The graphs below have the same shape. What is the equation of the graph of g(x)? A. g(x) = x^2 + 4
B. g(x) = x^2- 4
C. g(x) = (x - 4)^2
D. g(x) = (x + 4)^2

Answer:

a) 0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.

b) 0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.

c) 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 7.7 grams per mililiter.

This means that [tex]\mu = 65, \sigma = 7.7[/tex]

a. What is the probability that the amount of collagen is greater than 60 grams per.

This is 1 subtracted by the pvalue of Z when X = 60. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{60 - 65}{7.7}[/tex]

[tex]Z = -0.65[/tex]

[tex]Z = -0.65[/tex] has a pvalue of 0.2578

0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.

b. What is the probability that the amount of collagen is less than 90 grams per.

This is the pvalue of Z when X = 90.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{90 - 65}{7.7}[/tex]

[tex]Z = 3.25[/tex]

[tex]Z = 3.25[/tex] has a pvalue of 0.9994

0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.

c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?

Between Z = 1 and Z = -1, so the proportion is the pvalue of Z = 1 subtracted by the pvalue of Z = -1

Z = 1 has a pvalue of 0.8413

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826*100% = 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean

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Answer: 2

Explanation:

Remember Rise/Run

1/2

So if they went "Run" 4 units

then the equivalent to 1/2 is 2/4

Therefore the value of a is 2!

I hope this helped!

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- Zack Slocum

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Answer:

Step-by-step expVivian’s house area can be split into two rectangles: FLSU and MNSR.

area of rectangle FLSU

= length × width

= (FU) × (FL)

= 30 × 25

= 750 square feet

area of rectangle MNSR

= length × width

= (MS) × (MN)

= 38 × 25

= 950 square feet

area of Vivian’s house

= area of rectangle FLSU+ area of rectangle MNSR

= 750 square feet + 950 square feet

= 1,700 square feet

Answer: 13/30

Step-by-step explanation:

8/15 -1/10 = (2×8)/(2×15) - (3×1)/(3×10) = 16/30 - 3/30 = (16-3)/30 = 13/30

Answer:

13/30

Step-by-step explanation:

8/15 - 1/10 (first find a common denominator which can be 30 for example)

Multiply numerator and demomiator

16/30 (x2) - 3/30 (x3) =13/30.

Answer:

Answer: It´s correlated. Step-by-step explanation: The graph shows that the height of the tree increases as time passes, meaning that the more time that a three has been planted the more height it has, so there´s a direct correlation between the time passing and the height of the tree.

Answer:

radius = 51.70 cm

Step-by-step explanation:

Volume = (2/3) π r³

Volume = 92160 π

Radius = ?

Using the above formula

V = (2/3) π r³

r³ = v/((2/3) π)

r³ = ((92160 π) x 3) / (2 x π)

r³ = 276480/2 because (π/π) = 1

r³ = 138240

Taking cube root on both sides

r = 51.70 cm

Answer:

Step-by-step explanation:

Answer:

Out of the four employees, Alice is the one who has completed the least work time, since she only completed 12.5% of it.

Step-by-step explanation:

Since Phil has completed 1/4 of his shift; Darren has completed 3/7 of his shift; Alice has finished 1/8 of her shift of her; and Lisa has 1/5 of her shift remaining, to determine, out of the four employees, who has completed the least work time, the following calculation must be performed:

Phil: 4 - 1/4 = 3/4 = 0.75

Darren: 7 - 3/7 = 4/7 = 0.57

Alice: 8 - 1/8 = 7/8 = 0.875

Smooth: 5 - 1/5 = 4/5 = 0.8

Thus, of the four employees, Alice is the one who has completed the least work time, since she only completed 12.5% of it.

Answer:

[tex]\huge\boxed{13}[/tex]

Step-by-step explanation:

= 2k - x

Given that k = 9, x = 5

= 2(9) - 5

= 18 - 5

= 13

[tex]\rule[225]{225}{2}[/tex]

Hope his helped!

Answer:

i think c

i'm not sure tho

Step-by-step explanation:

Answer:

4 x 5 x 3 = 60

Step-by-step explanation:

4 x 5 = 20 ,   20 x 3 = 60

Answer:

y = 5x

y = amount of money all the friends spent.

x = cost of burgers, a bottle of apple juice, and a bag of chips all together

Step-by-step explanation:

Ion know which all apply but okay?

Answer:

D. x = 10, m<TRS = 60°

Step-by-step explanation:

m<QRS = 122° (given)

m<QRT = (7x - 8)° (given)

m<TRS = (6x)° (given)

m<QRT + m<TRS = m<QRS (angle addition postulate)

(7x - 8)° + (6x)° = 122° (substitution)

Solve for x

7x - 8 + 6x = 122

Add like terms

13x - 8 = 122

13x = 122 + 8

13x = 130

x = 130/13

x = 10

✔️m<TRS = (6x)°

Plug in the value of x

m<TRS = (6*10)° = 60°

Answer:

the answer is 134 hope this helps.

Answer:

18.33

Step-by-step explanation:

Answer:

96 dozen (or/aka) 1152 cupcakes

Step-by-step explanation:

I hope this is right, if not I'm very sorry just bad at math.

Answer:

x² - x - 2 = 0

Step-by-step explanation:

Given:

- 4(x - x²) = 8

Find:

Standards form

Computation:

- 4(x - x²) = 8

(x - x²) = -2

x - x² = -2

x² - x - 2 = 0

9514 1404 393

Answer:

  158,000

Step-by-step explanation:

Using the given square feet for x in the equation, we have ...

  y = 0.071×1483 +52.48 = 157.773

We presume this is supposed to represent the estimated value of the house in thousands.

The fair price is estimated to be 158,000.

hmm, how many cubes are there?

length times width times height

we have 6 cubes long, 6 wide and 6 tall

6*6*6=216 cubes

each is 1 cubic feet

216 times 1=216

216 cubic feet

A is answer

Answer:

[tex]\boxed{C. 32}[/tex]

Step-by-step explanation:

Hello There!

If you didn't know the exterior angle of a triangle is equal to the opposite interior angles

so

100 = 68 + x

subtract 68

100-68=32

68-68 cancels out

we're left with

x = 32

Answer:

this one

16(0.5x-0.75+2)

Step-by-step explanation:

Answer:

Third Option is the only equivalent equation :)

Step-by-step explanation:

First Option: NO

16(0.5x - 4y + 32)

distribute

8x - 64y + 512

Second Option: NO

16(0.5x - 0.75 + 32)

distribute

8x - 12y + 512

16(0.5x - 0.75 + 2)

distribute

8x - 12y + 32

Fourth Option:

16(0.5x + 4y + 2)

distribute

8x + 64y + 32

hope this helps :)

Answer:

20=0+5x

x=20/5

x=4

x=4

x=4

Answer:

exact form:

x=0, 1/2

decimal form:

x=0, 0.5

Answer:

(47.3, 54.1)

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{10.4}{\sqrt{35}} = 3.4[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 50.7 - 3.4 = 47.3

The upper end of the interval is the sample mean added to M. So it is 50.7 + 3.4 = 54.1

The answer is (47.3, 54.1).

Answer:

first, dilate triangle ABC with respect to the origin by scale factor of 2.

then rotate it 90 degrees counterclockwise about the origin

Step-by-step explanation:

Answer:

sorry but i need the points

Step-by-step explanation:

Answer:

1≤x≤9

0,1,0,1,2,3,4,5,6,7,8,9

x is a prime number 2,3,5,7