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Leya [2.2K]
3 years ago
10

Ms.Gartland bought x number of shirts for the new members of her chorus.The cost for x number of shirts,including $3.99 shipping

,was $77.49.Each shirt cost $12.25.There was no sales tax on his purchase.which equation could be used to find x?
Mathematics
2 answers:
lorasvet [3.4K]3 years ago
6 0

1

77.49 - 3.99 = $73.5

73.5 / 12.25 = 6 Shirts

Ann [662]3 years ago
3 0

\\
\text{Ms.Gartland bought x number of shirts for the new members of her chorus.}\\
\text{The cost of x shirts, was 77.49 dollars including a }\3.99 \text{ shipping charges}\\
\\
\text{Given that each shirt cost }\$12.25 \text{, so the cost of x shirts would be}\\
=12.25\times x=12.25x\\
\\
\text{hence the equation that represents this situation is:}\\
\\
\text{Total cost of x shirts at a rate of 12.25 dollars each + Shipping charges}=\$77.49\\
\\
\Rightarrow 12.25x+3.99=77.49

Hence the equation that can be used to find x is:

12.25 x + 3.99= 77.49

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As per the reference document attached thereby along with the question statement, if (∠SOX = 160°), [∠1 = (x + 14)], and [∠2 = (3x – 10)], then the measure of ∠2 in degrees will be 113°

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[∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)],

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Or, [{(x + 3x) + (14 - 10)} = 160°]

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Or, [(3x – 10) = {(3 * 41) - 10}°]

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Or, (∠2 = 113°)

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To learn more about Measures in Degrees, click on the link below.

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\cos^{-1}(x) is going to output an angle measurement in [0,\pi].

So we are looking to solve the following equation in that interval:

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This happens in the second quadrant on the given interval.

The solution to the equation is \frac{3\pi}{4}.

So we are saying that \cos(\frac{3\pi}{4})=\frac{-\sqrt{2}}{2} implies \cos^{-1}(\frac{-\sqrt{2}}{2})=\frac{3\pi}{4} since \frac{3\pi}{4} \in [0,\pi].

Answer is \frac{3\pi}{4}.

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Answer:

t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349      

p_v =P(t_9>10.349)=1.34x10^{-6}  

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

Step-by-step explanation:

1) Data given and notation      

\bar X=51.6 represent the sample mean

s=1.1 represent the standard deviation for the sample      

n=10 sample size      

\mu_o =48 represent the value that we want to test    

\alpha=0.05 represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)      

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the mean score is higher than 48, the system of hypothesis would be:      

Null hypothesis:\mu \geq 48      

Alternative hypothesis:\mu > 48      

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:      

t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)      

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic      

We can replace in formula (1) the info given like this:      

t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349      

Calculate the P-value      

First we find the degrees of freedom:

df=n-1=10-1=9

Since is a one-side upper test the p value would be:      

p_v =P(t_9>10.349)=1.34x10^{-6}  

Conclusion      

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.        

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