The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = −3.
x = −4, y = −6
The equation is y =

Answer:

the answer is B

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Answer:

Step-by-step explanation:

(-2, 2)   (2, -3)

(-3 - 2)/(2 + 2)

-5/4 the slope

y - 2 = -5/4(x + 2)

y - 2 = -5/4x - 5/2

y- 4/2 = -5/4x - 5/2

y = -5/4x - 1/2

To calculate your fuel consumption in gallons per hour, divide the speed (in miles per hour) by the fuel efficiency (in miles per gallon). This will give you the gallons per hour (GPH).

For example, if your speed is 50 mph and your fuel efficiency is 30 mpg, your fuel consumption would be 1.67 GPH (50/30). You can then use this result to estimate your fuel costs and overall fuel consumption over a certain period of time.

To understand this concept better, it is important to know that speed (in mph) and fuel efficiency (in mpg) are inversely related. This means that as your speed increases, your fuel efficiency decreases, and as your speed decreases, your fuel efficiency increases.

So, if you want to maximize your fuel efficiency, you need to drive at the lowest possible speed. Additionally, the higher the fuel efficiency, the lower the fuel consumption in GPH.

In short, you can use the readout from your odometer and fuel efficiency meter to calculate your fuel consumption in GPH by dividing the speed (in mph) by the fuel efficiency (in mpg). This result can help you estimate your fuel costs and overall fuel consumption.

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a) Deposit around $6,825.23 annually for 12 years with a 12% interest rate compounded monthly to have $250,000.  b) For continuous compounding, deposit approximately $5,308.94 annually.

a) To calculate the annual deposit required with a 12% interest rate compounded monthly, we can use the formula for the future value of an ordinary annuity:\[ FV = P \times \left( \frac{{(1 + r/n)^{n \times t} - 1}}{{r/n}} \right) \]

Where:FV = Future Value ($250,000)

P = Annual deposit

r = Interest rate per period (12% or 0.12)

n = Number of compounding periods per year (12)

t = Number of years (12)

Rearranging the formula and plugging in the values, we have:

\[ P = \frac{{FV \times (r/n)}}{{(1 + r/n)^{n \times t} - 1}} \]

\[ P = \frac{{250,000 \times (0.12/12)}}{{(1 + 0.12/12)^{12 \times 12} - 1}} \]

\[ P \approx \$6,825.23 \]Therefore, you would need to deposit approximately $6,825.23 annually.

b) If the interest is compounded continuously, we can use the formula for continuous compounding:\[ FV = P \times e^{r \times t} \]

Where:FV = Future Value ($250,000)

P = Annual deposit

r = Interest rate per year (12% or 0.12)

t = Number of years (12)

Rearranging the formula and substituting the given values:

\[ P = \frac{{FV}}{{e^{r \times t}}} \]

\[ P = \frac{{250,000}}{{e^{0.12 \times 12}}} \]

\[ P \approx \$5,308.94 \]Thus, you would need to deposit approximately $5,308.94 annually.



Therefore, a) Deposit around $6,825.23 annually for 12 years with a 12% interest rate compounded monthly to have $250,000.  b) For continuous compounding, deposit approximately $5,308.94 annually.

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I would have saved a total of $3800 in 12 months

From the question, the given parameters are:

The amount saved at the end of each month is represented as

Total amount = Initial amount of savings + Savings each month x Number of months

So, we have

y = 200 + 300x

Where x represents the number of months and y represents the total amount

For 12 months, we have

y = 200 + 300 x 12

Evaluate

y = 3800

Hence, the amount of money saved in 12 months is 3800

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Thomas considers cohesion to be the presence of strong positive bonds between members of a group. In his perspective, cohesion represents a sense of unity, attachment, and solidarity among individuals within the group.

Cohesion, according to Thomas, goes beyond mere cooperation or coordination of activities. It encompasses the emotional and social aspects of group dynamics, emphasizing the quality and strength of the relationships between members. The existence of strong positive bonds implies that individuals feel connected, trust each other, and have a shared sense of identity and purpose.

Thomas likely believes that cohesive groups are characterized by mutual support, collaboration, and a sense of belonging. Members are more likely to work together effectively, communicate openly, and have a higher level of commitment to group goals. Cohesion may also contribute to increased satisfaction, motivation, and overall well-being within the group.

Thomas's perspective aligns with the socio-emotional aspect of group cohesion, emphasizing the interpersonal connections and social dynamics that contribute to the cohesiveness of a group.

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Answer:

Yes, the runners number of strides will fit evenly into the length of the race.

Step-by-step explanation:

The bridge is 138,435 feet. You would divide this to get 46,145 as a whole number.

Answer:

Step-by-step explanation:

You are dividing 138435 by 3.

The quotient would be 46145 with no remainder. So the answer would be yes.

A 2nd way to do this is to see if 183435 is a multiple of 3.

Hope this helps!

Have a great day!

Answer:

\( F = mt +b\)

From the info given we know that m =-11 and we have a condition given:

\( F =90 , t =4\)

Using this condition we have:

\( 90 = -11*4 +b\)

And solving for b we got:

\( 90 +4*11 = 90 +44= 134\)

So then the original temperatue for this case is 134 F

Step-by-step explanation:

For this case we know that after four hours the temperature was 90 f and the temperature dropped 11 f per hour.

We can use a linear model to solve the problem given by:

\( F = mt +b\)

Where F represent the temperature, t the time in hours and m the slope and b the intercept.

From the info given we know that m =-11 and we have a condition given:

\( F =90 , t =4\)

Using this condition we have:

\( 90 = -11*4 +b\)

And solving for b we got:

\( 90 +4*11 = 90 +44= 134\)

So then the original temperatue for this case is 134 F

Answer:

(-2,6]

Step-by-step explanation:

to find the domain, just looks for the x axis

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

Explanation:

The domain spans from -2 to 6 on the x axis number line.

We exclude -2 because of the open hole; but we include 6 because of the closed circle endpoint.

We could say the domain is \(-2 < \text{x} \le 6\) but it's more compact to write it as (-2,6] which is in interval notation.

Use a curved parenthesis to exclude the endpoint. A square bracket includes the endpoint.

Answer:

the answer is 1470

Step-by-step explanation:

157+376+413+524

=1470

Answer:

This table represents a function

y is 1.3 times x

y=1.3x

Step-by-step explanation:

iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. 81.855%  of the population has an iq score between 70 and 115

What is z-score?

The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.

Using z tables, you may calculate the proportion of the population that is either below or above the score.

Now, according to the question;

IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.

A z score is determined as follows:

z = (x - μ)/σ

μ = mean of the distribution

σ = standard distribution of the sampling.

Calculation for the z score for x = 70 and  115

z= (70-100)/15

= -30/15

=-2

and x=115

z = (115 - 100)/15

= 15/15

z = 1.0

Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,

P( -2 < z < 1)= P(z<1) - P(z< -2)

                   =  0.8413 - 0.02275

                  = 0.81855

Therefore, the percent of the population has an iq between 70and 115 is 81.855%.

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Answer:

5/-9

Step-by-step explanation:

cuz it is just trust me

The probability that a randomly selected hot water heater has a life span of between 12 and 15 years is about 65.62%.

A Z-score is a numerical measurement that describes a cost's relationship to the suggestion of a group of values. Z-score is measured in terms of standard deviations from the suggested. If a Z-score is 0, it suggests that the statistics point's rating is identical to the mean rating.

According to the question;

Mean (μ) = 13 years

Standard deviation (σ) = 1.5 years

The z score can be used to find the probability of a random variable occurring over a normally distributed parameter if its mean and standard deviation is given. z = x- μ /  σ

The z score can then be used to find the probability of a randomly selected hot water heater lifespan being below that value: P ( Z < z)

First, find the z score for 12 and 15

z = 12 - 13 / 1.5 = - 0.6667

z = 15 - 13 / 1.5 = 1.333

Therefore,

P ( X < 12) = P ( Z < - 0.6667 ) ≈ 0.2525

P ( X < 15) = P ( Z < 1.333 ) ≈ 0.9087

To find the probability of a randomly selected hot water heater having a lifespan between 12 and 15 over this distribution, subtract the P for the lower value from the P for the higher value.

P ( - 0.6667 < X < 1.333 )  = P ( Z < 1.333 ) - P ( Z < - 0.6667 ) = 0.9087 - 0.2525 = 0.6562

P ( 12 < X < 15 ) ≈ 65.62%

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the solution to the system of equations is (x, y) = (1, -7).

How to solve?

The given system of equations is:

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

y = -7x ...(2)

To solve the system by substitution, we can substitute the value of y from equation (2) into equation (1) and solve for x.

Substituting y = -7x from equation (2) into equation (1), we get:

-7x = -3x + 4

Adding 7x to both sides, we get:

4x = 4

Dividing both sides by 4, we get:

x = 1

Now, substituting x = 1 into equation (2), we get:

y = -7(1) = -7

Therefore, the solution to the system of equations is (x, y) = (1, -7).

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Kay deposited (c)$93.44  in cash and coins.

Money or coins that are legal tender can be used to pay for goods, debts, or services. Additionally, as stated by a corporation, it occasionally includes the worth of assets that can be quickly converted into cash. In its physical form, cash is another name for money. Bank accounts and marketable securities, such as government bonds and banker's acceptances, are typically included in the definition of "cash" in a business context.

We proceed from the whole backward. The amount deducted for cash received is first added back,

498.01+213.51 = 711.52

Each cheque that was deposited is then subtracted:

711.52-40.25 = 671.27

671.27-57.68 = 613.59

613.59-520.15 = 93.44

She started with (c) $93.44 in cash and coins.

Correct Question :

How much did kay deposit in cash and coins? a. $404.57 b. $213.51 c. $93.44 d. $284.50

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The chi-square test for goodness of fit will produce a large value for chi-square under the circumstances where the observed frequencies significantly deviate from the expected frequencies based on the null hypothesis.

The chi-square test for goodness of fit is used to determine if there is a significant difference between the observed frequencies in a sample and the expected frequencies based on a specified distribution.

The test compares the observed frequencies in different categories or groups with the expected frequencies under the null hypothesis.

A large value for chi-square indicates a significant discrepancy between the observed and expected frequencies, suggesting that the null hypothesis is not supported.

This can occur in several circumstances.

First, if the sample size is large, even small differences between observed and expected frequencies can lead to a significant chi-square value.

Second, if there are substantial deviations between the observed and expected frequencies in one or more categories, the chi-square value will be large. This could indicate a lack of fit between the observed data and the expected distribution.

Additionally, if the assumptions of the chi-square test are violated, such as independence of observations or expected frequencies being sufficiently large, it can lead to inflated chi-square values.

These violations can distort the results and lead to a larger chi-square value.

In summary, the chi-square test for goodness of fit produces a large chi-square value when the observed frequencies significantly deviate from the expected frequencies, indicating a lack of fit between the observed data and the expected distribution.

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Answer:

Cheeeeseeeeii

Step-by-step explanation:

Cheeeeseee

The higher the standard deviation of an arrival process with an average interarrival time of 6 minutes, the more variability or dispersion there is in the arrival times.

Standard deviation measures the dispersion or spread of data points around the mean. In the context of an arrival process, it represents the degree of variability in the time intervals between arrivals. A higher standard deviation indicates that the arrival times are more scattered or deviate more from the average interarrival time of 6 minutes.

When the standard deviation is high, it suggests that the arrival process is less predictable or more random. The actual interarrival times may vary significantly from the expected average of 6 minutes. This can lead to less efficient scheduling or planning as the arrival times become less predictable.

In contrast, when the standard deviation is low, the arrival times tend to be more consistent and closely clustered around the average interarrival time. This indicates a more predictable and reliable arrival process.

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Answer: 360

Step-by-step explanation:

done

Answer:

1364 is the number of possibilities for positive integers less than 1,00,000.

Step-by-step explanation:

1. 5 digit numbers:

We have 5 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 5 digit numbers:

\(4 \times 4 \times 4 \times 4 \times 4\\ \Rightarrow 1024\)

2. 4 digit numbers:

We have 4 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 4 digit numbers:

\(4 \times 4 \times 4 \times 4 \\ \Rightarrow 256\)

3. 3 digit numbers:

We have 3 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 3 digit numbers:

\(4 \times 4 \times 4 \\ \Rightarrow 64\)

4. 2 digit numbers:

We have 2 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 2 digit numbers:

\(4 \times 4 \\ \Rightarrow 16\)

5. 1 digit numbers:

We have 1 place here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 1 digit numbers:

\(4\)

We can add all the above possibilities to find the total.

So,  number of positive integers less than 100,000 whose digits are among 1, 2, 3, and 4 = 1024 + 256 + 64 + 16 + 4 = 1364

Answer:

This is a waste of time. I'm sorry you have to do this, this is pointless. I did it too. I'll spare you the calculations — it's 1364.

Answer:

Proportionality constant k

When two variables are directly or indirectly proportional to each other, then their relationship can be described as y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.

Answer: Proportionality constant k

Step-by-step explanation:

below?

Answer:

225 units squared

Step-by-step explanation:

The area of a triangle is 1/2*base*height.

A = 1/2*b*h

base = 45

height = 10

Just plug into formula.

A = 1/2*(45)*(10) = 225

Answer:

x=10

Step-by-step explanation:

x-4=6

To isolate x, you can add 4 to both sides of the equation:

x-4+4=6+4

x=10

Hope this helps!

Step-by-step explanation:

x=10

Answer:

A=2m⁴+17m³+11m²+24m

Step-by-step explanation:

The area of rectangle is length × width

A=LW

A=(m+8)(2m³+m²+3m)

A= 2m⁴+m³+3m²+16m³+8m²+24m

A=2m⁴+m³+16m³+3m²+8m²+24m

A=2m⁴+17m³+11m²+24m

The histogram, time series, box plot, stem and leaf, and frequency polygon.

Dot plots, stem and leaf graphs, histograms, box plots, ogive graphs, and scatter plots are all used to graph numerical data. The dot plot: Stem and leaf: The stem represents the first digit of the number in these graphs, while the leaf/leaves indicate the second digit (s). A histogram or a polygon graph should be used for scores that fall on an interval or ratio scale. A bar is centered above each score (or interval) in a histogram, with the height corresponding to the frequency of that score or interval and the width according to the true boundaries of that score or period.

Scatterplot. Scatter plots are effective for displaying accurate, dense data visualizations, relationships, and groupings between variables.

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Answer:

The kinetic energy (KE) of an object with mass (m) moving at a velocity (v) can be calculated using the formula:

KE = 1/2 * m * v^2

Substituting the given values:

KE = 1/2 * 1200 kg * (8.33 m/s)^2

KE = 41,147.5 J

Therefore, the kinetic energy of the object is 41,147.5 Joules.

Step-by-step explanation:

x+2x+x=d is solution set of a linear system whose augmented matrix.

What does matrix mean?

First statement

[ 1 2 3 | d][x]

[ 1 2 3]x=d

x+2x+3x=d

Second statement

Ax=d

Given that A = [ 1 2 3]

[ 1 2 3]x=d

x+2x+3x=d

x+2x+x=d

Then, they are going to have the same solution

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