State whether or not the following statements are true. Justify your reasoning.
a. a . (b + c) = a . b + a . c
b. a x (b + c) = a × b + a x c
c. a x (b.c) = a x b . a x c

1. The score a competitor obtained from a figure skating competition: This random variable is quantitative and discrete. The score is a numerical value that represents a specific outcome in the competition. It is discrete because it takes on specific, distinct values (e.g., 7.5, 8.2, 9.0) and cannot take on any value between those values.

2. The bearing in which a boat is traveling: This random variable is qualitative and discrete. The bearing represents a direction, such as north, south, east, or west. It is discrete because it takes on specific, distinct values from a set of possible directions.

3. The condition of a used car you're thinking about purchasing: This random variable is qualitative. The condition represents different categories or states, such as excellent, good, fair, or poor. It is qualitative because it involves descriptive categories rather than numerical values.

4. The capacity of a stapler with respect to staples: This random variable is quantitative and discrete. The capacity represents the number of staples a stapler can hold, which is a numerical value and can only take on specific, distinct values (e.g., 50, 100, 200).

5. The time it takes for your car to get an oil change: This random variable is quantitative and continuous. The time represents a duration and can take on any real value within a certain range. It is continuous because it can have infinite possible values within that range.

6. The amount of dietary fiber in a bag of Psyllium Husk: This random variable is quantitative and continuous. The amount of dietary fiber represents a measurable quantity, such as grams or milligrams, and can take on any real value within a certain range. It is continuous because it can have infinite possible values within that range.

Learn more about Random Variables here: brainly.com/question/17016472

#SPJ11

Let x be the amount of flour that was in the bag to start. The jar already had 4.5 cups of flour and he added enough flour to fill a 12-cup jar completely.

which means that 12 − 4.5 = 7.5 cups of flour were added to the jar. There was still some flour left over in the bag. Therefore, x − 7.5 > 0.5x > 8The inequality which represents the problem is 0.5 < x < 8Solving the inequality;0.5 < x < 8The above inequality represents that the flour that was initially in the bag should be between 0.5 cups and 8 cups inclusive. Then, complete the sentence to describe the solution;There were more than 0.5 cups of flour in the bag to start.

Learn more about amount here:

https://brainly.com/question/32379654

#SPJ11

column four 8, 15, 40, 45, 52.

Answer:

It's C. With more trials, the frequency of heads up will equal the frequency of tails up.

Step-by-step explanation:

edge

Answer:

4

thank youuuu

Step-by-step explanation:

have a good day

Answer:

\( m\angle A = 72\degree \\

m\angle B = 108\degree \)

Step-by-step explanation:

ABCD is a parallelogram.

Since, opposite angles of a parallelogram are congruent.

\( \therefore m\angle A = m\angle C\\

\therefore (5y-3)\degree = (3y+27)\degree \\

\therefore 5y - 3= 3y +27\\

\therefore 5y-3y = 27+3\\

\therefore 2y = 30\\\\

\therefore y = \frac{30}{2} \\\\

\therefore y = 15\\

\because m\angle A = (5y-3)\degree \\

\therefore m\angle A = (5\times 15-3)\degree \\

\therefore m\angle A = (75-3)\degree \\

\huge{\red {\boxed {\therefore m\angle A = 72\degree}}} \\\\

\because m\angle A + m\angle B = 180\degree(opposite \: \angle 's\: of\:a\: \parallel ^{gm}) \\

\therefore m\angle B = 180\degree - 72\degree \\

\huge{\purple {\boxed {\therefore m\angle B = 108\degree}}} \)

9514 1404 393

Answer:

  x = ±√((d -c)/a)

Step-by-step explanation:

The usual "solve for ..." approach works fine in this case.

  ax^2 +c = d

  ax^2 = d - c . . . . . subtract c

  x^2 = (d -c)/a . . . . divide by a

  x = ±√((d -c)/a) . . . take the square root

_____

When there are numbers, a graphical solution could work. It depends on whether an exact or approximate solution is required.

_____

Comment on "solve for ..."

When solving an equation for a specific variable, it is worthwhile to consider the Order of Operations. Look at what has been done to the variable, then undo those operations in reverse order. Here, the variable has been squared, the product multiplied by 'a', that product added to c. So, the "undo" consists of subtracting 'c', dividing by 'a', and taking the square root.

Answer:

h=60 2h=120

Step-by-step explanation:

the sum of 4 angles of a quadrilateral is 360 degree. so h+h+2h+2h=360

h=60 and 2h=120

Answer:

I hope it helps mate

as I promised I will help you

I will always help you understanding your assingments

enjoy your day

#Captainpower:)

the scale factor of the dilation is k = 2.

As a result, the points on line r' are situated twice as far from the starting point as their counterparts on line r.

The scale factor is a numerical value used to compare two measurements or objects. It is used to determine the proportion between two objects that have different measurements. It is used to describe how much larger or smaller one measurement is in comparison to another.

A dilation is a transformation that changes the size of a figure. In the case of line r, the dilation is a transformation that changes the size of the line.

from the question;

We need to know how much the line is being stretched or contracted in order to calculate the scale factor k of the dilation that converts line r to line r'.

Any location on the original liner that is d distance from the origin will be mapped to a place on the dilated line r' that is k * d away from the origin since the origin is the center of the dilation.

Looking at the diagram, we can see that line r passes through the points (1,2) and (5,4), which are both a distance of\(\sqrt{(1^2 + 2^2)}\) = \(\sqrt{5}\) from the origin.

Line r' passes through the points (2,4) and (10,8), which are both a distance of sqrt\((2^2 + 4^2) = 2*\sqrt{5}\) from the origin.

k = 2

Hence, k = 2 is the scale factor for the dilation. As a result, the points on line r' are situated twice as far from the starting point as their counterparts on line r.

Learn more about scale here:

https://brainly.com/question/30215119

#SPJ1

Answer:  20%

Step-by-step explanation:

if 500 = 100kg

          = 10kg

     50 = 10kg

%Profit = S.P/B.P *100

%Profit = 60/50 *100

%Profit = 120%

%Profit = 120% -100% = 20%

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

1 day

Step-by-step explanation:

Assuming all the electricians work at the same rate, we can use the formula:

(time x workers) = constant

So, if 2 electricians took 5 days, we have:

(5 x 2) = (time x 10)

Simplifying, we get:

10 = time x 10

Dividing both sides by 10, we get:

time = 1

Therefore, it would take 10 electricians 1 day to wire the house.

Answer:

Eliana saves at a greater rate because her unit rate of $42 per week is greater than Lana's unit rate of $40 per week

hope this helps =3

sorry if im wrong

The rent expense allocated to each department is as follows: Jewelry department: $30,800, Cosmetics department: $46,200, Housewares department: $21,000, Tools department: $9,000, Shoes department: $18,000.

The retailer allocates 70% of the total rent expense to the first floor and 30% to the second floor. Then, the rent expense for each floor is allocated to the departments based on the square footage they occupy. By applying these allocation percentages and calculations, we determined the rent expense for each department.

Rent expense allocation:

- Jewelry department (1,760 sq ft on the first floor): ($130,000 * 70% * 1,760 sq ft) / (1,760 sq ft + 2,640 sq ft) = $30,800

- Cosmetics department (2,640 sq ft on the first floor): ($130,000 * 70% * 2,640 sq ft) / (1,760 sq ft + 2,640 sq ft) = $46,200

- Housewares department (1,848 sq ft on the second floor): ($130,000 * 30% * 1,848 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $21,000

- Tools department (792 sq ft on the second floor): ($130,000 * 30% * 792 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $9,000

- Shoes department (1,760 sq ft on the second floor): ($130,000 * 30% * 1,760 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $18,000

To know more about rent each year, click here: brainly.com/question/29133557

#SPJ11

A retailer pays \( \$ 130,000 \) rent each year for its two-story building. Space in this building is occupied by five departments as shown here.

Jewelry department - 1,760 square feet of first-floor space

Cosmetics department - 2,640 square feet of first-floor space

Housewares department - 1,848 square feet of second-floor space

Tools department - 792 square feet of second-floor space

Shoes department - 1,760 square feet of second-floor space

The company allocates 70% of total rent expense to the first floor and 30% to the second floor, and then allocates rent expense for each floor to the departments occupying that floor on the basis of space Occupied.

Determine the rent expense to be allocated to each department

The intersection of the parabola and the circle will be (6.865, 1.366) and (6.865, -1.366).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

y² = x - 5                   ...1

x² + y² = 49              ...2

From equations 1 and 2, then we have

x² + x - 5 = 49

x² + x - 54 = 0

Use the formula method to calculate the value of 'x'. Then we have

x = [- 1 ± √(1² - 4 · 1 · -54)] / 2

x = [- 1 ± √(1 + 216)] / 2

x = (- 1 ± 14.7309) / 2

x = (- 1 - 14.7309) / 2, (- 1 + 14.7309) / 2

x = -7.865, 6.865

Then the value of the variable 'y' is given as,

y² = x - 5

y² = 6.865 - 5

y² = 1.865

y = ± 1.366

The intersection of the parabola and the circle will be (6.865, 1.366) and (6.865, -1.366). And the graph is given below.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

A) Approx. 1067 is the required sample size to ensure 95% confidence that the sample proportion will not differ from the true proportion by more than 3%.

B) When the previous estimate is 65%, approx. 971 is the sample size needed to achieve 95% confidence that the sample proportion will not differ by more than 3% from the true proportion.

To determine the sample size needed for estimating the proportion of drivers exceeding the speed limit, we can use the formula for sample size calculation for proportions:

n = (Z² * p * (1 - p)) / E²

where:

n = the sample size.

Z = the Z-value associated with the confidence level of 95%.

p = the estimated proportion or previous estimate.

E = the maximum allowable error, which is 3% or 0.03.

We calculate as follows:

A. No previous estimate for p is available:

Here, we will assume p = 0.5 (maximum variance) since we don't have any prior information about the proportion. So, adding the values into the formula:

n = (Z² * p * (1 - p)) / E²

n = ((1.96)² * 0.5 * (1 - 0.5)) / 0.03²

n= (3.842 * 0.5 * (0.5))/0.03²

n = (1.9208*0.5)/0.0009

n ≈ 1067.11

Thus, to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%, a sample size of approximately 1067 is required.

B. Supposing previous studies found that the sample percentage of drivers who exceeded the speed limit is 65%:

Here, we have a previous estimate of p = 0.65:

Putting the values into the formula:

n = (Z²* p * (1 - p)) / E²

n = ((1.96)² * 0.65 * (1 - 0.65)) / 0.03²

n= (3.842 * 0.65 *(0.35))/0.0009

n ≈ 971

Hence, with the previous estimate of 65%, a sample size of approximately 971 is necessary to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%.

Learn more about sample size calculation at brainly.com/question/30647570

#SPJ4

Company A has a higher risk percentage (55%) compared to Company B (3%).

To compute the Coefficient of Variation (CV) for each company, we need to use the formula:

CV = (Standard Deviation / Mean) * 100

Let's calculate the CV for each company:

For Company A:

Risk Percentage = 55%

Return = 14%

For Company B:

Risk Percentage = 3%

Return = 14%

Since we don't have the standard deviation values for each company, we cannot calculate the exact CV. However, we can still compare the riskiness of the two companies based on the provided information.

The Coefficient of Variation measures the risk relative to the return. A higher CV indicates higher risk relative to the return, while a lower CV indicates lower risk relative to the return.

In this case, Company A has a higher risk percentage (55%) compared to Company B (3%), which suggests that Company A is riskier. However, without the standard deviation values, we cannot make a definitive conclusion about the riskiness based solely on the provided information. The CV would provide a more accurate measure for comparison if we had the standard deviation values for both companies.

To learn more about standard deviation

https://brainly.com/question/475676

#SPJ11

The reliability of a two-component product if the components are in parallel, with individual reliabilities of 0.95, and 0.80 is 0.99. The answer is option b.

The probability that a specific object will carry out its intended function for a specific amount of time under a specific set of circumstances without experiencing any failures is known as reliability.

The reliability definition is based on four criteria: function, fulfillment likelihood, duration, and environment. Maintainability and reliability are related because when a machine or product malfunctions, there may be a way to get it back into working order.

When we use the phrase "talking reliability-smart," we mean that any of the aspects that shape the device in parallel can be considered. This does not necessarily imply that they are physically parallel (in all circumstances), as parallel capacitors have a certain behavior in the circuit and may malfunction if one of them fails.

Parallel forms reliability is a measure of reliability obtained by giving the same set of people different versions of an assessment tool (each version must contain items that probe the same construct, talent, knowledge base, etc.

The complete question is given below:-

What is the reliability of a two-component product if the components are in parallel, with individual reliabilities of 0.95, and 0.80?

a. 0.875

b. 0.99

c. 0.95

d. 0.76

e. 0.80

Learn more about reliability here:

brainly.com/question/1265793

#SPJ4

Answer:

The first one is quadratic equation

Answer:

the alternate interior angles theorem.

Hope this helps.. Good Luck!

Answer:

  F' corresponds to point F

Step-by-step explanation:

When a point is the result of some transformation, we often designate that result using the base name of the original, with a prime (') added. In this case, we expect that F' is the transformation of point F.

__

Comment on point naming

Of course, points can be given any name you like. These conventions are adopted to aid in communication about transformations and correspondence between points. It would be unusual--even confusing, but not unreasonable, for point F' to correspond to point D, for example. In the case of certain transformations, point F' may actually be point D.

Answer:

C

Step-by-step explanation:

Point F.

Answer:

again i can not see the given point

Step-by-step explanation:

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

Learn more about Profitability index

https://brainly.com/question/30641835

#SPJ11

Answer:

The coordinates of its image are (2, -4)

Step-by-step explanation:

Let us revise the rules of reflection across the axes

∵ The point (2, 4) is reflected across the x-axis

→ By using the first rule above rx-axis (x, y) → (x, -y)

∴ Change the sign of its y-coordinate

∴ Its image is (2, -4)

∴ The coordinates of its image are (2, -4)

In this exercise, we are given two functions f and g, and an interval [a, b]. We are asked to find the area between the graphs of f and g from x=a to x=b using definite integrals and the Fundamental Theorem of Calculus. The process involves finding the antiderivatives of the functions f and g, and then subtracting the values of the antiderivatives at a and b.

In particular, for this problem, we have f(x) = 8(x) = 6 - |x - 2| and the interval [3, 7). We can split the interval into two parts: [3, 5) and [5, 7). On the first part, the function f(x) is equal to 8(x) = 6 - (2 - x) = x + 4. On the second part, the function f(x) is equal to 8(x) = 6 - (x - 2) = 8 - x. Therefore, we can write the integral for the area between the graphs of f and g as follows:

∫[3,5) [f(x) - g(x)] dx + ∫[5,7) [f(x) - g(x)] dx

Substituting the functions f and g, we get:

∫[3,5) [(x+4) - 3] dx + ∫[5,7) [(8-x) - 3] dx

Evaluating the integrals, we get:

[(1/2)x^2 + 4x - 3x] from 3 to 5 + [(8x - (1/2)x^2) - 15] from 5 to 7

Simplifying, we get:

8

Therefore, the exact area between the graphs of f and g from x=3 to x=7 is 8 square units.

To learn more about Fundamental Theorem, click here:

brainly.com/question/30761130

#SPJ11

The answer is A) Line y = 5x + 6 intersects the line y = −x − 7.

Here, we have,

given that,

the equations are:

y = 5x + 6

y = −x − 7

so, solving the given equations ,we get,

5x + 6 = -x - 7

6x + 6 = -7

6x = -13

x = -13/6

y = 5(-13/6) + 6

y = -29/6

The solution is (-13/6, -29/6) and that tells us that the two lines do not intersect at the origin or any of the two axis.

If they intersected at the origin, then the solution should have been (0, 0).

If they intersected at the x-axis, the solution should have been (x, 0).

If the two lines intersected at the y-axis, the solution would have been (0, y).

The answer is A) Line y = 5x + 6 intersects the line y = −x − 7.

To learn more on equation click:

brainly.com/question/24169758

#SPJ1

complete question:

Consider the following system of equations: y = 5x + 6 y = −x − 7 Which description best describes the solution to the system of equations?

Line y = 5x + 6 intersects line y = −x − 7.

Lines y = 5x + 6 and y = −x − 7 intersect the x-axis.

Lines y = 5x + 6 and y = −x − 7 intersect the y-axis.

Line y = 5x + 6 intersects the origin.

Answer:

we minus 0.25 from 35

Step-by-step explanation:

35_0.25

Answer:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion

You can carve out 150 cubes of side 0.1 m from the given block of wood.

To determine the number of cubes, we need to calculate the volume of the block and the volume of each cube.

The volume of the block is given by:

Volume = length × width × height

Volume = 75 cm × 50 cm × 40 cm

Converting the measurements to meters:

Volume = (75 cm / 100) m × (50 cm / 100) m × (40 cm / 100) m

Volume = 0.75 m × 0.5 m × 0.4 m

Volume = 0.15 m³

The volume of each cube is given by:

Volume of each cube = side³

Volume of each cube = (0.1 m)³

Volume of each cube = 0.001 m³

To find the number of cubes that can be carved out of the block, we divide the volume of the block by the volume of each cube:

Number of cubes = Volume of block / Volume of each cube

Number of cubes = 0.15 m³ / 0.001 m³

Number of cubes = 150

Therefore, you can carve out 150 cubes of side 0.1 m from the given block of wood.

For more information on volume visit: brainly.com/question/11608639

#SPJ11