The distribution of random variable r has mean 10 and standard deviation 4. The distribution of random variable s has mean 7 and standard deviation 3. If r and s are independent, what are the mean and standard deviation of the distribution of r−s ?.
If [tex]X,Y[/tex] are independent, we have the properties for expectation and variance,
[tex]\Bbb E[aX + bY] = a\,\Bbb E[X] + b\,\Bbb E[Y][/tex]
[tex]\Bbb V[aX + bY] = a^2\,\Bbb V[X] + b^2\,\Bbb V[Y][/tex]
where [tex]a,b\in\Bbb R[/tex] are fixed.
Then
[tex]\Bbb E[R - S] = \Bbb E[R] - \Bbb E[S] = 10 - 7 = \boxed{3}[/tex]
and
[tex]\Bbb V[R - S] = \Bbb V[R] + (-1)^2\, \Bbb V[S] = 4^2 + 3^2 = \boxed{5}\,{}^2 = 25[/tex]
(recall that standard deviation = √(variance))
10 ≤ 3x + 4 < 25
How do I solve
Answer: 2 ≤ x < 7
Step-by-step explanation:
10 ≤ 3x + 4 < 25 ==> solve for x, so work to isolate the x variable
10-4 ≤ 3x + 4-4 < 25-4
6 ≤ 3x < 21
6/3 ≤ 3x/3 < 21/3
2 ≤ x < 7
Answer:
I believe it's [2, 7). It has to be solve differently.
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GO Practice
Spiral Review Extra Practice
2. The table shows the time it took for Javier to
complete one repetition of different
exercises during his Monday workout.
.
Exercise
Squats 0.08
Crunches 0.03
Lunges 0.04
Curts 0.05
Javier likes to work out for 1 hour. If he
doesn't use the full hour on his exercises, he
runs on a treadmill for the remaining time. If
he completed 3 repetitions of each exercise,
how long did he run on the treadmill on
Monday? I need explication step bu step
Using the addition of all the exercise, Javier runs on the treadmill on Monday is 0.40 hours.
What is addition?Addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Given that Javier completed 3 repetitions of each exercise. thus by multiplication time taken by Javier to complete each exercise is as follows;
Squats = 0.8 x 3= 0.24 hour
Crunches = 0.03 x 3 = 0.09 hour
Lunges = 0.04 x 3 = 0.12 hour
curls = 0.05 x 3 = 0.15 hour
we can calculate the total time taken to complete all exercises as;
0.24 + 0.09 + 0.12 + 0.15
= 0.60 hour
Now the time took on treadmill by Javier;
1 hour - 0.60 hour
0.40 hour
Hence, If he completed 3 repetitions of each exercise, then he run 0.40 hours on the treadmill on Monday.
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Nora left her house and drove to the store. She stopped and Went inside . From there, she drove in the same direction until she got to the bank. She stopped it and went inside the bank. Then she drove home. The graph below shows the number of blocks away from home Nora in X minutes after after she left her house, until she got back home. How long was Nora in the bank
Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the
GFDT below.
Lengths (mm)
Frequency
220 - 229
1
230 239
16
240 - 249
71
250 - 259
108
260 - 269
83
270 - 279
18
280 289
3
What is the lower class boundary for the first class?
class boundary =
Answer:
330-339
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An isosceles triangle has at least two congruent sides. The perimeter of a certain isosceles triangle is at
most 12 in. The length of each of the two congruent sides is 5 in. What are the possible lengths of the
remaining side?
x ≤ 2 but must be greater than 0 . triangles are the possible lengths of the remaining side.
How is an isosceles triangle defined?
Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal.The length of one of the congruent side is 5
The total length of two congruent sides is 10
Perimeter at the most is 12 (meaning the maximum length of perimeter is 12)
The third side of the triangle must be 12-10 = 2 at the most
Writing this requirement as inequality we have
x ≤ 2 but must be greater than 0
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is this a function or not explain why
I WILL GIVE BRAINLIEST!!!
Please help me.
Translate all word problems into equations.
You only need to give equation+answer for number 7 and 9.
7. Between noon and midnight, the temperature
dropped 20°F. If the temperature was -8°F at
midnight, what was the temperature at noon?
8. If a strawberry pie is divided into 6 equal slices, each
slice has 240 calories. How many calories are in the
whole pie?
9. A chest was resting on the ocean floor 1000 ft below
the surface. It was lifted to the deck of a ship 8 ft
above the surface. How far was the chest lifted?
10. When all the kids who tried out for Little League
were divided into teams of 20 players, there were
exactly 8 teams. How many kids tried out?
Step-by-step explanation: They are word problems into equations. Have a good night. you will get them right.
7.) x - 20 = -8
8.) x/6 = 240
9.) - 1000 + x = 8
10.) x/20 = 8
Find the distance between
the two points rounding to the nearest tenth (if necessary).
(8, 7) and (1, -2)
Answer: 11.4
Step-by-step explanation:
Help If u can please show ur work thank you
Answer:
Step-by-step explanation:
What is the greatest common factor of 44 and 22?
Answer:
The greatest common factor of 44 and 22 is 22.
Step-by-step explanation:
First, you should list all the factors of 44 and 22. For 44, the factors are: 1, 2, 4, 11, 22 and 44
For 22, the factors are: 1, 2, 11 and 22
The greatest common factor is 22.
Answer: 22
Step-by-step explanation:
In order to find GCF of 44 and 22, take the prime factorization of the two numbers
22: 11*2
44: 11*4=11*2*2
Notice they both have 11*2 in their prime factorization.
11*2=22
GCF of 44 and 22 is 22
The use of electricity in the US in 1902 was 6.03 x 10^9 kilowatt-hours.
The use of electricity in the US in 1950 was 4.3 x 10^11 kilowatt-hours.
How many times more was the electricity used in 1950 than 1902? Express your answer in Scientific Notation.
a. 7.131 x 10
b. 10.33 x 10^20
c. 1.73 x 10^2
d. 2.6 x 10^20
Using scientific notation , the electricity used in 1950 was 7.131 × 10¹ times more than that used in 1902 .
Values that are either too huge or too little to be conveniently expressed in decimal form can be expressed using scientific notation (typically would result in a long string of digits). It is also referred to as scientific form, standard index form, and standard form in the UK. This base ten notation is often used by scientists, mathematicians, and engineers because it can make various mathematical procedures easier.
One can represent exceedingly large or extremely small quantities using scientific notation. In scientific notation, the result of multiplying an integer between 1 and 10 by a power of 10 is written. For instance, in scientific notation, 35,000,000 can be written as 3.5× 10⁷.
Given that the use of electricity in the US in 1902 was 6.03 x 10⁹kilowatt-hours and the use of electricity in the US in 1950 was 4.3 x 10¹¹ kilowatt-hours.
These are both represented in scientific notation.
Now we have to divide to find the number of times more electricity is used.
(4.3 x 10¹¹) ÷ (6.03 x 10⁹)
= 71.31011...
≈ 7.131 × 10¹
Hence the scientific representation is given by 7.131 × 10¹ times.
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walter, agnes, and holly are making beaded lizards. walter has 476 green beads and 32 red beads. agnes has 104 green beads and 16 red beads. holly has 281 green beads and 80 red beads. they all share their beads so as to make the largest possible number of lizards. if a beaded lizard requires 94 green beads and 16 red beads, what is the number of green beads left over?
The number of green beads left over = 15
Walter:
Number of green beads = 476
Number of red beads = 32
Agnes:
Number of green beads = 104
Number of red beads = 16
Holly:
Number of green beads = 281
Number of red beads = 80
Total number of red beads = 32+16+80 = 128 beads
Number of red beads required for making one lizard = 16
Since 128/16 = 8 , there will be no red beads left after making 8 lizards.
Total number of green beads = 476+104+281 = 861 beads
Number of green beads required for making one lizard = 94
Now 861/94 = [tex]9\frac{15}{94}[/tex]
That is , 15 is the remainder when 861 is divided by 94
So there will be 15 green beads left after making 9 lizards.
Therefore, the number of green beads left over = 15
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Which expression is equivalent to
3√50 x √22
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
lets solve ~
[tex]\qquad \sf \dashrightarrow \: 3 \sqrt{50} \times \sqrt{22} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \sqrt{2 \times 5 \times 5} \times \sqrt{2 \times 11} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \sqrt{2 \times 2 \times 5 \times 5 \times 11} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \times 2 \times 5 \times \sqrt{11} [/tex]
[tex]\qquad \sf \dashrightarrow \: 30 \sqrt{11} [/tex]
a box has four cards numbered 1, 2, 3, and 4. greg will toss a coin once and record the toss as heads (h) or tails (t). then he will randomly pick a card from the box and record the number chosen. give the sample space describing all possible outcomes. then give all of the outcomes for the event that the number chosen is 3. use the format h1 to mean that the coin toss is heads and the number chosen is 1. if there is more than one element in the set, separate them with commas.
Sample space when a coin is tossed is {H, T}
Sample space for drawing a card is {1, 2, 3, 4}
Sample space = {H1, H2, H3, H4, T1, T2, T3, T4}
Event that the coin toss is tails = {H1, H2, H3, H4}
The sample space describing all possible outcomes are (H1, H2, H3, H4, T1, T2, T3, T4).
What do you mean by fair coin?A series of independent Bernoulli trials with a chance of 1/2 on each trial is referred to as a fair coin in probability theory and statistics. A biased or unjust coin is one for which the probability is not equal to one-half.
The presumption that a coin is fair is sometimes made by making reference to an ideal coin in theoretical investigations. When John Edmund Kerrich experimented with flipping coins, he discovered that 679 times out of 1000, a coin fashioned of a wooden disc the size of a crown that was coated with lead on one side landed heads (wooden side up).
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image below, what are the domains and ranges?
Answer:
1. domain: -6 ≤ x ≤ 7
range: -6 ≤ y ≤ 4
2. domain: 5 > x
range: -5 < y
Step-by-step explanation:
1. domain: the farthest number left that the line reaches is -6, while the farthest right is 7. due to the line being closed as well as the points being filled in, you use the less than or equal to sign.
range: the farthest number down that the line reaches is -6, while the farthest is goes up is 4. again, since the points are filled in, you use the "or equal to" sign.
2. domain: since the only plotted point is 5, and the point is not filled in, you would say that 5 is greater than x due to the direction that the line moves
range: the lowest part of the line touches -5 and only goes up from there, therefore y is greater than -5
in the month of januray, i were able to sell 1,200 desserts. In februaryc, your dessert sales increased to 1,500. What is the percent of change
The increment in the percentage of dessert sales will be 25%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
I was able to sell 1,200 desserts throughout the month of January. Your dessert sales jumped to 1,500 in February.
Then the increment in the percentage will be given as,
P = [(1500 - 1200) / 1200] x 100
P = (300 / 1200) x 100
P = 0.25 x 100
P = 25%
The increment in the percentage of dessert sales will be 25%.
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i need help
sum body help
Answer:
p = independent
t = dependent
The amount of hired truckers will depend on the amount of produce that has to be shipped from California to New York.
Hope this helps :)
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $65 to come to his house and $55 for every hour they work. If the plumber charges Jerald a total of $296, how many hours did the plumber work? Write and solve an equation to determine the number of hours worked by the plumber.
A 55x − 65 = 296; x = 6.6 hours
B 55x + 65 = 296; x = 4.2 hours
C 65x − 55 = 296; x = 5.4 hours
D 65x + 55 = 296; x = 3.7 hours
Answer:
B 55x + 65 = 296; x = 4.2 hours
Step-by-step explanation:
The equation to determine the number of hours worked by the plumber is 65 + 55x = 296.
The number of hours worked by the plumber is 4.2
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Charges for home visit = $65
Charges for each hour = $55
Let the number of hours = x
Total charges = $296
We can make an equation:
65 + 55x = 296
The number of hours can be calculated.
65 + 55x = 296
Subtracting 65 on both sides.
65 + 55x - 65 = 296 - 65
55x = 231
Dividing both sides by 55.
x = 231 / 55
x = 4.2
Thus,
The equation to determine the number of hours worked by the plumber is 65 + 55x = 296.
The number of hours worked by the plumber is 4.2
Option B is the correct answer.
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17+|-12--5|--6
show how you got the answer
Answer:
I'm assuming the double minus marks meant 5 and 6 were negative. Answer is 30.
Step-by-step explanation:
[tex]17+\abs(-12--5)-(-6)\\17+\abs(-12+5)-(-6)\\17+\abs(-7)-(-6)\\17+7-(-6)\\17+7--6\\24--6\\24+6\\30[/tex]
Answer:The answer would be 28
Step-by-step explanation:17-6 is 11
The absolute value of -12-5 is 17
17+11=28
So therefore the answer would be 28.
State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
Answer:
E
Step-by-step explanation:
You already know that TS = AB and TU = BC because it shows that in the images using the tick marks. SSS Triangle Congruence Postulate is when two triangles are congruent to each other because all the corresponding side lengths are equal to each other. So we already have two side lengths that are equal to each other, and, in order for SSS to be true, we need all 3 side lengths to be equal to each other. The only two side lengths not equal to each other yet are US and CA so if those were to be equal to each other, all corresponding side lengths would be equal to each other.
Let me know if you have any questions.
the meteorologist made a forecast that a cold front was coming through and the temperature would steadily drop 24.8 degrees over the next six and one fourth hours. how much did the temperature drop each hour? 39.68 degrees 3.968 degrees 31.05 degrees 18.55 degrees
The temperature drop is B. 3.968 degrees each hour.
What is the temperature drop calculated?The temperature drop per hour can be computed by dividing the total temperature drop by the number of hours over which the temperature dropped.
Data and Calculations:The total steady drop in temperature = 24.8 degrees
Total number of hours for the temperature drop = 6¹/₄ hours
6¹/₄ hours = 6.25 hours
Temperature drop per hour = total drop/total hours of drop
= 2(4.8 ÷ 6¹/₄ hours)
= 3.968 degrees
Thus, the temperature drop is B. 3.968 degrees each hour.
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give an example of 2 inequalities that are equivalent inequalities
-4x < or = to -1 and x > or = 1/4
Explation
-4x/4 < or = to -1/-4 x > or = to 1/4find the length s of the arc that subtends a central angle of measure 6 rad in a circle of radius 4 cm.
The length of the arc for the given circle is 24cm.
What is the length of an arc of a circle?The Arc length refers to the distance between two points on a section of a curve or a circle.Length of the arc (L) = r Θ, where r = radius of the curve, Θ = angle subtended by the arc at the centre of the curve in radians.Given:
Angle = 6 radians = ΘRadius of circle = 4cm = rTo find: Length of the arc.
Finding:
On substituting the values of r and Θ in the formula of length of the arc, we get:
L = 4(6) = 24 cm.
Hence, the length of the arc for the given circle is 24cm.
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Which system of linear inequalities is represented by the graph?
y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x +
The system of linear inequalities is represented by the graph is y > x – 2 and y < x + 1.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
The given options are,
y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x + 1
Since,
The linear equation of a straight line is
y = mx + c,
where m is the gradient or slope, and
y = c is the value where the line cuts the y-axis.
The formula for slope of line with points (x1,y1) and (x2,y2) can be expressed as,
m = (y2 - y1) / (x2 - x1)
Now from y > x – 2 and y < x + 1
the first line passes through (0, 1) and (0, -1)
So,slope m = (0 - 1) / (0 - 1)
⇒ m = 1
Now the line intercept y-axis at (1, 1)
So, c = 1
So,equation of line is given as,
y < x + 1
the second line passes through (0, 2) and (0, -2)
So,slope m = (0 - 2) / (0 - 2)
⇒ m = 1
Now the line intercept y-axis at (-2, 0)
So, c = -2
So,equation of line is given as,
y < x - 2
So, we get y > x – 2 and y < x + 1.
Thus, the system of linear inequalities is represented by the graph is y > x – 2 and y < x + 1.
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The missing graph of the question is attached.
if you draw two cards from a deck, what is the probability that you will get the ace of diamonds and a black card?
The probability that the ace of diamonds and a black card will come is 1 / 51 .
Case A :
probability of first getting an ace of diamonds = 1 / 52
probability of getting a black card given first card is ace of diamond = 26 / 51
Hence , probability that the ace of diamonds and a black card will come is ( 1 / 52 ) * ( 26 / 51 ) = ( 1 / 102 )
Case B :
probability of first getting a black card = ( 26 / 52 )
probability of getting an ace , given first card is a black card = ( 1 / 51 )
Hence , the probability that the ace of diamonds and a black card will come is ( 26 / 52 ) * ( 1 / 51 ) = ( 1 / 102 )
P ( A ∪ B ) = P ( A ) + P (B ) + P ( A ∩ B )
= ( 1 / 102 ) + ( 1 / 102 )
= 1 / 51 .
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Laura invests £1290 in a bank account.
The account gathers compound interest at a rate of
0.5% per month.
How much money will be in the account after 8 months?
Give your answer in pounds to the nearest 1p.
Answer: £1342.5
Step-by-step explanation:
y = a(1 + R)^n
y = 1290(1 + 0.005)^8
y ≈ 1342.51
∴ £1342.5
Last week, Pablo drove 115 miles. This week, he drove k miles. Using k, write an expression for the total number of miles he drove in the two weeks. 2-Step Equation find me an answer or sum, and givve me 5 stars.
The expression for the total number of miles Pablo drove in the two weeks is (115+k) miles.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that Last week, Pablo drove 115 miles. This week, he drove k miles. Therefore, the total number of miles for which Pablo drove can be written as,
Total number of miles = Number of miles last week + Number of miles this week
= 115 miles + k miles
= (115 + k) miles
Hence, the expression for the total number of miles Pablo drove in the two weeks is (115+k) miles.
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Tim (t), isaac (i), and hannah (h) all sell individual insurance policies. isaac sells four times as much as tim, and hannah sells three times as much as isaac. create an equation in terms of tim (t) in order to find the portion he sells.
Using proportions, the equation in terms of Tim is given by:
T(t) = 17t.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we have that:
Isaac sells four times as much as Tim, hence I = 4t.Hannah sells three times as much as Isaac, hence H = 3I = 3 x 4t = 12t.Hence the total amount, as a function of Isaac's amount, is given by:
T(t) = I + H + t
T(t) = 4t + 12t + t
T(t) = 17t.
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In a proportional relationship when x=6 we know that y=14
Answer:
Given that y varies proportionally with x , with a constant of proportionality k=13 , find y when x=12 .
Write the equation of the proportional relationship.
The variable x varies proportionally with y with a constant of proportionality equal to 13
So,
Substitute the given x value.
Step-by-step explanation: