COULD SOMEMEMMEME PLEASEEE HELPP ME

COULD SOMEMEMMEME PLEASEEE HELPP ME

Answers

Answer 1

Answer:

1. 0.000345

2. 0.0345

3. 34.5

4. 3.45

do the powers

Then multiply 3.45 with the result of those powers

Answer 2
1)0.000345
2)0.0345
3)34.5
4)3.45
If it’s negative it moves to the left from the decimal and given exponent. If it’s positive it moves to the right from the decimal from the given exponent

Related Questions

class extends value undefined is not a constructor or null

Answers

What? What do you mean?

Help ASAP Question:
The Department of Transportation's salt and sand mixing sheds are in the shape of a cone. One of the sheds measures 50 ft
high and 40 ft in diameter. What is the approximate volume of this shed? Use 3.14 for pi, Round to the nearest whole
number

Answers

Answer:

HI 56

Step-by-step explanation:

A disk with a radius of 0.1 m is spinning about its center with a constant angular speed of 10 rad/sec. What are the speed and magnitude of the acceleration of a bug clinging to the rim of the disk?

1) 10 m/s and 10 m/s^2

2) 1 m/s and 0 m/^2 (Disk spins at constant speed)

3) 0.1 m/s and 1 m/s^2

4) 1 m/s and 10 m/s^2

Answers

A disk with a radius of 0.1 m is spinning about its center with a constant angular speed of 10 rad/sec. The speed of the bug is equal to the tangential speed of a point on the rim of the disk, which can be given by: v = rωWhere:r = 0.1 m (the radius of the disk)ω = 10 rad/sec (the angular speed of the disk)Therefore, the speed of the bug is: v = rω= 0.1 m x 10 rad/sec= 1 m/s

The acceleration of the bug can be given by: a = rαWhere:α = α (angular acceleration)The angular acceleration is zero because the disk is spinning at a constant angular speed. Hence, the acceleration of the bug is zero or a = 0 m/s². Therefore, the correct option is option 2) 1 m/s and 0 m/s² (Disk spins at a constant speed).

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Which costly, time-consuming studies are always needed for products requiring a Premarket Approval, AND what is the purpose of these studies?

Answers

The costly, time-consuming studies always needed for Products Requiring Premarket Approval are Preclinical Studies, Clinical Trials, Quality Control Testing.

Preclinical Studies are the studies that happens in the laboratory and are tried on animals before human trials. The purpose of animal trial is to ensure preliminary data on the product's pharmacology, toxicology, and potential risks.

Clinical Trials are trials of testing the products on human subjects under control conditions. These trials are done to ensure product safety and optimal dosage. They have multiple phases and involve larger group of participants.

Quality Control Testing is used to test the product's quality, purity, stability, and consistency. It is done to ensure, the product meets the required specifications and maintain it's integrity.

The purpose of this data is to provide comprehensive scientific evidence and data to regulatory authorities, used to demonstrate the product's quality, purity, stability. These studies are used to know the risks and benefit of the product, identify the side effects and make sure that product meets the required specifications and maintain it's integrity.

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(-4/7) ÷(16/49)
Find the answer​

(-4/7) (16/49) Find the answer

Answers

Step-by-step explanation:

cross product. Ise the butrerfly or cross and bones method. Multiply -4 and 49. Put that in the numerator. Then multiply 7 and 16. Put that in the denominator. Then reduce if u can.

- 1/7 = 1.75 I think

suppose that a particular nba player makes of his free throws. assume that late in a basketball game, this player is fouled and is awarded two free throws.
a. What is the probability that he will make both free throws? (to decimals) b. What is the probability that he will make at least one free throw? (to decimals) c. What is the probability that he will miss both free throws? (to decimals) d. Late in basketball game; team often intentionally fouls an opposing player in order to stop the game clock: The usual strategy is t0 intentionally foul the other team's worst free-throw shooter: Assume the team' worst free throw shooter makes 58% of his free throws Calculate the probabilities for this player as shown in parts (2), (b), and (c) and show that intentionally fouling this player who makes 58% of his free throws is better strategy than intentionally fouling the player who makes 89% of his free throws. Assume as in parts (a), (b), and (c) that two free throws will be awarded.
1. What is the probability that this player will make both throws? (to 4 decimals) 2. What is the probability that will make at least one tlrow? (to decimals) 3. What is the probability that thils player wIll mlss bolhi Urows? (to decimals)

Answers

Step-by-step explanation:

suppose you brought 45 shares of telecommunications company 4 years ago at a price of $63.00 per share. you just sold it for $71.50 per share. how much did you make

Suppose \( A \) and \( B \) are independent events where \( P(A)=35 \), and \( P(B \mid A)=.40 \). What is the \( P(B) \) ? \( 0.65 \) \( 0.40 \) \( 0.60 \) \( 0.35 \)

Answers

If events A and B are independent, with P(A) = 0.35 and P(B|A) = 0.40, then the probability P(B) can be calculated as 0.35.

Two events A and B are considered independent if the occurrence or non-occurrence of one event does not affect the probability of the other event. In this case, we are given that A and B are independent events.

P(B|A) represents the conditional probability of event B occurring given that event A has already occurred. Since A and B are independent, P(B|A) = P(B). We are given that P(B|A) = 0.40, which implies that P(B) = 0.40.

However, the question states that P(A) = 0.35. This indicates that there might be a discrepancy or error in the information provided. If P(A) = 0.35, then P(B) should also be 0.35 for the events to be independent.

Therefore, based on the given information, the correct answer is that P(B) is 0.35

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HELP FAST!! What is another way to write x 7/3?

HELP FAST!! What is another way to write x 7/3?
HELP FAST!! What is another way to write x 7/3?

Answers

The way that the exponent illustrated as x ^7/3 can be written is 3✓x^7

How to explain the exponent?

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Expressing large numbers in terms of powers is known as an exponent. Therefore, the exponent describes the number of times a number has been multiplied by itself.

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is written as bn. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to base multiplication when n is a positive integer; therefore, bn is the result of multiplying n bases:

In this case, it should be noted that x ^7/3 will simply be the cube root of x raised to power 7. This is illustrated as x ^7/3.

Therefore, the correct option is C.

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To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?

Answers

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Identify the linear equation?

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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What is 22 lb day in oz h?

Answers

Answer:

352 OZ

Step-by-step explanation:

One pound = 16 OZ

take 22 and multiply it by 16

22 x 16 = 352

Answer:

15 ounces per hour

Step-by-step explanation:

This is dimensional analysis, so we need to find conversion factors for ounces per pound and hours per day.  Once we have those we write the equation such that the units we need are left and the others cancel:

22lb/1 day  x  16 ounces/1 lb x 1 day/24hrs = 14.66666666666 ounces per hour

Since the problem was written with no decimals, our answer probably shouldn't either and in most cases like this we want to round to the nearest whole number, which is 15.

The cross section of a parabolic sound reflector at the Olympics has a diameter of 20 inches and is 25 inches deep. Write an equation that represents the cross section of the reflector with its vertex at ( ) 0, 0 and its focus to the left of the vertex.

Answers

Answer: 69

Step-by-step explanation: Sorry I do not know the answer because I am not smart.  I just need the points so I can answer more questions.  Have a great day though and I wish you luck with your question:)

an aircraft seam requires 27 rivets. the seam will have to be reworked if any of these rivets is defective. suppose rivets are defective independently of one another, each with the same probability. (round your answers to four decimal places.)

Answers

The probability of at least one defective rivet in a seam requiring 27 rivets, assuming they are independently defective with the same probability, is approximately 68.3%.

To solve this problem, we can use the concept of probability and the binomial distribution.

The probability of a rivet being defective is denoted by "p". Since each rivet is defective independently of the others, the probability of a rivet not being defective (i.e., being good) is 1 - p.

The seam will need to be reworked if any of the 27 rivets is defective. Therefore, we want to calculate the probability that at least one rivet is defective.

The probability of at least one defective rivet can be found using the complement rule: subtracting the probability of no defective rivets from 1.

The probability of no defective rivets is given by (1 - p) raised to the power of 27 (since each rivet is independent).

So, the probability of at least one defective rivet is:

P(at least one defective rivet) = 1 - P(no defective rivets)

P(at least one defective rivet) = 1 - (1 - p)^27

Now, we can substitute any desired value for the probability of a defective rivet, "p," to calculate the probability of at least one defective rivet.

For example, if we assume a defective rivet probability of p = 0.05 (5%), the calculation would be as follows:

P(at least one defective rivet) = 1 - (1 - 0.05)^27

P(at least one defective rivet) ≈ 0.683

Therefore, with a 5% probability of a rivet being defective, the probability of at least one defective rivet in the seam is approximately 0.683 or 68.3%.

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The parallelogram shown below has an area of 60 units^2

squared.
Find the missing base.

Answers

Answer:

The missing base is 6

Step-by-step explanation:

The base is 6 units.

What is parallelogram?

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, a parallelogram with one base 11, height 10 units and area 60 sq units.

We know that, area of a parallelogram = base x height

Therefore,

base x 10 = 60

base = 60 / 10

base = 6

Hence, the missing base is 6.

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point) if 1/x 1/y=5 and y(5)=524, (meaning that when x=5, y=524 ), find y′(5) by implicit differentiation.

Answers

If 1/x 1/y=5 and y(5)=524, by implicit differentiation the value of y'(5) is  20.96

Differentiate both sides of the equation 1/x + 1/y = 5 with respect to x to find y′(5).

Differentiating 1/x with respect to x gives:

d/dx (1/x) = -1/x²

To differentiate 1/y with respect to x, we'll use the chain rule:

d/dx (1/y) = (1/y) × dy/dx

Applying the chain rule to the right side of the equation, we get:

d/dx (5) = 0

Now, let's differentiate the left side of the equation:

d/dx (1/x + 1/y) = -1/x² + (1/y) × dy/dx

Since the equation is satisfied when x = 5 and y = 524, we can substitute these values into the equation to solve for dy/dx:

-1/(5²) + (1/524) × dy/dx = 0

Simplifying the equation:

-1/25 + (1/524) × dy/dx = 0

To find dy/dx, we isolate the term:

(1/524) × dy/dx = 1/25

Now, multiply both sides by 524:

dy/dx = (1/25) × 524

Simplifying the right side of the equation:

dy/dx = 20.96

Therefore, y'(5) ≈ 20.96.

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What ratio of sides from AADE defines tan 19° ?

What ratio of sides from AADE defines tan 19 ?

Answers

Answer:

\(\large \sf \boxed{ \sf \dfrac{DE}{AD} }\)

Explanation:

\(\sf tan(x) = \dfrac{opposite}{adjacent}\)

Here given angle: 19°

Opposite to this angle: DE

Adjacent to this angle: AD

Hypotenuse to this angle: EA

So ratio of sides that defines tan(19) = opposite/adjacent = DE/AD

what is the difference between slope and rate of change

Answers

The slope is the steepness of a line on a graph and represents the ratio of the vertical change to the horizontal change, the rate of change refers to the amount of change in one variable corresponding to a unit change in another variable.

The slope of a line is a measure of its steepness or incline. It is calculated by dividing the vertical change (change in y-values) by the horizontal change (change in x-values) between two points on the line. The slope indicates how much the dependent variable (y) changes with respect to a unit change in the independent variable (x). In other words, it represents the ratio of the rise (vertical change) to the run (horizontal change) on the graph.

On the other hand, the rate of change is a broader concept that applies to any relationship between two variables, not just linear relationships. It measures how one variable changes in response to a unit change in another variable. The rate of change can be positive, indicating an increase in one variable for every unit increase in the other variable, or negative, indicating a decrease. It can also vary across different intervals of the relationship, indicating that the relationship is not constant.

In summary, the slope specifically refers to the steepness of a line on a graph and is calculated as the ratio of the vertical change to the horizontal change. The rate of change, on the other hand, is a more general concept that describes how one variable changes in response to a unit change in another variable and can be applied to any type of relationship between variables.

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Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .

Can someone answer this question please please help me I really need it if its correct I will mark you

Answers

Formula for a quarter circle's perimeter: C = ((pi x 2 x radius) / 4) + r + r

17.85 = ((3.14 x 2 x r) / 4) + 2r

17.85 = (6.28r / 4) + 2r

17.85 = 1.57r + 2r

17.85 = 3.57r

r = 5 meters

Hope this helps! :)

If f(x) = 2x2 + 3x – 1 and g(x) = -x, then f(-1)+g( - 1) = O a.) 1 O b.) - 3 O c.) -5 O d.) - 1

Answers

If function f(x) = 2x2 + 3x – 1 and g(x) = -x, then f(-1)+g( - 1) = -1

To solve this problem, we need to plug in -1 for x in both f(x) and g(x).

f(-1) = 2(-1)2 + 3(-1) – 1 = 2 - 3 - 1 = -2

g(-1) = -(-1) = 1

Now, we can add f(-1) and g(-1):

f(-1) + g(-1) = -2 + 1 = -1


To solve f(-1) + g(-1), we need to first find the values of f(-1) and g(-1) individually.

For f(-1):
f(x) = 2x^2 + 3x - 1
f(-1) = 2(-1)^2 + 3(-1) - 1
f(-1) = 2(1) - 3 - 1
f(-1) = 2 - 3 - 1
f(-1) = -2

For g(-1):
g(x) = -x
g(-1) = -(-1)
g(-1) = 1

Now, let's add f(-1) and g(-1):
f(-1) + g(-1) = -2 + 1 = -1

So, the answer is d.) -1.

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FILL IN THE BLANK use the data in the table to complete the sentence. x y –2 7 –1 6 0 5 1 4 the function has an average rate of change of __________.

Answers

The function has an average rate of change of -1.

To find the average rate of change of a function, we can use the formula:

Average Rate of Change = (Change in y) / (Change in x)

Using the data provided in the table, we can calculate the average rate of change between each pair of consecutive points. Let's calculate it for each pair:

Between (-2, 7) and (-1, 6):

Change in y = 6 - 7 = -1

Change in x = -1 - (-2) = 1

Average Rate of Change = (-1) / (1) = -1

Between (-1, 6) and (0, 5):

Change in y = 5 - 6 = -1

Change in x = 0 - (-1) = 1

Average Rate of Change = (-1) / (1) = -1

Between (0, 5) and (1, 4):

Change in y = 4 - 5 = -1

Change in x = 1 - 0 = 1

Average Rate of Change = (-1) / (1) = -1

From the calculations, we can see that the function has a constant average rate of change of -1 between any two consecutive points in the table.

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basis. 3.1 Use the information in the table to answer the questions that follow Mrs Mabaspacked is a registered resident and she used 14 kl of water for the month of August 2022 calculate her water bill excluding VAT. The Polokwane Local municipality 2021 tariff for prepaid electricity appears below. 23 3.2 3.3 Pre-Paid system Basic Charge 11392 (cent) Consumption Block 1 (0-50) units Block 2 ((51-350) 50 300 units Block 3 (351-600) 250 units Block 4 (>600) Cost per unit (c/kWh) 118,24c 154,36c 227.88c 267,95c Source: (3) www.polokwane.gov.za Write down the fixed monthly electricity cost for the prepaid system in Rand. If a household uses 196 kWh of electricity in a month, how much would they pay for their electricity consumption, excluding VAT? (2) (4) [9] TOTAL: 50​

Answers

1. The fixed monthly electricity cost for prepaid system in Polokwane is 113.92 Rand.

2. The household would pay 445.02 Rand for 196 kWh of electricity consumption.

What is fixed costs for prepaid electricity and how much will be paid for 196 kWh of consumption?

Fixed monthly electricity cost = Basic Charge / 100

Fixed monthly electricity cost = 11392/100

Fixed monthly electricity cost = 113.92 Rand

For a household using 196 kWh of electricity.

The First 50 units at 118.24c/kWh:

= 50 x 118.24

= 5,912c

For next 250 units at 154.36c/kWh:

= 250 x 154.36

= 38,590c

The total cost unit will give:

= 5,912c + 38,590c / 100

= 445.02 Rand.

Full question:

Mrs Mabaspacked is a registered resident and she used 14 kl of water for the month of August 2022 calculate her water bill excluding VAT. Th

e Polokwane Local municipality 2021 tariff for prepaid electricity appears below. 23 3.2 3.3

Pre-Paid system Basic Charge 11392 (cent) Consumption Block 1 (0-50) units Block 2 ((51-350) 50 300 units Block 3 (351-600) 250 units Block 4 (>600) Cost per unit (c/kWh) 118,24c 154,36c 227.88c 267,95c Source: (3) www.polokwane.gov.za

1. Write down the fixed monthly electricity cost for the prepaid system in Rand.

2. If a household uses 196 kWh of electricity in a month, how much would they pay for their electricity consumption, excluding VAT?.

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Find x if f(x) = 2x + 7 and f(x) = -1.

Answers

the answer is positive 5

Answer:

\(x=-4\)

Step-by-step explanation:

We are given the function:

\(f(x)=2x+7\)

And we want to find x when f(x) = -1.

Substitute:

\(-1=2x+7\)

Subtract seven from both sides:

\(2x=-8\)

Divide both sides by two. Hence:

\(x=-4\)

Determine the values of x for which the rational expression is undefined. If there is more than one value, enter your answers as a comma separated list. If there is no value that makes the expression undefined enter "NONE".

Answers

The rational expression is undefined when the denominator is equal to zero because division by zero is undefined in mathematics. Therefore, we need to find the values of x that make the denominator equal to zero.

The given rational expression is not provided in the question. However, in general, if the rational expression is of the form f(x) / g(x), where g(x) represents the denominator, then we need to solve the equation g(x) = 0 to find the values of x that make the denominator equal to zero.

If there exists one or more such values, then the expression is undefined at those values. If there is no value that makes the denominator equal to zero, then the expression is defined for all real values of x.

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a manufacturer produces bearings, but because of variability in the production process, not all of the bearings have the same diameter. the diameters have a normal distribution with a mean of 1.5 centimeters (cm) and a standard deviation of 0.02 cm. the manufacturer has determined that diameters in the range of 1.46 to 1.54 cm are acceptable. what proportion of all bearings falls in the acceptable range? (round your answer to four decimal places.)

Answers

The proportion of all bearings falls in the acceptable range is 0.9544 (rounded to four decimal places).

The proportion of all bearings falls in the acceptable range is 0.9544. The given problem statement asks to determine the proportion of bearings produced in the acceptable range, given the mean, standard deviation and the acceptable range for bearing diameters.Solution: The given distribution is normal with mean (μ) = 1.5 cm and standard deviation (σ) = 0.02 cm. Also, the acceptable range of diameter is from 1.46 cm to 1.54 cm, hence the distance between the lower limit and mean is: $Z_{lower}=\frac{1.46-1.5}{0.02}=-2$Similarly, the distance between upper limit and mean is:$Z_{upper}=\frac{1.54-1.5}{0.02}=2$Using the standard normal table or calculator, we can obtain the probability (proportion) of the distribution that falls within the acceptable range (from $Z_{lower}$ to $Z_{upper}$).So, the proportion of all bearings that fall in the acceptable range is:$$P(-2≤Z≤2)=0.9544$$Therefore, the proportion of all bearings falls in the acceptable range is 0.9544 (rounded to four decimal places).

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Evaluate the expression when b=2 and y=-6.

-b+47

Help

Answers

45 cuz -2 + 47 is 45

Pleaaasseee help!!! BRAINLIEST FOR CORRECT ANSWER!! What is the transformation rule for a translation 3 units right?

Answers

Answer:

Rule: replace x by x - a where a is the number of units that you want to move right. a must be greater than 0. x - - a  would move left.

Step-by-step explanation:

You want f(x) to move 3 units to the right.

That would mean that  x would be replaced by x - 3.  Just to be sure let's try it.

Suppose you have f(x) = x^2 + 6x + 5       It is graphed as the red lineNow suppose you want to move 3 units right. It would replaced like f(x - 3) = (x - 3)^2 + 6(x - 3) + 5 which is the blue lineNotice nothing else is changed. The blue line looks exactly like the red line except that it is shifted 3 units to the right.

Pleaaasseee help!!! BRAINLIEST FOR CORRECT ANSWER!! What is the transformation rule for a translation

Often, conditional probabilities are worded with what​ phrase?

​"dependent"

​"given that"

​"either/or"

​"mutually exclusive"

Answers

The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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6 pounds of candy cost 22.44. What is the cost of one pound

Answers

Answer:

$3.74

Step-by-step explanation:

Proportions:

6 pounds ⇔ $22.44

1 pound ⇔ $ C

C = 22.44*1/6

C = $3.74

Dave collects model trains. So far he has 23 distinct train cars. How many ways can he put 7 cars together? = Answer 23 PAnswer 7 =23!(23−7)! =23!16! = Answer 23 ⋅ Answer 22 ⋅21⋅20⋅19⋅18⋅ Answer 17 = Answer

Answers

Answer:

He can put 7 cars together in 245,157 ways.

Step-by-step explanation:

The order in which the cars are put together is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

23 distinct train cars. How many ways can he put 7 cars together?

Combinations of 7 from a set of 23. So

\(C_{23,7} = \frac{23!}{7!(23-7)!} = \frac{23!}{7!16!} = 245157\)

He can put 7 cars together in 245,157 ways.

during an election, a group of 4 council members must be selected from a group of 18 people running for these positions. how many such selections are possible?

Answers

The possible number of ways of selection by using combination formula is 3060.

What is combination?

A grouping of items where the order in which they were chosen is irrelevant is known as combination.

Given that the number of people in the group is 18. Only 4 people will be member of the council.

The formula of combination is \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\) , where r number of objects are selected from n objects.

In the given question the value of n is 18 and the value of r is 2.

Substitute the value of n and r in \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\).

\(^{18}C_{4}=\frac{18!}{4!(18-4)!}\)

Solve the above expression:

18^C_4 = 18x17x16x15x14/4x14

18^C_4 = 18x17x16x15/4x3x2x1

3060 18^C_4 = 3060

The number of ways such selection is 3060.

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Horatio spends about 40 hours per week reading 2 different books in his spare
time. One book is more difficult, and one is lighter. He reads about 12 pages per
hour of the more difficult book and 25 pages per hour of the lighter book. If he
reads 610 pages per week, how many hours does Horatio spend on each book?

Answers

Horatio devotes 30 hours to the harder book and 10 hours to the easier one.

Calculations

Let X be the hours spent reading the more difficult book

Let Y be the hours spent reading the less difficult book

Total hours spent = X + Y = 40

Number of pages of difficult book in X hours at 12 pages per hour = 12X

Number of pages of easier book in Y hours at 25 pages per hour = 25Y

Total pages read = 12X + 25Y

So we have two equations in X and Y and we can solve them simultaneously. Equations are:

X + Y = 40                    (1)

12X + 25Y = 610             (2)

We can eliminate one of the variable terms by making the coefficients of the other term equal and then subtracting

Multiply (1) by 12 to make X terms equal

12(X + Y) = 12 x 40

12X + 12Y = 480                (3)

Subtract (3) from (2)

(2) - (3)

==> 12X + 25Y - (12X + 12Y) = 610 - 480

==> 12X + 25Y - 12X - 12Y = 130

==> 25Y - 12Y = 130                           (12X terms cancel)

==> 13Y = 130

==> Y = 130/13                                     (divide both sides by 13)

==> Y = 10

Using (1)

X + Y = 40

==> X + 10 = 40

==> X + 10 - 10 = 40 - 10

==> X = 30

So answer:

Horatio spends 30 hours on the more difficult book and 10 hours on the lighter book

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