Answer:
(x +1)(x +24)
Step-by-step explanation:
Factors of 24 that have a sum of 25 are 1 and 24. These are the constants you need in the binomial factors:
x^2 +25x +24 = (x +1)(x +24)
help me find the function pls
Answer:
see below
Step-by-step explanation:
The tangent function has been shifted upward by 2 units, but there has been no horizontal scaling. Any horizontal offset must be equal to some number of whole periods.
Choices A and B show tan( )+2, the correct vertical offset. However, choice A has a horizontal scale factor of 2. The correct choice is B, which has no horizontal scaling (the coefficient of x is 1) and a horizontal offset of π, one full period.
_____
Comment on horizontal scaling
Horizontal scaling is different from vertical scaling in that using k·x in place of x compresses the graph horizontally by a factor of k. On the other hand, using k·f(x) in place of f(x) expands the graph vertically by a factor of k.
Find the 91st term of the arithmetic sequence 4,6,8
Answer:
184
Step-by-step explanation:
Find the common difference first d = 6 - 4 = 2
first term a_1 = 4
a_n = (n -1)*d + a_1
a_91 = (91 - 1) * 2 + 4
a_91 is the 91st term:
a_91 = 90*2 + 4
a_91 = 180 + 4 = 184
The 91st term of the arithmetic sequence 4,6,8 is 184.
Explanation:
The question requires us to find the 91st term of the arithmetic sequence 4,6,8. In an arithmetic sequence, each term is equal to the previous term plus a constant difference. In this case, the common difference is 2 (6-4 or 8-6).
To find the 91st term of an arithmetic sequence, we use the formula a + (n-1)d, where a is the first term, n is the term number, and d is the common difference. Plugging in the values, we get: 4 + (91-1) * 2 = 4 + 180 = 184. So, the 91st term in the sequence is 184.
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Evaluate the expression. 2 • 15 – 7 + 4
Answer:
27
Step-by-step explanation:
PEMDAS
Helpppppppppppppppppp
Answer:
4*4*4*4*4
Step-by-step explanation:
Exponents are written as
b^x
where b is the base, and x is the number of times the base is being multiplied
We have
4^5
Therefore, 4 is the base, and it is being multiplied 5 times.
If we are to write it out, we have:
4*4*4*4*4
Therefore, the correct choice is B
The resultant vector from the cross product of two vectors is _____________ a) perpendicular to any one of the two vectors involved in cross product
b) perpendicular to the plane containing both vectors
c) parallel to to any one of the two vectors involved in cross product
d) parallel to the plane containing both vectors
Answer:
b) perpendicular to the plane containing both vectors
Step-by-step explanation:
The cross product is perpendicular to both contributing vectors. Consequently, it is perpendicular to the plane containing them.
The cross product of two vectors results in a vector that is perpendicular to the plane containing both input vectors. This is a key principle in vector physics.
Explanation:The resultant vector from the cross product of two vectors is perpendicular to the plane containing both vectors involved in the cross product. This is a fundamental principle in vector physics. To further illustrate, if you have two vectors A and B, and you perform a cross product, the resulting vector, often denoted as AxB, will be a vector perpendicular (or orthogonal) to the plane containing vectors A and B. Therefore, the correct option is 'b'.
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PLEASE HELP ASAP
Jessica brings her friends to a party. There are 40 people attending. Jessica brings 2 friends there. How many people are at the party without Jessica and her friends?
a. 37
b. 38
c. 40
d. 3
Answer:
a. 37
Step-by-step explanation:
"Jessica brings her friends to a party. There are 40 people attending. Jessica brings 2 friends there. How many people are at the party without Jessica and her friends?
"
40 total minus Jessica and her friends = 37
Hope this helps!
Answer:
C.) 37 I think
Step-by-step explanation:
SoRrY i'M nOt sMaRt. But i think it's 37 and then minus her and her 2 friends means:
[tex]40-3=37:)[/tex]
A Ferris wheel has a diameter of 40 feet. What is its circumference?
Round to the nearest tenth. Use 3.14 for .
Answer:125.6 feet
Step-by-step explanation:
diameter=40 feet
π=3.14
Circumference= π x diameter
Circumference=3.14 x 40
Circumference=125.6
you are allowed to work a total of no more than 30 hours each week at your two jobs. Lawn mowing pays $5 per hour and babysitting pays $8 per hour. You need to earn at least $300 per week. You decide to write a system of inequalities to help determine the amount of time you can work at each job, where x represents the number of hours you mow lawns y represents the number of hours you babysit. You write the first inequality as x+y<30. Write the second inequality you would use for this system .
Answer:
5X + 8Y >= 300; intersection at (-20, 50)
Step-by-step explanation:
let t = work hours
0 < t < 30
X = time lawn mowing
Y = time babysitting.
X + Y < 30
5X + 8Y >= 300
We could solve...
X < 30 - Y
5(30 - Y) + 8Y >=300
150 - 5Y + 8Y >= 300
3Y >=150
Y >=50
then X < -20
intersection at (-20, 50)
Answer:
Step-by-step explanation:
5x+8y > 300
_
Combine like terms.
8y2 + 8(4y2 − 7) =
Answer:
= 80y - 56 then it will be the answer, it may be incorrect so i apologize if it is.
Answer:
80y - 56
Step-by-step explanation:
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An investor randomly purchases 3 stocks listed on a stock exchange. Historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 49%. The number of stocks that increase in value is recorded.
Final answer:
No, the given probability experiment does not represent a binomial experiment because it does not meet the three conditions required for a binomial experiment.
Explanation:
No, the given probability experiment does not represent a binomial experiment. In order for an experiment to be considered a binomial experiment, it must meet three conditions:
1. There must be a fixed number of trials, denoted by 'n'. However, in the given experiment, the number of stocks that the investor purchases is not fixed.
2. There must be only two possible outcomes, called success and failure, for each trial. However, in the given experiment, the outcomes can have three possibilities: the stock can increase, decrease, or have no change in value.
3. The 'n' trials must be independent and repeated using identical conditions. However, in the given experiment, the success or failure of one stock can potentially influence the success or failure of another stock.
Jersey constructed a small wooden jewelry box, shown below, for her mother.
'Picture not drawn to scale
What is the volume of the jewelry box?
A. 234 cu in
B.
15
cu in
32 cu in
D.
117 cu in
Answer:
(D)117 Cubic Inches
Step-by-step explanation:
Dimensions of the box are:
Length[tex]=7\frac{1}{2}\:inch[/tex]
Width[tex]=4\frac{1}{3}\:inch[/tex]
Height[tex]=3\frac{3}{5}\:inch[/tex]
Volume of the Box =Length X Width X Height
[tex]=7\dfrac{1}{2}X4\dfrac{1}{3}X3\dfrac{3}{5}\\\\=\dfrac{15}{2}X\dfrac{13}{3}X\dfrac{18}{5}\\\\=\dfrac{15X13X18}{2X3X5}\\\\=\dfrac{3510}{30}[/tex]
=117 Cubic Inches
The volume of the box is 117 cubic inches.
Answer:
D) 117 cubic inches
Step-by-step explanation:
Have a wonderful day!
7. There are seven clarinet players in the concert band. In how
many ways can they be seated in seven chairs at a concert?
Use the Fundamental Counting Principle.
A. 5,040
C. 840
B. 2,520
D. 210
Answer:
Step-by-step explanation:
The number of people in the cabinet is 7.
n = 7.
Fundamental Counting Principle states that if there are m ways of doing a thing and there are n ways of doing other thing then there are total m*n ways of doing both things.
now using fundamental Counting Principle.
since 7 players can sit on chair in
7 , 6, 5 , 4, 3 , 2, 1 ways then together they can be seated in
7 * 6 * 5 * 4 * 3 * 2 * 1 ways = 5,040 ways.
To arrange this seven people in a straight cabinet, the number of way to arrange them is n!
Then,
n! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
There are 5040 ways of arranging them.
Option A is correct.
2 qurstions 100 points
1- What is the Molarity of 1.25 moles of NaOH in 250 mL of
water?
2- How do you dilute a 20 mL of a 5Molar solution to 0.5 Molar solution
Answer:
1). 1.25 / 250 = .005M
.005 = 1 liter
2). (20)(.5) = 10M
have a good day, and be safe
∵∴∵∴∵∴∵∴∵
⊕ΘΞΠΤ⊕
∵∴∵∴∵∴∵∴∵
On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (negative 6, 10), has a vertex at (negative 4, 6), and goes through (negative 2, 10).
What is the equation of the translated function, g(x), if
f(x) = x2?
g(x) = (x – 4)2 + 6
g(x) = (x + 6)2 – 4
g(x) = (x – 6)2 – 4
g(x) = (x + 4)2 + 6
Answer:
[tex]y = (x+4)^{2}+6[/tex]
Step-by-step explanation:
The parabola with vertex at point (h,k) is described by the following model:
[tex]y - k = C\cdot (x-h)^{2}[/tex]
The equation which satisfies the conditions described above:
[tex]y - 6 = (x+4)^{2}[/tex]
[tex]y = (x+4)^{2}+6[/tex]
The two points are evaluated herein:
x = -6
[tex]y =(-6+4)^{2}+6[/tex]
[tex]y = (-2)^{2}+6[/tex]
[tex]y = 4 + 6[/tex]
[tex]y = 10[/tex]
x = -2
[tex]y = (-2+4)^{2}+6[/tex]
[tex]y = 2^{2} + 6[/tex]
[tex]y = 4 + 6[/tex]
[tex]y = 10[/tex]
The equation of the translated function is [tex]y = (x+4)^{2}+6[/tex].
2/3x - 5/6 equal to or greater than 1/2
The solution to the inequality [tex]\( \frac{2}{3}x - \frac{5}{6} \geq \frac{1}{2} \)[/tex] is [tex]\( x \geq 2 \)[/tex].
Given inequality: [tex]\( \frac{2}{3}x - \frac{5}{6} \geq \frac{1}{2} \)[/tex]
Step 1: To simplify the equation, let's find a common denominator for the fractions. The least common multiple (LCM) of 3 and 6 is 6.
Step 2: Rewrite the fractions with the common denominator, which is 6.
So, [tex]\( \frac{2}{3}x - \frac{5}{6} \)[/tex] becomes [tex]\( \frac{4x}{6} - \frac{5}{6} \).[/tex]
Step 3: Now, we have the equation [tex]\( \frac{4x}{6} - \frac{5}{6} \geq \frac{1}{2} \).[/tex]
Step 4: Combine the fractions on the left side of the equation: [tex]\( \frac{4x - 5}{6} \geq \frac{1}{2} \)[/tex].
Step 5: To get rid of the denominator, multiply both sides of the equation by 6 to clear it.
[tex]\( 6 \times \frac{4x - 5}{6} \geq 6 \times \frac{1}{2} \)[/tex]
This simplifies to: [tex]\( 4x - 5 \geq 3 \)[/tex]
Step 6: Now, let's isolate [tex]\(x\)[/tex] by adding 5 to both sides:
[tex]\( 4x - 5 + 5 \geq 3 + 5 \)[/tex]
[tex]\( 4x \geq 8 \)[/tex]
Step 7: Finally, divide both sides by 4:
[tex]\( \frac{4x}{4} \geq \frac{8}{4} \)[/tex]
[tex]\( x \geq 2 \)[/tex]
Complete correct question:
Solve: [tex]\frac{2}{3} x-\frac{5}{6} \geq \frac{1}{2}[/tex]
At 400 miles per hour, how far can an airplane fly in 2 1/2 hours?
A. 600 miles
B.800 miles
C.650 MILES
D.1000 miles
E. None correct
Answer:
D. 1000 miles
Step-by-step explanation:
400 x 2.5 = 1000
The set {5, 6, 8, 9, 10} is part of a solution set for which inequality?
A. c+14<24
B. c+18≥24
C. c+18>24
D. c+14≤24
please help
Answer:
D. c+14 ≤ 24
Step-by-step explanation:
The solutions for these inequalities are ...
A. c < 10 -- does not include the value 10
B. c ≥ 6 -- does not include the value 5
C. c > 6 -- does not include the values 5 or 6
D. c ≤ 10 -- includes all of the values listed
The set given is part of the solution set of ...
c +14 ≤ 24
The scores for the Algebra 2 CFE are normally distributed with a mean score of 45 and a standard deviation of 5.6. If you score 52 on the test, what percentage of test takers scored lower than you?
87.49 %
89.44 %
90.32 %
91.15%
Answer:
89.44%
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 45, \sigma = 5.6[/tex]
If you score 52 on the test, what percentage of test takers scored lower than you?
This is the pvalue of Z when X = 52.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{52 - 45}{5.6}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944.
So 89.44% of test takers scored lower than you.
A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 6 hours and 24 minutes, but when there is a wind blowing from Penthaven to Jackson at 50 miles per hour, the trip takes 6 hours and 40 minutes. How many miles is the distance from Penthaven to Jackson?
(Assume that the plane flies at a constant speed, and that the turnaround time is negligible.)
Answer:800 miles
Step-by-step explanation:
Given
Round trip for Penthaven to Jackson takes 6 hr and 24 minutes in absence of wind
[tex]t_1=6+\frac{24}{60}=6.4\ hr[/tex]
When Wind blows from Penthaven to Jackson it takes 6 hr and 40 min i.e.
[tex]t_2=6+\frac{40}{60}=\frac{20}{3}\ hr[/tex]
Speed of wind [tex]v=50\ mph[/tex]
Suppose x be the distance between Penthaven and Jackson and u be the speed of plane
So initially
[tex]6.4=\frac{x}{u}+\frac{x}{u}[/tex]
[tex]6.4=\frac{2x}{u}[/tex]
[tex]x=3.2u \quad \ldots(i)[/tex]
When wind is blowing then,
[tex]\Rightarrow \frac{20}{3}=\frac{x}{u+v}+\frac{x}{u-v}[/tex]
[tex]\Rightarrow \frac{20}{3}=x[\frac{1}{u+50}+\frac{1}{u-50}][/tex]
[tex]\Rightarrow \frac{20}{3}=x[\frac{2u}{u^2-50^2}]\quad \ldots(ii)[/tex]
Substitute the value of x in [tex](ii)[/tex]
[tex]\Rightarrow \frac{20}{3}=\frac{2u[3.2u]}{u^2-50^2}[/tex]
[tex]\Rightarrow 10[u^2-50^2]=9.6u^2[/tex]
[tex]\Rightarrow 0.4u^2=50^2\times 10[/tex]
[tex]\Rightarrow u^2=\frac{50^2\times 10^2}{4}[/tex]
[tex]\Rightarrow u=250\ mph[/tex]
Thus [tex]x=3.2\times 250=800\ miles[/tex]
How many treaspoons are in 20mls
There are 4 teaspoons in 20 mils. I just learned this in class.
-Dhruva;)
Answer:
4.05768 or 4
Step-by-step explanation:
There are 0.202884 teaspoon in a millilitre. If you multiply 0.202884 by 20, you 4.05768.
I am 100% sure (:
Can i pls have brainliest?
-ME
Lauren makes bracelets using small beads. She uses
60 beads for each bracelet. How many beads does
Lauren need to make 7 bracelets?
A 42 beads
C 420 beads
B 67 beads
D 670 beads
Answer:
420
Step-by-step explanation:
She uses 60 beads per bracelet and is making 7 bracelets
7*60 = 420 beads total
Beth writes a number that shows 60 parts out of 100. Select all that could be Beth's number
Beth's number, which indicates 60 parts out of 100, can be expressed as 60%, 0.60, 60/100, or in simplest form, 3/5. These representations are commonly used in mathematics to show percentages and their equivalent values.
Beth writes a number that shows 60 parts out of 100. In mathematics, expressing a part out of 100 is essentially describing a percentage. So, Beth's number could be expressed in several ways that all represent 60 out of 100. The simplest form would be 60%, which directly translates to 60 per 100. Another possible representation could be 0.60, which is the decimal form equivalent to 60%. If we were to convert this percentage into a fraction, it would be
60/100, which can also be simplified to
3/5. It cannot be a number such as N(60, 5.477) which suggests a normal distribution with a mean of 60 and a standard deviation of 5.477, nor can it be .9990 which is not equivalent to 60 parts out of 100 in any common mathematical representation.
I don't undestand how to solve this problem
Answer:
Volume = 20
Step-by-step explanation:
To find volume of the shape you split the shape into two shapes: A triangle or pyramid and a rectangle
The volujme of a rectangle is W x L x H
A = 2 x 5 x 8
A = 80
The volume of a pyramid is
A = [tex]\frac{1}{2}[/tex]Bh The B is the area of the base so B = L x W = 5 x 2 = 10 so B = 10
A = [tex]\frac{1}{2}[/tex] 10 x 4
A = [tex]\frac{1}{2}[/tex] 40
A = 20
What is the distance between the following points?
Phytagoras Theorem :
c² = a² + b²
c² = 9² + 2²
c² = 81 + 4
c² = 85
c = √85
So, the distance between the following points is √85
Hope it helpful and useful :)
A swimming school claimed that the average seven-year-old would be able to swim across an Olympic-sized pool in less than 120 seconds after taking lessons from their instructors. To test this claim, a consumer psychologist arranged for eight randomly selected seven-year-old children to take lessons at the school and recorded how long it took each child to swim across a pool at the end of the lessons.
The times (in seconds) were 60, 120, 110, 80, 70, 90, 100, and 130.
What conclusion would the psychologist draw following a t test for a single sample using 120 seconds as the "known" population mean and the .05 significance level? 13 points) across an
a. Sample mean:
b. Sample sum of squares:
c. Degrees of freedom:
d. The estimated population variance:
Answer:
Step-by-step explanation:
The mean of the set of data given is
Mean = (60 + 120 + 110 + 80 + 70 + 90 + 100 + 130)/8 = 95
Standard deviation = √(summation(x - mean)/n
n = 8
Summation(x - mean) = (60 - 95)^2 + (120 - 95)^2 + (110 - 95)^2 + (80 - 95)^2 + (70 - 95)^2 + (90 - 95)^2 + (100 - 95)^2 + (130 - 95)^2 = 4200
Standard deviation = √(4200/8) = 22.91
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≤ 120
For the alternative hypothesis,
µ > 120
This is a right tailed test.
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 8,
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 95
µ = population mean = 120
s = samples standard deviation = 22.91
t = (95 - 120)/(22.91/√8) = - 3.09
We would determine the p value using the t test calculator. It becomes
p = 0.009
Since alpha, 0.05 > than the p value, 0.009, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the average seven-year-old would be able to swim across an Olympic-sized pool in more than 120 seconds after taking lessons from their instructors.
Using the one - sample t test, we can conclude that average 7year old will swim in less than 120 hours
Given the data :
60, 120, 110, 80, 70, 90, 100, and 130. Sample size, n = 8Using calculator :
Mean = ΣX/n = 760/8 = 95Standard deviation = 24.49The degree of freedom :
df = n - 1 df = 8 - 1 = 7The hypothesis :
[tex]H_{0} : μ > 120 [/tex]
[tex]H_{1} : μ ≤ 120 [/tex]
From the equality sign in the alternative hypothesis, we have a left-tailed test
Test statistic :
[tex] \frac{x - μ}{\frac{s}{\sqrt{n}}} [/tex]
Inputting the values :
[tex] \frac{95 - 120}{\frac{24.49}{\sqrt{8}}} [/tex]
[tex] \frac{-25}{8.658} = - 2.887 [/tex]
Calculating the P-value :
α = 0.05 ; df = 7 ;Pvalue = 0.012
Decison Region :
Reject Null if Pvalue is < αSince 0.012 < 0.05 ; we reject [tex]H_{0} [/tex] and conclude that average 7year old will swim in less than 120 hours.
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Determine the approximate value of x.
a.
b.
2.13
3.53
c. 4.39
d. 7.52
We have been given a right triangle. We are asked to find the value of x.
We can see that x is opposite side to angle that measures 62 degrees and adjacent side to angle is 4 units.
We know that tangent relates adjacent and opposite side of right triangle.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(62^{\circ})=\frac{x}{4}[/tex]
[tex]4\cdot \text{tan}(62^{\circ})=\frac{x}{4}\cdot 4[/tex]
[tex]4\cdot (1.880726465346)=x[/tex]
[tex]7.522905861384=x[/tex]
[tex]x=7.522905861384[/tex]
[tex]x\approx 7.52[/tex]
Therefore, the value of x is approximately 7.52 units and option 'd' is the correct choice.
Round $6.4442 to the nearest cent.
Answer:
6.40
Step-by-step explanation:
Find the number in the tenth place (the first 4) and look one place to the right for the rounding digit (the second 4).
Round up if this number is greater than or equal to 5
and round down if it is less than 5.
4 is less than five, therefore should be rounded down.
Answer:
6.44
Step-by-step explanation:
The nearest cent is the hundredths place (or two decimals)
6.4442 rounds to 6.44
The next number is less than 5 so we leave the hundredths place alone.
The face of a cube has a surface area of 9cm2
Answer:
D
Step-by-step explanation:
Because 9cm2 is 9 times 9 which equals 81 cm.
To find the length of one side of a cube with a surface area of 9 cm², set up the equation s² * 6 = 9. Simplify and solve for s to find that the length of one side is √(9/6) cm.
Explanation:The question is asking about the surface area of a cube. The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying that result by 6 since a cube has 6 faces. So, if the surface area of a cube is 9 cm², you can set up the equation: 9 = s² * 6. Simplifying, you get s² = 9/6. Taking the square root of both sides, you find that s = √(9/6). Therefore, the length of one side of the cube is √(9/6) cm.
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(15 pt., 5 pt. each) A player in the Powerball lottery picks five different integers between 1 and 69, inclusive, and a sixth integer between 1 and 26, inclusive, which may duplicate one of the earlier five integers. The player wins the jackpot (currently $43 million) if the first five numbers picked match the first five numbers drawn (in any order) and the sixth number picked matches the sixth number drawn. a. What is the probability that a player wins the jackpot
Answer:
The probability that a player wins the jackpot is [tex]\frac{1}{292201338}[/tex]
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the first five numbers are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
First five numbers:
Desired:
5 correct numbers, from a set of 5. So
[tex]D = C_{5,5} = \frac{5!}{5!(5-5)!} = 1[/tex]
Total:
5 numbers from a set of 69. So
[tex]T = C_{69,5} = \frac{69!}{5!(69-5)!} = 11238513[/tex]
Probability:
[tex]P_{5} = \frac{D}{T} = \frac{1}{11238513}[/tex]
-------------
Sixth number:
1 from a set of 26
Then
[tex]P_{6} = \frac{1}{26}[/tex]
-------------
Probability of winning the prize
[tex]P = P_{5} \times P_{6} = \frac{1}{11238513} \times \frac{1}{26} = \frac{1}{292201338}[/tex]
The probability that a player wins the jackpot is [tex]\frac{1}{292201338}[/tex]
To calculate the probability of winning the jackpot in the Powerball lottery, we need to consider the probability of choosing the first five numbers correctly and the probability of choosing the sixth number correctly. Multiply the probabilities from these two steps to find the overall probability.
Explanation:To calculate the probability of winning the jackpot in the Powerball lottery, we need to consider two parts: the probability of choosing the first five numbers correctly (regardless of order) and the probability of choosing the sixth number correctly.
The probability of choosing the first five numbers correctly is given by:The probability of choosing the sixth number correctly is simply 1 out of 26, since the player can pick any number between 1 and 26, inclusive.To find the overall probability, we multiply the probabilities from the two steps:
P(winning jackpot) = P(choosing first five numbers correctly) x P(choosing sixth number correctly) = [P(choosing one number correctly)]^5 x P(choosing one number correctly) = (5/69)^5 x 1/26
Calculating this expression gives us the probability of winning the jackpot in the Powerball lottery.
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A marketing survey involves brand recognition in New York and California. Of 147 New Yorkers surveyed, 79 were familiar with the brand while 78 out of 147 Californians knew this brand as well. Assume that you plan to test the claim that the proportion of New Yorkers who recognize this brand differs from the proportion of Californians who do the same, i.e., p1 ≠ p2. Use the given information to find the pooled sample proportion begin mathsize 14px style p with bar on top end style. Round your answer to three decimal places.
Answer:
[tex]z=\frac{0.537-0.531}{\sqrt{0.534(1-0.534)(\frac{1}{147}+\frac{1}{147})}}=0.103[/tex]
Now we can calculate the p value with the following probability taking in count the alternative hypothesis:
[tex]p_v =2*P(Z>0.103) =0.918 [/tex]
For this case since the p value is large enough we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that we have significant differences between the two proportions analyzed.
Step-by-step explanation:
Information provided
[tex]X_{1}=79[/tex] represent the number of New Yorkers familiar with the brand
[tex]X_{2}=78[/tex] represent the number of Californians familiar with the brand
[tex]n_{1}=147[/tex] sample of New Yorkers
[tex]n_{2}=147[/tex] sample of Californians
[tex]p_{1}=\frac{79}{147}=0.537[/tex] represent the proportion New Yorkers familiar with the brand
[tex]p_{2}=\frac{78}{147}=0.531[/tex] represent the proportion of Californians familiar with the brand
[tex]\hat p[/tex] represent the pooled estimate of p
z would represent the statistic
[tex]p_v[/tex] represent the value
System of hypothesis
We want to verify if the two proportions of interest for this case are equal, the system of hypothesis would be:
Null hypothesis:[tex]p_{1} = p_{2}[/tex]
Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]
The statistic would be given by:
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{79+78}{147+147}=0.534[/tex]
Repalcing the info given we got:
[tex]z=\frac{0.537-0.531}{\sqrt{0.534(1-0.534)(\frac{1}{147}+\frac{1}{147})}}=0.103[/tex]
Now we can calculate the p value with the following probability taking in count the alternative hypothesis:
[tex]p_v =2*P(Z>0.103) =0.918 [/tex]
For this case since the p value is large enough we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that we have significant differences between the two proportions analyzed.