To test upper h 0 : mu equals 72 versus upper h 1 : mu less than 72​, a simple random sample of size nequals20 is obtained from a population that is known to be normally​ distributed, and the sample standard deviation is found to be 6. complete parts ​(a) and ​(b) below.

ANSWER

[tex]{ \sec}(e) = \pm \: \sqrt{\frac{11}{8} } [/tex]

EXPLANATION

We use the Pythagorean Identity,

[tex] { \sec}^{2} (e) = 1 + { \tan}^{2} (e)[/tex]

It was given that,

[tex] { \tan}^{2} (e) = \frac{3}{8} [/tex]

We substitute the values into the identity to obtain,

[tex] { \sec}^{2} (e) = 1 + \frac{3}{8} [/tex]

[tex]{ \sec}^{2} (e) = \frac{11}{8} [/tex]

We take square root of both sides to get,

[tex]{ \sec}(e) = \pm \: \sqrt{\frac{11}{8} } [/tex]

Answer:

sec e = √(11/8) ⇒ answer B

Step-by-step explanation:

* Lets revise some identities in trigonometry

# sin²x + cos²x = 1

- Divide both sides by cos²x

∴ sin²x/cos²x + cos²x/cos²x = 1/cos²x

∵ sinx/cosx = tanx

∴ sin²x/cos²x = tan²x

∵ cos²x/cos²x = 1

∵ 1/cosx = secx

∴ 1/cos²x = sec²x

* Now lets write the new identity

# tan²x + 1 = sec²x

- Let x = e

∴ tan²e + 1 = sec²e

- Substitute the value of tan²e in the identity

∵ tan²e = 3/8

∴ 3/8 + 1 = sec²e

- Change the 1 to the fraction 8/8

∴ 3/8 + 8/8 = sec²e ⇒ add the fractions

∴ 11/8 = sec²e

- Take square root for the two sides to find sec e

∴ sec e = √(11/8)

∴ The answer is B

The area of the shaded region is 42.14 square inches.

How the area of the shaded region is determined:

We are given a square with side lengths of 14 inches, and each corner of the square has a quarter circle with a radius of 7 inches. We need to find the area of the shaded region, which is the area of the square minus the area of the quarter circles.

To calculate the area of the figure, we need to consider both the square and the quarter circles.

1. Calculate the area of the square:

The square has a side length of 14 inches.

Area of the square = [tex]side^2[/tex] = [tex]14^2[/tex] = 196 square inches

2. Calculate the area of the quarter circles:

The quarter circle has a radius of 7 inches.

The area of a full circle is given by:

Area of the circle = [tex]\pi r^2[/tex]

Area of the quarter circle = 4/4 x [tex]\pi r^2[/tex]

= 1 x 3.14 x [tex]7^2[/tex]

= 153.86 square inches

Therefore, the area of the shaded region = Area of the square - Area of the quarter circles:

= 196 - 153.86

= 42.14 square inches

Complete Question:

The square in the figure has a side length of 14 inches. The radius of the each quarter circle is 7 inches. What is the area of the shaded region?

Answer:

[tex]A=50(0.6)^x[/tex]

18 mg of medicine will be left in the patient's system after two hours.

Step-by-step explanation:

Given,

The initial quantity of the medicine, P = 50 mg,

Also, it decreases every hour at a constant rate of 40%

That is, r = 40 %,

Thus, the quantity of the medicine after x hours,

[tex]A=P(1-\frac{r}{100})^r[/tex]

[tex]=50(1-\frac{40}{100})^x[/tex]

[tex]=50(1-0.4)^x[/tex]

[tex]=50(0.6)^x[/tex]

Which is the required exponential decay function that models this scenario.

The quantity of the medicine after 2 hours,

[tex]A=50(0.6)^2=18\text{ mg}[/tex]

Answer:

Using theorem

AE=8.66

Thus radius of large circle is one third of equilateral triangle altitude.

Radius of larger circle=2.9 inch

And radius of inner circle will be 0.96 inch

Answer:

195 miles

Step-by-step explanation:

50*x=125

x=2.5

2.5*78=195miles

Answer:

A) Reflect the graph of the first function across the x-axis, translate it pi/4 units to the left, and translate it 2 units up

Answer:

[tex]ln(x - 1) = ln(\frac{6}{x})[/tex]

Step-by-step explanation:

[tex]ln(x - 1) = ln6 - lnx[/tex]

To solve for x we need to simplify the ln

To simplify logarithmic function we use log property

[tex]ln(a) - ln(b) = ln(\frac{a}{b})[/tex]

we apply the same property on the right hand side of the given equation

[tex]ln(x - 1) = ln6 - lnx[/tex]

[tex]ln(6) - ln(x) = ln(\frac{6}{x})[/tex]

[tex]ln(x - 1) = ln(\frac{6}{x})[/tex]

This is the first step in solving the given equation

Final answer:

The standard deviation of the given data set is 10.03, and the value that is one standard deviation below the mean is 32.67. Calculations involve finding the mean, computing squared deviations, calculating the sum of squared deviations, finding the variance, and taking the square root of the variance.

Explanation:

The mean is calculated as: (27 + 38 + 47 + 42 + 33 + 56 + 37 + 57 + 38 + 52) ÷ 10 = 427 ÷ 10 = 42.7.

Now we calculate each deviation from the mean, square it, and sum them:

(27 - 42.7)² = 246.49

(38 - 42.7)² = 22.09

(47 - 42.7)² = 18.49

(42 - 42.7)² = 0.49

(33 - 42.7)² = 94.09

(56 - 42.7)² = 176.89

(37 - 42.7)² = 32.49

(57 - 42.7)² = 204.49

(38 - 42.7)² = 22.09

(52 - 42.7)² = 86.49

A sum of squared deviations = 904.61.

The variance is 904.61 ÷ (10-1) = 100.51.

The standard deviation is the square root of the variance,
which is  √100.51 equal to approximately 10.03.

To find the value that is one standard deviation below the mean, we subtract one standard deviation from the mean: 42.7 - 10.03 = 32.67.

Therefore, the standard deviation to the nearest hundredth is 10.03, and the value that is one standard deviation below the mean is approximately 32.67.

To be clear, the given relation between time and female population is an integral:
[tex]t = \int { \frac{P+S}{P[(r - 1)P - S]} } \, dP [/tex]

The 90% confidence interval for the population mean [tex]\( \mu \)[/tex] is approximately (2.50, 3.21) .

To construct a 90% confidence interval for the population mean [tex]\( \mu \)[/tex], we can use the formula:

[tex]\[ \text{Confidence Interval} = \bar{x} \pm \left( \text{Critical Value} \times \frac{s}{\sqrt{n}} \right) \][/tex]

where:

- [tex]\( \bar{x} \)[/tex] is the sample mean,

- s is the sample standard deviation,

- n is the sample size, and

- the critical value corresponds to the desired confidence level and degrees of freedom.

Given:

- Sample mean [tex]\( \bar{x} = 2.86 \),[/tex]

- Sample standard deviation s=0.78

- Sample size n=15

- Confidence level = 90%.

First, we need to find the critical value corresponding to a 90% confidence level and 14 degrees of freedom (since ( n - 1 = 15 - 1 = 14 )). We can find this value using a t-distribution table or a statistical calculator. For a 90% confidence level and 14 degrees of freedom, the critical value is approximately 1.7613.

Now, let's calculate the confidence interval:

[tex]\[ \text{Confidence Interval} = 2.86 \pm \left( 1.7613 \times \frac{0.78}{\sqrt{15}} \right) \]\[ \text{Confidence Interval} = 2.86 \pm \left( 1.7613 \times \frac{0.78}{\sqrt{15}} \right) \]\[ \text{Confidence Interval} = 2.86 \pm \left( 1.7613 \times \frac{0.78}{3.87298} \right) \]\[ \text{Confidence Interval} = 2.86 \pm \left( 1.7613 \times 0.20172 \right) \]\[ \text{Confidence Interval} = 2.86 \pm 0.35587 \][/tex]

Lower Limit:

[tex]\[ 2.86 - 0.35587 \approx 2.5041 \][/tex]

Upper Limit:

[tex]\[ 2.86 + 0.35587 \approx 3.2141 \][/tex]

Answer:

Option D. 4/5

Step-by-step explanation:

we know that

The probability of scoring 1, 3, or 5 points with one randomly thrown dart is equal to divide the area of the largest circle by the area of the square game board

step 1

Find the area of the square game board

[tex]A=b^{2}[/tex]

we have

[tex]b=20\ cm[/tex]

substitute

[tex]A=20^{2}[/tex]

[tex]A=400\ cm^{2}[/tex]

step 2

Find the probability

[tex]P=320/400[/tex]

[tex]P=0.8=8/10=4/5[/tex]