Using a t-distribution calculator, it is found that the confidence level is of 95%.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In this problem, we have that t = 2.776, df = 5 - 1 = 4 for a two-tailed interval, hence looking at the t-table it is found that the confidence level is of 95%.
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The area of a rectangle is (81x^2 − 4y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.
Answer 81x^2 - 4y^2 Note this is the difference of 2 perfect squares
a^2 - b^2 = (a + b)(a - b)
so here we have a = 9x and b = 2y
and our factors are
(9x + 2y)(9x - 2y)
the dimensions are 9x + 2y and 9x - 2y
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Show Work
81x^2 - 4y^2 Note this is the difference of 2 perfect squares
a^2 - b^2 = (a + b)(a - b)
so here we have a = 9x and b = 2y
and our factors are
(9x + 2y)(9x - 2y)
The dimensions of the rectangle with an area of (81x² - 4y²) square units are (9x + 2y) and (9x - 2y) units, as the area expression is a difference of squares that has been factored accordingly.
The area of a rectangle is given by the expression (81x² − 4y²) square units. To determine the dimensions of the rectangle, we need to factor this expression completely.
This expression is a difference of squares and can be factored as follows:Use the difference of squares formula, which is a²- b² = (a - b)(a + b).Apply the formula: (81x² − 4y²) = (9x)² - (2y)² = (9x + 2y)(9x - 2y).Therefore, the dimensions of the rectangle can be 9x + 2y and 9x - 2y units.
Who drove the fastest 363 miles in 6 hours, 435 miles in 7 hours, 500 miles in 8 hours, or 215 miles in 5 hours.
Answer:
The 3rd person who drove 500 miles in 8 hours drove the fastest.
Step-by-step explanation:
1st person : 60.5 mph
2nd person : 62.14 mph
3rd person : 62.5 mph
4th person : 43 mph
you simply divide the total miles driven by the amount of time and then you get the miles per hour.
Hope this helps!
if you were to build a house, one with two-dimensional figures and the other with three-dimensional figures, which one will have a better chance of withstanding a hurricane and why
Answer:
both
Step-by-step explanation:
Depending on how u look at it, one is comprised of 2d figures and the other is of 3d, but the 2d shapes combine to make the faces of any 3d shape, so its basically the same.
Samantha is making special edition hazelnut and almond chocolate boxes to give to her friends. It costs Samantha $15 to make one hazelnut chocolate box and $30 to make one almond chocolate box. It takes her 20 minutes to make either box of chocolates. She wants to spend no more than $210 and 200 minutes making the chocolate boxes to give to her friends.
Answer:
6 hazelnut
4 almond
Step-by-step explanation:
Answer:
Samantha should make six hazelnut chocolate boxes and four almond chocolate boxes in order to maximize the number of chocolates she gives to her friends.
Step-by-step explanation: This is the right answer
Eric practiced the piano and guitar for a total of 8 hours this week he practiced the piano for 1/4 of that time how many hours did he practice piano this week
Answer: 2
Step-by-step explanation:
If 8 hours are spent the week, and there is only 1/4 used to play piano then you have to know how much 1/4 is of 8.
To get 1/4 of 8 you need to multiply 8 by 1/4.
The answer is 2.
Use the drop-down menus to complete each equation so the statement about its solution is true.
The drop down menus consist of numbers 0-9
A)
No solution--
No solution is obtained when there is a condition such that the equation gives a absurd condition.
Hence we write our equation as:
2x+9+3x+x=6x+1
Hence, we have:
6x+9=6x+1
i.e. we have: 9=1
which is a contradiction.
Hence, we get no solution.
B)
One solution--
One solution or unique solution is obtained when we obtain a unique value for our given variable.
i.e. if we write our equation as:
2x+9+3x+x=5x+1
i.e. 6x+9=5x+1
i.e. x= -8
Hence, we get a unique value for x.
C)
Infinite many solution--
The infinite many solution is where we get a condition such that we could not get a unique value for x but the equation is true.
Hence, we have:
2x+9+3x+x=6x+9
i.e. 6x+9=6x+9
as left hand side of equation is equal to right hand side of the equation for every ''x'' Hence, we get infinite many solution.
Answer:
1. 6x+1
2. 5x+1
3. 6x+9
Find the solution set.
x^2 – 5x = 0
Answer:
x=0 and x=5
Step-by-step explanation:
x^2 – 5x = 0
Factor out an x
x(x-5) = 0
Using the zero product property
x=0 and x-5 =0
Solving
x=0 x-5+5 = 0+5
x=0 and x=5
A country’s population in 1992 was 50 million. In 2992 it was 53 million. Estimate the population in 2010 using the exponential growth formula. Round your answer to the nearest formula.
Answer:
P ≈ 56 million
Step-by-step explanation:
Your question is attached in the picture below.
The exponential formula for these cases is
P = Po*e^(kt)
Where,
Po = initial population
k = is a constant used to define the growth rate
t = time transcurred since the time of the initial population
For this exercise,
Po = 50 million
Year 2002
2002 - 1992 = 10
53 million = 50 million *e^(k*10)
(53/50) = e^(k*10)
k*10 = ln(53/50)
k = 0.005827
The equation results
P = 50 million *e^(0.005827*t)
Year 2010
2010-1992 = 18
P = 50 million *e^(0.005827*18)
P = 50 million *(1.11058)
P = 55.53 million
P ≈ 56 million
Answer:
the answer is 56 just got it right
if you need population in 2010
Step-by-step explanation:
What is the lateral area of the cylinder?
Answer: second option.
Step-by-step explanation:
The formula used for calculate the lateral area of a cylinder is this one:
[tex]LA=2\pi rh[/tex]
Where "r" is the radius and "h" is the height
The formula for calculate the area of a circle (which is the base of a cylinder) is:
[tex]A=\pi r^2[/tex]
Knowing the area of the base, you can solve for the radius:
[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]
Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:
[tex]LA=2\pi (6units)(2units)[/tex]
[tex]LA=24\pi\ units^2[/tex]
Select Independent or Not independent for each situation.
A jar contains twenty coins. Two coins are picked randomly without replacement.
A coin is flipped three times.
A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.
A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.
Answer:
1. Not Independent
2. Independent
3. Not Independent
4. Independent
Step-by-step explanation:
Independent: An event is independent if the outcome of one event doesn't effect the outcome of the other event.
Not independent : An event is Not independent if the outcome of one event effect the outcome of other event.
1. A jar contains twenty coins. Two coins are picked randomly without replacement.
Not Independent because if coins are not replaced the outcome of next event will be effected.
2. A coin is flipped three times.
Independent because when a coin is flipped once its outcome doesn't effect the outcome of the coin flipped again
3. A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.
Not Independent because if balls are not replaced the outcome of next event will be effected.
4. A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.
Independent because when the spinner is spuned once its outcome doesn't effect the outcome of the spinner spun again
The correctcorrect probabilityprobability conditiony for each of the given situation as regards independent or not are;
A) Not Independent
B) Dependent
C) Not Independent
D) Dependent
Independent EventsAn independent event is one that doesn't depend on the probability of another one happening while a dependent event is one that depends on the probability of another one happening.
A) A jar contains twenty coins. Two coins are picked randomly without replacement; This is not independent because when we do not replace a selected coin, it affects the outcome of the next choice.
B) A coin is flipped three times; This is dependent because a flip doesn't depend on another flip.
C) A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement; This is not independent because when we do not replace a selected ball, it affects the outcome of the next choice.
D) A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice; This is independent because spinning doesn't affect the outcome of the next spin.
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Answer: try A I took the same test earlier
Step-by-step explanation:
Two number cubes, each with the numbers 1 through 6, are rolled. What is the probability that the sum of the rolled numbers is 2? PLEASE HELP ANYONE IN LIKE @20 min
The probability of rolling a sum of 2 with two dice is 1/36. This is calculated by determining the independent probabilities of rolling 1 on each die and multiplying these probabilities together.
Explanation:
The subject of this question is probability in mathematics, specifically involving the numbers on two rolled dice. The only way two dice (number cubes) can add up to 2 is if both rolled dice shows 1. Each die has 6 sides, so the probability for each dies rolling 1 is 1/6.
The probability of two independent events both occurring is founding by multiplying the probability of each event. As the two dice is rolled independently, the probability of both are showing 1 (and hence their sum is being 2) is (1/6) x (1/6), which simplifies to 1/36. Therefore, the probability that the sum of the numbers rolled on two dice is 2 1/36.
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Use the Geometric Mean Theorem to find the value of J if
G=3 and F=12
Answer:
6
Step-by-step explanation:
The Geometric Mean Theorem states that the altitude (in this case, j) is equal to radical(g*f).
Therefore, j=√(g*f), j=√(3*12), j=6
Answer:
[tex]\boxed{6}[/tex]
Step-by-step explanation:
The Geometric Mean Theorem states that the altitude to the hypotenuse of a right triangle is the geometric mean of the two segments it creates.
Thus, in your triangle,
j = √(fg)
If f = 12 and g = 3,
j = √(12 × 3) = √ 36 = 6
[tex]\boxed{j = 6}[/tex]
consider the sequence -3,7,17,27...
which function (with domain all integers n>=1) could be used to define and continue the sequence.
A f(n)= 10n-13
B f(n)=-3n+10
C f(n)=10n-3
D f(n)=-3(n-1)+10
Answer:
The function is f(n) = 10n - 13 ⇒ answer A
Step-by-step explanation:
* Lets revise the arithmetic sequence
- There is a constant difference between each two consecutive
numbers
- Ex:
# 2 , 5 , 8 , 11 , ……………………….
# 5 , 10 , 15 , 20 , …………………………
# 12 , 10 , 8 , 6 , ……………………………
* General term (nth term) of an Arithmetic sequence:
# U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
# Un = a + (n – 1)d, where a is the first term , d is the difference
between each two consecutive terms, n is the position of the
term in the sequence
* Now lets solve the problem
- The sequence is -3 , 7 , 17 , 27 , .........
∵ 7 - (-3) = 7 + 3 = 10
∵ 17 - 7 = 10
∵ 27 - 17 = 10
∴ The sequence is arithmetic with constant difference 10
∴ f(n) = a + (n - 1)d
∵ a = -3
∵ d = 10
∴ f(n) = -3 + (n - 1)(10) ⇒ lets simplify it
∴ f(n) = -3 + n(10) + (-1)(10) = -3 + 10n - 10 ⇒ add like terms
∴ f(n) = 10n - 13
* The function is f(n) = 10n - 13
Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.
To determine which function could be used to define and continue the given sequence (-3, 7, 17, 27...), we need to analyze the pattern of differences between consecutive terms and see which option best represents this pattern. The sequence increases by 10 each time, as can be seen from the differences (7 - (-3) = 10, 17 - 7 = 10, 27 - 17 = 10).
Looking at the functions provided:
Option A: f(n) = 10n - 13If we put n=1, f(1) = 10*1 - 13 = -3; If we put n=2, f(2) = 10*2 - 13 = 7; and so on. The pattern matches.Option B: f(n) = -3n + 10 If we put n=1, f(1) = -3*1 + 10 = 7, which does not match the first term of our sequence.Option C: f(n) = 10n - 3 If we put n=1, f(1) = 10*1 - 3 = 7, which does not match the first term of our sequence.Option D: f(n) = -3(n - 1) + 10 If we put n=1, f(1) = -3*(1 - 1) + 10 = 10, which does not match the first term of our sequence.Therefore, Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.
I am in urgent need of some help!! So uh....Please help me A quadrilateral has angles that measure 72 degrees, 98 degrees and 65 degrees what is the measure of the fourth angle??
So I could be completely wrong, or I could be completely right, but quadrilaterals interior angles equal 360 degrees.
So, if you ad up 98, 72, and 65 you end up with 235 degrees.
In order to find the fourth angle, you would just subtract 235 from 360 and get 125 degrees.
BUT, maybe see if someone else answers too, because I am not 100% sure.
Find the area please
=================================================
Explanation:
The base is 10 and the height is 6. So b = 10 and h = 6.
We don't use the 7 at all.
Let's use those b and h values into the formula below
A = b*h/2
A = 10*6/2
A = 60/2
A = 30
Answer:
30 square units
Step-by-step explanation:
Always remember that the equation for the area of a triangle is 1/2 times base times height. With an obtuse triangle, you must always ignore the slant. So, half of the base, which is 10, is equal to 5 and 5 times 6 is 30. Also, remember you can multiply in whichever order and the answer will always be the same because of the commutative property.
According to the general equation for conditional probability, if (image attached)
A. [tex]\frac{40}{49}[/tex]
B. [tex]\frac{24}{49}[/tex]
C. [tex]\frac{32}{49}[/tex]
D. [tex]\frac{16}{49}[/tex]
Answer: Option A
[tex]P(A|B) = \frac{40}{49}[/tex]
Step-by-step explanation:
In a probabilistic experiment, when two events A and B are dependent on each other, then the probability of occurrence A since B occurs is:
[tex]P(A|B) = \frac{P(A\ and\ B)}{P(B)}[/tex]
Then if [tex]P(A\ and\ B) = \frac{5}{7}[/tex] and [tex]P(B) = \frac{7}{8}[/tex] then:
[tex]P(A|B) = \frac{\frac{5}{7}}{\frac{7}{8}}\\\\P(A|B) = \frac{40}{49}[/tex]
Answer:
Correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].
Step-by-step explanation:
Given that [tex]P(A\cap B)=\frac{5}{7}[/tex], [tex]P(B)=\frac{7}{8}[/tex].
Now using those values , we need to find the value of [tex]P(A|B)[/tex].
So apply the formula of conditional probability:
[tex]P(A\cap B)=P(B) \times P(A|B)[/tex]
Plug the given values into above formula, we get:
[tex]\frac{5}{7}=\frac{7}{8} \times P(A|B)[/tex]
[tex]\frac{7}{8} \times P(A|B)=\frac{5}{7}[/tex]
[tex]P(A|B)=\frac{\frac{5}{7}}{\frac{7}{8}}[/tex]
[tex]P(A|B)=\frac{5}{7}\cdot\frac{8}{7}[/tex]
[tex]P(A|B)=\frac{40}{49}[/tex]
Hence correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].
How are possibilities observed in a game of poker?
Answer:
the number if different possible poker hands is found by counting the number of ways that 5 cards can be selected from 52 cards.
Step-by-step explanation:
this is a valid answer for e2020
Final answer:
In poker, the number of microstates when dealing with five cards from separate decks is 52^5, and the probability of getting 5 queens of hearts is (1/52)^5. The probability of drawing any specific hand is also 1 in 380,204,032. Poker hand values are inversely proportional to their entropy, with rarer hands having greater value.
Explanation:
Calculations Involved in Poker Probabilities
The game of poker involves a combination of skill and luck, with probabilities playing a significant role in the strategy. To answer the student's questions regarding probabilities in poker, we need to delve into some detailed calculations.
Microstates in Poker: A microstate refers to a specific arrangement of cards. When dealing five random cards from five separate decks, we consider each deck to have 52 unique cards. The number of microstates would be 52^5 (or 380,204,032) because for each card drawn there are 52 possibilities, and each draw is independent from the others.Probability of getting 5 queens of hearts: Given that each deck has one queen of hearts, the probability of drawing the queen of hearts from each deck in one try is (1/52)^5, which is 1 in 380,204,032.Probability of a specific hand: Since there are 52 possible cards for each of the five draws, the probability of getting any specific hand of five cards, regardless of suit or rank, is also 1 in 380,204,032.In analyzing poker hands and their respective values, we find that the value of a hand is typically inversely proportional to its entropy, meaning a less likely hand equates to a higher value.
Pascal's Wager as applied to gambling is not directly related to poker probabilities, but it is an interesting philosophical approach to decision-making under uncertainty. Rather than calculating monetary risk, it assesses the existential gamble of believing in a deity.
Understanding probabilities like these allows gamblers, politicians, teachers, doctors, and individuals in many other fields to make more informed decisions about probable outcomes.
New Question, I'll offer 40 points again. Please help me if you can. Thank you!!! Which statement best describes the association between variable X and variable Y?
A) moderate positive association
B) weak positive association
C) weak negative association
D) moderate negative association
Answer:
C) weak negative association
Step-by-step explanation:
As X increases, Y generally decreases. So this is a negative association. Because the points are widely scattered, it is also a weak association. So the answer is C.
the answer is c because the graph is going down
Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), xx seconds after Antoine threw it, is modeled by: h(x)=-2x^2+4x+16h(x)=−2x 2 +4x+16 What is the height of the ball at the time it is thrown?
Answer:
[tex]\boxed{\text{16 ft}}[/tex]
Step-by-step explanation:
h(x) = -2x² + 4x + 16
At the time the ball is thrown,
x = 0
h(0) = -2 × 0² + 4 × 0 + 16 = [tex]\boxed{ \textbf{16 ft}}[/tex]
Answer:
The height of the ball at the time it is thrown is 16 meters.
Step-by-step explanation:
To find the height of the ball at the time it is thrown, we have that we set the time accordingly. So the height of the ball at the time it is thrown is given by h(0) since the ball was thrown at second 0.
Now that we know the time, which is our x, we set all of our x's to 0.
[tex]h(0)=-2(0)^{2} +4(0)+16[/tex]
Next we solve,
[tex]=0+0+16[/tex]
[tex]=16[/tex]
In conclusion, the height of the ball at the time it is thrown is 16 meters.
Solved and got it right on Khan Academy!
Find an equation of a line that comes close to the points listed in below. Then use a graphing calculator to check that your line comes close to the points.
x (2,4,5,6,8)
y (12,10,6,6,1)
A.
y = 2 x + 2
B.
y = negative 2 x + 17
C.
y = negative 2 x + 18
D.
y = negative 1.3 x + 15
Answer:
Option B: y = -2x + 17.
Step-by-step explanation:
Lets calculate values for option B:
x = 2 , y = -4+17 = 13 ( B gives the value 12)
x = 4, y = -8+17 = 9 (10)
x = 5, y = -10+17 = 7 (6)
x = 6, y = -12+17 = 5 (6)
x = 8, y = -16+17 =- 1 (1)
Sum of the differences = 1 + 1 + 1 + 1 = 4.
These values are close to the ones given in the question.
Option A y = 6, 10, 12, 14, 18 - some of the values of y are a lot different than the given values.
Option C:
Working them out we get y = 14, 10, 8, 6, 2. which are not quite as good as Option B values The total difference is 5 compared with 4 for option B.
Option D.
y = 12.4, 9.8, 8.5, 7.2, 4.6 where some of the differences are large.
Use a calculator to solve for theta in the given interval
Answer:
d. [tex]1.82\: or\:4.46[/tex]
Step-by-step explanation:
The given trigonometric equation is;
[tex]\sec \theta=-4.0545[/tex]
Recall that;
[tex]\cos \theta=\frac{1}{\sec \theta}[/tex]
[tex]\implies \cos \theta=\frac{1}{-4.0545}[/tex]
[tex]\implies \cos \theta=-0.2466[/tex]
The cosine function is negative in the second and third quadrant.
[tex]\theta=\pi-\cos^{-1}(0.2466)\: or\:\pi+\cos^{-1}(0.2466)[/tex]
[tex]\theta=1.82\: or\:4.46[/tex]
A middle school has 490 students. Mae surveys a random sample of 60 students and finds that 24 of them have pet dogs. How many students are likely to have pet dogs?
Answer:
196
Step-by-step explanation:
Find the domain and range of the function. f(x)=|2x|-sin x
Answer:
Domain = (-∞,∞)
Range: [0,∞)
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached image below, to find more information about the graph
The equation is:
f(x)=|2x|-sin(x)
From the graph we can see that
- the domain is equal to all real numbers.
- The range goes from [0,∞)
The correct answer is option d, but bear in mind that the range includes zero as well, so it would be Range: [0,∞)
Answer:
Answer is D!!!
Step-by-step explanation:
HELP ASAP PLZ
the function f(x) is the height of a model rocket x seconds after launch. The rocket reaches its maximum height in 2 seconds and hits the ground at 4 seconds. What is the practical domain for the function f(x)?
Final answer:
The practical domain of the function f(x), representing the height of a model rocket after launch, is [0,4], including the launch at time x=0, reaching the maximum height at x=2 seconds, and landing at x=4 seconds.
Explanation:
The practical domain for the function f(x), which represents the height of a model rocket x seconds after launch, refers to the interval of time during which the rocket is in flight. Since the rocket is launched at time x=0, reaches its maximum height at x=2 seconds, and hits the ground at x=4 seconds, the practical domain of f(x) is [0,4].
This domain includes all times from the launch to when the rocket lands, as the function's values will only be meaningful or defined within this interval.
Which ordered pair is a solution of the equation y = 3x?
A. (-8, -18)
B. (-8, -3)
C. (-2, -9)
D. (-10, -30)
I believe it’s b or c... Hope this helps!
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Suppose the dial on the spinner is spun 2 times in a row.
X is the number of times the dial lands on region A.
Which table represents the probability distribution for the variable X?
Answer:
2nd table
Step-by-step explanation:
Because it’s split into 3 equal sections so each region is one third
Answer: d) 4/9, 4/9, 1/9
Step-by-step explanation:
Let's look at all of the possible combinations of 1st spin & 2nd spin:
AA BA CA
AB BB CB
AC BC CC
P (X=0): how many times is A not in the combination? 4 out of 9
P (X=1): how many times is A in the combination once? 4 out of 9
P (X=2): how many times is A in the combination twice? 1 out of 9
The measurement from the base of a tree to the tip of its shadow is 100ft.
Answer: it’s 200ft
Step-by-step explanation:
PLS HELP 15 POINTS
Find the missing part.
L=8 W=4 H=2
Find the diagonal (d) of the rectangular solid.
Answer:
2√21
Step-by-step explanation:
Diagonal =√(L²+W²+H²)
Diagonal =√(8²+4²+2²)=√(64+16+4)=√84=2√21
For 180° < 0 < 360°, which of the primary trigonometric functions may have positive values?
For angles between 180° and 360°, only cosine (cos) and cosecant (csc) may yield a positive value. This is because these angles fall in the third and fourth quadrants of the unit circle where only certain functions yield positive results.
Explanation:In the trigonometric functions, the sign of the function's result can vary depending on the size of the angle. For angles between 180° and 360°, only cosine (cos) and cosecant (csc), which is the reciprocal of sine, may have positive values.
In mathematics circle, these angles are in the third and fourth quadrants. In the third quadrant (180° ≤ θ < 270°), only the function tangent (tan) and its reciprocal cotangent (cot) can be positive. While in the fourth quadrant (270° ≤ θ < 360°), the functions cosine (cos) and its reciprocal secant (sec) can be positive.
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