence perimeter of 20 feet and a width of 2 feet, is 8 feet, equivalent to 96 inches.

Given: Perimeter (P) = 20 feet, Width (W) = 2 feet,

Conversion factor: 1 foot = 12 inches

Using the formula for perimeter: P = 2L + 2W

Substitute the given values: 20 = 2L + 2(2)

Simplify: 20 = 2L + 4

Subtract 4 from both sides: 16 = 2L

Divide by 2: L = 8 feet

Convert feet to inches: Length (in inches) = 8 feet * 12 inches/foot = 96 inches

So, the length of the rectangular yard is 96 inches.

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To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula and solve for the length in inches. The length of James' rectangular yard is 108 inches.

To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula. However, since we need the length in inches, we will convert the feet to inches using the conversion factor of 1 foot = 12 inches.

Let's solve:

The length of James' rectangular yard is 108 inches.

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The solution of the given inequality -x < -x + 7 ( x - 2 ) is given by x > 2.

As given in the question,

Inequality is given by :

-x < -x + 7 ( x - 2 )

Open the parenthesis of the given inequality we have,

⇒ -x < -x + 7x - 14

Collect all the like terms on the same side we get,

⇒ - x < 6x  - 14

Subtract 6x from both the side of the inequality we get,

⇒ - x - 6x < 6x - 6x - 14

⇒ -7x < -14

Divide both the side of the inequality by -7 we get,

⇒ -7x/ -7 > -14 / -7

⇒ x > 2

x has all the value greater than 2.

Therefore, for the given inequality the solution is given by x > 2.

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Answer:

(1.5, −0.5)

Step-by-step explanation:

Answer:

In 2022, the town's population is 2220.

Step-by-step explanation:

It currently the year 2022. Hence, 22 years have passed since 2000.

2022 − 2000 = 22

To solve for the town's population today, first multiply the years passed since 2000 by the percent decrease each year.

[tex]22 \, \textrm{years} \times \dfrac{3.2 \, \%}{\textrm{year}} = 70.4 \, \%[/tex]

Then, subtract that percent of the population in 2000 from the population in 2000.

[tex]7500-(70.4 \,\% \cdot 7500)[/tex]

[tex]= 7500 - 5280[/tex]

[tex]=2220[/tex]

For the given range of theta, cos(theta) is negative, which means that theta is in the third or fourth quadrant. In these quadrants, the sine function is positive, the tangent function is negative, and the cotangent function is negative.

Since cos(theta) = -3/5, we can use the Pythagorean identity to find the value of sin(theta):

sin^2(theta) + cos^2(theta) = 1

sin^2(theta) = 1 - cos^2(theta)

sin^2(theta) = 1 - (-3/5)^2

sin^2(theta) = 1 - 9/25

sin^2(theta) = 16/25

sin(theta) = sqrt(16/25) = 4/5

Therefore, the value of sin(theta) is 4/5.

We can also use the identity cot(theta) = 1/tan(theta) to find the value of cot(theta):

cot(theta) = 1/tan(theta)

cot(theta) = 1/(sin(theta)/cos(theta))

cot(theta) = cos(theta)/sin(theta)

cot(theta) = (-3/5)/(4/5)

cot(theta) = -3/4

Therefore, the value of cot(theta) is -3/4.

The values of the other trigonometric functions can be found using the definitions of these functions:

tan(theta) = sin(theta)/cos(theta) = (4/5)/(-3/5) = -4/3

csc(theta) = 1/sin(theta) = 1/(4/5) = 5/4

sec(theta) = 1/cos(theta) = 1/(-3/5) = -5/3

Therefore, the values of the trigonometric functions for the given range of theta are:

sin(theta) = 4/5

tan(theta) = -4/3

csc(theta) = 5/4

sec(theta) = -5/3

cot(theta) = -3/4

The alternative hypothesis for this problem b. HA: µD>0

What is meant by hypothesis?

In math, A hypothesis is an assumption made based on some evidence.

Here we have given that systems analyst is testing the feasibility of using a new computer system. He wants to see if the new system uses less processing time than the old system.

And we need to find the alternative hypothesis for this problem

While we looking into the given question we have identified the following values,

Old System: mean = 27.2 seconds, s = 3.2 seconds, n - 25

New System: mean = 24.3 seconds, s = 2.1 seconds, n = 25

Difference (Old -New): mean = 2.9 seconds, s = 1.4 seconds, n = 25

Basically, while written the hypothesis, we have to follow the order of the following,

=> (Old-New, Larger-Smaller>)

Therefore, the correct option is (B).

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Answer: 13.55 or 13 11/20.

Step-by-step explanation: First, you have to find a common denominator, in this case, it would be 20. 2 can go into 20 10 times, 4 can go into 20 5 times, and 10 can go into 20 2 times. Then, you would NOW have 3 10/20 + 4 15/20 + 5 6/20, to have all the equal denominators. When you add, you would get 12 31/20, but now you have to simplify. Now, you SHOULD get 13 11/20 after simplifying. As a decimal, it would be 13.55 I hoped this helped!

Answer:

Step-by-step explanation:

2sin x=-√3

[tex]sin~x=-\frac{\sqrt{3} }{2} =-sin~\frac{\pi }{3} =sin (\pi +\frac{\pi }{3} ),sin(2\pi -\frac{\pi }{3} )\\=sin(\frac{4\pi }{3} +2k\pi ),sin (\frac{5\pi }{3} +2k\pi )\\=sin(A+Bk\pi ),sin(C+Dk\pi )\\x=A+Bk\pi ,C+Dk\pi \\where~A=\frac{4\pi }{3} ,B=2\\C=\frac{5\pi }{3} ,D=2[/tex]

We Reject H₀ if t calculated > t tabulated and hence the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, we failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise

The Null and Alternate hypothesis is given by

Null hypotheses = H₀: μ₁ = μ₂

Alternate hypotheses = H₁: μ₁ ≠ μ₂

The test statistic is given by

Where  is the sample mean of people who do not exercise regularly.

Where  is the sample mean of people who do exercise regularly.

Where  is the sample standard deviation of people who do not exercise regularly.

Where  is the sample standard deviation of people who do exercise regularly.

Where  is the sample size of people who do not exercise regularly.

Where  is the sample size of people who do exercise regularly.

The given level of significance is

1 - 0.95 = 0.05

The degree of freedom is

df = 16 + 12 - 2 = 26

From the t-table, df = 26 and significance level 0.05,

t = 2.056 (two-tailed)

Conclusion:

We Reject H₀ if t calculated > t tabulated

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The value of x that makes sense for the expression is the domain of the expression
The value of x makes sense for √-2x² is 0
The value of x must not exceed 0 for  √(-2x)³ to make sense

What is Angle Sum Property?

The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angles.

√-2x²

For the above expression to have a defined value, the expression in the bracket must be positive.

However, x² will always be positive, and -2 will ensure that the expression is always negative, except when x = 0

Hence, the value of x makes sense for √-2x² is 0.

√(-2x)³

For the above expression to have a defined value, the expression in the square root must be positive.

However, the power of 3 will ensure that the expression is always positive only when x is less than or equal to 0

Hence, the value of x must not exceed 0 for √(-2x)³ to make sense.

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The x-coordinate for the point  (x, -8), if Y-intercept is 4, and the coordinates of the point is (14, -3), is 24, so option B is correct.

An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.

Given:

Y-intercept = 4,

Coordinates of point =  (14, -3), (x, -8)

Calculate the line equation as shown below,

y = m x + 4

Here, m is the slope,

Put point (14, -3) in the equation,

-3 = m × 14 + 4

m = -7 / 14

m = -1 / 2

Hence, the equation of a line is,

y = -1/2 x + 4

Put point (x, -8),

-8 = -1/2 x + 4,

-12 = -1/2x

x = 24

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Answer: if there is an option for -1,989 then it would be that one

Step-by-step explanation:

13 - 90 would give you -77 and then 50/90 is would give you 0.5555555. -77 + 0.5 would be -76.5 which then you multiply by 26 gives you -1,989.

Answer:

Step-by-step explanation:

x=-4

The factors of the expression 3(m + 2) are 3 and (m + 2) and the correct option is A. 3 and (m + 2).

A factor in an expression of number, variable, term or any other longer expression that is multiplied by another. In mathematics, a number or algebraic expression that divides another number or expression evenly without remainder is also called a factor.

The question have an algebraic expression; 3(m + 2)

considering the four options;

A. 3 and (m + 2)

B. m and 2

C. 3 and m

D. 3 and 2

Only option A. with 3 and (m + 2) can be said to be factors as multiplying them will give 3(m + 2) and can both divide the expression 3(m + 2) evenly without a remainder.

In conclusion, 3 and (m + 2) are factors for the given expression and option A. 3 and (m + 2) is correct.

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Answer:

55 1/10 yd

Step-by-step explanation:

26 + 10 + 3/5 + 10 + 1/5 + 8 + 3/10 =

= 54 + 4/5 + 3/10 =

= 54 + (8 + 3)/10 =

= 54 + 11/10 =

= 54 + 10/10 + 1/10 =

= 54 + 1 + 1/10 =

= 55 1/10

Answer:

55[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

Convert all the mixed numbers to fractions with a common denominator (10) then add them up:

26 + 53/5 + 51/5 + 83/10 =

26 + 106/10 + 102/10 + 83/10 =

26 + 291/10 =

26 + 29[tex]\frac{1}{10}[/tex] = 55[tex]\frac{1}{10}[/tex]

The transformation could be used to show that triangle Q is similar but not congruent to triangle P is Dilation.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

Given that, triangle P undergoes a transformations resulting in triangle Q.

We know, Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

Hence, The transformation could be used to show that triangle Q is similar but not congruent to triangle P is Dilation.

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Answer: 5/8

Step-by-step explanation:

Answer:

The division algorithm says when a number is divided by a number gives the quotient

Step-by-step explanation:

Answer:

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

Answer:

d= -3

Step-by-step explanation:

Rearrange variables to the left side of the equation: -4.3x 10d= -0.0043

Divide both sides of the equation by the coefficient of variable

Reduce the fraction

Convert fraction into negative exponential form

Convert both sides of the equation into terms with the same with same base

Simplify using exponent power rule

Based on the given conditions, corresponding exponents are equal

Answer:

1.1

Step-by-step explanation:

By subtracting and adding mixed numbers, we can see that at the end she has (5 + 7/8) tubes of paint.

We know that initially Allie had (4 + 3/4) tubes of purple paint, and she sed (2+ 1/4) tubes.

So at this point we need to take the difference between the two mixed numbers, we will get:

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

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

2 + 2/4  = 2 + 1/2

Then she founds (3 + 3/8) more. Now we need to add that:

2 + 1/2 + (3 + 3/8) = (2 + 3) + (1/2 + 3/8)

(2 + 3) + (1/2 + 3/8) = 5 + (4/8 + 3/8)

5 + (4/8 + 3/8) = 5 + 7/8

She has 5 + 7/8 tubes of purple paint.

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The probability that a random variable has a value less than 44 is 44.

The probability that a random variable has a value less than 44 can be determined by calculating the area under the curve to the left of 44.

In a uniform density curve, the probability of a random variable falling within a certain range is equal to the length of that range. To find the probability of a random variable having a value less than 44, we need to find the length of the range from 0 to 44.

The length of this range is 44 - 0 = 44.

Therefore, the probability that a random variable has a value less than 44 is 44.

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Answer:

the constant term in this problem is 8