QUESTION 7
What is the coefficient of y in the expression - y2 +4y-8?

Answer:

a) 75%.

b) 84%

c) Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem:

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by \(100(1 - \frac{1}{k^{2}})\).

In this question:

Mean: 6.3 hours

Standard deviation: 1.6 hours

(a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours.

3.1 = 6.3 - 2*1.6

9.5 = 6.3 + 2*1.6

Within 2 standard deviations, so the minimum percentage is 75%.

(b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours.

How many standard deviations from the mean?

One standard deviation is 1.6

These measures are 10.3 = 6.3 = 6.3 - 2.3 = 4. This is k standard deviations, in which

\(k = \frac{4}{1.6} = 2.5\)

The minimum percentage is:

\(100(1 - \frac{1}{k^{2}}) - 100(1 - \frac{1}{2.5^{2}}) = 84%\)

So 84%.

(c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day.

Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

Answer:

3/4 to 9/6

Step-by-step explanation:

Answer:

No, because the ratios of the sides that form the vertex angles are the​ same, but the vertex angles may not be congruent.

Step-by-step explanation:

I just took the quick check

If 18 is subtracted from the number, the digits are reversed.

Let the digit in the unit's place be x and the digit at the tens place be y.

The number obtained by reversing the order of the digits is = 10x + y

10y + x = 6(x + y) + 4

10y + x = 6x + 6y + 4

10y + x - 6x - 6y = 4

- 5x + 4y = 4

(10y + x) - 18 = 10x + y

10y + x - 10x - y = 18

- 9x + 9y = 18

- 9(x - y) = 18

x - y = - 18/9

4x - 4y = -8............(3)

5x - 4y = - 4

4x - 4y = - 8

(-) (+) (+)

----------------------

5x - 4y = - 4

5(4) - 4y = - 4

20 - 4y = - 4

- 4y = - 4 - 20

- 4y = - 24

y = 24/4

Now, Number = 10y + x = 10 × 6 + 4 = 60 + 4 = 64

Answer:

3

Step-by-step explanation:

21÷3=7

15÷3=5

18÷3=6

7 5 and 6 do not have a gcf except for 1.

Answer:

C. Subtract 4 from both sides.

Step-by-step explanation:

You need the equation in the form x² + ax + b = 0 to then either try factoring or use the quadratic formula.

In order to achieve that, you need to first:

Subtract 4 from both sides.

Answer: d. 25

Step-by-step explanation: This is correct because the graph starts at 75 and then jumps to 100. 75 + 25 is 100. This then goes from 100 to 125. Again, 100 + 25 is 125. Finally, it goes from 125 to 150. 125 + 25 equals 150. The final answer is 25 because each time the line increases, it increases by 25.

Let me know if this helped in the comments.

Answer:

the answer for this is 2.64575

√7=2.64

please mark this answer as brainlist

The intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

Option (D) is correct.

What is the intersection of two sets?

The intersection of two sets, A and B, is the set of elements that are common to both sets. It is often represented by A ∩ B.

In this case, Set A = {2, 4, 6, 8} and set B = {1, 2, 3, 4, 5, 6, 7, 8}. The set that represents A ∩ B is {2, 4, 6, 8} because these are the elements that are common to both sets A and B.

So the correct answer is {2, 4, 6, 8}

Hence, the intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

To learn more about the intersection of two sets, visit:

https://brainly.com/question/11439924

#SPJ1

Answer: 9.44 seconds

Step-by-step explanation:

A movement equation in the vertical axis is usually written as follows:

p(t) = (-g/2)*t^2 + v0*t + p0

where:

g is the gravitational acceleration, in this case is 32 ft/s^2, then -g/2 = -16ft/s^2

v0 is the initial velocity, in this case, 24 ft/s

p0 is the initial height, in this case, 1200ft

Then, when p(t)  = 0ft will mean that the pebble will hit the ground, then we need to calculate:

p(t) = -16t^2+24t+1200  = 0

and find the value of t, this is a quadratic equation, then we can use the Bhaskara equation to find the two solutions, these are:

\(t = \frac{-24 +- \sqrt{24^2 - 4*(-16)*1200} }{2*-16} = \frac{-24 +- 278.2}{-32}\)

Then the two solutions are:

t = (-24  + 278.2)/-32 = -7.94 seconds (we can discard this one, because the negative time is not really defined)

t = (-24 - 278.2)/-32 = 9.44 seconds

Then the pebble needs 9.44 seconds to hit the ground

Every case concerning the residual sums of squares for the restricted and unrestricted regressions - RRSS > URSS

\(R^{2}\) is the proportion of the total variability of y that is explained by the model.

R-squared (R2) is a statistical metric that shows how much of a dependent variable's variation is explained by one or more independent variables in a regression model. R-squared measures how well the variation of one variable accounts for the variance of the second, as opposed to correlation, which describes the strength of the link between independent and dependent variables.

To know more about R-squared visit: brainly.com/question/13324767

#SPJ4

Answer:

\(f(g(x)) =\dfrac{1}{\sqrt{x - 2} - 5}\)

\(D(f(g(x)) = (2;27) \cup (27; +\infty)\)

Step-by-step explanation:

\(f(x) = \dfrac{1}{x - 5}\)

\(g(x) = \sqrt{x - 2}\)

\(f(g(x)) = \dfrac{1}{g(x) - 5} = \dfrac{1}{\sqrt{x - 2} - 5}\)

\(D(f(g(x)):\)

\(\displaystyle \left \{ {{x - 2 > 0} \atop { \sqrt{x - 2} - 5 \neq 0 }} \right.\) \(\displaystyle \left \{ {{x > 2} \atop { \sqrt{x - 2} \neq 5 }} \right\) \(\displaystyle \left \{ {{x > 2} \atop { (\sqrt{x - 2})^{2} \neq 5^{2} }} \right\)  \(\displaystyle \left \{ {{x > 2} \atop { x - 2 \neq 25 }} \right\) \(\displaystyle \left \{ {{x > 2} \atop { x \neq 27 }} \right\)

\(D(f(g(x)) = (2;27) \cup (27; +\infty)\)

Answer:

12ft

Step-by-step explanation:

It is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a Wide range of factors

As an AI language model, I do not have access to up-to-date information about salaries of coaches in Jacksonville. However, in general, the salaries of coaches vary widely depending on a number of factors, such as the type of sport, the level of competition, the location, the success of the team, and the budget of the institution.

In terms of tennis and football, football is generally considered to be a more popular and high-profile sport than tennis in the United States, which could result in higher salaries for football coaches at the collegiate level. Football also typically generates more revenue and has larger budgets for athletic programs, which could also influence the salaries of coaches.

However, there are also factors that could affect the salaries of tennis coaches. For example, if a tennis program has a particularly successful season or has produced successful players, the coach may negotiate a higher salary. Additionally, some colleges may place a greater emphasis on tennis or have larger budgets for tennis programs, which could also impact the salaries of coaches.

Overall, it is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a wide range of factors. It is also important to note that salaries can vary widely between individual institutions, even within the same sport, and that negotiations between coaches and their institutions can play a significant role in determining salaries.

To know more about Wide range.

https://brainly.com/question/30389189

#SPJ11

The measure of the angle ∠FEB will be 70°.

An infinitely long row of evenly spaced dots that extends in both directions makes up a line. Its length is the only dimension it has. An illustration of a line is a horizontal mark made on a piece of paper. A figure made by two rays that intersect at the same endpoint is referred to as an angle.\

Given that the angle ∠EFB is 35° and BD is the angle bisector of ∠EFD. The measure of the angle ∠FEB will be;-

∠FEB = 2 x ∠EFB

∠FEB = 2 x 35

∠FEB  = 70°

Therefore, the value of the angle ∠FEB will be 70°.

To know more about lines and angles follow

https://brainly.com/question/25770607

#SPJ1

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

Learn more on age word problems here;

https://brainly.com/question/17043336

#SPJ1

Answer:

a.  all of the above are correct

b.  The pitcher will throw 30 pitches that are not curveballs.

Step-by-step explanation:

Considering the concept of independent events, we have that they are classified as follows:

a) Independent.

b) Dependent.

Independent events is when a success or failure in an event do not influence the probability of a success or failure in the other event.

For item a, in each roll of the dice, the probability of the number being even/odd will not change from previous trials, hence the events are independent.

For item b, the slip will be kept out of a hat, hence the number of total outcomes change, hence changing the probability(desired outcomes divided by total outcomes), and hence the events are dependent.

More can be learned about independent events at https://brainly.com/question/14478923

#SPJ1

Answer:

15 m

Step-by-step explanation:

perimeter of rectangle = 2 ( l + b )

l = 4.5

b = 3

p = 2 ×( 4.5 + 3)

p = 2 × ( 7.5)

p = 15 m

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

Answer:

A cold water tap takes 3 minutes to fill the bath. A hot water tap takes 2 minutes to fill the bath. How long does it take to fill the bath when both taps are open at the same time?

It is easiest just to let the bath be a given size.

My little bath will be 12 litres

cold water  4L/min          hot water = 6L/min      

together 10L/1 min

10*(12/10) L per  1*(12/10) minutes

12L per 1.2min

12L per 1min and 12sec

It will take 1 minute and 12 seconds to fill the bath.

Step-by-step explanation:

Answer:

It will take 5 minutes for both faucets together to fill the water cooler

Step-by-step explanation:

I'm kinda just guessing but I do have a reasonable explanation

So the average time it takes for the faucets INDIVIDUALLY to fill the water cooler is 10 minutes

But since both faucets are filling them TOGETHER, it should take half the time

And half of 10 is 5

So it should take 5 minutes for both faucets together to fill the water cooler

If that makes sense

The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

Know more about volumes,

https://brainly.com/question/17101095

#SPJ1

The value of -3√5 as the opposite of the square root is -75.

What in mathematics is a square root?

The factor we can multiply by itself to obtain a given number is the number's square root.

               Square root is represented by the symbol sqrt, which stands for square root of, end square root. Squaring an integer is the reverse of finding its square root.

-3√5

The opposite of the square root is the square, so,

-3√5 = -3 × 5²

-3√5 = - 3 × 25

-3√5 = - 75

Learn more about Square root

brainly.com/question/3120622

#SPJ1

In linear equation, 187 tickets do they need to sell.

What is a linear equation ?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.        

                                           The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." This is the basis for its designation as a "linear equation."

The drama club wants to raise at least $1500. They have already received donations of $565 so the amount left till target is:

= 1500 - 565

= $935

Tickets are being sold at $5 so the number of tickets needed to get to $935 is

= 935/5

= 187 tickets

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

Read more about probability,

https://brainly.com/question/30390037

Answer:

The initial value is the value of the y-coordinate when the x-coordinate is equal to 0. That is the same to say the value at which the graph intercepts the y-axis. So, you just have to pick the graph whose line intercepts the y-axis at 1/2.

Answers:

x = 7*sqrt(3)

y = 7

===========================================================

Explanation:

We have a 30-60-90 triangle here since the missing acute angle is 90-60 = 30 degrees. Or you could note how 30+60+90 = 180.

The side length y is the shorter leg as it's opposite the smallest angle. It's equal to half of the hypotenuse. So y = 14/2 = 7.

The longer leg x is equal to y*sqrt(3). We multiply the shorter leg by sqrt(3) to get the longer leg. This means

x = y*sqrt(3) = 7*sqrt(3)

----------

You could also use the pythagorean theorem if you knew that y = 7 and you had the hypotenuse value as well. You could solve like so

a^2 + b^2 = c^2

7^2 + b^2 = 14^2

b^2 = 14^2 - 7^2

b^2 = 147

b = sqrt(147)

b = sqrt(49*3)

b = sqrt(49)*sqrt(3)

b = 7*sqrt(3)

Which matches up with the value of x we found earlier.