What is the difference between the x-intercept and the y-intercept? Give examples with numbers for points.

The potters are qualified for the home loan as their total monthly payment is $831.02, which is less than $1000.00.

The total cost of the cottage along with the annual insurance and taxes is $118,000 + $710 + $2800 = $121,510.

The down payment made by the potters is $14,000. Therefore, the amount to be financed through a mortgage is $121,510 - $14,000 = $107,510.

Using the formula for the monthly payment of a mortgage, which is given by:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

where P is the principal (amount to be financed), i is the monthly interest rate, and n is the total number of monthly payments.

For a 5%, 15-year mortgage, the monthly interest rate is 0.05/12 = 0.0041667, and the total number of monthly payments is 15 x 12 = 180.

Plugging in the values, we get:

M = $107,510 [ 0.0041667 (1 + 0.0041667)^180 ] / [ (1 + 0.0041667)^180 - 1 ]

M = $831.02

Therefore, the total monthly payment for the mortgage and the annual insurance and taxes is $831.02 + $59.17 + $233.33 = $1123.52, which is more than the maximum allowed payment of $1000.00. Hence, the potters are qualified for the home loan.

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Answer:

(4,1)

Step-by-step explanation:

point b is at (-1, 4) and the rule for 90 degree clockwise rotations is (y, -x) so it's (4, 1)

Answer:

the answer is 4, 1

After 7 minutes, the tank contains 260 gallons of water.

The required linear function W that gives the number of gallons of water in the tank after t minutes is W(t) = -20t + 400.

 (a)Formula for a linear function W that gives the number of gallons of water in the tank after t minutes is given by

                                              W(t) = -20t + 400.

Here, the independent variable is t which denotes the time in minutes, and the dependent variable is W which denotes the volume of water in the tank.

The function has a slope of -20, which indicates the rate of water drained per minute, and an initial volume of 400 gallons.

(b) To determine the number of gallons of water in the tank after 7 minutes, substitute t = 7 in the linear function W,

We get;

                                    W(7) = -20(7) + 400 = -140 + 400 = 260 gallons

Therefore, after 7 minutes, the tank contains 260 gallons of water.

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We should administer 2.05 ml/hr.

A sort of neurotransmitter and hormone is dopamine. It affects a variety of vital bodily processes, such as mobility, memory, rewarding pleasure, and motivation. Dopamine levels are linked to a number of neurological and mental health conditions.

To determine the ml/hr to administer, we first need to calculate the dose of dopamine in mg/kg/min. We can use the following formula:

dose (mg/kg/min) = 4 mcg/kg/min x 10^-3 (to convert from mcg to mg)

dose (mg/kg/min) = 0.004 mg/kg/min

Next, we need to calculate the total dose in mg/min. We can use the following formula:

dose (mg/min) = dose (mg/kg/min) x weight (kg)

dose (mg/min) = 0.004 mg/kg/min x 64 kg = 0.256 mg/min

Now we need to convert the dose from mg/min to ml/hr, using the following formula:

ml/hr = dose (mg/min) x weight (kg) / concentration (mg/ml) x 60 min/hr

ml/hr = 0.256 mg/min x 64 kg / 400 mg/250 ml x 60 min/hr

ml/hr = 2.048 ml/hr

To round to the nearest tenth, we will round 2.048 to 2.05 ml/hr. Therefore, we should administer 2.05 ml/hr.

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The required unit of the measure of the mean is given as in Dollars. Option A is correct.

What does math's median mean?

When a data set's median value is used, 50% of the data points in the collection have values that are lower or equal to the median and 50% of them have values that are higher or equal to the median.

                               When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.

Due to that,

With a mean of $21,800 and a standard deviation of $400, the price distribution for a specific car model is roughly typical. Four of the model's cars will be chosen at random as the sample.

                                  It must be established which unit of measurement is appropriate for the mean of the sample distribution of the car's pricing.

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Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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11.1% of porcelain tile has strength up to 185 per square inch, while 6% has strength of 206.4 per square inch.

a. To find the percent of its popular porcelain tile that will have breaking strengths at most 185 pounds per square inch, we can use the Z-score formula. The Z-score formula is Z = (x - μ) / σ. In this problem, x is 185, μ is 200, and σ is 6.2. Plugging these values into the formula, we get Z = -2.42. To find the percent of tiles that have a breaking strength of at most 185 pounds per square inch, we can use a Z-score table. Looking up -2.42 on the Z-score table, we get a probability of 0.011, or 11.1%.

Z = (x - μ) / σ.

x=185

μ =200

σ = 6.2

Z = -2.42

Hence, probability = 0.011, or 11.1%.

b. The strongest 6% of its popular porcelain tile will have a breaking strength of 206.4 pounds per square inch. To find this value, we can use the Z-score formula again. This time, we will use a positive Z-score of 1.645, which corresponds to a probability of 0.06. Plugging this value into the formula, we get,

x = μ + (Z * σ).

Thus, x = 200 + (1.645 * 6.2) = 206.4.

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Answer:

Im gonna take a guess and say that the number of students is x and the $ collected is y

Step-by-step explanation:

Answer:

This is compound probability. You find the answer by taking each individual probability and multiplying them by each other. The answer to your problem depends on what happens after picking the first number. The common terminology in math is replacing or not replacing.For example, if you choose the odd number on the first pick the probability is 2/4 OR 1/2. If you replace the number you still have all 4 numbers. The probability of choosing an odd number the second time is the same, 1/2. As described earlier you multiply each probability by each other. P(odd number) x P(odd number): 1/2 * 1/2 = 1/4. The answer when replacing the original number is 1/4 Without replacing after the first drawn number your final answer looks different. The first draw remains the same, 2/4 OR 1/2. If you hold on to that number, the probability of drawing another odd number is 1/3 because there is only 1 odd number left and there is a total of 3 numbers remaining. You take 1/2 * 1/3 = 1/6. The answer without replacing after the first draw is 1/6.

Step-by-step explanation:

hope this helps if not let me know

The kinetic energy of the volleyball is 945 joules.

To calculate the kinetic energy of the volleyball, we can use the formula:

Kinetic Energy = 1/2 \(\times\) mass \(\times\) velocity^2

Mass of the volleyball (m) = 2.1 kg

Velocity of the volleyball (v) = 30 m/s

Plugging these values into the formula, we have:

Kinetic Energy = 1/2 \(\times\) 2.1 kg \(\times\) (30 m/s)^2

Simplifying the equation:

Kinetic Energy \(= 1/2 \times 2.1 kg\)  times \(900 m^2/s^2\)

Kinetic Energy \(= 0.5 \times2.1 kg \times 900 m^2/s^2\)

Kinetic Energy = 945 J (joules)

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Answer:

91. The probability that Caroline will be ready before Andrew is 0.25 (Option B). Since the service times are exponentially distributed with a mean 15 minutes, the remaining service time for Andrew when Caroline arrives is also exponentially distributed with the mean 15 minutes. The service time for Caroline is also exponentially distributed with mean 15 minutes. The probability that Caroline’s service time is less than Andrew’s remaining service time is given by the formula P(X < Y) = 1 / (1 + λY / λX), where λX and λY are the rates of the exponential distributions for X and Y respectively. Since both service times have the same rate (λ = 1/15), the formula simplifies to P(X < Y) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Andrew is 0.25.

92. The probability that Caroline will be ready before Bob is 0.35 (Option A). Since Bob arrived 10 minutes after Andrew, his remaining service time when Caroline arrives is exponentially distributed with mean 15 minutes. Using the same formula as above, we get P(X < Y) = 1 / (1 + λY / λX) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Bob is 0.35.

Answer:

1/6

Step-by-step explanation:

\(36^{-1/2}=\frac{1}{36^{1/2}}=\frac{1}{\sqrt{36}}=\frac{1}{6}\)

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

3 hours

Step-by-step explanation:

Step one:

given data

Dana charges

$64.95 fee, plus $45/h.

let the number of hours be x

and the total charges be y

y= 45x+64.95---------1

Tom charges

$79.95 fee, plus $40/h.

let the number of hours be x

and the total charges be y

y= 40x+79.95---------2

Step two:

Equate eqn 1 and 2 to find x

45x+64.95=40x+79.95

collect like terms

45x-40x=79.95-64.95

5x=15

divide by 15

x= 15/5

x= 3 hours

The slopes of the secant lines passing through P(4,2) and Q(x,f(x)) for x = 2, 5, and 8 are 0.500, 1.000, and 1.500 respectively.

The estimated slope of the tangent line to the graph of f at P(4,2) is 1.000. To improve the approximation of the slope, one can choose secant lines that are closer to P and nearly vertical.

In more detail, let's analyze the function f(x) = x and the point P(4,2) on its graph.

(a) To find the slope of each secant line passing through P(4,2) and Q(x,f(x)), we calculate the difference in y-values divided by the difference in x-values. The secant lines for x = 2, 5, and 8 are:

- For Q(2,f(x)), the slope is (f(2) - 2) / (2 - 4) = (2 - 2) / (-2) = 0.500.

- For Q(5,f(x)), the slope is (f(5) - 2) / (5 - 4) = (5 - 2) / 1 = 3.000.

- For Q(8,f(x)), the slope is (f(8) - 2) / (8 - 4) = (8 - 2) / 4 = 1.500.

(b) To estimate the slope of the tangent line to the graph of f at P(4,2), we can consider the secant lines that are closer to P and nearly vertical. From part (a), we can see that as we choose secant lines with points closer to P, the slopes approach 1.000. Therefore, we can estimate the slope of the tangent line to be 1.000.

To improve the approximation of the slope, we can choose even smaller intervals around P and calculate the slopes of the secant lines. By selecting points that are closer to P, the secant lines become more similar to the tangent line, resulting in a better approximation of the slope. Additionally, choosing secant lines that are nearly vertical allows us to better capture the instantaneous rate of change at P and improve the estimation of the slope of the tangent line.

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The slope of the equation is 0.6, which means that for every second, the computer downloads 0.6 megabytes of data, option C is correct.

The linear equation that represents the number of megabytes downloaded per second can be determined by dividing the total amount of data downloaded (3 MB) by the time taken to download it (5 seconds). This gives us the rate of download in megabytes per second (MB/s). Therefore, the equation is:

y = 0.6x

where y represents the number of megabytes downloaded per second and x represents the time taken to download the data. The negative slope values in the other options do not make sense, as the number of megabytes downloaded per second should be a positive value, option C is correct.

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Answer:

280

Step-by-step explanation:

The domain of this quadratic function is {-∞, ∞}.

The range of this quadratic function is {3, ∞}.

In Mathematics, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Generally speaking, the domain of this quadratic function are all the x-values (independent value) that are located on the x-axis of the graph, which include {-∞, ∞} or all real numbers.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞}.

Range = {3, ∞}

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The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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The probability that a randomly selected datum falls within 2 standard deviations of the mean as required is; 0.95.

By observation, it follows that the distribution as represented in the task content above is a normal distribution.

On this note, the empirical rule applies as follows;

For a standard normal distribution, 68% of the observations (datum) fall within 1 standard deviation of the mean; 95% of the datum lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean.

On this note, when expressed as a percentage; the probability that the randomly selected datum falls with 2 standard deviations is; 95/100 = 0.95.

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The number is 7 if the difference of five and one-tenth, and half of a number is one and six-tenths.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The difference between five and one-tenth, and half of a number is one and six-tenths.

Let x be the number:

= 5 1/10 - x/2 = 1 6/10

= 51/10 - x/2 = 16/10

x/2 = 51/10 - 16/10

x/2 = (51-16)/10

x/2 = 35/10

x = 7

Thus, the number is 7 if the difference of five and one-tenth, and half of a number is one and six-tenths.

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Answer:

"?" = 3

Step-by-step explanation:

The answer can be gotten by subtracting 4 from 7. The 4 is the exponent in (4a^4b), and the 7 is the exponent in 16a^7b. So:

7 - 4 = 3

Therefore, the "?" = 3

Hope this helps :)

Answer:

?=3

Step-by-step explanation:

Okay so with exponents, when multiplying exponents with the same base, you add them.

In your case, we have a^? * a^4=a^7 (this is the only part you need to solve)

so ?+4=7

?=7-4=3

Have a nice day!

Answer:

j = 8m + 48 is correct

Step-by-step explanation:

You see that the y-intercept where x is equal to is 48, and after one month it increases by 8, so we have j = 8m + 48. You were correct

Answer:

The bottom right answer.

Domain -5, -1, 0, 1, 2, 3

Range -4, 0, 2, 3, 4

Step-by-step explanation:

Domain is all the x coordinates, Range is all the y coordinates

To find the Domain, work left to right on the x-axis and list the x coordinates.

-5, -1, 0, 1, 2, 3

To find the Range, work from the bottom to the top of the y-axis and list the y coordinates.

-4, 0, 2, 3, 4

Answer:

a recursive definition for your sequence is

adding (6) to each one of the digits

Step-by-step explanation:

The given system of equations do not have a solution since their related line equations have the same slope.

The given system of equations is:

-x + 5y = 3   .......... (1)

2x - 10y = 4   ........(2)

In Equation (1), add both sides by (-5y)

-x + 5y + (-5y) = 3 + (-5y)

-x = -3 - 5y

Multiply by (-1)

x = 3 + 5y

Substitute x = 3 + 5y into equation (2)

2x - 10y = 4

2.(3 + 5y) - 10y = 4

6 + 10y - 10y = 4

6 = 4 (False)

Since the last equation is false, we might suspect that the given system of solution does not have solutions.

We need to check the slope of both equations:

-x + 5y = 3

⇒ 5y = x + 3

⇒ y = 1/5 x + 3/5

2x - 10y = 4

⇒ -10 y = -2x + 4

⇒ y = (2/10) x - 4/10

⇒ y = 1/5 x - 2/5

We can see that both equations have the same slope, i.e. 1/5.

Hence, they do not have solutions since the lines are parallel to each other.

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Step-by-step explanation:

when thuong real estate sold kate's house, she was charged in commission of $4,000. If the house sold for $80,000, what percent commission did the real estate company charge?

4,000 / 80,000 = 0.05

0.05 = 5% commission