The measure of the angle of elevation is 58°( nearest degree)
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The height of the pole will represent the opposite to the angle of elevation and the length of the shade will be the adjascent to the angle of elevation.
Represent the angle of elevation by x
Tan x = opp/adj
Tan x = 8/5
Tan x = 1.6
x = tan^-1(1.6)
x = 58° ( nearest degree)
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A farmer is tracking the amount of corn his land is yielding each year. He finds that the function f(x)=-x^2+20x+50 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 1 to year 10.
The average rate of change from year 1 to year 10 is: (150 - 69)/9 = 9 based on the given function.
The amount of maize the farmer's land is yielding in pounds per acre over x years is represented by the function f(x)=[tex]-x^2+20x+50[/tex].
We must compute the change in f(x) for the range [1,10] and divide by the interval's length to determine the average rate of change from year 1 to year 10.
f(1) = [tex]-(1)^2[/tex] + 20(1) + 50 = 69
f(10) = [tex]-(10)^2[/tex] + 20(10) + 50 = 150
Hence, the change in f(x) throughout the range [1,10] is as follows:
f(10) - f(1) = 150 - 69 = 81
And the interval [1,10] has the following length:
10 - 1 = 9
Thus, from year one to year ten, the average rate of change is:
(150 - 69)/9 = 9
By interpreting the average rate of change, we can conclude that from year 1 to year 10, the farmer's land's yield of maize per acre is growing at a pace of 9 pounds each year. This indicates that, on average, throughout the course of these ten years, the farmer can anticipate harvesting 9 extra pounds of maize per acre.
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!!!TIMED PLEASE HELP AS FAST AS POSSIBLE!!!!
Answer: 53
Step-by-step explanation:
90- 37 = 53
Two angles are Complementary when they add up to 90 degrees (a Right Angle)
1. In voting for the fifth-grade class president, only one third of the students
cast votes. What fraction of the whole class voted for Tim? for
Selena? Who received more votes?
Answer:
We cannot determine the exact number of votes for Tim or Selena without additional information. However, we can determine the fraction of the whole class that voted for each candidate based on the given information.
If only one third of the students cast votes, that means that two thirds did not vote. Therefore, the fraction of the whole class that voted for Tim and Selena is each equal to one third of the total number of students.
To calculate these fractions, we can use the following formula:
Fraction of class = Number of students who voted / Total number of students
Let's assume that there are N students in the class. Then, the number of students who voted for Tim is (1/3)N, and the number of students who voted for Selena is also (1/3)N.
So, the fraction of the whole class that voted for Tim is:
(1/3)N / N = 1/3
Similarly, the fraction of the whole class that voted for Selena is also 1/3.
Since we don't know the exact number of votes for each candidate, we cannot determine who received more votes.
Based on your knowledge of the two data sets described below, would you expect a scatter plot describing the
two data sets to have a positive, a negative, or no correlation?
amount of gas in a car's gas tank and the total distance the car has traveled since last being filled with gas
Based on my knowledge, I would expect a negative correlation between the amount of gas in a car's gas tank and the total distance the car has traveled since last being filled with gas.
As the car travels, the amount of gas in the tank decreases. Thus, if the car has traveled a long distance since being filled up, it is likely that there is less gas in the tank. Therefore, there should be a negative correlation between the amount of gas in the tank and the distance traveled, meaning that as the distance traveled increases, the amount of gas in the tank decreases.
A scatter plot of these two variables should show a downward-sloping trend, indicating the negative correlation.
Therefore the correct answer is negative correlation.
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8. Look at the spinner below. Allie spins the spinner 2 times.. K SA % What is the probability she will spin a on the first spin and & on the second spin? (if you can could you please explain how you got the answer)
If Allie spins the spinner 2 times. the probability that Allie spins A on the first spin and & on the second spin is: B. 1/16.
How to find the probability?Based on the information provided, the spinner has four possible outcomes: K, S, A, and %, each with equal probability of 1/4.
To find the probability that Allie spins A on the first spin and & on the second spin, we need to multiply the probability of spinning A on the first spin (1/4) by the probability of spinning & on the second spin (1/4), because the two events are independent.
Therefore, the probability is:
P(A on first spin and & on second spin) = P(A) × P(&) = (1/4) × (1/4) = 1/16
So the probability that Allie spins A on the first spin and & on the second spin is 1/16.
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a sprinkler distributes water in a circular pattern, supplying water to a depth of feet per hour at a distance of r feet from the sprinkler. a. what is the total amount of water supplied per hour inside of a circle of radius 14? per hour b. what is the total amount of water that goes throught the sprinkler per hour? per hour calculate the total amount of water supplied per hour inside a circle of radius , then let .
The total amount of water supplied per hour inside a circle of radius 14 is approximately79.90 ft^3 per hour, and the total amount of water that goes through the sprinkler per hour is approximately 2π ft^3 per hour. As R approaches infinity, the total amount of water supplied per hour approaches 2 ft^3 per hour.
To find the total amount of water supplied per hour inside of a circle of radius 14, we need to integrate the function e^(-r) over the region of the circle total amount of water = ∫∫ e^(-r) dA
where the integration is over the circular region of radius 14, and dA is the differential area element.
Using polar coordinates, we can write dA = r dr dθ, and the limits of integration are 0 ≤ r ≤ 14 and 0 ≤ θ ≤ 2π. Substituting these values, we get:
total amount of water = ∫(0 to 2π) ∫(0 to 14) e^(-r) r dr dθ
Integrating with respect to r first, we get:
total amount of water = ∫(0 to 2π) [-e^(-r)](0 to 14) dθ
total amount of water = ∫(0 to 2π) (1 - e^(-14)) dθ
total amount of water = (1 - e^(-14)) ∫(0 to 2π) dθ
total amount of water = 2π(1 - e^(-14))
Thus, the total amount of water supplied per hour inside of a circle of radius 14 is approximately 79.90 ft^3 per hour.
To find the total amount of water that goes through the sprinkler per hour, we need to integrate the function e^(-r) over the entire plane:
total amount of water = ∫∫ e^(-r) dA
where the integration is over the entire plane, and dA is the differential area element.
Using polar coordinates, we can write dA = r dr dθ, and the limits of integration are 0 ≤ r ≤ ∞ and 0 ≤ θ ≤ 2π. Substituting these values, we get:
total amount of water = ∫(0 to 2π) ∫(0 to ∞) e^(-r) r dr dθ
Integrating with respect to r first, we get:
total amount of water = ∫(0 to 2π) [-e^(-r)](0 to ∞) dθ
total amount of water = ∫(0 to 2π) (1) dθ
total amount of water = 2π
Thus, the total amount of water that goes through the sprinkler per hour is exactly 2π ft^3 per hour.
To calculate the total amount of water supplied per hour inside a circle of radius R, then let R → ∞, we can use the result from part B and multiply it by the ratio of the areas of the two circles:
total amount of water = (total amount of water inside circle of radius R) × (area of circle of radius R)/(area of entire plane)
total amount of water = (2πR^2(1-e^(-R))) / (πR^2)
total amount of water = 2(1-e^(-R))
Now we can let R → ∞:
total amount of water = 2
Thus, the total amount of water supplied per hour inside a circle of infinite radius is exactly 2 ft^3 per hour.
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--The given question is incomplete, the complete question is given
"A sprinkler distributes water in a circular pattern, supplying water to a depth of e^-r feet per hour at a distance of r feet from the sprinkler. A. What is the total amount of water supplied per hour inside of a circle of radius 14? ft^3 per hour B. What is the total amount of water that goes through the sprinkler per hour? ft^3 per hour Calculate the total amount of water supplied per hour inside a circle of radius R, then let R rightarrow infinity."--
Select all that are a radius of circle O.
A) OC
B) OB
C) PQ
D) AB
The parts that are called radius as shown from the diagram are: OC and OB (option A and B)
How do i know which part of the circle is called radius?The radius of a circle is defined as the distance from the center of the circle to any point on the circumference. However, the radius is also obtained by dividing the diameter of a circle by 2
Now, we shall consider the diagram given to determine the distance from the center to the circumference (i.e radius). This is shown below:
Line PQ is not a radius since it does not start from the centerLine OA is called a radius since it starts from the centerLine OB is called a radius since it starts from the centerLine OC is called a radius since it starts from the centerConsidering the options given from the question, we can conclude that the parts of the circle which is called the radius are: OC and OB (option A and B)
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What fraction of a semicircle is an angle that measures 29pi/18 radians? Express your answer as a fraction in simplest terms.
Answer:
A semicircle has an angle measure of pi radians. Therefore, the fraction of a semicircle that an angle of 29pi/18 radians represents is:
(29pi/18) / pi = 29/18
So the fraction of a semicircle that an angle of 29pi/18 radians represents is 29/18.
Step-by-step explanation:
Evaluate-+61
Enter your answer in the box.
- 7 when x = 18
The expression 61+x when x = 18 evaluates to 79.
What is expression?Expression is a combination of numbers, symbols and operators that represent a mathematical quantity or operation.
To find the value of the expression, we must first substitute 18 in for x. To evaluate this expression, we must add 61 and 18. 61+18 = 79. Therefore, the expression 61+x when x = 18 evaluates to 79.
To verify the answer, we can use the distributive property of multiplication to expand the expression. 61+x is equivalent to 61+18, which can be written as
61+18 = 61+1*18.
We can now distribute the 1 to the 18,
so 61+1*18 = 61+18 = 79.
Therefore, the expression 61+x when x = 18 evaluates to 79.
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Question: Evaluate-61+x
Enter your answer in the box.
Find the value of equation, when x = 18.
compute{i-j j-k k-i]
Answer:
Step-by-step explanation:
(i-j)×(j-k)×(k-i)
{(i×j)-(i×k)-(j×j)+(j×k)}×(k-i)
(k+j-i)×(k-i)
( j+i+k-j)
(i+k)
You have $
48
to order pizza for you and your friends. Slices of pizza are $
3.20
each. The inequality representing this scenario is 3.20
n
≤
48
, with n
representing the number of pizza slices you can order.
Select all the numbers that represent the amount of pizza slices you can order for you and your friends.
It's important to note that ordering more than 15 slices would exceed your budget of $48, while ordering fewer slices would allow you to save money for other expenses.
To determine how many pizza slices you can order with $48, we divide the total amount of money by the cost of each slice of pizza, which is $3.20. This gives us:
48 ÷ 3.20 = 15
So you can order up to 15 slices of pizza with $48. However, since you cannot order a fraction of a slice, the actual number of slices must be a whole number. Therefore, the possible numbers of pizza slices you can order are:
0 slices
1 slice
2 slices
3 slices
4 slices
5 slices
6 slices
7 slices
8 slices
9 slices
10 slices
11 slices
12 slices
13 slices
14 slices
15 slices
So, any of the above numbers represents the amount of pizza slices you can order for you and your friends. It's important to note that ordering more than 15 slices would exceed your budget of $48, while ordering fewer slices would allow you to save money for other expenses.
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Consider the basis of . Let be the linear transformation such thatSet. Compute .Consider the basis B = ([ 0 ] , [ 0 ] , [ 1 ] of R^3. [ 0 ] [ -1 ] [ -2 ][ 1 ] [ -1 ] [ 1 ]Let T:R^3→R^2 be the linear transformation such that T( [0] ) = [1] , T ([ 0 ]) = [3] , T([ 1 ]) = [ 0][0] [1] [ -1] [2] [ -2] [-1][1] [ -1] [ 1 ]Set v = [ -1 ] Compute T(v).[ 1 ][ -2 ]T(v) = [ .... ]
The value of T(v), express v as linear combination in the basis B and the matrix representation of T obtain is T(v) = [4, -4].
To find T(v), we need to express v as a linear combination of the basis vectors of R^3 with respect to B:
v = (-1)[0] + (-1)[0] + (1)[1]
This means that the coordinate vector of v with respect to B is [-1, -1, 1].
To find the matrix representation of T with respect to the standard bases of R^3 and R^2, we can apply T to each of the basis vectors:
T([1, 0, 0]) = [1, 3]
T([0, 1, 0]) = [-1, 1]
T([0, 0, 1]) = [2, -2]
We can arrange the results in a matrix:
[1 -1 2]
[3 1 -2]
The matrix [1 -1 2; 3 1 -2] represents T with respect to the standard bases of R^3 and R^2.
To find T(v), we can multiply the matrix representation of T with the coordinate vector of v with respect to B:
T(v) = [1 -1 2; 3 1 -2] * [-1; -1; 1] = [4; -4]
Therefore, T(v) = [4, -4].
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What organ system contains the heart and blood vessels?
The circulatory system's primary functions are listed above. Service for the body's cells is provided by the heart, blood, and blood vessels.
Through the system of veins, arteries, and capillaries, blood transports carbon dioxide towards the lungs (for expiration) and takes up oxygen. Both liquid and solid components make up your blood. Water, salts, and protein make up the liquid component, known as plasma.
Plasma makes up most of your blood. Red blood cells, white blood cells, and platelets make up the solid portion of your blood. The oxygen from your lungs is carried to human tissues and organs by red blood cells (RBC).
The study on quality, organization, location, and change is what arithmetic is all about. Mathematicians look for patterns and come up with new theories.
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The function f
has reference points (0, 1)
and (1, 2). What do the reference points become for the transformation given by g
?
g(x)=2⋅f(x)+2
the reference points for the transformation given by g(x) = 2*f(x) + 2 are (0, 4) and (1, 6).
The given function f has reference points (0, 1) and (1, 2). To find the reference points for the transformation given by g(x) = 2*f(x) + 2, we need to apply the transformation to each of the original reference points.
For the first reference point (0, 1), we have:
g(0) = 2f(0) + 2 = 21 + 2 = 4
So the transformed point is (0, 4).
For the second reference point (1, 2), we have:
g(1) = 2f(1) + 2 = 22 + 2 = 6
So the transformed point is (1, 6).
Therefore, the reference points for the transformation given by g(x) = 2*f(x) + 2 are (0, 4) and (1, 6).
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HELP DUE IN 2 HOURS 4.7y^2+5.3+4y-3.3-2y+y^2
Answer:
5.7y^2 +2y +2
Step-by-step explanation:
You want to simplify the expression 4.7y^2+5.3+4y-3.3-2y+y^2.
SimplifyIdentify like terms and combine their coefficients:
4.7y^2+5.3+4y-3.3-2y+y^2
= (4.7 +1)y^2 +(4 -2)y +(5.3 -3.3)
= 5.7y^2 +2y +2
What is the volume of a cake box that is 12 inches long, 9 inches wide, and 6 inches high? (1 point)
a
102 cubic inches
b
252 cubic inches
c
648 cubic inches
d
972 cubic inches
help
The volume of the cake box is c. 648 cubic inches.
Define volumeVolume refers to the amount of space occupied by an object or a three-dimensional figure. It is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).The volume of an object can be determined by multiplying its length, width, and height if it has a regular shape such as a rectangular prism or cube.
A rectangular box's volume is equal to its length, width, and height.
Substituting the given values, we get:
Volume of a cake box = 12 inches x 9 inches x 6 inches
Volume = 648 cubic inches
Therefore, the volume of the cake box is 648 cubic inches.
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the speeds of four vehicles were measured at the midpoint of a roadway section as 55, 50, 74, and 78 mph, respectively. if all vehicles were traveling at constant speed over this roadway section, what was the space-mean speed (rounded to the nearest mph) for the four vehicles?
The space-mean speed of the four vehicles is approximately 64 mph.
The given information about the speeds of four vehicles measured at the midpoint of a roadway section are as follows:Vehicle Speed (mph)A 55B 50C 74D 78The space-mean speed of the four vehicles can be found out by the following formula:Space-mean speed = {Sum of the individual speeds of the vehicles}/{Number of vehicles}Space-mean speed = (55 + 50 + 74 + 78)/4Space-mean speed = 257/4Space-mean speed ≈ 64 mph (rounded to the nearest mph)
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Find the area of the shaded region:
6 m
4 m
8 m
12 m
Therefore, the area of the shaded region is 72 square meters.
What is Triangle?A triangle is a three-sided polygon that is formed by connecting three straight lines or line segments. It is a basic geometric shape that is commonly studied in mathematics, geometry, and trigonometry. Triangles have a wide range of properties and characteristics that are important in various fields of study, including their angles, sides, and area. Triangles can be classified based on their angles (as acute, right, or obtuse triangles) or based on their sides (as equilateral, isosceles, or scalene triangles). The study of triangles is fundamental in many areas of mathematics and physics and is also important in practical applications such as engineering, architecture, and surveying.
by the question.
To find the area of the shaded region, we first need to find the area of the entire rectangle. The area of a rectangle is given by the formula: length x width.
The length of the rectangle is 12 meters, and the width is 8 meters, so the area of the entire rectangle is:
12m x 8m = 96 square meters
Next, we need to find the area of the triangle that is not shaded. The base of the triangle is 6 meters, and the height is 8 meters. The area of a triangle is given by the formula: 1/2 x base x height.
1/2 x 6m x 8m = 24 square meters
Finally, we can find the area of the shaded region by subtracting the area of the triangle from the area of the entire rectangle:
96 square meters - 24 square meters = 72 square meters
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For a party, Katrina wants to make a nut mixture
of pecans and cashews. Pecans (p) sell for $4.99
per pound and cashews (c) sell for $3.79 per
pound. She has $35 to spend on the nut
mixture.
Write the equation that models this situation.
The equation that represents the given equation model is: 4.99p + 3.79c = 35
How to find the linear equation model?The most common form of representing a linear equation model is:
y = mx + b
where:
m is slope
b is y-intercept
Let the number of pounds of Pecans she can buy be p
Let the number of pounds of cashews she can buy be c
We are told that:
Cost of pecans = $4.99 per pound
Cost of Cashews = $3.79 per pound
Thus, for $35 to spend we have the equation as:
4.99p + 3.79c = 35
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99 cookies were diveded into three piles in the ratios of 1:1/2:1/3. how many cookies were in the middle pile
To the total of 99 cookies, there are 27 cookies in middle pile.
Let's call the number of cookies in the first pile "x". Then, the number of cookies in the second pile is 1/2 of x, or (1/2)x, and the number of cookies in the third pile is 1/3 of x, or (1/3)x.
We know that the total number of cookies is 99, so we can write an equation:
x + (1/2)x + (1/3)x = 99
To solve for x, we can first find a common denominator:
(6/6)x + (3/6)x + (2/6)x = 99
(11/6)x = 99
x = (6/11) * 99
x = 54
So, there are 54 cookies in the first pile, (1/2)x = (1/2)*54 = 27 cookies in the second pile, and (1/3)x = (1/3)*54 = 18 cookies in the third pile. In the middle pile there are 27 cookies.
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two trains leave stations 418 miles apart at the same time and travel toward eact other. once treain trevels at 85 mph and the ohter treavels at 105 mph. how long willit take for the two trains to meet
It will take 2.2 hours for the two trains to meet.
We can find the time taken by the two trains to meet by using the formula,
large Time=Distance/Speed
Let's consider the time taken by the two trains to meet be "t".The distance between two trains = 418 miles.
Now, the first train is traveling at a speed of 85 mph and the second train is traveling at a speed of 105 mph.
Let's calculate the distance covered by both the trains in time "t".The distance covered by the first train in time "t"=85t.
The distance covered by the second train in time "t"=105t.
So, the total distance covered by both the trains in time "t" is,
Distance covered = 85t+105t=190t.
But we know the distance between the two trains is 418 miles.
Therefore,190t = 418
Now, solve for "t"t = 418/190t = 2.2 hours
Therefore, the two trains will meet in 2.2 hours.
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Calculate the volume of a pie
that has flat sides so that it is
shaped like a cylinder. The pie
has a radius of 3 inches and a
height of 2 inches.
Answer:
56.54 inches
Step-by-step explanation:
If the radius is 3 inches, to find the area of the circle your equation would be A = (pi) x r^2
Your equation would look like this:
A = (pi) x 3^2
A = 28.27
Now to get the volume of the pie, you would multiply 28.27 x 2 which gives you an answer of 56.54 inches.
consider a deck of 52 cards. one deals 4 cards in a row with no replacement. what is the probability that the first three cards are 3 aces and the last one is a king ?
The probability of the first three cards being 3 aces and the last one being a king is 1/66,300.
The probability of drawing an ace from a deck of 52 cards is 4/52 (since there are 4 aces in the deck), and the probability of drawing a king is 4/52 as well.
Since the cards are dealt with no replacement, the probability of drawing three aces in a row is
(4/52) × (3/51) × (2/50) = 1/5525
This is because after each card is drawn, there is one less ace in the deck, and one less card overall.
Now, we need to multiply this probability by the probability of drawing a king as the fourth card. Since there are only 48 cards left in the deck at this point (since three cards have already been drawn), the probability of drawing a king is
4/48 = 1/12
Therefore, the probability of drawing 3 aces and 1 king in a row is
(1/5525) × (1/12) = 1/66300
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Casey buys a bracelet. She pays for the bracelet and pays $0. 72 $0. 72dollar sign, 0, point, 72 in sales tax. The sales tax rate is 6% percent. What is the original price of the bracelet, before tax?
Answer:
$12
Step-by-step explanation:
You want to know the amount that has a tax of $0.72 when the tax rate is 6%.
TaxThe tax is computed by multiplying the price by the tax rate.
tax = price × (tax rate)
$0.72 = price × 0.06
price = $0.72/0.06 = $(72/6) = $12
The original price of the bracelet is $12.
A tank is shaped like an upside-down square pyramid, with base of
3m by 3m and a height of 16m. How fast does the height increase when the water is 9m deep if water is being pumped in at a rate of 2/3 m^3/s? Round to 3 decimal places. Note: The volume of a square pyramid is V=((s^2*)h)/3 where s is the length of one side of the base and h is the height
The rate at which the height of the water is increasing when water is being pumped in at a rate of 2/3 m/s and the water is 9m deep is 0.667 m/s.
We can start by using the formula for the volume of a square pyramid to find the volume of water in the tank. Let V be the volume of water in the tank and h be the height of the water.
V = (s² [h])/3
We know that the base of the pyramid is 3m by 3m, so s = 3. Also, the height of the pyramid is 16m, so we have:
V = (3² [h])/3
V = 3h
Now, we can find the rate of change of the volume with respect to time:
dV/dt = 3 [dh/dt]
We know that water is being pumped in at a rate of 2/3 m/s, so dh/dt = 2/3. We want to find how fast the height increases when the water is 9m deep, so h = 9. Substituting these values, we get:
dV/dt = 3 [dh/dt]
dV/dt = 3 [2/3]
dV/dt = 2
Therefore, the rate at which the volume of water is increasing is 2 cubic meters per second. To find the rate at which the height of the water is increasing, we need to solve for dh/dt:
dV/dt = 3 [dh/dt]
2 = 3 * dh/dt
dh/dt = 2/3
So the height of the water is increasing at a rate of 2/3 m/s when the water is 9m deep. Rounded to 3 decimal places, the answer is 0.667 m/s.
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Question 5 Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the equation (-4, 2); y = -x+6
Step-by-step explanation:
If it is parallel to the line y = -x + 6, they have the same gradient and the gradient is the coefficient of x which is -1.
We use the equation y=mx+c
Y is 2
M is -1
X is -4
2 = (-1×-4) + c
2 = 4 + c
C = 2 - 4 = -2
Y = -x -2
Ten people (labeled 1-10) have purchased raffle tickets for a fundraiser. However, they did not all purchase the same
number of tickets. One ticket is to be selected at random. Which of the following could be the probability distribution for
the winning ticket?
C
1
0.10
1
2
0.01 0.01
2
0.10
1
3
4
5
6
0.10 0.10 0.10 0.10
3
4
5
0.05 0.07 0.68
1
2
0.125 0.125
6
0.01
2 3
4
5
6
7 8 9 10
0.01 0.11 0.02 0.12 0.03 0.13 0.04 0.14 0.05 0.15
3
0.125
7
8 9 10
0.10 0.10 0.10 0.10
5
7 8 9 10
0.05
0.03 0.01 0.08
6
4
7
9
10
0.125 0.125 0.125 0.125 0.125 0.125 0.125
8
The correct option is A: the probability distribution for the winning ticket:
1 2 3 4 5 6 7 8 9 10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
Explain about the probability distribution?A frequency distribution that has been idealised is a probability distribution.
Each individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each possible value for a particular variable appears.The probability of occurrence of a value determines how frequently it appears in a sample. Probability is a value between 0 and 1 that indicates the likelihood that something will happen:Zero denotes impossibility.1 denotes a certainty.Total people = 10 (1 - 10)
One ticket is selected at random from each person.
As the selection is independent events of each other, each will have the same probability.
So,
probability = favourable outcome / total outcome.
probability = 1/10
probability = 0.10.
Thus, the correct option is A: the probability distribution for the winning ticket:
1 2 3 4 5 6 7 8 9 10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
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Vin has saved $ 62 so far this month. His goal is to save at least $ 100 by the end of the month. How much can Vin save from now until the end of the month to reach his goal?
1. Let s represent the amount Vin saves from now until the end of
the month. Write an expression that represents Vin’s total savings
this month.
2. Write an inequality that shows that Vin’s total savings for the
month are at least $ 100.
3. Solve the inequality from Exercise 2 and show
all of the possible solutions on the number line.
4. How much can Vin save from now until the end of the month to
meet his goal?
1. Let us suppose the amount saved = s. 2. The inequality is 62 + s ≥ 100. 3. The value of s is: s ≥ 38. 4. Vin can save at least $38 from now until the end of the month to meet his goal of saving at least $100.
What is inequality?A mathematical statement illustrating the relationship between two amounts or expressions that are not always equal is known as an inequality. To represent the connection between the two values, an inequality may employ a number of symbols, including (less than), > (greater than), (less than or equal to), or (greater than or equal to). In algebra and other branches of mathematics, inequalities are frequently used to indicate restrictions, such as limitations on a variable, and to address issues with variables or unknown numbers. An inequality's solution, which may be a range of values rather than a single value, is the collection of all values that meet the inequality.
1. Let us suppose the amount saved = s.
2. The inequality is 62 + s ≥ 100
3. Solving for s we have:
62 + s ≥ 100
s ≥ 100 - 62
s ≥ 38
On the number line, all values greater than or equal to 38 would satisfy this inequality.
4. Vin can save at least $38 from now until the end of the month to meet his goal of saving at least $100.
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Cuantos huevos representa los 3/5 de 4/7 de 420 docenas
Para resolver este problema, primero tenemos que multiplicar las fracciones:
3/5 x 4/7 = 12/35
Luego, encontramos cuántas docenas son 12/35 de 420 docenas:
(12/35) x 420 = 144
Así que 3/5 de 4/7 de 420 docenas (que es equivalente a 12/35 de 420 docenas) representa 144 docenas de huevos.
Para encontrar el número total de huevos, multiplicamos 144 docenas por 12 huevos por docena:
144 x 12 = 1,728
Por lo tanto, 3/5 de 4/7 de 420 docenas representa 1,728 huevos.
Explain how to determine whether two ratios are equivalent
Answer:
Ratios are fractions, right? Set the two fractions equal to each other and then cross-multiply them. If each side of the equation is equal, then the ratios are equal; if not, then the ratios are not equivalent.
Ex. 1
Comparing ratios 4:2 and 2:1
[tex]\frac{4}{2} = \frac{2}{1}[/tex]
Cross-multiplying, we get 4 = 4, but we can also simplify each side of the equation to get 2 = 2.
Ex. 2
Comparing ratios 3:5 and 6:7
[tex]\frac{3}{5} =? \frac{6}{7}[/tex]
Cross-multiply, we get 21 = 30, so the ratios are not equal. This is an example of a case where you can't simplify the ratios.
Ex. 3
Comparing rations 5:12 and 10:24
[tex]\frac{5}{12} = \frac{10}{24}[/tex]
Cross-multiply, 120 = 120 so the ratios are equal.
Hope this helps!