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DIA [1.3K]
1 year ago
9

Circle O has diameter FG and chord FH. Calculate the measure of < HFG if GH = 72°

Mathematics
1 answer:
Angelina_Jolie [31]1 year ago
5 0

Given the figure in the attached image.

Circle O has diameter FG and chord FH.

If arc GH is;

GH=72^{\circ}

we want to find the measure of angle HFG.

Recall that from circle geometry theorems;

"The angle at the center of a circle is twice the angle at the circumference of the circle."

So;

\begin{gathered} 2\times m\measuredangle HFG=m\measuredangle GOH \\ m\measuredangle HFG=\frac{1}{2}m\measuredangle GOH \\ m\measuredangle HFG=\frac{1}{2}GH \end{gathered}

substituting the value of GH;

undefined

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Step-by-step explanation:

(40-70) ÷ 70 = -30 ÷ 70 = -0.43 or -43%

Answer: The video game was reduced by 43%.

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Brums [2.3K]

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.        

5 0
3 years ago
Please help! Find the equation of the line (graph provided in attached picture) Use exact numbers. y =_ x+_ ( _ represent blanks
Dennis_Churaev [7]

Answer:

y = \frac{3}{4}x - 2

Step-by-step explanation:

Equation of a line is given as y = mx + b

Where,

m = slope of the line = \frac{y_2 - y_1}{x_2 - x_1}

b = y-intercept, which is the value at the point where the line intercepts the y-axis. At this point, x = 0.

Let's find m and b to derive the equation for the line.

m = \frac{y_2 - y_1}{x_2 - x_1}

Use the coordinate pair of any two points on the line. Let's use the following,

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Plug in the values and solve for m

m = \frac{1 - (-2)}{4 - 0}

m = \frac{1 + 2}{4}

m = \frac{3}{4}

b = -2 (the line intercepts the y-axis at this point)

Our equation would be =>

y = mx + b

y = \frac{3}{4}x + (-2)

y = \frac{3}{4}x - 2

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