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2 years ago

CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already

Mathematics

1 answer:

Ratling [72]2 years ago

6 0

Answer:

15.7 in

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

$\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}$

It checks.

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A label that wraps around a box of golf balls covers 75% of its lateral surface area. What is the value of x? The height is 2 th

GalinKa [24]

To find the area of the rectangular prism, use the formula:

A = width x height x length

A = 2 x 2 x 3

A = 12

Now multiply A with 0.75

12 x 0.75 = 9

x = 9 in³

hope this helps

5 0

2 years ago

Read 2 more answers

Using a 16-sided number cube, what is the probability that you will roll a multiple of 4 or an odd prime number? The number 1 is

iogann1982 [59]

<h3>Answer: 0.563 (choice C)</h3>

================================================

Explanation:

E = event space

E = set of outcomes we want to happen

E = rolling a multiple of 4 or rolling an odd prime number

E = {4,8,12,16 3,5,7,11,13}

n(E) = number of items in set E

n(E) = 9, (four multiples of 16+five ways to roll odd prime number)

-----

S = sample space

S = set of all possible outcomes (whether we want them to happen or not)

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}

n(S) = number of items in set S

n(S) = 16

-----

P(E) = probability of event space occurring

P(E) = probability of rolling a multiple of 4 or rolling an odd prime number

P(E) = n(E)/n(S)

P(E) = 9/16

P(E) = 0.5625

P(E) = 0.563

3 0

2 years ago

Let X represent the amount of time until the next student will arrive in the library parking lot at the university. If we know t

Ber [7]

Answer:

The probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.

Step-by-step explanation:

The random variable <em>X</em> is defined as the amount of time until the next student will arrive in the library parking lot at the university.

The random variable <em>X</em> follows an Exponential distribution with mean, <em>μ</em> = 4 minutes.

The probability density function of <em>X</em> is:

$f_{X}(x)=\lambda e^{\lambda x};\ x\geq 0, \lambda >0$

The parameter of the exponential distribution is:

$\lambda=\frac{1}{\mu}=\frac{1}{4}=0.25$

Compute the value of P (X > 10) as follows:

$P(X>10)=\int\limits^{\infty}_{10}{0.25e^{-0.25x}}\, dx$

$=0.25\times \int\limits^{\infty}_{10}{e^{-0.25x}}\, dx\\=0.25\times |\frac{e^{0.25x}}{-0.25}|^{\infty}_{10}\\=(e^{-0.25\times \infty})-(e^{-0.25\times 10})\\=0.0821$

Thus, the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.

3 0

2 years ago

A machine needs 2 of its gears replaced. You find 2 gears, one manufactured 5 years ago and the other manufactured 10 years ago.

Tcecarenko [31]

Probability that gear 1 will fail = 5/100 (upto 10 years)
and 8/100 (after 10 years)

Probability that both will fail = 5/100 * 8/100
= 40/10000
= 0.4 %

8 0

2 years ago

Find the truth set of each predicate. (If your answer is an interval, enter it using interval notation; otherwise enter it as a

makvit [3.9K]

(a) Predicate: 10d is an integer

The domain is $\mathbb{Z}$ . In fact, integers are closed under multiplication, and 10 is an integer. So, if d is an integer, 10d is a multiplication between integers, and thus an integer.

(c) $1\leq x^2\leq 4$

Since 1 and 4 are both squares, we have

$1\leq x^2 \leq 4 \iff 1^2\leq x^2 \leq 2^2$

And we deduce that x must be between 1 and 2. But since negative numbers become positive when squared, the numbers between -2 and -1 are also fine. So, the domain is

$[-2,-1]\cup [1,2]$

Predicates (b) and (d) are identical to (a) and (c)

6 0

2 years ago