The bookstore has 15 new copies and 15 used copies in stock. If 25 people come in one by one to purchase this text, what is the probability that all 25 will get the type of book they want from current stock

The number of units of each of the products are as follows

Information from the problem gives

If the carrier can carry 15,600 cubic feet and 18,300 pounds and is insured for $78,700

assuming product A = A, product B = B and product C = C

from the table the equation is derived as follows

24A + 40B + 80C = 15,600

40A + 30B + 60C = 18,300

150A + 170B + 300C = 78,700

solving simultaneously gives

A = 300, B = 110, and C = 50

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Answer:

180

Step-by-step explanation:

The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:

A=10×18

A=180

The area of the parallelogram is 180 square units

Answer:

The best buy is the 16-ounce drink

Step-by-step explanation:

here, we see that,

12 ounce = 3/4 (16 ounce)

So, the price should reflect that,

i.e,

price of 12 ounce drink = 3/4 (price of 16 ounce drink)

By this metric,

Price of 12 ounce drink = 3/4 ( 1.19)

Price of 12 ounce drink = $0.8925

So, 12-ounce drink should cost $0.8925 but the actual drink costs $0.99,

So, it is more expensive than it should be,

So, the best buy is the 16-ounce drink

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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The probability of randomly drawing seven vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles is low. One time throughout the simulation's 500 iterations, all seven tiles were vowels.

Part A: What is the probability of randomly drawing 7 vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles?

Part B: To imitate one repetition of the process, you would use a table of random digits or a calculator to randomly generate seven digits, each between 0 and 9. The variable you would measure is the number of vowels drawn.

Part C:

Random Digits: 4, 2, 5, 7, 8, 8, 4

Vowels: 2, 8, 8, 4

Part D: This result suggests that it is possible to randomly draw all vowels in one draw, although it is unlikely.

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Answer:

x=3

Step-by-step explanation:

subtract 2x from both sides then you are left with 3=4x-9

add 9 to both sides then you have 12=4x then divide both sides by 4 and x=3

Answer:

x=3

Step-by-step explanation:

2x+3=6x-9

subtract 3 both sides

2x=6x-12

subtract 6 x both sides

-4x=-6

divide 4 both sides

-x=-3 simplify (divide both sides by -1)

x=3

The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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Answer:

D No, the difference between the sample result and what is expected is not extreme enough. The probability of it occurring by chance alone is not unlikely.

Step-by-step explanation:

Got it right on unit test review

The probability of it occurring by chance alone is not unlikely.

We have given that,

An air-conditioning repair technician claims to complete 67% of repairs in under an hour. A random sample of 31.

repairs was chosen, and 22 of those were completed in under an hour. Let p = the proportion of the random.

The sample was completed in under an hour.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

The probability that 71% or more of this technician's repairs were completed in under an hour is 0.317.

D No, the difference between the sample result and what is expected is not extreme enough. The probability of it occurring by chance alone is not unlikely.

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Answer:

6a+48

Step-by-step explanation:

Distribute:

6(a+8)

6 x a = 6a

6 x 8 = 48

6a+48

Answer: 6a + 48

Step-by-step explanation: use the distributive property and multiply 6•a to get 6a and multiply 6•8 to get 48

Answer:

2 hours

Step-by-step explanation:

Let t represent the anount of time traveled by Chelsea

Katie

d= 18t

Chelsea

d= 6(4+t)

18t= 6(4+t)

18t= 24+6t

18t-6t= 24

12t= 24

Divide bith isdes by the coefficient of t which is 12

t= 24/12

t= 2

Hence Katie will have to travel for 2 hours before catching up with Chelsea,

Answer:

44

Step-by-step explanation:

Well if you see the picture

triangle 1 has an area of

\(\frac{3*4}{2}=6\)

triangle 2 has an area of

\(\frac{3*4}{2}=6\)

rectangle 3 has an area of

\(8*3=24\)

and triangle 4 has an area of

\(\frac{2*8}{2}=8\)

if we add then up

\(6+6+24+8=44\)

Answer:

Step-by-step explanation:

Money raised:

The equivalent expressions are B: 2(12m-6p+36) and (c): 12(2m-p+6)

From the question, we have the following parameters that can be used in our computation:

24m-12p+72

Factor out 2 from the expression

So, we have

2(12m-6p+36)

This represents the option (b)

Factor out 12 from the expression

So, we have

12(2m-p+6)

This represents the option (c)

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The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Answer:

After solving the pair of simultaneous equations we get x=5 and y=1. Solution Set = {5,1}

Step-by-step explanation:

We need to solve the pair of simultaneous equations

\(0.6x-4y=-1\\0.8x-3.5y=0.5\)

We can solve using substitution method.

Let:

\(0.6x-4y=-1--eq(1)\\0.8x-3.5y=0.5--eq(2)\)

Find value of x from eq(1) and put it in eq(2)

\(From \ eq(1):\\0.6x-4y=-1\\0.6x=-1+4y\\x=\frac{-1+4y}{0.6}\)

Putting in equation 2

\(0.8x -3.5y =0.5\\0.8(\frac{-1+4y}{0.6})-3.5y=0.5\\1.33(-1+4y)-3.5y=0.5\\-1.33+5.32y-3.5y=0.5\\-1.33+1.82y=0.5\\1.82y=0.5+1.33\\1.82y=1.83\\y=\frac{1.83}{1.82}\\y=1.00\)

So, we get value of y= 1.00

Now finding value of x by putting value of y in eq(1)

\(x=\frac{-1+4y}{0.6}\\x= \frac{-1+4(1.00)}{0.6}\\x=\frac{3}{0.6}\\x=5\)

We get value of x = 5

So, After solving the pair of simultaneous equations we get x=5 and y=1. Solution Set = {5,1}

Answer:

lines f and h are perpendicular because the products of their slopes is -1

Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Step-by-step explanation:

A car is on a slope of 10degree above the horizontal . a force 1000N is applied to the car up the line of the slope. the car has amass of 500 kg . what is the acceleration of the car

Answer:

The proportion of new typists that take at most two hours to learn the computer system is 0.9525 = 95.25%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes.

This means that \(\mu = 90, \sigma = 18\)

The proportion of new typists that take at most two hours to learn the computer system is

This is the pvalue of Z when X = 120 minutes = 2 hours. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{120 - 90}{18}\)

\(Z = 1.67\)

\(Z = 1.67\) has a pvalue of 0.9525.

The proportion of new typists that take at most two hours to learn the computer system is 0.9525 = 95.25%.

The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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Answer:

288

Step-by-step explanation:

Each taco is 1.25 dollars and you are trying to figure out how many tacos he sold to do this we make an equation.

Step 1

1.25 x = 360

x =is the amount of tacos sold.

Step 2

1.25 x = 360

/1.25      /1.25

to get x on its own we need to cancel out the 1.25 so we dived because it was multiplied to the x. we did the same on the other side to balance the equation.

Step 3

x = 288

we now need to identify what x is, we can see it is 288. If we trade x for what it means it is then this is your answer  the amount of tacos sold=288

i hope this helps ;)

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

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8.1

Remember cos = adjacent side (in this case X) / hypotenuse (10)

Answer:

D

Step-by-step explanation:

2y=10x

Divide both sides by 2.

y=5x

Now substitute this into the second equation.

Answer:

b. \(x^2/64 - 5y^2/36=1\)

Step-by-step explanation: a p e x

The percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt hours is 45.122% decrease.

Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value.

we know,

% change = (final- initial) / initial * 100

=(1125-2050)/1125 *100

=45.122%

Hence, percentage change be 45.122% decrease.

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Answer:

Attached is the box plot

Step-by-step explanation:

20, 21, 22, 22, 25, 25, 26, 27, 30, 31, 31, 31, 32, 32, 35

Minimum: 20

\(Q_1\): 22

Median or \(Q_2\): 27

\(Q_3\): 31

Maximum: 35

Hope this helps!

Answer:

Minimum = 20
First quartile = 22
Median = 27
Third quartile = 31
Maximum = 35

Step-by-step explanation:

Given the following question:

35, 22, 30, 31, 27, 20, 32, 21, 32, 22, 31, 25, 26, 31, 25

In order to find the five-number summary of the given data set we have to find five separate numbers.

Five-number summary consists of...

1. The minimum
2. The first quartile
3. The median
4. The third quartile
5. The maximum

Which means there will be five different answers for this data set:

Minimum:
To find the minimum we find the smallest value in our data set.
35, 22, 30, 31, 27, 20, 32, 21, 32, 22, 31, 25, 26, 31, 25

Minimum is equal to 20

First quartile/Third quartile:
By splitting the data set in four different groups and rearranging the numbers from least to greatest we can find he first/third quartile.

Q1 = 22
Q3 = 31

Median:
By rearranging the number from least to greatest and spliting the number in two groups. The middle value of the data set will also be the median.

35, 22, 30, 31, 27, 20, 32, 21, 32, 22, 31, 25, 26, 31, 25
20, 21, 22, 22, 25, 25, 26, 27, 30, 31, 31, 31, 32, 32, 35

Median is 27

Maximum:
The maximum is simply the largest number in the data set.
20, 21, 22, 22, 25, 25, 26, 27, 30, 31, 31, 31, 32, 32, 35

The maximum is 35.

Hope this helps.