40 POINTS!!!! Which sequence of transformations will result in an image that maps onto itself?

Answer:

99.36% probability that the sample proportion will differ from the population proportion by less than 6%

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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.

For a sample proportion p in a sample of size n, we have that the sampling distribution of the sample proportions has [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex].

In this question:

[tex]n = 306, p = 0.18, \mu = 0.18, s = \sqrt{\frac{0.18*0.82}{306}} = 0.0220[/tex].

What is the probability that the sample proportion will differ from the population proportion by less than 6%

This is the pvalue of Z when X = 0.18 + 0.06 = 0.24 subtracted by the pvalue of Z when X = 0.18 - 0.06 = 0.12. So

X = 0.24

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.24 - 0.18}{0.022}[/tex]

[tex]Z = 2.73[/tex]

[tex]Z = 2.73[/tex] has a pvalue of 0.9968

X = 0.12

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

[tex]Z = \frac{0.12 - 0.18}{0.022}[/tex]

[tex]Z = -2.73[/tex]

[tex]Z = -2.73[/tex] has a pvalue of 0.0032

0.9968 - 0.0032 = 0.9936

99.36% probability that the sample proportion will differ from the population proportion by less than 6%

Answer:

The y-coordinate of point C' is 4

Step-by-step explanation:

In the picture attached, pentagon ABCDE is shown.

Rotation 90° counterclockwise about the origin transforms point (x,y) into (-y,x).

C is located at (4, 3), then C' is located at (-3, 4)

Answer:

4

Step-by-step explanation:

The solution to the given function is determined as 13.

The solution of the function is calculated as follows;

[tex]\sqrt{x - 4} \ +\ 5 = 2[/tex]

collect similar terms together

 [tex]\sqrt{x - 4} \ = 2-5\\\\\sqrt{x - 4} \ = -3[/tex]

square both sides of the equation

[tex](\sqrt{x - 4} )^2 = (-3)^2\\\\x - 4 = 9\\\\x = 9 + 4\\\\x = 13[/tex]

Thus, the solution to the given function is determined as 13.

Learn more about solution of functions here: https://brainly.com/question/10439235

#SPJ9

Answer:

No solution

Step-by-step explanation:

Edge.

Answer:

$228.67

Step-by-step explanation:

Given that:

Terry has a monthly mortgage payment of $979.

Terry's annual taxes are $1200 per year. That implies that his escrow each month require to posses 1/12 of that amount.

i.e 1/12 × 1200 = $100 per month.

For his  homeowner's insurance which is $800 per year,

His escrow account each month is = 1/12 × 800 = $66.67

PMI = $62 per month.

Thus: The amount that is deposited  into Terry's escrow account each month is the sum total of $100 + $ 66.67 + $62 = $228.67

Answer:

You cannot do this because 2800 cm squared is area and liters is volume. however, if you mean 2800 cm cubed, then the answer is 2.8 liters.

Step-by-step explanation:

Answer:

78doalrse

Step-by-step explanation:

solos w

Answer:

$11.40

Step-by-step explanation:

This question asks us to find how much money the family should leave as their tip.

To find the tip, multiply the cost of the total bill by the tip rate.

cost of bill * tip rate

The total bill was $57, and they are leaving a 20% tip

$57 * 20%

Convert 20% to a decimal by dividing by 100 or moving the decimal place 2 spaces to the left.

20/100=0.20

20.0--> 2.0 --> 0.20

20%=0.20

$57 * 0.20

Multiply 57 and 0.20

11.4= $11.40

The family should leave a tip of $11.40

Answer:

(a) dy/dx = 4/(2y+1)^2.

(b) y = 4/9 x - 14/9

(c) d2y/dx2 = -64/243

Step-by-step explanation:

You have the following equation

[tex](2y+1)^3-24x=-3[/tex]   (1)

(a) You first derivative implicitly the equation (1) respect to x:

[tex]\frac{d}{dx}[(2y+1)^3-24x]=\frac{d}{dx}[-3]\\\\3(2y+1)^2(2\frac{dy}{dx})-24=0[/tex]

next, you solve the last result for dy/dx:

[tex]6(2y+1)^2\frac{dy}{dx}=24\\\\\frac{dy}{dx}=\frac{4}{(2y+1)^2}[/tex](2)

(b) The equation for the tangent line is given by:

[tex]y-y_o=m(x-x_o)[/tex]    (3)

with yo = -2 and xo = -1

To find the slope m you use the result of the equation (2), because dy/dx evaluated in (-1,-2) is the slope at such point:

m = [tex]\frac{dy}{dx}=\frac{4}{(2(-2)+1)^2}=\frac{4}{9}[/tex]

Hence, by replacing in the equation (3) you obtain:

[tex]y-(-2)=\frac{4}{9}(x-(-1))\\\\y+2=\frac{4}{9}x+\frac{4}{9}\\\\y=\frac{4}{9}x-\frac{14}{9}[/tex]

hence, the equation for the tangent line is y = 4/9 x - 14/9

(c) To find d2y/dx2 you derivative the result obtain in the equation (2):

[tex]\frac{d^2y}{dx^2}=\frac{d}{dx}[4(2y+1)^{-2}]\\\\\frac{d^2y}{dx^2}=-8(2y+1)^{-3}(2\frac{dy}{dx})\\\\\frac{d^2y}{dx^2}=-16(2y+1)^{-3}\frac{dy}{dx}[/tex]     (4)

the second derivative for the point (-1,-2) is obtained by replacing y=-2 and dy/dx=m=4/9 in the equation (4):

[tex]\frac{d^2y}{dx^2}=-16(2(-2)+1)^{-3}(\frac{4}{9})=-\frac{64}{243}[/tex]

hence, d2y/dx2 evaluated in (-1,-2) is -64/243

Answer:

(A) The value of  [tex]dy/dx=\frac{4}{(2y+1)^2}[/tex].

(B) The equation of the tangent is : [tex]y=(4/9)x-(14/9)[/tex]

(C) The value of  [tex]\frac{d^2y}{dx^2}=-64/243[/tex]

(D) The point (16,0) is not on curve so it can not be determined by the given equation.

Step-by-step explanation:

Given information:

The equation [tex](2y+1)^3-24x=-3[/tex]

(A) For the first derivative of the given equation:

[tex]\frac{d}{dx}[(2y+1)^3-24x ]= \frac{d}{dx}(-3)[/tex]

[tex]3(2y+1)^2(dy/dx)-24=0[/tex]

[tex](dy/dx)=\frac{4}{(2y+1)^2}[/tex]

Hence , from the above equation it is shown that the value of

[tex]dy/dx=\frac{4}{(2y+1)^2}[/tex]

(B) The equation of the tangent to the curve is given by:

[tex]y-y_o=m(x-x_0)\\[/tex]

On putting the given values in the above equation

We get:

[tex]m=\frac{4}{(2(-2))+1)^2}[/tex]

[tex]m=4/9[/tex]

Hence, the equation of the tangent can be written as :

[tex]y-(-2)=(4/9)(x-(-1))\\y+2=\frac{4}{9}x+\frac{4}{9}[/tex]

So, the equation of the tangent is :

[tex]y=(4/9)x-(14/9)[/tex]

(C) Now ,

To find [tex]d^2y/dx^2[/tex] for the equation

We have to find double derivative of the equation;

[tex]\frac{d^2y}{dx^2} =\frac{d}{dx}[4(2y+1)^{-2}]\\\frac{d^2y}{dx^2} = -16(2y+1)^{-3}\frac{dy}{dx}[/tex]

On putting the values from the given information in the above equation;

[tex]\frac{d^2y}{dx^2} =-16(2(-2)+1)^{-3}(4/9)[/tex]

[tex]\frac{d^2y}{dx^2}=-64/243[/tex]

(D) For the equation [tex](2y+1)^3-24x=-3[/tex]

First check for the given points (16,0) if it satisfies the given equation or not.

Now on checking for the same the point is not satisfying the given equation hence, we can not find the value of [tex](y-1)'(0)[/tex].

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Answer:

Step-by-step explanation:

r(t) = (7 cost + 7t sin t)i + (7 sin t - 7t cos t)j

[tex]\frac{d \bar r t}{dt} =(7\frac{d}{dt}\cos t + 7\frac{d}{dt} (t \sin t)i+(7\frac{d}{dt} \sin t-7\frac{d}{dt} t \cos t)j[/tex]

[tex]=(7(-\sin t)+7(1* \sin t+t \cos t))i+(7 \cost -7(1*\cos t - t \sin t))j\\\\=7((-\sin t+\sin t+t \cos t)i+(\cos t-\cos t+t \sin t)j)\\\\=7((t\cos t)i+(t\sin t)j)[/tex]

[tex]\bar r'(t)=\frac{d \bar r t}{dt} =(7t\cos t)i+(7t\sin t)j---(1)\\\\11\bar r(t)=\sqrt{(7t\cos t)^2+(7t\sin t)^2}\\\\=\sqrt{49t^2(\cos^2t+\sin^2 t)} \\\\=7t[/tex]

[tex]\bar T (t)=\frac{\bar r'(t)}{11\bar r(t)11} =\frac{(7t\cos t)i+(7t\sin t)j}{7t} \\\\\barT(t)=(\cos t)i+(\sin t)j[/tex]

[tex]\bar T'(t)=\frac{d}{dt} (\cos t)i+\frac{d}{dt} (\sin t) j\\\\\bar T'(t)=(-\sin t)i+(\cos t)j---(2)\\\\11\bar T'(t)=\sqrt{(-\sin t)^2+(\cos t)^2} \\\\=\sqrt{\sin^2t+\cos^2t} \\\\=1[/tex]

[tex]\bar N(t)=\bar T'(t)=\frac{(-\sin t)i+(\cos t)j}{(1)} \\\\ \large \boxed {\bar N(t)=(-\sin t)i+(\cos t)j}[/tex]

[tex]K(t)=\frac{|\b\r T'(t)|}{\bar r (t)|} \\\\=\frac{|-\sin t i+\cos t j|}{|7t\cos t +7t \sin t j|}[/tex]

Using eq (1) and (2)

[tex]K(t)=\frac{\sqrt{(-\sin t)^2+(\cos t)^2} }{\sqrt{(7t\cos t)^2+(7t\sin t)^2} }\\\\=\frac{\sqrt{\sin^2 t+\cos^2t} }{\sqrt{49t^2(\cos^2 t+\sin^2t)} }\\\\=\frac{\sqrt{1} }{\sqrt{49t^2\times 1} } \\\\ \large \boxed {K(t)=\frac{1}{7t} }[/tex]

Answer:

36,000

Step-by-step explanation:

So all we have to do is divide 360 by 0.01. that equals 36,000

Answer:

6720 ways different

Step-by-step explanation:

In this case, we must calculate the different ways using the permutation formula:

nPr = n! / (n - r)!

where n is the total number of people and r would come being the group of person that you want to put together the groups, therefore n = 8 and r = 5

replacing:

8P5 = 8! / (8 - 5)!

8P5 = 6720

That is to say that there are 6720 ways different winning groups are possible

Answer:

A. Probability the man is colorblind = 0.07

B. Probability the woman is not colorblind = 0.996

C. Probability neither the man or woman is colorblind = 0.926

D. Probability at least one of the woman or man is colorblind = 0.074

Note: The given question is missing some values. The question below is a sample question.

"The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosomes). Approximately 7% of American men and 0.4% of American women are red-green color-blind.

(a) If an American male is selected at random, what is the probability that he is red-green colorblind?

(b) If an American female is selected at random, what is the probability that she is NOT red-green color-blind?

(c) If one man and one woman are selected at random, what is the probability that neither are

red-green color-blind?

(d) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind?"

Step-by-Step Explanation:

Let cbM and cbW represent the events that a man or a woman is colorblind, respectively.

(a) 7% of men are colorblind, P(CBM) = 7/100 = 0.07.

(b) 0.4% of women are colorblind = 0.4/100 = 0.004

P(not cbW) = 1 - P(cbW)

P(not cbW) = 1 - 0.004 = 0.996.

(c) Probability the woman is not colorblind, P(not cbW) = 0.996,

Probability that the man is not color- blind, P(not cbM) = 1 - 0.07 = 0.93.

The two events are independent of each other, therefore, their probabilities are multiplied together:

P(neither is colorblind) = P(not cbM) × P(not cbW)

= 0.93 × 0.996 = 0.926.

(d) Probability that at least one is colorblind is the complement of the set P (neither is colorblind).

Therefore, P(at least one is colorblind) = 1 - P (Neither is Colorblind)

= 1 - 0.926 = 0.074

The right answer is 5538.96 units^2

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer: 5538.96

Step-by-step explanation: 3.14× 42×42

42×42=1764

∴ 3.14×1764= 5538.96

Answer:

Mostly correct

For Q3, you are doing great, you remembered that negative numbers can happen if the exponent is an odd number.

For Q4, I think you were confused with the fractions,

4(i)

[tex](\frac{2}{3} )^{4} = (\frac{2^{4}}{3^{4}}) = (\frac{16}{81}) =0.198[/tex]

4(ii) is also wrong but I'll let you try to fix it yourself following what I given you for 4(i). You should get 1/64

Hope this helps!

Answer:

i = correct

ii = correct

iii = correct

iv = correct

4

i = 16/81 => 0.1975308642

ii= 1/64

Answer:

Step-by-step explanation: idk

Answer:

x1 = 4

x2 = -5

Step-by-step explanation:

There is a formula to solve the quadratic equations, which is:

[-b +- √ (b² - 4 ac) ] / (2a)

Quadractic equations have this look:

ax² + bx + c = 0

You need to stablish the numbers:

where a, is the number with x², b the x and c, the independent term.

x²  + x - 20 = 0 For this case:

a = 1 ; b = 1 ; c = -20. We replace in the formula

[-1 +- √ (1² - 4 1 (-20)) ] / (2 .1)

(-1 + √81) / 2 = 4

(-1 - √81) / 2 = -5

Answer:

x1= 4     ,    x2= -5

Step-by-step explanation:

put in calculator MOD 5 3

a= 1   b= 1   c= -20

Answer:

Option (A)

Step-by-step explanation:

In the figure attached,

Quadrilateral ABCD has been translated to get an image quadrilateral A'B'C'D'.

To get the rule by which the pre-image ABCD has been translated, we will choose a point A(1, 1) from the given pre-image.

Coordinates of point A' are (3, -2).

So the change is,

A(1, 1) → A'(3, -2)

A(1, 1) → A'[(1 + 2), (1 - 3)]

A(x, y) → A'[(x + 2), (y - 3)]

Therefore, point A has been shifted 2 units right and 3 units down.

Option (A) will be the answer.

Answer:

y = 0.5x + 1.5

Step-by-step explanation:

I just graphed the points with GeoGebra. Hope this Helps!

Answer:

3889

Step-by-step explanation:

you add all the numbers to get the answer

Answer:3889

Step-by-step explanation:So what u want to do is add them

1034

1289

1566

3889

Answer:

We study if the composition of both functions equals the identity ("x"), that is if

[tex]f(g(x))=x[/tex]

Step-by-step explanation:

The composition of the two functions should render 'x" if one is the inverse of the other. That is, we need to find what  [tex]f(g(x))[/tex] renders. Notice as well that the same verification could be done with examining  [tex]g(f(x))[/tex].

Let's work with [tex]f(g(x))[/tex] :

[tex]f(g(x))=f(\frac{1}{5} x+5)=5\,(\frac{1}{5} x+5)-25= x+25-25=x[/tex]

So we see that the composition of both functions indeed render "x", and that way we have verified that one is the the inverse of the other.

Answer:

B. One-fifth (5 x minus 25) + 5

Step-by-step explanation:

Just got it right on the test.

Answer:

We conclude that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control.

Step-by-step explanation:

The complete question is : In a random sample of 360 women, 65% favored stricter gun control laws. In a random  sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women  favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a  significance level of 0.05.

Now, we are given that in a random sample of 360 women, 65% favored stricter gun control laws.

And in a random  sample of 220 men, 60% favored stricter gun control laws.

Let [tex]p_1[/tex] = proportion of women favoring stricter gun control laws.

[tex]p_2[/tex] = proportion of men favoring stricter gun control laws.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex]     {means that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1> p_2[/tex]     {means that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control}

The test statistics that would be used here Two-sample z-test for proportions;

                          T.S. =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of women favoring stricter gun control laws = 65%

[tex]\hat p_2[/tex] = sample proportion of men favoring stricter gun control laws = 60%

[tex]n_1[/tex] = sample of women = 360

[tex]n_2[/tex] = sample of men = 220

So, the test statistics  =  [tex]\frac{(0.65 -0.60)-(0)}{\sqrt{\frac{0.65(1-0.65)}{360}+\frac{0.60(1-0.60)}{220} } }[/tex]

                                     =  1.205

The value of z test statistics is 1.205.

Now, at 5% significance level, the z table gives critical value of 1.645 for right-tailed test.

Since, our test statistics is less than the critical value of z as 1.205 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control.

Answer:

AAAAAAAAAAAA answer is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

base x height divided by 2

4x3=12

12 divided by 2 = 6

6x5= 30

Answer:

Second quadrant = 120°.

Third quadrant = 210°

Step-by-step explanation:

We are given that:

[tex]sin^2(x) = 3cos^2(x)[/tex]

The following property is known:

[tex]sin^2(x) +cos^2(x)=1\\[/tex]

Combining both expressions:

[tex]sin^2(x) =1-cos^2(x)\\sin^2(x) = 3cos^2(x)\\\\1-cos^2(x) = 3cos^2(x)\\cos^2(x)=\frac{1}{4}\\cos(x)=\pm \frac{1}{2}[/tex]

If x lies in the second quadrant, then cos(x) = -1/2:

[tex]x=cos^{-1}(1/2)\\x=120^o[/tex]

The value of x that satisfies the equation if x lies in the second quadrant is 120°.

If x lies in the third quadrant, then cos(x) = -1/2:

[tex]x=120+90=210^o[/tex]

The value of x that satisfies the equation if x lies in the third quadrant is  210°

Answer:

The value of x that satisfies the equation if x lies in the second quadrant is 120

The value of x that satisfies the equation if x lies in the third quadrant is

240

Step-by-step explanation:

This is correct for Plato/Edmentum users :) Hope I could help !

Answer:

A and C

Step-by-step explanation:

CD and AB

Answer:

CD & AB

Hope this helps!

[tex](\frac{9}{4} )(\frac{15}{8} )[/tex]

[tex]\frac{135}{32}[/tex]

[tex]=4\frac{7}{32}[/tex]

1. So start off by asking yourself, how will I get this answer? Absolute values!

2. So what the question is asking is for you to build and equation that shows us how to solve for the highest and lowest grades that are 19 points above and below the average of 72.

3. So your unknown is x, and for us to be able to plug in our highest and lowest scores it will always have to = 19 (that’s the rule we got from the question)

So now this is where your absolute value comes in.

4. Set it up

| x - 72 | = 19

5. Solve it

72-19=53 Minimum

72+19=91 Maximum

6. | 53 - 72 | = 19

| 91 - 72 | = 19

Answer:

x = 30

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

100 = 70+x

Subtract 70 from each side

100-70 = 70+x-70

30 =x

Answer:

[tex]x = 30 \: \: degrees[/tex]

Step-by-step explanation:

The sum of the of the exterior angle is equal to sum of the opposite interior angles in a triangle.

[tex]70 + x = 100 \\ x = 100 - 70 \\ x = 30 \: \: \: degrees[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Rejection of the claim about aspirin is more serious because the wrong aspirin dosage could cause more serious adverse reactions than a wrong vitamin C dosage. It would be wise to use a greater significance level for testing the claim about the aspirin.

Step-by-step explanation:

The wrong dosage of aspirin will cause more damage than a wrong dosage of vitamin C. Then, if we perform an hypothesis test for each mean, the rejection of the claim about the aspirin content is more serious than the vitamin C content.

In the case of the aspirin, we want to minimize the Type II error (accepting a false null hypothesis). This can be achieved increasing the sample size or/and increasing the significance level. Then, a significative difference between the claimed content and the sample content will be easily detected.