assume that the fleet consists of 25 percent lexus, 30 percent infinity, and 45 percent mercedes automobiles. 35 percent of the lexus cars, 85 percent of the infinities, and 80 percent of the mercedes have cd players. use this information to answer the following questions. (1) what is the probability that a randomly selected car has a cd player? equation editor equation editor (2) what is the probability that a randomly selected car either is a mercedes or has a cd player?

The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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Answer:

b

Step-by-step explanation:

The equation that represents the graph will be y > 3x + 2. Then the correct option is B.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

From the graph, the two points are (0, 2) and (-3, -7). The region above the line is considered, then the equation is written as,

(y - 2) > [(2 + 7) / (0 + 3)] (x - 0)

y - 2 > 3x

y > 3x + 2

The equation that represents the graph will be y > 3x + 2. Then the correct option is B.

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Answer: There are no solutions.

Step-by-step explanation: Hope this help :D

Answer:

FD = 25.9

Step-by-step explanation:

13x - 16 = 4x + 11

9x = 27

x = 3

using Pythagorean theorem:

FD²  = 12² + [4(3) + 11]²

FD² = 144 + 23² = 144 + 529 = 673

FD = 25.94

The constant speed which is must so that he complete the journey of 250 km distance in 2 hours is equals to the 125 km/h.

Travelled average speed, V =100 km/h

Time taken by motorist travels to completes his journey = 2 1/2 hours

= 5/2 hours

Let the cost speed with which he travel to complete the journey in 2 hours be " x km/h". We have to calculate the value of x. A constant speed is something that changes steadily or no change over time and an average rate or speed is the overall speed of something that travels at different speeds or rates over time.

Average speed = total distance/ total time taken to travel the distance

Let us consider "L km" be the total distance travelled by motorist with an average speed of 100 km/h.

=> 100 km/h = L km/(5/2) hours

=> 100 = L/5/2

=> 100 = 2L/5

=> 500 = 2L

=> L = 500/2 = 250

so, travelled distance = 250 km

Now, The constant speed for travalling 250 km distance in 2 hours is calculated by Constant speed = distance/time

=> x = 250 km /2 hours

=> x = 125 km/h

Hence, required value of x is 125 km/h.

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Answer:

The length is 43 feet, the width is 15 feet, and the area is 645 square feet

Step-by-step explanation:

Let us solve the question

∵ The drawing plan shows a rectangle that is 17.2 inches by 6 inches

∴ The drawing length = 17.2 inches

∴ The drawing width = 6 inches

∵ The scale in the plan is 2 in.: 5 ft

→ By using the ratio method

→  inches: feet

→  2         : 5

→  17.2     : L

→  6         : W

→ By using the cross multiplication

∵ 2 × L = 17.2 × 5

∴ 2L = 86

→ Divide both sides by 2

∴ L = 43 feet

∴ The actual length is 43 feet

→ By using the cross multiplication

∵ 2 × W = 6 × 5

∴ 2W = 30

→ Divide both sides by 2

∴ W = 15 feet

∴ The actual width is 15 feet

∵ The area of the rectangle is A = L × W

∵ L = 43 feet

∵ W = 15 feet

→ Substitute them in the rule of the area

∴ A = 43 × 15

∴ A = 645 feet²

∴ The actual area is 645 square feet

Answer:

\(\dfrac{-7}{2}\)

Step-by-step explanation:

Here we are given a polynomial ,

\(\implies f(x) = 2x^3 + Ax^2 + 4x - 5 \)

And the value of ,

\(\implies f(2) = 5 \dots (i) \)

And we need to find out the value of A . Firstly substitute x = 2 in f(x) , we have ,

\(\implies f(2) = 2(2)^3+ A(2)^2 + 4(2) -5 \)

Simplify the exponents ,

\(\implies f(2) = 2(8) + A(4) + 8 - 5 \)

Simplify by multiplying ,

\(\implies f(2) = 16 + 4A + 3 \)

Add the constants ,

\(\implies f(2) = 19 + 4A \)

Now from equation (i) , we have ,

\(\implies 19 + 4A = 5 \)

Subtracting 19 both sides,

\(\implies 4A = 5-19 \)

Simplify,

\(\implies 4A = -14\)

Divide both sides by 4 ,

\(\implies A =\dfrac{-14}{4}=\boxed{ \dfrac{-7}{2}}\)

Hence the value of A is -7/2.

We are provided with the information that the high temperature of 79°F occurs at 6 PM and the average temperature for the entire 24-hour period is 61°F.

We know that the high temperature of 79°F occurs at 6 PM, which corresponds to 18:00 in a 24-hour format. Since the average temperature for the 24-hour period is 61°F, we can use this as the midline of the sinusoidal function.

The general form of a sinusoidal function is:

f(x) = A(sin(B(x - C))) + D,

where A is the amplitude, B determines the period, C is the horizontal shift, and D is the vertical shift.

In this case, the midline is 61°F, so D = 61. Since the amplitude is half of the difference between the high and low temperatures, A = (79 - 61)/2 = 9°F. The period of a sinusoidal function representing a 24-hour period is 24, so B = [2π/24] = π/12.

To find the horizontal shift, we need to calculate the time difference between the high temperature at 6 PM and 7 AM. This is 7 + 12 - 18 = 1 hour. Since 1 hour is 1/24 of the period, the horizontal shift is C = π/12.

Now we can plug in the values into the equation:

f(x) = [9(sin((π/12))(x - π/12))] + 61.

To find the temperature at 7 AM (x = 7), we evaluate the equation:

f(7) = [9(sin((π/12))(7 - π/12)) ]+ [61] ≈ 51.3°F.

Therefore, the temperature at 7 AM is approximately 51.3°F.

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Answer:

1.) \(5x^{2} -7x+1\)

2.)\(2(x^{2} -3x-3\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) (\(2x^{2}\) - 9x + 4) + (\(3x^{2}\) + 2x - 3)

= \(2x^{2}\) - 9x + 4 + \(3x^{2}\) + 2x - 3

= \(5x^{2}\) - 7x - 1

2) \(x^{2}\) - 4x - 3 + \(x^{2}\) -2x - 3

= \(2x^{2}\) - 6x - 6

Answer:

Step-by-step explanation:

The repeated part is 194805, six digits. Let the fraction be x.

Convert as follows:

Find prime factors of both numerator and denominator and simplify by cancelling common factors:

The common factors are:

When they cancel we are left with:

The value of the "7" in 432.0769 is 7/1000 or option A.

In the number 432.0769, the digit "7" is in the thousandths place, which means that it represents seven parts of one thousandth. The digit to the left of the thousandths place is the hundredths place, which represents one hundredth of a number. Therefore, the difference between the thousandths and hundredths place is a factor of ten, which means that the value of the digit "7" is ten times greater than the value of the digit to its right.

To put it in another way, the number 432.0769 can be broken down into its decimal representation:

4 hundreds + 3 tens + 2 ones + 0 tenths + 7 hundredths + 6 thousandths + 9 ten-thousandths

Hence the correct option is (a).

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Answer: b

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

you have to divide it so 7 1/2 ÷ 1 1/2

15/2 × 3/2 then you swap the 3/2 to 2/3 so it will be 15/2 × 2/3 you don't have to cross multiplication so you just multiply across so it would be 15×3=30 and then 2×3=6 so it would be 30/6 but that's not the final answer because it and improper fractions so you divide 30÷6=5 and that's how you get 5

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

The number of petrol cars, given the ratio of cars to vans and the proportion of types of cars, is 30 cars

First, find the number of cars made :

= Number of cars and vans made x Ratio of cars / ( Sum of ratio of cars and vans )

= 160 x 3 / ( 3 + 7 )

= 160 x 3 / 10

= 48 cars

The number of petrol cars would be:

= Number of cars made - Number of electric cars - Diesel cars

= 48 - ( 1 / 8 x 48 ) - ( 25 % x 48 )

= 48 - 6 - 12

= 30 cars

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The profit function for the company is Profit = (19x - 7x) - 105,000. When the company produces and sells 7500 book covers, the profit earned is $99,000. When the company produces and sells 8750 book covers, the profit earned is $152,500.

A. Profit = (19x - 7x) - 105,000

B. Profit = (19(7500) - 7(7500)) - 105,000 = $99,000

C. Profit = (19(8750) - 7(8750)) - 105,000 = $152,500

D. Profit = (19(11835) - 7(11835)) - 105,000 = $229,495

A. The profit for the company for a single book cover is the difference between the selling price and the production cost. The selling price is $19 and the production cost is $7. The difference is $12. The company's fixed cost is $105,000, so the profit function is Profit = (19x - 7x) - 105,000.

B. To find the profit earned by the company when it produces and sells 7500 book covers, substitute 7500 for x in the profit function. Profit = (19(7500) - 7(7500)) - 105,000 = $99,000.

C. To find the profit earned by the company when it produces and sells 8750 book covers, substitute 8750 for x in the profit function. Profit = (19(8750) - 7(8750)) - 105,000 = $152,500.

D. To find the profit earned by the company when it produces and sells 11,835 book covers, substitute 11,835 for x in the profit function. Profit = (19(11835) - 7(11835)) - 105,000 = $229,495.

The profit function for the company is Profit = (19x - 7x) - 105,000. When the company produces and sells 7500 book covers, the profit earned is $99,000. When the company produces and sells 8750 book covers, the profit earned is $152,500. When the company produces and sells 11,835 book covers, the profit earned is $229,495.

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Answer:

0.5 minutes

Step-by-step explanation:

Since we are provided the equation and the current height of the candle (which would be 25 inches) we can simply replace this current height with the variable h and then solve the rest of the equation to find out the value of m when the height of the candle is at 25 inches.

h = 32−14m

25 = 32−14m ... subtract both sides by 32

-7 = -14m ... divide both sides by -14

0.5 = m

Finally, we can see that after 0.5 minutes the candle would have melted down to 25 inches.

Answer:

The value of x is 6

Step-by-step explanation:

The perimeter of an equilateral triangle is P = 3 × S, where S is the length of each side

∵ The perimeter of an equilateral triangle is 63 inches

∴ P = 63 inches

→ By using the rule of the perimeter above

∵ P = 3 × S

→ Equate the right sides of P

∴ 3 × S = 63

→ Divide both sides by 3

∴ S = 21 inches

∴ The length of each side is 21 inches

∵ The length of each side is (4x - 3)

→ Equate (4x - 3) by the length of each side

∴ 4x - 3 = 21

→ Add 3 to both sides

∵ 4x - 3 + 3 = 21 + 3

∴ 4x = 24

→ Divide both sides by 4 to find x

∴ x = 6

∴ The value of x is 6

There are 11 positive three-digit integers that satisfy the given congruences.

Let n be the positive integer that we are looking for. According to the Chinese Remainder Theorem, we can solve the following system of linear congruences:

n ≡ 22 (mod 66)

n ≡ 55 (mod 99)

n ≡ 77 (mod 1111)

First, we can simplify the second congruence by dividing both sides by 11:

n ≡ 5 (mod 9)

Now, let's look at the first congruence. Since 66 = 2 x 3 x 11, we know that n must be divisible by 2 and 3, and satisfy the following congruence modulo 11:

n ≡ 0 (mod 11)

Using similar reasoning, we can write the third congruence as follows. Since 1111 = 11 x 101, we know that n must be divisible by 11, and satisfy the following congruence modulo 101:

n ≡ 66 + 22 = 88 (mod 101)

Now, we have reduced the problem to solving two simpler systems of linear congruences:

n ≡ 0 (mod 11)

n ≡ 5 (mod 9)

and

n ≡ 11k (mod 66)

n ≡ 88 (mod 101)

for some integer k. For the first system, we can use the Chinese Remainder Theorem again to get:

n ≡ 99 (mod 99)

For the second system, we can use the Extended Euclidean Algorithm to find a solution. First, we have:

66(-1) + 101(1) = 35

Then, we multiply both sides by 88:

66(-88) + 101(88) = 308

Therefore, the general solution to the second system is:

n ≡ 308 + 101(66k - 88) = 6433 + 6666k (mod 6666)

Thus, the positive three-digit integers that satisfy all three congruences are given by:

n = 99, 1098, 2097, ..., 9891 (11 terms)

Therefore, there are 11 positive three-digit integers that satisfy the given congruences.

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Answer:

D. 1/4

Step-by-step explanation:

The probability of flipping a tail is 1/2. To find the probability of flipping two tails, multiply.

1/2 x 1/2 = 1/4

Answer: Here we will learn how to find the probability of tossing two coins.

Let us take the experiment of tossing two coins simultaneously:

When we toss two coins simultaneously then the possible of outcomes are: (two heads) or (one head and one tail) or (two tails) i.e., in short (H, H) or (H, T) or (T, T) respectively; where H is denoted for head and T is denoted for tail.

Therefore, total numbers of outcome are 22 = 4

The above explanation will help us to solve the problems on finding the probability of tossing two coins.

Step-by-step explanation:

THE ANSWER MUST BE AT LEAST 1/4 OR 1/8

IF THAT IS WRONG LET ME KNOW!

AND IF YOU NEED A TUTOR I AM OPEN FOR HELP JUST CONTACT ME IF YOU HAVE ANY QUESTIONS!

Answer:

12 percent

Step-by-step explanation:

24 by 100 0f 50

24 ×50=1200

1200÷100 is 12

To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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The amount of inventory that Baryla can hold is **$16.1 million**.

The inventory turnover ratio is calculated as sales / inventory. To maintain an inventory turnover ratio of at least 5.6, Baryla's inventory must be no more than $90 million / 5.6 = $16.1 million.

Calculation:

```

sales = $90 million

gross profit margin = 35%

inventory turnover ratio = 5.6

inventory = sales / inventory turnover ratio = $90 million / 5.6 = $16.1 million

```

**b. Currently, some of Baryla's inventory includes $1.5 million of outdated and damaged goods that simply remain in inventory and are not salable. What inventory turnover ratio must the good inventory maintain in order to achieve an overall turnover ratio of at least 5.6 (including the unsalable items)?**

The good inventory must maintain an inventory turnover ratio of **9.4 times** in order to achieve an overall turnover ratio of at least 5.6.

The overall inventory turnover ratio is 5.6, and the unsalable inventory is $1.5 million. This means that the good inventory is $90 million - $1.5 million = $88.5 million.

The good inventory must maintain an inventory turnover ratio of $88.5 million / 5.6 = **9.4 times** in order to achieve an overall turnover ratio of at least 5.6.

overall inventory turnover ratio = 5.6

unsalable inventory = $1.5 million

good inventory = $90 million - $1.5 million = $88.5 million

good inventory turnover ratio = $88.5 million / 5.6 = 9.4 times

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Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer:

Assuming it’s a matter of rotations.

Since its 180 clockwise you go, well clockwise.

You put your needle on the point of rotation and stretch it to a random point “assuming it’s A”.

You put the pencil on A and needle on the point of rotation (X for now) and then draw a circle.

You then proceed to without changing the compass postion, put it on point A, and construct tiny arcs (like a hexagon), each tic (arc) is 60 degrees so constructed 3 of those. Each time you make an arc, go to the arc you made without changing your compass and repeat until 3 times.

On the third arc mark (assuming A), A prime or A'.

You then put your needle on (x) again then put the lead on lets say point B.
You repeat the steps until all points have a prime (').
You then just construct the primed letters and then connect them with a straight edge.
You now have a 180 degree clockwise rotation.

(if your trying to find which one looks like it, then its usually one who’s straight up flat on the same plane AKA a reflection)

Answer:

because red is colour which attracts more

Answer:

1/15

Step-by-step explanation:

Total number of marbles: 3 + 4 + 1 + 2 = 10

First pick:

p(red) = 3/10

Now there are a total of 9 marbles.

Second pick:

p(blue) = 2/9

Overall probability:

p(red then blue) = 3/10 * 2/9 = 6/90 = 1/15

The square root of twenty-four minus eight is 5.19615242271, and it would be plotted between 5 and 6, but closer to 5 on a number line.

A horizontal line with uniformly spaced numerical increments is referred to as a number line.

The way the number on the line can be replied will depend on the numbers on the line.

The number's intended use is described in the question that goes with it, such as when graphing a point.

Locating numbers, comparing numbers, fractions and mixed numbers, decimals, integers, absolute value, addition, subtraction, inequalities, multiples, common denominators, and other mathematical concepts may all be taught using number lines, which are incredibly versatile manipulatives.

We have the expression,

the square root of 35 minus 8.

In numeric form,

√(35-8)

Simplifying,

√(35-8)

= √(27)

= 3√(3)

= 5.19615242271

That means,

√(27) is  5.19615242271.

If we round that off, the number will be 5.

So, between 5 and 6,

but closer to 5.

Therefore, √(29) would be plotted between 5 and 6, but closer to 5 on a number line.

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