Answer:
A. maximum value at 30
Step-by-step explanation:
−x² + 10x + 5
First, factor out the leading coefficient from the first two terms:
-1 (x² − 10x) + 5
Take half of the next coefficient, square it, then add and subtract the result.
(-10/2)² = 25
-1 (x² − 10x + 25 − 25) + 5
-1 (x² − 10x + 25) + 25 + 5
-1 (x² − 10x + 25) + 30
Factor the perfect square.
-1 (x − 5)² + 30
The equation is now in vertex form. This is a downwards parabola with a vertex at (5, 30). Since the parabola points down, the vertex is a maximum.
A soccer ball is thrown upward from the top of a 204 foot high building at a speed of 112 feet per second. The soccer ball's height above ground can be modeled by the equation . When does the soccer ball hit the ground?
Answer:
8.5 seconds to hit the ground
Step-by-step explanation:
A soccer ball is thrown upward from the top of a 204 foot high building at a speed of 112 feet per second.
[tex]h(t)=-16t^2+V_0t+h_0[/tex]
Vo is the speed 112 feet per second
h0 is the initial height = 204 foot
So the equation becomes
[tex]h(t)=-16t^2+112t+204[/tex]
When the soccer ball hit the ground then the height becomes 0
[tex]0=-16t^2+112t+204[/tex]
Apply quadratic formula
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]t=\frac{-112+\sqrt{112^2-4 (-16) \cdot 204}}{2(-16)}[/tex]
[tex]t=\frac{-112+\sqrt{25600}}{-32}=-1.5[/tex]
[tex]\frac{-112-\sqrt{25600}}{-32}=8.5[/tex]
time cannot be negative
so it takes 8.5 seconds to hit the ground
MOBIL Gas Station sells different kinds of gasoline: regular, plus, premium. Mr.Adams spent $36.25 on 12.5 gallons of regular gasoline at MOBIL Gas Station. Determine the cost per gallon for regular gasoline.
The cost per gallon of regular gasoline will be $2.69 per gallon.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
MOBIL Service station sells various types of fuel: standard, besides, and premium. Mr.Adams burned through $36.25 on 12.5 gallons of standard fuel at the MOBIL Service station.
The cost per gallon for regular gasoline will be given as,
Rate = $36.25 / 12.5
Rate = $2.69 per gallon
The cost per gallon of regular gasoline will be $2.69 per gallon.
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Gas Mileage is how many miles you travel on one gallon of gasoline. A new Honda Accord Hybrid ( part electric, part gasoline ) testes our traveling 432 miles on 8 gallons of gasoline. What is the car's gas mileage? How fat can it travel on a full tank of 12 1/2 gallons of gas?
Answer: the distance it can travel on full tank is 675 miles
Step-by-step explanation:
Gas Mileage is how many miles you travel on one gallon of gasoline.
A new Honda Accord Hybrid ( part electric, part gasoline ) tests for its gas mileage by traveling 432 miles on 8 gallons of gasoline.
This means that its gas mileage is
Number of miles travelled / number of gallons of gasoline used.
Gas mileage = 432/8 = 54 miles per gallon
If a full tank containing 12 1/2 = 25/2 gallons is used, the distance that it can travel will be
Gas mileage × volume of the full tank. it becomes
54 × 25/2 = 675miles
Radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3 meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.7 meters?The intensity is______milliroentgens per hour. (Round to the nearest tenth as needed.)
The intensity at a distance of 2.7 meters is 77.17 milliroentgens per hour.
Given:
I= 62.5 milliroentgens per hour
Distance = 3 meters
If the intensity of radiation varies inversely as the square of the distance from the machine, use the inverse square law formula:
[tex]I = k/d^2[/tex]
Where:
I represents the intensity of radiation,
k is a constant,
d represents the distance from the machine.
Substituting the value back to formula as
62.5 = k/(3²)
62.5 = k/9
k = 62.5 x 9
k = 562.5
So, the intensity at a distance of 2.7 meters:
I = 562.5/(2.7²)
I = 562.5/7.29
I = 77.17 milliroentgens per hour
Therefore, the intensity is 77.17 milliroentgens per hour.
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The intensity of radiation from a machine at a distance of 2.7 meters is 77.16 milliroentgens per hour, according to the inverse square law in Physics.
Explanation:The question is related to inverse square law in Physics. The intensity (ℤ) of radiation varies inversely as the square of the distance (d) from the machine. Mathematically, this relationship is represented as ℤ = k/d^2 where k is a constant. Given that at a distance of 3 meters, the intensity is 62.5 milliroentgens per hour, we can find the constant k = ℤ * d^2, i.e., k = 3^2 * 62.5 = 562.5.
Now, you want to know the intensity at a distance of 2.7 meters, which we can find by substituting this value and the constant k in our equation: ℤ = k/d^2, which results in ℤ = 562.5/(2.7^2) = 77.16 milliroentgens per hour. Therefore, the intensity at a distance of 2.7 meters from the radiation machine is 77.16 milliroentgens per hour.
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There are 8 88 employees on The Game Shop's sales team. Last month, they sold a total of g gg games. One of the sales team members, Chris, sold 17 1717 fewer games than what the team averaged per employee. How many games did Chris sell? Write your answer as an expression
Answer:
The number of games sold by Chris = [tex](\frac{g}{8} - 17)[/tex]
Step-by-step explanation:
The total number of employees in the team = 8
The total number of games sold by the whole team = g
The number of games sold by Chris = Average Games sold by each member - 17
Now, [tex]\textrm{Average number of games sold by each} = \frac{\textrm{Total number of games sold by team}}{\textrm{Total number of people in team}}\\[/tex]
=[tex]\frac{g}{8}[/tex]
⇒The average number of games sold by each of the team member = g/8
Hence, the number of games sold by Chris = [tex](\frac{g}{8} - 17)[/tex]
Sally was shopping for a turkey tree for Thanksgiving she looked at 48 trees. Of those she found that 7/8 of them were too small. How many of the trees were too small?
Final answer:
Sally looked at 48 turkey trees and found 7/8 were too small. By multiplying 48 by the fraction 7/8, we find that 42 trees were too small.
Explanation:
The question asks us to calculate the number of turkey trees that were too small, based on the total number of trees Sally looked at and the fraction that were too small.
Sally looked at 48 trees in total and found that 7/8 of them were too small. To find the number of too small trees, we multiply the total number of trees by the fraction that were too small:
Number of too small trees = Total number of trees × Fraction too small
Number of too small trees = 48 × 7/8
Calculating this gives us:
Number of too small trees = 48 × 0.875
Number of too small trees = 42
Therefore, out of the 48 turkey trees Sally looked at, 42 of them were too small for her Thanksgiving needs.
Write an equation for the line that is parallel to the glven line and that passes
through the given point.
y = x-10;(-6, -29)
Answer:
The answer to your question is y = x - 23
Step-by-step explanation:
Process
1.- Get the slope of the line
If two lines are parallels, it means that they have the same slope.
y = 1x - 10
Slope = m = 1
2.- Get the equation of the line
y - y1 = m(x - x1)
y + 29 = 1(x + 6) Substitution
y + 29 = x + 6 Expanding
y = x + 6 - 29 Simplifying
y = x - 23
Answer:
y = x - 23
Step-by-step explanation:
All lines parallel to the given line y = x - 10 have the same slope (1), and the same form of equaiton: y = x + C, where C is a constant.
We know that the new line passes through (-6, -29). Replacing x with -6, y with -29, we get:
-29 = -6 + C, and thus we find that C = -23.
Thus, the desired equation is
y = x - 23
There are 16 cherry trees in Oliver's orchard, and he wants to plant more. It takes him an hour to plant each tree. Let h represent the number of hours Oliver spent planting and c represent the total number of cherry trees he will have.
Answer:
16+h=c
Step-by-step explanation:
A volleyball league collected $2,040 for both division of volleyball teams the blue division costs &160 per team and the red division costs $180 per team.How many teams will play in each division
Answer:
There are 6 teams will play for each team.
Step-by-step explanation:
Given;
Total amount of money = $ 2040
Cost for blue team = $ 160
Cost for red team = $ 180
Solution,
Let number of blue teams be x and the number of red teams be y.
Total cost =[tex]160x + 180y = 2040[/tex]
Since it is a league match and so both divisions must have equal teams.
∴ x=y
∴ [tex]160x + 180x = 2040[/tex]
[tex]340x = 2040\\x = 6[/tex]
Hence the number of teams in each division is 6.
A random sample of 64 bags of white cheddar popcorn weighed, on average, 5.23 ounces with a standard deviation of 0.24 ounce.
Test the hypothesis that µ = 5.5 ounces against the alternative hypothesis, µ < 5.5 ounces, at the 0.05 level of significance.
Answer:
We conclude that cheddar popcorn weighed less than 5.5 ounces.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ =5.5 ounces
Sample mean, [tex]\bar{x}[/tex] = 5.23 ounces
Sample size, n = 64
Alpha, α = 0.05
Sample standard deviation, σ = 0.24 ounce.
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 5.5\text{ ounces}\\H_A: \mu < 5.5\text{ ounces}[/tex]
We use One-tailed z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{5.23 - 5.5}{\frac{0.24}{\sqrt{64}} } = -9[/tex]
Now, [tex]z_{critical} \text{ at 0.05 level of significance } =-1.645[/tex]
Since,
[tex]z_{stat} < z_{critical}[/tex]
We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that cheddar popcorn weighed less than 5.5 ounces.
The z test is mathematically given as z=-1.86, and a>p value.
therefore we failed to accept null hypothesis.
What conclusion do we come to at the test of the hypothesis?
Question Parameters:
A random sample of 64 bags
weighed, on average, 5.23 ounces
the standard deviation of 0.24 ounce.
µ = 5.5 ounces
Generally, hypothesis is mathematically given as
H_0:\mu = 5.8 null
H_a:\mu < 5.8 alter
Using z test
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\\\z=\frac{5.74-5.8}{\frac{0.26}{\sqrt{65}}}[/tex]
z=-1.86
In conclusion,
p value = 0.0314
α = 0.10
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It’s not 3 but still need help with it
Answer:
13
Step-by-step explanation:
5-(-8)=13
Answer:
13
Step-by-step explanation:
The number line is really helpful in this case. All you have to do is count the spaces between -8, where A is, and 5, where C is. There's 13 spaces between them, therefore the length of AC is 13.
An event sold $608 worth of tickets. Adult tickets cost $11 and children's tickets cost $6. If 68 tickets were sold, how many were adult tickets and how many were children's tickets?
Answer: There were 40 adult tickets and 28 children's tickets
Step-by-step explanation:
Let x represent the number of adult tickets sold.
Let y represent the number of children's tickets sold.
An event sold $608 worth of tickets adult tickets cost $11 while children's tickets cost $6. It means that
11x + 6y = 608 - - - - - - 1
If 68 tickets were sold, it means that
x + y = 68
Substituting x = 68 - y into equation 1, it becomes
11(68 - y) + 6y = 608
748 - 11y + 6y = 608
- 11y + 6y = 608 - 748
- 5y = 140
y = 140/5 = 28
x = 68 - y = 68 - 28
x = 40
Ahab needs to mix 3.5 cups of liquid iced tea concentrate with 3 cups of water to make iced tea. Ahab has 21 cups of iced tea concentrate. How much iced tea can he make?
Answer:
39 cups
Step-by-step explanation:
If we assume that the 3.5 cups of concentrate make 3.5+3 = 6.5 cups of tea, we can use the proportion ...
6.5/3.5 = x/21
to find the x cups of tea Ahab can make with 21 cups of concentrate.
Multiplying by 21, we get ...
x = 21(6.5/3.5) = 39
Ahab can make 39 cups of tea.
Jane andre and maria pick apples .Andre picks three times as many pounds as maris .Jane picks two times as .A u pounds as andre .Tbw total weight of tbe apples is 840 pounds .How maby pounds of apples dose andre pick?
Answer: Andre picked 252 pounds of apples
Step-by-step explanation:
Let x = number of pounds of apple picked by Jane.
Let y = number of pounds of apple picked by Andre
Let z = number of pounds of apple picked by Maria
Andre picks three times as many pounds as maria. It means that
y = 3z
Jane picks two times as many pounds as Andre. It means that
x = 2y
The total weight of the apples is 840 pounds. It means that
x + y + z = 840 - - - - - - - - - 1
We will substitute z = y/3 and x = 2y into equation 1
2y + y + y/3 = 840
Cross multiplying with 3
6y + 3y + y = 2520
10y = 2520
y = 2520/10 = 252
x = 2y = 252× 2 = 504
z = y/3 = 252/3 = 84
The top and bottom margins of a poster are 4 cm and the side margins are each 5 cm. If the area of printed material on the poster is fixed at 388 square centimeters, find the dimensions of the poster with the smallest area.
Answer:
The smallest poster has dimension 25.6 cm by 32.05 cm.
Step-by-step explanation:
Let "x" and "y" be the length and the width of the poster.
The margin of a poster are 4 cm and the side margins are 5 cm.
The length of the print = x - 2(4) = x - 8
The width of the print = y - 2(5) = y - 10
The area of the print = (x- 8)(y -10)
The area of the print is given as 388 square inches.
(x-8)(y -10) = 388
From this let's find y.
y -10 = [tex]\frac{388}{(x - 8)}[/tex]
y = [tex]\frac{388}{x - 8} + 10[/tex] -------------------(1)
The area of the poster = xy
Now replace y by [tex]\frac{388}{x - 8} + 10[/tex], we get
The area of the poster = x ([tex]\frac{388}{x - 8} + 10[/tex])
= [tex]10x + \frac{388x}{x - 8}[/tex]
To minimizing the area of the poster, take the derivative.
A'(x) = [tex]10 + 388(\frac{-8}{(x-8)^{2} } )[/tex]
A'(x) = [tex]10 - \frac{3104}{(x-8)^2}[/tex]
Now set the derivative equal to zero and find the critical point.
A'(x) = 0
[tex]10 - \frac{3104}{(x-8)^2}[/tex] = 0
[tex]10 = \frac{3104}{(x-8)^2}[/tex]
[tex](x - 8)^2 = \frac{3104}{10}[/tex]
[tex](x - 8)^2 = 310.4[/tex]
Taking square root on both sides, we get
x - 8 = 17.6
x = 17.6 + 8
x = 25.6
So, x = 25.6 cm takes the minimum.
Now let's find y.
Plug in x = 25.6 cm in equation (1)
y = [tex]\frac{388}{25.6 - 8} + 10[/tex]
y = 22.05 + 10
y = 32.05
Therefore, the smallest poster has dimension 25.6 cm by 32.05 cm.
The minimum area of the poster given that the printed area is 388 sq.cm and the margins are 4cm top/bottom and 5cm on the sides, is found by using calculus and the area constraints. The problem can be solved by expressing width and height in terms of one another and then optimizing the area equation.
To solve the problem, we use calculus and the area constraint to find the dimensions with a minimum area. Let's denote that width of the poster is w and height is h. The entire area of the poster would then be expressed as:
(w+2*5cm)*(h+2*4cm) = poster area
On the other hand, we have a fixed constraint that states the printed area is 388cm², so we have:
w*h = 388 cm²
We can express h as 388/w and substitute this in the poster's area equation, and then use calculus to find the minimum area given these constraints.
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Joaquín invirtió su dinero a 12% y a 15% obteniendo unos intereses de $3000. Si las cantidades que invirtió hubieran sido intercambiadas, habría tenido un retorno de $2940. ¿Cuánto dinero invirtió a 15%?
Answer:
12,000
Step-by-step explanation:
espero que he ayudado
Suppose you and a friend each choose at random an integer between 1 and 8, inclusive. For example, some possibilities are (3,7), (7,3), (4,4), (8,1), where your number is written first and your friend’s number second. Find the following probabilities.
a. p(you pick 5 and your friend picks 8)
b. p(sum of the two numbers picked is < 4)
c. p(both numbers match)
Answer and explanation:
Given : Suppose you and a friend each choose at random an integer between 1 and 8, inclusive.
The sample space is
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) (2,8)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (3,8)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (5,7) (5,8)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (6,7) (6,8)
(7,1) (7,2) (7,3) (7,4) (7,5) (7,6) (7,7) (7,8)
(8,1) (8,2) (8,3) (8,4) (8,5) (8,6) (8,7) (8,8)
Total number of outcome = 64
To find : The following probabilities ?
Solution :
The probability is given by,
[tex]\text{Probability}=\frac{\text{Favorable outcome }}{\text{Total outcome}}[/tex]
a) p(you pick 5 and your friend picks 8)
The favorable outcome is (5,8)= 1
[tex]\text{Probability}=\frac{1}{64}[/tex]
b) p(sum of the two numbers picked is < 4)
The favorable outcome is (1,1), (1,2), (2,1)= 3
[tex]\text{Probability}=\frac{3}{64}[/tex]
c) p(both numbers match)
The favorable outcome is (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8) = 8
[tex]\text{Probability}=\frac{8}{64}[/tex]
[tex]\text{Probability}=\frac{1}{8}[/tex]
The probabilities for choosing specific integers or pairs with a particular sum between 1 and 8 are computed based on the total number of possible combinations, which is 64 (8x8).
Explanation:The probability of choosing a specific pair of integers when you and a friend each pick an integer at random between 1 and 8 can be found using the principles of probability. With 8 choices for each person, there are 64 (8 × 8) possible combinations.
P(you pick 5 and your friend picks 8): There is only 1 combination where you pick 5 and your friend picks 8 out of the 64 possible combinations, so the probability is 1/64.P(both numbers match): There are 8 combinations where both numbers match (1,1), (2,2), ..., (8,8) out of the 64 combinations, so the probability is 8/64 or 1/8.To compute the probability that the sum of the two numbers picked is < 4, notice that there are very few combinations: (1,1), (1,2), (2,1). So, P(sum < 4) is 3/64.
On Saturday,4 friends ordered a large pizza to share altogether they pay 9.80 for the pizza . They share the cost equally .How much does each person pay?
Answer:
each paid $2.45
Step-by-step explanation:
9.80/4 = 2.45
Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?(A) 11/30
(B) 9/20
(C) 3/5
(D) 11/15
(E) 5/6
Answer:
(B) 9/20
Step-by-step explanation:
The fastest machine can do 1/4 of the job in 1 hour. The second-fastest machine can do 1/5 of the job in 1 hour. Together, these two machines can do ...
(1/4) +(1/5) = (5+4)/(5·4) = 9/20
of the job in 1 hour.
9/20 of the job can be done in 1 hour by two of the machines.
Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB = 2(m∠CEA) ∠CEF is a straight angle. ∠AEF is a right angle.
The statements that must be true are:
a. m∠CEA = 90°
b. m∠CEF = m∠CEA + m∠BEF
e. ∠AEF is a right angle.
Here's why:
a. m∠CEA = 90°
The diagram shows a small square marking ∠CEA, which is the standard notation for a right angle, indicating it measures 90 degrees.b. m∠CEF = m∠CEA + m∠BEF
This statement is true by the Angle Addition Postulate, which states that the measure of an angle formed by two adjacent angles is equal to the sum of their individual measures. In this case, ∠CEF is formed by ∠CEA and ∠BEF, so its measure is the sum of their measures.c. m∠ CEB = 2(m∠ CEA)
This statement is not true. Since EB bisects ∠CEA, it divides it into two equal angles, meaning m∠CEB = m∠CEA, not twice its measure.d. ∠ CEF is a straight angle.
This statement is not necessarily true. A straight angle measures 180 degrees, and we don't have enough information to determine if ∠CEF has that measure.e. ∠ AEF is a right angle.
This statement is true. Since EB bisects ∠CEA, which is a right angle, it creates two right angles: ∠CEB and ∠AEF.you guysss pls help me
Answer:
option B)[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
According to the given conditions, the total number of outcomes are 24.
The probability that of drawing hearts card is
P=[tex]\frac{(total number of hearts cases)}{(total number of cases)}[/tex]
total number of hearts cases= 6
thus P= [tex]\frac{6}{24} = \frac{1}{4}[/tex]
now the probability of 4 or 6 is,
P=[tex]\frac{(total number of 4 or 6 cases)}{(total number of cases)}[/tex]
thus P= [tex]\frac{8}{24} = \frac{1}{3}[/tex]
thus, by multiplication law,
final probality is P= [tex](\frac{1}{4})(\frac{1}{3})[/tex]
P= [tex]\frac{1}{12}[/tex]
7x-9-11=3x+4+2x
how did u get 12?
Answer:
x = 12
Step-by-step explanation:
Given expression is \[7x-9-11=3x+4+2x\]
Simplifying: \[7x -(9+11) = (3x+2x)+4\]
Or, \[7x - 20 = 5x + 4\]
Bringing all terms containing x to the left side of the equation and all the numeric terms to the right side:
\[7x-5x = 20 + 4\]
=> \[(7-5)x = 24\]
=> \[2x = 24 \]
=> x = \[\frac{24}{2}\]
=> x= 12
Hence the value of x which satisfies the given equation \[7x-9-11=3x+4+2x\] is 12
circles pls help decent amount of points
Help me please!!
Find x
Check the picture below.
About how many cubes were used to make this figure? A. about 40 B. about 70 C. about 100 D. about 140
Answer:
Around 100,i.e. 105
Step-by-step explanation:
In the given cube
Length of the cube = 7 unit cells
Breadth of the cube = 3 unit cells
Height of the cube = 5 unit cells
Therefore the number of unit cubes required to make such big cube is nothing but the volume of the big cube = length*breadth*height
⇒Number of cubes used to make that big cube= 7*5*3
= 105
Hence, option D (around 100) is the correct answer
Can someone answer this question correctly please don't answer if you don't know the answer and please show work I need it right now please : )
Answer:
The result is [tex]-\frac{371}{6}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{7}{-2.5+8.5}+\frac{0.6(8+13)}{-0.2}[/tex]
First, we solve the denominator of the left-hand fraction
[tex]\frac{7}{6}+\frac{0.6(8+13)}{-0.2}[/tex]
Then we find the sum in the numerator of the right-hand fraction
[tex]\frac{7}{6}+\frac{0.6(21)}{-0.2}[/tex]
Now we solve the second fraction
[tex]\frac{7}{6}-63[/tex]
The final result is the subtraction of both expressions
[tex]-\frac{371}{6}[/tex]
The volume of a cylinder is 4x3 cubic units and its height is x units.
Which expression represents the radius of the cylinder, in units?
2x
4x
2pi x²
4pi x2
Answer:
The answer to your question is r = 2x
Step-by-step explanation:
Volume of a cylinder = V = π r² h
r = radius
h = height = x
Volume = 4x³
Then
r² = [tex]\frac{volume}{\pi h}[/tex]
r² = [tex]\frac{4x^{3} }{\pi x}[/tex]
r² = 4x²
r = 2x
Numbers from zero to nine are individually selected at random and combined to make a code that contains a six-digit number. Numbers can be repeated. If you were given ten tries to guess the code what would be the probability of guessing the correct code? Give you answer as a fraction. Do not include commas in your answer, for example, 31,000 would be written as 31000.
The probability of guessing correctly within ten tries is 10/1,000,000, simplifying to 1/100,000.
Explanation:This problem is related to probability. The total number of ways to form a six-digit code with numbers from 0 to 9, where numbers can be repeated, is 10^6 because there are 10 possible choices for each of the 6 places. Thus there are 1,000,000 possible codes.
The probability of you correctly guessing the code on any one try would then be 1/1,000,000. If you try ten times, each attempt independent of the others, you still have a 1/1,000,000 chance each try. Combining these ten independent events, the total probability of guessing the correct code in ten tries would be 10/1,000,000.
Therefore, your probability is 10/1,000,000, which simplifies to 1/100,000.
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Show your work to prove that the inverse of f(x) is g(x).
[tex]f(x) = \frac{x+9}{4}\\g(x)=4x-9[/tex]
Answer:
Below.
Step-by-step explanation:
If g(x) is the inverse of g(x) then g(f(x)) = x.
g(f(x)) = 4 (x + 9)/ 4 - 9
= x + 9 - 9
= x.
So it is the inverse.
Also if you find f((g(x)) it is also = to x.
A simple random sample of size nequals=8181 is obtained from a population with mu equals 77μ=77 and sigma equals 27σ=27. (a) Describe the sampling distribution of x overbarx. (b) What is Upper P (x overbar greater than 81.5 )P x>81.5? (c) What is Upper P (x overbar less than or equals 69.5 )P x≤69.5? (d) What is Upper P (73.4 less than x overbar less than 84.05 )P 73.4
Answer:
a) [tex]P(\bar X>81.5)=1-0.933=0.067[/tex]
b) [tex]P(\bar X<69.5)=0.0062[/tex]
c) [tex]P(73.4<\bar X<84.05)=0.8755[/tex]
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:
[tex]X \sim N(\mu=77,\sigma=27)[/tex]
And let [tex]\bar X[/tex] represent the sample mean, the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
On this case [tex]\bar X \sim N(77,\frac{27}{\sqrt{81}})[/tex]
Part a
We want this probability:
[tex]P(\bar X>81.5)=1-P(\bar X<81.5)[/tex]
The best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we apply this formula to our probability we got this:
[tex]P(\bar X >81.5)=1-P(Z<\frac{81.5-77}{\frac{27}{\sqrt{81}}})=1-P(Z<1.5)[/tex]
[tex]P(\bar X>81.5)=1-0.933=0.067[/tex]
Part b
We want this probability:
[tex]P(\bar X\leq 69.5)[/tex]
If we apply the formula for the z score to our probability we got this:
[tex]P(\bar X \leq 69.5)=P(Z\leq \frac{69.5-77}{\frac{27}{\sqrt{81}}})=P(Z<-2.5)[/tex]
[tex]P(\bar X\leq 69.5)=0.0062[/tex]
Part c
We are interested on this probability
[tex]P(73.4<\bar X<84.05)[/tex]
If we apply the Z score formula to our probability we got this:
[tex]P(73.4<\bar X<84.05)=P(\frac{73.4-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{84.05-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]
[tex]=P(\frac{73.4-77}{\frac{27}{\sqrt{81}}}<Z<\frac{84.05-77}{\frac{27}{\sqrt{81}}})=P(-1.2<z<2.35)[/tex]
And we can find this probability on this way:
[tex]P(-1.2<z<2.35)=P(z<2.35)-P(z<-1.2)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-1.2<z<2.35)=P(z<2.35)-P(z<-1.2)=0.9906-0.1151=0.8755[/tex]