Answers
As we have shown that both AE is congruent to CE and BE is congruent to DE.
Now, let's focus on the diagonals of the parallelogram, AC and BD. We are told that they intersect at point E.
To prove that AE is congruent to CE, we can use the fact that opposite sides of a parallelogram are congruent. Since AC is a diagonal of the parallelogram, it divides it into two congruent triangles, AEC and CED. This is because AE is parallel to CD (as they are opposite sides of the parallelogram), and EC is common to both triangles.
Therefore, by the Side-Angle-Side (SAS) congruence theorem, we can conclude that triangle AEC is congruent to triangle CED. In particular, this means that AE is congruent to CE.
Similarly, to prove that BE is congruent to DE, we can use the same reasoning. Since BD is a diagonal of the parallelogram, it divides it into two congruent triangles, AEB and DEC. This is because BE is parallel to AC (as they are opposite sides of the parallelogram), and ED is common to both triangles.
Therefore, by the SAS congruence theorem, we can conclude that triangle AEB is congruent to triangle DEC. In particular, this means that BE is congruent to DE.
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Related Questions
Q2: The population of a herd of deer is represented by the function P(t) = 205(1.13)t where t is given in years. To the nearest whole number, what will the herd population be after 6 years?
Answers
Answer:
584
Step-by-step explanation:
To find the herd population after 6 years, we need to evaluate P(6) using the given function:
P(6) = 205(1.13)^6
Using a calculator, we get:
P(6) ≈ 584
Rounding this to the nearest whole number, we get:
The herd population after 6 years ≈ 584.
You work independently as a copier salesperson. Last month, you sold 26 printers at a cost of $1,750 each. The cost of goods sold for each printer is $975. Additional operating expenses include your salary ($3,000/month), advertising ($50/month), and office lease ($550/month). Use this information to calculate (a) your gross profit and (b) your net income.
Answers
(A) The gross profit is $20,150.
(B) The net income is $16,550
To solve this problem(A) To calculate the gross profit, we need to subtract the cost of goods sold from the total revenue generated by selling the printers.
Total revenue = 26 x $1,750 = $45,500
Cost of goods sold = 26 x $975 = $25,350
Gross profit = Total revenue - Cost of goods sold
Gross profit = $45,500 - $25,350
Gross profit = $20,150
Therefore, the gross profit is $20,150.
(B) To calculate the net income, we need to subtract all the operating expenses from the gross profit.
Gross profit = $20,150
Salary = $3,000
Advertising = $50
Office lease = $550
Total operating expenses = $3,600
Net income = Gross profit - Total operating expenses
Net income = $20,150 - $3,600
Net income = $16,550
Therefore, the net income is $16,550.
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #2
Answers
Answer:
Whenever the base of an exponential function is less than 1 (5/7 < 1), the graph exhibits exponential decay and when the base is greater than 1, the graph exhibits exponential decay (7 > 1).
Final answer: a base of 7 will cause the graph to increase as you go from left to right in both the x coordinates and the y coordinates.
I provided a picture of a graph that shows both bases just in case you want to alter my answer slightly, but aren't sure how the graph would look
A wildlife group is trying to determine how many wild hogs are in a certain area. They trapped, tagged, and released 20 wild hogs. Later, they counted 8 wild hogs out of the 40 they saw.
What can the wildlife group estimate is the total population of wild hogs in that area
A. 80
B. 90
C. 100
D. 16
Answers
Answer:
The correct answer is 16
Step-by-step explanation:
Answer:
C. 100
Step-by-step explanation:
Assuming that the proportion of tagged hogs in the population is the same as the proportion of tagged hogs in the sample that was later observed, we can set up a proportion to estimate the total population of wild hogs:
tagged hogs in population / total population = tagged hogs in sample / size of sample
We know that 20 wild hogs were tagged and released, and that 8 out of 40 hogs observed were tagged. So we can plug these numbers into the proportion and solve for the total population:
20 / total population = 8 / 40
Simplifying this equation, we get:
total population = (20 * 40) / 8 = 100
Therefore, the wildlife group can estimate that the total population of wild hogs in the area is 100. Answer choice C is correct.
Hope this helps!
Question 5
Which of the following functions best describes this graph?
4
Ay=x²-2x+4
OB. y +9x+18
OC. ys (x+5)(x-4)
Answers
Answer:
D. y = (x - 3)(x - 6)
Step-by-step explanation:
The graph shows a parabola and the parabola intersects the x-axis at (-6, 0) and at (-3, 0). When a function intersects the x-axis, the y value must automatically equal 0, since there is only horizontal movement on the x-axis.
(x-3)(x-6) is a binomial expression that will make a quadratic equation when expanded. We refer to the coordinate where a parabola intersects the x-axis as roots, which are numbers that make the quadratic equation equal 0.
We know from the zero-product property, that when the product of two numbers is 0, at least on the numbers must be 0 (e.g., 4 * 0 = 0 or even 0 * 0 = 0). Thus, we can solve any quadratic equation in the the x-intercept form (i.e., the form tha (x-3)(x-6) is currently in) by setting both expressions equal to 0 and solving for x. This wil give an x-coordinate both times, but since you set the equations equal to 0, you know that your y-coordinate each time is 0:
Solution for x - 3 = 0:
x - 3 = 0
x = 3
Solving for x - 6 = 0
x - 6 = 0
x = 6
You can check by plugging in 3 for x and 6 for x and see if you get 0:
3 for x:
(3 - 3)(3 - 6) = 0
0 * -3 = 0
0 = 0
6 for x:
(6 - 3)(6 - 6) = 0
3 * 0 = 0
0 = 0
answer with explanation
Answers
Answer:
Area = 20 [tex]units^{2}[/tex]
Perimeter = 18 units
Step-by-step explanation:
Helping in the name of Jesus.
Professional Golfers’ Earnings Two random samples of earnings of professional golfers were selected. One sample was taken from the Professional Golfers Association, and the other was taken from the Ladies Professional Golfers Association. At , is there a difference in the means? The data are in thousands of dollars. Use the critical value method with tables.
PGA:
446, 1147, 9188, 5687, 4910
8553, 7573, 375
LPGA
76, 122, 466, 863, 100
1876, 2029, 4364, 2921
use u1 for the mean earnings of pga golfers. assume the variables are normally distributed and the variances are unequal
h0:
h1:
this hypothesis test is (one tailed or two tailed)
critical value(s)
t=
reject or do not reject the null hypothesis
is there enough evidence to support the claim
Answers
As per the hypothesis, t (1.7518) is less than the critical value (1.7823), we fail to reject the null hypothesis.
For this scenario, our null and alternative hypotheses can be stated as follows:
H0: u₁ - u₂ = 0 (There is no significant difference between the mean earnings of PGA and LPGA golfers)
H1: u₁ - u₂ > 0 (There is a significant difference between the mean earnings of PGA and LPGA golfers)
Assuming a level of significance (alpha) of 0.05, the degrees of freedom can be calculated as follows:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
where s₁ and s₂ are the sample standard deviations, n₁ and n₂ are the sample sizes.
For the PGA sample, we have n₁ = 8, s₁ = 3139.71
For the LPGA sample, we have n₂ = 8, s₂ = 1232.59
Using the above formula, we get df = 12.61
Using a t-distribution table with 12 degrees of freedom and a one-tailed test, we find the critical value to be 1.7823.
Next, we need to calculate the test statistic t, which can be calculated as follows:
t = (x₁ - x₂) / √[s₁²/n₁ + s₂²/n₂]
where x₁ and x₂ are the sample means.
For the PGA sample, we have x₁ = 4358.22
For the LPGA sample, we have x₂ = 1128.50
Using the above formula, we get t = 1.7518.
Now, we can compare the test statistic t to the critical value 1.7823. Since In other words, we do not have enough evidence to support the claim that there is a significant difference between the mean earnings of PGA and LPGA golfers.
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Andre wants to buy a new car. Gas is so expensive; Andre wants to purchase a
car that has the best gas millage rate.
•
Car 1 has gas mileage that can be described as y = 25x, where x is the
number of gallon of gas used and y is the total miles driven.
Car 2 has he gas mileage rate displayed in the table below.
Number of
Gallons of
Gas
2
5
7
8
11
60
150
210
240
330
Which car should Andre buy? How many more miles per gallon can he
drive in this car than the other car?
Answers
Answer: Andre should buy Car 2. Brainliest?
Step-by-step explanation:
To compare the gas mileage of the two cars, we need to find out how many miles each car can travel per gallon of gas.
For Car 1: y = 25x
This means that for every gallon of gas used (x), the car can travel 25 times that amount in miles (y). So, the gas mileage for Car 1 is 25 miles per gallon (mpg).
For Car 2: we can calculate the miles per gallon by dividing the total miles traveled by the number of gallons of gas used:
For 2 gallons of gas, the car can travel 60 miles. So, the gas mileage is 30 mpg (60 miles ÷ 2 gallons).
For 5 gallons of gas, the car can travel 150 miles. So, the gas mileage is 30 mpg (150 miles ÷ 5 gallons).
For 7 gallons of gas, the car can travel 210 miles. So, the gas mileage is 30 mpg (210 miles ÷ 7 gallons).
For 8 gallons of gas, the car can travel 240 miles. So, the gas mileage is 30 mpg (240 miles ÷ 8 gallons).
For 11 gallons of gas, the car can travel 330 miles. So, the gas mileage is 30 mpg (330 miles ÷ 11 gallons).
Therefore, Car 2 has a consistent gas mileage of 30 mpg.
From the above calculations, we can see that Car 2 has a better gas mileage compared to Car 1. Car 2 can travel 30 miles on a gallon of gas, while Car 1 can only travel 25 miles on a gallon of gas.
Therefore, Andre should buy Car 2 if he wants to get the best gas mileage. Car 2 can travel 5 more miles per gallon than Car 1.
Determine the length of a chord whose central angle is 80° in a circle with a radius of 4 centimeters. Question 9 options: 3.94 cm 2.57 cm 5.14 cm 7.88 cm
Answers
The length of the chord whose central angle is 80° in a circle with a radius of 4 centimeters is 5.14 cm using the law of cosines.
Given that,
Central angle of a chord = 80°
Radius of the circle = 4 centimeters
There will be a triangle formed by the chord and the two radius.
Let a be the length of the chord.
Using the law of cosines,
a² = 4² + 4² - (2 × 4 × 4) cos (80°)
a² = 16 + 16 - 32 cos (80°)
a² = 32 - 32 cos (80°)
a² = 26.4433
a = 5.14
Hence the length of the chord is 5.14 cm.
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Find the final amount of money in an account if $7, 300 is deposited at 2% interest compounded semi annually and the money is left for 7 years
Answers
The final amount of money in the account after 7 years would be $8,790.56.
To calculate the final amount of money in an account, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)[/tex]
where A is the final amount of money, P is the initial amount of money, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we have P = $7,300, r = 0.02 (since the interest rate is 2%), n = 2 (since the interest is compounded semi-annually), and t = 7 (since the money is left for 7 years). Plugging these values into the formula, we get:
A = $7,300(1 + 0.02/2)¹⁴
A = $7,300(1.01)¹⁴
A = $8,790.56
This means that the initial investment of $7,300 earned $1,490.56 in interest over the 7-year period due to the compounding effect of the semi-annual interest payments.
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Margarita borrows $14,000 from her uncle and agrees to repay it in monthly installments of $400. Her uncle charges 0.9% interest per month on the balance.
(a) If her balance An in the nth month is given recursively by A0 = 14,000 and An = k · An − 1 − 400, what is k?
(b) Find her balance after two months. (Round your answer to the nearest cent.)
Answers
Answer:
Step-by-step explanation:
(a) We know that the balance An in the nth month is given by:
An = k · An-1 - 400
where A0 = 14,000. Substituting n = 1, we get:
A1 = k · A0 - 400
A1 = k · 14,000 - 400
We also know that her uncle charges 0.9% interest per month on the balance. This means that the balance after one month should be:
A1' = A0 + 0.009 · A0 - 400
A1' = 14,000 + 0.009 · 14,000 - 400
A1' = 14,126
Setting A1 = A1', we can solve for k:
k · 14,000 - 400 = 14,126
k = 1.009
Therefore, k is approximately 1.009.
(b) To find her balance after two months, we can use the recursive formula with n = 2:
A2 = k · A1 - 400
A2 = 1.009 · 14,126 - 400
Using a calculator, we get:
A2 ≈ 14,272.34
Therefore, her balance after two months is approximately $14,272.34.
18. Un comerciante vende una vaca por S/700.
Si le había costados S/500, ¿qué parte
representa la ganancia sobre el costo?
a) 2/5
b) 3/5
c) 4/5
d) 1/5 e) 6/5
Answers
Find the critical value zc necessary to form a confidence interval at the level of confidence shown below.
c =0.81
Answers
Hence, the critical value for the 81% confidence interval is 1.311 occurs while comparing equations (1) and (2).
Explain about the Critical Values:The cut-off scores used during confidence intervals, hypothesis testing, and other statistical techniques are known as the crucial values. They are used to establish the boundaries of confidence intervals in the case of confidence intervals.
Level of confidence c = 0.81
The degree of assurance c = 81%.
Now, the overall confidence level is shown as (1−α) , where α is the significance level.
= 1.0 - 0.81
= 0.19
Thus, the 81% confidence level suggests a significance level of 0.19.
Critical value Z(α/2) is:
P(Z > Z(α/2)) = (α/2)
= 0.19/2
P(Z > Z(α/2)) = 0.095 ...eq 1
Using the z-table online, check the p-value for the z 0.095.
P(Z > 1.311) = 0.095 ...eq 2
Hence, the critical value for the 81% confidence interval is 1.311 occurs while comparing equations (1) and (2).
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A planter box has dimensions 30 in × 15 in × 18 in (Length × Width × Height).
a. Find the volume of the box in cubic feet and in cubic yards.
b. Potting soil is sold in 1.5 cubic-foot bags, and each bag weighs 11.2 pounds. How many
pounds of soil does the box hold?
c. You’d like to paint the sides (but not the bottom) of the planter box. You plan on
applying one coat of paint. How many square feet of paint will you need?
88
Answers
Okay, let's solve this step-by-step:
a)
Length = 30 in = 2.5 ft
Width = 15 in = 1.25 ft
Height = 18 in = 1.5 ft
Volume (cubic ft) = Length x Width x Height
= 2.5 x 1.25 x 1.5 = 3.75 cubic ft
Volume (cubic yards) = 3.75 / 27 = 0.14 cubic yards
b)
Since the box volume is 3.75 cubic ft and potting soil bags are 1.5 cubic ft,
you will need 3.75 / 1.5 = 2.5 bags of soil.
Each bag weighs 11.2 lbs, so 2.5 bags will weigh 2.5 * 11.2 = 28 lbs of soil.
c)
To paint the sides of the box, you need:
Length (2 sides) = 30 in x 2 = 60 in
Width (2 sides) = 15 in x 2 = 30 in
Height (4 sides) = 18 in x 4 = 72 in
Total inches of sides = 60 + 30 + 72 = 162 in
Conversion: 162 in / 12 in = 13.5 square ft
So you will need about 14 square feet of paint.
Let me know if you have any other questions!
Super Markets Incorporated, is considering expanding into the Scottsdale, Arizona, area. You, as director of planning, must present an analysis of the proposed expansion to the operating committee of the board of directors. As a part of your proposal, you need to include information on the amount people in the region spend per month for grocery items. You would also like to include information on the relationship between the amount spent for grocery items and income. Your assistant gathered the following sample information.
Household Amount Spent Monthly Income
1 $ 555 $ 4,340
2 489 4,510
. . .
. . .
. . .
39 1,206 9,814
40 1,145 9,835
picture Click here for the Excel Data File
a-1. Draw a scatter diagram.
1. On the graph below, use the point tool to plot the point corresponding to the Monthly Income and the Amount Spent (Amount 1).
2. Repeat the process for the remainder of the sample (Amount 2, Amount 3, … ).
3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.
a-2. Based on these data, does it appear that there is a relationship between monthly income and amount spent?
b-1. Determine the correlation coefficient. (Round your answer to 4 decimal places.)
b-2. Can we conclude that there is a positive correlation between monthly income and amount spent? Use the 0.05 significance level.
c. Determine the coefficient of determination. (Round your answer to 4 decimal places.)
d. Determine the standard error of estimate. (Round your answer to 4 decimal places.)
e. Would you recommend using the regression equation to predict amount spent with monthly income?
multiple choice
Yes
No
PrevQuestion 13 of 16 Total13 of 16Visit question mapNext
Answers
The above is an analysis of data related to income and expenditure. See the working below as well as the attached information.
What is the analysis of the given data?Scatter diagram is attachedpoints are plotted on the graphCorrelation coefficient (r) = 0.9451
R Calculation
Note that:
X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X - Mx & Y - My: Deviation scores
(X - Mx)2 & (Y - My)2: Deviation Squared
(X - Mx)(Y - My): Product of Deviation Scores
X Values
∑ = 273195
Mean = 6829.875
∑(X - Mx)2 = SSx = 119242794.375
Y Values
∑ = 33625
Mean = 840.625
∑(Y - My)2 = SSy = 2396869.375
X and Y Combined
N = 40
∑(X - Mx)(Y - My) = 15978328.125
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 15978328.125 / √((119242794.375)(2396869.375)) = 0.9451
Thus, the value of R is 0.9451.
4. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).
5) The value of R², the coefficient of determination, is 0.8932.
To drive this, just square the coefficient of determination. That is
R² = 0.9451² = 0.8932
5. To compute the standard errors of the estimate:
SE = √(SSE / (n-2))
where SSE is the sum of squared errors and n is the sample size.
From the regression output, we have SSE = 0.9326 and n = 40.
SE = √ (0.9326 / (40-2)) = 0.1570
Therefore, the standard error of estimate is 0.1570.
6) Yes, because the coefficient of determination is high (0.8932), indicating that 89.32 % of the variability i n the amount spent can be explained by the linear relationship with monthly income.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached.
quadratic equations. A positive real number is 4 more than another. If the sum of the squares of the two numbers is 56, find the numbers.
Answers
Answer:
2√6 +2 and 2√6 -2
Step-by-step explanation:
You want two numbers such that one is 4 more than the other and the sum of their squares is 56.
SetupLet x represent the smaller number. The the sum of the squares of the two numbers is ...
x² +(x +4)² = 56
SolutionSimplifying the equation, we have ...
2x² +8x +16 = 56
x² +4x = 20 . . . . . . . . . subtract 16, divide by 2
x² +4x +4 = 24 . . . . . . add 4 to complete the square
(x +2)² = 2²·6 . . . . . . . write in terms of squares
x = 2√6 -2 . . . . . . . . positive square root, subtract 6
The two numbers are 2√6 -2 and 2√6 +2.
__
Additional comment
Their approximate decimal values are 6.8990 and 2.8990. As you expect, the sum of the squares of the rounded values differs slightly from 56.
Ms. Rosen sells computers. Last month she sold 72 computers, and her
goal is to sell 12% more computers this month than she sold last month.
How many computers does she need to sell to reach her goal?
Answers
81
72 + (12% of 72) = 80.64 and since you can't sell .64 computers, she needs to sell 81.
Mamadou has 64 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 247 square meters. Solve for the dimensions (length and width) of the field.
Answers
Answer: The length and width are 13 and 19
Step-by-step explanation:
This is because the factors of 247 are 1, 13, 19, and 247. 13 times 19 is 247, but if 13 and 19 are the sides, the perimeter would be 64 as well.
27. Find the value of x. Then tell whether the side lengths form a Pythagorean triple.
27.
X =
Triple?
Need 27
Answers
The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given:
Let us consider one length i.e. 16 to be Perpendicular and other length i.e. 19 to be Width.
According to the Pythagoras theorem:
[tex]\text{Hypotenuse}^2=\text{Perpendicular}^2+\text{Base}^2[/tex]
Let us consider the value of Hypotenuse to be x.
[tex]x^2=19^2+16^2[/tex]
[tex]x^2=361+256[/tex]
[tex]x^2=617[/tex]
[tex]x=\sqrt{617}[/tex]
[tex]x=24.84[/tex]
Thus, from the value of x we can infer that the given lengths are not forming Pythagorean triple.
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Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised appear in the table below. Price per Photo $56 $52 $24 Number of Photos Sold 4 5 12 Revenue $224 $260 $288 Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos are sold, and what price per photo will maximize her revenue?
Answers
a. A bag contains 4 red marbles, 5 yellows marbles, and 7 whites marbles. If a marble is drawn from the bag, replaced, and another marble is drawn,
what is the probability of drawing first a marble and then a marble?
Answers
Answer: 5/64
Step-by-step explanation:
The probability of drawing a red marble on the first draw is 4/16 = 1/4 (since there are 4 red marbles out of 16 total marbles).
After replacing the first marble, the probability of drawing a yellow marble on the second draw is 5/16 (since there are 5 yellow marbles remaining out of 16 total marbles).
Therefore, the probability of drawing a red marble and then a yellow marble is (1/4) x (5/16) = 5/64
Identify the domain and range of the function. y=√x−4
A. Domain: x≥−4, Range: y≥0
B. Domain: x≥4, Range: y≥0
C. Domain: x≤4, Range: y≤0
D. Domain: x≥0, Range: y≥4
Answers
Using the function y = √ (x-4) has the following:
Domain: x≥−4, Range: y≥0.
Correct answer is A.
Define a function?A function is a relationship between each element of a non-empty set A and at least one element of another non-empty set B. A relation f between a set A (the function's domain) and a set B is how a function is defined in mathematics (its co-domain). Anytime an A and b B exist, f = (a,b)|
The domain of the function y=√ (x-4) is restricted by the square root of a non-negative number, which means that x-4 must be greater than or equal to zero. Thus, we have:
x-4 ≥ 0
x ≥ 4
Therefore, the domain of the function is x≥4.
The range of the function is determined by the output values of the function. Since the square root of any non-negative number is always non-negative, the output values of the function y=√x-4 will always be non-negative. Thus, the range of the function is y≥0.
Therefore, the correct answer is A. Domain: x≥−4, Range: y≥0.
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CO (
Which of the following is the result of the operation below?
123 6
1.1
-2
0 2
1.
15
11
-R1+R2+R2
Answers
The result of the matrix operation is
1 2 3 6
0 -1 -2 -8
0 2 1 5
Identifying the result of the matrix operation?From the question, we have the following parameters that can be used in our computation:
Matrix A
Such that the matrix is
1 2 3 6
1 1 1 -2
0 2 1 5
The matrix operation is -R1 + R2 = R2
So, we have
1 2 3 6
0 -1 -2 -8
0 2 1 5
Hence, the result is the matrix above
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The ordered pairs represent an absolute value function (f): (-3,9) (-1,1) (2,5)
Describe the relationship between that function and g(x)=4|x+5|-3.
The graph of f is translated ___ units up and ___ units to the left from the graph of g.
Answers
The relationship between the functions f(x) and g(x) is not by translation
Describing the relationship between the functionsFrom the question, we have the following parameters that can be used in our computation:
Function f(x) = (-3, 9), (-1, 1) and (2, 5)Function g(x) = 4|x + 5| - 3When the ordered pairs and the graph g(x) are plotted on a graph, we can see that the function f(x) is not and cannot be translated in any way to get the function g(x)
This means that the relationship between the functions is not by translation
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An integer A written in an n-based number system is 647, while written in an (n+2)-based number system is 513. Write the number A in the 10 number system! (n is of course a positive integer)
Answers
Answer:
79
Step-by-step explanation:
Let's start by writing out what we know:
A = 647 in base-n
A = 513 in base-(n+2)
To find A in base-10, we need to use the place value system and the definition of each base. Let's first convert A to base-10 using the given information.
In base-n, A is equal to:
A = 6n^2 + 4n + 7
In base-(n+2), A is equal to:
A = 5(n+2)^2 + 1(n+2) + 3
A = 5(n^2 + 4n + 4) + (n + 2) + 3
A = 5n^2 + 21n + 20
Now we have two expressions for A, so we can set them equal to each other and solve for n:
6n^2 + 4n + 7 = 5n^2 + 21n + 20
Simplifying and rearranging, we get:
n^2 + 8n + 13 = 0
Using the quadratic formula, we can solve for n:
n = (-8 ± sqrt(8^2 - 4(1)(13))) / (2(1))
n = (-8 ± 2) / 2
n = -3 or n = -5
Since n is a positive integer, we can disregard the negative solution and conclude that n = 3.
Now that we know n, we can substitute it back into the expression for A in base-n and solve for A in base-10:
A = 6n^2 + 4n + 7
A = 6(3^2) + 4(3) + 7
A = 79
Therefore, the number A written in base-10 is 79.
Hope this helps!
Dejon saves eight dollars in a week author saves four times the amount Dejon saves in the same week
Answers
The amount that Author saves in the same week is $32.
What is a simple equation?An equation which has a variable of unknown value is referred to as a simple equation. Thus, the value of the variable is to be determined.
From the given question, it can be deduced that;
Dejon saves $8 per week, while Author saves four times that of Dejon.
Thus, this implies that;
the amount that Author saves same week = 4 * $8
= $32
Therefore, the amount that Author save in the same week is $32.
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Which graph shows the image of ABC after a rotation about the origin
Answers
Answer:
I would say C. Because it shows ABC, and all the others are either upside down or lopsided. I hope it was correct for you
adam bought a skateboard that is on sale for 35% off the original cost is 150 what is the sale price
Answers
Answer:
$97.50
Step-by-step explanation:
To calculate the sale price of the skateboard, we need to apply a discount of 35% to the original cost of $150:
Discount amount = 35% x $150 = $52.50
The sale price is the original cost minus the discount amount:
Sale price = $150 - $52.50 = $97.50
Therefore, the sale price of the skateboard after a 35% discount is $97.5
The sale price of the skateboard is $97.50.
To calculate the sale price, we need to first determine the amount of the discount, and then subtract that discount from the original price.
The discount is 35% of the original price:
Discount = 0.35 x 150 = 52.50
So the sale price is the original price minus the discount:
Sale price = 150 - 52.50 = 97.50
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Make a rap about why a parallelogram is the best shape. Must be appropriate and at least a minute long. Giving brainless to whoever answers!!!
Answers
Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:
Yo, listen up, the parallelogram is where it's at,
A shape so brilliant, the angles are sat.
Parallel sides that never converge,
Internal angles that never diverge.
Each side an equal length,
A geometry prodigy's dream length.
The diagonals intersect, another line through the middle they meet,
Creating symmetry so neat.
A rectangle it could be,
But it's oblong, not square, can't you see?
With depth and width in perfect balance we see,
A two-dimensional form of complexity.
While the square is simple, the parallelogram is hip,
A mathematical masterpiece, skip, skip, skip!
four right angles keep the shape so tight,
Parallel lines dominate left and right.
Rotated or reflected without a care,
Its structural integrity beyond compare.
triangles form at each corner you'll note,
Acute or obtuse, depends on the protractor's groove.
A versatile shape with reason and purpose galore,
The parallelogram, simply, carries the floor.
From geometry to art, its angles they intrigue,
As a basis for patterns, its potential we can truly plug.
A forgotten form that deserves more acclaim,
Put the parallelogram on geometry's game!
This shape so underrated, rarely appreciated it seems,
But with logic and virtue, strong foundations it gleams.
The parallelogram, the parallelogram, Hooray!
This is why the parallelogram is the best shape, I say!
In In a study of the effects of college student employment on academic performance, two random samples (one from students who worked and the other from students who did not work) were selected from college students at a large university. The following summary statistics for GPA were reported. Employed students sample size 114
Mean GPA 3.15
Std deviation 0.485
Non-employed students
Sample size 114
Mean GPA 3.23
std deviation 0.524
Compute a 90% confidence interval for the mean GPAs of non-employed students. Assume that the normal condition is met.
a. Identify the variables needed to solve the problem.
b. Find the standard deviation.
c. Calculate the point estimate and margin of error.
d. Calculate the confidence interval
Answers
The standard deviation for non-employed students is given as 0.524,
the margin of error is 0.083 and the 90% confidence interval for the mean GPAs of non-employed students is (3.147, 3.313).
Variables needed to solve the problem Sample size (n)
Sample mean, Sample standard deviation (s), Confidence level (CL)
Margin of error (E)
b. The standard deviation for non-employed students is given as 0.524.
c. Point estimate:
The point estimate for the mean GPA of non-employed students is the sample mean, which is given as 3.23.
Margin of error:
We can use the formula for the margin of error:
E = z(s/√n)
For a 90% confidence level, the critical value is 1.645.
E = 1.645(0.524/√114) = 0.083
Therefore, the margin of error is approximately 0.083.
d. Confidence interval:
The confidence interval is given by the formula:
(3.23 - 0.083, 3.23 + 0.083)
= (3.147, 3.313)
Therefore, the 90% confidence interval for the mean GPAs of non-employed students is (3.147, 3.313).
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