IQ scores are collected from a sample of 36 students
at a large university. The scores are summarized in
the histogram below.


Which of the following statements is true of the mean
and median?

O The mean is equal to the median IQ.

O The mean is less than the median IQ

O The mean is greater than the median IQ.

O It cannot be determined because we cannot tell the
exact values of the IQ scores in the sample.

Answer:

The function would be:

Since y should be positive or zero:

So x can get values from 0 to 6.

The domain is:

Answer:

function= y=20-3x

Domain= 1,2,3,4,5,6

To calculate how long it would take to pay off 60% of the debt,

we can use the same facts as in problem #16. Let's go through the steps:

1. Determine the total amount of debt: Find the original debt amount given in problem #16.

2. Calculate 60% of the debt: Multiply the total debt by 0.6 to find the amount that represents 60% of the debt.

3. Divide the amount obtained in step 2 by the monthly payment: This will give us the number of months it will take to pay off 60% of the debt.

Now, let's apply these steps to the options provided:

a. About 45 months: To determine if this is the correct answer, we need to perform the calculations outlined above using the original debt amount and the monthly payment given in problem #16.

b. About 50 months: Same as option a, perform the calculations using the original debt amount and the monthly payment.

c. About 55 months: Perform the calculations outlined above using the original debt amount and the monthly payment.

d. About 37 months: Perform the calculations outlined above using the original debt amount and the monthly payment.

After performing the calculations for each option, compare the results with the options provided to find the correct answer.

To Learn more about amount of debt:

https://brainly.com/question/28929846

#SPJ11

The equation which shows the number of minutes it will take for the two containers to have same amount of water is 200+4t=0.

Given that container A has 800 ml and water is increasing by 6 ml per minute, container B has 1000 ml and water is increasing by 10 ml per minute.

We are required to find the equation that shows the minutes it will take for the two containers to have the same amount of water.

Water in container A=800 ml

Rate of increase of water in container A=6 ml per minute

Water in container B=1000 ml

Rate of increase of water in container B=10 ml per minute

According to the question the amount of water in both the containers is same.

let the number of minutes be t.

So,the equation will be:

800+6t=1000+10t

1000-800+10t-6t=0

200+4t=0

Hence the equation which shows the number of minutes it will take for the two containers to have same amount of water is 200+4t=0.

Learn more about equations at https://brainly.com/question/2972832

#SPJ9

Answer:

85° and 95°

Step-by-step explanation:

Given that , x and x + 10 are a pair of angles .

=> x + x + 10° = 180°

=> 2x = 180° -10°

=> 2x = 170°

=> x = 170°/2

=> x = 85° .

Answer:

For every one pound there are 16 ounces.

Step-by-step explanation:

We can simply see that by dividing the ounces by pounds, 32/2 = 16, and 48/3 = 16.

Number of ounces: 16, 32, 48, 64, 80, 96

Number of pounds:  1, 2, 3, 4, 5, 6

Answer:

5.75

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + b^2 = 7^2

16 + b^2 = 49

49 - 16 = 33

√33 = 5.75

Answer:

second number = - 28

Step-by-step explanation:

let the first number be x and the second number y , then

x + y = - 18 , that is

10 + y = - 18 ( subtract 10 from both sides )

y = - 28 , that is

the second number is - 28

Answer:

Step-by-step explanation:

The equation that represents the situation is -28 + 10 = -18

The second number is -28.

Poppy's sister used approximately 3.14 inches more wire per wall hanging than Poppy.

To find the amount of wire used by both Poppy and her sister, we'll calculate the circumference of their respective wall hangings using the formula:

C = 2πr

Since the diameter is twice the radius, we can find her sister's radius as follows:

Poppy's radius = 6.25 inches

Poppy's diameter = 2 * 6.25 = 12.5 inches

Sister's diameter = Poppy's diameter + 1 = 12.5 + 1 = 13.5 inches

Sister's radius = 13.5 / 2 = 6.75 inches

Now, we'll calculate the circumferences using the given value for π:

Poppy's circumference = 2 x 3.14 x 6.25 ≈ 39.25 inches

Sister's circumference = 2 x 3.14 x 6.75 ≈ 42.39 inches

Difference = Sister's circumference - Poppy's circumference

Difference = 42.39 - 39.25 = 3.14 inches

Find out more on wire at https://brainly.com/question/29205033

#SPJ1

An equivalent expression to \(7k^2\), where k is an even number, is \(28n^2\), where n is an integer.

If k is an even number, then we can write k as 2n, where n is some integer. Substituting this into \(7k^2,\) we get:

\(7(2n)^2= 7(4n^2)\)

\(= 28n^2\)

Therefore, an equivalent expression to \(7k^2\), where k is an even number, is \(28n^2\), where n is an integer.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z.

Integers come in three types:

Zero (0)

Positive Integers (Natural numbers)

Negative Integers (Additive inverse of Natural Numbers)

To know more about integers visit:

https://brainly.com/question/15276410

#SPJ4

The usual speed of the bus is 60 km/hr.

Speed is the rate of change in location of an item, expressed in meters per second.

Given,

Let x be the usual speed.

Speed = Distance/ Time

Time = Distance/Speed

Bus usually travels 350 miles.

It takes time for it to get there = 350/x h

The bus departs this week at 6:10, though.

The 70-minute bus delay = 70/60 = 7/6 h

The bus's current speed is (x+10) miles per hour.

The new window of time for getting there is \(\frac{350}{x+10}\)

\(\frac{350}{x}\) + \(\frac{350}{x+10}\) = \(\frac{7}{6}\)

350(\(\frac{x+10-x}{x(x+10)}\) ) = \(\frac{7}{6}\)

350 ( \(\frac{10}{x^{2} +10x}\) )= \(\frac{7}{6}\)

7(x² +10x) = 6(350)(10)

x² + 10x = 3000

x² + 10x - 3000 = 0

x² -60x + 50x - 3000 = 0

x( x - 60) + 50(x - 60) = 0

(x + 50)(x - 60) = 0

x = -50 , x = 60

The usual speed of the bus is 60 km/hr.

To learn more about speed, visit:

https://brainly.com/question/15203844

#SPJ4

The given figure appears to be a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In the given figure, we can see that opposite sides are parallel, so it is a parallelogram.

We can also find that the measure of angle A is 120 degrees because the adjacent angles to angle A are 30 and 30 degrees, and the sum of adjacent angles in a parallelogram is 180 degrees. Similarly, the measure of angle C is 60 degrees.

The formula to find the area of a parallelogram is:

Area = base x height

We can choose any base and its corresponding height to find the area of the parallelogram. In the given figure, we can choose AB as the base and the perpendicular distance from AB to line DC as the height. Let's call this distance h.

From the figure, we can see that triangle ADE is a 30-60-90 triangle. The ratio of the sides in a 30-60-90 triangle is 1:sqrt(3):2. So, if AD is x, then DE is x*sqrt(3) and AE is 2x.

Since AE is parallel to DC, we can say that the height h is the same for triangles ADE and CFB. So, we can use triangle CFB to find the value of h.

Triangle CFB is a right triangle with angles 30, 60, and 90 degrees. The length of CB is 4 units and the length of CF is 2 units. So, the length of FB is 2*sqrt(3) units (using the ratio 1:sqrt(3):2). Therefore, the area of triangle CFB is:

Area = (1/2) x base x height

Area = (1/2) x 4 x 2

Area = 4

Since the area of triangle CFB is equal to the area of triangle ADE, we can say that:

Area of parallelogram ABCD = 2 x area of triangle CFB

Area of parallelogram ABCD = 2 x 4

Area of parallelogram ABCD = 8 square units

So, the area of the parallelogram is 8 square units.

The 95% confidence interval for the population mean, based on a sample size of n=8 with the outlier 25 included, is [1.53, 8.47]. When the outlier is replaced with 8, the confidence interval becomes [2.04, 6.96]. The presence of the outlier significantly affects the width of the confidence interval, causing it to be wider and less precise.

A confidence interval is a range of values that is likely to contain the true population mean with a certain level of confidence. In this case, we are constructing a 95% confidence interval, which means that there is a 95% probability that the true population mean falls within the interval.

The formula for calculating the confidence interval for the population mean, assuming a normal distribution, is:

\(CI = x^-\)±\(t * (s / \sqrt{n})\)

Where:

CI represents the confidence interval

\(x^-\) is the sample mean

t is the critical value from the t-distribution table based on the desired confidence level and degrees of freedom

s is the sample standard deviation

n is the sample size

In the given scenario, the initial sample contains the outlier 25, resulting in a wider confidence interval. When the outlier is replaced with 8, the confidence interval becomes narrower.

The presence of an outlier can have a significant impact on the confidence interval. Outliers are extreme values that are far away from the rest of the data. In this case, the outlier value of 25 is much larger than the other observations. Including this outlier in the calculation increases the sample standard deviation, which leads to a wider confidence interval. Conversely, when the outlier is replaced with a value closer to the rest of the data (8), the standard deviation decreases, resulting in a narrower confidence interval.

In conclusion, outliers can distort the estimate of the population mean and increase the uncertainty in the estimate. They can cause the confidence interval to be wider and less precise, as observed in the comparison of the two confidence intervals calculated with and without the outlier.

Learn more about confidence intervals  here:

https://brainly.com/question/31753211

#SPJ4

Answer: the answer is B

Step-by-step explanation:

Answer:

B. 16.2

Step-by-step explanation:

The angle is equal to a right angle so

90 - 73.8 = 16.2

x = 16.2

Answer: 13

Step-by-step explanation:

Initially, the tank contains 60 kg of salt, calculated by multiplying the salt concentration (0.06 kg/L) by the water volume (1000 L).

In the given scenario, the tank starts with a known salt concentration and water volume. By multiplying the concentration (0.06 kg/L) with the water volume (1000 L), we find that the initial amount of salt in the tank is 60 kg.

After 4.5 hours, considering the rate of water entering and leaving the tank, the net increase in solution volume is 810 L. Multiplying this by the initial concentration (0.06 kg/L), we determine that the amount of salt in the tank after 4.5 hours is 48.6 kg.

As time approaches infinity, with a constant inflow and outflow of solution, the concentration of salt in the tank stabilizes at the initial concentration of 0.06 kg/L.

Learn more about Multiplying click here :brainly.com/question/25834626

#SPJ11

The solution of the given equation is\(u(x,t) = ∑(-1)n+1 4/(nπ) sin(nπ/4) sin(nπx / 2) exp(-n^2 π^2 t / 4)\)

The given equation is Ut = 4uxx, 0 < x < 2,t > 0u(0,t) = 1, u(2,t) = 2, u(x,0) = sin(17x) — 4 sin(Tt x/2)

The general form of the solution is given as:

\(u(x,t) = B0 + B1 x + ∑[Bn cos(nπx / L) + Cn sin(nπx / L)] exp(-n^2 π^2 t / L^2)\)

Where,\(Bn = (2/L) ∫f(x) cos(nπx / L) dx; from x = 0 to L . . . . . (1)\)

\(Cn = (2/L) ∫f(x) sin(nπx / L) dx; from x = 0 to L . . . . . (2)\)

\(L = 2Bn\)

First we need to find the values of B0 and B1.

Given initial conditions are\(u(x,0) = sin(17x) — 4 sin(Tt x/2)\)

We can write \(u(x,0) = B0 + B1 x + ∑[Bn cos(nπx / L) + Cn sin(nπx / L)]\)

From the given function, comparing the coefficients of the Fourier series, we have

\(B0 = 0, B1 = 0, Bn = (2/L) ∫f(x) cos(nπx / L) dx; from x = 0 to L = 0; for n = 1, 2, 3, .......\)

\(Cn = (2/L) ∫f(x) sin(nπx / L) dx; from x = 0 to L = (-1)n+1 4/(nπ)sin(nπ/4); for n = 1, 2, 3, .......L = 2.\)

Using the values of Bn and Cn, we can write the solution as \(u(x,t) = ∑(-1)n+1 4/(nπ) sin(nπ/4) sin(nπx / 2) exp(-n^2 π^2 t / 4)\)

Therefore, the solution of the given equation is\(u(x,t) = ∑(-1)n+1 4/(nπ) sin(nπ/4) sin(nπx / 2) exp(-n^2 π^2 t / 4)\)

Know more about equations here:

https://brainly.com/question/17145398

#SPJ11

Answer:

C. The circle was translated down 5 units in dilated by factor of 1/3

Step-by-step explanation:

The circle was translated down 5 units in dilated by factor of 1/3

Answer:

C

Step-by-step explanation:

Answer:

Sorry but i can't help u.

Step-by-step explanation:

The slope intercept form of a line which passes through the points (-2, 5) and (6, -4)  is  y = (-9/8)x + 11/4.

According to the question.

A line passes through the two points (-2, 5) and (6, -4).

As we know that, the slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

So, the slope of the line = -4 -5/(6 + 2) = -9/8

And, the slope intercept form of a line which passes through the points (-2, 5) and (6, -4) is given by

y = (-9/8)x + b

Since, the line passes through (-2, 5) and (6, -4). So, both the points must statisfy the above equation.

⇒ 5 = (-9/8)(-2) + b

⇒ 5 = 9/4 + b

⇒ b = 5 - 9/4

⇒ b = (20 - 9)/4

⇒ b = 11/4

Therefore, the slope intercept form of a line which passes through the points (-2, 5) and (6, -4)  is  y = (-9/8)x + 11/4.

Find out more information about slope intercept form of a line here:

https://brainly.com/question/9682526

#SPJ4

Answer:

12 would be a common denominator

Step-by-step explanation:

2 4 6 8 10 (12)

3 6 9 (12)

4 8 (12)

Answer:

25 cubic feet

Step-by-step explanation:

You need to convert all units to feet and then multiply the dimensions.

24 inches is 2 feet

30 inches is 2.5 feet

So, you would multiply 5X2X2.5= 25.

Step-by-step explanation:

3.000976×10⁹ would be how I will write in standard form

Answer:

x² - 8x + 12

Step-by-step explanation:

(x - 2) (x - 6)

x² -6x -2x + 12

x² - 8x + 12
The picture shows the equation like that, so I solve it that way!

Answer:

Step-by-step explanation:

\(\tt (x-2)(x-6)\)

Use the FOIL method:-

→ \(\boxed{\bf (a+b)(c+d)=ac+ad+bc+bd}\)

\(\tt x^2-6x-2x+12\)

Combine like terms:-

\(\tt x^2+(-6x-2x)+12\)

Simplify:-

\(\tt x ^2-8x+12\)

______________________

Hope this helps! :)

Answer:

The answer is H. I think :)

Answer:

12 is a rational number because it can be expressed as the quotient of two integers: 12 ÷ 1.

12 belongs to the sets of natural numbers, integer numbers, rational numbers, and real numbers.

First, we can see that it is a whole number, so it is an integer number.

Also, all positive integers are natural numbers, so 12 is also a whole number.

Now, we also can rewrite 12 as:

12 = 12/1

So it is a quotient between two integer numbers, thus, 12 is also a rational number.

Finally, the trivial answer, 12 belongs to the set of the real numbers (the set that contains all the numbers).

Concluding:

12 belongs to the sets of whole numbers, integer numbers, rational numbers, and real numbers.

If you want to learn more about sets of numbers:

https://brainly.com/question/20118982

#SPJ1

The required statements and reasons to prove that DE is equal to CE is explained.

The triangle congruence theorem is a theorem that can be used to prove that two or more triangles are the same, considering the corresponding properties of the triangles. The properties are length of the sides, and measure of internal angles.

The statements and reasons to prove that DE is equal to CE are explained below using the triangle congruence theorem.

         STATEMENT                            REASON

1. AD = BC                                          Given

2. <BCD = <ADC                                Given

3. DC = DC                                         Reflexive property

4. ΔADC ≅ ΔBCD                              SAS

5. <EDC ≅ <ECD                                CPCTC

6. AC = BD                                          Definition of diagonal

7. DE = CE                                           Congruent sides of isosceles triangle

Learn more about the triangle congruence theorem at https://brainly.com/question/18922904

#SPJ1

Answer:

Using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

What is the right rectangular prism?

The right rectangular prism has four rectangle-shaped side faces and two parallel end faces that are perpendicular to each of the bases.

Parallelograms make up the sides of an oblique prism, a non-right rectangular prism.

A cuboid is yet another name for a right rectangle prism.

So, the volume of the right rectangular prism:

V = wlh

Insert values:

V = wlh

V = 6*8*4.5

V = 216cm³

Now, the volume of the cube:

V = a³

V = 2³

V = 8cm³

Then, the number of cubes that can be fitted in the right rectangular prism:

216/8 = 27

Therefore, using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

Know more about the right rectangular prism? here:

brainly.com/question/3317747

#SPJ1

Correct question:

How many cubes, with side measures of 2 cm, will fit inside a right rectangular prism with dimensions of 6 cm by 8 cm by 4 1/2 cm?

Group of answer choices

a. 24

b. 27

c. 108

d. 54

The final answer is 27

To determine how many cubes will fit inside the right rectangular prism, we need to find the volume of the prism and the volume of the cubes, then divide the volume of the prism by the volume of the cubes.

Volume of a cube (V_cube) = side^3
V_cube = 2 cm * 2 cm * 2 cm = 8 cubic cm

Volume of the right rectangular prism (V_prism) = length * width * height
V_prism = 6 cm * 8 cm * 4.5 cm = 216 cubic cm

Now, divide the volume of the prism by the volume of the cubes:
Number of cubes = V_prism / V_cube = 216 cubic cm / 8 cubic cm = 27 cubes

Therefore, 27 cubes with side measures of 2 cm will fit inside the right rectangular prism.

To know more about cubes visit : https://brainly.com/question/28134860

#SPJ11