To solve the question, we will follow the steps below:
[tex]f(x)=x^2-1[/tex]To find f(f(x)), we will simply replace x by x² - 1 in the function x² - 1
That is:
f((fx)) = (x²-1)² - 1
Then we open the parenthesis
f(f(x)) = (x² - 1)(x² -1) - 1
=x²(x²-1)-1(x²-1) - 1
= x⁴ - x² - x² + 1 - 1
= x⁴ - 2x²
So the correct option is option D. which is x⁴ - 2x²
The number of yards Y is equal to the number of feet F divided by 3 find formula and graph it
Respuesta:
Si el número de yardas (Y) es igual al número de pies (F) dividido por 3, entonces podemos establecer la siguiente ecuación:
[tex]Y=\frac{F}{3}\text{.}[/tex]La gráfica de esta ecuación es una linea recta con pendiente 1/3 y que pasa por el origen, como sigue:
A parachute speed during a free fall reaches 135 miles per hour. What is this speed in feet per second? At this speed, how many feet will the parachute fall during 5 seconds free fall? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answer.
The parachutes speed during free fall will be : 990 feet per second
Given: A parachute speed during a free fall = 135 miles per hour.
This means Unit rate = 135 miles per hour
= 135 × [tex]\frac{5280}{60X60}[/tex] feet per second
Because it is given that 1 mile = 5280 feet per second
= [tex]135 X \frac{5280}{3600}[/tex]
On dividing 5280 by 3600
we get:
= 135 × 1.46
= 198.00 feet per second
Thus in 5 seconds the parachutes speed during free fall will be :
990 feet per second.
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What does the variable r represent?The population correlation coefficientThe sample correlation coefficientThe coefficient of determinationThe critical value for the correlation coefficient
Given:
Variable r
To determine the what variable r represents, we first note that it is a common way to indicate a correlation value. We also note that coefficient of determination, r^2, is simply the square of the sample correlation coefficient (i.e., r).
Therefore, variable r means:
The sample correlation coefficient
A farmer is going to divide her40 acre farm between two crops. Seed for crop A costs $30 per acre. Seedfor crop B costs $15 per acre. The farmer can spend at most $1050 on seed.If crop B brings in a profit of $70 per acre, and crop A brings in a profit of $180 per acre, how many acres ofeach crop should the farmer plant to maximize her profit?acres of crop Aacres of crop B
Given: A farmer is going to divide her40 acre farm between two crops
To Determine: How many acres of each crop should the farmer plant to maximize her profit
Solution
[tex]\begin{gathered} x=acres\text{ for crop A} \\ y=acres\text{ fro corp B} \end{gathered}[/tex][tex]\begin{gathered} Therefore: \\ x+y\leq40 \\ 30x+15y\leq1050 \\ Profit\text{ functon is} \\ P=70y+180x \end{gathered}[/tex]The graph of the inequalitiesis as shown below
Neglecting the negative axis, the point that will maximize the profit are te points shown above with their coordinates
The coordinates will maximum profits are
[tex]\begin{gathered} Point1:(0,40) \\ Point2:(35,0) \\ Point3:(30,10) \end{gathered}[/tex]Substitute the 3 points into the profit functions to determine thepoint that will given the maximum profit
[tex]\begin{gathered} P=180x+70y \\ Point1 \\ P1=180(0)+70(40) \\ P1=0+2800 \end{gathered}[/tex][tex]\begin{gathered} Point2 \\ P2=180(35)+70(0) \\ P2=6300+0 \\ P2=6300 \end{gathered}[/tex][tex]\begin{gathered} Point3 \\ P3=180(30)+70(10) \\ P3=5400+700 \\ P3=6100 \end{gathered}[/tex]Hence, the point that will maximize profit is (35, 0), which is
35 acres of crop A, and
0 acre of crop B
John saves 2/5 of his take-home pay. After
6 paychecks, he has saved $4,800. How much is John's paycheck?
A. $800
C. $2,000
B. $1,920
D. $3,500
John's paycheck is $2,000.
According to the question,
We have the following information:
John saves 2/5 of his take-home pay.
After 6 paychecks, he has saved $4,800.
Now, let's take John's paycheck to be $x.
Now, 2/5 of this paycheck will be $2x/5.
So, this is the amount saved from 1 paycheck of John.
Now, to find the amount saved in 6 paychecks will be:
6*(2x/5)
Now, we can equate this to the amount saved by John after 6 paychecks.
6*(2x/5) = $4,800
12x/5 = 4800
12x = (4800*5)
x = (4800*5)/12
Now, dividing 4800 by 12:
x = 400*5
x = $ 2000
Hence, the correct option is C ($2,000).
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Recall that the volume of the a right circular cone with height h and radius …
Given:
The change in volume by time is, (dV/dt) = 10 cubic feet per minute.
The diameter and height of the right circular one are equal, 2r = h.
Height of the pile is, h = 21 ft.
The objective is to find the rate of increase in height of the pile.
Explanation:
The general formula of volume of cone is,
[tex]V=\frac{1}{3}\pi r^2h\text{ . . . . . (1)}[/tex]From the given data, radius of the cone can be calculated as,
[tex]\begin{gathered} 2r=h \\ r=\frac{h}{2} \end{gathered}[/tex]Substitute the value of r in equation (1).
[tex]\begin{gathered} V=\frac{1}{3}\pi(\frac{h}{2})^2h \\ V=\frac{1}{3}\pi(\frac{h^2}{4})^{}h \\ V=\frac{1}{12}\pi h^3\text{ . . . . . (2)} \end{gathered}[/tex]To find rate of increase in height of the pile:
Now, differentiate equation (2) with respect to time t.
[tex]\begin{gathered} \frac{dV}{dt}=\frac{\pi}{12}\times\frac{d}{dt}(h^3) \\ \frac{dV}{dt}=\frac{\pi}{12}\times3h^2\frac{dh}{dt} \\ \frac{dV}{dt}=\frac{\pi}{4}\times h^2\frac{dh}{dt}\text{ . . . . (3)} \end{gathered}[/tex]Substitute (dV/dt) and h in equation (3).
On plugging the obtained values in eqation (3),
[tex]\begin{gathered} 10=\frac{\pi}{4}\times(21)^2\frac{dh}{dt} \\ \frac{dh}{\mathrm{d}t}=\frac{10\times4}{21^2\times\pi} \\ \frac{dh}{dt}=0.02887164\ldots.\text{.} \\ \frac{dh}{dt}\approx0.029\ldots\text{ ft/min} \end{gathered}[/tex]Hence, the rate of increase in height of the pile is 0.029 ft/min.
in and perform the symmetry test on each of the folha (b) 9x - y = 9 (d) 25x - 36y? = 900 (1)-25x + 4y = 100 (h) -x + 4y = 16 endpoints of the conjugate axis fundament for each
therefore the center of the hyperbole is (0,0) and it's symmetry axis is the y-axis and the x-axis. The intercepts are (0,-1) and (0,1)
enrique needs our help again. He has 310 dollars he can afford to put towards a new car each month. he wants to be done in 5 years.
a. if he were to be approved for loan at 8% apr compounded monthly, what would the size loan granted to him be? what is he were approved for 3% compounded monthly?
b. one of your values should be higher then the other. Explain why it makes sense that your higher loan value paired with the apr that produced it makes sense?
The monthly payment of $310 compounded monthly at 8% and 3% will have a principal of $15,288.71 and $17,252.23 respectively
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
In order to solve this question, we can use the formula of monthly payment we can use a simple formula for that
[tex]A = p \frac{r(1+r)^n}{(1+r)^n-1}[/tex]
A = monthly paymentr = rate n = number of times compoundedPrincipal on the loanIn the first scenario, we can find the monthly payment at 8%
Substituting the values into the equation and solve
The principal at 8% is $152888.71 and the principal at 3% is at $17252.23
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I am just all around confused with this. Well explanation needed!
Given:
m∠A = (4x - 2) degrees
m∠B = (11x + 17) degrees
Let's find the value of x if the angles A and B are complementary angles.
Complementary angles are angles that sum up to 90 degrees.
Hence, we have:
m∠A + m∠B = 90
(4x - 2) + (11x + 17) = 90
Let's solve for x.
• Remove the parentheses:
4x - 2 + 11x + 17 = 90
• Combine like terms:
4x + 11x - 2 + 17 = 90
15x + 15 = 90
• Subtract 15 from both sides:
15x + 15 - 15 = 90 - 15
15x = 75
• Divide both sides of the equation by 15:
[tex]\begin{gathered} \frac{15x}{15}=\frac{75}{15} \\ \\ x=5 \end{gathered}[/tex]Therefore, the value of x = 5
ANSWER:
x = 5
The length of the long leg in a 30°-60°-90° triangle is 3√2 cm. What is thelength of the short leg?
Answer
x = √6
Explanation
We will first sketch this triangle.
Let the short leg of the triangle be x
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
So, after noting the three sides in a right triangle, we will then use trignometric ratios to solve for any of the unknown. If the non-right-angle angle given is θ, the trignometric ratios in short forms are written as
SOH, CAH and TOA
SOH means Sin θ = (Opp/Hyp)
CAH means Cos θ = (Adj/Hyp)
TOA means Tan θ = (Opp/Adj)
So, the one to be used depends on the sides of the triangle that are provided.
For this triangle, using the angle 60° as the non-right-angle angle
Hypotenuse = ?
Opposite = 3√2
Adjacent = x
Angle = 60°
TOA means Tan θ = (Opp/Adj)
Tan 60° = (3√2)/x
Tan 60° = √3
Tan 60° = (3√2)/x
√3 = (3√2)/x
Cross multiply
x = (3√2)/(√3)
x = (√3) (√2)
x = √6
Hope this Helps!!!
Answer:
x = √6
Step-by-step explanation:
Find the mean of the following numbers:
8
0
3
3
1
7
4
1
4
4
Answer:
the answer is 3.5 i think
8+3+3+1+7+4+1+4+4= 35
35/10=3.5
Write the correct expression for the following statement.
The quotient of x and three
Answer:
[tex]\frac{x}{3}[/tex] or x/3 or x÷3
Mr. Emmer gave a test in his Chemistry class. The scores were normally distributed with a mean of 82 and a standard deviation of 4. A student is randomly chosen. What is the probability that the student scores an 88 or below?
Answer:
93.32 %
Step-by-step explanation:
88 - 82 = 6 points
this is 6 /4 = z-score + 1.5
from z score table , this corresponds to .9332 or 93.32 %
continued - calculating gross payRemember, this is money round to the nearest Penny/hundredths place.
ANSWER:
Regular pay is $383.2
Overtime rate is $14.37
Overtime pay is $114.96
Gross pay is $498.16
STEP-BY-STEP EXPLANATION:
Assuming the overtime multiplier is 1.5 and the standard work week is 40 hours. Therefore, we calculate the regular payment like this:
[tex]RP=40\cdot9.58=383.2[/tex]The overtime rate would be the value of the normal payment times the overtime multiplier, like this
[tex]OTR=9.58\cdot1.5=14.37[/tex]Then we multiply the number of additional hours to the 40 hours allowed, that is, 8 (48 - 40), for which one gives overtime pay
[tex]OTP=8\cdot114.96=114.96[/tex]Now the gross pay would be the sum of the regular payment with the overtime payment:
[tex]GP=114.96+383.2=498.16[/tex]Find odds in favor of winning ring and find against winning the ring
We have a randomly selected prize out of 9 objects (4 rings, 4 headsets and 1 camera).
a) We have to calculate the odds in favor of Mary winning a ring.
The odds can be expressed as the proportion (or quotient) between the probabilities of winning a ring and the probabilities of not winning a ring.
This will also be equal to the number of outcomes that will be a ring (4 elements are rings) divided by the number of outcomes that are not a ring (5 elements are not a ring):
[tex]o_{wr}=\frac{4\/9}{5\/9}=4:5[/tex]b) Now, we have to calculate the odds against Mary winning a ring.
This will be the inverse of the previous result, as we have to divide the probability of not winning a ring by the probability of winning.
We can then write:
[tex]o_{nwr}=\frac{5\/9}{4\/9}=5:4[/tex]Answer:
a) 4 : 5
b) 5 : 4
is the reflection of a figure in the x axis equivalent to the rotation of that same figure 180° (clockwise) about the origin?
The reflection across x-axis has the following rule applied
[tex](x,y)\rightarrow(x,-y)[/tex]The rotation of 180° about the origin has the rule
[tex](x,y)\rightarrow(-x,-y)[/tex]In this case, the new image are not the same, that is to say
Therefore, they are not the same.
Last year, Kaitlyn had $30,000 to invest. She invested some of it in an account that paid 5% simple interest per year, and she invested the rest in an account that paid 9% simple interest per year. After one year, she received a total of $2580 in interest. How much did she invest in each account?First account:Second account:
Answer:
She invested an amount of $3,000 in the first accont and $27,000 in the second account
Explanation:
Here, we want to get the amount invested in each of the accounts
To get this,let us write the simple interest formula
Mathematically, we have this as:
[tex]I\text{ = }\frac{PRT}{100}[/tex]Let the amount invested in the first account be $x, while that of the second account be $y
P represent the amounts invested
R is the rate of investment
T is the time (1 year)
The sum of these two is the $30000 she has to invest
Mathematically, we have this as:
[tex]x\text{ + y = 30000}[/tex]Let us get the interests on each of the accounts
For the first account, we have the interest as:
[tex]I_1\text{ = }\frac{x\times5\times1}{100}\text{ = }\frac{5x}{100}[/tex]For the second account, we have the interest as:
[tex]I_2\text{ = }\frac{y\times9\times1}{100}\text{ =}\frac{9y}{100}[/tex]The sum of these two is the interest value, which is as follows:
[tex]\begin{gathered} I_1+I_2\text{ = }\frac{5x}{100}+\frac{9y}{100}\text{ = 2580} \\ \\ 5x\text{ + 9y = 258000} \end{gathered}[/tex]So, we have two equations to solve simultaneously
The two equations are:
[tex]\begin{gathered} x\text{ + y = 30000} \\ 5x\text{ + 9y = 258000} \end{gathered}[/tex]We can solve this by substitution
Let us substitute for y
[tex]y\text{ = 30000-x}[/tex]Insert this into the second equation, we have this as:
[tex]\begin{gathered} 5x\text{ + 9(30000-x) = 258000} \\ 5x\text{ + 270000-9x = 258000} \\ 9x-5x\text{ = 270000-258000} \\ 4x\text{ = 12000} \\ x\text{ = }\frac{12000}{4} \\ x\text{ = 3,000} \end{gathered}[/tex]Recall:
[tex]y\text{ = 30000-x = 30000-3000 = 27000}[/tex]What this mean is that:
She invested an amount of $3,000 in the first accont and $27,000 in the second account
Find the interest and future value of a deposit of $8,750 at 3% for twenty years.
Answer
Interest = $5,250
Future value = $14,000
Explanation
Given:
Principal, P = $8,750
Rate, R = 3%
Time, T = 20 years
What to find:
The interest and future value.
Step-by-step solution:
The Interest
The interest can be calculated using the simple interest formula below.
[tex]Interest=\frac{P\times R\times T}{100}=\frac{\$8,750\times3\times20}{100}=\$5,250[/tex]The interest of $8,750 at 3% for twenty years is $5,250
The future value
Future value = Amount = Principal + Interest
Future value = $8,750 + $5,250
Future value = $14,000
For the exponential function f, find f^-1 analytically and graph both f and f^-1.f(x)=6^x-8
First, replace f(x) by y. This is done to make the rest of the process easier.
[tex]y=6^x-8[/tex]Now, replace every x with y and a every y with an x:
[tex]x=6^y-8[/tex]Now, solve this equation for y. Then, we must move -8 to the left hand side as +8. It yields
[tex]x+8=6^y[/tex]Now, we can apply logarithms in both sides:
[tex]\log (x+8)=\log 6^y[/tex]For the properties of logarithms, we have
[tex]\log 6^y=y\log 6[/tex]then, we have
[tex]\log (x+8)=y\log 6[/tex]and we obtain
[tex]y=\frac{\log(x+8)}{\log6}[/tex]Finally, replace y with f^1. Then, the inverse funcion is
[tex]f^{-1}(x)=\frac{\log(x+8)}{\log6}[/tex]The graphs of the function and its inverse are:
Temperature is usually measured on the Fahrenheit scale (°F) or the Celsius scale (°C). Use the formula F = 1.8C+ 32 to convert from one scale to the other. The highest temperature ever recorded in Virginia Beach, Virginia, was 104°F. Find the temperature in degrees Celsius. 219°C 26°C b. 155°C d. 40°C
Answer:
The temperature in degrees Celsius is;
[tex]40^0C[/tex]Explanation:
Given the formula for converting Temperature from Celsius to Fahrenheit as;
[tex]F=1.8C+32[/tex]Where;
F = temperature in Fahrenheit
C = temperature in Celsius
To convert from Fahrenheit to Celsius, let us make C the subject of formula;
[tex]\begin{gathered} F-32=1.8C \\ C=\frac{F-32}{1.8} \end{gathered}[/tex]To convert 104°F to Celsius, let us substitute the value into the derived formula;
[tex]\begin{gathered} C=\frac{F-32}{1.8} \\ C=\frac{104-32}{1.8} \\ C=40^0C \end{gathered}[/tex]Therefore, the temperature in degrees Celsius is;
[tex]40^0C[/tex]
PLS HELP DUE TODAY THE IXL
Answer:
Step-by-step explanation:
Answer:
Explain the meaning of 5!
a. 1+2+3+4+5
b.5-4-3-1-0
c.0×1×2×3×4×5
d. 5•4•3•2•1
The number 5 in mathematics denotes a quantity or value of 5. Five is the entire number between four and six. Five is the name of the number. Sam the little shows off five fingers.
What does 5 represent?The distance between 5 and 0 is the absolute value of 5. Then you go 1, 2, 3, 4, and 5. To the immediate right of zero, 5 is located. As a result, 5 has an absolute value of 5.
It denotes the sum of all succeeding integers, inclusively from 1 to 5.
That ' s 5! = 5*4*3*2*1 =120.
Also known as five factorials.
What's the name of a five-digit number?Ten-thousands
Answer and justification A five-digit figure is one that is in the tens of thousands. This is due to the fact that 10,000 is the smallest positive whole number with five digits.
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Please help me I’ll mark u brainly
Answer:
A: (-3,0)
B:(-3,-5)
C:(-6,0)
Step-by-step explanation:
invert the signs on all numbers to flip it 180 degrees, then add 4 to each y point to translate up 4
Solve for x:
X=
76⁰
9x+1
40°
The value of x is 7 and the measure of unknown angle is 64°.
The angles of triangle are given 76°, (9x+1)° and 40°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Now, sum of three angles of a triangle is
76°+(9x+1)°+40°= 180°
⇒ 116+9x+1 = 180
⇒ 9x + 117 = 180
⇒ 9x = 63
⇒ x = 7
So, 9x+1=64°
Therefore, the value of x is 7 and the measure of unknown angle is 64°.
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The model represents an equation. What value of x makes the equation true? Enter your answer in the box below
the value of x are that makes it true
You earn $\$34.50$ selling items at a craft show. Newton earns $5$ times as much as you. Descartes earns $0.1$ times as much as Newton does. How much do the three of you earn in all?
All the three person earn $230.75 in all.
What is mean by Addition?
The process of combining two or more numbers is called the Addition.
Given that;
You earn in selling items = $35.50
Newton earn 5 times as much you.
Descartes earns 0.1 times as much as Newton does.
Now,
You earn in selling item = $35.50
Newton earn in selling = 5 x $35.50
= $177.5
Descartes earn in selling = 0.1 x $177.5
= $17.75
So, Total earn = $35.50 + $177.5 + $17.75
= $230.75
Therefore, All the three person earn $230.75 in all.
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HELPP PLEASE
Choose A
( A is the answer <3)
Write the fraction as a percent. Round to the nearest tenth of a percent if necessary.1/6A) 60%B) 16.7%C) 1.7%D) 27.8%
SOLUTION:
[tex]\frac{1}{6}=(\frac{1}{6}\times\frac{100}{1})\%=\frac{100}{6}\%[/tex]This can be simplified to give;
[tex]16.7\%[/tex]The measure of an angle and it’s complement differ by 22 degrees. Find the larger angle.
The measure of an angle and its complement differ by 22 degrees and the larger is 56°
What are Complementary Angles?The total of the two angles' measurements determines their complement and supplement. The pair of angles is said to be complimentary if the product of the two angles equals the measurement of a right angle.
1. If the total of two angles equals 90°, the angles are considered to be complements of one another.
2. Let x° and y° be the two angles. Since they complement one another, the two angles' sum will be 90 degrees.
= x + y = 90°. (Assume equation 1 is used.)
3. The two angles differ by 22 degrees, hence the equation will be,
= x - y = 22°. (Put equation 2 in.
4. To determine the values of x and y, solve equations 1 and 2.
Add equations 1 and 2 together.
= x + y + x - y = 90 + 22,
= 2x = 112°,
= x = 56°.
5. In equation 1, change the value of x.
= 56° + y = 90°,
= y = 90 -56,
= y = 34°.
So, the measure of the two angles is 56°, and 34°.
And the larger angle is 56°
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f(x)=7x-3 for f(x)= -38
Answer:
f(x)= -269
Step-by-step explanation:
f(x)=7x-3
Since we know f(x)= -38, we can substitute x for -38.
So:
f(-38)=7(-38)-3
f(-38)= -266-3
f(x)= -269
Answer:
-7x=38+3
-7x=41/-7=5.8