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melamori03 [73]
3 years ago
7

How many teaspoons are in a quart

Mathematics
1 answer:
dmitriy555 [2]3 years ago
3 0
There are 192 teaspoons in 1 quart
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Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a norm
Artemon [7]

Answer:

a) 0.5.

b) 0.8413

c) 0.8413

d) 0.6826

e) 0.9332

f) 1

Step-by-step explanation:

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.

In this problem, we have that:

\mu = 6, \sigma = 0.2

(a) P(x > 6) =

This is 1 subtracted by the pvalue of Z when X = 6. So

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

Z = \frac{6-6}{0.2}

Z = 0

Z = 0 has a pvalue of 0.5.

1 - 0.5 = 0.5.

(b) P(x < 6.2)=

This is the pvalue of Z when X = 6.2. So

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

Z = \frac{6.2-6}{0.2}

Z = 1

Z = 1 has a pvalue of 0.8413

(c) P(x ≤ 6.2) =

In the normal distribution, the probability of an exact value, for example, P(X = 6.2), is always zero, which means that P(x ≤ 6.2) = P(x < 6.2) = 0.8413.

(d) P(5.8 < x < 6.2) =

This is the pvalue of Z when X = 6.2 subtracted by the pvalue of Z when X  5.8.

X = 6.2

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

Z = \frac{6.2-6}{0.2}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 5.8

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

Z = \frac{5.8-6}{0.2}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

(e) P(x > 5.7) =

This is 1 subtracted by the pvalue of Z when X = 5.7.

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

Z = \frac{5.8-6}{0.2}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

1 - 0.0668 = 0.9332

(f) P(x > 5) =

This is 1 subtracted by the pvalue of Z when X = 5.

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

Z = \frac{5-6}{0.2}

Z = -5

Z = -5 has a pvalue of 0.

1 - 0 = 1

5 0
3 years ago
What is thesum of the two polynomials ? (-x^2+9)+(-3x^2-11x+4)
True [87]
-x^2 + 9 - 3x^2 - 11x + 4
-4x^2 - 11x + 13
3 0
3 years ago
Solve the equation <br> |x-3| -10=-5
Deffense [45]

Answer:

x=8                     x=-2

Step-by-step explanation:

|x-3| -10=-5

Add 10 to each side

|x-3| -10+10=-5+10

|x-3| =5

Now separate into two equations , one positive and one negative

x-3 = 5           x-3 = -5

Add 3 to each side

x-3+3 = 5+3    x-3+3 = -5 +3

x=8                     x=-2

5 0
3 years ago
Read 2 more answers
What is the inverse function for h(x) = <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B7%7D%20-1" id="TexFormula1" title="\sqrt
Blizzard [7]

Step-by-step explanation:

y =  \sqrt{x + 7}  - 1

Replace x and y.

x =  \sqrt{y + 7}  - 1

Solve for y.

x + 1 =  \sqrt{y + 7}

Square both sides.

(x + 1) {}^{2}  = y + 7

(x + 1) {}^{2}  - 7 = y

This is the inverse function or you can also say

{x}^{2}  + 2x - 6 = y

5 0
2 years ago
Factor f(x) into linear factors given that k is a zero of f(x).
Studentka2010 [4]

Step-by-step explanation:

step 1. if k is a zero then (x - 1) is a factor of 4x^3 + 23x^2 - 34x + 7.

step 2. we "can" use long division but synthetic division is easier!

step 3. 1 4 23 -34 7

4. 4. 27. -7.

4 27. -7. 0 (must get 0)

step 4. so the factors are (x - 1)(4x^2 + 27x - 7).

step 5. please note if you multiply these factors together you will get the original polynomial!

3 0
2 years ago
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