The values of the composite functions are
(1) (f + g)(x) = 4x² + 2x - 2
(2) (fg)(x) = 8x³ - 4x² - 2x + 1
(3) (fⁿ)(x) = (4x² - 1)ⁿ
How to evaluate the composite functionsFrom the question, we have the following functions that can be used in our computation:
f(x) = 4x² - 1
g(x) = 2x - 1
Using the above as a guide, we have the following:
(f + g)(x) = f(x) + g(x)
(f + g)(x) = 4x² - 1 + 2x - 1
Evaluate the like terms
(f + g)(x) = 4x² + 2x - 2
(fg)(x) = f(x) * g(x)
(fg)(x) = (4x² - 1) * (2x - 1)
Evaluate the products
(fg)(x) = 8x³ - 4x² - 2x + 1
(fⁿ)(x) = (f(x))ⁿ
So, we have
(fⁿ)(x) = (4x² - 1)ⁿ
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In a survey of 320 college graduates, 36% reported that they stayed on their first full-time job less than 1 year. If 15 of those subjects are randomly selected without replacement for a follow-up survey, find the probability that exactly 5 of them stayed on their job for less than one-year.
Name the variables in the context of the problem.
State the requirements for binomial distribution for this problem.
Use the long formula above to find P(x)
Using the binomial distribution, there is a 0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, there is a fixed number of independent trials, each with only two possible outcomes, hence the binomial distribution is used. The values of the parameters are:
n = 15, p = 0.36.
The probability is P(X = 5), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.36)^{5}.(0.64)^{10} = 0.2094[/tex]
0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.
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solve the equation: z^ +4z+20+iz(a+1)=0 Where A is constant, has complex conjuget root. if one of roots this quadratic is z=B+2i?
The complex conjugate roots exists A = -1 - 4i or A = -1 + 12i.
How to estimate complex conjugate roots?
If one of the roots exists w = B + 2i, then the other root exists its conjugate w = B - 2i. So we can factorize the quadratic to
[tex]z^2+4z+20+iz(A+1) = (z-(B+2i))(z-(B-2i))[/tex]
Expand the right side and collect all the coefficients.
[tex]z^2+(4+(A+1)i)z+20 = z^2-2Bz+B^2+4[/tex]
From the z and constant terms, we have
[tex]$\left \{ {{4+(A+1)i = -2B} \atop {20 = B^2+4}} \right.[/tex]
From the second equation, we get
[tex]B^2 = 16[/tex]
B = ± 4
Then 4+(A+1)i = ± 8
(A + 1)i = 4 or (A + 1)i = -12
Since [tex]$\frac{1}{i} = -i[/tex], we have
[tex]$\frac{-A+1}{i} =4[/tex] or [tex]$\frac{-A+1}{i} =-12[/tex]
A+1 = -4i or A+1 = 12i
A = -1-4i or A = -1+12i
Therefore, the complex conjugate roots exists A = -1-4i or A = -1+12i.
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the sum of the measures of three angles is 200. these measures are in the ration 3:5:12. Find the measure of the three angles.
Answer:
30, 50, and 120
Step-by-step explanation:
3/20 × 200 = 30
5/20 × 200 = 50
12/20 × 200 = 120
The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.
Given that:
The sum of the measures of three angles = 200.
Let the ratios be x.
The ratio of first angle be 3x
The ratio of second angle be 5x
The ratio of third angle be 12x
According to the question,
3x+ 5x+ 12x = 200
20x = 200
Divide both sides by x
x = 200/20
x = 10
The ratio of first angle be 3x = 3(10) = 30 degrees
The ratio of second angle be 5x = 5(10) = 50 degrees
The ratio of third angle be 12x = 12(10) = 120 degrees
The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.
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Se dispone de 800 000 para invertir. Una cuenta paga el 18% de interés anual, y otra paga el 21%. ¿Cuánto debe invertirse en cada cuenta para ganar 150 000 en intereses en un año?
Se debe depositar $ 600 000 en la cuenta con 18 % de interés anual y $ 200 000 en la cuenta con 21 % de interés anual para recibir $ 150 000 en intereses.
¿Cuánto se debe invertir en cada cuenta para alcanzar las ganancias deseadas en un período dado?
En este problema tenemos un depósito repartido en dos cuentas, que adquiere ganancias de manera continua en el tiempo. En consecuencia, tenemos por interés compuesto la siguiente ecuación a resolver:
x · (18/100) + (800 000 - x) · (21/100) = 150 000
168 000 - (3/100) · x = 150 000
(3/100) · x = 18 000
x = 600 000
Se debe depositar $ 600 000 en la cuenta con 18 % de interés anual y $ 200 000 en la cuenta con 21 % de interés anual para recibir $ 150 000 en intereses.
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1. Quadratics.
The path of the longest shot put by the Women's track team at Sun Devil U is modeled by h(x) = -0.017x² + 1.08x + 5.8, where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground. (Both x and h(x) are measured in feet.)
a. 4 points. Determine h(24). Round your answer to 2 decimal places. Then explain what your answer means in the context of the problem. ("In the context of the problem" means "in terms of the shot put's horizontal distance from the start and in terms of the height of the shot put above the ground.")
b. 4 points. Determine the numerical value of the vertical intercept and explain what this means in the context of the problem.
c. 4 points. Determine the numerical values of the vertex coordinates and explain what they mean in the context of the problem.
d. 4 points. How far from the start did the shot put strike the ground? Round your answer to 2 decimal places.
h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.
What is the value of h(24)?Given,
h(x) = -0.017x² + 1.08x + 5.8
Put h = 24,
h(24) = -0.017(24)² + 1.08(24) + 5.8
h(24) = -9.792 + 25.92 + 5.8
h(24) = 21.93
The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.
What is the value of the vertical intercept?Vertical intercept, x = 0
h(0) = -0.017(0)² + 1.08(0) + 5.8
h(0) = 5.8
The height of the shot put above the ground is 5.8 feet at the start.
What is the values of the vertex coordinates?vertex coordinates,
(h,k) = [(-b/2a),-(b²- 4ac)/4a]
(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]
(h,k) = [(1.08/0.034),(1.5608)/0.068)]
(h,k) = (31.76,22.95)
The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.
How far from the start did the shot put strike the ground?Put h(x) = 0,
-0.017x² + 1.08x + 5.8 = 0
Use quadratic formula for solving x,
x = (-b±√b²- 4ac)/2a
Here a = -0.017, b=1.08, c=5.8
x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)
x = [-1.08±√1.5608]/-0.034
x = [-1.08-1.2493]/-0.034 and x = [-1.08+1.2493]/-0.034
x = 68.509 and x = - 4.98
Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²
= √73.49²
= 73.49 feet
Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.
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Which of the following has the least steep graph?
Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 99%, sample size 10.
Answer:
1.894
3.169
2.064
3.690
Step-by-step explanation: 90% ; sample size = 8
Degree of freedom, df = n - 1
t(1 - α/2, 7) = t0.05, 7 = 1.894
Find the interest rate for a principal of $6514 and charged $45415 in interest for 15 years.
Answer:
the answer is 46.47937775048613
Which of the following is a radical equation?
x StartRoot 3 EndRoot = 13
x + StartRoot 3 EndRoot = 13
StartRoot x EndRoot + 3 = 13
x + 3 = StartRoot 13 EndRoot
Using it's concept, a radical equation is given as follows:
[tex]\sqrt{x} + 3 = 13[/tex].
What is a radical equation?A radical equation is an equation in which the variable is inside the radical.
Hence, among the equations given, the radical equation is:
[tex]\sqrt{x} + 3 = 13[/tex].
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Answer:
C
Step-by-step explanation:
took edge test and got 100
!!GIVING BRAINLISET!! HELP IF ANYONE CAN
SOLVE THIS FOR ME 1-7 JUST ANSWERS
The solution to the given polynomial in their degree are:
5m²p³ + 6 - binomial5q^-4 + 6q - binomial7ab + 6b² - 2a³ - TrinomialPolynomial5m²p³ + 6 - binomial5q^-4 + 6q - binomial7ab + 6b² - 2a³ - Trinomial2a + 4a³ - 5a² - 1
= 4a³ - 5a² + 2a - 1
The leading coefficient is 4a³
4z - 2z² - 5z⁴
= -5z⁴ - 2z² + 4z
The leading coefficient is -5z⁴
(-3d² - 8 + 2d) + (4d - 12 + d²)
= -3d² - 8 + 2d + 4d - 12 + d²
= -2d² + 6d - 20
(y + 5) + (2y + 4y² - 2)
= y + 5 + 2y + 4y² - 2
= 4y² + 3y + 3
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You randomly select an integer from 0 to 9 (inclusively) and then randomly select and integer from 0 to 7 what is the probability of selecting a 2 both times
Reason:
Set A = {0,1,2,3,4,5,6,7,8,9}
Set B = {0,1,2,3,4,5,6,7}
The probability of getting a "2" from set A is 1/10 since there is one copy of "2" that we want out of ten values total.
The probability of getting a "2" from set B is 1/8 for similar reasoning. This time there are eight numbers in this set.
Multiply those fractions mentioned (1/10)*(1/8) = 1/80
This fraction converts to the exact decimal value of 0.0125, meaning there's exactly a 1.25% chance of getting "2" twice in a row.
Q19. When a resistor is placed across 230M supply (de) the
current is 12A. What is the value of resistor that must
De connected in parallel to increase the load current
to 16a
The value of the resistor that must be connected in parallel is 57.47 ohms
How to determine the resistor connected across the 230 V supplyVoltage (V) = 230 VCurrent (I) = 12 AResistor 1 (R₁) =?V = IR
230 = 12 × R₁
Divide both sides by 12
R₁ = 230 / 12
R₁ = 19.17 ohms
How to determine the total resistanceVoltage (V) = 230 VCurrent (I) = 16 ATotal resistance (Rₜ) =?V = IR
230 = 16 × Rₜ
Divide both sides by 12
Rₜ = 230 / 16
Rₜ = 14.375 ohms
How to determine the resistor connected in paralleResistor 1 (R₁) = 19.17 ohms Total resistance (Rₜ) = 14.375 ohmsResistor 2 (R₂) = ?1/Rₜ = 1/R₁ + 1/R₂
Collect like terms
1/R₂ = 1/Rₜ - 1/R₁
R₂ = (Rₜ × R₁) / (R₁ - Rₜ)
R₂ = (14.375 × 19.17) / (19.17 - 14.375)
R₂ = 57.47 ohms
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Arnez Company’s annual accounting period ends on December 31. The following information concerns the adjusting entries to be recorded as of that date. The Office Supplies account started the year with a $3,850 balance. During the year, the company purchased supplies for $15,901, which was added to the Office Supplies account. The inventory of supplies available at December 31 totaled $3,388. The Prepaid Insurance account had a $27,744 debit balance at December 31 before adjusting for the costs of any expired coverage for the year. An analysis of prepaid insurance shows that $20,004 of unexpired insurance coverage remains at year-end. The company has 15 employees, who earn a total of $1,800 in salaries each working day. They are paid each Monday for their work in the five-day workweek ending on the previous Friday. Assume that December 31 is a Tuesday, and all 15 employees worked the first two days of that week. Because New Year’s Day is a paid holiday, they will be paid salaries for five full days on Monday, January 6 of next year. The company purchased a building at the beginning of this year. It cost $725,000 and is expected to have a $45,000 salvage value at the end of its predicted 25-year life. Annual depreciation is $27,200. Since the company is not large enough to occupy the entire building it owns, it rented space to a tenant at $3,400 per month, starting on November 1. The rent was paid on time on November 1, and the amount received was credited to Rent Revenue. However, the tenant has not paid the December rent. The company has worked out an agreement with the tenant, who has promised to pay both December and January rent in full on January 31. On November 1, the company rented space to another tenant for $3,080 per month. The tenant paid five months' rent in advance on that date. The payment was recorded with a credit to the Unearned Revenue account. Assume no other adjusting entries are made during the year. Required: 1. Use the information to prepare adjusting entries as of December 31. 2. Prepare journal entries to record the first subsequent cash transaction in January of the next year for parts c and e.
1. The preparation of the adjusting entries as of December 31 for Arnez Company is as follows:
Adjusting Journal Entries:1. Debit Office Supplies Expenses $16,363
Credit Office Supplies $16.363
2. Debit Insurance Expenses $7,740
Credit Prepaid Insurance $7,740
3. Debit Salaries Expenses $54,000
Credit Salaries Payable $54,000
4. Debit Rent Receivable $3,400
Credit Rent Revenue $3,400
5. Debit Unearned Rent Revenue $6,160
Credit Rent Revenue $6,160
2. The preparation of the journal entries to record the first subsequent cash transactions in January of the next year for Arnez Company is as follows:
Journal Entries:Debit Salaries Payable $54,000
Credit Cash $54,000
Debit Cash $6,800
Credit Rent Receivable $3,400
Credit Rent Revenue $3,400
Adjusting Transaction Analysis:1. Office Supplies Expenses $16,363 Office Supplies $16.363 ($3,850 + $15,901 - $3,388)
2. Insurance Expenses $7,740 Prepaid Insurance $7,740 ($27,744 - $20,004)
3. Salaries Expenses $54,000 Salaries Payable $54,000 ($1,800 x 15 x 2)
4. Rent Receivable $3,400 Rent Revenue $3,400
5. Unearned Rent Revenue $6,160 Rent Revenue $6,160 ($3,080 x 2)
January Transactions:Salaries Payable $54,000 Cash $54,000
Cash $6,800 Rent Receivable $3,400 Rent Revenue $3,400
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ienes una cuerda que mide 90 cm. Hay que partir la cuerda en 2 segmentos (A y B). La cuerda B debe ser 5 veces más grande que la cuerda A. ¿Cuánto mide la cuerda B?
Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.
¿Cuánto mide cada segmento de cuerda?
En este problema debemos hallar dos segmentos de cuerda que cumple la siguiente relación, basada en el enunciado citado:
5 = (90 cm - x)/x (1)
5 · x = 90 cm - x
6 · x = 90 cm
x = 15 cm
Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.
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Robin can make 8 puppets with the material she already has. For each additional sheet of felt she buys, she can make 5 more puppets. What is an equation that shows how the total number of puppets she can make, y, depends on the number of sheets of felt she buys?
How much should be invested now at an interest rate of 6.5% per year, compounded continuously, to have $1500 in two years?
Do not round any intermediate computations, and round your answer to the nearest cent.
If necessary, refer to the list of financial formulas.
Answer:
$1317.14
Step-by-step explanation:
compounded continuously formula is A=Pe^rt
given that you want to have $1500 in 2 years while the rate is 6.5%, you have A, r, and t of the formula and you are just looking for the P.
plugging everything in...
1500=P (e)^2x0.065
P=1500/1.139
P=1317.14
-11r is greater than or less than -20
If a cylinder has a volume of 300 m3 and a radius of 5 m, what is its height (in meters)? (Round your answer to two decimal places.)
also second question:
The diameter is 6 feet 6 inches. The height is 12 feet 3 inches. Determine the surface area (in square feet) and volume (in cubic feet) of the following. (Round your answers to one decimal place.)
The height of the cylinder is 3.82 m
2. The surface area is 316.5 ft²
The volume is 406.5 ft³
Calculating volume of a cylinderThe volume of a cylinder is given by the formula,
V = πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
V = 300 m³
r = 5 m
h = ?
Putting the parameters into the formula, we get
300 = π × 5² × h
300 = π × 25× h
∴ h = 300/25π
h = 3.82 m
Hence, the height of the cylinder is 3.82 m
2.
Diameter = 6 feet 6 inches = 6.5 feet
∴ Radius = 3.25 feet
Height = 12 feet 3 inches = 12.25 feet
Surface area of a cylinder is given by
Surface area = 2πr(r + h)
Where r is the radius
and h is the height
Surface area = 2π×3.25(3.25 + 12.25)
Surface area = 316.5 ft²
For the volume
V = πr²h
V = π × 3.25² × 12.25
V = 406.5 ft³
Hence, the volume is 406.5 ft³
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divide 7.39 divide 0.72 rounded quotient of the nearest hundredth
Answer:
10.26 I believe you wanted me to divide 7.39/0.72. If so, you get 10.2638 that rounds to 10.26
Step-by-step explanation:
Can u give me brainliest please
The value of the expression 7.39 ÷ 0.72 is 10.26 to the nearest hundredths.
We have,
Expression:
7.39 ÷ 0.72
Now,
The expression can be written as,
= 7.39 / 0.72 ______(1)
Simplify the numerator and denominator.
Numerator = 7.39 = 739/100 _____(2)
Denominator = 0.72 = 72/100 ______(3)
Now,
From (1), (2), and (3).
7.39 / 0.72
= (739/100) / (72/100)
= 739/100 x 100/72
100 is the common factor so it gets canceled.
= 739/72
= 10.2638888.....
Rounding to the nearest hundredths.
= 10.26
Thus.
The value of the expression 7.39 ÷ 0.72 is 10.26 to the nearest hundredths.
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I need answers please and thank you!
Will give brainliest
Answer:
Step-by-step explanation:
will give brainiest wrrwrwvrwvr
Solving for the area.
Area
1/2(sum of parallel sides)height1/2(50+65)(30)1/2(115)(30)15(115)1150+5751725ft²Answer:
1725 ft²
Step-by-step explanation:
The formula to find the area of a trapezoid is :
Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height
Let us solve it now.
Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height
Area = [tex]\frac{1}{2}[/tex] × ( 65 + 50 ) × 30
Area = [tex]\frac{1}{2}[/tex] × ( 115 ) × 30
Area = [tex]\frac{1}{2}[/tex] × 3450
Area = 1725 ft²
Determine whether the graph is bipartite.
The graph isn't bipartite because it isn't possible to assign either Blue or Red to each vertex, without having connected vertices with the same color.
What is the bipartite graph theorem?The bipartite graph theorem states that a graph is considered to be bipartite only if it's possible to assign either Blue or Red to all the vertex, such that no two (2) connected vertices would have the same color.
By critically observing the image after assigning the colors to each vertices (see attachment), we can logically deduce that the graph isn't bipartite because it isn't possible to assign either Blue or Red to all the vertex, without having connected vertices with the same color.
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The sum of two numbers is 42. The greater number is equal to 5 times the smaller number. Find the numbers.
Answer:
35 and 7
Step-by-step explanation:
5x + 1x =42
6x=42
x=7
Answer:
Greater number: 35
Smaller number: 7
Step-by-step explanation:
1) Set up system of equations.
Let x = greater number
Let y = smaller number
----------------------------------------------
x + y = 42
x = 5y
2) Solve them using elimination or substitution.
x + y = 42
x - 5y = 0
----------------
6y = 42
y = 42/6
y = 7
3) Substitute the found answer into one of the two equations to find the value of x.
x = 5(7)
x = 35
Therefore, the greater number is 35, and the smaller number is 7.
For many years organize crime rent a number game that is now run illegally by minis states government the player select a three digit number from 0 to 999 there are 1000 such members a bet of two dollars is placed on a number say number 115 if the number is selected the player wins $700 if any other number is selected the player wins nothing find the expected value for this game and describe what it means
Using a discrete distribution, the expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Considering the situation described in this problem, the distribution for the earnings is given as follows:
P(X = 700) = 1/1000.P(X = -2) = 999/1000.Hence the expected value is given as follows:
[tex]E(X) = 700\frac{1}{1000} - 2\frac{999}{1000} = \frac{700 - 2(999)}{1000} = -1.298[/tex]
The expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.
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I need some help on this question
Using slopes, the table that could represent Relationship B is the second table.
What is the slope of a relationship?The slope of a relationship is given by the change in y divided by the change in x.
For relationship A, we have points (2,3) and (4,6), hence the slope is:
mA = (6 - 3)/(4 - 2) = 3/2 = 1.5.
Then, the slopes in the table are given as follows:
m = (8.4 - 6.3)/(4 - 3) = 2.1 > mA, hence the first table cannot be representation B.m = (4.5 - 2.25)/(6 - 3) = 0.75 < mA, hence the second table could represent Relationship B.m = (7.2 - 5.4)/(4 - 3) = 1.8 > mA, hence the third table cannot be representation B.m = (9.6 - 4.8)/(6 - 3) = 1.6 > mA, hence the fourth table cannot be representation B.More can be learned about slopes at https://brainly.com/question/24674549
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You can build two triangles that have the same side lengths but are not
congruent.
A. True
B. False
Answer: False .
Step-by-step explanation: mark me brainliest
Answer:
false because l don't know
your restaurant serves 50 bowls of French onion soup daily and each serving has 8 ounces of onion per portion. Do you think it would be better to purchase whole onions at $1.99 per pound, and cut them yourself, or purchase pre-sliced onions at $2.99 per pound?
I would be better to purchase whole onions at $1.99 per pound, and cut them yourself
Optimization of costNumber of bowls = 50
Weight of each bowl = 8
Total weight of the onion soup = 8 x 50 = 400 ounces
Note that:
1 pound = 16 ounces
Total weight in pounds = 400/16
Total weight in pounds = 25 pounds
If you buy the whole onions and purchase at $1.99 per pound
Total cost = 25 x 1.99 = $49.75
If you purchase pre-sliced onions at $2.99 per pound
Total cost = 25 x $2.99 = $74.75
Since it is cheaper to purchase whole onions at $1.99 per pound, it is the better choice
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A ternary string of length n is a sequence of n digits in which only 0, 1, or 2 appear.
For example, (0,1,0,2) and (1,1,2,2) are ternary strings of length 4 and can be seen as: 0102 and 1122.
How many ternary strings of length 2n are there in which the zeros appear only in odd positions?
dunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunno
dunno
The function y=f(x is graphed below. What is the average rate of change of the function f(x)on the interval 0≤x≤5?
[tex]m = \frac{f(5) - f(0)}{5 - 0} [/tex]
[tex]m = \frac{ - 10 - 10}{5} = \frac{ - 20}{5} = - 4[/tex]
Step-by-step explanation:
the average rate of change is
(f(high interval end) - f(low interval end))/(high interval end - low interval end)
in our case here
(f(5) - f(0)) / (5 - 0)
(-10 - 10) / 5 = -20/5 = -4