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harkovskaia [24]
3 years ago
9

The model below represents an equation. Write the equation that is modeled then find what value of x makes the equation true.

Mathematics
1 answer:
LenaWriter [7]3 years ago
4 0
6x-5=4x+5
x=5
I hope this helps you
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Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately norm
iragen [17]

Answer:

a. 0.691

b. 0.382

c. 0.933

d. $88.490

e. $58.168

f. 5th percentile: $42.103

95th percentile: $107.897

Step-by-step explanation:

We have, for the purchase amounts by customers, a normal distribution with mean $75 and standard deviation of $20.

a. This can be calculated using the z-score:

z=\dfrac{X-\mu}{\sigma}=\dfrac{85-75}{20}=\dfrac{10}{20}=0.5\\\\\\P(X

The probability that a randomly selected customer spends less than $85 at this store is 0.691.

b. We have to calculate the z-scores for both values:

z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{65-75}{20}=\dfrac{-10}{20}=-0.5\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{85-75}{20}=\dfrac{10}{20}=0.5\\\\\\\\P(65

The probability that a randomly selected customer spends between $65 and $85 at this store is 0.382.

c. We recalculate the z-score for X=45.

z=\dfrac{X-\mu}{\sigma}=\dfrac{45-75}{20}=\dfrac{-30}{20}=-1.5\\\\\\P(X>45)=P(z>-1.5)=0.933

The probability that a randomly selected customer spends more than $45 at this store is 0.933.

d. In this case, first we have to calculate the z-score that satisfies P(z<z*)=0.75, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

P(z

Then, we can calculate X as:

X^*=\mu+z^*\cdot\sigma=75+0.67449\cdot 20=75+13.4898=88.490

75% of the customers will not spend more than $88.49.

e. In this case, first we have to calculate the z-score that satisfies P(z>z*)=0.8, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

P(z>-0.84162)=0.80

Then, we can calculate X as:

X^*=\mu+z^*\cdot\sigma=75+(-0.84162)\cdot 20=75-16.8324=58.168

80% of the customers will spend more than $58.17.

f. We have to calculate the two points that are equidistant from the mean such that 90% of all customer purchases are between these values.

In terms of the z-score, we can express this as:

P(|z|

The value for z* is ±1.64485.

We can now calculate the values for X as:

X_1=\mu+z_1\cdot\sigma=75+(-1.64485)\cdot 20=75-32.897=42.103\\\\\\X_2=\mu+z_2\cdot\sigma=75+1.64485\cdot 20=75+32.897=107.897

5th percentile: $42.103

95th percentile: $107.897

5 0
3 years ago
1. Simplify the expression<br> 11x + 3x
Natali [406]

Answer:

14x

Step-by-step explanation:

Step 1: Collect like terms by adding their coefficients

(11+3)x

Step 2: Add the numbers

14x

4 0
3 years ago
Read 2 more answers
The amount c in grams of a 100 gram sample of carbon-14 remaining after t years is represented by the equation c= 100 (0.99988)t
tigry1 [53]

Answer: The amount of carbon-14 remaining after 4 years is 99.95 grams.

Step-by-step explanation:

Hi, to answer this question we simply have to substitute t=4 in the equation given and solve for c.

c= 100 (0.99988)^t

c =100 (0.99988)^4

c = 100 x 0.999520086

c= 99.95200864 ≅99.95 grams (rounded)

The amount of carbon-14 remaining after 4 years is 99.95 grams.

Feel free to ask for more if needed or if you did not understand something.

8 0
3 years ago
A child takes a nap averaging three hours and get an average of 12 hours of sleep at night . Nap time and night time sleep can e
algol13
That should be all of them. Hope it helps
8 0
3 years ago
What is 2867 divided by 61 using box method
anyanavicka [17]

Answer:

47

Step-by-step explanation:

this is due to when 286 is divided by 61 it gets 40 and the remainder gets you 7 as a result it is 47

4 0
3 years ago
Read 2 more answers
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