NEED HELP ASAP!
The sum of two numbers is 105. The larger number is 6 less than twice the smaller
number. What are the numbers?
Answers
Answer: x=68, y=37
Step-by-step explanation:
The equation for the sum of two numbers is 105 would be x+y=105. You can say the larger number would be x and the smaller would be y. So, x=2y-6. then you plug that into the x in the first equation.
2y-6+y=105
3y-6=105
3y=111
y=37
Then you would plug in the y to one of the equations. I will do the second one but you can do either one.
x=2y-6
x=2*37-6
x=74-6
x=68
Related Questions
What is KJG? REASON:
Answers
Answer:
55
Step-by-step explanation:
this is because FJI & HJG are congruent. They are both 90*. So, subtract 35 from 90 to get the answer
Answer:
Step-by-step explanation:
I'm sorry I was trying to get out of this and the submited the answer
please help asap ;-;
Answers
Answer:
D.
Step-by-step explanation:
Both have a slope or "rate of change" of 1/2 because going from (0,5)-->(2,6) on the first one you go right 2 units and up 1 and slope is rise over run or y/x values in this case it would be 1/2 and on the bottom function you can see it goes from (0,-2)-->(4,0) and this goes right 4 units and up 2 units same principal applies you get 2/4 which is equal to 1/2 also it being negative or not doesn't change whether the two functions have the same rate of change.
I don't get what to do with this!
Answers
Answer:
76+76=152
Step-by-step explanation:
let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b) find sin (θ+y)
Answers
In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement
\(\sin (\theta)=\frac{3}{5}\)Describes the following triangle
To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation
\(x^2+3^2=5^2\)Solving for x, we have
\(\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}\)The missing length of the first triangle is equal to 4.
For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression
\(\tan (y)=\frac{12}{5}\)Describes the following triangle
Using the Pythagorean Theorem again, we have
\(5^2+12^2=h^2\)Solving for h, we have
\(\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}\)The missing side measure is equal to 13.
Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.
The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles
\(\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}\)To calculate the sine and cosine of the sum
\(\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}\)We can use the following identities
\(\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}\)Using those identities in our problem, we're going to have
\(\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}\)
Writing expressions form context of MX+B
Answers
The linear equation that represent the total cost over x GB is given as 10x + 20. The total cost when over 2 GB is $40
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The slope intercept form of linear equation is:
y = mx + b
Where m is the rate of change and b is the initial value of y
Let y represent the total cost over x GB of data.
y = mx + b
The data plan cost $20 per month and $10 per GB over 3 GB.
Hence:
m = 10, b = 20; y = 10x + 20
Total cost when over by 2 GB = 10(2) + 20 = $40
Total cost when over by x GB = 10x + 20
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What is the lbs for 80kg?
Answers
80 kilograms is equivalent to around 176.37 lbs.
Use the formula below to convert 80 kilograms' (kg) to pounds (lbs.):
1 kilograms = 2.20462 pounds
So, you may multiply 80 by 2.20462 to convert 80 kg to lbs:
80 kg x 2.20462 pounds/kg = 176.3696 lbs (rounded to four decimal places)
The term "lb" stands for pounds, a weight unit that is frequently employed in the United States and in other nations that use imperial units. The approximate weight of a pound in kilos is 0.4536. (kg).
The International System of Units' basic unit of mass, the kilogram, is denoted by the notation "kg" (SI). The standard unit for measuring mass or weight in the majority of nations is the kilogram. A kilogram is about equivalent to 2.20462 pounds (lbs).
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Assume that a sample is used to estimate a population proportion μ . Find the margin of error M.E. that corresponds to a sample of size 49 with a mean of 69.3 and a standard deviation of 18.9 at a confidence level of 99.8%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. =
Answers
he margin of error M.E. is 8.0 (rounded to one decimal place because the sample statistics are presented with this accuracy).The margin of error (ME) for a sample of size n is given by the formula below
:ME = zα/2(σ/√n) where zα/2 is the z-score obtained from the standard normal distribution table that corresponds to the desired level of confidence, σ is the standard deviation of the population and n is the sample size. Given that a sample of size 49 is used to estimate a population proportion μ. Also, the sample has a mean of 69.3 and a standard deviation of 18.9 at a confidence level of 99.8%. We can find the margin of error M.E as follows:For a 99.8% confidence level, α = 1 - 0.998 = 0.002. Thus, the area of the two tails of the standard normal distribution is (1 - 0.002) / 2 = 0.999 / 2 = 0.4995.Using the z-score table, the z-score for a standard normal distribution that corresponds to 0.4995 area is z = 2.96773.M.E. = zα/2(σ/√n)= (2.96773) (18.9/√49)= (2.96773) (2.7)= 8.014951 ≈ 8.0 (rounded to one decimal place since the sample statistics are presented with this accuracy)., t
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The margin of error is M.E. = 0.2 (rounded to one decimal place).
Given information: A sample is used to estimate a population proportion μ.
Sample size = n
= 49
Sample mean = 69.3
Sample standard deviation = 18.9
Confidence level = 99.8%
To find: The margin of error that corresponds to these parameters.
Solution:
As given, the sample is used to estimate a population proportion. Therefore, it is given that we are dealing with proportions.
Hence, we will use the standard normal distribution formula for proportions.
The formula is:
z = (p - μ) / σ
where, p is the sample proportion,
μ is the population proportion,
σ is the standard deviation of the distribution of sample proportions.
We can simplify the formula as follows:
p = sample mean
= 69.3
μ = population mean
= x / n
= 69.3 / 49
= 1.4143
σ = standard deviation
= √(pq / n)
where q = 1 - p
We need to find the z-score that corresponds to a 99.8% confidence level.
Using the standard normal distribution table, we find that the z-score for a 99.8% confidence level is:
z = 2.967
We can use the formula for the margin of error:
ME = z * σ, where z is the z-score, and σ is the standard deviation of the distribution of sample proportions.
Substituting the values, we get:
ME = 2.967 * sqrt(pq / n)
Now, we need to find p and q.
p = 69.3 / 100
= 0.693
q = 1 - p
= 1 - 0.693
= 0.307
Substituting the values of p, q, and n, we get:
ME = 2.967 × √(0.693 × 0.307 / 49)
= 0.1867
≈ 0.2 (rounded to one decimal place)
Answer: M.E. = 0.2 (rounded to one decimal place)
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Hi
Need help ASAP please
Answers
it's 3/2 because it rises three and goes over two. hope this helps !!
calculate the area, in square units, bounded above by x=−9−y−−−−√ 3 and x=−12y 6 and bounded below by the x-axis.
Answers
The area bounded above by the curves x = -9 - √(3y) and x = -12y and below by the x-axis is 24 square units.
What is the area enclosed by the curves x = -9 - √(3y) and x = -12y, with the x-axis as the lower boundary?The given problem asks us to calculate the area enclosed by two curves. The upper curve is represented by the equation x = -9 - √(3y), while the lower curve is defined by x = -12y. The region we are interested in lies below the x-axis. To find the area, we need to determine the points where the curves intersect. Setting the two equations equal to each other, we get -9 - √(3y) = -12y. By solving this equation, we find y = -1/3 and y = -3. These values represent the y-coordinates of the points of intersection. Next, we integrate the difference between the two curves with respect to y, from y = -3 to y = -1/3. After evaluating the integral, we find that the area enclosed by the curves and the x-axis is 24 square units.
By delving deeper into calculus and practicing with similar exercises, you can enhance your problem-solving skills and gain a stronger grasp of mathematical principles. Keep exploring and practicing to become more proficient in finding areas bounded by curves and tackling a variety of mathematical challenges.
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the sum of a number q and sixty-four divided by eighty-three
Answers
Answer:
(q + 64) ÷ 83
Step-by-step explanation:
(q + 64) ÷ 83
The answer is (q + 64) ÷ 83
215.7 is what percent of 192
Answers
112.34375%
215.7 is 112.34400% of 192
Figure J'K'L'M' is the image of figure JKLM after a series of transformations.
(graph is in photo attached)
Part A: Name the congruent side and angle pairs for the
two figures.
Sides:
Angles:
Part B: On the coordinate plane above, draw figure J"K"L"M", the image of figure JKLM after it is rotated 180° around the origin. Describe how the use of transformations proves that all three figures are congruent.
PLEASE HELP ASAP I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Answers
The final figure J"K"L"M" is congruent to the initial figure JKLM since each transformation maintains distance, angle measure, and orientation. The three figures are therefore all consistent.
Congruent Sides: How Do You Discover Them?Congruent sides are sides in any shape that have equal lengths on all sides. For instance, two triangles are said to be congruent if all three of their sides are the same length and equal to one another. SSS is the name of this congruence rule (side-side-side).
According to the given information:Sides:
Side JK is congruent to side K'M'
Side KL is congruent to side L'M'
Side LM is congruent to side M'J'
Side JM is congruent to side K'L'
Angles:
Angle JKM is congruent to angle K'M'J'
Angle KLM is congruent to angle L'M'K'
Angle LJM is congruent to angle M'J'K'
Angle JML is congruent to angle K'L'M'
Part B:
To see that all three figures are congruent, we can use the following sequence of transformations:
Start with figure JKLM.
Apply a translation to obtain figure J'K'L'M'.
Apply a reflection to obtain figure JK'L'M'.
Apply a rotation to obtain figure J"K"L"M".
Since each transformation preserves distance, angle measure, and orientation, the resulting figure J"K"L"M" is congruent to the original figure JKLM. Therefore, all three figures are congruent.
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What number is exponent?
Answers
Answer:
2
Step-by-step explanation:
The base B represents the number you multiply and the exponent "x" tells you how many times you multiply the base, and you write it as "B^ x." For example, 8^3 is 8X8X8=512 where "8" is the base, "3" is the exponent and the whole expression is the power.
Anita and Susanna are in a 5-mile bike race. The graph
shows each racer's distance from the start as a function of
time. What could describe Anita's race from minute 3 to
minute 5?
6
Susanna
5
Anita
She started to climb up a hill and
slowed down.
Distance (miles)
She stopped to change a flat tire.
2
1
0
1
2
3
7
8
9 10
She sped up and passed Susanna.
4 5 6
Time (minutes)
She won the race.
Answers
Answer: she stopped to change a flat tire
Step-by-step explanation:
A group of people were asked how many TVs they each have at home. Their responses are given below. Copy the table and record the responses in the tally column. What frequencies should replace A, B, C and D? Responses 1 0 2 2 1 1 0 0 2 1 3 1 1 Number of TVs 0 1 2 3 Tally Frequency A B с D
Answers
The frequencies for this problem are given as follows:
A = 3/13.B = 6/13.C = 3/13.D = 1/13.How to obtain the frequencies?The total number of people in this problem is given as follows:
13.
Out of 13 people, 3 have zero TV's, hence the frequency A is given as follows:
A = 3/13.
Out of 13 people, 6 have one TV, hence the frequency B is given as follows:
B = 6/13.
Out of 13 people, 3 have two TV's, hence the frequency C is given as follows:
C = 3/13.
Out of 13 people, 1 have three TV's, hence the frequency D is given as follows:
D = 1/13.
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What fraction is equal to 50% of 1/3
Answers
Answer:
1/6
Step-by-step explanation:
50% is 0.5 or 1/2 so you just multiply 1/3 by 1/2 to get 1/6
Answer:
your answer is 1/6
Step-by-step explanation:
1/3 of 50% so what you do is 1/3*50% which 50% in fraction form is 1/2
so you do this
\(\frac{1}{2}*\frac{1}{3}\)
and that equals 1/6
thats better
Interval notation of x<2
Answers
interval notation of x<2
x=1
a random sample of 784 10-ounce cans of fruit nectar is drawn from among all cans produced in a run. prior experience has shown that the distribution of the contents has a mean of 10 ounces and a standard deviation of .10 ounce. what is the probability that the mean contents of the 784 sample cans is less than 9.995 ounces? a) 0.131 b) 0.081 c) 0.101 d) 0.111 e) 0.121 f) none of the above
Answers
The probability that the mean contents of the 784 sample cans are less than 9.995 ounces is 0.081. The correct option is B
Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. Probability has been introduced in mathematics to determine how likely events are to occur.
Given mean = 10
standard deviation = 0.10
sample = 784
The probability that the 784 sample cans' average contents will be less than 9.995 ounces
P ( X < 9.995 ) = x - μ/ σ / √n
= 9.995-10/0.10/√784
= -0.005 / 0.10 /28
= -1.400
P(Z < -1.400) = 0.081
Therefore the probability that the mean contents of the 784 sample cans are less than 9.995 ounces is 0.081
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in making a section of an air duct, 18 sq ft of sheet metal is used. this section is cut from a 24 sq ft sheet. what percent of the sheet is used? answer in decimal form.
Answers
75% or 0.75 of the sheet metal is used to make the section of the air duct.
To find the percentage of the sheet metal used, we divide the area of the section by the area of the whole sheet and multiply by 100.
The area of the section is 18 sq ft and the area of the whole sheet is 24 sq ft.
So, the percentage of the sheet metal used is (18/24) * 100 = 75%.
Therefore, the answer in decimal form is 0.75.
In conclusion, 75% or 0.75 of the sheet metal is used to make the section of the air duct.
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Construct a stem and leaf plot of the data. how does it suggest that the sample mean and median will compare
Answers
To construct a stem and leaf plot, you first need to separate each data point into a stem and a leaf. The stem represents the leading digit(s) of the data point, while the leaf represents the trailing digit(s).
Once you have organized the data in this way, you can create the plot. The stems are listed vertically, and the leaves are placed horizontally next to their corresponding stems. Make sure to arrange the leaves in ascending order.
Regarding how the stem and leaf plot suggests the sample mean and median will compare, we can look at the distribution of the data. If the leaves are evenly distributed across the stems, it suggests a symmetrical distribution. In this case, the sample mean and median will be similar.
However, if the leaves are concentrated in certain stems, it suggests an asymmetrical distribution. In this scenario, the sample mean and median may differ. The median tends to be less affected by extreme values, while the mean can be influenced by outliers.
Therefore, by examining the stem and leaf plot, you can get a sense of whether the sample mean and median will be similar or different based on the distribution of the data.
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Problem 2: (16 marks) Six and a half years ago, you purchased at par, a 10-year 7% coupon bond that pays semi- annual interest. Today the market rate of interest is 8% and you are considering selling the bond.
a. What was the market rate of interest at the time you purchased the bond?
b. Suppose you wish to sell the bond today
i. How much should you sell the bond for?
ii. What is the quoted price of the bond?
iii. What is the current yield on the bond?
iv. What will be your annual holding period return on the bond?
Suppose your friend offers you a price of $950 for the bond today. Would you be willing to sell the bond to her? Explain your answer.
C.
Answers
Calculation of market rate of interest at the time of purchasing the bondThe information given in the problem is as follows:FV = $1000PMT = (7% of 1000)/2 = $35 (semiannual)N = 10 * 2 = 20 (semiannual)Semi-annual yield = 7% (coupon rate)/2 = 3.5%
Using the above-given information, the value of the bond can be calculated as follows: The price of the bond at the time of purchase = $1000 = PV= $832.67This implies that the market rate of interest at the time of purchasing the bond was 8.5%.b)
Calculation of selling the bond todayThe market rate of interest is now 8%. Using the given formula, the value of the bond can be calculated as follows:
PMT = (7% of 1000)/2 = $35 (semiannual)N = 10 * 2 = 20 (semiannual)The price of the bond today = $881.57
Quoted price of bond = 88.16% = 0.8816 x $1000 = $881.6Current yield on bond = (70/881.6) x 100 = 7.94%Annual holding period return on bond = [(881.57-832.67) / 832.67] / 6.5 = 0.59%Suppose the bond is offered at $950, the holding period return will be calculated as follows:
Holding period return = [(950-832.67) / 832.67] / 6.5 = 1.42%As per the given scenario, the annual holding period return on the bond is 0.59%. So, it can be concluded that the friend's offer is better than the current return. So, it is recommended to sell the bond to the friend.
The market rate of interest at the time of purchasing the bond was 8.5%.The price of the bond today = $881.57.The quoted price of the bond is $881.6.The current yield on bond is 7.94%.The annual holding period return on bond is 0.59%.The holding period return if bond is sold to a friend for $950 is 1.42%.
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The proof below may or may not be correct. If the proof is incorrect, determine the
first step number that is not justified and the reason it is not justified.
Answers
Answer:
Step-by-step explanation: step 5
they have not proved the ASA postulate i.e. they the are missing a step to proove angle BEF = angle CED (Verticle angles)
so, correct answer is step number 5 and reason 'missing prior step'
Caroline wants to buy 100 g of spice mix from a British or French website.
The conversion rate is €1 = £0.85
What is the price, including delivery costs, that Caroline would pay for the spice mix from the cheaper website? Give your answer in pounds (£).
British website: £0.90 for 25 g Free delivery.
French website: €1.20 for 50 g €0.80 delivery per order.
Answers
The website which is cheaper for Caroline to buy the spice mix is French website.
Given data ,
Let's calculate the total cost for Caroline from both websites and determine which one is cheaper.
British website:
Price for 100 g = (£0.90 / 25 g) * 100 g = £3.60
Since the British website offers free delivery, the total cost remains £3.60.
French website:
Price for 100 g = (€1.20 / 50 g) * 100 g = €2.40
Delivery cost = €0.80
On simplifying the equation , we get
To convert the price and delivery cost to pounds, we'll use the conversion rate: €1 = £0.85.
Price in pounds = €2.40 * £0.85 = £2.04
Delivery cost in pounds = €0.80 * £0.85 = £0.68
Total cost = Price in pounds + Delivery cost = £2.04 + £0.68 = £2.72
Comparing the total costs:
British website: £3.60
French website: £2.72
Hence , Caroline would pay £2.72 for the spice mix from the cheaper website, which is the French website.
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A composite figure is formed by placing a half-sphere atop a cylinder. The half-sphere and the cylinder both have a radius of 3 centimeters. The height of the cylinder is 10 centimeters.
What is the exact volume of the composite figure?
Enter your answer in the box.
Answers
Answer:
72π
Step-by-step explanation:
The volume of the composite figure can be calculated by finding the sum of the volumes of the half-sphere and the cylinder. Hence, the exact volume of the composite figure is 108π cubic centimeters.
What is a volume?Volume is a three-dimensional measurement of the amount of space a thing takes up. It is usually measured in cubic meters, cubic centimeters, or cubic feet. It is computed by multiplying the length, breadth, and height of the shape, or by using particular formulae for other forms such as cylinders, cones, or spheres. The volume of a thing indicates how much space it takes up.
The volume of the composite figure can be calculated by finding the sum of the volumes of the half-sphere and the cylinder.
The formula for the volume of a cylinder is
V = π\(r^2h\),
where r is the radius and h is the height.
Substituting the values given in the problem, we get:
Volume of cylinder = π\((3)^2(10)\)
= 90π cubic centimeters.
The formula for the volume of a half-sphere is
V = (2/3)π\(r^3\)
Substituting the value of r given in the problem, we get:
Volume of half-sphere = (2/3)π\((3)^3\)
= 18π cubic centimeters.
Therefore, the total volume of the composite figure is:
Volume of composite figure = Volume of cylinder + Volume of half-sphere
= 90π + 18π
= 108π cubic centimeters.
Hence, the exact volume of the composite figure is 108π cubic centimeters.
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. Kyle is 24 years older than his daughter Hannah. Kyle is 48 years old. How old is Hannah?
Answers
Answer:
Hannah is 24years of age
how do i do this question
Answers
Answer: Okay this is the formula for slope: y=mx+b 2 would be the slope and -1 would be the y intercept so select b.
Step-by-step explanation:
guys i really can't solve this one
make b the subject of the formula T= 2π√a/b
Answers
Answer:
see explanation
Step-by-step explanation:
assuming the equation is
T = 2π\(\sqrt{\frac{a}{b} }\) ( divide both sides by 2π )
\(\frac{T}{2\pi }\) = \(\sqrt{\frac{a}{b} }\) ( square both sides to clear the radical )
( \(\frac{T}{2\pi }\) )² = \(\frac{a}{b}\) , that is
\(\frac{T^2}{4\pi ^2}\) = \(\frac{a}{b}\) ( cross- multiply )
b T² = 4aπ² ( divide both sides by T² )
b = \(\frac{4a\pi ^2}{T^2}\)
Let f(x) = sin x and g(x) = x² + 1. Find the following derivatives. d (a) (f(g(x))) (b) = (g(f(x))) dx dx d sin (x²+1) • sin(x²)+1 dx dx = cos(x²+1)(2x)
Answers
To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.
(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.
df/dx = df/dg * dg/dx
df/dx = cos(g(x)) * (2x)
(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.
dg/dx = dg/df * df/dx
dg/dx = 2f(x) * cos(x)
Hence, the derivatives are:
(a) d/dx(f(g(x))) = cos(g(x)) * (2x)
(b) d/dx(g(f(x))) = 2f(x) * cos(x)
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Please help marking brainiest
Answers
Answer:
can you blow the image up or tell me what it says
Step-by-step explanation:
Suppose a business records the following values each day the total number of customers that day (X) Revenue for that day (Y) A summary of X and Y in the previous days is mean of X: 600 Standard deviation of X: 10 Mean of Y: $5000, Standard deviation of Y: 1000 Correlation r= 0.9 Calculate the values A,B,C and D (1 mark) Future value of X Z score of X Predicted y average of y+ r* (Z score of X)* standard deviation of y 595 A B 600 0 $5000 D 615 IC You will get marks for each correct answer but note you are encouraged to show working. If the working is correct but the answer is wrong you will be given partial marks
Answers
The predicted values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350, therefore, the correct option is IC.
Given,
Mean of X = 600
Standard deviation of X = 10
Mean of Y = $5000
Standard deviation of Y = 1000
Correlation r= 0.9
Future value of X = 595
Z score of X = (X- Mean of X) / Standard deviation of X= (595-600) / 10 = -0.5
Using the formula, Predicted y = average of y+ r* (Z score of X)* standard deviation of y
Predicted y = $5000 + 0.9 * (-0.5) * 1000 = $4750
The predicted value of Y for X = 595 is $4750.
Now, to find the values of A, B, C, and D; we need to calculate the Z score of X = 615 and find the corresponding predicted value of Y.
Z score of X = (X- Mean of X) / Standard deviation of X= (615-600) / 10 = 1.5
Predicted y = average of y+ r* (Z score of X)* standard deviation of y
Predicted y = $5000 + 0.9 * (1.5) * 1000 = $6350
The predicted value of Y for X = 615 is $6350.
Hence, the values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350
Therefore, the correct option is IC.
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