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3 years ago

10

A baker uses 1.5 tsp of vanilla extract in each cake. how much vanilla extract in liters should the baker order to make 800 cake

s? (1 tsp = 5 ml)

1 answer:

aleksandrvk [35]3 years ago

8 0

1.5 tsp x 800 cakes = 1200 tsp.

1 tsp = 5 ml

1200 x 5 = 6000 ml

1 ml = 0.001 liter

6000 x 0.001 = 6 liters

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An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you th

anastassius [24]

Answer:

0.288

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 17.48, \sigma = 3.25, n = 10, s = \frac{3.25}{\sqrt{10}} = 1.027740$

Find the probability that the mean printing speed of the sample is greater than 18.06 ppm.

This is 1 subtracted by the pvalue of Z when X = 18.06. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{18.06 - 17.48}{1.027740}$

$Z = 0.56$

$Z = 0.56$ has a pvalue of 0.712

1 - 0.712 = 0.288

The answer is 0.288

7 0

3 years ago

saw5 [17]

Answer:

$4,500

Step-by-step explanation:

For simple interest,

I = prt,

where

I = interest

p = principal

r = annual interest rate

t = number of years

We have p = $5,000, r = 9% = 0.09; t = 1 year

I = $5,000 × 0.09 × 1

I = $450

5 0

3 years ago

Read 2 more answers

Please help me with this question. Algebra 2 is hard!!

trapecia [35]

Answer:

domain: {x ∈ ℝ : x ≤ 5}
range: {y ∈ ℝ : y ≤ -1}

Step-by-step explanation:

<u>Domain</u>

The domain of a function is the set of x values for which the function is defined. Here, the domain is limited by the values of x that make the square root defined. That is, the expression under the radical cannot be negative:

-3x +15 ≥ 0

15 ≥ 3x . . . . . . add 3x

5 ≥ x . . . . . . . . divide by 3

x ≤ 5 . . . . . . . . put x on the left (swap sides)

The rest of the notation in the domain expression simply says x is a real number.

domain: {x ∈ ℝ : x ≤ 5} . . . . . . matches the first choice

__

<u>Range</u>

The range of a function is the set of values that f(x) can have. We know the square root can be zero or any positive number. When it is zero, f(x) = -1.

When it is a positive number, that value is multiplied by -4 and added to -1, so f(x) is a number more negative than -1. Then the range of the function is all numbers -1 and below:

range: {y ∈ ℝ : y ≤ -1} . . . . . . matches the last choice

_____

<em>Comment on domain/range problems</em>

When working domain and range problems, it works well to have a good understanding of the domain and range limitations of the functions we usually work with: polynomials, square root, logarithm, trig functions, exponential functions. Domain and range problems generally involve combinations of these or ratios of combinations of these.

3 0

3 years ago

Hugh says that “one less than four times a number” can be written as two expressions: 1 - 4n and 4n - 1. Why is Hugh incorrect?

Basile [38]

Answer:

N times 4-1

Step-by-step explanation:

4 times number is not a squared number where you multiply- the number

by it's self and then you subtract 1

8 0

3 years ago

raketka [301]

Answer:

y -10 = -1/9 (x-9)

Step-by-step explanation:

Point slope form is

y-y1 = m (x-x1)

y -10 = -1/9 (x-9)

4 0

3 years ago