Answers
Given
[tex]S=\mleft\lbrace1,2,3,4,5,6,7,8,9\mright\rbrace[/tex]by selecting two numbers from S, the number of possible outcomes is
[tex]n(S)=9\times9=81[/tex]Let E be the event that selecting two numbers randomly and their sum is 12 with replacement.
[tex]E=\lbrack(3,9),(4,8),(5,7),(6,6),(7,5),(8,4),(9,3)\}[/tex][tex]n(E)=7[/tex]The probability is
[tex]P(E)=\frac{n(E)}{n(S)}[/tex]Substitute values, we get
h is
[tex]P(E)=\frac{7}{81}[/tex]b)without replacement
Areplacementout
[tex]A=\mleft\lbrace(3,9\mright),(4,8),(5,7),(7,5),(8,4),(9,3)\}[/tex][tex]n(A)=6[/tex][tex]P(A)=\frac{n(A)}{n(S)}[/tex]Substitute the values, we get
[tex]P(A)=\frac{6}{81}=\frac{2}{27}[/tex]The probability that the sum is 12 if selecting two numbers without replacement
[tex]P(A)=\frac{2}{27}[/tex]Related Questions
please help me solve these as much as possible urgent neeeddd.
i think its easy but im just not smart
solve as many as you can. one is enough (but more is better)
Answers
Answer:
7. 45
8. 19
9. 15
10. 24
11. 23
12. 6
13. 8
14. 15
15. 12
16. 3
17. 26
18. 12
19. 21
20. 34
21. 2
hope this helps!:)
The graph of y = f(x) is shown below. Find all values of x where f(x) = 0
Answers
The values of x when f(x) = 0 are 2 and 8
Graphs are used mostly to show the relationship between two variables (usually x and y).
The graph of y = f(x) is attached
To get the values of x when f(x) = 0 , we consider where the line of the graph crosses the x-axis.
The graph crosses the x-axis at:
x = 2
x = 8
This means that the values of x when f(x) = 0 are 2 and 8
Therefore, in the graph of y = f(x), the values of x where f(x) = 0 are 2 and 8
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Disclaimer : The question mentined is not provided with a graph, the above solution is done as per the graph attached.
A company takes 16 minutes to wash 24 cars. How many cars can be
washed in 1 minute?
Answers
Answer:1.5 cars can be washed in 1 minute but realistically only 1 car can be washed
Step-by-step explanation: 24/16 =1.5 and that get you your answer of 1.5 but the correct answer is 1.5 or 1 depending on if they are asking you to round down or not.
Write equations for the vertical and horizontal lines passing through the point (-9, 5).
Answers
Answer:
the vertical line is:
x = 5
The horizontal line is:
y = -9
Step-by-step explanation:
A vertical line has a fixed x-value, while a horizontal line has a fixed y-value.
Then we can write a vertical line as:
x = a
and a horizontal line as
y = b
Then, if we want a vertical line that passes through the point (5, -9), remember that the x-vale will be fixed, then we fix the x-value at the same x-value of the point, which we know that is 5, then the vertical line that passes through the point (5, -9) is:
x = 5
Step-by-step explanation:
what is 10.88+10.88+10.88
Answers
Answer:
32.64
Step-by-step explanation:
9. The amount of water used by a washing
machine varies directly with the weight of the
load being washed. The washing machine uses
28 gallons to wash 7 pounds of clothing. How
many gallons of water will the machine
use to wash 24.5 pounds of laundry?
Answers
The machine will use 90 gallons of water to wash 24.5 pounds of laundry.
What is Direct Variation?If two quantities change by the same amount, they are said to follow a direct variation. As a result, when one quantity changes, the other follows suit, increasing when the first increases and decreasing when the first decreases. To put it another way, two quantities are said to be directly proportional to one another if the ratio of the first to the second is a constant term. The coefficient or constant of proportionality is the name given to this constant quantity. Assuming that x and y are two quantities that are directly varying, they are stated as follows:y ∝ x
Consequently, y = kx, where k is the proportionality constant.
Given:
The amount of water used by a washing machine varies directly with the weight of the load being washed.
Let's assume,
The amount of water used by a washing machine is y.
The weight of the load being washed is x.
According to the question,
y = 28 gallons
x = 7 pounds
Putting the values we get,
y = kx
28 = k × 7
k = 4
Now, we have to find y when x = 24.5
y = 4 × 24.5 = 98
Hence the machine will use 90 gallons of water to wash 24.5 pounds of laundry.
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Mr. Mole left his burrow and started digging his way down.
AAA represents Mr. Mole's altitude relative to the ground (in meters) after ttt minutes.
A=-2.3t-7A=−2.3t−7A, equals, minus, 2, point, 3, t, minus, 7
How fast did Mr. Mole descend?
Answers
Mr mole descend at the rate of 2.3 meters per minutes.
A rate in mathematics is the comparison of two related values expressed in dissimilar units.
The numerator of the ratio expresses the equivalent rate of change in the other (dependent) variable if the denominator of the ratio is presented as a single unit of one of these quantities and it is expected that this number may be altered systematically (i.e., is an independent variable).Examples of rates that are usually represented as "per unit of time" are speed, heart rate, and flux. An example of a ratio having a non-time denominator is the electric field ratio. Other examples include exchange rates and literacy rates (in volts per meter).The given equation to represent the position of Mr. Mole is
A = -2.3 t - 7
where A denotes the depth and t is the time.
Now the rate can be found out by dividing the change in depth by the change in time.
Differentiating we get
ΔA = -2.3 Δt
or, ΔA / Δt = -2.3
hence the rate of the mole is 2.3 meters per minutes.
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Customer number two gives you a
15% off coupon. What is the new cost
of the order? 11.50
Answers
Answer:
$8.50 ? let me know if im wrong
Step-by-step explanation:
Name the subset of the real numbers to which each number belongs 2/3
Answers
The given number 2/3 belongs to the subset of rational numbers.
What are subsets?
All numbers on the number line, from negative to plus infinity, are considered to be real numbers. They are breaking up into the following groups:
1. We can count the components of a set using natural numbers.
2. Natural numbers and their opposites in the negative, such as zero, are known as integers.
3. Fractions can be used to express rational numbers.
4. Non-periodic infinite decimals are indicative of irrational quantities.
The answer to the given question is : It belongs to the rational numbers because it is a fraction.
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I need to make sure these are correct thank you in advance!
Answers
Using the unit rate, the graphs that best represent the amount they earn for different amount of time is: C.
How to Interpret the Slope?The slope of a graph can be interpreted as the unit rate of the scenario that is being represented by the graph. For example, money earned in dollars per hour worked is the unit rate or slope of the graph given in this scenario.
The larger the unit rate value, the steeper the slope of the line of the graph.
Let Lin's unit rate be represented as x, therefore,
Lin's unit rate = x
Diego's unit rate = 2x
Jada's unit rate = 2(2x) = 4x
This shows that unit rate of Jada is the highest, and therefore, the graph that would represent how much Jada earns would be the steepest, followed by Diego's, and the least is Lin's.
Therefore, the all the graphs would be: C.
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The mean of five numbers is 8.2. Four of the numbers are 8, 10, 12 and 10.
Work out the fifth number.
Answers
Answer:
1
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
let x be the fifth number , then
[tex]\frac{8+10+12+10+x}{5}[/tex] = 8.2 ( multiply both sides by 5 to clear the fraction )
40 + x = 41 ( subtract 40 from both sides )
x = 1
the fifth number is 1
An artist has been commissioned to make a stained glass window in the shape of a regular octagon. the octagon must fit inside an square space. determine the length of each side of the octagon. round to the nearest hundredth of an inch.
Answers
Using an assumed value that the octagon must fit inside an 11 inch square space, tthe length of each side of the octagon would be 8.23 inches.
Since an assumed side of the square is 11 inches
Here, y is the two equal sides of the right-angle triangle
So y + x + y = 11
Using Pythagoras's theorem for the right angle triangle
y² + y² = x²
2y² = x²
y² = (x²)/2
y = x /√2
So substitute the value of y = x /√2 in the equation
x /√2 + x + x /√2 = 11
2x /√2 + x = 11
2x /√2 + x√2 /√2 = 11
x[2/√2 + √2 /√2] = 11
x[(2 + √2) /√2] = 11
x(2 + √2) = 11√2
x = 11√2/(2 + √2)
x = 15.5563/3.4142 = 12.1421
Round to the nearest hundredth of an inch
x = 12.1
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There are 80 houses in the neighborhood 1/4 of the houses have a chain-link fence in the backyard 2/5 of the houses have a privacy fence in the backyard the rest of the houses have no fence how many houses have no fence in the backyard
Answers
Based on the number of houses in the neighborhood and those that have a chain-link fence and a privacy fence, the number of houses with no fence in the backyard are 28 houses
How to find the number of houses with no fence?First, find the number of houses in the neighborhood that have a chain-link fence:
= Number of houses x Proportion with a chain-link fence
= 80 x 1/4
= 20 houses
Then find the number of houses in the neighborhood that have a privacy fence:
= Number of houses x Proportion with a privacy fence
= 80 x 2/5
= 160 / 5
= 32 houses
The number of houses in the neighborhood that have no fence is:
= Total number of houses - Houses with a chain-link fence - Houses with a privacy fence
= 80 - 20 - 32
= 28 houses with no fence
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Which equation has the correct sign on the product?
OA. (-8)(-8)= -64
OB. (-18)4 = -72
OC. 13-3-39
OD. 45(-4)= 180
Answers
Evaluate the following expressions.
Answers
Answer:
[tex]a.[/tex] [tex]\frac{49}{50}[/tex]
[tex]b.[/tex] [tex]8[/tex]
Step-by-step explanation:
[tex]a.[/tex] [tex]\frac{1}{2} +\frac{2}{5} +\frac{2}{25}[/tex]
To solve this, we must first find the LEAST COMMON MULTIPLE (LCM).
To find the LCM, we must list the multiples of the denominators, then find the smallest multiple that all three numbers have in common.
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
25: 25, 50
The LCM is 50.
Now that we have found the LCM, we will change the fractions so that all three have a denominator of 50.
To do this, we multiply the numerator and the denominator by the same number.
[tex]\frac{1}{2} *\frac{25}{25} =\frac{25}{50}[/tex]
[tex]\frac{2}{5} *\frac{10}{10} =\frac{20}{50} \\[/tex]
[tex]\frac{2}{25} *\frac{2}{2} =\frac{4}{50}[/tex]
Now that all fractions have the same denominator, we can add them. Remember, when adding fractions, the denominators stay the same. Only add the numerators.
[tex]\frac{25}{50} +\frac{20}{50} +\frac{4}{50} \\\\=\frac{49}{50}[/tex]
_______________________________________________________
[tex]b.[/tex] [tex]\frac{2}{3} *\frac{30}{7} *\frac{14}{5}[/tex]
To multiply fractions, multiply the numerators, then the denominators. Lastly, simplify the product.
[tex]2*30*14=840\\3*7*5=105[/tex]
[tex]\frac{840}{105} =\frac{8}{1}[/tex]
Help and please explain how answer is right
Answers
The new conditional statement that follows from the pair of true statement is If 4x + 5 = 13; then -5x = -10
What is law of syllogism?The law of Syllogism states that if the following two statements are true:
Statement 1: If x , then y
Statement 2: If y , then z
Then we can derive a third true statement:
Statement 3: If x , then z
From the given;
Statement 1: If x , then y
If 4x + 5 = 13; then x = 2
Statement 2: If y , then z
If x = 2; then -5x = -10
Statement 3: If x , then z
If 4x + 5 = 13; then -5x = -10
In conclusion, according to the law of Syllogism, the statement that follows from the pair of true statement is If 4x + 5 = 13; then -5x = -10
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- 1 2/5 - 3 1/3. Please help.
Answers
Answer:
-4 11/15
Step-by-step explanation:
Lisa spent $27 on fruit at the grocery store. She spent a total of $30 at the store. What percentage of the total did she spend on fruit?
Answers
Lisa spent 90% of the total money on the fruits.
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Given is Lisa spent $27 on fruits at the grocery store. She spent a total of $30 at the same store.
Money spent by Lisa on fruits = $27
Total money spent by Lisa = $30
Therefore, percentage of the total money she spend on fruits will be -
(27/30) x 100 = 90%
Hence, Lisa spent 90% of the total money on the fruits.
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Two-fifths of a number decreased by 3 is 1. Find the number.
Answers
By using the basics of the number system the calculated number from the given statement is 10.
What is number system?
In mathematics, the number system can be used to express the numbers in a way of writing to make the mathematical expression. Basically, it provide the unique representation of the number with the help of the algebraic structures and operations.
According to the question, the expression can be formed by the given statement is as follows:
Let us assume the number be 'a'
Using basics of the number system for the formation of an expression:
Therefore,
(2/5)a - 3 = 1
⇒ (2/5)a = 4
⇒ a = 10
Hence, by using the basics of the number system the calculated number from the given statement is 10.
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Given m\_EBC = (3x + 20)° and m \_ABC = (17x-40)° find m\_ EBC and m LABC.
Answers
Answer:
18. m<EBC = 43°, m<CBD = 47°
19. m<EBC = 50°, m<ABC = 130°
Step-by-step explanation:
18. Find m<EBC and m<CBD
m<EBC = (5x + 8) and m<CBD = (6x + 5)
these two angles add up to a right angle, therefore their sum is 90°
5x + 8 + 6x + 5 = 90
11x + 13 = 90 , 11x = 77 , x = 7
m<EBC: 5(7) + 8 = 43
m<CBD: 6(7) + 5 = 47
19. Find m<EBC and m<ABC
m<EBC = (3x + 20) and m<ABC = (17x - 40)
these two angles are supplementary, meaning that they add up to 180°
3x + 20 + 17x - 40 = 180
20x - 20 = 180, 20x = 200, x = 10
m<EBC: 3(10) + 20 = 50
m<ABC: 17(10) - 40 = 130
Jose used to budget $500 each month for groceries. He decided to change his budget
for groceries to $425 this month. By what percentage was Jose's budget for groceries
reduced this month?
Answers
Answer:
15 percent change
Step-by-step explanation:
1) 500 - 425 = 75
2) 75 / 500 = 0.15
3) 0.15 * 100= 15
Amanda is driving a racecar. The table below gives the distance D (1) (in meters) she has driven at a few times t (in seconds) after she startsTimer(seconds)Distance D (1)(meters)
Answers
From the question;
we are to calculate average rate of change of distance with respect to time
The average rate of change is given as
[tex]\text{Average rate of change = }\frac{D_2-D_1}{T_2-T_1}[/tex]From the question we are given the table below
a. we are to find the average rate of change of the distance driven from 0 secons to 3 seconds
From the information
we have
[tex]undefined[/tex]an ecologist wishes to mark off a circular sampling region having radius 13 m. however, the radius of the resulting region is actually a random variable r with the following pdf.
Answers
The expected area of a circular sampling region is 531.56 m²
Given,
The radius of the circular sampling region = 13m
f(r) = [tex]\left \{ {\frac{3}{4} } \atop {0}} \right.[/tex] [1 - (13 - r)²] 12 ≤ r ≤ 14
We have to find the area of the circular sampling region = E (π r²)
E (π r²) = π E (r²)
Lets find E (r²)
E (r²) =₁₂ [tex]\int\limits^[/tex]¹⁴ r² f(r) dr
= ₁₂∫¹⁴ (3r²/4) (1 - (13 -r)²) dr
= 3/4 ₁₂∫¹⁴ r² (1 - 169 - r² + 26r) dr
= 3/4 ₁₂∫¹⁴ r² (26r³ - r⁴ - 168r²) dr
= 3/4 [ 26r⁴/4 - r⁵/5 - 168r³/3]₁₂¹⁴
= 3/4 [ (26 × 14⁴)/4 - 14⁵/5 - (168 × 14³)/3] - [ (26 × 12⁴)/4 - 12⁵/5 (168 × 12³)/3]
= 3/4 [ (26 × 38416)/4 - 537824/5 - (168 × 2744)/3] - [ (26 × 20736)/4 - 248832/5 - (168 × 1728)/3]
= 3/4 [ 249704 - 107564.8 - 153664] - [ 134784 - 49766.4 - 96768]
= 3/4 [-11524.8] - [-11750.4]
= 3/4 [225.6]
= 169.2
∴ E(r²) = 169.2
Now lets find the expected area of the circular sampling region:
Area = E(π r²) = π E (r²)
Here, E(r²) = 169.2
So, area = π × 169.2 = 531.56 m²
That is, the expected area of a circular sampling region is 531.56 m²
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The points (0,k) and (1,4) fall on a line with a slope of 9. What is the value of k?
Answers
Answer:
Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2), where x and y are the coordinates of the points.
(k-4)÷(0-1) = 9
k-4 = 9(0-1)
k-4 = -9
k = -5
lin and her brother earn 15 dollars for shoveling snow for their grandma and 35 dollars for cleaning the garage how much money does lin get if she split the money equally with her brother
Answers
Answer:
35+15 =50
50/2= 25 dollars
2 If x and y vary directly and y=32 when x=18, then which of the following equations correctly represents
the algebraic relationship between x and y?
(A)y=16/9x
(B)y=x+14
(C) x+y=50
(D)y=9/16x
Answers
The equation would be y = 16/9x which represents the algebraic relationship between x and y which is the correct answer would be an option (A).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Given that x and y vary directly and y = 32 when x = 18
Direct variation equation can be written as:
y = kx where "k" is a constant.
Substitute the values of y = 32 and x = 18 in the direct variation equation and solve for k:
⇒ 32 = k(18)
⇒ k = 32/18
⇒ k = 16/9
The direct variation equation :
⇒ y = 16/9x
Therefore, the equation would be y = 16/9x which represents the algebraic relationship between x and y.
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Hi ! Please help, this came up as one of my questions and I don’t know how to do it well. Thanks!
Answers
Answer:
y = (3/2)x + 3
Step-by-step explanation:
Comment
The general equation is
y = mx + b
Finding m
The equation for the slope is
m = (y2 - y1)/(x2 - x1)
Givens
y2 = 3
y1 = 0
x2 = 0
x1 = - 2
m = (3 - 0)/(0 - -2)
m = 3 / 2
m = 3/2
Finding b
b is the y intercept which is (0,3)
x = 0
y = 3
3 = 0*3 + b
b = 3
So the equation is
y = (3/2) x + 3
What is the least common multiple of 34, 17, and 31?
Answers
Answer: 31, 34, 17
Step-by-step explanation:
I’ll try to give brainliest to the first answer
Answers
Answer:
[tex]-2(x+5) = -2x -10[/tex]
Step-by-step explanation:
Hi there,
For us to answer the question we have to check if whether the end product on the both LHS and RHS are equal or not , so lets take each equation is whether both the sides are similar or not :
First eq :-
[tex]-2(x-5) = -2x + 5\\giving\\-2x+10\neq -2x+5[/tex]
Since it is not equal it is incorrect.
Second eq:-
[tex]-2(x+5) = -2x-5\\giving\\-2x-10\neq -2x-5[/tex]
Since it is not equal it is incorrect.
Third eq:-
[tex]-2(x+5) = -2x -10\\giving\\-2x-10=-2x-10\\[/tex]
Now we got the equation that equals both in LHS and RHS.
So our Answer is
[tex]-2(x+5) = -2x -10[/tex]
Hope this helped you out if so do mark me as the brainliest,
a fellow mate,
cheers!
Activity 4: Fair Share!
Directions: apply the rules in multiplication of integers in answering the following activity.
Answers
Answer:
1. P
2. U
3. K
4. A
5. M
6. C
7. E
8. J
9. L
10. I