Answers
Answer:
x = 46
Step-by-step explanation:
Use the triangle angle bisector theorem.
58/63.8 = (x + 4)/55
63.8(x + 4) = 55 * 58
63.8x + 255.2 = 3190
63.8x = 2934.8
x = 46
Related Questions
Want Brainliest? Get this correct Which of the following is the product of the rational expressions shown below?
Answers
We multiply the numerators together to get x*2x = 2x^2 as the numerator for the answer.
The denominators pair up and multiply to get (x-5)(x+4) = x^2+4x-5x-20 = x^2-x-20. You can use the distributive property, FOIL, or the box method to expand out (x-5)(x+4)
So that's how we end up with (2x^2) all over (x^2-x-20) as the answer.
Question 4
If 20 percent of a certain number is 16, what is 25 percent of that number?
Answers
Answer:
the answer is 40.
hope u get it...
Which is a possible paycheck deduction? Select all that apply.
commission
federal income tax
health insurance premium
overtime hours
state income tax
Answers
Answer:
Federal income taxes, health insurance premium, state income tax
Step-by-step explanation:
Commission may be a bonus from a sale you made and overtime hours are extra hours over 40.00 that you worked during the week
2 things are certain in life death and taxes
A rookie quarterback is negotiating his first NFL contract.His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows:________.
1 2 3 4
Contract 1 $3,000,000 $3,000,000 $3,000,000 $3,000,000
Contract 2 $2,000,000 $3,000,000 $4,000,000 $5,000,000
Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,000
As his advisor, which contract would you recommend that he accept?
Answers
Answer:
He should accept contract 2 because it has a higher present value.
Step-by-step explanation:
we need to find the present value of each contract:
Contract 1 = $3,000,000/1.1 + $3,000,000/1.1² + $3,000,000/1.1³ + $3,000,000/1.1⁴ = $2,727,273 + $2,479,339 + $2,253,944 + $2,049,040 = $9,509,596
Contract 2 $2,000,000/1.1 + $3,000,000/1.1² $4,000,000/1.1³ + $5,000,000 /1.1⁴ = $1,818,182 + $2,479,339 + $3,005,259 + $3,415,067 = $10,717,847
Contract 3 $7,000,000/1.1 + $1,000,000/1.1² + $1,000,000/1.1³ + $1,000,000/1.1⁴ = $6,363,636 + $826,446 + $751,315 + $683,013 = $8,624,410
According to a government commision, 70% of all the nation’s households have vcrs. In a random sample of 15 households, what is the probability that exactly 10 have vcrs
Answers
Answer: P(10,15,0.7)=3003*0.7^10*0.3^5=approx 0.2061
Step-by-step explanation:
The required probability P(10,15,0.7)= C15 10 *p^10*q^(15-10) where
C15 10= 15 !/10!/5!= 11*12*13*14*15/(2*3*4*5)=11*12*13*14/(2*4)=11*3*13*7=
=77*39=3003
p=0.7 q=1-p =1-0.7= 0.3 (probability of not having vcrs)
So P(10,15,0.7)=3003*0.7^10*0.3^5=approx 0.2061
forex is the name of the U.S. stock exchange.
-true
-false
Answers
Answer:
false
Step-by-step explanation:
hello
this is false
FOREX means Foreign Exchange
it refers to the foreign exchange market
hope this helps
Answer:
true, forex trading is a profitable than staking cryptocurrency. forex trading is the best thing I will refer someone I love because learning never stops and no on is above blowing accounts when beginning Forex
The price of a vase was increased by 10% to £22.What was the price before the increase
Answers
Answer: £20.
Step-by-step explanation:
Let the old price = £x
Percent increase. = 10%
Increment. = 10% of £x
= 10x/100
Now new price = £22
To determine the old price we have
x + 10x/100. = 22
We now multiply everything by 100 to make it a linear expression
100x + 10x = 2200
110x = 2200, therefore
x. = 2200/110
= £20
Therefore, the price before the increase. = £20.
A rectangle is placed around a semicircle as shown below. The length of the rectangle is 12 cm. Find the area of the shaded region.
Use the value 3.14 for at, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Answer:
15.48 ft^2
Step-by-step explanation:
According to the image we have the following information:
the length of the rectangle = diameter of the semicircle, therefore it is 12 feet
, the radius of the semicircle (half the diameter) = width of the rectangle = 12/2 ft = 6 ft
We also know that the area of the shaded region would be equal to the area of the rectangle minus the area of the semicircle.
Therefore, we replace:
Area of the rectangle = width * length
Ar = 6 ft * 12 ft = 72 ft ^ 2
Area of the semicircle = [1/2] * π * (r ^ 2)
As = [1/2] * 3.14 * (6 feet) ^ 2 = 56.52 ft ^ 2
We replace in the area of the shaded region
shaded region area = 72 ft ^ 2 - 56.52 ft ^ 2 =
Shaded region area = 15.48 ft ^ 2
Use the following information to answer problems 14-16: Suppose that in a large metropolitan area, 82% of all households have cable tv. Suppose you are interested in selecting a group of six households from this area. Let X be the number of households in a group of six households from this area that have cable tv. For what proportion of groups will exactly four of the six households have cable tv?
Answers
Answer:
66.6% or 0.66
Step-by-step explanation:
82% or 0.82 of All households have cable TV.
X = The number of households in a group of 6, that have cable TV.
You wish to find the proportion or percentage of groups for which EXACTLY 4 of 6 households will have cable TV.
82% of 6 is = 4.92
Approximately 4.92 out of 6 households, have cable TV.
Using this figure, you can now find out what % of 6 will give you 4.
Cross multiply:
0.82 - 4.92
M - 4
M = (4×0.82) ÷ 4.92 = 3.28÷4.92 = 0.666
Hence, 66.6% of 6 households, have cable TV. In other words, exactly 4 households (X=4) have cable TV.
To test, you can find what 66% of 6 is. You will get 4.
make d the subject of the formula; n=k/d^2
Answers
Answer:
[tex]n = \frac{k}{ {d}^{2} } [/tex]
[tex] {d}^{2} = \frac{k}{n} [/tex]
[tex]d = \sqrt{ \frac{k}{n} } [/tex]
Here is the required firmula....Answer:
d = √(k/n)
Step-by-step explanation:
n = k/d²
n/1 = k/d²
Cross multiply.
k = nd²
Divide both sides by n.
k/n = nd²/n
k/n = d²
Take the square root on both sides.
√(k/n) = √(d²)
√(k/n) = d
is 0.790 greater than or equal to 0.79?
Answers
It's the same vallue. If they were different, i could argue that 2.000 is greater than 2.00. Impossible, because 2 is equal to 2.
A number increased by negative eight is equal to fourteen. Which equation could be used to find the number?
Answers
Answer:
-8 + x = 14
Number = 22
Step-by-step explanation:
Let x be the number.
First, we know that we'll be using addition to find the number because the problem says "increased" which means add or addition.
Next, We also know that the starting number is -8 and the answer to the equation is 14.
That's why the equation is -8 (starting number) + x = 14 (ending number)
Therefore the answer would be: -8 + x = 14
Please help me with this question!!
Answers
Answer:
rationalirrationalirrationalirrational√7, it is irrationalStep-by-step explanation:
A rational number is one that can be expressed as the ratio of two integers. All fractions that have integer numerators and (non-zero) denominators are rational numbers. Any finite decimal number, or any repeating decimal number, is a rational number. These can always be expressed as the ratio of two integers. For example, 0.4040... = 40/99, and 0.286 = 286/1000.
To make an irrational sum, at least one of the contributors must be irrational. You want an irrational 2-number sum that has 7/8 as one of the contributors. Since 7/8 is rational, the other contributor must be irrational.
__
Step 1. The number 7/8 is rational.
Step 2. The desired sum is irrational.
Step 3. The rule rational + irrational = irrational applies.
Step 4. An irrational number must be chosen.
Step 5. √7 will produce an irrational sum, because it is irrational.
1. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Berwick sample is________.
a. 60
b. 75
c. 80
d. 90
2. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Milton sample is________.
a. 60
b. 75
c. 80
d. 90
3. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Leesburg sample is________.
a. 60
b. 75
c. 80
d. 90
4. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square test statistic for these samples is_______.
a. 1.49
b. 2.44
c. 4.15
d. 5.33
5. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The degrees of freedom for the chi-square critical value is_______.
a. 1
b. 2
c. 3
d. 4
6. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square critical value using alpha = 0.05 is_______.
a. 2.706
b. 3.841
c. 5.991
d. 7.815
7. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
Using alpha = 0.05, the conclusion for this chi-square test would be that because the test statistic is
A. More than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
B. Less than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
C. More than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
D. Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Answers
Answer:
1) Option B is correct.
Expected frequency of satisfied customers from the Berwick sample = 75
2) Option D is correct.
Expected frequency of satisfied customers from the Milton sample = 90
3) Option A is correct.
Expected frequency of satisfied customers from the Leesburg sample = 60
4) Option B is correct.
The chi-square test statistic for these samples = 2.44
5) Option B is correct.
The degrees of freedom for the chi-square critical value = 2
6) Option C is correct.
The chi-square critical value using alpha = 0.05 is 5.991
7) Option D is correct.
The conclusion for this chi-square test would be that because the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Step-by-step explanation:
Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Since this is a chi test that aims to check if there are differences in the proportion of expected number of customers for each location, we state the null and alternative hypothesis first.
The null hypothesis usually counters the claim we hope to test and would be that there is no difference between the proportion of expected frequency of satisfied customers at the three locations.
The alternative hypothesis confirms the claim we want to test and is that there is a significant difference between the proportion of expected frequency of satisfied customers at the three locations.
So, the total proportion of satisfied customers is used to calculate the expected number of satisfied customers for each of the three locations.
80+85+60= 225
Total number of customers = 100 + 120 + 80 = 300
Proportion of satisfied customers = (225/300) = 0.75
1) Expected frequency of satisfied customers from the Berwick sample = np = 100 × 0.75 = 75
2) Expected frequency of satisfied customers from the Milton sample = np = 120 × 0.75 = 90
3) Expected frequency of satisfied customers from the Leesburg sample = np = 80 × 0.75 = 60
4) Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Proportion for unsatisfied ccustomers = 0.25
So, expected number of unsatisfied customers for the three branches are 25, 30 and 20 respectively.
Chi square test statistic is a sum of the square of deviations from the each expected value divided by the expected value.
χ² = [(X₁ - ε₁)²/ε₁] + [(X₂ - ε₂)²/ε₂] + [(X₃ - ε₃)²/ε₃] + [(X₄ - ε₄)²/ε₄] + [(X₅ - ε₅)²/ε₅] + [(X₆ - ε₆)²/ε₆]
X₁ = 80, ε₁ = 75
X₂ = 85, ε₂ = 90
X₃ = 60, ε₃ = 60
X₄ = 20, ε₄ = 25
X₅ = 35, ε₅ = 30
X₆ = 20, ε₆ = 20
χ² = [(80 - 75)²/75] + [(85 - 90)²/90] + [(60 - 60)²/60] + [(20 - 25)²/25] + [(35 - 30)²/30] + [(20 - 20)²/20]
χ² = 0.3333 + 0.2778 + 0 + 1 + 0.8333 + 0 = 2.4444 = 2.44
5) The degree of freedom for a chi-square test is
(number of rows - 1) × (number of columns - 1)
= (2 - 1) × (3 - 1) = 1 × 2 = 2
6) Using the Chi-square critical value calculator for a degree of freedom of 2 and a significance level of 0.05, the chi-square critical value is 5.991.
7) Interpretation of results.
If the Chi-square test statistic is less than the critical value, we fail to reject the null hypothesis.
If the Chi-square test statistic is unusually large and is greater than the critical value, we reject the null hypothesis.
For this question,
Chi-square test statistic = 2.44
Critical value = 5.991
2.44 < 5.991
test statistic < critical value
The test statistic is Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Hope this Helps!!!
Find an equation of the tangent line to the curve at the given point.x2+2xy−y2+x=101, (7,9) (hyperbola)
Answers
Answer:
The equation of the tangent line of the given curve
[tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]
The tangent of the given curve at the point
[tex](\frac{dy}{dx})_{(7,9)} = \frac{33}{4}[/tex]
Step-by-step explanation:
Explanation :-
Step(i):-
Given equation of the parabola
x²+2xy−y²+x=101 ...(i)
apply derivative Formulas
a) [tex]\frac{dx^{n} }{dx} = n x ^{n-1}[/tex]
b) [tex]\frac{d U V }{dx} = U \frac{dV}{dx} + V \frac{dU}{dx}[/tex]
Step(ii):-
Differentiating equation (i) with respective to 'x' , we get
[tex]2 x + 2 ( x \frac{dy}{dx} + y) - 2 y \frac{dy}{dx} +1 = 0[/tex]
[tex]2 x + 2 x \frac{dy}{dx} +2 y - 2 y \frac{dy}{dx} +1 = 0[/tex]
on simplification , we get
[tex]( 2 x - 2 y) \frac{dy}{dx} = - (2x +2y +1)[/tex]
[tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]
The tangent of the given curve at the point ( 7,9)
[tex](\frac{dy}{dx})_{(7,9)} = \frac{- ((2(7) +2(9) +1))}{( 2 (7) - 2 (9)}[/tex]
[tex](\frac{dy}{dx})_{(7,9)} = \frac{- (33)}{( -4} = \frac{33}{4}[/tex]
Final answer :-
The equation of the tangent line of the given curve
[tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]
The tangent of the given curve at the point
[tex](\frac{dy}{dx})_{(7,9)} = \frac{33}{4}[/tex]
Nine balls, each marked with a number from 1 to 9, are placed in a bag and one
Ball is taken out at random. What is the probability that the number on the ball is:
(a) odd, (b) a multiple of 3, (c) 5, (d) not a 7
Answers
Answer:
a =5/9 b=1/3 c=1/9 d=8/9
Step-by-step explanation:
there are total 9 numbers
in a
there are 5 odd numbers
in b
there are 3 multiplier of 3
in c
there is only one 5
in d
there are 8 numbers except 7
a) 5/9 b) 1/3 c) 1/9 d) 8/9
Step-by-step explanation:
a) odd numbers between 1 to 9 are 1,3,5,7,9. so there are 5 odd numbers.
total balls are 9
=> probability is 5/9
b) multiples of 3 = 3, 6,9 there are 3 numbers.
=> probability is = 3/9 = 1/3
c) 5. only one 5 is there between 1 to 9 numbers.
=> probability is 1/9
d) not a 7.
removing 7. there will 8 numbers.
=> probability is 8/9
On a piece of paper, graph f(x) = 3^x Then determine which answer choice
matches the graph you drew.
Answers
Answer: Make a chart of x values and corresponding outputs as y-values
Plot the points, draw the curve
Step-by-step explanation: Example of chart
x . y
-1 . 1/9
0 1
1 . 3
2 . 9
3 . 27
Once you do this you will have something similar to graph a or b.
It is difficult to tell from the photo; which graphed curve passes through (2,9) ?
The graph of the given exponential function [tex]\rm f(x) = 3^x[/tex] is attached below and this can be determined by using the given data.
Given :
[tex]\rm f(x) = 3^x[/tex]
The following steps can be used in order to determine the correct choice that matches the graph you drew:
Step 1 - Write the given exponential function.
[tex]\rm f(x) = 3^x[/tex]
Step 2 - The domain of the function [tex]\rm f(x) = 3^x[/tex] is [tex](-\infty,\infty)[/tex].
Step 3 - The range of the function [tex]\rm f(x) = 3^x[/tex] is [tex](0,\infty)[/tex].
Therefore, the correct option is B) and the graph of the function [tex]\rm f(x) = 3^x[/tex] is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
Which side lengths form a right triangle?
Answers
Answer:
B) 1, 8, √65
Step-by-step explanation:
For 3 side lengths to form a triangle the sum of two random sides must be bigger than the third side and their differences must be smaller than the third side.
1+8 > √65 because √65 is approximately 8.1
8-1 < √65
Answer:
B. 1,8,(65)½
Step-by-step explanation:
For the side lengths to form a right triangle they have to obey the Phythagorean Theorem which when paraphrased says " the square of the longer side is equal to the sum of the squares of the other sides"
A . 2² + 15² = 4 + 225 = 229
17² = 289
Not a Phythagorean triple
B. 1² + 8² = 1 + 64 = 65
(65½)² = 65
A Phythagorean triple
C. 2² + (80½)² = 4 + 80 = 84
9² = 81
Not a Phythagorean triple.
if the insured insures a $6,000 in-network medical bill after the annual deductible of $2,500 has been paid how much will the health plan pay?
Answers
Answer:
The total money the health plan will pay is $8500
Step-by-step explanation:
In-network medical bill of the insured to insure = $6000
Annual deductible = $2500
Total amount = $2500 + 6000
Total amount =$8500
The amount the insurance company will pay on the health plan if anything goes wrong will be the total money .
The total money the health plan will pay is $8500
Which point is located at (Negative 3.5, Negative 4.5)? On a coordinate plane, point A is 3.5 units to the left and 4.5 units down. Point K is 3.5 units to the right and 4.5 units up. Point R is 3.5 units to the left and 4.5 units up. Point Y is 4.5 units to the left and 3.5 units down. point A point K point R point Y
Answers
Answer:
Point A
Step-by-step explanation:
We know that on a coordinate plane, negative numbers can be found by moving down or moving to the left. This point must be found by moving down and left. To establish whether it is point A or point Y, we can remember that x coordinates move left and right and y coordinates move up and down. So, we would need to move 3.5 units left for x and then 4.5 units down for y. This leads us to point A.
hope this helps!
Answer:
it is point A
Step-by-step explanation:
Which of the following statements must be true, given that ABC XYZ and AB = 10 cm?
A.
AC = 10 cm
B.
XZ = 10 cm
C.
YZ = 10 cm
D.
XY = 10 cm.
Answers
Answer:
Option D is correct.
XY = 10 cm
Step-by-step explanation:
Complete Question
Which of the following statements must be true, given that ABC = XYZ and AB = 10 cm?
The diagram for the question is missing.
Solution
The diagram for the question isn't attached.
But from the condition, ABC = XYZ, it is evident that the two triangles are similar according to the SSS congruent theorem.
If all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar. And from the condition given, we can predict, without seeing the diagram for the question, that
(AB/XY) = (BC/YZ) = (CA/ZX)
We can also predict that the triangles are exactly the same and the proportionality bbetween is 1.
AB = XY
BC = YZ
CA = ZX
Hence, AB = XY = 10 cm.
Hope this Helps!!!
No idea how to graph this
Answers
Answer:
you can write up to 3 coordinate but you can also continue also .you have to remember to keep the value of variable on right side before computing the value of variable on right side to get good answer.
[PLEASE HELP] Each of these statements describe a transformation of a graph of y = x, The which of the statements correctly describe the graph of y =x + 7???
Answers
Answer:
B
Step-by-step explanation:
Adding the 7 to the input (x) will increase the output (y) by 7. Therefore, the graph is translated 7 units up.
Answer:
The answer is B
Step-by-step explanation:
well the equation of a line is : y = mx + b
in this question the equation is y = x
so the line y = x +7 will be 7 units up than y = x
Now that we have our linear regression model, let’s try to make a prediction for the sales given a new set of advertising budgets as follows: new.dat <- data.frame(TV=200, Radio=10, Newspaper=20) You are required to report the predicted sales as well as the lower and upper bound for the 95% prediction interval. What will you report?
Answers
Answer:
The predicted sales for the new set of advertising budgets is 14.
Step-by-step explanation:
The linear regression model is:
[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]
Compute the value of sales for:
TV = 200,
Radio = 10,
Newspaper = 20
[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]
[tex]=2.9389+0.0458\cdot(200)+0.1885\cdot(10)-0.0010\cdot(20)\\=2.9389+9.16+1.885-0.0002\\=13.9837\\\approx 14[/tex]
Thus, the predicted sales for the new set of advertising budgets is 14.
2(x + 25) =100 hellppppppp meee
Answers
Answer:
x=25
Step-by-step explanation:
2(x+25)=100
2x+50=100
2x=50
x=25
Number of non sqaure number are there between 36² and 37²
Answers
Answer:
A 1,296
B 1,369
36 answer
20. The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of units over the ten-year span, (number of units sold, profit) for specific recorded years: (46,250), (48, 305), (50,350), (52, 390), (54, 410) a) Use linear regression to determine a function y, where profit in thousands of dollars depends on the number of units sold in hundreds. b) Predict when the profit will exceed one million dollars.
Answers
Answer:
20
Step-by-step explanation:
The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015.
What is a linear function?
A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given pair of (number of units sold y, profit x)
Linear equation slope and y-intercept
A linear equation or function is given as ;
y = mx + c
Here, c is the y-intercept and m is the slope.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope m = (y₂ - y₁)/(x₂ - x₁)
Therefore slope of (46,250), (48, 305)
m = (305 - 250)/(48 - 46) = 27.5
Put, m = 27.5 and (46,250)
250 = 27.5(46) + c
c = -1015
y = 27.5x - 1015
Hence "The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015".
For more about the linear function,
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If f(x)=2x−1, show that f(f(x))=4x−3. Find f(f(f(x))).
Answers
Answer: f(f(f(x)))=8x-7
Step-by-step explanation:
Since we were given f(x) and f(f(x)), We plug that into f(x) again to get f(f(f(x))).
2(4x-3)-1 [distribute]
8x-6-1 [combine like terms]
8x-7
A sample of bacteria is decaying according to a half-life model. If the sample begins with 800 bacteria, and after 13 minutes there are 320 bacteria, after how many minutes will there be 15 bacteria remaining? Round your answer to the nearest whole number.
Answers
Answer:
56.42 minutes
Step-by-step explanation:
The initial sample= y0 = 800
After 13 minutes , amount = 320
Y= y0e-kt
320 = 800e-k(13)
320/800 = e-k13
0.4 = e-k13
In0.4 = -k13
-0.91629= -k13
0.07048= k
Y = 800e-0.07048t
Minutes when the bacterial present will be 15
15 = 800e-0.07048t
15/800= e-0.07048t
0.01875 = e-0.07048t
In 0.01875 = -0.07048t
-3.97656 = -0.07048t
-3.97656/-0.07048= t
56.42 = t
56.42 minutes
Phil Nelson deposited $35,000 at Wachovia Bank at 3.5% interest
compounded quarterly. How much money will be in this account at
the end of the year?
Answers
Answer:
$36,241.20
Step-by-step explanation:
Compounded Interest Rate Formula: A = P(1 + r/n)^nt
Since we are given P, r, n, and t, simply plug it into the formula:
A = 35000(1 + 0.035/4)⁴⁽¹⁾
A = 35000(1 + 0.00875)⁴
A = 35000(1.00875)⁴
A = 35000(1.03546)
A = 36241.2