A college’s data about the incoming freshmen indicates that the mean of their high school GPAs was 3.4, with a standard deviation of 0.35; the distribution was roughly mound-shaped and only slightly skewed. The students are randomly assigned to freshman writing seminars in groups of 25. What might the mean GPA of one of these seminar groups be? Describe the appropriate sampling distribution model—shape, center, and spread— with attention to assumptions and conditions. Make a sketch using the 68–95–99.7 Rule.

The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]

Step-by-step explanation:

We have to add the fractional weight of both boxes to find the combined weight of both boxes.

Given

Weight of Box 1: [tex]8\frac{2}{9}[/tex] kilograms

Weight of Box 2: [tex]3\frac{2}{10}[/tex] kilograms

So the total weight will be:

[tex]= 8\frac{2}{9} + 3\frac{2}{10}[/tex]

Simplifying the fractions

[tex]=\frac{74}{9} + \frac{32}{10}\\\\= \frac{74(10)+32(9)}{90}\\\\=\frac{740+288}{90}\\\\=\frac{1028}{90}\\\\=11\frac{38}{90}\\\\=11\frac{19}{45}\\[/tex]

Hence,

The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]

Keywords: Fractions, addition

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Answer:

Area of each tile = 19.5 inches^2

Step-by-step explanation:

Rhombus:-

A rhombus is a type of quadrilateral whose opposite sides are parallel and equal.Also, the opposite angles of a rhombus are equal and the diagonal intersect each other perpendicularly.

To find the area of a rhombus when the measures of its height and side length are given, use the formula

A = Base X height

Area of a rhombus = 6.5 X  3

                          A      = 19.5 inches^2

The area of each rhombus-shaped tile is 19.5 square inches for the given dimensions. Thus, each tile has an area of 19.5 square inches.

To find the area of a rhombus, you can use the formula

⇒ Area = base × height

In this case, the height is given as 3 inches and the length of each side is 6.5 inches, but the length of the sides is not needed, as we are working with the base and height directly.

So, the area can be calculated as follows:

⇒ Base = 6.5 inches

⇒ Height = 3 inches.

⇒ Area = base × height.

⇒ Area = 6.5 inches × 3 inches

= 19.5 square inches.

Therefore, the area of each rhombus-shaped tile is 19.5 square inches.

Answer:

The expression that represents the number of hits he got in the rest of the​ games is [tex]t=52-h[/tex].

Step-by-step explanation:

Given:

Number of hits in one season = 52 hits

Number of hits in one game = 'h'

We need to write expression that represents the number of hits he got in the rest of the​ games.

Solution:

Let the number of hits he got in the rest of the​ games be 't'.

Now we can say that;

The number of hits he got in the rest of the​ games is equal to Number of hits in one season minus Number of hits in one game.

framing in equation form we get;

[tex]t=52-h[/tex]

Hence expression that represents the number of hits he got in the rest of the​ games is [tex]t=52-h[/tex].

Answer:

52 - h

Step-by-step explanation:

Simplify: 52 - h

Answer:

B

Step-by-step explanation:

The discrete type of data contains observations that can be counted and consists of finite set of data. In the given problem the votes received by Derek consists of finite set of value and votes received by Derek are countable.

Hence the votes received by Derek  is discrete data set because there is finite number of values.

The distance between the harbor and the island is 20 nautical miles.

To find the distance between the harbor and the island, we need to calculate the average speed of the motorboat for the entire trip. Since the average speed on the outbound trip was 10 knots and the average speed on the return trip was also 10 knots, we can conclude that the boat traveled at a constant speed throughout the trip. Let's assume the distance between the harbor and the island is 'd'.

Since speed = distance / time, we can calculate the time taken for each leg of the trip using the average speeds and the total time of 4.0 hours:

Time taken for the outbound trip = d / 10 knots

Time taken for the return trip = d / 10 knots

Since the total time is 4.0 hours, we can write the equation: d / 10 + d / 10 = 4.0

Simplifying the equation, we get: 2d / 10 = 4.0

Multiplying both sides by 10, we get: 2d = 40

Dividing both sides by 2, we get: d = 20

Therefore, the distance between the harbor and the island is 20 nautical miles.

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The equations that are true according to the exponent rules for powers of 10 include: [tex]10^5 / 10^3 = 10^5-3, 10^5 * 10^3 = 10^5+3,[/tex] and [tex]10^5 / 10^3 = 10^5-3.[/tex]

The subject in question deals with exponent rules for powers of 10. Here, we'll identify which equations are true based on these rules:

a. (10^5)^3 = 10^5×3. This is not correct. According to the power of a power rule, we should multiply the exponents, so the answer should be 10^15.

b. [tex]10^5 / 10^3 = 10^5-3.[/tex] This is correct. When dividing bases that are the same, we subtract the exponent of the denominator from the exponent of the numerator, hence 10^(5-3) = 10^2.

c. 10^5 × 10^3 = 10^5+3. This is correct. When multiplying bases that are the same, we add the exponents, hence 10^(5+3) = 10^8.

d. [tex]10^5 / 10^3 = 10^5-3[/tex]. This is correct, as explained in point b. The answer is 10^2.

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Final answer:

Equation c [tex](10^5*10^3 = 10^{(5+3)})[/tex] and equations b and d [tex](10^5/10^3 = 10^{(5-3)})[/tex] are correct. To multiply or divide numbers in scientific notation, multiply or divide the coefficients and add or subtract the exponents, respectively. This method can be used to calculate without converting to standard form.

Explanation:

The equations that are true out of the ones provided are as follows:

To evaluate (8.552 × 10^6) ÷ (3.129 × 10^3) without entering scientific notation into your calculator, first divide the coefficients (8.552 ÷ 3.129) and then subtract the exponents for the powers of 10 (10^6 ÷ 10^3 = 10^(6-3) or 10^3). The result is approximately 2.73189 × 10^3.

Answer:

[tex]\sqrt{29}[/tex]

Step-by-step explanation:

The complex number x + yi can be expressed in coordinate form as

x + yi → (x, y ), thus

4 + 3i → (4, 3 )

6 - 2i → (6, - 2 )

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (6, - 2)

d = [tex]\sqrt{(6-4)^2+(-2-3)^2}[/tex]

   = [tex]\sqrt{2^2+(-5)^2}[/tex]

   = [tex]\sqrt{4+25}[/tex]

   = [tex]\sqrt{29}[/tex]

Answer:

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

The perimeter of a rectangle is 48 in. It means that

48 = 2(L + W)

L + W = 48/2

L + W = 24 - - - - - - - - - 1

the length of the rectangle is 6 in greater than the width. It means that

L = W + 6

Substituting L = W + 6 into equation 1, it becomes

W + 6 + W = 24

2W + 6 = 24

2W = 24 - 6 = 18

W = 18/2 = 9

L = W + 6 = 9 + 6 = 15

Final answer:

The student's problem involves finding the length and width of a rectangle given its perimeter and the fact that the length is 6 inches greater than the width. To solve it, we defined the width as a variable, set up an equation based on the perimeter, and used substitution to find that the width is 9 inches and the length is 15 inches.

Explanation:

The perimeter of a rectangle is given by the formula 2(length + width). In the stated problem, we are given the total perimeter (48 inches) and told that the length is 6 inches greater than the width. We can define the width as w and the length as w + 6. So, the perimeter equation is:

2(w + (w + 6)) = 48

Now that we have the width, we can find the length using substitution:

w + 6 = 9 + 6 = 15

Therefore, the width is 9 inches and the length is 15 inches.

Answer:the point slope form is

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

Step-by-step explanation:

The point slope form of a line is expressed as

y - y1 = m(x - x1)

Where

m represents the slope of the line.

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

From the information given,

slope, m = - 1/2

y1 = - 1

x1 = 6

Therefore, the point slope eqy would be

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

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

Answer:

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

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

Step-by-step explanation:

Answer:

i say its c or b

Step-by-step explanation:

Answer:

  C.  1 3/4 - (a fraction less than 3/4)

Step-by-step explanation:

Your number sense should be able to help you with this one.

A. 5 × 1/10 = 1/2, not a number greater than 1

B. 4/9 + 1/3 = 7/9, not a number greater than 1

C. 1 3/4 -1/2 = 1 1/4, a number greater than 1 (see below for more explanation)

D. 7/8 × 1/2 = 7/16, not a number greater than 1.

__

More explanation

Let x represent a number less than 3/4. Then we want to make sure that ...

  y = 1 3/4 - x

will be greater than 1.

Solving for x, we get ...

  x = 1 3/4 - y

Applying the requirement that x < 3/4, we have ...

  x < 3/4

  (1 3/4 -y) < 3/4

  1 3/4 < y + 3/4 . . . . . . add y

  1 < y . . . . . . . . . . . . . . .subtract 3/4

We see that the condition on x makes sure that y is always greater than 1.

When y = 3, the value of z is 2.

Since x is directly proportional to y and inversely proportional to z, we can write this relationship as:
[tex]x = k \frac{y}{z}[/tex]
where k is a constant of proportionality.

We are given the values x = 3, y = 6, and z = 4. Let's use these values to find k.

[tex]3 = k \frac{6}{4}[/tex]

Simplifying this, we get:

[tex]3 = k \cdot 1.5[/tex]

Solving for k:

[tex]k = \frac{3}{1.5} = 2[/tex]

Now we know the constant k. We can use it to find z when y = 3.

We know the relationship:

[tex]x = 2 \frac{y}{z}[/tex]

We need to find z when x = 3 and y = 3.

[tex]3 = 2 \frac{3}{z}[/tex]

Rearranging to solve for z:

[tex]3 = 6 \div z[/tex]

[tex]z = 2[/tex]

Answer:

Line segment is part of a line bounded by two endpoints

Step-by-step explanation:

Line segment is part of a line bounded by two endpoints

Answer: B

Step-by-step explanation:

Mathematical statements are those that can be objectively proven true or false. Among the options provided, statements B and F qualify as mathematical statements. Therefore, the correct answer choice is A.

The student asks which of the following statements are mathematical statements:

A: All the ladies love me.
B: 5 = 7
C: Contemporary Math is the best class ever.
D: Bye, Felicia!
E: The square root of 64 is 8 something, right?
F: If the storm is coming, then the sky is blue.

Mathematical statements are statements that can be objectively proven true or false.

Thus, the correct answer is A. B, F

Answer: 38

Step-by-step explanation:

14 - 2xy

(substitute x and y)

14 - 2 (-6) (2)

14 + 24

38

Answer:

its 38

Step-by-step explanation:

Do xy first and you get -24 and 14-(-28) would be a double negative so you add them together.

Answer:

  £375

Step-by-step explanation:

The tax changed from 17.5% of the car's price to 20% of the car's price, an increase of 2.5% of the car's price.

The increased tax amount is ...

  0.025 × £15000 = £375

The price of the car went up by £375 due to the increase in VAT.

Answer:

The answer to your question is A coordinate plane with a line passing through (0, -3) and (2,0)

Step-by-step explanation:

Line

                             3x - 2y = 6

Solve for y

                              -2y = -3x + 6

                                 y = 3/2 x - 3

Find "y" when x = 0

                                 y = 3/2(0) - 3

                                 y = -3                      Point (0, -3)

Find "x" when y = 0

                                0 = 3/2x - 3

                                 3 = 3/2 x

                                x = 6/3

                                x = 2                       Point (2, 0)

The graph of the equation 3x - 2y = 6 passes through the points (0, -3) and (2, 0). This conclusion is reached after rearranging the equation into the slope-intercept form and comparing the slope and the y-intercept with coordinates of the given lines.

To find the correct graph for the equation 3x - 2y = 6, we first need to rearrange the equation in the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.

We rearrange our equation as follows: 3x - 6 = 2y. Simplifying, we get y = 1.5x - 3.

This equation tells us that the y-intercept (where the line crosses y-axis) is -3, and the slope is 1.5, in other words, for each step in positive x-direction, y increases by 1.5 steps.

Now looking at our coordinate plane options, the graph that fits this description is the one with a line passing through the points (0, -3) and (2, 0). Hence, this is the graph of the given equation.

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Answer:

After evaluating the given expression we get the value as 4.

Step-by-step explanation:

Given:

[tex]\frac{j}{k}-0.2k[/tex]

We need to evaluate the expression when j =25 and k =5

Solution:

On substituting the values of k and j in the expression we get;

[tex]\frac{25}{5}-0.2\times5[/tex]

We will use PEDMAS which means first operation performed will be division.

So we can say that;

[tex]5-0.2\times5[/tex]

Now next Operation to be performed is multiplication.

So we can say that;

[tex]5-1[/tex]

Finally we will use subtraction operation and then we will get;

[tex]4[/tex]

Hence After evaluating the given expression we get the value as 4.

Answer:

6

Step-by-step explanation:

Answer: the number of hotdogs that were sold is 35

the number of orders of fries is 52

Step-by-step explanation:

Let x represent the number of hotdogs that were sold.

Let y represent the number of orders of fries.

You sold a total of 87 hotdogs and orders of fried combined. This means that

x + y = 87

Each hot dog costs 1.50 and each order of fries costs 0.50. At the end of the night you made a whopping $78.50! This means that

1.5x + 0.5y = 78.5 - - - - - - - - - - -1

Substituting x = 87 - y into equation 1, it becomes

1.5(87 - y) + 0.5y = 78.5

130.5 - 1.5y + 0.5y = 78.5

- 1.5y + 0.5y = 78.5 - 130.5

- y = - 52

y = 52

Substituting y = 52 into x = 87 - y, it becomes

x = 87 - 52

x = 35

Answer:

Smallville is growing at a greater rate

Step-by-step explanation:

use the formula for percentage increase to find what percentage the population of Bigville increased.

(Increase ÷ original number) * 100 = % of increase

increase = 571,533 - 387,480 = 184,053

(184,053 ÷ 387,480) * 100 = 47.5

Bigville percent of increase is 47.5%

Smallville percent of increase is 53.67%

since, smallville has a bigger percentage, it is growing at the greater rate  

Answer:

$828

Step-by-step explanation:

15% = 0.15

0.15 x 720 = 108

total cost = $720 + $108 = $828

Final answer:

To find the total cost of an iPad that is on sale at 15% off with a 6% sales tax, calculate the discount, subtract it from the original price, determine the sales tax, and add it to the discounted price.

Explanation:

To find the total cost of the iPad:

Calculate the discount: $720 * 15% = $108 discount

Subtract the discount from the original price: $720 - $108 = $612

Calculate the sales tax: $612 * 6% = $36.72

Add the sales tax to the discounted price: $612 + $36.72 = $648.72

Answer:

  40 mph

Step-by-step explanation:

We assume "outbound" refers to the trip to the lake. The ratio of speeds is inversely proportional to the ratio of times, so ...

  outbound speed : inbound speed = 4 : 3

These differ by one ratio unit, so that one ratio unit corresponds to the speed difference of 10 mph. Then the 4 ratio units of outbound speed will correspond to ...

  4×10 mph = 40 mph

Paul's average speed on the outbound trip was 40 mph.

___

The distance to the lake was 120 mi.

Answer:Paul's average speed on the outbound trip is 40mph

Step-by-step explanation:

Let x represent Paul's outbound trip which is the trip to the lake.

The trip to the lake took 3 hours.

Distance travelled = speed × time

It means that

Distance covered on the trip to the lake would be

3 × x = 3x

the trip back took 4 hours. He averaged 10 mph faster on the trip there than on the return trip. It means that his speed would be

x - 10

Therefore, distance travelled on return trip would be

4(x - 10) = 4x - 40

Since the distance travelled is the same, it means that

3x = 4x - 40

4x - 3x = 40

x = 40

The truck, experiencing a force of 1500 N, skids a distance of 25 meters, resulting in a change in kinetic energy of 37,500 J. Now, let's break down the concept of kinetic energy and the given data:

Definition of Kinetic Energy:

Kinetic energy, in physics, is the energy possessed by a moving object.

It represents the effort required to accelerate an object of a specific mass from rest to a particular velocity.

The body retains its kinetic energy even with slight speed variations, maintaining the energy acquired during acceleration.

Kinetic Energy Conservation:

When the body decelerates from its current velocity to a state of rest, the same amount of energy is expended.

Formal Definition:

Kinetic energy is formally described as any quantity exhibiting a gradient with respect to time in the Lagrangian of a system.

Given Data:

Force (F) = 1500 N

Distance (d) = 25 m

Calculation of Change in Kinetic Energy:

Utilize the formula for change in kinetic energy: ΔK.E = F × d

Substitute the values: ΔK.E = 1500 × 25

This results in ΔK.E = 37,500 J.

Therefore, the observed change in kinetic energy for the truck, moving a distance of 25 meters with a force of 1500 N, is precisely 37,500 J.

Complete questions

A truck skids for a distance of 25 m with the road pushing on its tires with force of 1500 N as its brakes are applied. What is the change in kinetic energy for the truck? Round the answer to two significant digits.J

Answer:

The answer is C

Step-by-step explanation:

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. Example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (5,-4)

Answer:

The answer is 118.

Step-by-step explanation:

First we need to subtract the meal cost from average unit cost for each meal:

[tex]7-5.75=1.25[/tex]

A restaurant profits 1.25$ for each meal. If we divide fixed cost to profit for each meal:

[tex]147.5/1.25=118[/tex]

The restaurant have to sell 118 meals at least each day for the owner to break even

Answer:the equation relating E to H is

E = 20H

Step-by-step explanation:

Let E represent her earnings (in dollars) after tutoring for H hours.

For each hour that she tutors, she earns 20 dollars. This means that in H hours, her total earnings would be

E = 20H

To find Mai's earnings after tutoring for 17 hours, we would substitute H = 17 into the equation. It becomes

E = 20 × 17

E = $340

Mai's earnings [tex](\(E\))[/tex] after tutoring for 17 hours would be $340, calculated as [tex]\(E = 20 \times 17\).[/tex]

To relate Mai's earnings [tex](\(E\))[/tex] to the number of hours she tutors [tex](\(H\))[/tex], we can use the following equation:

[tex]\[E = 20H\][/tex]

This equation represents that Mai earns $20 for each hour she tutors. By multiplying the number of hours [tex](\(H\))[/tex] by the rate of $20 per hour, we get her total earnings [tex](\(E\))[/tex].

Now, to find Mai's earnings after tutoring for 17 hours, we can plug in [tex]\(H = 17\)[/tex] into the equation:

[tex]\[E = 20 \times 17\][/tex]

[tex]\[E = 340\][/tex]

So, Mai's earnings after tutoring for 17 hours would be $340.

Answer:

Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2

(i) Monday

(ii) Tuesday

(iii) Wednesday

(iv) Thursday

Ans

(iv)Thursday

Step-by-step explanation:

Forecast for

Monday +4 Abs |+4| = 4

Tuesday –6 Abs |-6| = 6

Wednesday +7 Abs |+7| = 7

Thursday –2 Abs |-2| = 2

The most accurate is the day closest the temperature forecast is closest to observed temperature, which is

Thursday (-2)

Answer:

it is thursday

Step-by-step explanation:

hope it helps

Answer:

729

Step-by-step explanation:

The first term is 1 in the geometric sequence 1, −3, 9, −27, . .

First find out the nth term formula for the geometric sequence

[tex]a_n=a_1(r)^{n-1}[/tex]

where a_1 is the first term =1

r is the common ratio,

[tex]\frac{-3}{1}=-3[/tex]

[tex]\frac{9}{-3}=-3[/tex]

[tex]\frac{-27}{9}=-3[/tex]

r=-3, a_1=1

[tex]a_n=a_1(r)^{n-1}[/tex]

[tex]a_n=1(-3)^{n-1}[/tex]

Now find out the seventh term, n=7

[tex]a_7=1(-3)^{7-1}=729[/tex]

To find the seventh term of the geometric sequence 1, −3, 9, −27, ..., we calculate the common ratio and use it in the formula for the n-th term. The common ratio is −3 and the seventh term turns out to be 729. So the correct option is  E.

Calculating the SEVENTH Term of a Geometric Sequence

The given geometric sequence is 1, −3, 9, −27, ... and we are asked to find the seventh term. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio (r). To find the common ratio, we can divide the second term by the first term, or the third term by the second term, and so on.

Common ratio (r) calculation:
Divide the second term (−3) by the first term (1), which gives us r = −3.

To find the seventh term, we use the formula for the n-th term of a geometric sequence, which is:
a_n = a_1 × r^(n-1), where a_n is the n-th term, a_1 is the first term, and n is the term number.

Seventh term calculation:
a_7 = 1 × (−3)^(7-1) = 1 × (−3)^6. Since −3 to an even power is positive, the answer is 1 × 3^6 = 729.

Therefore, the seventh term of the geometric sequence is 729.