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anzhelika [568]
3 years ago
9

13. A shop owner spent $540 to purchase a stock of

Mathematics
1 answer:
Daniel [21]3 years ago
3 0

Answer:

Step--by--step explanation:

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Can you help? Having a hard time figuring this out. Thanks
Dmitrij [34]

Answer:

3a) The value of  x = 56

3b) The measure of ∠ H T M = 90°

3c) The radius of the circle = 53

Step-by-step explanation:

3a) ∵ A F is a tangent to the circle O at point F

∵ Secant AH intersects circle O at point T

∴ (A F)² = (A T)(A H)

∴ 7( x + 7) = (21)² ⇒ ÷ 7

∴ x + 7 = 63

∴ x = 63 - 7 = 56

3b) ∵ HM is a diameter

∴ The measure of the arc HM = 180° ⇒ semi-circle

∵ ∠ H T M is inscribed angle subtended by the arc HM

∴ m ∠ H T M = half the measure of arc HM

∴ m ∠ H T M = 180° ÷ 2 = 90°

3c) ∵ Δ H T M is a right angle triangle at T

∴ (H M)² = (M T)² + (H T)² ⇒ Pythagorean theorem

∴ (H M)² = (90)² + (56)²

∴ (H M)² = 11236

∴ HM = \sqrt{11236} = 106

∴ OM = 106 ÷ 2 = 53

∵ OM is the radius of the circle O

∴ The radius  = 53

4 0
3 years ago
You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment option
kozerog [31]
Ngzktzkg mf kg247;77. Kyzjfsktxhgtvt
7 0
3 years ago
Help I need to pass test
rewona [7]

Answer: I know that the answer is 47.

Step-by-step explanation: add up all the angles to get 180 degrees.

8 0
3 years ago
Read 2 more answers
The sum of a number and twelve is twenty-one. What is the number? 21 n 12 8 9 10 33
Sonbull [250]

Answer:

9

Step-by-step explanation:

Subtract 1 2 12 12 from both sides of the equation + 1 2 = 2 1 + 1 2 − 1 2 = 2 1 − 1 2 2 Simplify Solution = 9

4 0
2 years ago
Read 2 more answers
Assume that a simple random sample has been selected from a normally distributed population. State the hypotheses, find the test
BaLLatris [955]

Solution

Hypotheses:

- The population mean is 132. In order to test the claim that the mean is 132, we should check for if the mean is not 132.

- Thus, the Hypotheses are:

\begin{gathered} H_0:\mu=132 \\ H_1:\mu\ne132 \end{gathered}

Test statistic:

- The test statistic has to be a t-statistic because the sample size (n) is less than 30.

- The formula for finding the t-statistic is:

\begin{gathered} t=\frac{\bar{X}-\mu}{\frac{s}{\sqrt{n}}} \\  \\ where, \\ \bar{X}=\text{ Sample mean} \\ \mu=\text{ Population mean} \\ s=\text{ Standard deviation} \\ n=\text{ Sample size} \end{gathered}

- Applying the formula, we have:

\begin{gathered} t=\frac{137-132}{\frac{14.2}{\sqrt{20}}} \\  \\ t=\frac{5}{3.1752} \\  \\ t\approx1.5747 \end{gathered}

Critical value:

- The critical value t-critical, is gotten by reading off the t-distribution table.

- For this, we need the degrees of freedom (df) which is gotten by the formula:

\begin{gathered} df=n-1 \\ df=20-1=19 \end{gathered}

- And then we also use the significance level of 0.1 and the fact that it is a two-tailed test to trace out the t-critical. (Note: significance level of 0.1 implies 10% significance level)

- This is done below:

- The critical value is 1.729

P-value:

- To find the p-value, we simply check the table for where the t-statistic falls.

- The t-statistic given is 1.5747. We simply check which values this falls between in the t-distribution table. It falls between 1.328 and 1.729. We can simply choose a value between 0.1 and 0.05 and multiply the result by 2 since it is a two-tailed test.

- However, we can also use a t-distribution calculator, we have:

- Thus, the p-value is 0.13183

Final Conclusion:

- The p-value is 0.13183, and comparing this to the significance level of 0.1, we can see that 0.13183 is outside the rejection region.

- Thus, the result is not significant and we fail to reject the null hypothesis

7 0
1 year ago
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