A spinner with repeated colors numbered from 1
to 8 is shown. Sections 1 and 8 are purple.
Sections 2 and 3 are yellow. Sections 4, 5, and 6
are blue. Section 7 is orange.
Which statement about probability is true?
The probability of landing on orange is greater
than the probability of landing on purple.
The probability of landing on yellow is less than
the probability of landing on blue.
The probability of landing on orange is equal to
the probability of landing on yellow.
The probability of landing on purple is equal to
the probability of landing on blue.
Answers
Answer: The probability of landing on orange is equal to the probability of landing on purple
Step-by-step explanation:
The spinner has a total of 8 equally-sized sections, and each section has a unique color. Therefore, the probability of landing on any particular section is 1/8 or 0.125.
Looking at the colors on the spinner, we can see that there are two purple sections, two yellow sections, three blue sections, and one orange section.
Therefore, the probability of landing on orange is 1/8 or 0.125, which is equal to the probability of landing on purple (sections 1 and 8). So the statement "The probability of landing on orange is equal to the probability of landing on purple" is true.
On the other hand, the probability of landing on yellow is 2/8 or 0.25, which is greater than the probability of landing on blue (sections 4, 5, and 6), which is 3/8 or 0.375. So the statement "The probability of landing on yellow is less than the probability of landing on blue" is false.
Therefore, the correct statement about probability is "The probability of landing on orange is equal to the probability of landing on purple."
Related Questions
1. 3 6 12 24 2. 2 9 16 23 3. 53 46 39 32 4. 5 12 26 54 5. 5 20 50 110
FIND 3 NEXT TERMS
Answers
Answer:
Step-by-step explanation:
1. 48 96 192 (multiplying by 2)
2. 30 37 44 ( adding 7)
3. 25 18 11 ( subtracting 7)
4. 110 232 456 ( adding 7, 14, 28, 56 and so on)
5. 230 470 950 (adding 15, 30, 60 120 and so on)
Finding equations of exponential function
Answers
The exponential function are y = 10(2)^x, y = 1.270(1.389)^x, y = 5.656(0.957)^x and y = 6.567(0.870)^x.
What is the equation of the exponential function1. (a) To find the equation of the exponential function that passes through the points (0,10) and (3,80), we can use the formula:
y = a(b)^x
where a and b are constants that we need to find.
First, we can use the point (0,10) to solve for a:
10 = a(b)^0
10 = a
Next, we can use the point (3,80) to solve for b:
80 = 10(b)^3
8 = b^3
b = 2
Therefore, the equation of the exponential function is:
y = 10(2)^x
(b) To find the equation of the exponential function that passes through the points (0.18, 2.8) and (2, 8), we can use the same formula:
y = a(b)^x
First, we can use the point (0.18, 2.8) to solve for a:
2.8 = a(b)^0.18
Next, we can use the point (2, 8) to solve for b:
8 = a(b)^2
Dividing the second equation by the first, we get:
2.857 = (b)^1.82
b = 1.389
Substituting this value of b back into one of the equations to solve for a, we get:
2.8 = a(1.389)^0.18
a = 1.270
Therefore, the equation of the exponential function is:
y = 1.270(1.389)^x
2. (a) To find the equation of the exponential function that passes through the points (2, 5.12288) and (1.92, 2.192), we can again use the formula:
y = a(b)^x
First, we can use the point (2,5.12288) to solve for a:
5.12288 = a(b)^2
Next, we can use the point (1.92,2.192) to solve for b:
2.192 = a(b)^1.92
Dividing the second equation by the first, we get:
0.427 = (b)^(0.08)
b = 0.957
Substituting this value of b back into one of the equations to solve for a, we get:
5.12288 = a(0.957)^2
a = 5.656
Therefore, the equation of the exponential function is:
y = 5.656(0.957)^x
(b) To find the equation of the exponential function that passes through the points (1.192,5) and (5,0.75), we can use the same formula:
y = a(b)^x
First, we can use the point (1.192,5) to solve for a:
5 = a(b)^1.192
Next, we can use the point (5,0.75) to solve for b:
0.75 = a(b)^5
Dividing the second equation by the first, we get:
0.149 = (b)^3.808
b = 0.870
Substituting this value of b back into one of the equations to solve for a, we get:
5 = a(0.870)^1.192
a = 6.567
Therefore, the equation of the exponential function is:
y = 6.567(0.870)^x
3. To find the equation of the exponential function that passes through the points (2.14,7) and (7,205), we can use the same formula as before:
y = a(b)^x
First, we can use the point (2.14,7) to solve for a:
7 = a(b)^2.14
Next, we can use the point (7,205) to solve for b:
205 = a(b)^7
Dividing the second equation by the first, we get:
29.285 = (b)^(4.86)
b = 5.474
Substituting this value of b back into one of the equations to solve for a, we get:
7 = a(5.474)^2.14
a = 0.00061
Therefore, the equation of the exponential function is:
y = 0.00061(5.474)^x
Rounding a and b to the nearest hundred, we get:
a = 0.0006
b = 5.47
So, the final equation of the exponential function is:
y = 0.0006(5.47)^x
We can check if the points (2.14,7) and (7,205) fall on the curve by plugging them into the equation:
y = 0.0006(5.47)^x
When x = 2.14:
y = 0.0006(5.47)^2.14 ≈ 7
When x = 7:
y = 0.0006(5.47)^7 ≈ 205
So, the points do fall on the curve, which means that the equation we found is correct.
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if you have 220 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
Answers
Answer:
6050 square meters
Step-by-step explanation:
You want to know the largest rectangular area that can be enclosed using 220 meters of fencing for 3 sides.
DimensionsFor enclosure length x, the width of the enclosure is half the remaining fence: (220 -x)/2. The area is the product of length and width.
A = (x)(220 -x)/2
This is the equation of a parabola that opens downward. Its vertex (maximum) is halfway between the zeros, which are x=0 and x=220. This means the area is maximized when x=110 and the width is (220-110)/2 = 55.
The maximum area is (110 m)(55 m) = 6050 m².
__
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The answer is 2025 sq. meter.
If you have 220 meters of fencing and want to enclose a rectangular area up against a long, straight wall, the largest area you can enclose is 4840 square meters. Explanation: To determine the largest possible area, we have to find out how to divide the 220 meters of fencing so that we can maximize the space enclosed by it. If one side of the rectangle is x meters long, the other side is (110 - x) meters long (because we have one straight wall to use as a side).The perimeter of the rectangle can be calculated by adding up all four sides of the rectangle. Hence:2x + (110 - x) + (110 - x) = 220We simplify the equation to solve for x:2x + 220 - 2x = 220-x = 55Therefore, one side of the rectangle is 55 meters long, and the other side is (110 - 55) = 55 meters long as well. The area of a rectangle is given by its length multiplied by its width. In this case, the area is:55 x 55 = 3025.
Therefore, the largest area that can be enclosed is 3025 square meters.
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A scatter plot is shown on the coordinate plane.
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8
Which of the following graphs shows a line on the scatter plot that fits the data?
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8, with a line passing through the coordinates 5 comma 7 and 10 comma 9
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8, with a line passing through the coordinates 2 comma 7 and 6 comma 7
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8, with a line passing through the coordinates 1 comma 4 and 5 comma 6
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8, with a line passing through the coordinates 1 comma 4 and 3 comma 8
Answers
The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates [tex](1,4)[/tex] and [tex](5,6)[/tex] .
What is a graph?The best way to determine which graph shows a line that fits the data is to plot the line on the scatter plot and see how well it fits with the points.
Let's start with option A, which shows a line passing through the coordinates 5 comma 7 and 10 comma 9. When we plot this line on the scatter plot, we can see that it doesn't fit the data very well.
The line doesn't pass through many of the points and seems to be a poor representation of the relationship between the x and y values.
Option B shows a line passing through the coordinates 2 comma 7 and 6 comma 7. Again, when we plot this line on the scatter plot, we can see that it doesn't fit the data very well.
The line passes through some points, but not all of them, and it doesn't seem to represent the relationship between the x and y values very well.
Option C shows a line passing through the coordinates 1 comma 4 and 5 comma 6. When we plot this line on the scatter plot, we can see that it fits the data fairly well. The line passes through several of the points and seems to capture the overall trend of the data.
Option D shows a line passing through the coordinates 1 comma 4 and 3 comma 8. When we plot this line on the scatter plot, we can see that it fits the data fairly well. The line passes through several of the points and seems to capture the overall trend of the data.
Therefore, The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates [tex](1,4)[/tex] and [tex](5,6)[/tex] .
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The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates (1,4) and (5,6).
What is the best-fit line?A line of best fit is a straight line that minimizes the distance between it and some data. It is used to express a relationship in a scatter plot of different data points.
Option A Some points are too far from the line when we draw a line through the points (5, 7, and 10). It is not the minimum distance between the line and the scattered data. So, it's not a line on the scatter plot that fits the data.
Option B When we draw a line through (2,7) and (6,7) then the distance between the line and the scattered is still much. So, it's not a line on the scatter plot that fits the data.
Option C When we draw a line through (1,4) and (5,6) then most of the points are nearer to the line and it defines a relation between the points and the line more efficiently. So, this line is the best-fit line for this scattered graph.
Option D When we draw a line through (1,4) and (3,8) then some points are too far from this line. It is not the minimum distance between the line and the scattered data. So, it's not a line on the scatter plot that fits the data.
Therefore, the graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates (1,4) and (5,6).
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If someone work 48.5 hours in a week, they would get how many amount of overtime hours?
Answers
If someone works 48.5 hours in a week and their regular work week is 40 hours, then they would have worked 8.5 hours of overtime.
What is meant by a week?
A week is a unit of time equal to seven days, usually beginning on Monday and ending on Sunday. It is commonly used to measure and organize time.
What is meant by hours?
Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.
According to the given information
In most cases, overtime pay is calculated as 1.5 times the employee’s regular hourly rate.
If someone works 48.5 hours in a week and their regular workweek is 40 hours, then they would have worked 8.5 hours of overtime.
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Graph the following equation on the coordinate plane.
y = -3x + 8
Answers
Answer:
See the picture below
Step-by-step explanation:
To graph this linear function, you need two things: slope and y-intercept.
y-intercept:
This is where the line crosses the x axis. It will cross when x = 0. (0,b). The b is the y-intercept. You see this in the equation at the end. In this case the y-intercept it 8.
Slope:
This is the change in y over the change in x. On the graph I highlighted two points (0,8) and (1,5). If you start at (0,8) and go to (1,5), you go straight down 3 units and 1 unit right. This is your slope. Going down is a negative direction and going right is a positive direction. The slope would be the change in y over the change in x. [tex]\frac{-3}{1}[/tex] which simplified would be -3. The slope is -3.
Helping in the name of Jesus.
Solve for x. Round your answer to the nearest tenth
Answers
Hence, value of variable y in the triangle is 7.5
Define triangle proportionalityTriangle proportionality is a relationship that exists between the sides of a triangle when a line is drawn parallel to one side of the triangle, intersecting the other two sides. Specifically, the line divides the two sides in proportion to the length of the third side.
We know that, if a line is drawn parallel to one side of a triangle, then the line divides the other two sides in proportion.
AB/AC=2y+5/2y+25
We know that
AB=BC=1/2AC
½=2y+5/2y+25
2y+25=4y+10
2y=15
y=7.5
value of variable y in the triangle is 7.5.
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20
Your friend won't get many stars like this! What changes
would you make to the equation to help your friend
collect all the stars? Why are those changes going to
work?
-16
.
-12
✓
Share With Class
-8
12
16
y= $x+4{x<2}
-4
Answers
Answer:
Step-by-step explanation:
10-16=to 4
I need help with this problem please
5+3{4-3+2)×9^2+100
Answers
Answer:
834
Step-by-step explanation:
5 + 3(4 - 3 + 2) x [tex]9^{2}[/tex] + 100
5 + 3(3) x 81 + 100
5 + 9 x 81 + 100
5 + 729 + 100
834
Helping in the name of Jesus.
What is the equation of the line that passes through the point
(
5
,
0
)
(5,0) and has a slope of
6
5
5
6
Answers
The equation of the line that passes through the point (5, 0) and has a slope of 6/5 is:
y = (6/5)x - 6To find the equation of the line that passes through the point (5, 0) and has a slope of 6/5,
we will use the point-slope form of the equation of a line, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Step 1: Plug in the given point (5, 0) as (x1, y1) and the slope (6/5) as m.
y - 0 = (6/5)(x - 5)
Step 2: Simplify the equation.
y = (6/5)(x - 5)
Step 3: Distribute the slope (6/5) on the right side.
y = (6/5)x - 6
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A carnival charges $3 for kids and $10 for adults. On Saturday, there were 500 visitors, and the total amount taken at the gate was $3,600. The
equation representing the number of visitors is k + a = 500, where k represents the number kids and a represents the number of adults. The
equation representing the amount of money collected is 3k + 10a = 3,600. How many kids and adults visited the carnival?
Answers
hope this helps
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 5, 10, 15, 20, ... an =
Answers
Answer:
[tex]a_{n}[/tex] = 5n
Step-by-step explanation:
there is a common difference between consecutive terms, that is
10 - 5 = 15 - 10 = 20 - 15 = 5
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 5 and d = 5 , then
[tex]a_{n}[/tex] = 5 + 5(n - 1) = 5 + 5n - 5 = 5n
an = 5n
Step-by-step Explanation:
The sequence goes up by 5 each time, so we can represent it using the formula:
an = 5n
Where n represents the position of the term in the sequence. To find a specific term, we substitute the value of n into the formula. For example, to find the 6th term:
a6 = 5(6)
a6 = 30
So the 6th term in the sequence is 30.
What does y equal?
5(2y-1)<-15
Answers
Answer:
To solve for y in the inequality 5(2y - 1) < -15, we can simplify the expression on the left-hand side as follows:
5(2y - 1) < -15
10y - 5 < -15 // Distribute the 5 on the left side
10y < -10 // Add 5 to both sides
y < -1 // Divide both sides by 10 and flip the inequality
Therefore, the solution is y < -1.
if f(x) = 2x^2 + 3x - 1 and g(x)= 4x+ 10 then (f . g) (x) is whar rype of function?
Linear
Cubic
Quartic
Quadratic
PLSS HELPPP
Answers
Answer:
quadratic
Step-by-step explanation:
see image above for explanation.
Apply the distributive property to factor out the greatest common factor. 24a−18b
Answers
Step-by-step explanation:
The GCF of 24 and 18 is '6'...factor that out to get
6 ( 4a-3b) that is all you can do....
what is the equation of a line that passes through 1,3 and has a slope of 5/4
Answers
Answer: y-3= 5/4(x-1) is the point slope form answer, y = 1.25x + 1.75 is the slope intercept form answer.
Step-by-step explanation:
Determine the unknown angle measures of △def. round to the nearest degree. m∠d = ° m∠f = °
Answers
Answer: [tex]\angle F = 44\°\\angle D= 46\°[/tex]
Step-by-step explanation:
I need help!!!!!!!!!!!!!!1
Answers
Answer:
∠2 = 125°
Step-by-step explanation:
∠1 and ∠2 form a straight angle of 180° (∠3 and ∠4 aswell)
∠1 = ∠3, because they are cross angles (∠3 and ∠4 aswell)
We can write an equation according to this and find y:
(8y - 9)° = (6y + 7)°
8y - 6y = 7 + 9
2y = 16 / : 2
y = 8
∠1 = 8 × 8 - 9 = 55°
∠2 = 180° - 55° = 125°
∠3 =∠1 = 6 × 8 + 7 = 55°
∠4 = 180° - 55° = 125°
Please help!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
It will cost $1200 to cover both sides of the green roof with plants at a cost of $0.75 per square foot.
To calculate the cost of covering both sides of the green roof, we first need to find the area of the roof. We can use the formula for the area of a rectangle:
area = length x width
Since the roof is 40 feet long, we need to find the width to calculate the area. We can estimate the width from the picture, but it's not given explicitly. So, we can make a reasonable assumption that the width is the same as the length of the shorter side of the roof, which appears to be about 20 feet.
Using this assumption, we can calculate the area of one side of the roof:
area = length x width = 40 ft x 20 ft = 800 sq ft
Since there are two sides to the roof, the total area is twice this amount:
total area = 2 x 800 sq ft = 1600 sq ft
To find the total cost of covering both sides of the roof, we can multiply the area by the cost per square foot of plants:
total cost = area x cost per sq ft
= 1600 sq ft x $0.75/sq ft
= $1200
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Keisaun was covering a square bulletin board with paper. One side of the bulletin board measure 3 feet. How much paper did he need?
Answers
-------------------------------------------------------------------------------------------------------------
Answer: 9 square feet
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Keisaun needs to cover a square. One side is 3 feet}[/tex]
Find: [tex]\textsf{We need to find how much paper he needs}[/tex]
Solution: Using the information that was given to us we know that we need to determine the area of the square that Keisaun needs to cover. We know that the area formula for a square is side * side. We are also given the information that a single side of the board is measured to be 3 feet. Therefore, using that information we can plug the value into the square area formula and solve.
[tex]\textsf{Area of a square = side * side}[/tex][tex]\textsf{Area of a square = 3 feet * 3 feet}[/tex][tex]\textsf{Area of a square = 9 feet}^2[/tex]Therefore, the answer to the question would be that Keisaun would need 9 square feet of paper to cover the square bulletin board.
Gabriel goes out to lunch. The bill, before tax and tip, was $9.50. A sales tax of 7.5% was added on. Gabriel tipped 15% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answers
Answer:
Gabriel left $1.53 in tips.
Step-by-step explanation:
Sales tax: 9.50*0.075=0.7125
9.50+0.71=10.21
Total with Sales Tax: $10.21
Tip: 10.21*0.15=1.5315
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.
Answer part a, b, and c for brainliest!!
Answers
The sample space when 2 lollipops are randomly selected with replacement is S_with_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}
The sample space when lollipops are selected without replacement is S_without_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}.
The experiment with replacement (Part A) shows independent events because the probability of each lollipop being chosen is the same for both selections.
How to find the sample space ?When selecting 2 lollipops with replacement, we put the first lollipop back into the bag before choosing the second one. When selecting 2 lollipops without replacement, we do not put the first lollipop back into the bag before choosing the second one.
The outcome of the first event does not affect the probability of the second event.
The experiment without replacement (Part B) shows dependent events because the probability of the second lollipop being chosen is affected by the outcome of the first event. When one lollipop is removed from the bag, there are fewer options available for the second selection, and the probabilities of the remaining lollipops change.
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A meter reader determines that a business has used 3550 kW•h of energy in two months. If electricity costs 10 cents per kW•h, calculate the bill.
Answers
Answer:
The first step is to calculate the total cost of energy used in two months. To do that, we need to multiply the amount of energy used by the cost per kilowatt-hour:
3550 kW•h x $0.10/kW•h = $355.00
So the total cost of energy used in two months is $355.00. This is the amount of the bill that the business will receive for its electricity usage.
Step-by-step explanation:
Answer:
To calculate the bill, we need to multiply the amount of energy used (3550 kW•h) by the cost per kW•h (10 cents).
3550 kW•h x 10 cents/kW•h = $355.00
Therefore, the bill for the business is $355.00.
Step-by-step explanation:
please pa brainliest po thanks.
confirm that the expected counts are large enough to use a chi-square distribution to calculate the p-value. what degrees of freedom should you use?
Answers
The expected counts are large enough to use a chi-square distribution to calculate the p-value because the predicted-counts are at least 5, the degree-of-freedom that should be used is 2.
The "degree-of-freedom" is defined as the number of independent parameters or variables that must be specified to completely describe a system or equation.
We see that the projected counts(expected-counts) are large enough to use a chi-square distribution if all predicted counts are at least 5,
So, This condition is satisfied and it satisfies that the expected counts are large enough to use a chi-square distribution to calculate the p-value.
In the table we see that the number of categories are three : {Red, Black, Green},
So, degree of freedom is = (number of categories) - 1 = 3 - 1 = 2.
Therefore, the degree of freedom is 2.
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The given question is incomplete, the complete question is
Confirm that the expected counts are large enough to use a chi-square distribution to calculate the p-value. The information table is given below.
What degrees of freedom should you use?
What is the radius of a cone with diameter d? An ice cream cone is filled exactly level with the top of the cone. The cone has a -cm diameter and -cm depth. Approximate how much ice cream (in ) is in the cone? Use 3.14 for .
Answers
Answer: radius is 2.5 and volume of ice cream is 58.9 cm cubed
Step-by-step explanation:
imagine that these cards are face down, and you pick at random.
A A A B B C
Answers
Answer:
1:A
2:B
3:A
that's the answer I think
Justine just ran her first race. Her distance from the finish line decreased as she ran.
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation?
Answers
The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero.
What is linear equation?
A linear equation is a mathematical equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.
What is y-intercept?
In a linear equation of the form y = mx + b, the y-intercept (b) is the point where the line intersects the y-axis.
According to given information:The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero. In the context of Justine's race, the y-intercept would represent her starting distance from the finish line.
It would be the distance from the finish line when she began the race, or the distance she would have to run to reach the finish line if she started at the beginning. The slope of the line would tell you how much the distance decreases as she runs.
Together, the y-intercept and slope of the line can provide useful information for understanding and analyzing Justine's race.
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The answer of the given question based on the linear relationship is , the y-intercept gives information about Justine's initial position or starting point before she started running the race.
What is Linear relationship?A linear relationship is a type of relationship between two variables where their relationship can be described by a straight line. In other words, the change in one variable is directly proportional to the change in the other variable. This means that as one variable increases or decreases, the other variable also changes in a consistent and predictable way. Linear relationships are commonly studied in mathematics, statistics, and other fields as they provide a useful framework for understanding the relationship between two variables and making predictions based on that relationship.
In the context of this linear relationship, the y-intercept represents the starting point of Justine's race. It is the point where her distance from the finish line is zero, which is the beginning of the race. Therefore, the y-intercept gives information about Justine's initial position or starting point before she started running the race.
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you are testing a new medication to see if it lowers high blood pressure. subjects with high blood pressure volunteered to take part in the experiment. 290 subjects were randomly chosen to receive the medicine (population 1: treatment) and 170 received a placebo (population 2: control). blood pressure was lowered to healthy levels in in 157 of the treatment group and 90 of the controls. test the claim that the new beta-blocker medicine is effective at a significance level of
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The new beta-blocker medicine is effective in lowering high blood pressure.
A hypothesis test can be used to test the claim that a new beta-blocker is effective at the significance level α (significance level).
Let us define the null and alternative hypotheses as follows:
Null Hypothesis (H0):
This drug does not affect high blood pressure.
Alternative hypothesis (Ha):
The drug is effective in lowering high blood pressure.
To test this hypothesis, we can use a two-sample proportional z-test comparing rates of success (lowering blood pressure) in two independent populations (treatment and control groups).
First, we need to calculate the sample proportions and the standard errors of their differences. Let p1 = treatment group success rate,
p2 = control group success rate,
and p = pooled rate.
p1 = 157/290 = 0.541
p2 = 90/170 = 0.529
p = (157 + 90) / (290 + 170) = 0.536
The standard error of the difference in proportions can be calculated as:
SE = sqrt[p*(1-p)(1/n1 + 1/n2)]
= square[0.536(1-0.536)*(1/290 + 1/170)]
= 0.056
Then you can compute the test statistic z.
z = (p1 - p2) / SE
= (0.541 - 0.529) / 0.056
= 2.143
Finally, we can compute the p-value associated with the test statistic z, assuming a standard normal distribution.
p-value = P(Z > 2.143) = 0.0169
The p-value (0.0169) is less than the significance level α, so we neglect the null hypothesis and can say that this drug is effective in lowering high blood pressure.
The chosen importance is not specified in the question, so it is not sure if it's important at that level. If α is given, you can compare the p-value to α and make a decision based on that.
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1. Kourtney invests $10,000 in an account that earns 4% interest compounded continuously.
What is the total amount of her investment after 12 years? Round to the nearest cent.
Answers
Answer: $14,983.50
Step-by-step explanation:
the area of this parallelogram is 51.5 cm2. work out the value of x
Answers
Answer:
The formula for area of a parallelogram is A=bh
x=10.3
Step-by-step explanation:
We don't have the base but we have the height.
the base is x and the height is 5
if the area is 51.5
we should divide the height to find the base.
51.5÷5=10.3
so the base is 10.3
Check if answer is correct:
b=10.3
h=5
a= 51.5
10.3(5)=51.5
a= 51.5cm²
I hope this helps as long as you know the formula it's easy :D