The cone below has a radius of 1 inch and height of 4 inches. What is the slant height in inches?

a. √-5

b. √−−17

c. 15

d. 17

The Kathleen should be able to pay approximately $702.82 today to cover her $750 loan payment due in six months.

To calculate the present value of Kathleen's loan payment, we can use the formula for present value of a future sum of money:

Substituting the values into the formula:

Calculating the present value:

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Answer:

61 ft

Step-by-step explanation:

since it's equal

u look cute in that pfp

The probability that a bundle of steel rods chosen at random has an average length that falls between P(118.7-cm M 119.8-cm) = -2.1018

We have the following information from the question is:

Steel rods are produced by a firm. Steel rod lengths have a mean of 118.7 cm and a standard deviation of 2.2 cm, and they are regularly distributed. 17 steel rods are packaged together for shipping.

Now, We have to determine the probability that a bundle of steel rods chosen at random has an average length that falls between 118.7- cm and 119.8-cm. P(118.7-cm M 119.8-cm).

We know that,

Mean =μ= 118.7

Standard deviation = σ = 2.2

n = 17

P(118.7 ) = (M-μ)/σ =  P[118.7 - 118 /2.2] = 0.3182

P(119.8) = (M-μ)/σ = P [119.8 - 118.7/2.2] = 2.42

P[118.7-cm <  M < 119.8-cm] = P(0.3182 < M < 2.42)

Using the z table:

0.3182 - 2.42

= -2.1018

Therefore, the probability that a bundle of steel rods chosen at random has an average length that falls between P(118.7-cm M 119.8-cm) = -2.1018

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Answer:

x = -4 and 2

Step-by-step explanation:

When x = -4 and 2, y = 0 so -4 and 2 are the roots

Answer:

c for both

Step-by-step explanation:

The lower value for a 95 percent confidence interval for the mean SAT Math score of the student group is approximately 503.06.

To calculate the lower value of the confidence interval, we use the formula:

Lower value = x - z * (σ / √n)

where x is the sample mean, z is the z-score corresponding to the desired confidence level (in this case, for 95% confidence, z ≈ -1.96), σ is the population standard deviation, and n is the sample size.

Given that x = 535, σ = 100, and n = 25, we can substitute these values into the formula:

Lower value = 535 - (-1.96) * (100 / √25)

Simplifying the expression:

Lower value = 535 + 1.96 * (100 / 5)

Lower value = 535 + 1.96 * 20

Lower value ≈ 535 + 39.2

Lower value ≈ 574.2

Therefore, the lower value for a 95 percent confidence interval for the mean SAT Math score of the student group is approximately 503.06.

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Answer:

4 kilometers.

Step-by-step explanation:

Answer:

Question A)

[tex]=\sqrt{6}x[/tex]

Question B)

[tex]=3a\sqrt{a}[/tex]

Question C)

[tex]=5\sqrt{2}b^2[/tex]

Step-by-step explanation:

A)

We are given:

[tex]\sqrt{6x^2}\, \text{ where } x\geq 0[/tex]

We can rewrite the expression:

[tex]=\sqrt{6}\cdot \sqrt{x^2}[/tex]

The square root and square will cancel each other out. Thus:

[tex]=\sqrt{6}x[/tex]

B)

We are given:

[tex]\sqrt{9a^3}[/tex]

Rewrite:

[tex]=\sqrt{9}\cdot \sqrt{a^3}[/tex]

Note that the square root of 9 is simply 3. We can also factor the second part:

[tex]=3\cdot \sqrt{a^2\cdot a}[/tex]

Rewriting:

[tex]=3\cdot\sqrt{a^2}\cdot\sqrt{a}[/tex]

Simplify:

[tex]=3a\sqrt{a}[/tex]

C)

We are given:

[tex]\sqrt{50b^4}[/tex]

Rewrite. Note that 50 = 25(2):

[tex]=\sqrt{25}\cdot \sqrt{2}\cdot \sqrt{b^4}[/tex]

Simplify. We can rewrite the factor as:

[tex]=5\cdot \sqrt{2}\cdot \sqrt{(b^2)^2}[/tex]

The square and square root will cancel out. Thus:

[tex]=5\sqrt{2}b^2[/tex]

Answer:

Vince is not correct because he should have interpreted the solution as having to save a minimum of $103.55.

Step-by-step explanation:my

my sister which is in college helped me with one.

Answer: its D

Step-by-step explanation:

Answer:

0.09 or 9%

Step-by-step explanation:

Formula:

I = Prt

r = I/(Pt)

Given:

I = 1350

P = 5000

t = 3

Finding r:

r = I/(Pt)

r = 1350/(5000 x 3)

r = 1350/15000

r = 0.09

0.09 or 9%

Answer:

11

Step-by-step explanation:

Each side on the smaller quadrilateral is half the length of the larger one. So since the corresponding side is 22, then half of that is 11.

ta da!

hope this helped :)

Answer:

Yes. See explanation below.

Step-by-step explanation:

The central angle and the degree arc measure of a sector of a circle are  equal. Doubling the arc measure, doubles the central angle measure and vice versa.

Area of the the original sector:

[tex] A_{sector} = \dfrac{n}{360^\circ}\pi r^2 [/tex]

where n = measure of the central angle of the sector

Since the central angle and the arc measure of the sector are equal, changing the arc measure has the same effect as changing the central angle measure.

Let's double the central angle to 2n which is the same as doubling the arc measure.

Area of the sector with a doubled central angle or a doubled arc measure:

[tex] A_{sector} = \dfrac{2n}{360^\circ}\pi r^2 [/tex]

Now we divide the area of the doubled sector by the area of the original sector.

[tex]\dfrac{\frac{2n}{360^\circ}\pi r^2}{\frac{n}{360^\circ}\pi r^2} =[/tex]

Simplify:

[tex]= \dfrac{2n}{n} \times \dfrac{360^\circ \pi r^2}{360^\circ \pi r^2}[/tex]

[tex] = \dfrac{2n}{n} [/tex]

[tex] = 2 [/tex]

The ratio of the areas is 2, so the area of the sector is indeed doubled.

Answer: Yes.

Answer:

the unit rate of pesos to dollars is 1 MXN = 0.04960 USD

Step-by-step explanation:

Quick Conversions from Mexican Peso to United States Dollar : 1 MXN = 0.04960 USD

$ or MEX$ 10 $, US$ 0.50

$ or MEX$ 50 $, US$ 2.48

$ or MEX$ 100 $, US$ 4.96

$ or MEX$ 250 $, US$ 12.40

Answer:

A.

0.5

Step-by-step explanation:

Ignoring minor details, one can think of the circulation of a vector field f along c as the line integral f along c given by. The statement is False. The statement is incomplete and lacks the necessary information to determine its truth value.

It seems to be referring to the circulation of a vector field along a curve, which is commonly represented by a line integral. However, without specifying the complete expression for the line integral or providing further context, it is not possible to definitively determine if the statement is true or false.

The statement provided is incomplete and lacks context, making it difficult to provide a comprehensive explanation. However, it seems to suggest a relationship between the circulation of a vector field and the line integral along a curve. In vector calculus, the circulation of a vector field represents the flow or rotation of the field around a closed curve. This can be computed by evaluating the line integral of the vector field along the curve. However, without specific details or equations, it is challenging to provide a more precise explanation within the given word limit. Additional information or context would be required to clarify the statement further.

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Answer:

a2 + 2al (or) a2 + √a24+h2 a 2 4 + h 2

Step-by-step explanation:

Answer:

SA=L²+2L√(L²/4+H²)

Step-by-step explanation:

Where H is the height and L is the length

Answer:

5^2

Step-by-step explanation:

Answer:

[tex]5^{2}[/tex]

Step-by-step explanation:

when dividing exponents with the same base (the number on the bottom) you subtract the exponents.

9514 1404 393

Answer:

  AB = [[-6, -1][-4, 6][-15, 10]]

Step-by-step explanation:

Any of a number of on-line, spreadsheet, or calculator tools will find the matrix product for you.

The input and output of one such tool is shown below.

__

As you know, each term in the product matrix is the sum of products of a row in the left matrix and a column in the right matrix. The coordinates of that row and column are the coordinates of the result in the product matrix.

For example, row 2, column 1 of the product matrix is the sum of products ...

  (4)(-3) +(-2)(-4) = -12 +8 = -4 . . . . row 2, column 1 of the result

we have shown that if [tex]$a_1, a_2, \ldots, a_n$[/tex] are n distinct real numbers, exactly [tex]$n-1$[/tex] multiplications are used to compute their product, regardless of how parentheses are inserted into the product.

What is the principle of mathematical induction?

The principle of mathematical induction is a powerful proof technique used to establish the validity of an infinite sequence of statements.

To prove that exactly [tex]$n-1$[/tex] multiplications are used to compute the product of n distinct real numbers, regardless of how parentheses are inserted into their product, we will use the principle of mathematical induction.

[tex]\textbf{Base Case:}[/tex]

For [tex]$n=2$[/tex], we have two distinct real numbers [tex]a_1$ and $a_2$.[/tex] The product is simply [tex]a_1 \cdot a_2$,[/tex] which requires only one multiplication. Thus, the base case holds true.

[tex]\textbf{Inductive Step:}[/tex]

Assume the statement holds true for [tex]$n=k$[/tex], where [tex]k \geq 2$.[/tex] That is, when multiplying k distinct real numbers, exactly [tex]$k-1$[/tex] multiplications are used.

Now, consider the case for [tex]$n=k+1$[/tex], where we have [tex]$k+1$[/tex] distinct real numbers [tex]$a_1, a_2, \ldots, a_{k+1}$[/tex]. The product can be computed by multiplying [tex]$a_1$[/tex] with the product of the remaining k numbers, which can be denoted as [tex]$(a_2 \cdot a_3 \cdot \ldots \cdot a_{k+1})$[/tex].

By our induction hypothesis, computing the product of k distinct real numbers requires [tex]$k-1$[/tex] multiplications. Therefore, multiplying[tex]$a_1$[/tex] with the product of the remaining [tex]$k$[/tex] numbers requires an additional multiplication, resulting in a total of k multiplications.

Hence, we have shown that if [tex]a_1, a_2, \ldots, a_n$ are $n$[/tex] distinct real numbers, exactly [tex]$n-1$[/tex] multiplications are used to compute their product, regardless of how parentheses are inserted into the product.

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Answer:

$11.25

Step-by-step explanation:

55.50 divided by 6 = 9.25

9.25 + 2 = 11.25

The author uses the actions of Roger Chillingworth to characterize him. Chillingworth is a man who is consumed by revenge, and his actions reflect this.

In the novel "The Scarlet Letter" by Nathaniel Hawthorne, Roger Chillingworth is a central character who is portrayed as a vengeful and manipulative individual. Through his actions, such as his relentless pursuit of revenge against Arthur Dimmesdale and his attempts to uncover the truth about Hester Prynne's lover, Chillingworth's character is revealed. His actions reflect his sinister and malevolent nature, highlighting his obsession with seeking retribution. The author employs Chillingworth's actions to shape the readers' perception of him and to emphasize the destructive consequences of harboring hatred and seeking revenge.

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To find a function that satisfies the given criteria, we can start by determining the requirements for its derivative, f'(x).

Let's break down the given properties and find the corresponding requirements for f'(x): f(x) is decreasing at x = -6: This means that the slope of the function should be negative at x = -6. Therefore, f'(-6) < 0. f(x) has a local minimum at x = -3: At a local minimum, the slope changes from negative to positive. Thus, f'(-3) = 0. f(x) has a local maximum at x = 3: At a local maximum, the slope changes from positive to negative. Hence, f'(3) = 0.

Now, let's integrate f'(x) to obtain f(x): Integrating f'(x) = -6 < x < -3 will give us a decreasing function on that interval. Integrating f'(x) = -3 < x < 3 will give us an increasing function on that interval. Integrating f'(x) = 3 < x < 6 will give us a decreasing function on that interval. To simplify the process, let's assume that f'(x) is a quadratic function with roots at -6, -3, and 3. We can represent it as: f'(x) = k(x + 6)(x + 3)(x - 3), where k is a constant that affects the steepness of the curve. By setting f'(-3) = 0, we find that k = -1/18.

Therefore, f'(x) = -1/18(x + 6)(x + 3)(x - 3). Integrating f'(x) will give us f(x): f(x) = ∫[-6,x] -1/18(t + 6)(t + 3)(t - 3) dt. Evaluating this integral is a bit complicated. Let's denote F(x) as the antiderivative of f(x): F(x) = ∫[-6,x] -1/18(t + 6)(t + 3)(t - 3) dt. Now, we can find f(x) by differentiating F(x): f(x) = d/dx[F(x)]. To get an explicit equation for f(x), we need to calculate the integral and differentiate the resulting antiderivative. Once you have the equation for f(x), you can plot it on the provided graphing option to verify that it matches the criteria mentioned in the question.

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Answer:

I think the answers would be :

a . 4/3

b. 1/5

c . - 5/4

hope it helps u ^^

Using cylindrical coordinates, the volume of the solid region bounded on the top by the paraboloid z = 12 − x^2 − y^2 and bounded on the bottom by the cone z = x^2 y^2 can be found. The explanation below provides the step-by-step process.

In cylindrical coordinates, we can express the paraboloid and the cone equations as follows:

Paraboloid: z = 12 -[tex]r^2[/tex]

Cone: z = [tex]r^2 cos^2(θ) sin^2(θ)[/tex]

To find the volume of the solid region, we need to determine the limits of integration. The region is bounded by the paraboloid on top and the cone on the bottom. The paraboloid and the cone intersect when 12 - [tex]r^2[/tex] = [tex]r^2 cos^2(θ) sin^2(θ)[/tex]. Simplifying this equation, we get 12 = [tex]r^2[/tex](1 - [tex]cos^2(θ)[/tex] [tex]sin^2(θ[/tex])). Since r is always non-negative, we can rewrite the equation as 12 =[tex]r^2[/tex][tex]sin^2(θ) (1 - sin^2(θ)[/tex]). This equation defines the boundary curve in the polar coordinate plane (r, θ).

To determine the limits of integration for r, we need to find the values of r that satisfy the equation above for each θ. For a fixed value of θ, the equation becomes 12 = [tex]r^2 sin^2(θ) (1 - sin^2(θ))[/tex]. This equation represents a circle with radius [tex]\sqrt(12 sin^2(θ) (1 - sin^2(θ)))[/tex]. Thus, the limits for r are 0 and [tex]\sqrt(12 sin^2(θ) (1 - sin^2(θ)))[/tex].

For the limits of integration for θ, we need to consider the range in which the paraboloid and the cone intersect. The cone is defined in the range 0 ≤ θ ≤ π, and the paraboloid intersects the cone when θ satisfies 12 = [tex]r^2 sin^2(θ) (1 - sin^2(θ))[/tex]. By solving this equation, we find that 0 ≤ θ ≤ π/2.

To calculate the volume, we integrate over the cylindrical coordinates as follows:

V = ∫∫∫ dV

= ∫[0,π/2]∫[0,√[tex](12sin^2(θ)(1-sin^2(θ)))]∫[r^2cos^2(θ)sin^2(θ),12-r^2][/tex] r dz dr dθ

Evaluating this triple integral will yield the volume of the solid region bounded by the given surfaces.

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Answer:

its 16 books

Step-by-step explanation:

iv had this problwm b4

Answer:

i just got it right.

Step-by-step explanation:

Answer:

y = 0.5,  1,  1.5,  2

Step-by-step explanation:

x is twice as much as y, so when you multiply the input for y by 2, it should get the value of x. Example: if y is 1, then x is 2, because 1*2 = 2

hope this helped!

Answer:

a = √39 (exact)

a = 6.24 (dec.)

Step-by-step explanation:

a^2 + b^2 = c^2

a^2 + 5^2 = 8^2

a^2 + 25 = 64

a^2 = 39

a = √39 (exact)

a = 6.24 (dec.)

Answer:

9(x+3)²=27

Step-by-step explanation:

hello :

9(x+3)²=27   means : (x+3)²=27/9

(x+3)²=3  because 3 is not the perfect square