Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
Scientists studied two animal populations. Function f(x) = 830(0.8)^x models a bear population in a given region x years after the study began. The table models the cougar population in the same region.
Year after study began: 0, 1, 2, 6, 15
Cougar population: 790, 735, 683, 511, 266
In the year the study began, how many more bears than cougars were in the given region.
Answer:
There were 40 more bears than cougars when the study started.Step-by-step explanation:
Givens:
[tex]f(x)=830(0.8)^{x}[/tex]; where [tex]x[/tex] refers to years after the study began, about bear population.Table given is for cougar population.So, the problem is asking how many more bears than cougars were in the given region. From the table, we know that there where 790 cougar when the study started.
Now, we have to calculate the initial condition of the function, because it's modelling bear population. Initial condition means when the study started, which is when [tex]x=0[/tex].
So, we have:
[tex]f(0)=830(0.8)^{0}=830(1)=830[/tex]
So, there were 830 bears when the study started.
If we compare, we find that there were 40 more bears than cougars when the study started, because 830-790 = 40.
The next three terms of the sequence 20, 40, 80, 160,… are 320, 640, and 1280.
In addition to the trigonometric ratios, what other methods can be used to solve a right triangle? Give situations for when you might want to use them
Is a triangle with sides of length 7 ft, 24 ft, and 25 ft a right triangle? Explain.
Mr. Thompson borrowed $3,000. He repaid the loan with an interest charge of $500 in 36 equal monthly payments. What approximate annual percentage rate did he pay? Find the answer to the nearest tenth of a percent.
On her first stroke, Maria hit a golf ball 140 yards, 2 feet, 9 inch. On her second she hit it 170 yards, 1 foot, 6 inches. How far did the ball go all together
2 feet 9 inches + 1 foot 6 inches = 3 feet 15 inches
15 inches = 1 foot 3 inches
3 feet + 1 foot = 4 feet
2 ft 9 inches + 1 ft 6 inches = 4 ft 3 inches
1 yard = 3 feet
4feet 3 inches = 1 yard, 1 foot 3 inches
140+170 = 310 yards
310 + 1 = 311
so it traveled 311 yards 1 foot and 3 inches
Answer:
311 yards and 1 feet and 3 inches
Step-by-step explanation:
What's the mean of 0,1,3,2
The value of 4 in 943,268
The value of the digit 4 in the number 943,268 is 40,000 because it is in the ten thousand place.
The value of the digit 4 in the number 943,268 depends on its place value in the number.
In 943,268:
- The digit 4 is in the ten-thousands place.
So, the value of the digit 4 in 943,268 is:
4 × 10,000 = 40,000
Therefore, the value of the digit 4 in 943,268 is 40,000.
CAN SOMEBODY PLEASE HELP ME? I will mark you as a BRAINLIST!!!
Sally found that a solution of x = 2 was extraneous for her function. What would be a possible denominator in Sally's function?
4x + 8
2x + 12
x^2 − 4
x^2 − 16
Answer:
[tex]x^2-4[/tex]
Step-by-step explanation:
Sally found that a solution of x = 2 was extraneous for her function.
Extraneous solution is a solution that makes the denominator 0
Possible denominator are given . LEts plug in 2 for x and check which option gives us 0
[tex]4x+8=4(2)+8= 16[/tex]
[tex]2x+12=2(2)+12=4+12= 16[/tex]
[tex]x^2-4= (2)^2-4= 4-4=0[/tex]
[tex]x^2-16= (2)^2-16= 4-16= 12[/tex]
[tex]x^2-4[/tex] gives us 0 when we plug in 2 for x.
So x=2 was extraneous solution for [tex]x^2-4[/tex]
What do the vertical lines mean?
Final answer:
In art, vertical lines suggest stability and structure, contrasting with calming horizontal lines and dynamic diagonal lines. These lines help define shapes, indicate motion, and guide the viewer through the composition.
Explanation:
The term vertical lines in the context of art and design, refers to lines that run up and down the canvas or design space, perpendicular to the horizon. These lines can convey a variety of meanings and emotions in visual compositions. According to a description by Oliver Harrison, vertical lines are seen as visually stable and can be associated with structures like tree trunks or classical columns, suggesting strength and stability.
What is the solution of \sqrt(2x+4)=16?
x = 6
x = 72
x = 126
no solution
The solution of the expression will be;
⇒ x = 126
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 expression is,
⇒ √(2x + 4) = 16
Now,
Solve the expression as;
The expression is,
⇒ √(2x + 4) = 16
Square both side, we get;
⇒ 2x + 4 = 16²
⇒ 2x + 4 = 256
⇒ 2x = 256 - 4
⇒ 2x = 252
⇒ x = 126
Thus, The solution of the expression will be;
⇒ x = 126
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Let f(x) = x + 8 and g(x) = x2 − 6x − 7. find f(g(2)). −7 −3 10 33 open study
The center of a circle is A (-3,3), and B (1,6) is on the circle. Find the area of the circle in terms of pi.
the quadratic equation whose roots are the am and hm between the roots of the equation 2x2 - 3x+5=0
The first thing to do is to find the roots.
The sum of the roots, x1 + x2 = -b / a
x1 + x2 = 3 / 2
The product of the roots, x1 * x2 = c / a
x1 * x2 = 5 / 2
The AM means arithmetic mean and is calculated using the formula:
AM = (x1 + x2) / 2
AM = (3 / 2) / 2
AM = 3 / 4 = y1
The HM means harmonic mean and is calculated using the formula:
2 / HM = 1 / x1 + 1 / x2
or
2 / HM = (x1 + x2) / x1 * x2
Rewriting in terms of HM alone on the left side:
HM = 2 x1*x2 / (x1 + x2)
HM = 2 (5 / 2) / (3 / 2)
HM = 10 / 3 = y2
Creating an equation from y1 and y2:
(y – ¾) (y – 10/3) = 0
y^2 – 10/3 y – ¾ y + 30/12 = 0
y^2 - 49/12 y + 30/12 = 0 (ANSWER)
or
y^2 – 4.083y + 2.5 = 0
In basketball, when monica takes her first free throw, she has a 50% chance of scoring. if she takes an additional throw, she has a 75% chance of scoring on this throw if she scored on the immediately previous throw, but only a 25% chance of scoring on this throw if she didn't score on the immediately previous throw. suppose she has to take a set of three free throws in a row, and she doesn't score on the first one. what is the probability that she scores at least once on one of the subsequent two throws?
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a.
What is the area of the pool cover?
b.
What is the length of the rope?
so use a basic formula here:
area of a circle = πr²
and the circumference of a circle = πd
a)
therefore the area of the pool cover is π multiplied by the radius² (which is the diameter of the pool cover plus the extra 12 inches divided by two, so the radius is 21/2 or 10.5) is 346.36(to two decimal places.)
b)
Using the same diameter, we can work out the length of the rope by multiplying the diameter (10.5) by π, which is 32.99 (to two decimal places).
The domain of the following relation R {(6, −2), (1, 2), (−3, −4), (−3, 2)} is
{−3, −3, 1, 6}
{−4, −2, 2, 2}
{−4, −2, 2}
{−3, 1, 6}
Answer:
Option 4th is correct
the domain of the following relation R is:
[tex]\{-3, 1, 6\}[/tex]
Step-by-step explanation:
Domain is the set of all values of x-coordinates where function is defined.
Given the Relation:
[tex]R = \{(6, -2), (1, 2), (-3, -4), (-3, 2)\}[/tex]
The ordered pairs are in the form of (x, y)
Domain = Set of all values of x.
In the given relation:
x-values = { 6, 1, -3}
⇒[tex]\text{Domain} = \{-3, 1, 6\}[/tex]
therefore, the domain of the following relation R is:
[tex]\{-3, 1, 6\}[/tex]
if a sprinkler waters 1/18 of a lawn in 1/3 hour, how much time will it take to water the entire lawn
3/3 would be 1 hour
3/18 of the lawn would be done in 1 hour
18/3=6
6*1 = 6
it would take 6 hours to do the whole lawn
It will take 360 minutes to water the entire lawn
What is cross multiplication?Cross multiply can be defined as the process of multiplying the numerator of the first fraction on one side of the equals to symbol, with the denominator of the second fraction on the other side of the equals to symbol.
1/18 lawn is watered in 1/3 of hour = 20 min
Whole lawn will be watered in 20 × 18 = 360 min
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Find the probability that 3 randomly selected people all have the same birthday. ignore leap years. round to eight decimal places.\
The probability that 3 randomly selected people all have the same birthday is 1 in 48,627,125.
Explanation:In order to find the probability that 3 randomly selected people all have the same birthday, we need to consider the total number of possible outcomes and the number of favorable outcomes. There are 365 days in a year (excluding leap years) and each person's birthday is independent of the others. Therefore, the probability of each person having the same birthday as the previous person is 1/365. To calculate the probability that all 3 people have the same birthday, we multiply the probabilities together:
P(3 people have the same birthday) = (1/365) * (1/365) * (1/365) = 1/48,627,125
Thus, the probability that 3 randomly selected people all have the same birthday is approximately 0.0000000206, rounded to eight decimal places.
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What is 10 1/2 divided 2 1/4
attached below. 20pts will thanks rate and give best answer
What's the answer help me out please ?
Factor completely then place the answer in the proper location on the grid. Write the answer in descending powers if x
6x^4+15x^3y^2+3x^2y^3
Since the population size is always larger than the sample size, then the sample statistic:
Which of the binomials below is a factor of this trinomial?
x² + 2x - 48
A. x + 8
B. x - 3
C. x - 8
D. x + 3
Given: WA = NO, WS = NT, W = N.
A)SSS
B) SAS
C) ASA
D)AAS
Answer with explanation:
It is given that ,
In two triangles, ΔWAS and ΔNOT
1. WA = NO
2. W S = NT
3. ∠W=∠N
≡ΔWAS ≅ ΔNOT
The Angle is included between two sides .
So,these two triangles are congruent by ,SAS.
Option B:→ S AS
What is the cardinality of the set {ø, {ø}, {ø, {ø}}}?
B is between a and c ac=15.8 and ab=9.9. find bc
Answer:
The value of bc is 5.9 units.
Step-by-step explanation:
Given information: b is between a and c, ac=15.8 and ab=9.9.
We need to find the measure of bc.
Since b is between a and c, therefore the segment ac is the sum of two segments ab and bc.
[tex]ac=ab+bc[/tex]
Substitute ac=15.8 and ab=9.9 in the above equation.
[tex]15.8=9.9+bc[/tex]
Subtract 9.9 from both sides.
[tex]15.8-9.9=9.9+bc-9.9[/tex]
[tex]5.9=bc[/tex]
Therefore the value of bc is 5.9 units.
If assumption of Collinearity is not for granted, then the length of Segment BC is defined by [tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex], for [tex]\beta \in [0^{\circ}, 180^{\circ}][/tex].
Reminder - Given that statement seems to be incomplete, we assume that we are talking about Line Segments and that Segments AC and BC may be Collinear.
By Geometry and, being more specific, by definition of Triangles, if we assume that all segment are not necessarily Collinear, then a Triangle may exist and can be modelled by the Law of Cosine:
[tex]BC = \sqrt{AC^{2}+AB^{2}-2\cdot AC\cdot AB\cdot \cos \beta}[/tex] (2)
Where [tex]\beta[/tex] is the angle at point B, in sexagesimal degrees and is between 0° and 180°.
If we know that [tex]AC = 15.8[/tex] and [tex]AB = 9.9[/tex], then the expression for the length of BC is:
[tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex]
If assumption of Collinearity is not for granted, then the length of Segment BC is defined by [tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex], for [tex]\beta \in [0^{\circ}, 180^{\circ}][/tex].
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