Heights for teenage boys and girls were calculated. The mean height for the sample of 46 boys was 195 cm and the variance was 58. For the sample of 66 girls, the mean was 165 cm and the variance was 75. Estimate how much taller teenage boys are using a 85% confidence level. Round answers to the nearest hundredth and provide the point estimate together with the margin of error.

Answer:

E[x] is larger

Step-by-step explanation:

I think E[x] is larger because the expected number of students on the bus of a randomly chosen student is larger.

This is because the higher the number of students present in a bus, the higher the probability that a randomly selected student would have been on that bus.

Whereas, for every driver to be chosen, the probability of any bus being chosen is 1/4 irrespective of the number of students in that particular bus

Answer:

its a postulate

Step-by-step explanation:

The statement represents a geometric postulate.

A postulate is one of the basic concepts of geography, and indicates an assumption that is accepted as true in the given theory.  

In this way, the main characteristic of the postulate is its general acceptance by the spectrum that studies it, that is, by the totality or vast majority of the scientists who are dedicated to its analysis.

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Answer: B

Step-by-step explanation:

Answer:B

Step-by-step explanation: I took the edge quiz and it was right.

Answer:

-1.031 m/s or  [tex]\frac{-\sqrt{17} }{4}[/tex]

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =  [tex]\frac{dx}{dt}[/tex] = ?

for x = 4

Applying Pythagorean Theorem we have

[tex]1^{2} +x^{2} =y^{2}[/tex]    .... equ 1

solving, where x = 4, we have

[tex]1^{2} +4^{2} =y^{2}[/tex]

[tex]y^{2} = 17[/tex]

[tex]y = \sqrt{17}[/tex]

Differentiating equ 1 implicitly with respect to t, we have

[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]

substituting values of

x = 4

y = [tex]\sqrt{17}[/tex]

[tex]\frac{dy}{dt}[/tex] = -1

into the equation, we get

[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]

[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s

Answer:

115 mi

Step-by-step explanation:

speed = distance/time

distance = speed * time

0.5 hours at 50 mph

distance = 50 mph * 0.5 h = 25 mi

1.5 hours at 60 mph

distance = 60 mph * 1.5 h = 90 mi

total distance = 25 mi + 90 mi = 115 mi

Answer:

ace hardware store

Step-by-step explanation:

Ace is the place with the helpful hardware folks!

Answer:

   (-10, -3)

Step-by-step explanation:

Replacing x with x+1 in a function moves its graph 1 unit to the left. The point that is 1 unit to the left of (-9, -3) is (-10, -3).

Answer:

1/10

Step-by-step explanation:

1/2= 5/10 - make it an equivalent fraction with the same denominator as the other fraction.

3/5= 6/10

5/10-6/10- subtract

=1/10

Answer:

X= 50°

Y= 70°

Z= 30°

BDE= 30°

2BDE= 60°

Step-by-step explanation:

(2x -70 )+z+(2x+20)=180...(sum of angle on a straight line)

2x -70 = BDE... alternate angles

Y + (2x-70)+(50+x-20) = 180...(sum of angles in a triangle)

X-20 = z ... alternate and opposite angles

(2x -70 )+z+(2x-+20)=180

2x-70 + x-20 +2x +20= 180

5x -70= 180

5x = 250

X= 50°

X-20 = z

50-20= z

30° = z

2x -70 = BDE

2(50) -70 = BDE

100-70 = BDE

30°= BDE

Y + (2x-70)+(50+x-20)

Y + 100-70 +50 +50 -20 = 180

Y + 200-90=180

Y= 70°

2BDE = 2*30

2BDE= 60°

Answer:

x=2 y=4

Step-by-step explanation:

Answer:

(D) -2,-3

Step-by-step explanation:

From the origin, we can find the current position of point B by counting.

B is 2 to the left of the y-axis, meaning that it's x value is -2.

B is 3 down of the x-axis, making it's y value -3.

Therefore, the coordinates of point B are -2,-3.

Hope this helped!

Answer: (D) -2,-3

Step-by-step explanation:

Answer:

10 miles

Step-by-step explanation:

3 mi/1 hr  x (h hours + 2/3 hr) = 5 mi/1 hr  x  h hours

3h + 2 = 5h

2 = 2h

h = 1 hour

3mi/hr  x 1 2/3 hr = 5 miles

5 mi/hr x  1 hr = 5 miles

He hiked 10 miles. (

Answer:

Vertical asymptote: [tex]x=3[/tex]

Horizontal asymptote: [tex]f(x) =2[/tex]

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

[tex]f (x) = -\dfrac{1 }{ x-3} +2[/tex]

One root, [tex]x = 3.5[/tex]

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

Roots of f(x) means the value of x where f(x) = 0

[tex]0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5[/tex]

One root, [tex]x = 3.5[/tex]

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) [tex]\rightarrow \infty[/tex]

For all, other values of [tex]x[/tex] , [tex]f(x)[/tex] is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is [tex]\frac{1}{x-3}[/tex].

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) [tex]\rightarrow \infty[/tex].

[tex]-\dfrac{1 }{ x-3} +2 \rightarrow \infty[/tex]

It is possible only when

[tex]x-3=0\\\Rightarrow x=3[/tex]

[tex]\therefore[/tex] vertical asymptote: [tex]x=3[/tex]

Horizontal Asymptote is the value of f(x) , where value of x [tex]\rightarrow \infty[/tex].

[tex]x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2[/tex]

[tex]\therefore[/tex] Horizontal asymptote: [tex]f(x) =2[/tex]

Please refer to the graph of given function as shown in the attached image.

Answer:

2.25

Step-by-step explanation:

The computation of the number c that satisfied is shown below:

Given that

[tex]f(x) = \sqrt{x}[/tex]

Interval = (0,9)

According to the Rolle's mean value theorem,

If f(x) is continuous in {a,b) and it is distinct also

And, f(a) ≠ f(b) so its existance should be at least one value

i.e

[tex]f^i(c) = \frac{f(b) - f(a)}{b -a }[/tex]

After this,

[tex]f(x) = \sqrt{x} \\\\ f^i(x) = \frac{1}{2}x ^{\frac{1}{2} - 1} \\\\ = \frac{1}{2}x ^{\frac{-1}{2}[/tex]

[tex]f^i(x) = \frac{1}{{2}\sqrt{x} } = f^i(c) = \frac{1}{{2}\sqrt{c} } \\\\\a = 0, f (a) = f(o) = \sqrt{0} = 0 \\\\\ b = 9 , f (b) = f(a) = \sqrt{9} = 3\\[/tex]

After this,

Put the values of a and b to the above equation

[tex]f^i(c) = \frac{f(b) - f(a)}{b - a} \\\\ \frac{1}{{2}\sqrt{c} } = \frac{3 -0}{9-0} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{3}{9} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{1}{3} \\\\ \sqrt[2]{c} = 3\\\\\sqrt{c} = \frac{3}{2} \\\\ c = \frac{9}{4}[/tex]

= 2.25

Answer:

10

Step-by-step explanation:

To find 20% of 50 you need to times 20 with 50 and divide by 100.

20×50÷100

=10

Answer:

1575 ft

Step-by-step explanation:

Convert 1/10 to decimal to make the math simpler.

1/10 = 0.1

Divide 3.5 by 0.1.

3.5/0.1 = 35

Multiply 35 by 45.

35 × 45 = 1575

The train will travel 1575 feet in 3.5 seconds.

The distance covered by the train in 3.5 seconds will be 1575 feet.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

A train travels 45 feet in 1/10 in a second.

Then the speed will be

Speed = 45 / (1/10)

Speed = 45 x 10

Speed = 450 feet per second

The distance covered by the train in 3.5 seconds will be

Distance = 450 x 3.5

Distance = 1575 feet

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Answer: 0.06x

Step-by-step explanation:

The given statement:  A number is 30% of 20% of the number x.

The required algebraic expression would be:

30% of 20% of x

[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex]  [we divide a percentage by 100 to convert it into decimal]

[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]

Hence, the required algebraic expression would be :

0.06x

Answer:

Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%.

Step-by-step explanation:

In this case we need to test whether the popular charity has expenses that are higher than other similar charities.

The hypothesis for the test can be defined as follows:

H₀: The popular charity has expenses that are higher than other similar charities, i.e. μ > 0.31.

Hₐ: The popular charity has expenses that are less than other similar charities, i.e. μ < 0.31.

As the population standard deviation is not known we will use a t-test for single mean.

Compute the sample mean and standard deviation as follows:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{10}\cdot[0.26+0.12+...+0.26]=0.238\\\\s= \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 0.0674 }{ 10 - 1} } =0.08654\approx 0.087[/tex]

Compute the test statistic value as follows:

[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{0.238-0.31}{0.087/\sqrt{10}}=-2.62[/tex]

Thus, the test statistic value is -2.62.

Compute the p-value of the test as follows:

 [tex]p-value=P(t_{\alpha, (n-1)}<-2.62}[/tex]

                [tex]=P(t_{0.05,9}<-2.62)\\=0.014[/tex]

*Use a t-table.

Thus, the p-value of the test is 0.014.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.014 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Thus, concluding that there is sufficient evidence to conclude that the mean is less than 31%.

Answer:

[tex]y(x)=100+0.1x[/tex]

Step-by-step explanation:

Let y represent the total fee (in dollars) of a trip where they climbed x vertical meters.

We know that there is an initial fee of $100, so we know that if we climb x=0 meters, we have a fee of y(0)=100.

[tex]y(0)=100[/tex]

As there is a constant fee (lets called it m) for each vertical meter climbed, we have a linear relationship as:

[tex]y(x)-y(0)=m(x-0)\\\\\\y(x)-100=mx\\\\\\y(x)=100+mx[/tex]

We know that for x=3000, we have a fee of $400, so if we replace this in the linear equation, we have:

[tex]y(3000)=100+m(3000)=400\\\\\\100+3000m=400\\\\3000m=400-100=300\\\\m=300/3000=0.1[/tex]

Then, we have the equation for the total fee in function of the vertical distance:

[tex]y(x)=100+0.1x[/tex]

Answer:  $323.33

Step-by-step explanation:

($17,000 + $4,900 - $2,500) ÷ 60 months = $323.33 per month

    ↓                ↓              ↓

 price        finance      down payment

Answer:

15

Step-by-step explanation:

Answer:

first we find the slope, m=(4-0)/(4+1)

Step-by-step explanation:

first, we find the slope, m=(4-0)/(4+1)=4/5

y-4=4/5 (x-4), y=(4/5)x+4/5

Answer:

A) P(A|B) = 0.01966

B) P(A'|B') = 0.99944

Step-by-step explanation:

A) We are told that A is the event "the person is infected" and B is the event "the person tests positive".

Thus, using bayes theorem, the probability that the person is infected is; P(A|B)

From bayes theorem,

P(A|B) = [P(A) × P(B|A)]/[(P(A) x P(B|A)) + (P(A') x P(B|A'))]

Now, from the question,

P(A) = 1/400

P(A') = 399/400

P(B|A) = 0.8

P(B|A') = 0.1

Thus;

P(A|B) = [(1/400) × 0.8)]/[((1/400) x 0.8) + ((399/400) x (0.1))]

P(A|B) = 0.01966

B) we want to find the probability that when a person tests negative, the person is not infected. This is;

P(A'|B') = P(Not infected|negative) = P(not infected and negative) / P(negative) = [(399/400) × 0.9)]/[((399/400) x 0.9) + ((1/400) x (0.2))] = 0.99944

Answer:

395

Step-by-step explanation:

15.8=d/25

multiply both sides by 25 to remove the denominator

25×15.8=d

d=395

Answer:

(a) The value of x is 5.

(b) The value of y is 15.

Step-by-step explanation:

Let the random variable X represent the number of electric toasters produced that require repairs within 1 year.

And the let the random variable Y represent the number of electric toasters produced that does not require repairs within 1 year.

The probability of the random variables are:

P (X) = 0.20

P (Y) = 1 - P (X) = 1 - 0.20 = 0.80

The event that a randomly selected electric toaster requires repair is independent of the other electric toasters.

A random sample of n = 20 toasters are selected.

The random variable X and Y thus, follows binomial distribution.

The probability mass function of X and Y are:

[tex]P(X=x)={20\choose x}(0.20)^{x}(1-0.20)^{20-x}[/tex]

[tex]P(Y=y)={20\choose y}(0.20)^{20-y}(1-0.20)^{y}[/tex]

(a)

Compute the value of x such that P (X ≥ x) < 0.50:

[tex]P (X \geq x) < 0.50\\\\1-P(X\leq x-1)<0.50\\\\0.50<P(X\leq x-1)\\\\0.50<\sum\limits^{x-1}_{0}[{20\choose x}(0.20)^{x}(1-0.20)^{20-x}][/tex]

Use the Binomial table for n = 20 and p = 0.20.

[tex]0.411=\sum\limits^{3}_{x=0}[b(x,20,0.20)]<0.50<\sum\limits^{4}_{x=0}[b(x,20,0.20)]=0.630[/tex]

The least value of x that satisfies the inequality P (X ≥ x) < 0.50 is:

x - 1 = 4

x = 5

Thus, the value of x is 5.

(b)

Compute the value of y such that P (Y ≥ y) > 0.80:

[tex]P (Y \geq y) >0.80\\\\P(Y\leq 20-y)>0.80\\\\P(Y\leq 20-y)>0.80\\\\\sum\limits^{20-y}_{y=0}[{20\choose y}(0.20)^{20-y}(1-0.20)^{y}]>0.80[/tex]

Use the Binomial table for n = 20 and p = 0.20.

[tex]0.630=\sum\limits^{4}_{y=0}[b(y,20,0.20)]<0.50<\sum\limits^{5}_{y=0}[b(y,20,0.20)]=0.804[/tex]

The least value of y that satisfies the inequality P (Y ≥ y) > 0.80 is:

20 - y = 5

y = 15

Thus, the value of y is 15.

Answer:

No.

Step-by-step explanation:

Substitute 4 (as x) and 2 (as y) into the 2 equations to see if they fit.

y = x - 2

2 = 4 - 2

2 = 2

The first equation is true for (4,2).

Now try the 2nd one.

y = 3x + 4

2 = 3(4) + 4

2 ≠ 16

So the 2nd equation is not true for (4,2).

Either one not true makes the solution incorrect.

No, (4, 2) is not the solution for system of Equation.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.

To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

Equations:

y= x-2 ............(1)

y= 3x+ 4.................(2)

Put the value of y from equation 1 to equation (2), we get

x- 2 = 3x+ 4

x- 3x = 4+ 2

-2x = 6

x= -3

and, y= -3 -2 = -5

So, the solution to the system is (-3, -5)

and, (4, 2) can only satisfy the Equation y= x-2 but does not satisfy y= 3x+ 4.

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Answer:

The correct answer that corresponds with that graph is B: y ≤-3x+2.

Step-by-step explanation:

1) First we need to figure out what kind of symbol the line is, greater or less than equations (< , >) then the line are dotted,and if its greater than or equal to or less than or equal to equations ( ≤, ≥) since the line are solid.

2) Now we need to figure out which side should be shaded, if the symbol is a less than or a less than or equal to then the shaded side should be on the left, if the symbol is a greater than or a greater than or equal then the shaded side should be on the right.

In this case we have a solid line and a shaded left side which mean the symbol that been used here is a less than or equal to symbol ( ≤ ).

So our answer is B: y ≤-3x+2.

Remember:

- greater or less than equations (< , >) = dotted line

- greater than or equal to or less than or equal to equations ( ≤, ≥) = solid line

- less than or a less than or equal to = shaded left side

- greater than or greater than or equal to = shaded right side

Answer:

a = 6, b = 7, c = 8, d = 7 and e = 6

Step-by-step explanation:

Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.

The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.

When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be a = 6 + 0 = 6 ft

When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be b = 6 + 1 = 7 ft

When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.

So the height will be c = 6 + 2= 8 ft

When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be d = 6 + 1 = 7 ft

When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be e = 6 + 0 = 6 ft

So the answers are:

a = 6, b = 7, c = 8, d = 7 and e = 6

Answer:

6, 7, 8, 7, 6

Step-by-step explanation:

Answer:

cosΘ = - [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

Given that Θ is in the third quadrant then cosΘ < 0

Given

tanΘ = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

Then 5 and 12 are the legs of a right triangle (5- 12- 13 ) with hypotenuse = 13

Thus

cosΘ = - [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{12}{13}[/tex]