Answer:
–x^3 + 5x^2 – 8x + 1
Step-by-step explanation:
You can observe that expanding f(2-x) will give you a sum that includes (2-x)³, so will have a -x³ term. This narrows the choices to one of the first two.
If x=0, then you have ...
... f(2) = 2^3 -2^2 -3 = 8 - 4 - 3 = 1 . . . . corresponds to the first selection
_____
Worked in detail
f(2-x) = (2-x)³ -(2-x)² -3 . . . . substitute 2-x for x in the expression for f(x)
... = (2³ -3·2²x +3·2x² -x³) -(2² -2·2x +x²) -3
... = -x³ +5x² -8x +1 . . . . . matches the first selection
_____
Using ...
... (a+b)³ = a³ + 3a²b +3ab² +b³
... (a+b)² = a² +2ab +b²
the table below shows the time, in seconds that it takes to fill to 20-ounce bottles with water.
Answer:
1 min and 40 sec
Step-by-step explanation:
well for every ounce it takes 5 sec
5 x 20 = 100
I hope i did this right ^_^
Answer:
100 seconds
Step-by-step explanation:
We are given the following data in the question:
Time: 0 30 60 90 120
Ounces of Bottles filled: 0 6 12 18 24
Where time is in seconds and the bottles are filled in ounces.
Amount of water filled in 30 seconds = 6 ounces
Amount of time taken to fill 1 ounce of water = [tex]\frac{30}{6}[/tex] = 5 seconds
We need to find the time to fill 20 Ounces
It is clear from the data that 18 ounces of water will fill in 90 seconds.
We have to find the time to fill 2 ounces of water.
Time taken to fill two ounces of water = [tex]2\times 5[/tex] seconds = 10 seconds.
Total time taken to fill 20 ounces of water = 990 + 10 = 100 seconds = 1 Minute 40 Seconds
Pls I need help with this one. Find the value of y in the equation
Answer:
y = 2 3/8
Step-by-step explanation:
Multiply by the denominator. This gives a linear equation that can be solved in the usual way.
... 3 = 8(y -2)
Divide by 8.
... 3/8 = y - 2
Add 2
... 2 3/8 = y
_____
In problems involving rational expressions, it often works well to multiply by the product of the denominators, or by their least common multiple, if that is easy to find. Doing this eliminates fractions. Here there is only one denominator (y-2), so we multiply by that.
last year 950 people attended a town's annual parade. This year $1,520 people attended. What was the percent increasse in ttendancce from last year to this year
60%
Step-by-step explanation:The percent change can be found from ...
... ((new value)/(old value) -1) × 100%
... (1520/950 -1) × 100% . . . . . . filling in your numbers
... (1.6 - 1) × 100% = 60% . . . . . . simplify
Attendance this year was 60% higher than last year.
The point (0, 5) lies on circle A with the center at the origin. Does the point (0, −5 ) lie on the circle? A. Yes, because both points are equidistant from the center of the circle. B. Yes, because the distance between the two points is half the distance from the center to one of the points. C. No, because both points are not equidistant from the center of the circle. D. No, because the distance between the two points is twice the distance from the center to one of the points.
A. Yes, because both points are equidistant from the center of the circle.
Step-by-step explanation:The point (0, 5) is 5 units from the point (0, 0).
The point (0, -5) is 5 units from the point (0, 0).
The given points are equidistant from the circle center at (0, 0), so both will lie on the circle—along with any other points that are 5 units from (0, 0).
Danny gets paid $8 per hour. What is the rate of change?
A) m=4
B) m= 1/2
C) m=8
Someone please help for grade‼️
Answer:
x=8
Step-by-step explanation:
Since this is an isosceles triangle, the angles in the triangle are 4x, 4x, and 84. The sum of the three angles in a triangle are 180.
4x+4x+ 84 = 180
Combine like terms
8x+84 = 180
Subtract 84 from each side
8x+84-84 = 180 - 84
8x = 96
Divide each side by 8
8x/8 = 96/12
x = 8
Pleaaasssee hellpppp. The farm has cows and turkeys. Between all the animals, there are 148 legs and sixty heads. How many cows and how many turkeys does the farm have?
Answer:
Step-by-step explanation:
14 cows
46 turkeys
Step-by-step explanation:If all the animals were turkeys, there would be 120 legs. There are 28 more than that. Replacing a turkey with a cow adds 2 legs, so there must be 14 such replacements.
There are 14 cows and 46 turkeys.
_____
Check
14×4 + 46×2 = 56 + 92 = 148 . . . . legs
14 + 46 = 60 . . . . . . heads
Which set of points matches the line above?
A.
(0,9) (6,8)
B.
(8,6) (3,11)
C.
(0,9) (11,3)
D.
(9,0) (3,11)
Answer:
C
Step-by-step explanation:
When x = 0, y = 9
When x = 11, y = 3
Find 11 on the horizontal line and go up to the crossing and the follow the line till the y-axis(going to the left direction(. Did you see the 3?
That is the (11 | 3) point
The perimeter of the rectangular playing field is 430 yards.The length of the field is 5 yards less than triple the width. What are the dimensions of the playing field?
Answer:
Answer - 160
Step-by-step explanation:
2L+2W = 430
L = 3W-5
2(3W-5)+2W = 430
6W-10+2W = 430
8W = 440
W = 55 and L = 3(55)-5 = 160
Answer:
Length = 160 and width = 55 yards
Step-by-step explanation:
Perimeter = 2L + 2W where L = the length and W = the width.
L = 3W - 5 (given).
So substituting for L is the formula for the perimeter:-
2(3W - 5) + 2W = 430
6W - 10 + 2W = 430
8W = 440
W = 55 yards.
So the Length L = [430 - 2(55]) / 2 = 160 yards.
Who's beaker has the greatest amount of liquid left in it?
Jay 0.8
Alana 1.05
Evan 1.2
Stacey 0.75
Evan has the most in his beaker.
This is because:
0.75 < 0.8 < 1.05 < 1.2.
PLEASE HELP WITH MATH CONSTRUCTED RESPONSE!!
1. Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable.
2. What is the best estimate for the average cost of tuition at a 4-year institution starting in 2000.
3. What is the best estimate for the average cost of tuition at a 4-year institution starting in 2020.
4. What does the slope mean in context of the situation?
5. Most students are not able to afford this tuition for 4 years. What are some ways that you can lower the cost of your college tuition? If you don’t plan to attend college, what things can do you post- HS graduation to continue your education or provide for yourself financially?
Answer:
y = 0.937976x +12.765$12,765$31,524the cost increase each yearStep-by-step explanation:
1. For this sort of question a graphing calculator or spreadsheet are suitable tools. The attached shows the linear regression line to have the equation ...
... y = 0.937976x + 12.765
where x is years since 2000, and y is average tuition cost in thousands.
2. The y-intercept is the year-2000 tuition: $12,765.
3. Evaluating the formula for x=20 gives y ≈ 31.524, so the year-2020 tuition is expected to be $31,524.
4. The slope is the rate of change of tuition with respect to number of years. It is the average increase per year (in thousands). It amounts to about $938 per year.
5. [not a math question]
cos(−θ)=√3/4 , sinθ<0
What is the value of sinθ ?
Answer:
as written, sin(θ) = -√13/4perhaps, sin(θ) = -1/2Two answers are given because the question is "unexpected." cos(θ) = √(3/4) is more commonly seen in such problems than is cos(θ) = (√3)/4, which is what you have written here. Choose the answer that matches your intent.
Step-by-step explanation:
The cosine function is an even function, so cos(θ) = cos(-θ).
The relationship between sin(θ) and cos(θ) is ...
... sin(θ) = ±√(1 -cos(θ)^2)
For sin(θ) < 0 and cos(θ) = (√3)/4, ...
... sin(θ) = -√(1 -3/16) = -√(13/16)
... sin(θ) = -(√13)/4
For sin(θ) < 0 and cos(0) = √(3/4), ...
... sin(θ) = -√(1 -3/4) = -√(1/4)
... sin(θ) = -1/2
Answer:
-√13/4 took the test.
The mean of a set of data is 4.68 and its standard deviation is 2.83. find the z score of the value
Answer:
z=-0.35 ( Depending on value given)
Step-by-step explanation:
Let the value be x. For calculation purposes, let us take x as 3.68. ( as mean is 4.68). We may assume a higher value as well. Depends on the given value.
The formula for z score is given as-
z=(value-mean)/Standard Deviation
z=(3.68-4.68)/2.83
z=-0.35
−10x+3y=5 ASAP
x=y−4
x ?
y?
Answer:
x = 1 and y = 5
Step-by-step explanation:
Use substitution because you know that x = y - 4, and plug this into the first equation to get -10(y - 4) + 3y = 5, or -10y + 40 + 3y = 5. This is -7y = -35 so y = 5. Plug this into the 2nd equation to get that x = 1 and y = 5.
Given: ∆ABC, AB = CB BD − median to AC E∈ AB ,F∈ BC AE = CF Prove: △ADE ≅ △CDF ΔBDE ≅ ΔBDF
Answer:
1) By SAS theorem, ΔADE≅ΔCDF
2) By SSS theorem, ΔBDE≅ΔBDF
Step-by-step explanation:
Consider isosceles triangle ABC (see diagram).
1. In triangles ADE and CDF:
AD≅DC (since BD is median, then it divides side AC in two congruent parts);AE≅CF (given);∠A≅∠C (triangle ABC is isosceles, then angles adjacent to the base are congruent).By SAS theorem, ΔADE≅ΔCDF.
2. In triangles BDE and BDF:
side BD is common;DE≅DF (ΔADE≅ΔCDF, then congruent triangles have congruent corresponding sides);BE≅FB (triangle ABC is isosceles, AB≅BC, AE≅CF, then BE=AB-AE, FB=BC-CF).Be SSS theorem, ΔBDE≅ΔBDF.
Express 4 as a fraction. A) 1 1 B) 1 4 C) 4 1 D) 4 4
The answer is C) 41 hope this helped
**WILL GIVE BRAINIEST! PLEASE HELP!**
d. $50.94
Step-by-step explanation:The deposit is for 1 year (4 quarters) at an annual rate of 5% (1.25% per quarter). The table value for those parameters is 1.05094. Multiply this value by the $1000 amount Miguel deposited to find his ending balance.
... ending balance = $1000 × 1.05094 = $1050.94
Since his deposit amount was $1000, the interest earned is ...
... $1050.94 -1000.00 = $50.94
In ΔABC (m∠C = 90°), the points D and E are the points where the angle bisectors of ∠A and ∠B intersect respectively sides BC and AC . Point G ∈ AB so that DG ⊥ AB and H ∈ AB so that EH ⊥ AB .
Prove that ΔCEH and ΔCDG are isosceles.
The problem is symmetrical, so proof for ΔCDG can serve as a model for proof for ΔCEH.
Step-by-step explanation:∠DGA ≅ ∠DCA ≅ 90° . . . . given
∠GAD ≅ ∠CAD . . . . definition of angle bisector AD
AD ≅ AD . . . . reflexive property
ΔDGA ≅ ΔDCA . . . . AAS congruence theorem
CD ≅ GD . . . . CPCTC
∴ ΔCDG is isosceles . . . . definition of isosceles triangle (2 sides congruent)
_____
To do the same for ΔCEH, replace "D" with "E", replace "G" with "H", and replace "A" with "B". The rest of the logic applies.
The sum of two numbers is 67 and the difference is 13 . What are the numbers?
Answer:
27 and 40
Step-by-step explanation:
Final answer:
The sum of two numbers is 67 and the difference is 13. The two numbers are 40 and 27.
Explanation:
Let's solve this problem step by step:
Let's call one number x and the other number y.We know that x + y = 67 and x - y = 13.To find the numbers, we can solve this system of equations.Adding the two equations together, we get 2x = 80.Dividing both sides by 2, we find that x = 40.Substituting x = 40 into either equation, we find that y = 27.Therefore, the two numbers are 40 and 27.
Which postulate or theorem proves ∆WXY ≅ ∆WZY ?
SSS Congruence Theorem
SAS Congruence Postulate
HL Congruence Theorem
Answer:
HL Congruence Theorem
Step-by-step explanation:
Answer:
HL congruence theorem
Step-by-step explanation:
Given that WZX is an isosceles triangle with sides WX=WZ
Also given that WY is altitude on side XZ
Consider triangles WXY and WZY
WX=WZ Given
WY=WY REflexive property
Angle wyz =angle wyx Right angle
Hence by HL congruence theorem, since one leg and hypotenuse are equal we get the two triangles to be congruent.
Jeff answered all 25 questions on his chemistry test. For each right answer, he got 4 points and for each wrong answer he lost 2 points. If he got a score of 70 points, how many questions did he get right?
Answer:
Jeff got 20 answers right.
Step-by-step explanation:
The maximum number of points Jeff can get is 100. (25 * 4) However, for each question he gets wrong, he's actually losing 6 points because he doesn't get the four points for getting right, and has the additional -2 points for getting it wrong. Since he only got a score of 70, that means he lost 30 points.
30/6 = 5. So he missed 5 question and got 20 question right.
As per the given values, Jeff got 20 questions right.
Explanation:Total questions answered = 25
Total points for each correct answer = 4
Total points for each incorrect answer = 2
To find the number of questions Jeff got right, we can set up the equation:
4x - 2(25 - x) = 70,
where x represents the number of questions he got right.
Simplifying the equation, we get -
6x - 50 = 70.
Adding 50 to both sides, we have 6x = 120.
Dividing both sides by 6, we get x = 20.
Therefore, Jeff got 20 questions right.
Learn more about Finding the number of questions answered correctly here:https://brainly.com/question/40214390
#SPJ2
A computer and printer cost a total of $1060 . The cost of the computer is three times the cost of the printer. Find the cost of each item.
Answer:
Printer cost 265
Computer cost 795
Step-by-step explanation:
1060 / 4 = 265
he cost of the printer is $265, and the cost of the computer is $795.
The question involves solving a system of equations to find the cost of two items based on their total cost and the ratio of their costs. To find the cost of a computer and a printer, we can set up the equations based on the given information: the total cost is $1060, and the cost of the computer is three times the cost of the printer.
Let's define C as the cost of the computer and P as the cost of the printer. According to the problem, we have two equations: C + P = $1060 (total cost) and C = 3P (cost relationship). We can substitute the second equation into the first to find P: 3P + P = $1060, so 4P = $1060. Dividing both sides by 4, we get P = $265. Using this value, we can find C by multiplying P by 3, giving us C = 3 * $265 = $795.
Thus, the cost of the printer is $265, and the cost of the computer is $795.
Choose the correct conic section to fit the equation. 49x 2 - 16y 2 = 784 Circle Ellipse Parabola Hyperbola
Answer:
hyperbola
Step-by-step explanation:
49x^ 2 - 16y^ 2 = 784
Divide each side by 784
49/784x^ 2 - 16/784y^ 2 = 784
x^2/16 - y^2/49 = 1
This is a hyperbola centered at (0,0)
If it has subtraction, it has to be a hyperbola
Answer:
Thus, The conic which fits the given equation correctly is hyperbola
Step-by-step explanation:
The equation is given to be : 49x² - 16y² = 784
Now, we need to find the correct conic section which fits this given equation
So, to find the correct conic, we will reduce the given equation into the standard form :
So, make R.H.S. 1 by dividing each term by 784
[tex]\frac{49x^2}{784}-\frac{16y^2}{784}=\frac{784}{784}[/tex]
[tex]\implies \frac{x^2}{16}-\frac{y^2}{49}=1[/tex]
[tex]\implies\frac{x^2}{4^2}-\frac{y^2}{7^2}=1[/tex]
This is the standard equation of hyperbola, where a = 4 and b = 7
Thus, The conic which fits the given equation correctly is hyperbola
Clint's salary increased from $24000 to $36000 over a three-year period. Helen's salary increased from $29000 to $43, 500 over the same period. Whose salary increased more in absolute terms? In relative terms? Explain.
Answer:
Helen's salary increased more.
Step-by-step explanation:
We know that Clint's salary increased from $24000 to $36000 over a three-year period.
So the increase in Clint's salary will be = 36000 - 24000 = $12000
While Helen's salary increased from $29000 to $43, 500 over the same period of 3 years.
So the increase in Helen's salary will be = 43500 - 29000 = $14500
Therefore, in absolute terms, Helen's salary has increased more.
If z is a standard normal variable, find the probability. The Probability that z is greater than -1.82.
A. -0.0344
B. 0.9656
C. 0.0344
D. 0.4656
Answer:
C.) 0.9656
Step-by-step explanation:
Using a z-table look for -1.82 and we obtain : 0.0344. So what's the probability that z > -1.82 is the same as saying when is z > 0.0344? Since we're talking about probabilities of an outcome from ranging from 0% to 100% meaning 0 through 1 in decimals then:
1 - 0.0344 = 0.9656
So the probability that z>-1.82 is C.) 0.9656
Using the normal distribution, it is found that there is a 0.9656 probability that z is greater than -1.82, option B.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. The probability of finding a value above X, that is, having a z-score above the one found, is 1 subtracted by the p-value of Z.In this problem:
z = -1.82 has a p-value of 0.0344.
1 - 0.0344 = 0.9656.
0.9656 probability that z is greater than -1.82, option B.
A similar problem is given at https://brainly.com/question/5954134
Which is a third degree polynomial with –3 and 2 as its only zeros?
x^2 + x – 6
x^3 + 2x^2 – 5x – 6
x^3 + 4x^2 – 3x – 18
x^3 + x^2 – 8x– 12
The third-degree polynomial with – 3 and 2 as its only zeros is x³ + x² – 8x – 12, which can be factored as (x+3)(x-2)(x-2).
Explanation:A third-degree polynomial with – 3 and 2 as its only zeros must be in the format of A(x+3)(x-2)(x-C), where A and C are constants, and C is possibly another zero of the polynomial.
Given the four options, the only polynomial that fits this format and has – 3 and 2 as zeros is x³ + x² – 8x – 12.
To verify, we can factor it: (x+3)(x-2)(x-2), which shows that 2 is a zero of multiplicity 2, and – 3 is also a zero.
There are no other real zeros besides these, so it is the correct polynomial.
The sum of two numbers is 60 . The smaller number is 12 less than the larger number. What are the numbers?
Answer:
36 and 24
Step-by-step explanation
36 - 24 = 12
36 + 24 = 60
please help!
1. Find the volume for 5 different spheres by randomly choosing different radii.
Using the same radii values, find the volume of 5 cylinders where the height of the cylinder is the same as the diameter of the sphere.
Answer:
[tex]\begin{array}{ccc}\text{Radius}&\text{Volume of sphere}&\text{Volume of cylinder}\\&&\\1&\dfrac{4}{3}\pi &2\pi \\&&\\2&\dfrac{32}{3}\pi &16\pi \\&&\\3&36\pi &54\pi \\&&\\4&\dfrac{256}{3}\pi &128\pi \\&&\\5&\dfrac{500}{3}\pi &250\pi\end{array}[/tex]
Step-by-step explanation:
Use formulas for the volumes:
[tex]V_{sphere}=\dfrac{4}{3}\pi r^3,\\ \\V_{cylinder}=\pi r^2h=\pi r^2\cdot 2r=2\pi r^3.[/tex]
1. When r=1,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 1^3=\dfrac{4}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 1^3=2\pi.[/tex]
2. When r=2,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 2^3=\dfrac{32}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 2^3=16\pi.[/tex]
3. When r=3,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 3^3=36\pi,\\ \\V_{cylinder}=2\pi \cdot 3^3=54\pi.[/tex]
4. When r=4,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 4^3=\dfrac{256}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 4^3=128\pi.[/tex]
5. When r=5,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 5^3=\dfrac{500}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 5^3=250\pi.[/tex]
Note that for all r,
[tex]\dfrac{V_{sphere}}{V_{cylinder}}=\dfrac{\frac{4}{3}\pi r^3}{2\pi r^3}=\dfrac{2}{3}.[/tex]
Answer:
Please, see the attached file.
Thanks.
Step-by-step explanation:
Please, see the attached file.
Thanks.
everyday each maid a-milking gets 3 gallons of milk from her cow. How much milk to the maids gets in one day?
\(•_•)
( )Z
/ \
Answer:
3 gallons? haha
Step-by-step explanation:
The question did not make that much sense but the only amount of anything given in the question was 3 gallons.
The questions says the maid gets 3 gallons of milk from the cow everyday. SO if we are wondering how much she makes in one day it has to be 3 gallons because it does not give any other information...
Assuming the traditional context of 'The Twelve Days of Christmas' with 8 maids a-milking, each maid gets 3 gallons of milk from her cow, so they would collectively get 24 gallons of milk in one day.
The student is asking how much milk the maids a-milking would get in one day if each maid gets 3 gallons of milk from her cow. To find the total amount of milk gathered by the maids in one day, we need to know the number of maids a-milking. Assuming a traditional context of the song 'The Twelve Days of Christmas', there are 8 maids a-milking. Therefore, the calculation would be:
8 maids x 3 gallons per maid = 24 gallons
So, the maids a-milking would get a total of 24 gallons of milk in one day.
It is important to note that the unit of measurement appropriate for such a quantity of milk is gallons, which is useful for larger capacities, such as the amount produced by a dairy farm operation.
John can create 3 apps in 6 weeks while Ben can do the same job in 2 weeks. How many weeks would it take them to create 10 apps together?
plzzz answer i rlly need help
Answer:
5 weeks
Step-by-step explanation:
John creates apps at the rate ...
... (3 apps)/(6 weeks) = 1/2 app/week
Ben creates apps at the rate ...
... (3 apps)/(2 weeks) = 3/2 app/week
Together, they create ...
... (1/2) app/week + (3/2) app/week = 2 app/week
So, the time for 10 apps is ...
... (10 app)/(2 app/week) = 5 week
_____
Comment on the problem
If the guys actually work at a uniform rate like this, the result after 5 weeks will be 9 completed apps and 2 half-completed apps. Their rate is 10 apps in 5 weeks, but their actual output in that time period may not be 10 completed apps.
One should beware of the "mythical man-month." Rates of job completion depend on many factors. Individual average rates cannot always be summed when folks "work together."