Solve the system of equations.
−5y+3x=3
−8y+9x=−12

To calculate the Loan to Value (LTV) ratio, we divide the loan amount by the purchase price of the property and express the result as a percentage. LTV = 80%

Given: Purchase price of the building: $8,000,000 Loan amount: $6,400,000 LTV = (Loan amount / Purchase price) * 100 LTV = ($6,400,000 / $8,000,000) * 100 LTV = 0.8 * 100 LTV = 80%

Therefore, the Loan to Value (LTV) ratio in this scenario is 80%. This means that the bank has provided a loan equivalent to 80% of the purchase price of the building.

The remaining 20% of the purchase price, which is $1,600,000 in this case, would be the down payment or equity contribution made by the borrower. Correct answer is 80%

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Answer:

Step-by-step explanation:

The formula for the perimeter of a rectangle is often written as P = 2l + 2w, where l is the length of the rectangle and w is the width of the rectangle. The area of a two-dimensional figure describes the amount of surface the shape covers

Answer:

56

Step-by-step explanation:

To find the area of a shape use this formula

Plug in

Area is equal to 56

By the Law of Sines,

\(\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \sin B=\frac{b \sin A}{a} \\ \\ =\frac{244\sin 37.8^{\circ}}{229} \\ \\ B \approx 37.42^{\circ}, 142.58^{\circ}\)

Of these, only 37.42° is a possible value of B (sum of angles of a triangle is 180°).

So, we have that:

\( a=229, b=244, A=37.8^{\circ}, B=\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)\)

Angles of a triangle add to 180°, so:

\(C=180^{\circ}-A-B=142.2^{\circ}-\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)

\)

Using the Law of Sines again,

\(\frac{c}{\sin C}=\frac{a}{\sin A} \\ \\ c=\frac{a \sin C}{\sin A} \\ \\ =\frac{244\sin \left(142^{\circ}-\arcsin \left(\frac{244 \sin 37.8^{\circ}}{229} \right) \right)}{\sin 37.8^{\circ}}\)

So, there is one possible triangle, where:

\(a=229 \\ \\ b=244 \\ \\ c=\frac{244\sin \left(142^{\circ}-\arcsin \left(\frac{244 \sin 37.8^{\circ}}{229} \right) \right)}{\sin 37.8^{\circ}} \\ \\ A=37.8^{\circ} \\ \\ B=\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right) \\ \\ C=142.2^{\circ}-\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)\)

Answer:

38

Step-by-step explanation:

32 + 10 = 42         subtract 42-4 = 38

Answer:

\(2m=45\)

Step-by-step explanation:

He earned twice as much washing cars, which is \(2m\). This is given to be equal to 45.

The domain and range using set notation is {-6, -3, 0, 1, 2, 3} and {2, 1, 0}, respectively

The function is given as:

{(-6,2),(-3,1),(0,0),(1,1),(1,2),(3,0)}

Rewrite the function as:

(x, y) = {(-6,2),(-3,1),(0,0),(1,1),(1,2),(3,0)}

Split the pairs

x = -6, -3, 0, 1, 2, 3

y = 2, 1, 0, 1, 2, 0

Remove repetition

x = -6, -3, 0, 1, 2, 3

y = 2, 1, 0

Hence, the domain and range using set notation is {-6, -3, 0, 1, 2, 3} and {2, 1, 0}, respectively

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Answer:

D.7y(-4x + 5)

Step-by-step explanation:

Answer: d

Step-by-step explanation:

Given points, point A = (2, -5) and point B = (-3, -7).We need to find the translation vector that takes B to A.For any two points A(x1, y1) and B(x2, y2) in a coordinate plane, the translation vector that takes B to A is given by:

Translation Vector = [x1 - x2, y1 - y2]

Here, x1 = 2, y1 = -5, x2 = -3, and y2 = -7

Translation Vector = [x1 - x2, y1 - y2]= [2 - (-3), -5 - (-7)]= [2 + 3, -5 + 7]= [5, 2]

Therefore,

the coordinates of the translation vector that takes B to A are (5, 2).

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Answer:

2/5

Step-by-step explanation:

3/5 x 2/3 = 6/15

6/15 = 2/5

The symbol for an ordered pair is a set of round or parentheses ( ) and it is written as (x,y), where x and y are the coordinates.

Answer:

-12

Ydbzushsbsksjsbsksudjeke

Answer:

ZERO

Step-by-step explanation:

A slope of zero means the line is horizontal. A horizontal line means you will get a slope of zero.

Answer:

Step-by-step explanation:

C.

Answer:

no it's not because is not

Answer:No because you can’t simplify 3/8 more and 1/4=2/8

Step-by-step explanation:

Answer:

Calculate distance first - so using the image we know that if we use pythogorean theorm we can get 2 vectors of this line, 1 completely vertical and one completely horizontal. Apply pythogorean theorm to the line and use for all other question. So 6^2+2^2=c^2

36+4=c^2

distance √40 half of it is √10

So we can use for this for it. (4-√10, 0-√10) so its (4-√10, -√10) for first one

Now that we dont have the image for the line we can apply the distance formula because we dont have clear view of points for #2. -2-6 = -8 then we need 5-1 = 4, -8^2+4^2 = c^2 so then sqrt(80) is distance. 2√5 is half. So then we subtract from (-5, 2) highest point on graph.( -5-√20, 2-√20).

Since this is heavily on writing I expect you to do the rest. Calculating the distance and pythogorean theorm on your own.

First 2 answers are

(4-√10, -√10)

( -5-√20, 2-√20)

The types of triangles which can be used as a counterexample to the statement " all angles in a triangle are acute " are:

Obtuse

Right

Counter example in math's is defined as an attempt at showing that a mathematical statement is false.

Now, in this case we want to find the counter example that all angles in a triangle are acute angles.

Now, an acute angle is defined as an angle that is less than 90 degrees.

Now, A right angle fits the counter example statement because at least one angle is not less than 90 degrees.

Similarly, an Isosceles triangle does not fit the counter example argument because in an isosceles triangle, two angles are equal and it is possible for three of the angles to be less than 90 degrees.

An obtuse triangle means that one of the angles are greater than 90 degrees and as such this fits our counter example.

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The simplified form of the given expression is -18. The correct option is the third option-  -18

From the question, we are to simplify

|3-10| - (12 ÷ 4 + 2)²

Simplifying

|3-10| - (12 ÷ 4 + 2)²

|-7| - (3 + 2)²

7 - (5)²

7 - 25

= -18

Hence, the simplified form of the given expression is -18. The correct option is the third option-  -18

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The corrals that satisfies the population constraint that requires at least 20 square meters of area per animal is option (d) corral 4

To determine which corral meets the population constraints of at least 20 square meters for each animal, we need to calculate the area of each corral and divide it by the number of animals in that corral. If the result is at least 20 square meters, then the corral meets the requirement.

Corral 1: Area = length x width = 50 x 40 = 2000 square meters. Number of animals = 110. Area per animal = 2000/110 = 18.18 square meters. Therefore, Corral 1 does not meet the requirement.

Corral 2: Area = length x width = 60 x 35 = 2100 square meters. Number of animals = 115. Area per animal = 2100/115 = 18.26 square meters. Therefore, Corral 2 does not meet the requirement.

Corral 3: Area = length x width = 55 x 45 = 2475 square meters. Number of animals = 125. Area per animal = 2475/125 = 19.8 square meters. Therefore, Corral 3 meets the requirement.

Corral 4: Area = length x width = 65 x 40 = 2600 square meters. Number of animals = 130. Area per animal = 2600/130 = 20 square meters. Therefore, Corral 4 meets the requirement.

Therefore, the answer is (d) Corral 4.

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Answer:

D. Corral 4

Hope this helps!

Step-by-step explanation:

Answer:

p(t) = 339,996,563(1.005^t)

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

-9/2

Step-by-step explanation:

Answer: a=-9/2 (Exact Form) a=-4.5 (Decimal form) a=-4 1/2 (mixed Number form)

Step-by-step explanation:

Answer:

1.50 $

Step-by-step explanation:

Hope this helps!

The explanatory variable or factor in this study is the type of drug given to the volunteers.

In the study, the researchers are comparing the effects of two different drugs on the severity of depression. They are interested in determining whether the new drug is more effective in treating severe depression compared to the existing drug.

Therefore, the type of drug (new drug or existing drug) is the explanatory variable or factor being investigated in this study.

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We are given that the inside diameter of a piston ring is a random variable with mean value 10 cm and standard deviation 0.07 cm.

We are asked to find the sampling distribution of the sample mean diameter for two different random samples of n=16 and n=64 piston rings, respectively, and to calculate the standard deviation of each sampling distribution.

The sampling distribution of the sample mean diameter is the distribution of all possible sample means that could be obtained from a given sample size n.

The central limit theorem tells us that for large enough sample sizes (typically n ≥ 30), the sampling distribution of the sample mean is approximately normal, regardless of the shape of the underlying population distribution.

The mean of the sampling distribution of the sample mean is equal to the population mean, and the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size.

For the first random sample of n=16 piston rings, the center of the sampling distribution of the sample mean diameter is still 10 cm, as this is the population mean.

However, the standard deviation of the sampling distribution is equal to the population standard deviation of 0.07 cm divided by the square root of 16, which is 0.0175 cm. Therefore, the standard deviation of the sampling distribution of the sample mean diameter for the first random sample is 0.0175 cm.

For the second random sample of n=64 piston rings, the center of the sampling distribution of the sample mean diameter is still 10 cm, but the standard deviation of the sampling distribution is equal to the population standard deviation of 0.07 cm divided by the square root of 64, which is 0.00875 cm.

Therefore, the standard deviation of the sampling distribution of the sample mean diameter for the second random sample is 0.00875 cm.

Finally, we are asked which of the two random samples is more likely to have a sample mean diameter within 0.01 cm of 10 cm. Since the standard deviation of the sampling distribution of the sample mean decreases as the sample size increases, the second random sample of n=64 piston rings is more likely to have a sample mean diameter within 0.01 cm of 10 cm.

This is because the decreased variability of the sampling distribution means that the sample means are more tightly clustered around the population mean of 10 cm. Therefore, we can conclude that the second random sample is more precise than the first random sample.

In statistics, a random sample is a subset of a larger population that is selected in such a way that each member of the population has an equal chance of being included in the sample.

Random sampling is a crucial tool for drawing conclusions about a population based on a smaller subset of data. In this problem, we will explore the sampling distribution of the sample mean for two different random samples of piston rings.

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Answer:

the answer would be A.)

Step-by-step explanation:

The 90% confidence interval for the slope β is approximately (0.079 to 0.106), which is option b.

Part I:
The slope of the least-squares regression line is 0.092498, which is option b.

Part II:
To find the confidence interval for the slope β, we use the formula:
β ± t* (s/√n)
where t is the t-value for a 90% confidence interval with (n-2) degrees of freedom, s is the standard error of the estimate, and n is the sample size.
From the output, we have s = 466.2 and n = 19.
To find the t-value, we can use a t-distribution table or a calculator. For a 90% confidence interval with 17 degrees of freedom, the t-value is approximately 1.734.
Substituting the values, we get:
0.092498 ± 1.734 * (466.2/√19)
Simplifying, we get:
0.092498 ± 0.099
Therefore, the 90% confidence interval for the slope β is approximately (0.079 to 0.106), which is option b.

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Answer:

350 customers

Step-by-step explanation:

Since this is a ratio question and we only have variable that we need to solve (total people that entered last week), Then we can use the Rule of Three to solve this problem. We do this by multiplying the diagonal values of the following model and dividing by the third value in order to find the variable, like so...

18% of customers  <====>  63 customers

100% of customers  <====>  x customers

(100 * 63) / 18 = x

6,300 / 18 = x

350 = x

Finally, we can see that a total of 350 customers entered the store last week.

Linear equation is equation in which each term has at max one degree. The correct option is B.

Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on cartesian plane with axes of those variables, give a straight line.

Given the When the car begins, it is 200 miles from Kingston. After 2 hours, it is 80 miles from Kingston. Therefore, the speed of the car can be written as,

m = (200-80) miles / (0-2)hours = -60miles per hour

Since, the total distance is 200 miles, and the relation between the distance and the time is linear we can write the function that describes the car's distance from kingston is,

y = -60x + 200

Hence, the correct option is B.

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