Please answer this correctly

Answer:

3.46 meters

Step-by-step explanation:

In the right triangle, Using Trigonometry

[tex]\tan 60^\circ = \dfrac{6}{x} \\$Cross multiply\\x\tan 60^\circ =6\\$Divide both sides by \tan 60^\circ\\x=\dfrac{6}{\tan 60^\circ}\\\\x=3.46$ meters[/tex]

The ladder is 3.46 meters from the foot of the wall.

Answer: 15

Step-by-step explanation:

(gоf)(4) means g of f of 4. You would plug in f(4) into g(x).

f(4)=(4²)-3=16-3=13

Now that we know f(4) is 13, we would plug in 13 to g(x).

g(13)=13+2=15

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:

Step-by-step explanation:

Weather is usually referring to current condition of an area. For eg, the weather in NYC is sunny on this day with 68F.

However, Climate is referring to the average weather of that area (usually taken over more than 25 years). For eg, the climate in NYC is chilly with temperatures ranging from 68-78F.

Completely made up data but hope that clears my point. Weather is assessed temporarily whereas, Climate is usually prepared long term.

Answer:The length of time over which conditions are measured

Step-by-step explanation:

Answer:

The probability that all three have type B​+ blood is 0.001728

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have type B+ blood, or they do not. The probability of a person having type B+ blood is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that a person in the United States has type B​+ blood is 12​%.

This means that [tex]p = 0.12[/tex]

Three unrelated people in the United States are selected at random.

This means that [tex]n = 3[/tex]

Find the probability that all three have type B​+ blood.

This is P(X = 3).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.12)^{3}.(0.88)^{0} = 0.001728[/tex]

The probability that all three have type B​+ blood is 0.001728

Answer:

x= .75

Step-by-step explanation:

The equation can be solved by using the distributive property and using FOIL

I can include a full step by step if you need it. Just reply and ask

Answer:

[tex]y=\frac{13}{6}x+7[/tex]

Step-by-step explanation:

Please see the attached photo. Please mark this brainliest.

Answer:

23/50

Step-by-step explanation:

11/20=0.55

23/50=0.46

0.5-0.46=0.04

0.543-0.5=0.043

0.5-0.458=0.042

Answer:

E(x) = 5.83

Step-by-step explanation:

There are 36 possible outcomes.

There is a 6 in 36 chance that the difference between the dice is zero (square is also zero):

{1,1} {2,2} {3,3} {4,4} {5,5} {6,6}

There is a 10 in 36 chance that the difference between the dice is one (square is also 1):

{1,2} {2,1} {2,3} {3,2} {3,4} {4,3} {4,5} {5,4} {5,6} {6,5}

There is a 8 in 36 chance that the difference between the dice is two (square is 4):

{1,3} {3,1} {2,4} {4,2} {3,5} {5,3} {4,6} {6,4}

There is a 6 in 36 chance that the difference between the dice is three (square is 9):

{1,4} {4,1} {2,5} {5,2} {3,6} {6,3}

There is a 4 in 36 chance that the difference between the dice is four (square is 16):

{1,5} {5,1} {2,6} {6,2}

There is a 2 in 36 chance that the difference between the dice is four (square is 25):

{1,6} {6,1}

Therefore, the expected value for X is:

[tex]E(X) = \frac{6}{36}*0+\frac{10}{36}*1+\frac{8}{36}*4+\frac{6}{36}*9+\frac{4}{36}*16+\frac{2}{36}*25\\E(X) = 5.83[/tex]

The expected value is E(x) = 5.83

Answer:

C. ± 2.326 years.

Step-by-step explanation:

We have the standard deviation for the sample. So we use the t-distribution to solve this question.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.98}{2} = 0.01[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.01 = 0.99[/tex], so [tex]z = 2.326/tex]

Now, find the width of the interval

[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

[tex]\sigma = 5, n = 25[/tex]

So

[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]W = 2.326*\frac{5}{\sqrt{25}}[/tex]

The correct answer is:

C. ± 2.326 years.

Answer:

g(-5) = 2

g(0) = -2

g(1) = 2

Step-by-step explanation:

g(-5) satisfies x <-2, since -5 is less than -2.

g(0) satisfies -2≤x≤1 since 0 is greater than 2 but less than 1. When we plug in 0 into (x+1)^2 -2, we get -2.

g(1) satisfies -2≤x≤1 since it says that x is less than OR EQUAL TO 1. We then plug in 1 into (x+1)^2 -2 and get 2.

Answer:

x=1/3 is the answer

Step-by-step explanation:

6x+15=3x+14

substracting 3x on both sides

6x-3x+15=3x-3x+14

3x+15=14

subtracting 15 on both sides

3x+15-15=14-15

3x=1

x=1/3

i hope this will help you

Answer:

[tex]solution \\ 6x + 5 = 3x + 14 \\ or \: 6x - 3x = 14 - 5 \\ or \: 3x = 9 \\ or \: x = \frac{9}{3} \\ x = 3[/tex]

hope this helps ..

Good luck on your assignment...

Answer:

a) The null and alternative hypothesis are:

[tex]H_0: \pi=0.2\\\\H_a:\pi\neq 0.2[/tex]

b) Test statistic z = -1.3258

c) P-value = 0.1849

Step-by-step explanation:

a) As the reseracher want to determine  if the proportion of their users who use Firefox is significantly different from 0.2, it is a two-tailed test, as a proportion significantly low or significantly high gives evidence to support the alternative hypothesis.

Then the null and alternative hypothesis are:

[tex]H_0: \pi=0.2\\\\H_a:\pi\neq 0.2[/tex]

b)  The sample has a size n=200.

The sample proportion is p=0.16.

[tex]p=X/n=32/200=0.16[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.2*0.8}{200}}\\\\\\ \sigma_p=\sqrt{0.0008}=0.028[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.16-0.2+0.5/200}{0.028}=\dfrac{-0.038}{0.028}=-1.3258[/tex]

c) This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=2\cdot P(z<-1.3258)=0.1849[/tex]

As the P-value (0.1849) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of their users who use Firefox is significantly different from 0.2

Answer: The equation has a solution .

Step-by-step explanation:

Since we have given that

[tex]\sqrt{x+1}=7-2\sqrt{x}[/tex]

Squaring on both the sides, we get that,

[tex]x+1=(7-2\sqrt{x})^2\\\\x+1=49+4x-28\sqrt{x}\\\\3x+48-28\sqrt{x}=0[/tex]

Let [tex]\sqrt{x}=y\implies x=y^2[/tex]

So, our equation becomes,

[tex]3y^2-28y+48=0\\\\y=\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3}\\\\\sqrt{x}=\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3}\\\\x=(\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3})^2[/tex]

So, [tex]x=\dfrac{248}{9}\pm \dfrac{56\sqrt{13}}{9}[/tex]

Hence, the equation has a solution .

Answer:

A. (2b + 7)2

Step-by-step explanation:

4b2 + 28b + 49 = (2b + 7)2

Answer:

A. (2b + 7)2

Step-by-step explanation:

Answer:

Haha proofs are an interesting thing. Usually, nothing is to scale, which is why you can't measure anything. They are pretty annoying, but it helps to know why certain things are the way that they are and develop justification skills for higher level math.

Sorry to discourage you, but you're going to see "Justify" quite a lot in calculus and beyond which is basically a more informal version of a proof

you can never escape it tbh lol

We can't just measure the two figures to see if they are congruent as congruence is about shape and size.

It should be noted that congruence simply means that the shapes have identical length, angles, and size.

Therefore, we can't just measure the two figures to see if they are congruent as congruence is about shape and size.

Learn more about geometry on:

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Answer:

A.   minus 10,

Step-by-step explanation:

The distance travelled must be positive.

Therefore minus 10 would not be a reasonable answer.

Answer:

78

Step-by-step explanation:

Probably wrong

Answer:

the answer is B

Step-by-step explanation:

D: 0 ≤ g ≤ 20

R: 0 ≤ M(g) ≤ 340

I had the same problem. pls mark as brainliest

Answer:

A 98% confidence interval for the true proportion of Americans who were satisfied with the gun control laws in 2018 is (0.213, 0.387).

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].

For this problem, we have that:

[tex]n = 150, \pi = 0.3[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 2.327\sqrt{\frac{0.3*0.7}{150}} = 0.213[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 2.327\sqrt{\frac{0.3*0.7}{150}} = 0.387[/tex]

A 98% confidence interval for the true proportion of Americans who were satisfied with the gun control laws in 2018 is (0.213, 0.387).

Answer:

im guessing thats on khan so 4=4  and 8 = 2:)

Step-by-step explanation:

Answer: Both

Step-by-step explanation: Both equal y intercept

Answer:

[tex]3-4i[/tex]

Step-by-step explanation:

The x-axis represents [tex]x[/tex] and [tex]x[/tex] is 3. The y-axis represents [tex]iy[/tex] and [tex]y[/tex] is -4 so [tex]iy[/tex] is -4i.

A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit. The complex number that is represented by the graph is 3-4i.

A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit, and satisfies the equation i² = 1; every complex number may be represented as a + bi, where a and b are real numbers.

The complex numbers are represented on the graph where x represents the real number marked across the horizontal axis.

The y represents the imaginary part of the number and is marked across the vertical axis.

Hence, the complex number that is represented by the graph is 3-4i.

Learn more about Complex Number:

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Answer:

$23161.10

Step-by-step explanation:

Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t

Step 1: Convert months to years

60 months/12 month/year = 5 years

Step 2: Plug in known variables

A = 18400(1 + 0.0471)^5

Step 3: Solve

When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.

Step-by-step explanation:

Joe mama

Answer:

Step-by-step explanation:

Null hypothesis: u = 0.72

Alternative hypothesis: u =/ 0.72

Using the z score formula

z = p-P / √(P(1-P)/n)

Where p (sample proportion) is 0.75, P (population proportion) is 0.72, and n = 900.

z = 0.75-0.72 / √(0.72(1-0.72)/900)

z = 0.03/√(0.72(0.28)/900)

z = 0.03/√(0.2016/900)

z = 0.03/ √0.000224

z = 0.03/0.015

z = 2.0

To determine the p-value at an assumed significance level of 0.05 for a two tail test using a z score of 2, using the p value calculator, the p value is 0.0455.

Answer:

318$

Step-by-step explanation:

6*53 = 318$

Answer:

  y = (x +1)^3(x -2)

Step-by-step explanation:

The graph is generally U-shaped and opens upward. This means the polynomial is of even degree and has a positive leading coefficient.

The x-intercepts are -1 and +2, so there will be factors of (x -(-1)) and (x -2). (An x-intercept of p corresponds to a factor (x-p).)

The curve has a flat spot at x=-1, so the multiplicity of that factor will be greater than 1. Since the axis is crossed there (not just touched), the multiplicity will be odd.

The smallest exponent of the factor (x+1) that will meet all the requirements is 3. (The sum of exponents must be even, the exponent of (x+1) must be an odd number greater than 1.)

An equation could be ...

  y = (x +1)^3(x -2)

_____

Comment on what's to understand?

Every x-intercept of a polynomial curve corresponds to a binomial factor with a real number constant. (Above, we called the factor (x-p) for x-intercept x=p.) If the factor has odd multiplicity, the curve will cross the x-axis; if not, the curve will "touch" the x-axis at the x-intercept point. The higher the multiplicity (exponent of the factor), the "flatter" the curve is at the x-intercept.

The leading coefficient of the polynomial tells you the sign of the y-value when x takes on large positive values. If the degree of the polynomial is even, the general shape of the curve will be U-shaped, opening upward or downward depending on the sign of the leading coefficient. If the degree of the polynomial is odd, the curve will have a / or \ general shape, again depending on the sign of the leading coefficient. (\ for negative). This description is of the shape at large scales, ignoring any wiggles on the curve.

Answer:

The difference between the upper and lower limits of the confidence interval would be 0.22344, or answer choice E.

Step-by-step explanation:

To find the width of the confidence interval, one only needs to know the standard error and the confidence level, not the point estimate.

In the problem we are given that the standard deviation is .057.

They say that the confidence level is 95%, which is equal to 1.96 (that value can be found using the inverse normal function on a calculator or from a z-table).

.057×1.96=.11172. This is the value that would be added on to the point estimate to find the upper bound and subtracted to find the lower bound. Using this logic, there would be two of this number between the upper and lower limits of the confidence interval, so .11172×2=.22344.

Answer:

a) 96.64% probability that maximum speed is at most 50 km/h

b) 24.67% probability that maximum speed is at least 48 km/h

c) 86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

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 = 46.8, \sigma = 1.75[/tex]

A. What is the probability that maximum speed is at most 50 km/h?

This is the pvalue of Z when X = 50. So

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

[tex]Z = \frac{50 - 46.8}{1.75}[/tex]

[tex]Z = 1.83[/tex]

[tex]Z = 1.83[/tex] has a pvalue of 0.9664

96.64% probability that maximum speed is at most 50 km/h.

B. What is the probability that maximum speed is at least 48 km/h?

This is 1 subtracted by the pvalue of Z when X = 48.

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

[tex]Z = \frac{48 - 46.8}{1.75}[/tex]

[tex]Z = 0.685[/tex]

[tex]Z = 0.685[/tex] has a pvalue of 0.7533

1 - 0.7533 = 0.2467

24.67% probability that maximum speed is at least 48 km/h.

C. What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?

Z = 1.5 has a pvalue of 0.9332

Z = -1.5 has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664

86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

Answer:

Equations:

k + m = 48

m = 3k

Answer: Mark is 12; mom is 36

Step-by-step explanation:

Let k = Mark's age

Let m = mom's age

k + m = 48

m = 3k

k + 3k = 48

4k = 48

k = 12

m = 3k = 3(12) = 36

Equations:

k + m = 48

m = 3k

Answer: Mark is 12; mom is 36

Answer:

240

Step-by-step explanation:

Answer:

[tex]240[/tex]

Step-by-step explanation:

[tex]\left(26\cdot 25\right)-\left(25\cdot 24\right)+\left(24\cdot 23\right)-\left(23\cdot 22\right)+\left(22\cdot 21\right)-\left(21\cdot 20\right)+\left(20\cdot 19\right)-\left(19\cdot 18\right)+\left(18\cdot 17\right)-\left(17\cdot 16\right)+\left(16\cdot 15\right)-\left(15\cdot 14\right)[/tex]

[tex]650-600+552-506+462-420+380-342+306-272+240-210[/tex]

[tex]=240[/tex]