Answer:
[tex]\frac{x}{x+3}[/tex]
Step-by-step explanation:
[tex]\frac{x(x-3)}{(x+3)(x-3)}[/tex]
[tex]\frac{x}{x+3}[/tex]
Using the above graphic, it takes about _____ years to transition from using no oil to consuming 100 million barrels per day whereas it takes about______ years to transition from using 100 million to 200 million barrels per day.
A. 60, 10
B. 10, 60
C. 120, 50
D. 50, 120
It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.
As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.
The right axis indicates the global consumption rate of oil in millions of barrels per day.
To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.
The bottom axis is time in years.
The graph attached at the end of the solution.
Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.
Let the number of years of transition from using 100 million to 200 million barrels per day be b.
From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.
But it takes 50 years to go from 100 million to 200 million.
This is known as exponential growth.
Therefore, the value of a is 120 and the value of b is 50.
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A punter kicks a football. Its height h, in yard, t seconds after the kick is given by the equation h(t)=-4.9t^2+18.24t+0.8. The height of an approaching blocker's hand is modeled by the equation h(t)=-1.43t+4.26, using the same time. Can the blocker knock down the punt (do they intersect)? If so, at what point will that happen (the point of intersection)?
Part 1
[tex]-4.9t^2 +18.24t+0.8=-1.43t+4.26\\\\-4.9t^2 +19.67t-3.46=0\\\\\Delta =(19.67)^2 -4(-4.9)(-3.46)=319.0929 > 0[/tex]
Therefore, the blocker can knock down the punt.
Part 2
Using the quadratic formula,
[tex]t=\frac{-19.67 \pm \sqrt{319.0929}}{2(-4.9)}\\\\t \approx 0.18437, 3.82992[/tex]
Considering the graphs, it is clear to take the smaller solution. Thus, the point of intersection is [tex](0.18437, h(0.18437))=\boxed{(0.18437, 3.99635)}[/tex].
A sinusoidal function whose period is π2
, maximum value is 10, and minimum value is −4 has a y-intercept of 10.
What is the equation of the function described?
Responses
f(x)=7cos(4x)+3
f ( x ) = 7 cos ( 4 x ) + 3
f(x)=7sin(4x)+3
f ( x ) = 7 sin ( 4 x ) + 3
f(x)=7cos(4πx)+3
f ( x ) = 7 cos ( 4 π x ) + 3
f(x)=7sin(4πx)+3
The equation of the function described as; y = 7 sin ( 4x + π/2 ) + 3
The general equation of the sine curve can be written as;
y = a sin ( nx + α ) + b
where : a is the amplitude, n = 2π/period, b = shift in the direction of y
α°= shift in the direction of x
We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.
Thus,
a = (maximum - minimum)/2 = (10 - -4)/2
a = 7
n = 2π/period = 2π/(π/2)
n = 4
b = maximum - a = 10 - 7
b= 3
To find α as y-intercept = 10
y = 10 at x = 0
Substitute in the general function;
y = a sin ( nx + α ) + b
10 = 7 sin ( 4*0 + α ) + 3
Thus, we have;
sin α = 1
α = π/2
So, the equation of the function described is;
y = 7 sin ( 4x + π/2 ) + 3
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Bobby and Rick are in a 16-lap race on a one-mile oval track. Bobby, averaging 86 mph, has completed six laps just as Rick is getting his car onto the track. What speed does Rick have to average to be even with Bobby at the end of
the sixteenth lap?
To be even with Bobby at the end of the sixteenth lap, Rick has to average a speed of __ mph.
(Type an integer or a decimal.)
Hence, the speed that Rick must be driving on to even with Bobby at the end of the 16th lap should be: Distance = Speed × Time16=1084× Speed Speed=16×8410=134.4 mph.
The time taken by Bobby to complete 10 laps will be:
[tex]$$\begin{aligned}\text { Distance } & =\text { Speed } \times \text { Time } \\10 & =84 \times \text { Time } \\\text { Time } & =\frac{10}{84} \text { hours }\end{aligned}$$[/tex]
Hence, the speed that Rick must be driving on to even with Bobby at the end of the 16 th lap should be:
[tex]$$\begin{aligned}\text { Distance } & =\text { Speed } \times \text { Time } \\16 & =\frac{10}{84} \times \text { Speed } \\\text { Speed } & =\frac{16 \times 84}{10}=134.4 \mathrm{mph} .\end{aligned}$$[/tex]
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. Find the solution(s) to the systems of equations algebraically
{(y=x^2-2x+4),(y=3x):} (Use Substitution and factoring)
(multiple choice)
A.(0,0)
B.(4,12)
C.(4,1)
D.(0,4)
E.(1,3)
The solution to the systems of equations is (4,1). Option C. is the answer
How to find the solution(s) to the systems of equations algebraically?An algebraic equation is when two expressions are set equal to each other, and at least one variable is included
Given the: equations {(y=x²-2x+4), (y=3x):}
y= x²-2x+4 and y = 3x
substitute y = 3x into y= x²-2x+4. That is:
y= x²-2x+4
3x = x²-2x+4
x²-2x -3x+4 = 0
x²-5x+4 = 0
By factoring:
x²-4x -1x+4 = 0
x(x-4) -1(x-4) = 0
(x-4)(x-1) = 0
x-4 = 0 or x-1 = 0
x= 4 or x = 1
Thus, the solution is (4,1)
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A racetrack charges $85 for each seat in the lower section, $60 for each seat in the upper sections, and $35 for field tickets. There are three times the amount of seats in the upper section as compared to the lower section. The revenue from selling all 22,800 seats is $948,000. How many seats are in the upper section of the racetrack?
Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.
What is a system of equations?A system of equations, also called simultaneous equations, is two or more equations solved concurrently.
We can use any of the following methods to solve simultaneous equations:
GraphicalSubstitutionEliminationMatrix.In this situation, after forming the equations, we can use substitution and elimination methods to solve them.
Racetrack charge per lower seat = $85
Racetrack charge per upper seat = $60
Racetrack charge per field ticket = $35
Let lower seats = x
Let upper seats = 3x
Let field tickets = y
4x + y = 22,800 ... Equation 1
y = 22,800 - 4x ...Equation 3
85x + 60(3x) + 35y = 948,000
85x + 180x + 35y = 948,000 ... Equation 2
Substitute Equation 3 in Equation 2 to eliminate y:
85x + 180x + 35(22,800 - 4x) = 948,000
85x + 180x + 798,000 - 140x = 948,000
125x = 948,000 - 798,000
125x = 150,000
x = 1,200
Determining the number of seats:
Seats in the Lower section = 1,200
Seats in the Upper section = 3,600 (1,200 x 3)
Field tickets, y = 22,800 - 4x
y = 22,800 - 4(1,200)
= 18,000
Check:
85x + 180x + 35y = 948,000
85(1,200) + 180(1,200) + 35(18,000) = 948,000
102,000 + 216,000 + 630,000 = 948,000
948,000 = 948,000
Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.
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In the last 24 days, it rained 18 days. What is the ratio of rainy days to total days written as a percent?
The ratio of rainy days to total days written as a percent will be 75%.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.
Since in the last 24 days, it rained 18 days.
Number of rainy days = 18.
Number of total days = 24
The ratio of rainy days to total days written as a percent will be:
= Number of rainy days / Total days × 100
= 18/24 × 100
= 3/4 × 100
= 75%
Therefore, the ratio is 3:4 which is 75%.
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Please Help me!!!!! Will give brainliest 4 an EXPLAINATION!
The angles after solving the equations will be equal to 50°, and both angles will be the same as the corresponding angles. Hence, option B is correct.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the given information in the question,
The equations for the angles are:
7x + 1 = 6x + 8
7x - 6x = 8 - 1
x = 7
So, the angles will be,
7x + 1 = 7(7) + 1 = 50°
6x + 8 = 6(7) + 8 = 50°
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In a class activity, all the 15 students wear hats. 7 students wear red hats, 6 students wear green hats and 2 students wear white hats. (I) two of the 15 students are picked at random. Show that the probability that these two students wear hats of the the same colour is 37/105. (I) three of the 15 students are picked at random. Find the probability that at least 2 of these students wear red hats.
The probabilities, using the hypergeometric distribution, are given as follows:
i) Two wear the same color: 37/105: 0.35238 = 37/105.
ii) At least 2 wear red: 0.4461.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are presented as follows:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The probability of two red is given as follows:
[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]
The probability of two green is given as follows:
[tex]P(X = 2) = h(2,15,2,6) = \frac{C_{6,2}C_{9,0}}{C_{15,2}} = 0.14286[/tex]
The probability of two white is given as follows:
[tex]P(X = 2) = h(2,15,2,2) = \frac{C_{2,2}C_{13,0}}{C_{15,2}} = 0.00952[/tex]
Then the probability of two wearing the same color is given as follows:
0.2 + 0.14286 + 0.00952 = 0.35238 = 37/105.
The probability that out of 3 people, at least 2 wear red, is given as follows:
[tex]P(X = 2) = h(2,15,3,7) = \frac{C_{7,2}C_{8,1}}{C_{15,3}} = 0.3692[/tex]
[tex]P(X = 3) = h(3,15,3,7) = \frac{C_{7,3}C_{8,0}}{C_{15,3}} = 0.0769[/tex]
Hence:
0.3692 + 0.0769 = 0.4461.
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Solve. Write answers as an imaginary number
y^2+11=2
The solution of the equation written as an imaginary number is y = 3i or -3i
How to solve an equation and write the answer as an imaginary number?An imaginary number is a number of the form ai, where a is a real number and i is the square root of -1. Imaginary numbers are often denoted with the letter "i".
Given: y² + 11 = 2
y² + 11 = 2
y² = 2 - 11
y² = -9
y = ±√-9
y = ± 3i
y = 3i or -3i
(Note: √9 = 3 and √-9 = 3i)
Thus, the solution is y = 3i or -3i
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In AUVW, m/U = (3x - 10)°, m/V = (6x + 5)°, and m/W = (4x - 10)°. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
U +V +W = 180°
(3x -10)° +(6x +5)° +(4x -10)° = 180°
13x -15 = 180 . . . . . . . divide by °, collect terms
13x = 195 . . . . . . . add 15
x = 15 . . . . . . . divide by 13
The value of x is 15.
You brought popular game on sale for $20 and want to sell it on eBay. You want to mark up the toy 60%. What did you sell it for?
use the data above to test the claim that marble color preference and club membership are related, as follows: (2 pts) carefully state the hypotheses. Hypothesis is
H0: marble color preference and income class are independent
H1: marble color preference and income class are dependent
The Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".
The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample. Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.
We can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypotheses. However, the hypotheses can also be phrased in a general way that applies to any test.
We are given that to test the claim that marble color preference and club membership are related.
Thus, the Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".
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An area code has three digits. How many different area codes are possible
Answer:
1000
Step-by-step explanation:
If any of the digits 0-9 can be used then there are 10^3 possible codes.
10^3 = 1000
Is 5x-8+7y=y-6 linear or nonlinear
Answer:
Step-by-step explanation:
The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.
Lucy wants to buy a small car. She speaks to her bank and they offer her a loan of £5000 over 5 years at a simple interest rate of 5%. How much simple interest will Lucy have to pay back in total?
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
What is simple interest?To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.
A = $6,250.00
I = A - P = $1,250.00
Formula: A = P(1 + rt)
First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.
Fixing our equation
A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
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The gardening club at school is growing vegetables. The club has 300 square feet of planting
beds.Cucumber plants require 6 square feet of growing space, and tomato plants require 4
square feet of growing space. The students want to plant some of each type of plant and have at
least 60 plants.
Select the combination of equations or inequalities that could describe this situation. Let c represent the number of cucumber plants and t represent the number of tomato plants.
Answer:
The answer is :
E - 6c + 4t < 300
Solve the equation 2x + 3y = 5 for x.
Answer:
x = [tex]\frac{5-3y}{2}[/tex]
Step-by-step explanation:
2x + 3y = 5
isolate variable: 2x = 5-3y
divide by 2: x = [tex]\frac{5-3y}{2}[/tex]
The enrollment at MSU is described by the function
f(x) = 250x + 6000, where x is the number of years since 2010.
I. Find the enrollment in 2016.
II. In what year will the enrollment reach
10,000?
1) The enrollment in 2016 will be 7500.
2) In 2026 year the enrollment reach 10,000.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function f(x) represents the number of enrollment.
Defined as;
⇒ F(x) = 250x + 6000
Where x represents year since 2010.
(1) Now for finding the enrollment in 2016;
Put x = 2016 - 2010 = 6 in the function
⇒ F(6) = 250x6 + 6000
= 7500
Thus, The required number of enrollment = 7500
(2) Now we have to find the year in which enrollment reach 10,000;
i.e f(x) = 10,000
=> 250x + 6000 = 10000
=> 250x = 4000
=> x = 16
Thus, The required year = 2010 + 16
= 2026 answer.
1) The enrollment in 2016 will be 7500.
2) In 2026 year the enrollment reach 10,000.
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The length of a rectangular poster is 8 more inches than three times its width. The area of the poster is 256 square inches. Solve for the dimensions (length and width) of the poster
The dimensions are
inches ___ by ____ inches.
When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.
What is area?The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.
Here,
let length be l and width be w.
l=3w+8
l*w=256
(3w+8)*w=256
3w²+8w=256
3w²+32w-24w-256=0
3w(w-8)+32(w-8)=0
(3w+32)(w-8)=0
w=-32/3, 8
w=8 inch
l=3*8+8
l=32 inch
The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.
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Need Awnser asap
Right Awnser gets branliest
Answer:
x1,y16 is the rate of change
Step-by-step explanatI subtracted 13-32 which gives me 16, then I added 16 to 32 to be sure and it gave me 48 so the change on the Y axis is going up by 16 and x axis is going up by 1
Examine the drawing below, which could be a value for x?
The value of 'a' can be 20. The correct option is C, 20.
What is triangle inequality theorem?As per the triangle inequality theorem, the sum of any two sides of the triangle should be greater than the third side.
As per triangle inequality theorem, the sum of the two sides of the triangle should be greater than the third side of the triangle.
As per the triangle inequality theorem, if 'a' is the longest side of the triangle then,
21 + 6 > a
27 > a
If a is not the longest side of the triangle,
21 + a > 6
a > -21 + 6
a > -15
6 + a > 21
a > 21 - 6
a > 15
Therefore, the value of a should be greater than 15 and less than 27. Since the only option under this condition is 20.
Hence, The correct option is C, 20.
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Height (in inches) Mean Minimum Q1 Median Q3 Std Dev 4.21 Maximum 79 68.2 67 , 71 , Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches. Height (in inches) Q3 Mean 68. 2 Std Dev .21 Minimum 62 4 Q1 63 Median 67 Maximum 79 Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches. (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches.
Standard deviation will be √3.3516 .
To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².
After that , we have to calculate the Xbar by using
Xbar = ∑fiXi / N
for which we need the value of fi , Xi and N
N = 100
fiXi = 6478
we have calculated the values from the given data ,
Therefore ,
Xbar = 6478 / 100
= 64.78
Var(X) = αx² - ∑fiXi² / N - (Xbar²)
= 419980 / 100 - (64.78)²
= 4199.80 -4196.4484
=3.3516
Thus,
standard deviation ax = √var(X)
= √3.3516
Therefore , the standard deviation will be √3.3516
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One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.) dy dt = ky 1-y. (b) Solve the differential equation. Assume y(0) = C. y = 1-ce-kt +1 (c) A small town has 1300 inhabitants. At 8 AM, 100 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round the final answer to one decimal place.) hours after the beginning
(a) The differential Equation that is satisfied by y is dy/dt = k × y × (1 - y) ,
(b) Solution of the differential equation assuming y(0) = c is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
In the question ,
Part (a)
let the fraction of people who heard the rumor is = y
So , the fraction who have not heard the rumor is = 1 - y .
the rate of rumor spread is ⇒ dy/dt = k×y(1 - y)
dy/y(1-y) = k.dt ...where k is the constant of proportionality .
So , the differential equation is ..
dy/dt = k × y × (1 - y)
Part (b)
So , 1/y(1-y) = 1/y + 1/(1 - y) ....equation(1)
integrating equation(1) , we get
∫dx/(1 + ax) = ㏑(1 + ax)/a ,....where a is the constant
㏑y + ㏑(1-y)/(-1) = kt + d ,.....where d is the constant
By using , ㏑a - ㏑b = ㏑(a/b) and taking exponential . we get ,
y/(1 - y) = c₁[tex]e^{k\times t}[/tex]
for t = 0 and y(0) = c
solving further , we get
c₁ = c/(1 - c)
So , y = (1-y)c₁[tex]e^{k\times t}[/tex]
y(1 + c₁[tex]e^{k\times t}[/tex]) = c₁[tex]e^{k\times t}[/tex]
y = c₁[tex]e^{k\times t}[/tex]/(1 + c₁[tex]e^{k\times t}[/tex])
taking c₁[tex]e^{k\times t}[/tex] common , and substituting the value of c₁ we get ,
the solution as , y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
Therefore , (a) the differential equation is dy/dt = k × y × (1 - y) and
(b) the solution is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
The given question is incomplete , the complete question is
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.
(a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.)
(b) Solve the differential equation. Assume y(0) = C.
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find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius r.
The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
Now, According to the question:
The given sphere is of radius R.
Let h be the height and r be the radius of the cylinder inscribed in the sphere.
We know that:
Volume of cylinder
V = [tex]\pi R^2h[/tex] .....(1)
In right Triangle OBA
[tex]AB^2 + OB^2 = OA^2[/tex]
[tex]R^2 + \frac{h^2}{4} = r^2[/tex]
So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]
Putting the value of [tex]R^2[/tex] in equation (1), We get
V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]
V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex] ....(2)
dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)
For, Stationary point, dV/dh = 0
[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0
[tex](r^2 - \frac{3h}{4} )[/tex] => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]
Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]
[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex] = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0
Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]
Maximum volume is :
[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]
[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
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Find the Probability of, A King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.
As per the given data,
we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
We know that,
Probability(Event) =Number of Favorable Outcomes/Total number of
Outcomes = x/n.
Total number of Outcomes is 52 (given)
So, we will calculate Number of Favorable Outcomes as follows:
The total no. of King in deck of card is 4
The total no. of queen in deck of card is 4.
The total no. of ace in deck of card is 4.
The total no. of jack in deck of card is 4.
Therefore, the number of favorable outcomes is 4+4+4+4= 16
Now, putting values in the above stated formula of probability, we get:
Probability= 16/52=4/13
Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.
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look at attached photo
The correct answer is A) y = 9000x + 65,000.
Find a linear equation that models the value of the house after x years?The correct answer is A) y = 9000x + 65,000.
This is an equation in slope-intercept form, where "y" is equal to the value of the house after x years, "9000x" is the slope (or rate of change) of the equation, and 65,000 is the y-intercept (or the initial value of the house). The equation can be derived from the given information.The initial value of the house is 65,000, so the y-intercept must be 65,000. To find the slope, we can use the formula "rise/run", or change in y/change in x.The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).
The equation y = 9000x + 65,000
models the value of the house after x years, where y is the value of the house,
9000x is the slope of the equation,
and 65,000 is the y-intercept.
This equation can be used to calculate the value of the house after any given number of years.To learn more about linear equation in slope-intercept form refer to:
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Solve the following equation by first writing the equation in the form a x squared = c: t squared minus 49 = 0 a. t = 49 b. t = plus-or-minus 49 c. t = 7 d. t = plus-or-minus 7 Please select the best answer from the choices provided A B C D
By solving the equation we get ,t = ± 7 using concept of square roots.
How to find the square roots ?
Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.
For example, 2 is the square root of 4, and this is expressed as √4 = 2.
We know that every squared number has two square roots one is positive and another is negative.
In given que,
given condition is t squared minus 49 = 0
Form of equation is ax^ 2 = c.
given condition can also be written as t^2 - 49 = 0
i.e. t^2 = 49
where a = 1
x = t
c = 49
So, the square root are 7 and -7.
So, equation become t = ± 7.
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Ravi sells real estate. Based on previous data, he knows that 5% of home tours result in a sale. Assume that the results of these tours are independent from each other. Which of the following choices are binomial random variables? Choose all answers that apply: A. Take a random sample of 30 tours and let L = the number of tours that result in a sale. B. Take a random sample of 3 tours and let K = the number of tours that result in a sale. C. Take a random sample of 3 tours and let M = the amount of sales (in dollars) generated by the tours.
The options that represent binomial random variable are;
A. Take a random sample of 30 tours and let L = the number of tours that result in a sale.
B. Take a random sample of 3 tours and let K = the number of tours that result in a sale.
How to Identify Binomial Random Variables?There are 4 primary conditions for a random variable to be classified as binomial random variable and they are;
1. The number of observations n is fixed.
2. Each observation is independent.
3. Each observation represents one of two outcomes ("success" or "failure").
4. The probability of "success" p is the same for each outcome.
No, in this case, since 5% of home tours result in a sale, it therefore tells us that number of home tours is the independent variable while the amount of sales generated is the dependent variable.
From the above, we can access the given options and say that the last option is not a binomial random variable because the variable M is dependent and so does not satisfy one of the four conditions.
However, options A and B satisfy the 4 conditions and we say they are binomial random variables.
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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
70
Step-by-step explanation:
