The probability of event A is 0.0012 and the probability of event B is 0.0288
How to find the probabilities?There are 7 people and 4 prices.
A) The probability that Ann wins the first prize is 1/7, assuming that all 7 people have the same probability of winnig.
Then Jim is second, now the probability is 1/6 (because we don't count Ann anymore).
Soo wins the third one, with a probability 1/5.
Kira wins the last one, with a probability of 1/4.
The joint probability is the product of all the individual ones:
P(A) = 1/7*1/6*1/5*1/4 = 0.0012
B) Now we just want that Soo, Ann, Ravi, and Hans win, but the order does not matter.
So we have the same probability than above, but now we need to include the permutations of the 4 elements, so we add a factor 4!.
P(B) = 4!*0.0012 = 4*3*2*1*0.0012 = 0.0288
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what is this equation rewritten in the form that reveals the minimum of the function
We are given the quadratic function c(p) = p^2 - 28p + 250 and we need to rewrite this in such a way that the minimum value is easy to find.
Remember that the vertex
[tex]f(x)=a(x-h)^2+k[/tex]where (h, k) is the vertex or the minimum point.
We use completing the squares method to do this. We divide the second term, -28p, by 2p, then square it.
[tex](\frac{-28p}{2p})^2=(-14)^2=196[/tex]We add 196 to p^2 - 28p to make it equal to (p - 14)^2, but since it will change the value of the equation, we need to subtract the same value from 250 so that the net effect is zero.
[tex]\begin{gathered} c(p)=p^2-28p+250 \\ c(p)=(p^2-28p+196)+250-196 \\ c(p)=(p-14)^2+54 \end{gathered}[/tex]The equation is c(p) = (p - 14)^2 + 54.
A plane traveled 3465 miles with the wind in 5.5 hours and 3245 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.
The speed of the plane in still air is
The speed of the wind is
The most appropriate choice for speed will be given by-
Speed of plane in still air = 610 miles/hour
Speed of wind = 20 miles/hour
What is speed?
Distance travelled by a body in unit time is called speed.
Let the speed of plane in still air be x miles/hour
Speed of wind be y miles/hour
A plane traveled 3465 miles with the wind in 5.5 hours
So,
x + y = [tex]\frac{3465}{5.5}[/tex]
x + y = 630.......(1)
The plane travelled 3245 miles against the wind in the same amount of time
so,
x - y = [tex]\frac{3245}{5.5}[/tex]
x - y = 590.......(2)
Adding (1) and (2),
2x = 1220
x = [tex]\frac{1220}{2}[/tex]
x = 610 miles/hour
Putting the value of x in (1),
610 + y = 630
y = 630 - 610
y = 20 miles/hour
Speed of plane in still air = 610 miles/hour
Speed of wind = 20 miles/hour
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Use the figure for 5 and6.
And 7
Can I please get help on this math problem always been bad at math.If X=-5 and y=-3 what is the value of x (y-10) i can't provide pictures
Given
[tex]x(y-10)[/tex][tex]\begin{gathered} x(y-10) \\ x=5,y=3 \\ 5(3-10) \\ 5(-7) \\ -35 \end{gathered}[/tex]How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if repeating the digits are allowed? A.100 B. 125 C. 150
olution:
Recall the Fundamental Counting principle; if there are m ways to make a selection and n ways to make a second selection, then there are m x n number of ways in which two selection can be made.
ut of the provided digits, if the number ends with 3
ase 1: Tnumber of one digit numbers.
ut of the digits provided, only one way to fil;l the box that is with one.
Thus, there is one digit odd integer here.
Case 2: The number of two digits.
Out of the digits provided, only one way to fill the last box is with digit 3, and any one of the 4 digits can filled in it as 0 cannot filled in either of the box.
Thus, number of ways are;
[tex]4\times1=4[/tex]Aase 3: The number of three digit numbers.
ut of the digits provided, only one way to flll the last box is with digit 3, and any one of the 5 digits can be filled in second box, and thus any one of the 4 digits can be filled in first box as 0 cannot be fixed in the box.
Thus, number of ways are;
[tex]4\times5\times1=20[/tex]Lastly;
: The numbver of four digit numbers.
he number of ways are;
[tex]4\times5\times5\times1=100[/tex]Thus, the total number of ways to select are;
[tex]100+20+4+1=125[/tex]INAL ANSWER: 125
Hi can you help me find the correct answer to this problem?
we have the equation
[tex]\begin{gathered} \sqrt{10x-1}=7 \\ \end{gathered}[/tex]Solve for x
Step 1
squared both sides
[tex]\begin{gathered} 10x-1=7^2 \\ 10x-1=49 \\ 10x=49+1 \\ 10x=50 \\ x=\frac{50}{10} \\ \\ x=5 \end{gathered}[/tex]The answer is x=5
Some cars depreciate at rates as high as 75% per year for the first two years; this means that after one year the car is only worth 25% of the original cost. Suppose that you purchase a car for $16,500 that has a depreciation rate of 75%, then what will be the value of your car in 2 years? Hint: use f(x) = 16500(0.25)*, where x is the time in years. Round your answer to the nearest = dollar. $1.568 7765 then
Given:
Depreciation rate = 75% per year.
[tex]\begin{gathered} f(x)=a(1-0.75)^x \\ \\ f(x)=a(0.25)^x \end{gathered}[/tex]Let's find the value of the car in 2 years.
Given:
Cost = $16,500
Depreciation rate = 75%
From the equation we have:
Present value, a = 16500
x is the number of years = 2
Thus, we have:
[tex]\begin{gathered} f(2)=16500(0.25)^2 \\ \\ f(x)=16500(0.0625) \\ \\ f(x)=1031.25\approx1031 \end{gathered}[/tex]Therefore, the value of the car in 2 years is $1,031
ANSWER:
$1,031
Question 19 Here are the fuel efficiencies (in mpg) of 8 new cars. 44, 19, 51, 12, 34, 21, 15, 24 What is the percentage of these cars with a fuel efficiency less than 24 mpg?
The percentage of these cars with a fuel efficiency less than 24 mpg is 50 %.
What is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Given data:
44, 19, 51, 12, 34, 21, 15, 24
fuel efficiency less than 24 mpg is 19, 12, 21, 15
So, the percentage is
=4 / 8 x 100
= 1/2 x 100
= 50%
Hence, the percentage of these cars with a fuel efficiency less than 24 mpg is 50 %.
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Given the equation of a line
y = mx + 1, for what values of m will the line be increasing? Enter (<,>,=).
greater than 1. If its less than, it will be decreasing.
As an estimation we are told £3 is €4. Convert £12 to euros.
Well, here is the answer . . .
£12 = 13.73€
Seema used compatible numbers to estimate the product of (–25.31)(9.61). What was her estimate?
If Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.
Total estimateGiven data or information :
Product = ( – 25. 31 ) (9. 61)
Now let estimate the product by first approximating the product to the nearest tenth.
Approximation :
So,
-25.31 = - 25 ( Approximately )
9.61 =10 ( Approximately )
Hence , her estimate can be calculated as :
Estimate :
Estimate = (-25) (10)
Estimate =-250
Therefore based on the information or data given if Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.
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What is the direction and strength of the association between the variables?
Given the graph of a function f. Identify the function by name. Then Graph, state the domain and range, use set notation forA) 1/2f(x)B) 2f(x)
From the graph, we can determine that the function f(x) is quadratic. The function f(x) is defined as:
[tex]f(x)\text{ = }x^2[/tex]The graph of (a) 1/2 f(x):
This implies that f(x) is compressed vertically by a factor of 1/2.
Using the points:
(-4, 8) , (-2, 2), (0,0), (2,2), (4, 8)
The graph of the function using a graphing calculator is shown below:
The graph of (b) 2 f(x)
This implies that the original function was stretched vertically by a factor of 2
Using the points:
(-4, 32), (-2, 8), (0,0), (2,8), (4,32)
The graph using a graphing calculator is shown below:
The domain:
This is a set of allowable x-values
Using interval notation:
[tex](-\infty,\text{ }\infty)\text{ or All real numbers}[/tex]The range:
This is a set of allowable y-values:
Using interval notation:
[tex]\lbrack0,\text{ }\infty)\text{ }[/tex]HELPP! Algebra 2
If the length of one side of a square is triple and the length of an adjacent side is increased by 10, the resulting rectangle has an area that is 6 times the area of the original square. Find the length of a side pf the original square.
Answer:
Side = 10 units
Step-by-step explanation:
Original square area = s x s =s^2
now change the sides and this equals 6s^2
3s * ( s+10) = 6 s^2
3s^2 -30s = 0
s ( 3s-30) = 0 so s = 0 or 10
Evaluate ∫(15x2+x2‾‾√34) dx. Here C is the constant of integration.
We use the following formula for integration:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}+C[/tex]We have the following integral:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx[/tex]Separate into two integrals:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx=\int15x^2dx+\int\frac{\sqrt[3]{x^2}}{4}dx[/tex]Calculate the first integral. Take the coefficient out of the integral:
[tex]\int15x^2dx=15\int x^2dx[/tex]Apply the integration formula:
[tex]\int15x^2dx=15\frac{x^3}{3}+C=5x^3+C[/tex]Calculate the second integral. Take the coefficient out of the integral:
[tex]\int\frac{\sqrt[3]{x^2}}{4}dx=\frac{1}{4}\int\sqrt[3]{x^2}dx[/tex]Express the radical as a fractional exponent:
[tex]\frac{1}{4}\int\sqrt[3]{x^2}dx=\frac{1}{4}\int x^{2/3}dx[/tex]Apply the integration formula:
[tex]\frac{1}{4}\cdot\frac{x^{5/3}}{5/3}+C=\frac{3}{20}\sqrt[3]{x^5}+C[/tex]The total integral is:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx=5x^3+\frac{3}{20}\sqrt[3]{x^5}+C[/tex]I need help please with number 5 initially. I have attached a scanned document of my book problems.
Considering the z-test formula, it is found that:
a) Increasing the difference between the sample mean and the original population mean increases the test statistic.
b) Increasing the population standard deviation decreases the test statistic.
c) Increasing the sample size increases the test statistic.
What is the z-test formula?Considering a z-test, the formula for the test statistic is given by the following rule:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In item a, increasing the difference between the sample mean and the original population mean is increasing the numerator [tex]\overline{x} - \mu[/tex], meaning that the test statistic z will be increased.
In item b, increasing the population standard deviation [tex]\sigma[/tex] means that the denominator of the formula will be increasing, hence the test statistic will be decreased.
In item c, increasing the sample size n means that the denominator will be decreased, as the denominator is a fraction which is inverse proportional to the sample size, hence the test statistic z will be increased.
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If I eat pizza after midnight, then I'll
have a stomach ache.
Choose the equivalent statement.
A. If I don't have a stomach ache, then I didn't eat pizza after
midnight.
B. If I don't eat pizza after midnight, then I won't have a stomach
ache.
C. If I have a stomach ache, then I ate pizza after midnight.
Answer:
B. If I don't eat pizza after midnight, then I won't have a stomach ache.
Write an equation of the line with a
slope of 0 and y -intercept of 5
y=
Answer:
Step-by-step explanation:
it is y
Answer: Y=0x +5
Step-by-step explanation
its going up by 0 so 0x and you start at 5 so plus 5
Send answers for the question please and thanks.
Answer:
7⁻²=[tex]\frac{1}{49}[/tex]
3⁻⁴ [tex]=\frac{1}{81}[/tex]
9⁰=1
11⁻¹=[tex]\frac{1}{11}[/tex]
The polynomial -17x^2 + 165x + 14,481 represents the electricity generated (in gigawatts) by geothermal sources during 2002-2007. The polynomial 879x^2 - 72x + 10,140 represents the electricity generated (in gigawatts) by wind power during 2002-2007. In both polynomials, x represents the number of years after 2002. Find a polynomial for the total electricity generated by both geothermal and wind power during 2002-2007.
The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is given by adding the two other ones, we will get:
862x^2 + 93x + 24,621
How to find the polynomial for the total electricity?Here we have two polynomials:
Polynomial -17x^2 + 165x + 14,481 represents the electricity generatedby geothermal sources during 2002-2007. Polynomial 879x^2 - 72x + 10,140 represents the electricity generated by wind power during 2002-2007Both of these are in gigawatts, so are in the same units, which means that we can directly add the two polynomials to get a polynomial for the total electricity.
-17x^2 + 165x + 14,481 + 879x^2 - 72x + 10,140
Now we group like terms:
(-17x^2 + 879x^2) + (165x - 72x) + (14,481 + 10,140)
862x^2 + 93x + 24,621
This polynomial represents the total electricity generated during 2002-2007
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a line intercepts the points (13,-4) and (1, 12) whats the slope
Answer:
m=-4/3
Explanation:
Given the points: (13,-4) and (1, 12)
To determine the slope of the line that joins the point, use the formula below;
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substitute the given points:
[tex]\begin{gathered} m=\frac{12-(-4)}{1-13} \\ =\frac{12+4}{-12} \\ =-\frac{16}{12} \\ =-\frac{4}{3} \end{gathered}[/tex]The slope is -4/3.
In a jail cell, there are 5 Democrats and 6 Republicans. Four of these people will be randomly chosen for
early release. What is the probability that a group consisting of 2 Democrats and 2 Republicans will be chosen
for early release?
The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be 5/11.
What is probability?It should be noted that probability simply means the likelihood that a particular event will happen.
In this case, there are there are 5 Democrats and 6 Republicans and rour of these people will be randomly chosen for early release.
The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be:
Number of Democrats = 5
Number of Republicans = 6
Total number = 5 + 6 = 11
This will be illustrated through the combination formula:
= (5C2 × 6C2) / 11C4
= (10 × 15) / 330
= 150/330
= 5/11
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$(x) = x2 – 25 and g(x) = x + 5Step 2 of 4 : Find (J - 8)(x), Simplify your answer,Answer( -8)(x) =
Solve for (f - g)(x)
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ (f-g)(x)=(x^2-25)-(x+5) \\ (f-g)(x)=x^2-25-x-5 \\ \; \\ \text{Therefore,} \\ (f-g)(x)=x^2-x-30 \end{gathered}[/tex]Decide whether there is enough information to prove mn.
m
O Yes
O No
You
An
If so, state the theorem you can use. If not, answer "cannot" for the blank below.
✓prove mn
Yes, there is enough information to prove m||n.
By using the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem we can prove that line m is parallel to line n.
In the given figure,
Let the given angles formed by transversal r, adjacent to line m be angle 1, and to line n be angle 2.
Now, the vertically opposite angle to angle 1 will be equal to it as they both are congruent.
The vertically opposite angle equal to angle 1 would be corresponding to angle 2 and corresponding angles formed by a transversal are equal and congruent.
Moreover, angle 1 and angle 2 are alternate exterior angles and by Alternate Exterior Angles Theorem, they are congruent.
Hence, it is proved by the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem that line m is parallel to line n (m||n).
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If the quotient of a number and 8 is added to 1/4 the result is 7/8. Find the number.
Answer:
5
Step-by-step explanation:
Let n be the unknown number.
The quotient is the result obtained by dividing one number by another.
Therefore, the quotient of a number and 8 is ⁿ/₈.
If the quotient of a number and 8 is added to 1/4 the result is 7/8:
[tex]\implies \dfrac{n}{8}+\dfrac{1}{4}=\dfrac{7}{8}[/tex]
To solve, make the denominators of all the fractions the same:
[tex]\implies \dfrac{n}{8}+\dfrac{1 \cdot 2}{4 \cdot 2}=\dfrac{7}{8}[/tex]
[tex]\implies \dfrac{n}{8}+\dfrac{2}{8}=\dfrac{7}{8}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{n+2}{8}=\dfrac{7}{8}[/tex]
Multiply both sides by 8:
[tex]\implies \dfrac{8(n+2)}{8}=\dfrac{7 \cdot 8}{8}[/tex]
[tex]\implies n+2=7[/tex]
Subtract 2 from both sides:
[tex]\implies n+2-2=7-2[/tex]
[tex]\implies n=5[/tex]
Therefore, the number is 5.
Given that f(x) = x² - 3 and g(x) = 3x + 5, find (g- f)(9), if it exists.
(3x+5)-([tex]x^{2} - 3[/tex])=9
[tex]x^{2}[/tex]-3x-8=-9
[tex]x^{2}[/tex]-3x=-1
[tex]x^{2}[/tex]-3x+1=0
What are the minimum and maximum possible measures of 31 centimeters
The the minimum and maximum possible measures of 31 centimeters is {30.5. 31.5}
How do you find the minimum and maximum measurements?To find it, one need to add the biggest possible inaccuracy to each measurement, then multiply to get the biggest volume you can. Also Subtract the largest potential mistake from each measurement, then multiply, to to know the smallest volume that can be produced.
Note that the smallest value in the data set is the minimum. The highest value in the data collection is called the maximum.
Since only one data set is given, the possible measures can only be around it hence the largest and the smallest value close to it.
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when x is decreasd by 2 and then that number is divided by 2, the result is 2. what is the number
Answer:
lets denote x as 6
so,
(x-2)÷2
(6-2)÷2
4÷2
2(proved)
Which expression is equivalent to −40+(−20)+(−60) ?
Responses
−40−(20−60)
negative 40 minus open parenthesis 20 minus 60 close parenthesis
−(40−20)+(−60)
negative open parenthesis 40 minus 20 close parenthesis plus open parenthesis negative 60 close parenthesis
40 + 20 + 60
40 + 20 + 60
−20+(−40)+(−60
PLEASE HELP!
The expression equivalent to [-40 + (-20) + (-60)] is [−20 + (−40) + (−60)]
As per the question statement, we are provided with a linear expression of [-40 + (-20) + (-60)], and four options.
We are supposed to determine the one expression from the given options, that is equivalent to the question mentioned expression of [-40 + (-20) + (-60)].
To solve this question, we will first calculate the value of the question mentioned equation, and then, calculate and compare the values of individual expressions provided in the options, to obtain our desired answer.
Therefore, [-40 + (-20) + (-60)] = [-40 - 20 -60]
or, [-40 + (-20) + (-60)] = -( 40 + 20 + 60)
or, [-40 + (-20) + (-60)] = -120.
Now, coming to the first option, expression [−40 − (20 − 60)] equates to
[-40 - (-40)] = (-40 + 40) = (40 - 40) = 0,
And [0 ≠ (-120),
Hence, [−40 − (20 − 60)] is not the equivalent expression to
[-40 + (-20) + (-60)].
Now, coming to the second option, expression [-(40 − 20) + (-60)] equates to [-(20) + (-60)] = (-20 - 60) = -(20 + 60) = (-80),
But again, [(-80) ≠ (-120)],
Hence, [-(40 − 20) + (-60)] is not the equivalent expression to
[-40 + (-20) + (-60)].
Coming to the third option, expression [40 + 20 + 60] equates to (120)
But again, [120 ≠ (-120)],
Hence, [40 + 20 + 60] is not the equivalent expression to
[-40 + (-20) + (-60)].
Finally, Coming to the last option, expression [−20 + (−40) + (−60)] equates to (-20 - 40 - 60) = -(20 + 40 + 60) = (-120).
And [(-120) = (-120)],
Hence, [−20 + (−40) + (−60)] is the required equivalent expression to
[-40 + (-20) + (-60)].
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Answer:
−20+(−40)+(−60)
Step-by-step explanation:
they add up to the same thing and the order doesn't matter I think.
A model rocket is launched straight up into the air. The height y (in feet) of the rocket after t seconds can be modeled by y=-16t^2+128t. How many seconds is the rocket in the air?
Answer:
8
Step-by-step explanation:
To find the time the rocket is in the air, we can find the time when the height is 0 (remember this time is not 0).
[tex]-16t^2+128t=0 \\ \\ t^2-8t=0 \\ \\ t(t-8)=0 \\ \\ t=0,8 \\ \\ t \neq 0 \implies t=8[/tex]