44 students completed some homework and the histogram shows the times taken.
work out an estimate of the interquartile range.
in your work you must show the lower and upper quartiles

\(D:2x > 0\wedge x+2 > 0\\D:x > 0 \wedge x > -2\\D: x > 0\)

\(\log_42x+\log_4(x+2)=2\\\log_4(2x(x+2))=2\\2x^2+4x=4^2\\2x^2+4x-16=0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4\)

\(-4\not\in D\)

Therefore \(x=2\).

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;

Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴

Given the cash flows;

Year 0: $0

Year 1: $600

Year 2: $500

Year 3: $400

Then the Future value of uneven cash flow

= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³

= $600/1.11 + $500/1.23 + $400/1.36

=$540.54 + $405.28 + $293.00

=$1,238.82

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

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Given:

The arrow diagram of a relation.

To find:

Whether the given relation is a function or not.

Solution:

A relation is a called a function it there exist a unique y-value or unique output value for each x-value or input value.

From the given arrow diagram it is clear that y=2 and y=-1 for x=-1.

Since we have more than one value of y at x=-1, therefore, the given relation is not a function.

Hence, the correct option is B.

Answe and Step-by-step explanation:

Looking at the question the way it was asked, it is easy because it said they have been labelled, so you don't have to stress yourself. Although, if what is intended is, the labelling got wrong along the way and how do you identify the correct one? Then this is what to do:

Go to the one labelled RB. Since I'm assuming that the labelling got wrong, if you pick a red, it means what we have should be a RR and if we picked a black, it means what we have is a BB and we can't have a RB because it was labelled wrongly.

Let's assume he saw a red,

We know that the BB box was labelled wrongly, and we already determined that the box with RB is a RR. Therefore, the box BB can never be RR(because we've seen it already) and it's certainly not BB (due to the fact that they were labelled wrongly). So we have only one option left which is it being RB and whatever we have left will be BB.

If we assume what was picked from the wrongly labelled RB is black.

We know that the RR box was labelled wrongly, and we already determined that the box with RB is a BB. Therefore, the box RR can never be BB and it's certainly not RR (due to the fact that they were labelled wrongly). So we have only one option left which is it being RB and whatever we have left will be RR.

Answer:

c

Step-by-step explanation:

Answer:

This in fact would be a bar graph

Using a bar graph you can see the amount of people who like a specific type of ice cream

Hope this helps :)

Have a great day love :)

Answer:

Step-by-step explanation:

As,

- 0.0084

When estimated,

= - 0.008

\( = \frac{ - 8}{1000} \)

Then,

\( - 8 \times \frac{1}{1000} \)

\( = - 8 \times {10}^{ - 3} \)

Here,

Power of ten as observed is -3

Answer: D. 80 miles

Step-by-step explanation:

if 1 inch is 20 miles, then 4 inches is 4 x 20 = 80 miles what is real distance between City A and City B

Answer:

D. 80 miles

Step-by-step explanation:

If the map distance between Cities A and B is 4 in, and the map scale is 1 in = 20 mi, then the actual distance between Cities A and B is:

\(\frac{4\text{ in}}{1}\times\frac{20\text{ mi}}{1\text{ in}}=\frac{80\text{ mi}}{1}=80\text{ mi}\)

In other words, every one inch on the map equates to 20 miles in actual distance. Therefore, 4 inches equates to 80 miles.

Answer:

8

Step-by-step explanation:

Answer:

it will be 8

Step-by-step explanation:

The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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if you want to declare an integer variable that can be set to a valueless state, you would use the following declaration:

int? myNullableInt; You can then set it to a valueless state: myNullableInt = null;

1. Choose the base data type for your variable (e.g., int, float, bool, etc.).

2. Add a question mark (?) after the base data type to make it a Nullable type (e.g., int?, float?, bool?).

3. Declare the variable with the Nullable type.

4. Set the variable to a valueless state by assigning it the value "null".

For example, if you want to declare an integer variable that can be set to a valueless state, you would use the following declaration:

int? myNullableInt; You can then set it to a valueless state: myNullableInt = null;

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The equation for temperature change is T = -1.5t + 29 and the number line is plotted.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

Let T represent the temperature in degrees Celsius, and let t represent the time in hours after lunchtime.

Then write an expression for the situation as follows:

T = -1.5t + 29

Here, -1.5t represents the decrease in temperature per hour, since the temperature is dropping at a rate of 1.5 degrees Celsius per hour.

Adding 29 to -1.5t gives the initial temperature of 29 degrees Celsius at lunchtime.

To illustrate this situation on a number line diagram, we can plot the temperature T as a function of time t.

The diagram would have time t on the horizontal axis and temperature T on the vertical axis.

Label the point (0, 29) on the diagram to represent the temperature at lunchtime, and the point (x, 16) to represent the temperature at sunset, where x is the number of hours after lunchtime.

Then draw a straight line connecting these two points to represent the linear relationship between temperature and time.

The line slopes downward from left to right, indicating that the temperature is decreasing over time.

Therefore, the number line diagram is plotted.

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On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

A reasonable estimate of the constant of variation include the following: A. 0.25 kWh per day.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using the various data points from table D as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 0.5/2 = 1/4

Constant of proportionality, k = 0.25

Therefore, the required linear function is given by;

y = kx

y = 0.25x

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The optimal price for the product is $168. It is calculated by adding the variable cost of $52 per unit to the desired profit margin of $116, ensuring a minimum price that no one will pay.



To calculate the optimal price for this product, we need to consider the lowest price no one will pay and the variable cost per unit.The optimal price can be determined by adding a desired profit margin to the variable cost per unit. The profit margin represents the amount of profit you want to earn on each unit sold.

Let's assume you want to achieve a profit margin of $X per unit. Therefore, the optimal price would be the sum of the variable cost and the desired profit margin:

Optimal Price = Variable Cost + Desired Profit Margin

In this case, the variable cost per unit is $52, and the lowest price no one will pay is $168. So, we need to determine the desired profit margin.

To calculate the desired profit margin, we subtract the variable cost from the lowest price no one will pay:

Desired Profit Margin = Lowest Price No One Will Pay - Variable Cost

Desired Profit Margin = $168 - $52

Desired Profit Margin = $116

Now, we can calculate the optimal price:

Optimal Price = Variable Cost + Desired Profit Margin

Optimal Price = $52 + $116

Optimal Price = $168

Therefore, the optimal price for this product is $168.

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Answer:169.52

Step-by-step explanation:

=(26)(6.52)

Answer:

the answer is 3.(6.5)9 that's the answer to the equation

Answer:

17253.52

Step-by-step explanation:

100-9.5=90.5

19064.67*0.905=17253.52

Quadratic formula : x = ( - b ± √(b² - 4ac) ) / 2a

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

Let's proof quadratic formula by method of completing squares.

we have, ax² + bx + c = 0​

Now, solving this equation will be tough as it  have power 2 .

So, to overcome with this problem we have to rearrange it and x will appear only once. And, we can do with by the method of completing squares.

so, our aim is x² + 2dx + d² i.e, (x+d)²

Let's do the proof,

start with ax² + bx + c = 0​

Divide the equation with 'a'

x² + bx/a + c/a = 0

Take c/a in RHS

x² + bx/a = - c/a

Add b/a on both the sides,

x² + bx/a + (b/2a)² = -c/a + (b/2a)²

The LHS have the whole square formula i.e   x² + 2dx + d²  = (x+d)²

Complete the squares,

(x+b/2a)² = -c/a + (b/2a)²

Now, solve for 'x'

(x+b/2a)² = -c/a + (b/2a)²

(x+b/2a) = (±) √(-c/a+(b/2a)²)

Take b/2a to RHS,

x = -b/2a (±) √(-c/a+(b/2a)²)

Now, we have solve for 'x'

so, just simplify a bit,

x = [ -b (±) √(-(2a)² c/a + (2a)²(b/2a)²) ] / 2a

x = ( - b ± √(b² - 4ac) ) / 2a

We got the quadratic formula.

a.)

Proof :  Sum of roots = -b/a

we have, x = ( - b ± √(b² - 4ac) ) / 2a

Now, split into two roots r1 and r2,

r1 = ( - b + √(b² - 4ac) ) / 2a   and r2= ( - b - √(b² - 4ac) ) / 2a

sum of roots = r1 + r2

put the values of r1 and r2

r1 + r2 =  { ( - b + √(b² - 4ac) ) / 2a } +  {( - b - √(b² - 4ac) ) / 2a}

Take the LCM,

r1 + r2 =  [- b + √(b² - 4ac  - b - √(b² - 4ac) ] / 2a

          = -2b/ 2a

r1 + r2 = -b/a

b.)

Proof : Product of roots = c/a

we have, x = ( - b ± √(b² - 4ac) ) / 2a

Now, split into two roots r1 and r2,

r1 = ( - b + √(b² - 4ac) ) / 2a   and r2= ( - b - √(b² - 4ac) ) / 2a

product of roots = r1 * r2

r1 * r2 =  { ( - b + √(b² - 4ac) ) / 2a } *  {( - b - √(b² - 4ac) ) / 2a}

          = [b² + b√(b² - 4ac) - b√(b² - 4ac) - (b² - 4ac) ] / 4a²

          = b² - b² + 4ac / 4a²  = 4ac/4a²

r1 * r2 = c/a

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The value of z such that 0.15 of the area lies to the right of z can be found using the standard normal distribution table or a statistical calculator.

First, we need to determine the area to the left of z, which is 1 - 0.15 = 0.85. This is the area under the standard normal curve up to z.

Next, we need to find the corresponding z-score for this area. We can use the inverse normal distribution function, which is available in most statistical calculators. Alternatively, we can use the standard normal distribution table to find the value of z that corresponds to an area of 0.85.

Using the standard normal distribution table, we can look up the area 0.85 in the body of the table or the cumulative area column. The corresponding z-score is 1.04. This means that 85% of the area under the standard normal curve lies to the left of z = 1.04, and 15% of the area lies to the right of z = 1.04.

Therefore, the value of z such that 0.15 of the area lies to the right of z is z = 1.04, rounded to two decimal places. This means that if we have a standard normal distribution with a mean of 0 and a standard deviation of 1, then approximately 15% of the values will be greater than 1.04 standard deviations above the mean.

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Answer:

60 runs

Step-by-step explanation:

Given that:

Score in first innings = 30 runs

Change in score during second inning = + 30

The score in the second inning will be :

Score in first inning + change in score during second inning

30 + (+30)

30 + 30

= 60 runs

Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

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Answer:

x > 5

Step-by-step explanation:

2x + 3 < 4x - 7 ( subtract 2x from both sides )

3 < 2x - 7 ( add 7 to both sides )

10 < 2x ( divide both sides by 2 )

5 < x , then

x > 5

The answer is , (a) the probability of scoring above 400 is 0.79. , (b)  the probability that a student who scored above 400 reviewed for the test is 0.754.

a) The probability of scoring above 400

The total probability of scoring above 400 is given by;

P(Above 400) = P(Above 400 | Review)P(Review) + P(Above 400 | No Review)P(No Review)

In this case;

P(Above 400 | Review) = 0.85P(Above 400 | No Review)

= 0.65P(Review)

= 0.70P(No Review)

= 0.30

Substitute these values into the formula to obtain:

P(Above 400) = (0.85)(0.70) + (0.65)(0.30)

= 0.595 + 0.195

= 0.79

Therefore, the probability of scoring above 400 is 0.79.

b) The probability of reviewing if scored above 400

Let R be the event that a student reviewed for the test, and S be the event that a student scored above 400.

We are required to find P(R | S) that is, the probability that a student reviewed given that he/she scored above 400.

Using Bayes' theorem, we have,

P(R | S) = P(S | R)P(R)/P(S)

We know that;

P(S | R) = 0.85P(R)

= 0.70P(S)

= 0.79

Substitute these values to obtain;

P(R | S) = (0.85)(0.70)/0.79

= 0.754

Therefore, the probability that a student who scored above 400 reviewed for the test is 0.754.

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Answer:

$75.50

Step-by-step explanation:

In order to determine whether the project should be accepted or not when the discount rate is 12.5 percent, we can use the profitability index (PI) which is calculated by dividing the present value of cash inflows by the initial investment.

The formula for PI is:PI = (PV of cash inflows) / (initial investment)

A project should be accepted if the profitability index is greater than 1. Therefore, we need to calculate the profitability index (PI) of the project using the given information and determine whether it is greater than 1 or not.

The given answer choices are:

No; because the Pl is 3.3

Yes; because the PI is 3.0

No; because the Pl is 0.8

Yes; because the PI is 2.6

Yes; because the PI is 2.2

However, there is no information given regarding the Pl (present value of cash inflows) for any of these answer choices.

Therefore, we cannot use these answer choices to determine whether the project should be accepted or not when the discount rate is 12.5 percent. So, we need to calculate the PI using the given information and check if it is greater than 1 or not.

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The 95% confidence interval for the difference between the percent of residents who are younger than 50 and who are 50 and older that visited the park in the past year is  (-0.1076, 0.1076).

To calculate the 95% confidence interval for the difference between the percent of residents who are younger than 50 and who are 50 and older that visited the park in the past year, we can use the following formula:

CI = (p1 - p2) ± z*(sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2))

where:

p1 = the sample proportion of residents younger than 50 who visited the park

p2 = the sample proportion of residents 50 and older who visited the park

n1 = the sample size of residents younger than 50

n2 = the sample size of residents 50 and older

z* = the critical value from the standard normal distribution for a 95% confidence interval, which is 1.96

From the table, we can see that 60 out of 120 residents younger than 50 visited the park in the past year, while 40 out of 80 residents 50 and older visited the park in the past year. Therefore:

p1 = 60/120 = 0.5

p2 = 40/80 = 0.5

n1 = 120

n2 = 80

Plugging these values into the formula, we get:

CI = (0.5 - 0.5) ± 1.96*(sqrt(0.5*(1-0.5)/120 + 0.5*(1-0.5)/80))

Simplifying, we get:

CI = 0 ± 0.1076

Therefore, the 95% confidence interval the visit in the park in the past year is (-0.1076, 0.1076).

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Answer:

y = -3x + 800

Step-by-step explanation:

You start out with 800 eggs and go down 3 eggs with each customer

The function for the number of eggs left y after x customers is

y = 800 - 3x

A function is a relationship between inputs where each input is related to exactly one 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,

Number of eggs the diner starts in a week = 800

The number of eggs each customer gets = 3

Now,

The number of y eggs after x customers.

y = 800 - 3x

Thus,

The function is y = 800 - 3x.

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Answer:

15 female students in her sample

Step-by-step explanation:

134/1065 x 120 = 15.1

The given statement "For a sample with a standard deviation of s = 8, a score of x = 42 corresponds to z = -0.25. The mean for the sample is m = 40." is False because the calculated z-score does not match the given value.

To calculate the z-score, we use the formula z = (x - m) / s, where x is the score, m is the mean, and s is the standard deviation. Substituting the given values, we have z = (42 - 40) / 8 = 0.25. However, the given statement states that the z-score is -0.25, which is incorrect. Therefore, the statement is false.

The correct z-score for x = 42 with a mean of m = 40 and standard deviation of s = 8 is 0.25, not -0.25.

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