prove that
1/(sec A - tan A) =sec A + tan A​

Answer:

A

Step-by-step explanation:

The area of a kite is half of the product of the length of the diagonals, or in this case 16*12/2=96 square feet. Hope this helps!

Answer:

a. 96 ft^2

Step-by-step explanation:

You can cut the kite into 2 equal triangle halves vertically.

Then you can use the triangle area formula and multiply it by 2 since there are 2 triangles.

[tex]\frac{1}{2} *12*8*2=\\6*8*2=\\48*2=\\96ft^2[/tex]

The kite's area is a. 96 ft^2.

Answer:

We need a sample of at least 1937.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For this problem, we have that:

[tex]\pi = 0.72[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample should be if you want your estimate to be within 0.02 with 95% confidence.

We need a sample of at least n.

n is found when M = 0.02. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.96\sqrt{0.72*0.28}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.72*0.28}}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.72*0.28}}{0.02})^{2}[/tex]

[tex]n = 1936.16[/tex]

Rounding up to the nearest number.

We need a sample of at least 1937.

Complete question is;

In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.

Answer:

P(has diabetes | positive) = 0.442

Step-by-step explanation:

Probability of having diabetes and being positive is;

P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)

We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.

Thus;

P(positive & has diabetes) = 0.08 × 0.95 = 0.076

P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)

P(negative & has diabetes) = 0.004

P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)

We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease

Thus;

P(positive & no diabetes) = 0.92 × 0.1 = 0.092

P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)

P(negative &no diabetes) = 0.828

Probability that a person selected having diabetes actually has the disease is;

P(has diabetes | positive) =P(positive & has diabetes) / P(positive)

P(positive) = 0.08 + P(positive & no diabetes)

P(positive) = 0.08 + 0.092 = 0.172

P(has diabetes | positive) = 0.076/0.172 = 0.442

Using formula:

[tex]P(\text{diabetes diagnosis})\\[/tex]:

[tex]=\text{P(having diabetes and have been diagnosed with it)}\\ + \text{P(not have diabetes and yet be diagnosed with diabetes)}[/tex]

[tex]=0.08 \times 0.95+(1-0.08) \times 0.10 \\\\=0.08 \times 0.95+0.92 \times 0.10 \\\\=0.076+0.092\\\\=0.168[/tex]

[tex]\text{P(have been diagnosed with diabetes)}[/tex]:

[tex]=\frac{\text{P(have diabetic and been diagnosed as having insulin)}}{\text{P(diabetes diagnosis)}}[/tex]

[tex]=\frac{0.08\times 0.95}{0.168} \\\\=\frac{0.076}{0.168} \\\\=0.452\\[/tex]

Learn more about the probability:

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Answer:

1/5

Step-by-step explanation:

20*5 = 100, so 20 is 1/5

Answer:

  see the attachment for a graph

Step-by-step explanation:

The vertex of f(x) is (0, 0). The transformation g(x) = f(x -h) +k moves the vertex to (h, k). That is, the graph is translated right by h units, and up by k units.

Your transformation has h = -2, and k = -4. That is, the original graph is translated left 2 units and down 4 units. The result is the blue curve in the attachment.

Answer:

Hiking: 28%

Canoeing: 16%

Swimming: 24%

Fishing: 32%

Step-by-step explanation:

21 + 12 + 18 + 24 = 75 (there are 75 campers)

21 out of 75 = 28%

12 out of 75 = 16%

18 out of 75 = 24%

24 out of 75 = 32%

Hope this helps!

Please mark Brainliest if correct

Answer:

3

Step-by-step explanation:

Step 1: Isolate y

5y < 20

y < 4

When we figure out the inequality, we see that y has to be less than 4. Therefore, the highest integer value will have to be 3.

Answer:

Step-by-step explanation:

i think its 3

Answer:

0

Step-by-step explanation:

You cannot make any triangles with this angle

Answer:

Let's solve your equation step-by-step.

[tex]x^7+64x^4=0[/tex]

Step 1: Factor left side of equation.

[tex]x^4(x+4)(x^2-4x+16)=0[/tex]

Step 2: Set factors equal to 0.

[tex]x^4=0[/tex]  or  [tex]x+4=0[/tex]  or  [tex]x^2-4x+16=0[/tex] 

[tex]x^4=0[/tex]  or  [tex]x=0[/tex]  

Answer:

I hope this help you :)

Answer:

Step-by-step explanation:

Ray

Answer:

ray

Step-by-step explanation:

ray is a part of a line that has an endpoint in one side and extends indefinitely on the opposite side. hence, the answer is ray

hope this helps

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

[tex]Z = \frac{X - \mu}{s}[/tex]

X = 205

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{205 - 200}{5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413.

X = 195

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{195 - 200}{5}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{210 - 200}{5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772.

X = 195

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{190 - 200}{5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

(a): The required probability is [tex]P(195 < \bar{x} < 205)=0.6826[/tex]

(b): The required probability is [tex]P(190 < \bar{x} < 200)=0.9544[/tex]

A numerical measurement that describes a value's relationship to the mean of a group of values.

Given that,

mean=200

Standard deviation=50

[tex]n=100[/tex]

[tex]\mu_{\bar{x}}=200[/tex]

[tex]\sigma{\bar{x}} =\frac{\sigma}{\sqrt{n} } \\=\frac{50}{\sqrt{100} }\\ =5[/tex]

Part(a):

within [tex]5=200\pm 5=195,205[/tex]

[tex]P(195 < \bar{x} < 205)=P(-1 < z < 1)\\=P(z < 1)-P(z < -1)\\=0.8413-0.1587\\=0.6826[/tex]

Part(b):

within [tex]10=200\pm 10=190,200[/tex]

[tex]P(190 < \bar{x} < 200)=P(-1 .98 < z < 1.98)\\=P(z < 2)-P(z < -2)\\=0.9772-0.0228\\=0.9544[/tex]

Learn more about the topic Z-score:

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Answer:

[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]

Step-by-step explanation:

We are given the coordinates of points P(1,-6,7) and Q(-9,10,-5).

The values in the form of ([tex]x,y,z[/tex]) are:

[tex]x_1=1\\x_2=-9\\y_1=-6\\,y_2=10\\z_1=7\\z_2=-5[/tex]

[tex]$\vec{PQ}$[/tex] can be written as the difference of values of x, y and z axis of the two points i.e. change in axis.

[tex]\vec{PQ}=<x_2-x_1,y_2-y_1,z_2-z_1>[/tex]

[tex]\vec{PQ} = <(-9-1), 10-(-6),(-5-7)>\\\Rightarrow \vec{PQ} = <-10, 16,-12>[/tex]

The equation of line in vector form can be written as:

[tex]\vec{r} (t) = <1,-6,7> + t<-10,16,-12>[/tex]

The standard parametric equation can be written as:

[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]

Answer:

En álgebra, el teorema del factor es un teorema que vincula factores y ceros de un polinomio. Es un caso especial del teorema del resto polinómico.

Step-by-step explanation:

Answer:

a prism is a three dimensional shape with the same width all the way through.

Step-by-step explanation:

Step-by-step explanation:

i think this will help.

Answer: height = 13.24 m

Step-by-step explanation:

Draw a picture (see image below), then set up the proportions to find the length of QB.  Then input QB into either of the equations to find h.

Given: PQ = 10

          ∠TPB = 23°

          ∠TQB = 32°

[tex]\tan P=\dfrac{opposite}{adjacent}\qquad \qquad \tan Q=\dfrac{opposite}{adjacent}\\\\\\\tan 23^o=\dfrac{h}{10+x}\qquad \qquad \tan 32^o=\dfrac{h}{x}\\\\\\\underline{\text{Solve each equation for h:}}\\\tan 23^o(10+x)=h\qquad \qquad \tan 32^o(x)=h\\\\\\\underline{\text{Set the equations equal to each other and solve for x:}}\\\tan23^o(10+x)=\tan32^o(x)\\0.4245(10+x)=0.6249x\\4.245+0.4245x=0.6249x\\4.245=0.2004x\\21.18=x[/tex]

[tex]\underline{\text{In put x = 21.18 into either equation and solve for h:}}\\h=\tan 32^o(x)\\h=0.6249(2.118)\\\large\boxed{h=13.24}[/tex]

Answer: $3267.40

Step-by-step explanation:

A = P (1+r/n)^nt

A= 2500 (1+0.055)^nt

A= 2500 x 1.30696

A = 3267.40

Answer:

[tex]1/\sqrt{2}[/tex]

Answer:

B

Step-by-step explanation:

Answer: x=45°

Step-by-step explanation:

Angles opposite from each other are equal. The angle 160 degrees in red on the bottom encompasses two angles: BEG and CEG. Angle BEG is on the opposite side as FEA which means it is equal to x.

Since angle FED on the other side is 115, you subtract 115 from 160 to get 45 degrees.

Answer: x=45°

The angle BEG, which is opposite to the angle FEA, is determined to be 45 degrees.

According to the information provided, in a figure with an angle of 160 degrees (red angle on the bottom), there are two angles labeled as BEG and CEG. It is stated that the angle BEG is opposite to the angle FEA, making them equal, so we can represent this angle as x.

Additionally, it is mentioned that the angle FED on the other side measures 115 degrees.

To find the value of x, we subtract 115 degrees from the angle of 160 degrees.
=160-115
= 45

Thus, the solution is x = 45°.

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Answer:

24

Step-by-step explanation:

Since you are given almost everything, you just simply divide by 5=>

120/5 = 24

Hope this helps

Answer: x = -5

Step-by-step explanation:

If you factor each denominator, you can find the LCM.

[tex]\dfrac{2}{x^2-x-12}=\dfrac{1}{x^2-16}\\\\\\\dfrac{2}{(x-4)(x+3)}=\dfrac{1}{(x-4)(x+4)}\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\\dfrac{2}{(x-4)(x+3)}\bigg(\dfrac{x+4}{x+4}\bigg)=\dfrac{1}{(x-4)(x+4)}\bigg(\dfrac{x+3}{x+3}\bigg)\\\\\\\dfrac{2(x+4)}{(x-4)(x+4)(x+3)}=\dfrac{1(x+3)}{(x-4)(x+4)(x+3)}\\[/tex]

Now that the denominators are equal, we can clear the denominator and set the numerators equal to each other.

2(x + 4) = 1(x + 3)

2x + 8 = x + 3

x  + 8 =       3

x        =      -5

Answer:

P(X=2) = 0.302

Step-by-step explanation:

With the conditions mentioned in the question, we can model this variable as a binomial random variable, with parameters n=9 and p=0.2.

The probability of having k defective items in the sample of nine chips is:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{9}{k} 0.2^{k} 0.8^{9-k}\\\\\\[/tex]

Then, the probability of having 2 defective chips in the sample is:

[tex]P(x=2) = \dbinom{9}{2} p^{2}(1-p)^{7}=36*0.04*0.2097=0.302\\\\\\[/tex]

Answer:

A warranty of 6.185 years should be provided.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 8.2, \sigma = 1.3[/tex]

What warranty should be provided so that the company is replacing at most 6% of their blenders sold?

The warranty should be the 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.55.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.55 = \frac{X - 8.2}{1.3}[/tex]

[tex]X - 8.2 = -1.55*1.3[/tex]

[tex]X = 6.185[/tex]

A warranty of 6.185 years should be provided.

Answer:

9.34%

Step-by-step explanation:

p = 4%, or 0.04

n = Sample size = 667

u = Expected value = n * p = 667 * 0.04 = 26.68

SD = Standard deviation = [tex]\sqrt{np(1-p)} =\sqrt{667*0.04*(1-0.04)}[/tex] = 5.06

Now, the question is if the manager is correct, what is the probability that the proportion of flops in a sample of 667 released films would be greater than 5%?

This statement implies that the p-vlaue of Z when X = 5% * 667 = 33.35

Since,

Z = (X - u) / SD

We have;

Z = (33.35 - 26.68) / 5.06

Z = 1.32

From the Z-table, the p-value of 1.32 is 0.9066

1 - 0.9066 = 0.0934, or 9.34%

Therefore, the probability that the proportion of flops in a sample of 667 released films would be greater than 5% is 9.34%.

Answer:

no solutions

Step-by-step explanation:

6-3x=4-x-3-2x

Combine like terms

6-3x =1 -3x

Add 3x to each side

6 -3x+3x = 1-3x+3x

6 =1

This is not true so there are no solutions

Answer:

No solutions.

Step-by-step explanation:

6 - 3x = 4 - x - 3 - 2x

Add or subtract like terms if possible.

6 - 3x = -3x + 1

Add -1 and 3x on both sides.

6 - 1 = -3x + 3x

5 = 0

There are no solutions.

Answer:

x = 2

Step-by-step explanation:

the equation of the line can be found using the slope intercept form

y = mx +b

y= -3/2 x + 3

x intercept is found by setting y=0 bc that will give you the x-value at which the line crosses the x -axis so

0 = -3/2x+3 (subtract the 3 on both sides) would cancel out the + 3 and would

-3 = -3/2 x  (divide by -3/2 on both sides to cancel out the -3/2)  

x = 2

The radioactive compound has a half-life of around 3.09 hours.

The period of time needed for a radioactive substance's initial quantity to decay by half is known as its half-life. The half-life of a drug may be calculated as follows if the rate of decay is proportionate to the amount of the substance existing at time t:

Let t be the half-life of the substance, then after t hours, the amount of the substance present will be,

100 mg × [tex]\dfrac{1}{2}[/tex] = 50 mg.

At time 6 hours, the amount of the substance present is,

100 mg × (1 - 3%) = 97 mg.

Given that the amount of material available determines how quickly something degrades,

The half-life can be calculated as follows:

[tex]t = 6 \times \dfrac{50}{ 97} = 3.09 \ hours[/tex]

Therefore, the half-life of the radioactive substance is approximately 3.09 hours.

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Using the Central Limit Theorem, it is found that the measures are given by:

a) 2,500,000.

b) 88,388.35.

c) 2,500,000.

By the Central Limit Theorem, the sampling distribution of sample means of size n for a population of mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] has the same mean as the population, but with standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

Hence, we have that for options a and c, the mean is of 2,500,000 users, while for option b, the standard deviation is given by:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{625000}{\sqrt{50}} = 88,388.35.[/tex]

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

Answer:

- The center line is at 16.5 ounces.

- The standard deviation of the sample mean = 0.112 ounce.

- The UCL = 16.836 ounces.

- The LCL = 16.154 ounces.

Step-by-step explanation:

The Central limit theorem allows us to write for a random sample extracted from a normal population distribution with each variable independent of one another that

Mean of sampling distribution (μₓ) is approximately equal to the population mean (μ).

μₓ = μ = 16.5 ounces

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

where σ = population standard deviation = 0.25 ounce

N = Sample size = 5

σₓ = (0.25/√5) = 0.1118033989 = 0.112 ounce

Now using the 3 sigma limit rule that 99.5% of the distribution lies within 3 standard deviations of the mean, the entire distribution lies within

(μₓ ± 3σₓ)

= 16.5 ± (3×0.112)

= 16.5 ± (0.336)

= (16.154, 16.836)

Hope this Helps!!!

Answer:

The second graph.

Step-by-step explanation:

0-9: 6 numbers

10-19: 2 numbers

20-29: 1 number

30-39: 3 numbers

40-49: 1 number

50-59: 2 numbers

60-69: 0 numbers

70-79: 5 numbers

80-89: 3 numbers

90-99: 1 number