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3 years ago

how do the graphs of f(x) = sin x and g(x) = sin2x+3 compare. Must make two selections of the following that apply.

Mathematics

2 answers:

ivolga24 [154]3 years ago

4 0

Answer:

C. and E.

Step-by-step explanation:

Elena L [17]3 years ago

3 0

Answer:

The correct options are:

g(x) is shifted three units higher than f(x).

g(x) has a period that is half the period of f(x).

Step-by-step explanation:

We have to compare the graphs of the function:

$f(x)=\sin x$

and $g(x)=\sin 2x+3$

We have to select the correct options among the following:

As we know that the period of sine function is 2π.

i.e. Period of function f(x) is: 2π.

The period of sin(2 x) is π.

Hence, the period of the function g(x) function is π.

Hence, the period of g(x) is half the period of f(x).

Also we could observe that g(x) is shifted 3 units upward.

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Colin borrowed some money at 7.16%/a compounded quarterly. Three years later, he paid $5000 toward the principal and the interes

attashe74 [19]

Based on the calculations below, the amount originally borrowed by Colin is $10,006.67.

<h3>How do we calculate the original amount using PV formula?</h3>

To solve this question, the following present value (PV) formula will be used:

PVn = Pn / (1 + r)^n ........................... (1)

Where:

PVn = Present value of an amount paid in year n

P = Amount paid in year n

r = quarterly interest rate = 7.16% / Number of quarters in a year = 0.0716 / 4 = 0.0179

n = number of quarters = Number of years * Number of quarters in a year = Number of years * 4

Using equation (1), we can therefore proceed as follows:

PV3 = PV of $5,000 paid after three years = $5,000 / (1 + 0.0179)^(3 * 4) = $4,041.18

PV5 = PV of $5,000 paid after another 2 years (after 3 years + 2 years = 5) = $5,000 / (1 + 0.0179)^(5 * 4) = $3,506.45

PV10 = PV of $5,000 paid after another 5 years (after 3 years + 2 years + 5 years = 10) = $5,000 / (1 + 0.0179)^(10 * 4) = $2,459.04

Therefore, we have:

Original amount borrowed = PV3 + PV5 + PV10 = $4,041.18 + $3,506.45 + $2,459.04 = $10,006.67

Learn more about borrowing here: brainly.com/question/4239348.

#SPJ1

6 0

2 years ago

Find two ratios equivalent to the ratio in exercise 1<br><br> 8:5<br> 4:19<br> 6:23

Ne4ueva [31]

To find equivalent ratios just factor the same number to both numerator and denominator. I will make the ratios simple by multiplying 2/2 and 3/3 to the originals. To check, set as fraction and cross multiply and you should have the same number. I will show you how to check by doing it to the first ratio.

8:5 16:10 24:15

Check:
8/5 = 16/10
(8)(10)=(5)(16)
80=80

8/5=24/15
(8)(15)=(5)(24)
120=120

4:19 8:38 12:57

6:23 12:46 18:69

5 0

3 years ago

The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approxi

bazaltina [42]

Answer:

$425.6 should be budgeted for weekly repairs and maintenance.

Step-by-step explanation:

Normal Probability Distribution:

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

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean $400 and standard deviation $20.

This means that $\mu = 400, \sigma = 20$

How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?

This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

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

$1.28 = \frac{X - 400}{20}$