PLEASE HELP ME! I WILL BE GIVING 50 POINTS!

The standard form of each of the numbers is given as follows:

a) 2.35 x 10^-3 = 0.00235.

b) 2.35 x 10³ = 2350.

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

For item a, to obtain the standard form of the number, we must move the decimal points three places to the left, hence:

2.35 x 10^-3 = 0.00235.

For item b, to obtain the standard form of the number, we must move the decimal points three places to the right, hence:

2.35 x 10³ = 2350.

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If the small "coffee-shop" owner is trying to determine the preference of her customers by conducting a survey among a group of customers who visit the shop during a specific time frame, then this group would be a sample rather than a population.

A "Sample" is defined as a subset of the population that is selected to represent the entire population. In this case, the owner is trying to determine the preference of her customers by surveying a specific group of customers.

So, this group of customers is a sample of the population of all customers who visit the coffee shop.

To obtain meaningful results from the survey, the sample should be selected randomly and should be representative of the population. The results obtained from the sample could then be used to make inferences about the preferences of the entire population of customers who visit the coffee shop.

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The given question is incomplete, the complete question is

A small coffee shop owner wants to know which brand of coffee her customers prefer.

Is the data considered a "population" or "sample", Explain?

The equation to represent the relationship is a = [tex]\frac{3}{4}[/tex] b.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here the given two quantities in proportional relationship . Then,

=> a∝ b

=> a=kb

Where k is constant. Then, put a=-3 and b=-4 rhen,

=> -3=-4k

=> k = 3/4

Then the equation is ,

=> a = [tex]\frac{3}{4}[/tex] b.

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Step-by-step explanation:

so, she drove the 12,000 miles with an SUV that gave her 15 miles per gallon.

that means she used

12000 / 15 = 800 gallons of gasoline.

if she would have used a car that gave her 48 miles per gallon, she wound have needed

12000 / 48 = 250 gallons of gasoline.

so, she would have saved

800 - 250 = 550 gallons of gasoline.

In the equation , it take 2 hours for the experienced crew to paint the apartment.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here let us take x as time taken by new crew of painters apartment and y as time taken by experienced crew of painters apartment .

Now a new crew of painters takes two times as long to paint a small apartment as the experienced crew  then,

x = 2y ----> 1

both crews can paint the apartment in 6 hours then,

=> x+y = 6

Now put  equation 1  into x+y=6 then,

=> 2y+y=6

=> 3y = 6

=> y = 6/3 = 2 hours.

Hence it take 2 hours for the experienced crew to paint the apartment.

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The probability solutions are given as follows;

- P(CS Major and Not Hired) = 43.6% (Marginal)

- P(Other Major) = 31.5% (Marginal)

- P (Hired + CS Major) = 36.3% (Conditional)

- P (Not Hired + Other Major) = 48.5% (Conditional)

First we need to clarify the meaning of Joint, Marginal, and conditional probability.

Note that the table of values are attached.

So, the calculation is shows as follows:

P(CS Major and Not Hired) = 102/234 = 43.6% (Marginal)

- P(Other Major) = 74/234 = 31.5% (Marginal)

- P (Hired + CS Major) =  58/160 =  36.3% (Conditional)

- P (Not Hired + Other Major) = 36/74 48.5% (Conditional)

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Answer:

(2,5] or (7,∞)

Step-by-step explanation:

The value of x is given as follows:

B. 6.

The value of x is obtained applying the two secant segment theorem, which means that the following equation will hold true:

4(x + 4) = 5(5 + 3)

(we add the two parts), with the outer part being the multipler.

Expanding the operations, the value of x is obtained as follows:

4x + 16 = 40

4x = 24

x = 6.

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Answer:

No

Step-by-step explanation:

The angles of a triangle must add up to 180. 140+15+15 = 140 +30 = 170. This is not 170, so no. Hope this helps!

Answer:

It is not possible to draw a triangle with these angles because 140 + 15 + 15 = 170, triangle angles must add up to 180 and 180=170 is a false statement.

Step-by-step explanation:

The equation of the line through the points is 7y = -2x - 15.

The equation of a line that passes through two given points is calculated as follows;

y - y1 = m(x - x1)

Where;

The slope is calculated as;

m = (y2 - y1) / (x2 - x1)

m = (-3 + 1) / (3 + 4)

m = -2/7

The equation of the line is calculated as;

y - y1 = m(x - x1)

y - (-1) = (-2/7)(x - (-4))

y + 1 = (-2/7)(x + 4)

y + 1 = (-2/7)x - (8/7)

y = (-2/7)x - (15/7)

7y = -2x - 15

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The formula that will be useful in finding the area of the triangle is: Pythagoras theorem

The formula to find the area of the triangle is expressed by the formula:

A = ¹/₂bh

Where:

b is base

h is height

Now, we have the base but we don't have the height.

Pythagoras Theorem is defined as the way in which we find the missing length of a right angled triangle.

The triangle has three sides, namely the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

where c is the hypotenuse

Thus, to find the height of the triangle, we will use Pythagoras theorem to get:

h = √(6² - 4²)

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Answer:

1500 pounds Or 0.75 tons

Step-by-step explanation:

To solve this problem, we need to convert all units to the same unit, either tons or pounds. Let's convert 1 ton and 500 pounds to pounds:

1 ton = 2000 pounds

1 ton and 500 pounds = 2000 + 500 = 2500 pounds

Now we can subtract the amount of grain that was unloaded from the total amount:

2 tons = 2 * 2000 = 4000 pounds

4000 pounds - 2500 pounds = 1500 pounds

Therefore, the trucker still has 1 ton and 500 pounds, or 1500 pounds, of grain left on the truck.

To convert 1500 pounds to tons, we can use the conversion factor:

1 ton = 2000 pounds

Dividing both sides by 2000, we get:

1 pound = 1/2000 tons

Multiplying both sides by 1500, we get:

1500 pounds = 1500/2000 tons

Simplifying the fraction, we get:

1500 pounds = 0.75 tons

Therefore, 1500 pounds is equivalent to 0.75 tons.

An equation to determine p is 12 = 3p/4.

The total number of players at the baseball game is 16 players.

In order to write a linear equation to describe this situation, we would a assign variable to the total number of players at the baseball game, and then translate the word problem into a linear equation as follows:

Let the variable p represent the the total number of players at the baseball game.

Since the players had the choice of having a bottle of water or a box of juice., and of all of the players, only 12 chose a bottle of water, which was of the total number of players, a linear equation that can be used to model this situation is given by;

12 = 3/4 × p

48 = 3p

p = 48/3

p = 16 players.

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On the basis of the data presented, it would be advisable to sell the machinery based on the differential analysis.

For selling the machinery,

Revenues = $277,800

Costs = 277,800 × 5% = $13,890

Profit = Revenues - Cost = $277,800 - $13,890 = $263,910

For leasing the machinery,

Revenues = $286,800

Costs = $24,900

Profit = Revenues - Cost = $286,800 - $24,900 = $261,900

Here the profit generated by selling the machinery is greater, which is the better option.

Hence selling the machinery is the better option.

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On the basis of the data presented, it would be advisable to sell the machinery based on the differential analysis.

For selling the machinery,

Revenues = $277,800

Costs = 277,800 × 5% = $13,890

Profit = Revenues - Cost = $277,800 - $13,890 = $263,910

For leasing the machinery,

Revenues = $286,800

Costs = $24,900

Profit = Revenues - Cost = $286,800 - $24,900 = $261,900

Here the profit generated by selling the machinery is greater, which is the better option.

Hence selling the machinery is the better option.

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In the conversion of fractions to decimals, the fraction should be thought of as a division problem.

A fraction represents the division of the numerator (n) by the denominator (d). So, when you have a fraction like n/d, you can convert it to a decimal by dividing n by d.

Answer:

A. g(x) = -x^2 - 2

Step-by-step explanation:

Okay so it has the same slope as f(x) which means it's x^2, however, it's negative and going the other way so it's -x^2

Since the y-intercept is -2,

g(x) = -x^2 - 2

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Answer:

A

Step-by-step explanation:

It is a double angle identity.

sin2x = 2sinxcosx

Answer: 2sinxcosx

Step-by-step explanation:

Answer:

The common ratio of this geometric sequence is -1/2, so we have

a(7) = 16 × -1/2 = -8, a(8) = -8 × -1/2 = 4.

Dividing by -1/2 is the same as multiplying by -2. Working backwards, we have:

a(5) = -2 × 16 = -32

a(4) = -2 × -32 = 64

a(3) = -2 × 64 = -128

a(2) = -2 × -128 = 256

a(1) = -2 × 256 = -512

Answer:

100

Step-by-step explanation:

We can estimate 485% as 500%. We know that 500% is equal to 5.

Therefore,

20 × 500%

= 20 × 5

= 100

Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

The value of the car went down by an average of $1,725 each year over the six-year period.

Depreciation is the loss in value of an asset due to factors such as age, wear and tear, market conditions, and obsolescence. It is usually calculated on a linear basis, meaning that the same amount of depreciation is spread evenly over a period of time.

In this case, the car was purchased for $22,995, and six years later it was worth $12,645.

To calculate the linear depreciation of the car, we need to subtract the value at the end of the period from the value at the beginning, and divide by the number of years:

Depreciation = ($22,995 - $12,645) / 6

Depreciation = $1,725

This means that the car depreciated by an average of $1,725 each year. In other words, the value of the car went down by an average of $1,725 each year over the six-year period.

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Answer:

-1/2

Step-by-step explanation:

The information provided about the line is that the line passes through the points (2, 2) and (6, 0)

Therefore, the first step consists in computing the slope. The formula for the slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, by plugging the corresponding numbers is , we get that the slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-2}{6-2} =-\frac{1}{2}[/tex]

So then, we find that the slope is [tex]m=-\frac{1}{2}[/tex] and that the line passes through the point [tex](2,2)[/tex].

Conclusion: Based on the data provided, we conclude that the slope of the line is [tex]m=-\frac{1}{2}[/tex].

The simplified expression is (z -3)/z - 5. Option C

From the information given, we have to simply the expressions by solving the quadratic equation;

From the information given, we have that;

z² -5zx + 6

Find the pair factors and substitute the values

z² - 2z - 3z + 6

Group in pairs, we have;

z(z - 2) - 3(z - 2)

For the denominator, we have;

z² - 7x + 10

Find the factors

z² - 5z - 2z + 10

Group in pairs, we have;

z(z - 5) - 2(z - 5)

Then, we have the simplified form;

(z -3)/z - 5

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In a case wherebyMr. Pearson drives a bus for the city of Greenwood and Last month, he kept track of the number of bus riders each day the least number of bus riders is 50.

The least number can be described as the number that serves as the smallest among the given number.

Based on the record that was kept, t can be deduced that the highestnumber is 100 whereby the least of the number is 50 which implies that option A is correct because it is considered to be smallest number hence te least number.

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compete question;

Mr. Pearson drives a bus for the city of Greenwood. Last month, he kept track of the number of bus riders each day.

Bus riders

50

60

70

80

90

100

What was the least number of bus riders?

Answer:

There were 480 customers on Friday.

To calculate the increase from Thursday to Friday, we can use the following formula:

```

Increase = (percent increase / 100) * starting value

```

In this case, the percent increase is 1/5, and the starting value is 400 customers. So, the increase is:

```

Increase = (1/5 / 100) * 400 = 8

```

This means that there were 8 more customers on Friday than there were on Thursday. So, the total number of customers on Friday is:

```

Total = Starting value + Increase

= 400 + 8

= 480

```

Step-by-step explanation:

The value of angle x is determined as 55⁰.

The measure of angle x can be calculated by applying circle theorem which states that the angle at the center of a circle is twice the angle at the circumference of a circle.

This theorem is known as, "Angle at the Center Theorem" or "Central Angle Theorem". It states that the angle formed by two radii (lines segment from the center of the circle to any point on the circumference) of a circle is always twice the size of the angle formed by the same arc (portion of the circumference) when measured at the circumference.

The value of angle x is calculated as follows;

from the given figure;

m ∠MOL = 2 m∠MNL

110⁰ = 2x

x = ¹/₂ x 110⁰

x = 55⁰

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The function is never negative.

option D is the correct answer.

A negative function is a function in which the resulting y value is negative.

Also, a negative function is a function that has y values that are less than zero for any x values. In other words, a negative function has a negative sign in front of its output.

From the given graph, the x and y values started from 0 and increases into the positive direction, so we can conclude that the function can never be negative.

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The calculated value of the surface area of the shape is 192 square cm

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

The triangle (see attachment)

The surface area is calculated as

Area = 1/2 * Base * Height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 24 * 16

Evaluate

Area = 192

Hence, the surface area is 192 sq cm

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