Bob is shopping for houses in Fullerton. Recently, a 1200 square foot home sold for $600,000, and a comparable 1300 square foot home sold for $640,000. Assuming there is a linear relationship between the square footage of the home and y = the sale price, find an equation for y in terms of x. Write your equation in the form y = mx + b

Answer:

50,20

Step-by-step explanation:

let the two numbers be x and y respectively.

According to the question,

y=2/5 times of x

Or,

y= 2x/5 ..........(1)

Again,

or, x+y=70

or, x+2x/5=70

or, (5x+2x)/5=70

or, 7x=350

therefore x=50

putting the value of y in equation (1)

y=2x/5

y= (2×50)/5

therefore, y=20

Answer:

x = 175

Step-by-step explanation:

given:

A number is 2 /5 times another number. Their sum is 70.

find: the numbers (coefficient)

solution:

cross multiply

2 ( x ) = 70

5

2 (x) = 70 (5)

2 (x) = 350

x = 350

       2

x = 175

check:

2 ( x ) = 70

5

2 ( 175 ) = 70

5

350 = 70

 5

70 = 70

Step-by-step explanation:

end behavior

as x approaches infinity,y also approaches infinity

as x approaches negative infinity, y also approaches negative infinity

domain, x is all real numbers

range f(x) is all real numbers

2 2/3 of a fraction

________________

2 full and 2/3

- Jackson

Answer:

C

Step-by-step explanation:

I got it right

Answer:

The sixth rod is 35.20 cm.

Step-by-step explanation:

Get the total length of the 6 rods.

Total length = 6(44.2cm)

= 265.20 cm

Get the total length of 5 rods

Length of 5 rods = 5(46cm)

=230cm

The length of the sixth rod is the difference between the two.

Length of the sixth rod = 265.20 cm - 230 cm

length = 35.2 cm

In the above case, the possible point system will be:

1st choice vote: 4 points

2nd choice vote: 2 points

In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:

Lets say:

1st choice vote: 4 points

2nd choice vote: 2 points

Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.

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answer:

72

step-by-step explanation:

your question doesn't make mathematical sense how can 12 = 6 then subract 90?

maybe you meant 12 + 6 - 90

if so

the answer is

72

(my work)

12 + 6 = 18

18 - 90 = 72

hope this helped <3

The economist can conclude that the mean FICO score is less than 720 with a 95% confidence level.

To answer this question, we can use a one-sample t-test with a significance level of α=0.05.

First, we need to calculate the t-statistic:

t = (sample mean - hypothesized mean) / (standard deviation / √(sample size))

t = (695 - 720) / (65 / sqrt(60))
t = -2.81

Next, we need to find the critical t-value using a t-distribution table with 59 degrees of freedom (sample size - 1) and a significance level of α=0.05.

The critical t-value is -1.67 (one-tailed test).

Since the calculated t-statistic (-2.81) is less than the critical t-value (-1.67), we can reject the null hypothesis and conclude that the mean FICO score is significantly lower than 720. In other words, based on the sample data, the economist can conclude that the mean FICO score is less than 720 with a 95% confidence level.

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Answer:

Completing the square

Put the equation into the form ax 2 + bx = – c.

Make sure that a = 1 (if a ≠ 1, multiply through the equation by. before proceeding).

Using the value of b from this new equation, add. ...

Find the square root of both sides of the equation.

Solve the resulting equation.

Step-by-step explanation:

there

Answer: Put the equation into the form ax 2 + bx = – c.

Make sure that a = 1 (if a ≠ 1, multiply through the equation by. before proceeding).

Using the value of b from this new equation, add.

Find the square root of both sides of the equation.

Solve the resulting equation.

Step-by-step explanation: Hope this helps!

Answer:

(6,-2)

Step-by-step explanation:

graph and see the point where they cross and that is the solution

As per the trigonometric substitution the value of the integrals are

a) ∫ x² + 4 / x² dx is 2 tan θ

b) ∫ (16 - 9x²) / x² dx is (4/3) sec θ

c) ∫ (5x² - 3) / x² dx is (1/√3)tanθ

Let's take a look at the given integrals:

a) ∫ x² + 4 / x² dx

For this integral, we can use the trigonometric substitution x = 2tanθ. This substitution simplifies the integral and allows us to solve it using trigonometric identities.

b) ∫ (16 - 9x²) / x² dx

To solve this integral, we can use the trigonometric substitution x = (4/3)secθ. This substitution simplifies the expression under the integral sign and allows us to use trigonometric identities to solve the integral.

c) ∫ (5x² - 3) / x² dx

For this integral, we can use the trigonometric substitution x = (1/√3)tanθ. This substitution simplifies the integral and allows us to use trigonometric identities to solve it.

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The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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Answer:

10.75

-5/4

2 7/24

Step-by-step explanation:

1.)

__+-3.5=7.25

Let missing number = x

x - 3.5 = 7.25

x = 7.25 +3.5

x = 10.75

2.)

-3/4-__=1/2

Let missing number = x

-3/4 - x = 1/2

-3/4 - 1/2 = x

(-3 - 2) / 4 = x

-5/4 = x

3.)

-2 3/8-(-4 2/3) = x

-2 3/8 + 4 2/3 = x

-19/8 + 14/3 = x

(-57 + 112) / 24 = x

55 / 24 = x

2 7/24

Answer:

Area = 294 cm^2

Volume = 343 cm^3

Step-by-step explanation:

Simply plug in s = 7 into the given equations.

\(6s^{2} = 6*7^{2} = 294 cm^{2}\)

\(s^{3} = 7^{3} = 343 cm^{3}\)

Answer:

0 = -3x -10y -80

Step-by-step explanation:

Standard form means all numbers are whole numbers, so to get -3/10 to be whole, simply have everything on one side and multiply each term by 10:

y = -3/10x - 8

0 = -3/10x - y - 8

0 = -3x -10y -80

The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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No, it is not possible for Player B to have a higher batting average for the entire season if Player A has a greater batting average in both the first and second halves of the season.

Since Player A has a greater batting average in both halves of the season, it means that Player A has more hits per at-bat compared to Player B in each half. Therefore, Player A would have a higher overall average for the entire season.

If Player B were to have a higher batting average for the entire season, it would mean that Player B performed significantly better in the second half compared to the first half to offset the lower average in the first half. However, the given information states that Player A has a higher average in both halves, making it impossible for Player B to have a higher average for the entire season.

Therefore, the answer is that it is not possible for Player B to have a higher batting average for the entire season.

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Answer:

Step-by-step explanation:

Dont do it. Just take the detention

an equation showing a way to estimate to the neasrt inch the total rainfall for the two day 2.45 + 1.72 ≈ 4.2 inches

1. Add the two amounts of rainfall together: 2.45 + 1.72

2. Round the answer to the nearest inch: 4.2 inches

3. The equation to estimate the total rainfall for the two days is 2.45 + 1.72 ≈ 4.2 inches.

This equation provides a simple way to estimate the total rainfall for two days. By adding the two amounts of rainfall, we can then round the answer to the nearest inch to obtain the estimated total rainfall. This equation can be used to quickly and accurately estimate rainfall totals for any two-day period.

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The value of f(g(x)) is x^2 + 1/x

A function is an expression that describes the relationship between an independent variable and dependent variable.

Given the functions;

f(x) =

\( \sqrt[3]{x} \)

g(x) =

\( \frac{ x+ 1}{ {x}^{3} } \)

How to determine the function

Substitute the value do x as the value of the function g(x)

f(g(x)) =

\( \sqrt[3]{ \frac{x + 1}{ {x}^{3} } } \)

Find the cube root of the expression

f(g(x)) =

\( \frac{ {x}^{3} + {1}^{3} }{x} \)

Find the cube of the values

f(g(x)) =

\( \frac{ {x}^{3} + 1 }{x} \)

Divide through by x, we have;

f(g(x)) = x^2 + 1/x

Thus, the value of f(g(x)) is x^2 + 1/x

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Answer:

Agency A:  y = 12x

So Agency A pays a rate of $12 per hour

Agency B:  y = 10x + 20

So Agency B pays an initial fee of $20 plus a rate of $10 per hour.

Step-by-step explanation:

Agency A

To create a straight line equation for the data in table, use  \(y = mx + b\), where m is the slope and b is the y-intercept.

To find the slope m, take 2 points from the table and use the slope formula.

Let \((x_1,y_1)\) = (3, 36)

Let \((x_2,y_2)\) = (5, 60)

Slope formula: \(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{60-36}{5-3}=12\)

Now use the point-slope formula to create the final equation:

\(y-y_1=m(x-x_1)\)

\(\implies y-36=12(x-3)\)

\(\implies y=12x\)

Therefore, Agency A pays a rate of $12 per hour.

Agency B

From inspection, the function is a straight line.

Therefore we can use the straight line equation \(y = mx + b\),

where m is the slope and b is the y-intercept.

From inspection, we can see that the line crosses the y-axis at (0,20).  Therefore, the y-intercept is 20.

\(\implies y=mx+20\)

Taking 2 points on the line and using the slope formula to find the slope m:

Let \((x_1,y_1)\) = (0, 20)

Let \((x_2,y_2)\) = (3, 50)

Slope formula: \(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{50-20}{3-0}=10\)

Therefore, the final equation is:  \(y=10x+20\)

Therefore, Agency B pays an initial fee of $20 plus a rate of $10 per hour.

This warm-up serves two purposes. It refreshes the concept of distance, rate, and time of travel from grade 6, preparing students to use scale drawings to solve speed-related problems.

It also allows students to estimate decimal calculations.

Students are likely to approach the question in a few different ways. As students work, notice students using each strategy.

By finding or estimating the speed of the train in miles per hour and comparing this to the speed of the car

By finding the distance the car travels in 4 hours and comparing it to the distance the train travels in 4 hours

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The probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.

The cumulative distribution function of X is:\(F(x)= 1- 10/x\)  ( for x > 10)

X = the entire lifespan of a definite type of electronic device in hours, then the probability function of X,

here we use the cumulative distribution function, which is used to specify random variables,

F(X)= 1 - 10/X is cumulative distribution function,

then the probability that at least 3 devices will work for 15 hours

P(X\(\geq\)15)= 1- P(X<15)

            = F(15)

            = 1- 10/15

            =5/15

            =0.333

Hence, the probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.

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Answer:

2x+20

Step-by-step explanation:

Given

Age of Ethen = x

If Raj is 8 years older than Ethen, then;

Raj = x + 8

6 years time

Ethen age = x+ 6

Raj = x+8+6 = x+14

Sum of ages in 6 years time = x+6+x+14

Sum of ages in 6 years time = 2x + 20

Hence the required sum of ages is 2x+20

The solution of the given initial value problem is,

⇒ y = (t³/3 + t) + 7

The given differential equation is,

dy/dt = t² + 1,    t ≥ 0

This is a separable differential equation,

Which means we can separate the variables "y" and "t" on opposite sides of the equation and integrate both sides.

Starting with the given equation:

⇒ dy/dt = t² + 1

We can separate the variables:

⇒ dy = (t²  + 1) dt

Now, we can integrate both sides:

⇒ ∫ dy = ∫ (t^2 + 1) dt

⇒ y = (t³/3 + t) + C

Where C is a constant of integration.

Using the initial condition y = 7 when t = 0,

we can solve for C,

⇒ 7 = (0³/3 + 0) + C

⇒ C = 7

Therefore, the solution to the differential equation is:

⇒ y = (t³/3 + t) + 7

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Answer:

10 and 11

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

Step-by-step explanation:

\( log_{b}(6) = 1.79\)

Change of Base Formula,

\( \frac{ log(6) }{ log(b) } = 1.79\)

\( \frac{ log_{}(b) }{ log(6) } = \frac{1}{1.79} \)

\( log_{6}(b) = \frac{1}{1.79} \)

or

0.55865.... round if neededd

The present ages of the man and his son are 60 years and 25 years, respectively.

Let's assume the present age of the son is x years. According to the given information, five years ago, the man was thrice as old as his son, so the man's age at that time was 3(x - 5) years.

Now, let's consider the future scenario. In 10 years, the man's age will be (3(x - 5) + 10) years, and the son's age will be (x + 10) years.

According to the second given information, the man will be twice as old as his son in 10 years, so we can write the equation:

3(x - 5) + 10 = 2(x + 10)

Simplifying the equation:

3x - 15 + 10 = 2x + 20

3x - 5 = 2x + 20

3x - 2x = 20 + 5

x = 25

Therefore, the present age of the son is 25 years. Substituting this value into the equation for the man's age five years ago:

Man's present age = 3(x - 5) = 3(25 - 5) = 3(20) = 60 years

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