The constant c that satisfies the condition of probability mass function of the random variable are 1/55, 1/30, 1/56
What is the constant that satisfies the variable
(a) For f(x) to be a probability mass function, it must satisfy the following conditions:
1. f(x) ≥ 0 for all x
2. Σf(x) = 1, where the sum is taken over all possible values of X
Here, x can take values 1, 2, 3, 4
So, Σf(x) = f(1) + f(2) + f(3) + f(4) = c + 4c + 9c + 16c = 30c
For Σf(x) = 1, we need 30c = 1. So, c = 1/30.
(b) Here, x can take values 1, 2, 3,...,10
For Σf(x) = 1, we need c(1+2+3+...+10) = c(55) = 1. So, c = 1/55.
(c) Here, x can take values 1, 2, 3,...
For Σf(x) = 1, we need c(14+142+143+...) = c(14)(1+2+3+...) = c(14)∞ = 1. So, c = 1/(14∞).
(d) Here, x can take values 0, 1, 2, 3
For Σf(x) = 1, we need c(12+22+32+42) = c(1+4+9+16) = c(30) = 1. So, c = 1/30.
(e) Here, x can take values 1, 2, 3,...,n
For Σf(x) = 1, we need c(1+2+3+...+n) = c(n(n+1)/2) = 1. So, c = 2/(n(n+1)).
(f) Here, x can take values 0, 1, 2, 3
For Σf(x) = 1, we need c(12×3+22×4+32×5+42×6) = c(56) = 1. So, c = 1/56.
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Both Marker Farms and Jackson Farms sell apples at the farmer’s market. Maker offers 23 apples in 2 Baskets. Jackson farms offers 39 apples in 3 baskets. if price were the same for which farm provides a better value for a customer wanting apples
The farmer will make 14 baskets containing each of 5 apples and 7 peaches.
What is CGF?In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.
here, we have,
How many baskets can be made which contain both apples and peaches and each basket should contain the same combinations of fruits?
Given:
A farmer harvests 70 apples and 98 peaches.
They want to make baskets that have both apples and peaches to sell at the market.
Each basket should contain the same combinations of fruit.
They want to sell all the apples and peaches and as many baskets as possible.
Find:
How many baskets can the farm make having x apples and y peaches in the baskets?
Solution:
So, for solving this kind of question first we have to find the greatest common factor, we get;
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
So, the farmer will make 14 baskets each of 5 apples and 7 peaches.
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I need a answer and explaination.
Answer:
x = 33°
Step-by-step explanation:
Vertically opposite angles:Vertically opposite angles are congruent.
∠AOB = ∠DOC
4x - 6 = 2x + 60
Add 6 to both sides,
4x = 2x + 60 + 6
4x = 2x + 66
Subtract 2x from both sides,
4x - 2x = 66
2x = 66
Divide both sides by 2
x = 66 ÷ 2
[tex]\boxed{x = 33}[/tex]
∠AOB = 4x - 6
= 4*33 -6
= 132 - 6
∠AOB = 126°
∠DOC = 126°
Isabella scored 76% on her first math test this quarter. Her next two scores were 80%
and 84%. If she continues to improve at this rate,
A. What would be her score on the fifth (and final) test for the quarter?
B. Assuming each test is worth 100 points, what is Isabella's percentage for tests?
Answer:
your welcome
Step-by-step explanation:
A. she scored 89 %
B. 89 points
Find the equation of the straight lines Parallel to the line y + 8 = 0 and passes through (2; 1).
Answer:
[tex]y = 1[/tex]
Step-by-step explanation:
Rearranging the equation:
[tex]y = -8[/tex]
Three points to be considered:
1. Above is a horizontal line cutting through the y-axis at y value of [tex]-8[/tex].
2. A horizontal line has a slope (or gradient) of 0.
3. Parallel lines have the same slope (or gradient)
∴The straight line passing through (2, 1) will also have a zero slope. In addition, this is a horizontal line, which cuts the y-axis at y value of 1.
The equation of straight line:
y = 1
I NEED HELP ASAP HAS TO BE TURNED IN TMR
According to the information, the surface area of the pyramids is as follows: 1.377 inches², 2.208 inches², 3.160 inches².
How to find the surface area of the pyramids?To find the surface area of the pyramids we must perform the following mathematical operations.
A. Find the surface area of the base:
1. 13 * 13 = 169 in²2. 5.2 * 4.5 / 2 = 11.7 in²3. 7 * 10 = 70 in²B. We must find the surface area of the faces:
1.
8 * 13 = 10452 * 4 = 2082.
11.7 * 3 = 35.13.
6*7=4242 / 2 = 2110 * 4.8 = 4848 / 2 = 2421 + 24 = 4545 * 2 = 90 in²How to find the area of the total surface of the figures?To find the total area of the total surface of the figures we must perform the following procedure:
C. Add the area of the base to the area of the faces:
1.
169 + 208 = 377 in²2.
11.7 + 35.1 = 46.8 in²3.
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100 points help i will mark branilyest
Answer:
[tex]\frac{2}{11}[/tex]
Step-by-step explanation:
[tex]\frac{6}{11} * \frac{1}{3}[/tex]
since 6 and 3 are opposite of each other in this multiplication problem, you can divide them by 3 since they are both divisible by 3
[tex]\frac{2}{11} * \frac{1}{1} = \frac{2}{11}[/tex]
Brad has a $27 online gift
card. He plans to buy as many
books as he can. The cost of each
book is $3. How many books can
he buy without spending more
than his gift card amount?
Answer:
Step-by-step explanation:
Just divide the amount of the giftcard between the unit cost of the books.
[tex]\frac{gift-card-amount}{cost-of-books}=\frac{27}{3}=9[/tex]
Brad can buy 9 books with his gift card
. Rachel mows a rectangular lawn that is twelve yards-long and eight and two-thirds yards wide. In square yards what is the area of the lawn Rachel mows? Represent your answer using an area model.
The area of the rectangular lawn Rachel mows is 100 square yards
How to determine the area of the lawn
The formula for calculating the area of a rectangle is expressed with the formula;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values as given,
length = 12 yards
Width = 8 1/3 = 25/3 yards
Then,
Area = 12 × 25/3
Divide the factors
Area = 4(25)
Multiply the values
Area = 100 square yards
Hence, the value is 100 square yards
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The picture has a side of 7 inches.
What is the area of the picture?
Answer:
Step-by-step explanation:
So here is what I did. If the picture is square then you would multiply Length times the Width to get 49 square inches. But if it’s not a square then you would still multiply Length by Width.
Give the circumference and the area of a circle with diameter 4yd use the value of 3.14 for pi
Answer:
Circumference = 12.56 yd
Area = 12.56 yd²
Step-by-step explanation:
Equations we need to know:
Circumference of circle - 2πr
Area of circle - πr²
1) Circumference
2 x 3.14 x 2 = 12.56
2) Area
3.14 x 2² = 12.56
We have to make sure the we are using the radius and not the diameter otherwise our answer would be wrong
Hope this helps, have a lovely day! :)
Answer:
Area=12.56yd^2, Circumfrence=12.56yd
Step-by-step explanation:
the formula for the area of a circle is pi*r^2 and since pi is 3.14 and r is 2 so r^2 is 4 and 4*3.14 is 12.56 (r is the radius)
the formula for the circumference of a circle os 2*pi*r and r is 2 so its 2*3.14*2 multiplying all these terms again gives us 12.56 but be careful with the units as with the area comes yd^2 and with the circumference comes yd only
Find the number of sides (n) of the polygons with the angle values shown in the items below.
a) The sum of the interior angles is 10,440∘
b) The value of each interior angle is 171∘
As per the concept of polygon,
a) The sum of the interior angles is 10,440° then the number of sides is 58
b) The value of each interior angle is 171°, then the number of sides is 36
A polygon is a two-dimensional geometric shape made up of straight lines and angles. The number of sides a polygon has is directly related to the sum of its interior angles.
a), we can use the formula for the sum of the interior angles of a polygon, which is (n-2) times 180 degrees, where n is the number of sides. To find n, we can rearrange the formula to
=> n = (sum of interior angles / 180) + 2.
Plugging in the value of 10,440 degrees for the sum of interior angles, we get
=> n = (10440 / 180) + 2 = 58.
Therefore, the polygon in item a) has 58 sides.
For item b), we can use the formula for the value of each interior angle of a regular polygon, we get
=> n = (180(n-2)) / 171 = (180n - 360) / 171.
Solving for n, we find that the polygon in item b) has 36 sides.
In conclusion, polygons with the angle values shown in items a) and b) have 58 and 36 sides respectively. These formulas can be applied to any polygon to find the number of sides based on its interior angle values.
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Karen and Bill collect coins. Karen has x coins. Bill has 9 coins fewer than two times the number of coins Karen has. Write and simplify an expression for the total number of coins Karen and Bill have.
Answer: Let's call the total number of coins Karen and Bill have "t".
We can start by writing an expression for the number of coins Bill has:
2x - 9 = 9 + 2x
So the total number of coins Karen and Bill have is:
t = x + (2x - 9)
Simplifying the expression for t:
t = 3x - 9
So the total number of coins Karen and Bill have is equal to 3 times the number of coins Karen has minus 9.
Step-by-step explanation:
any " Which of the following numbers have a remainder of I when divided by 2? (There is more than one answer) A) 327 B) 400 C) 751 D) 148 E) 1,356
A. 327 and C.751 have a remainder of 1 when divided by 2
What is an Even Number?Even Numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2. They are numbers that are a multiple of 2. Examples are: 2, 4, 6, 8, 10, and so on are even numbers.
How to determine this,
By dividing each words by 2
327 divided by 2 = 163 remainder 1
So, this is not an even number when divided by 2
400 divided by 2 = 200 remainder 0
This is an even number
751 divided by 2 = 375 remainder 1
This is not an even number
148 divided by 2 = 74 remainder 0
This is an even number
1356 divided by 2 = 678 remainder 0
So, this is an even number
Therefore, only 327 and 751 have a remainder of 1 when divisible by 2.
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A campus contains buildings numbered 1 through 70. What is the probability that a student will enter a building that is not a multiple of 12?.
The probability that a student will enter a building that is not a multiple of 12 is 0.914
We can find the probability by finding the number of buildings that are not a multiple of 12 and dividing it by the total number of buildings (70).
The buildings that are multiples of 12 are:
12, 24, 36, 48, 60, and 70
So there are 6 buildings thar are multiple of 12.
So, the number of buildings that are not a multiple of 12 is
70 - 6 = 64
Therefore, the probability that a student will enter a building that is not a multiple of 12 is
= 64/70
= 0.914
= 91.4 %
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(3) A framed print measures 36 in by 22 in. If the print is enclosed by a 2-inch matting, what is the length of the diagonal of the print? Round to the nearest tenth. See illustration. 2 in 12 in 36 in a. 36.7 in b. 39.4 in c. 26.5 in d. 50 in 22 in
The length of the diagonal of the print would be = 36.7 in . That is option A (to the nearest tenth).
How to calculate the diagonal length of the print?The print has the shape of a rectangle which is a type of a quadrilateral that has four sides with two sides parallel to each other.
The diagonal length of the print can be calculated by the use of the Pythagorean formula;
That is c² = a² + b²
C = hypothenuse = ?
a = 22 - 4 = 18in
b = 36 - 4 = 32 in
c² = 18² + 32²
c² = 324 + 1024
c² = 1348
C= √1348
C = 36.7 in ( nearest tenth)
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A car dealership increased the price of a certain car by 14% The original price was 32,600
Answer: 37164
Step-by-step explanation:
14% of 32,600 is 4564
-To find the new value of the car, you must add the 14% of the original value and the original value together
-4,564 + 32,600 = 37164
All of the following are correct about the triangles shown, except which?
In △ABE, the sin(A) is the same as the tan(F) in △ACF because the triangles are 45-45-90 triangles and therefore similar.
In △ABE, the cos(A) is the same as the sin(F) in △ACF because the triangles are 45-45-90 triangles and therefore similar.
In △ADG, the tan(G) is the same as the tan(A) in △ACF because the triangles are 45-45-90 triangles and therefore similar.
In △ACF, the sin(F) is the same as the sin(E) in △ABE because the triangles are 45-45-90.
The false statement regarding the trigonometric ratios is given as follows:
In △ABE, the sin(A) is the same as the tan(F) in △ACF because the triangles are 45-45-90 triangles and therefore similar.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.For similar triangles, the ratios are equal, as the side lengths are proportional.
In a 45-45-90 triangle, the sine is equals to the cosine.
However, similar triangles have different values of sine and tangent, hence the first statement is false.
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Harry needs wood pieces to complete a project in woodshop class. He needs two pieces of wood that have a length of two and three eighths feet and four pieces of wood that are one and one third feet. What is the total amount of wood that Harry will need for the project?
three and four elevenths feet
three and seventeen twenty fourths feet
four and one third feet
ten and one twelfth feet
Thx!
The total amount of that Harry will need for the project is nineteen and seven twentieth feet. option A
Addition of Fraction
Wood 1:
Length of each = 2 5/8 feet
Number of pieces = 6
Total = Length of each × Number of pieces
= 2 5/8 × 6
= 21/8 × 6
= 126 / 8
= 15 3/4 meters
Wood 2:
Length of each = 1 1/5 feet
Number of pieces = 3
Total = Length of each × Number of pieces
= 1 1/5 × 3
= 6/5 × 3
= 18/5
= 3 3/5 meters
Total amount of wood needed for the project = 15 3/4 meters + 3 3/5 meters
= 126/8 + 18/5
= (630+144) / 40
= 774/40
= 19 14/40
= 19 7/20 meters
Therefore, the total amount of wood that Harry will need for the project is nineteen and seven twentieths feet. option A
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Let [tex]f(x)=-5x+3[/tex] and [tex]g(x)=6x-2[/tex]. Find f times g and its domain.
The result of f times g is; -30x² + 28x - 6 while it's domain as required is the set of all real numbers.
What is the domain of f times g?As evident in the task content;
f(x) = -5x + 3 while g(x) = 6x - 2.
Hence, the result of f times g is; (-5x + 3) (6x - 2).
open parenthesis
f × g = -5x(6x) - 5x(-2) + 3(6x) + 3(-2)
= -30x² + 10x + 18x - 6
f × g = -30x² + 28x -6.
By observation, the function above is a quadratic function and hence, it's domain is the set of all real numbers.
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Patrick ran from his home to a shop 400m away at an average speed of 2 m per second he walked back to his home at an average speed of 1 m per second find the average speed for the whole journey if he did not stop at the shop
The average speed that Patrick used to run from his home to a shop and walk back to his home is 1.33 m per second.
What is the average speed?The average speed is the total distance divided by the total time.
The average or mean is the quotient of the total value and the total time or number of items in a data set.
The distance from Patrick's home to a shop = 400 m
Running speed from home to the shop = 2 m per second
The total time used in running to the shop = 200 seconds (400/2)
The distance from the shop to Patrick's home = 400 m
Walking speed from shop to the home = 1 m per second
The total time used in walking back to the home = 400 seconds (400/1)
The total distance to and from shop = 800 m (400 x 2)
The total time used to run to and walk from the shop = 600 seconds (200 + 400)
The average speed for the whole journey = Total Distance/Total Time
= 800/600 = 1.33 m per second
Thus, for covering a total distance of 800 m in 600 seconds, Patrick's average speed was 1.33 m per second.
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Points A, B, C and D are collinear, with B between A and C, and C between B and D. What is the measure of CD, if AB = 4x-1, BC= 6x-2, BD = 11x + 5, and AD = 64?
A. 15 units
B. 22 units
C. 25 units
D. 27 units
E. 33 units
Answer:
D. 27 units.
Step-by-step explanation:
See my attachments.
Please help me with this.
Which question are you seeking the answer to?
A family went on a cross-country road trip for their summer vacation. The following table shows the number of days and the total amount of miles their car had driven.
Number of Days 2 5 6 8 12
Miles Driven 425 967 1,253 1,253 2,648
Which of the following graphs is most appropriate to construct for the data given in the table to observe how the miles change over a certain number of days? Explain.
A scatter plot, because it would show the association, or relationship, between the two variables
A scatter plot, because it would show how a variable changes over time between each individual data point
A line graph, because it would show the association, or relationship, between the two variables
A line graph, because it would show how a variable changes over time between each individual data point
Thus, a line graph would be more appropriate for this particular data set to observe the changes in the miles driven over a certain number of days.
What is data?Data refers to any collection of facts, figures, or information that can be processed, analyzed, and interpreted to gain insights and knowledge. It can be in various forms such as text, images, audio, video, or numerical values, and can be collected from various sources such as surveys, sensors, social media, or transactions.
Given by the question: -
The most appropriate graph to construct for the given data is a line graph because it would show how the miles driven change over time between each individual data point. A line graph is useful for showing trends or changes over time, and it allows us to see the progression of the miles driven during the trip. This graph would have days on the x-axis and miles driven on the y-axis, with a line connecting the data points. This would help to visualize any patterns or trends in how the miles driven change over time during the trip.
On the other hand, a scatter plot would show the relationship between the two variables, but it would not show the changes over time. While scatter plots are useful for showing relationships between variables, they do not show the order or progression of the data points over time.
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Determine the missing measures for the parallelogram below.
need help on this one
Based on the information in the graph, the angles of the parallelogram would be 68° and 112°, while the length of its sides would be 15 and 8.
How to identify the length and angles of this figure?To identify the length and angles of this figure we must carefully look at the lengths shown and the angles shown. Taking into account the shape of the parallelogram, we can infer that the values that correctly complete the dimensions of the figure are:
A = 112°B = 68°C = 112°basis = 15side = 8This is because the parallelogram has two equal sides and equal bases, so if the upper one measures 15, the lower one must measure the same. Additionally, if the side measures 8 the other side must measure 8. In the case of the angles it would be the same.
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Mr. Rideout is in charge of washing the windows on a bus. He washes 25 of the 30 windows before lunch. After lunch he washes 7 of the remaining windows. How many windows does Mr. Rideout still need to wash?
The remaining number of windows is given by the equation A = 11 windows
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The total number of windows that needs to be washed = 30 windows
The number of windows that was washed before lunch = ( 2/5 ) of the total
Substituting the values in the equation , we get
The number of windows that was washed before lunch = ( 2/5 ) x 30
The number of windows that was washed before lunch = 2 x 6
The number of windows that was washed before lunch = 12 windows
So , the remaining number of windows = 30 - 12 = 18 windows
And ,
The number of windows that was washed after lunch = 7 windows
So , the remaining number of windows that needs to be washed A = remaining number of windows - number of windows that was washed after lunch
On simplifying the equation , we get
The remaining number of windows that needs to be washed A = 18 - 7
The remaining number of windows that needs to be washed A = 11 windows
Hence , the equation is A = 11 windows
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find x, please show the work
What is the value of f divided by 13
When f=52
Answer:
4
Step-by-step explanation:
We know
f = 52
What is the value of f divided by 13
52 divided by 13 = 4
So, the value of f divided by 13 is 4.
A is the point (-1, 5). Let (x, y) be any point on the line y = 3x.
(3 marks)
a Write an equation in terms of x for the distance between (x, y) and A(-1, 5).
b Find the coordinates of the two points, B and C, on the line y = 3x which are a distance
of √74 from (-1, 5).
(3 marks)
e Find the equation of the line that is perpendicular to y = 3x and goes through the
point (-1, 5).
Find the coordinates of the point of intersection between ₁ and y = 3.x.
e Find the area of triangle ABC.
(2 marks)
The distance is√(x+1)²+(3x-5)², coordinates are B: (-4/3, -4) and C: (2/3, 2), y = (-1/3)x + (14/3) is equation of the line that is perpendicular to y = 3x, point of intersection is (7/5, 21/5).
What is Distance?The length along a line or line segment between two points on the line or line segment.
The distance formula is Distance=√(x₂-x₁)²+(y₂-y₁)²
Equation in terms of x for the distance between (x, y) and A(-1, 5) and y = 3x. be any point on the line
Distance=√(x+1)²+(3x-5)²
b. We need to find coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1, 5).
√(x₁+1)²+(3x₁-5)² =√74
√(x₂+1)²+(3x₂-5)² =√74
Simplifying each equation and solving for x, we get:
x₁ = -4/3 or x₁ = -2
x₂ = 2/3 or x₂ = -4
Simplifying each equation and solving for x, we get:
x₁ = -4/3 or x₁ = -2
x₂ = 2/3 or x₂ = -4
Substituting each value of x into y = 3x, we get the coordinates of B and C:
B: (-4/3, -4)
C: (2/3, 2)
The slope of y = 3x is 3,
Slope of any line perpendicular to it is -1/3.
Using the point-slope form of a line, we get the equation of the line passing through (-1, 5) with slope -1/3:
y-5=-1/3(x+1)
The point of intersection between y = 3x and the line y = (-1/3)x + (14/3), we can set the two equations equal to each other and solve for x:
3x = (-1/3)x + (14/3)
x = 14/10 = 7/5
y = 3(7/5) = 21/5
So the point of intersection is (7/5, 21/5).
To find the area of triangle ABC, we can use the distance formula between the points B and C:
d = √2/3 - (-4/3))² + (2 - (-4))²)
d=2√10
The base of the triangle is the distance between the x-coordinates of B and C, which is 2.
The area of the triangle is:1/2×b×h
=2√10
Hence, the distance is√(x+1)²+(3x-5)², coordinates are B: (-4/3, -4) and C: (2/3, 2), y = (-1/3)x + (14/3) is equation of the line that is perpendicular to y = 3x, point of intersection is (7/5, 21/5).
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Find the value of each variable
The triangle on the left is a 45 45 90 triangle and the triangle on the right is a 30 60 90 triangle.
In a 45 45 90 triangle, the length of the hypotenuse is equal to the length of either one of the legs times the square root of 2. So that means that a and c are both 18.
In a 30 60 90 triangle, the length of the hypotenuse is twice that of the leg opposite the 30 degree angle. So that means that b is 36. The length of the leg opposite the 60 degree angle is the length of the other leg times the sq root of 3. So that would give you d = 18 sq root 3.
The table below represents a linear function for the cost of a gym membership based on the number of months of membership.
What is the slope and y-intercept of the linear function.
The equation of line is y = 30x + 75 , where the slope is m = 30 and the y intercept is 75
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 1 , 105 )
Let the second point be Q ( 3 , 165 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 165 - 105 ) / ( 3 - 1 )
Slope m = ( 60 / 2 )
Slope m = 30
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 105 = 30 ( x - 1 )
On simplifying the equation , we get
y - 105 = 30x - 30
Adding 105 on both sides of the equation , we get
y = 30x + 75
Hence , the equation of line is y = 30x + 75
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