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2 years ago

Robert is planning to spend the day baking c batches of cookies and b batches of

Mathematics

1 answer:

Usimov [2.4K]2 years ago

6 0

Answer:12c + 30b ≤ 360

Step-by-step explanation:

Your math problem requires us to convert the word problem into math before we can solve the math. So let's try to do that first.

First, let's make a math equation to represent the amount of time.

The amount of time to bake "c" batches of cookies = (# of minutes per batch) x (# of batches) = 12 x c = 12c

Similarly for the amount of time to bake "b" batches of brownies = (# of minutes per batch) x (# of batches) = 30 x b = 30b

This is going to look like a format of:

(amount of time to bake cookies) + (amount of time to bake brownies) ≤ (total amount of time)

This person wants the (total amount of time) to be "at most 6 hours" but we can't just put "6" as our number because the other amounts of time are in "minutes".

6 hours * 60 minutes in an hour = 360 minutes

So our first equation becomes:

12c + 30b ≤ 360

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The scheduled arrival time for a daily flight from Boston to New York is 9:30 am. Historical data show that the arrival time fol

Galina-37 [17]

Answer:

Step-by-step explanation:

Let x be a random variable representing the flight arrival time from Boston to New York.

For a uniform probability distribution, the notation is

X U(a, b) where a is the lowest value of x and b is the lowest value of x

The probability density function, f(x) = 1/(b - a)

Mean, µ = (a + b)/2

Standard deviation, σ = √(b - a)²/12

From the information given, the time difference in minutes is 9:57 - 9:07 = 50 minutes. Therefore,

a = 0

b = 50

µ = (0 + 50)/2 = 25

σ = √(50 - 0)²/12 = 14.43

b) converting to minutes, it is 9:30 - 9:07 = 23 minutes

the probability that a flight arrives late(later than 9:30 am) is expressed as P(x > 23)

f(x) = 1/(50) = 0.02

P(x > 23) = (50 - 23)0.02 = 0.54

7 0

3 years ago

Help please for today

miskamm [114]

Answer:

y: (0 , 2.5)

x: (3.5 , 0)

Step-by-step explanation:

Y-intercept : (0 , 2.5)

X-intercept: (3.5 , 0)

When looking at the intersection on the y-axis, the x-coordinate will be 0. And when looking at the intersection on the x-axis, the y-coordinate will be 0.

8 0

3 years ago

A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. (a) What must be true

valentina_108 [34]

Answer:

(a) The distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b) The value of $P(\bar X$ is 0.7642.

Step-by-step explanation:

A random sample of size n = 10 is selected from a population.

Let the population be made up of the random variable X.

The mean and standard deviation of X are:

$\mu=68\\\sigma=15$

(a)

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. n = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

Then, the mean of the distribution of the sample mean is given by,

$\mu_{\bar x}=\mu=68$

And the standard deviation of the distribution of the sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{10}}=4.74$

Thus, the distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b)

Compute the value of $P(\bar X$ as follows:

$P(\bar X$

$=P(Z$

*Use a z-table for the probability.

Thus, the value of $P(\bar X$ is 0.7642.

(c)

Compute the value of $P(\bar X\geq 69.1)$ as follows:

Apply continuity correction as follows:

$P(\bar X\geq 69.1)=P(\bar X> 69.1+0.5)$

$=P(\bar X>69.6)$

$=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{69.6-68}{4.74})$

$=P(Z>0.34)\\=1-P(Z$

Thus, the value of $P(\bar X\geq 69.1)$ is 0.3670.

7 0

3 years ago

Please help me if you can

Luda [366]

A) 100 degrees (congruent angle)
B) 45 degrees (congruent angle)
C) 90 degrees (right angle)
D) 99 degrees (congruent angle)
E) 30 degrees (congruent angle)
F) 30 degrees (180-150=30, that is to find the other angle that is congruent to f)

5 0

2 years ago

Evaluate the following double integral: xy dA D where the region D is the triangular region whose vertices are (0, 0), (0, 3), (

natulia [17]

Answer:

I= 84

Step-by-step explanation:

for

$I=\int\limits^{}_{} \int\limits^{}_D {x*y} \, dA = \int\limits^{}_{} \int\limits^{}_D {x*y} \, dx*dy$

since D is the rectangle such that 0<x<3 , 0<y<3

$I=\int\limits^{}_{} \int\limits^{}_D {x*y} \, dA = \int\limits^{3}_{0} \int\limits^{3}_{0} {x*y} \, dx*dy = \int\limits^{3}_{0} {x} \, dx\int\limits^{3}_{0} {y} \, dy = x^{2} /2*y^{2} /2 = (3^{2} /2 - 0^{2} /2)* (3^{2} /2 - 0^{2} /2) = 3^{4} /4 = 81/4$

4 0

3 years ago