Robert is 40 years older than Brittany. the sum of their ages is 82. find their ages.

Answer:

Step-by-step explanation:

base x height divided by 2

4x3=12

12 divided by 2 = 6

6x5= 30

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:

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%

Step-by-step explanation:

federal= $4180

(9500*0.11*4)

private=$2660

(9500*0.07*4)

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:

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:

36,000

Step-by-step explanation:

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

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

The function whose graph is given is y = sin (x - 2).

Option B is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph of y = sin(x - 2) is a sinusoidal function that is shifted 2 units to the right from the standard sine function y = sin(x).

The sine function oscillates between -1 and 1 as x increases, and the value of x at which the function reaches its minimum or maximum value is a multiple of π.

When we subtract 2 from x in the equation y = sin(x - 2), the entire graph is shifted to the right by 2 units, which means that the minimum and maximum points occur at x-values that are 2 units greater than they would be for the standard sine function.

The graph of y = sin(x - a) is a sinusoidal function that is shifted a units to the right from the standard sine function.

So, in this case, the graph of y = sin(x-2) looks like the standard sine function shifted 2 units to the right.

The amplitude and period of the function remain the same as the standard sine function, but the phase shift changes.

Thus,

The function whose graph is given is y = sin (x - 2).

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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:

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:

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:

obtuse

isosceles

Step-by-step explanation:

It has one angle bigger than 90 so it is obtuse

It has two angles that measure the same so it has two sides that measure the same so it is isosceles

The given triangle is an Obtuse triangle.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

All the angles are,

100°

40°

40°

Here, It has one angle bigger than 90 so it is obtuse.

And, It has two angles that measure the same so it has two sides that measure the same so it is isosceles.

Thus, The given triangle is an Obtuse triangle.

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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:

Answer:

Step-by-step explanation: idk

Answer:

y = 0.5x + 1.5

Step-by-step explanation:

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

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

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

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

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:

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:

(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:

AAAAAAAAAAAA answer is A

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 and C

Step-by-step explanation:

CD and AB

Answer:

CD & AB

Hope this helps!

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:

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:

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.

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.

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Answer:

No solution

Step-by-step explanation:

Edge.

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