Solve the equation for n

y=nx+m

N=?

Answers

Answer 1

Answer: n= (y-m)/x

y minus m over x

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Sky needs $6700 for school and has two options. Option A: 5 years at 5% interest with monthly payments of $126.44 Option B: 6 years at 3.5% interest with monthly payments of $103.30 Calculate the total payback on each loan and calculate how much Sky will save by choosing option B.

Answers

Answer:

148.80

Step-by-step explanation:

Take 126.44 multiply by 60 months equals 7586.40

Take 103.30 multiply by 72 months equals 7437.60

Subtract 7437.60 from 7586.40

Final answer:

The total payback for Option A would be $7,586.4 and for Option B it would be $7,437.60. The difference of $148.8 indicates the savings Sky would have by choosing Option B over Option A.

Explanation:

Firstly, to calculate the total payback for each loan, you multiply the number of payments by the monthly payment amount. For Option A, that's 5 years times 12 payments per year, times a monthly payment of $126.44. Which gives us a total payback of 5 * 12 * 126.44 = $7,586.4. Next, calculate the payback for Option B in the same way: 6 years times 12 payments per year, times a monthly payment of $103.30. Which gives us 6 * 12 * 103.30 = $7,437.60.

Then, we subtract the total payback of Option B from that of Option A to find the savings: $7,586.4 - $7,437.60 = $148.8. So, by choosing option B, Sky would save $148.8.

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Identifying a Proportional Relationship in a TableWhich takle represents a proportional relationship?
x
y
4
*
.
09
y
8
5
2
12
7
18
20
26
12
28
60
84
18
20

Answers

9514 1404 393

Answer:

see below

Step-by-step explanation:

A proportional relationship is one in which the ratio of y to x is a constant for all non-zero values of x and y.

Of the tables shown here, this is the case only for the one shown below. It has ...

y = 1.4x

Answer:

The middle one

Step-by-step explanation:

The middle one

y = (7/5)x

x y

5 7

20 28

60 84

Create and solve
an equation with
2 variables(x).

Answers

Answer:

5x-2=3x+4

x=3

Step-by-step explanation:

Hope I helped!

An author argued that more basketball players have birthdates in the months immediately following July 31, because that was the age cutoff date for nonschool basketball leagues. Here is a sample of frequency counts of months of birthdates of randomly selected professional basketball players starting with January: 390, 392, 360, 318, 344, 330, 322, 496, 486, 486, 381, 331 . Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency? Do the sample values appear to support the author's claim?

Answers

Answer:

There is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.

Step-by-step explanation:

In this case we need to test whether there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

$\chi^(2)=\sum{((O-E)^(2))/(E)}$

The values are computed in the table.

The test statistic value is $\chi^(2)=128.12$ .

The degrees of freedom of the test is:

n - 1 = 12 - 1 = 11

Compute the p-value of the test as follows:

p-value < 0.00001

*Use a Chi-square table.

p-value < 0.00001 < α = 0.05.

So, the null hypothesis will be rejected at any significance level.

Thus, there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.

The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If she is willing to replace only 3% of the motors that fail, how long a guarantee should be offered? Assume that the lifetime of a motor follows a normal distribution.

Answers

Answer:

A guarantee of 6.24 years should be offered.

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:

$Z = (X - \mu)/(\sigma)$

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:

$\mu = 10, \sigma = 2$

If she is willing to replace only 3% of the motors that fail, how long a guarantee should be offered?

The 3rd percentile, that is, the value of X when Z has a pvalue of 0.03. So X when Z = -1.88.

$Z = (X - \mu)/(\sigma)$

$-1.88 = (X - 10)/(2)$

$X - 10 = -1.88*2$

$X = 6.24$

A guarantee of 6.24 years should be offered.

Last year, a baseball team paid $20 per bat and $12 per glove, spending a total of $552. They bought 34 pieces of equipment. What are a system of equations and an augmented matrix that can represent this situation

Answers

Answer:

20b +12g = 552
b + g = 34

$\left[\begin{array}{cc|c}20&12&552\n1&1&34\end{array}\right]$

Step-by-step explanation:

Two equations can be written: one for the total expense, and one for the number of pieces of equipment. The unknowns in this scenario are the numbers of bats and gloves, which we can represent using the variables b and g. Then the system of equations is ...

20b +12g = 552 . . . . . . equation for total expense

b + g = 34 . . . . . . . . . . . equation for pieces of equipment

The augmented matrix is the matrix of the coefficients in these equations:

$\left[\begin{array}{cc|c}20&12&552\n1&1&34\end{array}\right]$

_____

The solution to these equations is ...

(b, g) = (18, 16)

Final answer:

The system of equations representing this situation is 20b + 12g = 552 and b + g = 34. In augmented matrix form, this is [[20,12,552],[1,1,34]].

Explanation:

In this situation, we can represent the number of bats and gloves a baseball team bought as variables, let's say 'b' and 'g' respectively. From the query, we have two pieces of information which provide two equations: