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ivann1987 [24]
3 years ago
13

The time required for a skilled worker to produce x shirts is given by the function T(x) = 4x + 2, where T is measured in hours.

The salary the she is paid is given by the function S(T) = 15T, where S is measured in dollars.
A. If the worker produces 18 units, what will she be paid?

B. How many units would the worker need to produce to be paid $3,030?
Mathematics
1 answer:
solong [7]3 years ago
5 0

Answer:

A. $1,110

B. 50 units.

Step-by-step explanation:

A. Substitute x=18 into the function T(x)=4x+2 for calculate the time in hours required for the worker to produce 18 units:

T(18)=4(18)+2=74

Now you need to substitute T=74 into the function S(T)=15T to calculate the amount in dollars she will be paid for 74 hours:

S(74)=15(74)=1,110

She will be paid $1,110.

B. To calculate the number of units that the worker needs to produce to be paid $3,030 , you need to substitute S(T)=3,030 into the function S(T)=15T and solve for T (to find the number of hours she requires to work to be paid $3,030)

3,030=15T\\\\T=\frac{3,030}{15}\\\\T=202

Now, substitute T(x)=202 into T(x)=4x+2 and solve for x, to calculate the number of units she produces in 202 hours:

202=4x+2\\\\202-2=4x\\\\x=\frac{200}{4}\\\\x=50

She would need to produce 50 units to be paid $3,030

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Bruce drove 360 miles in 6 hours. If he continues at a consistent speed, how many more hours would he need to drive another 300
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Answer:

5 hours

Step-by-step explanation:

If he drove 360 miles in 6 hours, that means he drives 60 miles per hour.

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2 years ago
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Audryn left a $12 tip on a $68.73 restaurant bill. What percent tip did she leave? Round to the nearest tenth of a percent.
Fiesta28 [93]
So, if we take 68.73 to be the 100%, what is 12 in percentage off of it?

\bf \begin{array}{ccll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
68.73&100\\
12&p
\end{array}\implies \cfrac{68.73}{12}=\cfrac{100}{p}\implies p=\cfrac{12\cdot 100}{68.73}

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4 0
3 years ago
To find the standard deviation of the diameter of wooden​ dowels, the manufacturer measures 19 randomly selected dowels and find
loris [4]

Answer:

Option D -  [0.12

Step-by-step explanation:

Given : The manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s=0.16.

To find : The​ 95% confidence interval for the population standard deviation sigma?

Solution :

Number of sample n=19

The degree of freedom is Df=n-1=19-1=18

The standard deviation of the sample is s=0.16

Applying chi-square table to find critical value,

Upper critical value of \chi^2 is UC=\chi(\frac{0.05}{2},18) = 31.5264

Lower critical value of \chi^2 is  

LC=\chi(1-\frac{0.05}{2},18) = 8.2307

Lower limit of the 95% confidence interval for the population variance

L=\frac{(df)\times (s^2)}{UC}

L=\frac{18\times (0.16^2)}{31.5264}

L=\frac{18\times0.0256}{31.5264}

L=\frac{0.4608}{31.5264}

L=0.0146

Upper limit of the 95% confidence interval for the population variance

U=\frac{(df)\times(s^2)}{LC}

U=\frac{18\times (0.16^2)}{8.2307}

U=\frac{18\times0.0256}{8.2307}

U=\frac{0.4608}{8.2307}

U=0.0559

So, The 95% confidence interval for the population variance is [0.0146, 0.0560]

Now, The 95% confidence interval for the population standard deviation is

[\sqrt{0.0146}

[0.1208

or  [0.12

Therefore, Option D is correct.

The 95% confidence interval for the population standard deviation is  [0.12

6 0
3 years ago
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