Which graph is the sequence defined by the function f(x) = 3(2)x-1?

The school playground is in the shape of a pentagon. There is a drinking fountain at each of the 5 corners of the playground. Th

PIT_PIT [12445]

The answer is 21 distinct paths.

7 0

2 months ago

The weights of certain machine components are normally distributed with a mean of 8.01 g and a standard deviation of 0.06 g. Fin

PIT_PIT [12445]

Answer:

Option D) 7.90 g and 8.12 g

Step-by-step explanation:

The details provided in the question are:

Mean, μ = 8.01 g

Standard Deviation, σ = 0.06 g

The weights are distributed in a bell-shaped normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We need to determine the value of x for which the probability is 0.03.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 8.01}{0.06})=0.03$

$= 1 -P( z \leq \displaystyle\frac{x - 8.01}{0.06})=0.03$

$=P( z \leq \displaystyle\frac{x - 8.01}{0.06})=0.97$

Using the standard normal z table, we find that,

$\displaystyle\frac{x - 8.01}{0.06} = 1.881\\\\x = 8.12$

Thus, the value of 8.17 g separates the upper 3% of the weights.

P(X < x)

$P( X < x) = P( z < \displaystyle\frac{x - 8.01}{0.06})=0.03$

From the standard normal z table, we derive,

$\displaystyle\frac{x - 8.01}{0.06} = -1.881\\\\x = 7.90$

Consequently, 7.90 separates the lower 3% of the weights.

Option D) 7.90 g and 8.12 g

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7 0

2 months ago

Mr. Brown owned a house, which he rented for $60 a month. The house was assessed at $9000. In 1975 the rate of taxation was incr

AnnZ [12381]

First, we determine the percentage increase for the tax.

Initial amount = 25×9 = 225 ⇒ The 9 signifies 9 lots of thousands representing the house's value.
New amount = 28×9 = 252

Tax increase = 252 - 225 = 27
Percentage increase = (27÷225) ×100 = 12%

Therefore, the yearly rent should rise by 12%

Monthly rent is $60
Yearly rent = 60×12 = $720
With a 12% increase = 720×1.12 = 806.4 ⇒ Here, 1.12 is the multiplier derived from 100%+12%=112%=1.12

Monthly rent becomes 806.4÷12 = $67.20, resulting in an additional $7.20 each month.

5 0

2 months ago

Mike earned x dollars the first week of his new job. He earned 5% more the second week than the first week. Which expression rep

zzz [12365]

The expression indicates that the total earnings of Mike over the two weeks amount to 2.05x dollars

Solution:

It is given that Mike earned x dollars during the first week at his new job,

While in the second week, he earned 5% more than the earnings of the first week.

To determine: Total earnings over the two weeks

From the information provided,

Earnings in the first week = "x" dollars

Earnings in the second week = 5% more than first week earnings

Thus,

Earnings in the second week = x + 5% of x

$\rightarrow x + 5 \% \times x\\\\\rightarrow x + \frac{5}{100} \times x\\\\\rightarrow x + 0.05x = 1.05x$

Therefore, earnings in the second week equal to 1.05x dollars

The total earnings over the two weeks:

Total earnings = Earnings from first week + Earnings from second week

$Total\ Amount = x + 1.05x = 2.05x$

Thus, the expression for the total earnings of Mike for both weeks is 2.05x dollars

5 0

3 months ago

"Which pairs of angles in the figure below are vertical angles? Check all that apply.

lawyer [12517]

Angles known as vertical angles are those that are located across from each other at a common vertex where two lines intersect.

In the illustration, there exists only one pair of vertical angles.

These are Angle TSW and Angle ISN, both converging at the vertex labeled S.

<span>Answer is: B. Angle ISN and Angle TSW.</span>

5 0

3 months ago

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