2.
To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for
each hour of labor.
y (dollars)
4,000
3,000
2,000
1,000
10
20
30 40 50
x (hours)
1. How much would the painting company charge to paint a house that needs
20 hours of labor? A house that needs 50 hours?
Scom
60
2. Draw a line representing the relationship between x, the number of hours it
takes the painting company to finish the house, and y, the total cost of
painting the house. Label the two points from the earlier question on your
graph.
3. Find the slope of the line. What is the meaning of the slope in this context?

Answer:

c

Step-by-step explanation:

(a) The inductance of the solenoid can be found using the formula L = μ₀N²A / l, where μ₀ is the permeability of free space, N is the number of turns, A is the cross-sectional area, and l is the length of the solenoid. (b) The rate of change of current necessary to produce an electromotive force (emf) can bebe determined using the formula emf = -L (di/dt), where L is the inductance and di/dt is the rate of change of current.

(a) To find the inductance (L) of the solenoid, we can use the formula L = μ₀N²A / l, where μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), N is the number of turns (640), A is the cross-sectional area (πr², where r is the radius), and l is the length of the solenoid. Plugging in the given values, we can calculate the inductance.
(b) To determine the rate of change of current (di/dt) required to produce an electromotive force (emf) of 70.0 mV, we can use the formula emf = -L (di/dt), where L is the inductance. Rearranging the formula, we find di/dt = -emf / L. Substituting the given values of emf and the previously calculated inductance, we can find the magnitude of the rate of change of current necessary to generate the specified emf.

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The event is randomly selecting one card from a standard deck of 52 playing cards. We need to determine the number of outcomes in this event and whether it is a simple event or not.

In a standard deck of 52 playing cards, there are 4 suits (hearts, diamonds, clubs, spades) and each suit has 13 cards (Ace, 2-10, Jack, Queen, King). Therefore, there are 52 possible outcomes or cards to choose from in this event.
Now, let's determine if this event is a simple event or not. A simple event is an event that consists of a single outcome. In this case, since we are randomly selecting one card from the deck, the event of selecting a specific card (e.g., Ace of Hearts) would be a simple event because it has a single outcome. However, if the event is defined as selecting a card of a specific suit or a card of a specific rank (e.g., selecting a heart or selecting a King), then it would not be a simple event as there are multiple outcomes associated with that event.
When randomly selecting one card from a standard deck of 52 playing cards, there are 52 possible outcomes in the event. The event of selecting a specific card, like the Ace of Hearts, would be a simple event with a single outcome. However, events defined by selecting cards of a specific suit or rank would not be simple events as they have multiple outcomes.

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The gallon used by the first car is 35 gallons and the gallon used by the first car is 25 gallons.

The first step is to form a system of linear equation:

35a + 20b = 1725 equation 1

a + b = 60  equation 2

Where:

The elimination method would be used to solve this question.

Multiply equation 2 by 35:

 35a + 35b = 2100  equation 3

Subtract equation 1 from equation 3:

15b = 375

Divide both sides of the equation by 15:

b = 375 / 15

b = 25

Substitute for b in equation 2 :

a + 25 = 60

a = 60 - 25

a = 35

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The variable y takes the value -7 when we have x = -3.

Here we have the linear equation:

y = x - 4

We want to find the value of x such that y = -7, to get that, we only need to replace the variable y by the number -7 in the linear equation above:

-7 = x - 4

Now we can solve the linear equation for x.

-7 = x - 4

-7 + 4 = x

-3 = x

That is the solution.

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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Answer:

neither i think..

Step-by-step explanation:

Answer:

niether

Step-by-step explanation:

Answer: The constant of variation, k , is 54

Step-by-step explanation: Step 1: Check whether the graph is a straight line. If the graph is not a straight line, it does not represent a proportional relationship. Step 2: Check whether the line goes through the origin. If the graph does not go through the origin, it does not represent a proportional relationship.

The slope of the line on the graph is -1/2

The given parameters are the points on the line

From the above line, we have the following points

(x₁, y₁) = (9, -5)

(x₂, y₂) = (1, -1)

The slope of a line can be calculated using the following slope formula

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x₁, y₁) = (9, -5) and (x₂, y₂) = (1, -1)

Substitute the known values in the above equation

So, we have the following equation

Slope = (-1 + 5)/(1 - 9)

Evaluate the quotient

Slope = -1/2

Hence, the slope is -1/2

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Answer:

1267.18

Step-by-step explanation:

8.03x106=851.18

4.0x104=416

851.18+416=1267.18

The relation R=((1,2), (2, 1), (3,0), (0,-1), (2,2)) fails to be a function for the real number 2 because it violates the property that each input in the domain must have a unique corresponding output in the range.

A relation is considered a function if every input in the domain is associated with a unique output in the range. In the given relation R, we have the pair (2,1) and (2,2), where the input 2 is associated with two different outputs, namely 1 and 2. This violates the definition of a function, as an input cannot have more than one corresponding output.

To illustrate this, let's consider the mapping of the input 2. According to the relation R, the input 2 is associated with the outputs 1 and 2. In a function, each input should have only one output. However, in this case, we have two different outputs for the same input, which makes R fail to be a function.

Therefore, by choosing the real number 2 as the input, we can see that the relation R=((1,2), (2, 1), (3,0), (0,-1), (2,2)) fails to be a function.

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Answer:

(-5) ^ 11

Step-by-step explanation:

(-5) ^5 / (-5) ^ -6

We know that a^ b / a^ c = a^ ( b-c)

(-5)^ (5 - -6)

(-5) ^ (5+6)

(-5) ^ 11

Answer:

-5

Step-by-step explanation:

Mathaway

The range of 90% confidence interval representing true proportion of the CEOs extremely concerned about cyber threat are (0.2576, 0.3570).

Sample size is large enough for the valid analysis.

Total number of CEOs = 481

Number of CEOs concerned about cyber threats = 148

Confidence interval = 90%

Use the formula,

confidence interval = point estimate ± (critical value) x (standard error)

Point estimate is the sample proportion,

Critical value is determined by the desired level of confidence and the sample size

Standard error is a measure of the variability of the sampling distribution of the sample proportion.

Using the given information, we have,

Point estimate,

148/481 = 0.3073

Standard error,

√[(0.3073)(1-0.3073)/481]

= 0.0302 (rounded to four decimal places)

Critical value,

Critical value for a 90% confidence interval is approximately 1.645.

Margin of error,

(critical value) x (standard error)

= 1.645 x 0.0302

= 0.0497 (rounded to four decimal places)

90% confidence interval for the population proportion of CEOs in the country who are extremely concerned about cyber threats is,

0.3073 ± 0.0497

= (0.2576, 0.3570)

Therefore,  90% confident interval that the true proportion of CEOs in the country who are extremely concerned about cyber threats is between 0.2576 and 0.3570.

Sample size is 481 > 30 is large enough for this to be a valid analysis.

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Answer:

(3,4)

Step-by-step explanation:

Answer:

4,3

Step-by-step explanation:

The probability of - (a) no cracks is approximately 0.0000, (b)at least one crack is 0.3935.The assumption of a Poisson distribution is not valid (0), as the variability in vehicle load may affect the occurrence of cracks.

(a) To find the probability that there are no cracks requiring repair in 15 miles of highway, we can use the Poisson distribution formula. In this case, the mean (λ) is given as 2 cracks per mile, so the mean for 15 miles would be

2 * 15 = 30.

The probability of observing zero cracks is calculated as

\(P(X = 0) = e^(-λ) * (λ^0) / 0!.\)

Substituting the values, we get

\(P(X = 0) = e^(-30) * (30^0) / 0! ≈ 9.3576e-14.\)

(b) To find the probability that at least one crack requires repair in 1/4 mile of highway, we can again use the Poisson distribution.

Here, the mean (λ) is given as 2 cracks per mile, so the mean for 1/4 mile would be 2 * (1/4) = 0.5.

The probability of observing at least one crack is calculated as

P(X ≥ 1) = 1 - P(X = 0).

Using the formula from part (a), we know

P(X = 0) ≈ 9.3576e-14.

Therefore, P(X ≥ 1) ≈ 1 - 9.3576e-14 ≈ 1.

(c) The assumption of a Poisson distribution for the number of cracks requiring repair for all sections might not be valid if the vehicle load on the highway varies significantly.

The Poisson distribution assumes that events occur independently and at a constant rate, which may not hold true if certain sections have a heavy vehicle load while others have a light load.

Factors such as traffic congestion, road conditions, and maintenance practices can affect the occurrence of cracks.

Therefore, a Poisson distribution may not accurately model the variability in the number of cracks in different sections of the highway.

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Answer: She had left 54% of the money which is $1620.

Step-by-step explanation:

40% of $3000 = $1200

15% of $1200 = $180

$3000 - ($1200 + $180)

$3000 - $1380 = $1620

$1620 is the money she had left.

$1620 is 54% of $3000

She had 54% left of the money.

Hope that helped~!

Answer:

y = -5/3x - 6/5

Step-by-step explanation:

Brainliest pls

The area of a 2D form is the amount of space within its perimeter. The area of the school will be equal to 35/108 miles².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the school is the product of length and width. Given the length is 7/12 mile, while the width is 5/9 mile. Therefore, The area of the school campus will be,

Area = (7/12) × (5/9)

        = (35/108) miles²

Hence, the area of the school will be equal to 35/108 miles².

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The missing terms in the sentence are "Inclination" and "Vertical."

Inclination is the angle of tilt below the imaginary horizontal plane oriented 90-degrees to the vertical direction. It refers to the angle at which an object or surface deviates from being perfectly horizontal or flat. It measures the slope or tilt of the object or surface in relation to the vertical direction.

The vertical direction is the imaginary line or axis that points directly up or down, perpendicular to the horizontal plane. It is oriented at a 90-degree angle to the horizontal direction, which is typically considered the direction parallel to the ground or any other reference plane.

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The solution for x is 621.5424 M \(s^{-1}\), with units of molar per second (M \(s^{-1}\)).

To solve for x in the equation x = (6.4×10^3 M^(-2) s^(-1))(0.46M)^3, we can simplify the expression and calculate the result. Let's break it down step by step: x = (6.4×10^3 M^(-2) s^(-1))(0.46M)^3

First, let's simplify (0.46M)^3: (0.46M)^3 = (0.46^3)(M^3) = 0.097336M^3

Now, substitute this back into the equation:

x = (6.4×10^3 M^(-2) s^(-1))(0.097336M^3)

Next, multiply the terms: x = 6.4×10^3 × 0.097336 M^(-2) s^(-1) M^3

When multiplying the terms with the same base, we add the exponents:

x = 6.4×10^3 × 0.097336 M^(-2 + 3) s^(-1)

Simplifying the exponent: x = 6.4×10^3 × 0.097336 M^(1) s^(-1)

Now, multiply the numerical values: x = 621.5424 M s^(-1)

Therefore, the solution for x is 621.5424 M s^(-1), with units of molar per second (M s^(-1)).

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Answer:

The pool is 400 square meters

Step-by-step explanation:

To figure out the are of a slanted shape such as this, we must turn it into a shape that is non-slanted, like a rectangle or square (which is a type of rectangle). For this parallelogram, we can separate the shape into three parts: the two slanted bits on the outside, and a rectangle (7*2) in the middle (or on the inside).

We can see that each slanted part can take up half of two squares, and therefore one square. From here on out, we can do this one of two ways:

1. Figure out the area of the inside rectangle, then add the two slanted parts/two squares separately

OR

2. Since each slanted area equals one square, or since each is half of two square, we can add both sides together (for 1/2 + 1/2 = 1, or in this case,        1 +1 = 2), to make a full or complete rectangle, before figuring out the area of the shape as a whole (8*2).

8*2 = 16

Each square is 1 cm squared, which is in proportion to 25 meters squared (each cm is 5 meters (1:5), so the square, which is 1 cm by 1 cm, is proportionate to 5 meters by 5 meters).

16*25 = 400

The pool is therefore 400 square meters.

Answer:

interestinggggggggggggg

The probability that a standard normal random variable z is between -2.4 and 0.4 is approximately 0.6472.

To find the probability that a standard normal random variable z is between -2.4 and 0.4, we can follow these steps:

Step 1: Look up the cumulative probability corresponding to -2.4 in the standard normal distribution table. The cumulative probability at -2.4 is approximately 0.0082.

Step 2: Look up the cumulative probability corresponding to 0.4 in the standard normal distribution table. The cumulative probability at 0.4 is approximately 0.6554.

Step 3: Subtract the cumulative probability at -2.4 from the cumulative probability at 0.4 to find the probability between the two values:

P(-2.4 < z < 0.4) = 0.6554 - 0.0082

= 0.6472.

Therefore, The probability that z is between -2.4 and 0.4, when z is a standard normal random variable, is approximately 0.6472. This means that there is a 64.72% chance that a randomly selected value from a standard normal distribution falls within the range of -2.4 to 0.4.

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Answer:y=9

Step-by-step explanation:

y=mx+9

Swap sides so that all variable terms are on the left hand side.

mx+9=y

Subtract 9 from both sides.

mx=y−9

The equation is in standard form.

xm=y−9

Divide both sides by x.

x

xm

​

=

x

y−9

​

Dividing by x undoes the multiplication by x.

m=

x

y−9

​

Solve for x

{

x=

m

y−9

​

,

x∈R,

​

m



=0

y=9 and m=0

​

Answer:

Y=1

Step-by-step explanation:

(3,1)

(x,y)

Y=mx+c

1=m3+c

Step-by-step explanation:

decrease value is 1353

value 31,647

===========================================

Work Shown:

Applying the law of cosines

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 8^2 + 5^2 - 2*8*5*cos(88)

c^2 = 64 + 25 - 80*cos(88)

c^2 = 86.2080403

c = sqrt(86.2080403)

c = 9.2848285

c = 9

Technically he needs 10 meters of rope because of the extra 0.28 portion, but I'll stick with 9 meters since your teacher said to round to the nearest whole number.