A solid of revolution is generated by rotating the region between the z-axis and the graphs of f(x) = x^2 + 4x +5, x=-4, and x = -1 about the x-axis. Using the disk method, what is the volume of the solid? Enter your answer in terms of pi.

Answer:

b and c

Step-by-step explanation:

The Triangle Inequality Theorem lets us know that the sum of the two shortest sides of the triangle must be greater than the third side of the triangle.

In both A and D, the sum of the shortest two sides are equal to, not greater than the third side, so they will not form a triangle.

In B, 12+20 is 32, which is greater than 25. And in C, 18+24 is 42, which is greater than 30, so they both will form a triangle.

Using the Pythagorean Theorem, it is found that possible side lengths of a right triangle are given by:

c. 18 cm, 24 cm, 30 cm

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

The length of the hypotenuse is always greater than the length of the legs. The Pythagorean Theorem has to hold true, which holds only for option C, as:

18² + 24² = 30²

900 = 900

More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982

#SPJ2

Answer:

Greater, Less than, Greater

Step-by-step explanation:

Remember anything close to zero will always be greater in negative numbers. Example. -1>-2. Negative one is greater since it it closer to zero than 2.

Step-by-step explanation:

you question isn't clear enough

find the area of what actually?

Answer:

square = 34

triangle = 17

Step-by-step explanation:

Answer:

1/5 of 1,212

Step-by-step explanation:

Note that 25% = 1/4 and 30% = 3/10.

The least value is achieved when we take the smallest fraction, which is 1/5.

Answer:

1/5 of 1212 is the smallest value

Step-by-step explanation:

if we convert 25% to a fraction we have 1/4

if we convert 30% to a fraction we have 3/10

now we convert each of the four fractions into equivalent fractions using lowest common denominator of 60

1/3 = 20/60

1/5 = 12/60

1/4 = 15/60

3/10 = 18/60

the smallest fraction is 12/60, or 1/5

therefore 1/5 of 1212 is the smallest value

A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.

The number of sides (n) of the pentagon is:

n =5

The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).

To draw the pentagon onto itself, the pentagon has to be rotated.

The angle of rotation is:

θ \(= \frac{360}{n}\)

θ  \(=\frac{360}{5} = 72\)

Other possible angles of rotation must be multiple of 72. i.e.

θ= 72, 144, 216, 288...

Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.

Read more about the pentagon:

https://brainly.com/question/11759904

#SPJ4

The complete question is:

A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?

a. A reflection across line m

b. A reflection across the x-axis

c) A clockwise rotation of 144 degrees about the origin

The given function is f(x) = (4-x)/29. We need to find the x-values where f is not continuous and determine whether the discontinuities are removable or nonremovable.

For this function, there are no nonremovable discontinuities. The only type of discontinuity that could occur is a removable discontinuity. This occurs when a point is undefined, but the limit exists and is finite. In other words, the function can be made continuous by redefining it at that point.

To find any possible removable discontinuities, we need to find the values of x for which the denominator becomes zero, because division by zero is undefined. The denominator is always 29, which is never zero, so there are no values of x for which the denominator is zero. Therefore, there are no removable discontinuities.

In conclusion, the function f(x) = (4-x)/29 is continuous for all values of x, and there are no removable or nonremovable discontinuities.

To learn more about denominator, click here:

brainly.com/question/15007690

#SPJ11

The normal distribution has only positive values. Option A is the correct answer.

The normal distribution is a continuous probability distribution that is symmetric around the mean, and its values are only positive. The other distributions listed, such as the chi-square, f, and t distributions, are all skewed and have values that can be negative or positive. The z-distribution is similar to the normal distribution but has a mean of 0 and a standard deviation of 1, and thus can also have negative values. Therefore, the only distribution that has only positive values is the normal distribution, making option A the correct answer.

You can learn more about normal distribution at

https://brainly.com/question/4079902

#SPJ11

The area of the pentagon is approximately 15 square inches.

To find the area of the pentagon, we can use the formula for the area of a regular pentagon:

Area = (5/4) * (s²) * (1/tan(π/5)),

where "s" is the length of the side of the pentagon.

Given that the sides of the pentagon are as follows:

Two smallest sides = 2 inches,

Two largest equal sides = 4 inches,

One other equal side = 3 inches.

Since the pentagon is not a regular pentagon, we need to find the area by dividing it into different shapes and then calculating their individual areas.

The pentagon can be divided into three shapes: a rectangle and two triangles.

Rectangle:

The two smallest sides (2 inches) form the length and width of the rectangle.

Area of the rectangle = Length * Width = 2 inches * 2 inches = 4 square inches.

Triangle 1:

The two largest equal sides (4 inches) and one of the 3-inch sides form a triangle.

To calculate the height (h) of the triangle, we can use the Pythagorean theorem, since it is a right triangle.

h² = (4 inches)² - (1.5 inches)², [1.5 inches is half of the 3-inch side]

h² = 16 inches² - 2.25 inches²,

h² = 13.75 inches²,

h ≈ 3.7 inches.

Area of Triangle 1 = (1/2) * Base * Height = (1/2) * 3 inches * 3.7 inches ≈ 5.55 square inches.

Triangle 2:

The two largest equal sides (4 inches) and the other 3-inch side form another triangle.

Using the same height (3.7 inches) from Triangle 1:

Area of Triangle 2 = (1/2) * Base * Height = (1/2) * 3 inches * 3.7 inches ≈ 5.55 square inches.

Now, to find the area of the pentagon, we add the areas of the rectangle and the two triangles:

Total Area = Area of Rectangle + Area of Triangle 1 + Area of Triangle 2

Total Area = 4 square inches + 5.55 square inches + 5.55 square inches

Total Area ≈ 15.1 square inches.

Therefore, the area of the pentagon is approximately 15.1 square inches.

To know more about area of the pentagon click here :

https://brainly.com/question/29683405

#SPJ2

Answer:

\(b=20\sqrt{2}\) units

Step-by-step explanation:

Recall the Law of Sines

\(\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\)

Solve for side "b" given ∠A, ∠B, and side "a"

\(\frac{sinA}{a}=\frac{sinB}{b}\\ \\\frac{sin(30^\circ)}{20}=\frac{sin(45^\circ)}{b}\\ \\ bsin(30^\circ)=20sin(45^\circ)\\\\b(0.5)=20(\frac{\sqrt{2}}{2})\\ \\0.5b=10\sqrt{2}\\\\b=20\sqrt{2}\)

Therefore, \(b=20\sqrt{2}\) units

Answer:28

Step-by-step explanation:

Answer:

b = 7, c = -3 and a = 1

Step-by-step explanation:

So I'm assuming you know the quadratic formula, x=-b +- root (b^2-4ac)/2a

so knowing this, it is given that b^2 - 4ac = 61

it is also given 2a = 2 (the bottom of the fraction) which means a =1

and the -b = -7 (the start of the expression), which means b = 7

now we have b = 7, and a = 1

now we can sub it into b^2 - 4 x a x c = 61

b^2 is 7 x 7 = 49

4 x a x c = 4c

so we have 49-4c=61

-4c = 61-49

-4c = 12

c = -3

therefore we have b = 7, c = -3 and a = 1

Answer:

We know that in the box there are:

4 twix

3 kit-kat

Then the total number of candy in the box is:

4 +3 = 7

a)

Here we want to find the probability that we draw two twix.

All the candy has the same probability of being drawn from the box.

So, the probability of getting a twix in the first drawn, is equal to the quotient between the number of twix and the total number of candy in the box, this is:

p = 4/7

Now for the second draw, we do the same, but because we have already drawn one twix before, now the number of twix in the box is 3, and the total number of candy in the box is 6.

this time the probability is:

q = 3/6 = 1/2

The joint probability is the product of the individual probabilities, so here we have

P = p*q = (4/7)*(1/2) =  2/7

b) same reasoning than in the previous case:

For the first bar, the probability is:

p = 3/7

for the second bar, the probability is:

q = 2/6 = 1/3

The joint probability is:

P = p*q = (3/7)*(1/3) = 1/7

c) Suppose that first we draw a twix.

The probability we already know that is:

p = 4/7

Now we want another type, so we need to draw a kit-kat, the probability will be equal to the quotient between the remaining kit-kat bars (3) and the total number of candy in the box (6)

q = 3/6

The joint probability is:

P = p*q = (4/7)*(3/6) = 2/7

But, we also have the case where we first draw a kit-kat and after a twix, so we have a permutation of two, then the probability in this case is:

Probability = 2*P = 2*2/7 = 4/7

The variance of the length of the critical path is 5.76.

Option A is the correct answer.

We have,

To calculate the variance of the length of the critical path in the Critical Path Method (CPM) with three-time estimates (PERT), we can use the formula:

Variance = (Standard Deviation)²

Given that the standard deviation is 2.4, we can substitute it into the formula:

Variance = (2.4)² = 5.76

Therefore,

The variance of the length of the critical path is 5.76.

Learn more about variance here:

https://brainly.com/question/31432390

#SPJ1

(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

To learn more about scaling matrix click here : brainly.com/question/16662440

#SPJ11

Answer:

10 months

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

both angles equal each other

I hope this helps

Answer: \(4x^{2}\)

Step-by-step explanation:

to show the work go to this webiste and type in the problem https://www.mathpapa.com/algebra-calculator.html

The weight-loss pill advertisement claims that users lose an average of 1.8 pounds in one week with a standard deviation of one pound or more, implying some variability in individual weight loss outcomes.

To determine the probability of losing 1.8 pounds or more after one week using the weight-loss pill, we can use the concept of standard deviation and the Z-score.

The Z-score measures the number of standard deviations a data point is from the mean. We can use it to calculate the probability of obtaining a value equal to or greater than a specific value.

Given:

Mean (μ) = 1.8 pounds

Standard deviation (σ) = 1 pound

To calculate the Z-score, we use the formula:

Z = (X - μ) / σ

Where X is the value we want to find the probability for.

In this case, we want to find the probability of losing 1.8 pounds or more. So, X = 1.8 pounds.

Z = (1.8 - 1.8) / 1 = 0

Since the Z-score is 0, we need to find the probability of getting a value equal to or greater than 0.

To find this probability, we can refer to the Z-table or use a calculator that provides the cumulative probability function. The cumulative probability function gives us the probability of obtaining a Z-score less than or equal to a given value.

In this case, we want to find the probability of obtaining a Z-score greater than or equal to 0, which represents the probability of losing 1.8 pounds or more.

Looking up the Z-table or using a calculator, we find that the cumulative probability for a Z-score of 0 is 0.5.

Therefore, the probability of losing 1.8 pounds or more after one week using the weight-loss pill is 0.5 or 50%.

Learn more about standard deviation here:

https://brainly.com/question/29073906

#SPJ11

Answer:

9 3/5

Step-by-step explanation:

4 cups is 8 times the amount, so multiply 1 1/5 by 8 which gets you to 9 3/5

hope this helps

Answer:

To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Step-by-step explanation:

SA=2*4*5+2*4*6+2*6*5

=148 cmStep-by-step explanation:

The value of ∠ABD is 120 degrees if given an isosceles trapezoid ABCD with median XY

What is trapezoid ?

A trapezoid is a quadrilateral (a four-sided polygon) with at least one pair of parallel sides. The parallel sides of a trapezoid are called bases, and the non-parallel sides are called legs.

Since ABCD is an isosceles trapezoid, the length of AB is equal to the length of CD. Let's assume that AB = CD = a, and BC = d.

The length of XY is equal to half the sum of the lengths of the non-parallel sides AB and CD. Therefore, XY = (1/2)(AB+CD) = (1/2)(a+a) = a.

So, the length of the median XY is a.

Since ABCD is an isosceles trapezoid, the base angles A and D are congruent. Let's assume that m∠ABD = x.

Since XY is the median of ABCD, it bisects the legs AB and CD at M and N, respectively. Therefore, AM = MB = (AB/2) and DN = NC = (CD/2).

Since AD and BC are parallel, we have ∠AMB = ∠DNC (corresponding angles). Also, ∠AMB + ∠BMD = 180° (linear pair), so ∠BMD = 180° - ∠AMB.

Similarly, we have ∠CND + ∠DNC = 180° (linear pair), so ∠CND = 180° - ∠DNC.

Since AD and BC are parallel, we have ∠ABD + ∠BMD = 180° (co-interior angles), so ∠ABD = 180° - ∠BMD.

Similarly, we have ∠DCB + ∠CND = 180° (co-interior angles), so ∠DCB = 180° - ∠CND.

Since ABCD is an isosceles trapezoid, we have AB = CD, so AM + MC = DN + NB. Substituting the values, we get (a/2) + d = (a/2) + d. Therefore, d = d.

Now, we can use the fact that ∠BMD = ∠CND to get an equation in terms of x: x + ∠ABD = 180° - x + ∠DCB. Substituting d = d, we get x + ∠ABD = 180° - x + ∠ABD. Therefore, x = (1/2)*(180° - ∠ABD).

Since ABCD is an isosceles trapezoid, we have ∠ABC = ∠DCB. Also, we know that ∠ABD and ∠CBD are supplementary angles. Therefore, ∠ABD + ∠CBD = 180°. Substituting the value of x, we get (1/2)*(180° - ∠ABD) + ∠ABD = 180°. Simplifying, we get ∠ABD = 120°.

Therefore, The value of ∠ABD is 120 degrees if given an isosceles trapezoid ABCD with median XY

To learn more about Trapezoid from given link.

https://brainly.com/question/12623349

#SPJ1

Answer:

a. 44 cm b. 126 cm

Step-by-step explanation:

a. it is semi circle

perimeter is πd

22/7*14

44 cm

b. it is equilateral triangle

so perimeter is side* 3

42 *3 = 126cm

Answer:

Step-by-step explanation:

(a)

The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.

The length of a circle is  L₀ = πd, where d is the diameter.

Therefore:

\(\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}\)

(b)

A full circle it is 360°, so the circle sector of 60° is  \(\frac{60^o}{360^o}=\frac16\)  of the circle. So the arc of 60° is ¹/₆ of the full circle length.

The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).

Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.

The length of a circle is  L₀ = 2πr, where r is a radius.

Therefore:

\(\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}\)

Linear Pair of Angles: two angles that form a straight line - they are supplementary.A linear pair of angles refers to two adjacent angles that add up to 180 degrees.

It is important to note that the sum of the angles in a linear pair of angles will always equal 180 degrees. A linear pair of angles must be adjacent, meaning that they share a common vertex and a common side but no other interior points.

Linear pairs of angles can be used to solve problems involving complementary, supplementary, and vertical angles. Since they add up to 180 degrees, they are considered to be supplementary angles. This is because supplementary angles are two angles that add up to 180 degrees.

Therefore, a linear pair of angles is also supplementary because it contains two adjacent angles that add up to 180 degrees. In other words, if two angles form a straight line, then they are considered to be supplementary.

The use of linear pairs of angles is prevalent in geometry problems involving parallel lines, triangles, and polygons.

The concept of a linear pair of angles is also important in understanding the different types of angles, including acute, obtuse, and right angles. For instance, an acute angle can form a linear pair with an obtuse angle, while a right angle can only form a linear pair with another right angle.

For more such questions on 180 degrees

https://brainly.com/question/31298990

#SPJ8

Answer:

B) \(\$8395.80\)

Step-by-step explanation:

\(A=P(1+rt)\\A=7996(1+0.06\cdot\frac{10}{12})\\A=7996(1+0.05)\\A=7996(1.05)\\A=\$8395.80\)

This is all assuming that r=6% is an annual rate, making t=10/12 years

Given problem represent Fundamental Counting Theorem.

Fundamental Counting Theorem states that if an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m×n.

Here Taylor has 5 baskets and there are 6 balls in each basket.

That is m = 5 and n = 6

Therefore Taylor have m×n= 5×6 =30 balls

Hence here we use Fundamental counting theorem.

To know more about Fundamental counting theorem here

https://brainly.com/question/16025130

#SPJ1

Answer:

$3.00

Step-by-step explanation:

$5.00 = 5

$2.00 = 2

5

-2

_

3

3 = $3.00

Answer:

$3.00

Step-by-step explanation:

Answer:

It is decay  because the value of the car keeps falling.

for example, the value next year, would be 12250 x (100% - 11%) = $10,902.50

If it were a growth, the value would increase yearly

12250 x (0.89)^time

Step-by-step explanation:

the equation to represent exponential decay = Amount x ( 1 - rate)^time

Answer:

Step-by-step explanation:

#a

\(\\ \sf{:}\dashrightarrow -2(-4.5)=9.0\)

#b

\(\\ \sf{:}\dashrightarrow (-8.7)(-10)=8.7\)

#c

\(\\ \sf{:}\dashrightarrow (-7)(-2)=14\)

#d

\(\\ \sf{:}\dashrightarrow (-9)(-10)=90\)

Answer:

if you can please explain more of the context (what do they mean by turn around sentence) I'd be happy to help!

Answer: Hello! I'm JK!.....

Yes there is!

First, divide the large number by a small number.

If the remainder is left, then divide the first divisor by remainder.

If the remainder divides the first divisor completely, then it is the HCF or highest common factor of the given two numbers.

Step-by-step explanation:

I hope this helps you! <3 XoXoGoldenMaknae