Use circumcenter to draw a circle through three non-collinear points.
a) Draw diameter, construct equilateral triangle with one vertex at center and other two on circle.
b) Draw diameter, construct regular hexagon with one vertex at center and other vertices on circle.
What is diameter?Step 1: To construct a circle through three points not on a line, we can use the circumcenter of a triangle. We first construct the perpendicular bisectors of any two sides of the triangle. The point where these two lines intersect is the circumcenter of the triangle. We can then draw a circle with this point as the center, which passes through all three vertices of the triangle.
Step 2:
a) To construct an equilateral triangle inscribed in a circle, we can draw a diameter of the circle and then construct an equilateral triangle with one of the endpoints at the center of the circle and the other two endpoints on the circle itself.
b) To construct a regular hexagon inscribed in a circle, we can draw a diameter of the circle and then construct a regular hexagon with one of the vertices at the center of the circle and the other vertices on the circle itself.
c) To construct a square inscribed in a circle, we can draw a diameter of the circle and then construct a square with one of the vertices at the center of the circle and the other vertices on the circle itself.
Step 3:
a) To construct a tangent to a circle through a point on the circle, we can draw a radius of the circle to the point of tangency, and then construct the perpendicular bisector of this radius. The line where the perpendicular bisector intersects the circle is the tangent line.
b) To construct a tangent to a circle through a point outside the circle, we can draw a line from the point to the center of the circle, and then construct the perpendicular to this line at the point of tangency. The line where the perpendicular intersects the circle is the tangent line.
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Determine whether the graph of the equation is symmetric with respect to the
The graph of the equation y = x² + 5 is symmetric with respect to the y-axis, the correct option is (b).
To determine the symmetry of the graph, we can substitute (-x) for x in the equation and simplify:
y = (-x)² + 5
y = x² + 5
Since the equation is unchanged when x is replaced by (-x), the graph is symmetric with respect to the y-axis.
We can also see that the graph is not symmetric with respect to the x-axis or the origin. To check for symmetry with respect to the x-axis, we can substitute (-y) for y in the equation:
(-y) = x² + 5
y = -(x² + 5)
The equation is not the same as the original equation, so the graph is not symmetric with respect to the x-axis. Similarly, to check for symmetry with respect to the origin, we can substitute (-x) and (-y) for x and y in the equation:
(-y) = (-x)² + 5
y = x² + 5
The equation is not the same as the original equation, so the graph is not symmetric with respect to the origin.
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The complete question is:
Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, origin, or none of these
y = x² + 5
Check all the answers
a. The graph is symmetric with respect to the x-axis
b. The graph is symmetric with respect to the y-axis
c. The graph is symmetric with respect to the origin
d. none of the above
write the opposite of -4 1/2 and explain how it's related to -4 1/2. Use a number line as a reference in your explanation. Use the number line to think about the location of the number 2 and the number n, where n is greater than 3. write an inequality comparing the opposite of 2 and the opposite of n. explain how the number line shows that your inequality is correct
We can use the number line to see that 2 and any number greater than 3 are to the right of -4 1/2. By finding the Opposites of 2 and n and comparing them, we can write an inequality that is correct based on the number line.
The opposite of -4 1/2 is 4 1/2. This is because the opposite of a number is the number that is the same distance from 0 on the number line, but in the opposite direction. On a number line, -4 1/2 is to the left of 0, so its opposite, 4 1/2, is to the right of 0.
Looking at the number line, we can see that the number 2 is to the right of -4 1/2, but to the left of 4 1/2. Any number greater than 3, represented by n, is also to the right of -4 1/2.
The opposite of 2 is -2 and the opposite of n is -n. So, the inequality we can write is:
-n < -2
This is because -2 is to the left of -n on the number line. We can see that this inequality is correct on the number line because -2 is closer to 0 than -n, which means that -n is less than -2.
In summary, the opposite of -4 1/2 is 4 1/2, and it is related to -4 1/2 because they are the same distance from 0 on the number line, but in opposite directions. We can use the number line to see that 2 and any number greater than 3 are to the right of -4 1/2. By finding the opposites of 2 and n and comparing them, we can write an inequality that is correct based on the number line.
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It starts to snow at 10:54 AM it snows for two hours 16 minutes without stopping what time does a snow stop ?
Please help with this problem
To arrive at this answer, you can add the duration of the snowfall to the starting time to get time 1:10 PM
what is duration?
Duration refers to the length of time that something lasts or continues. It is the amount of time between the start and end of an event or activity. For example, the duration of a movie could be two hours, the duration of a concert could be three hours,
In the given question,
If it starts snowing at 10:54 AM and it snows for two hours and 16 minutes without stopping, then the snow will stop at 1:10 PM.
To arrive at this answer, you can add the duration of the snowfall to the starting time.
10:54 AM + 2 hours 16 minutes = 1:10 PM
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Write an equation tomorrow, the statement, the product of -8 and (y+3) is 32. How you can use the equation to reason about the value of Y?
The equation to model the statement is [tex]-8(y + 3) = 32[/tex] and the value of y is -7.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given statement is the product of – 8 and [tex](y + 3)[/tex] is 32.
Product means the operation is multiplication.
So the equation can be written as,
[tex]-8 (y + 3) = 32[/tex]
Dividing both sides by 8,
[tex]-(y + 3) = 4[/tex]
[tex]y + 3 = -4[/tex]
[tex]y = -4 - 3 = -7[/tex]
Hence the value of y is -7.
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in a randomized controlled trial, sometimes patients agree to receive an intervention but later decide to stop taking the medication. moreover, some patients who were assigned to placebo decide to stop taking the placebo pill and buy the drug on their own (even when they do not know that they are taking a placebo pill). when this happens, researchers typically do the analysis according to the original assignment of the treatment regardless of the actual treatment received. what is the name of this procedure to analyze the data?
The procedure used to analyze the given data is intention-to-treat analysis.
The procedure to analyze data according to the original assignment of the treatment regardless of the actual treatment received is called the intention-to-treat (ITT) analysis. It is considered the gold standard in clinical trial analysis because it preserves the randomization and avoids bias that may arise from differential dropouts or non-compliance. By analyzing all patients according to their randomized group, the ITT analysis provides an unbiased estimate of the treatment effect and better reflects the real-world effectiveness of the intervention.
The intention-to-treat (ITT) analysis is different from other types of analyses because it includes all patients according to their original randomized group, regardless of whether they received the assigned treatment or not. This is in contrast to per-protocol analysis, where only patients who completed the study without any major protocol deviations are included, or as-treated analysis, where patients are analyzed according to the actual treatment received.
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how do you multiply 7(b-5)(b-4) step by step
To multiply 7(b-5)(b-4), you can follow these steps:
1.
Start by distributing the 7 to the terms inside the parentheses:
7(b-5)(b-4) = 7 * b * (b-4) - 7 * 5 * (b-4)
2.
Simplify each term using the distributive property:
= 7b^2 - 28b - 35b + 140
3.
Combine like terms:
= 7b^2 - 63b + 140
So, the final answer is 7b^2 - 63b + 140.
The remainders obtained when px³ + qx² + 4x − 2 is divided by x-1 and x + 2 are
equal. Show that 3p - q = -4. If also the remainder is -18 when the polynomial is
divided by x-2, find the value of p and of q.
Our first equation yields p = 0. We obtain q = 3p = 0 by substituting this in the second equation. Hence, p = q = 0. As a result, the values of p and q are both zero.
what is polynomial ?A polynomial is a mathematical equation composed of variables and coefficients that is solved using mathematical operations like combination, deletion, multiplication, and quel integer exponents.
given
The result of dividing the same polynomial by x + 2 is
(p[tex]x^{2}[/tex] + (2p-q)x + (5q-2))(x+2) + (q[tex]x^{3}[/tex] + q[tex]x^{2}[/tex]+ 4[tex]x^{2}[/tex]) (12p-9q-2)
p+2q-2 = 12p-9q-2
When we simplify this equation, we obtain:
11p + 2q = 0
=> 3p - q = -4 (by adding 22p to both sides and multiplying both sides by 2)
Now, we also understand that the polynomial, when divided by x – 2, leaves a remainder of -18. Synthetic division or polynomial long division yields the following results:
= (p (x-2)³ + (7p-2q)(x-2) (x-2)² + (18q-8p)(x-2)) - 18
When we compare coefficients, we find:
p = 7p - 2q = 18q - 8p = 0
Our first equation yields p = 0. We obtain q = 3p = 0 by substituting this in the second equation. Hence, p = q = 0. As a result, the values of p and q are both zero.
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You estimate that it requires fifty minutes to serve 85 customers through a cafeteria line. If your normal lunch crowd averages 200 customers, about how much time will it take for the lunch crowd to go through the cafeteria line (assuming a constant flow of customers)? To the nearest minutes
Answer:
If 85 customers can be served in 50 minutes, then we can find the number of minutes per customer by dividing 50 by 85: 50 minutes / 85 customers ≈ 0.588 minutes per customer To estimate the time required for 200 customers, we can multiply the time per customer by the number of customers: 0.588 minutes per customer x 200 customers ≈ 117.6 minutes Rounding to the nearest minute, we can estimate that it will take about 118 minutes for the lunch crowd of 200 customers to go through the cafeteria line.
Nicole is 1.55 meters tall. At 2 p.m., she measures the length of a tree's shadow to be 30.05 meters. She stands 25.6 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
approximately 1.81 meters.
Step-by-step explanation:
Let's call the height of the tree "h". We can set up a proportion based on the similar triangles formed by Nicole, her shadow, the tree, and the tree's shadow:
(height of Nicole) / (length of Nicole's shadow) = (height of tree) / (length of tree's shadow)
Substituting the given values, we get:
1.55 / 25.6 = h / 30.05
Simplifying and solving for h, we get:
h = (1.55 / 25.6) * 30.05
= 1.81181640625
Rounding to the nearest hundredth, we get:
h ≈ 1.81 meters
the height of the tree is approximately 1.81 meters.
←
What is the total cost of a $704 tablet computer that is on sale at 13% off if the local sales tax rate is 4%?
The total cost of the tablet is S
(Round to two decimal places as needed.)
Answer:
636.98
Step-by-step explanation:
[tex]704 * .13 = 91.52 (discount)\\704 - 91.52 = 612.48 (price after discount)\\612.48 * .04 = 24.4992 (tax)\\612.48 + 24.4992 = 636.9792(Price with tax)\\round= 636.98[/tex]
the sales tax applies to the price after the discount is applied
4. Given the following: X(7, 0), Y(7, 5) and Z(0, 5), calculate the distance or
length of XY, YZ, and XZ. What is the perimeter of the triangle?
a. 6.8 units
b. 11.3 units
c. 15.8 units
d. 20.6 units
Answer:
To calculate the distance or length of XY, YZ, and XZ, we can use the distance formula: Distance = √[(x2 - x1)^2 + (y2 - y1)^2] For XY: Distance = √[(7 - 7)^2 + (5 - 0)^2] Distance = √[0 + 25] Distance = √25 Distance = 5 units For YZ: Distance = √[(0 - 7)^2 + (5 - 5)^2] Distance = √[49 + 0] Distance = √49 Distance = 7 units For XZ: Distance = √[(0 - 7)^2 + (5 - 0)^2] Distance = √[49 + 25] Distance = √74 Therefore, the length
Harper is working two summer jobs, making $12 per hour babysitting and $8 per hour landscaping. Harper must earn no less than $140 this week. Write an inequality that would represent the possible values for the number of hours babysitting, b b, and the number of hours landscaping, l l, that Harper can work in a given week.
The inequality that represents the possible values for the number of hours babysitting and the number of hours landscaping is 12b + 8l ≥ 140.
What is Inequality:A mathematical inequality is a statement that two quantities or expressions are not equal. Inequalities are used to compare the relative sizes of numbers or variables and represent constraints or conditions in various contexts, such as optimization problems, systems of linear equations, or financial planning.
Here we have
Harper is working two summer jobs, making $12 per hour babysitting and $8 per hour landscaping. Harper must earn no less than $140 this week.
Let Harper work for 'b' hours in the baby setting and l hours in landscaping
The amount earned by Haper by babysitting = $ 12 × b = 12b
The amount earned by Haper by landscaping = $ 8 × l = 8l
Here the amount should not be less than $ 140
=> 12b + 8l ≥ 140
Hence,
The inequality that represents the possible values for the number of hours babysitting and the number of hours landscaping is 12b + 8l ≥ 140.
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70 divided by 5 long division
Answer:
14
Step-by-step explanation:
70/5 is 14
ez cheesey toes
the probability of choosing two green balls without replacement is 1150, and the probability of choosing one green ball is 1225.what is the probability of drawing a second green ball, given that the first ball is green?
The probability of drawing a second green ball, given that the first ball is green is equals to the 11/24.
We have specify the probabilities values for selecting balls without replacement,
Probability of choosing two green ball
= 11/50
Probability of choosing one green ball
= 12/25
We have to determine the probability of drawing a second green ball, given that the first ball is green. Let us consider the two events as
A = Probability of second ball green
B = probability first ball is green = 12/25
P (A and B) = P (Both balls are green)
= 11/50
Fir determining the required probability we use conditional probability formula,
P ( A/B ) = P( A and B) / P (B)
Plug all known values in above formula,
P ( A/ B) = ( 11/50)/(12/25)
= (11 × 25)/(50×12)
= 11/24
Hence, required probability value is equals to 11/24.
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I need helppppppppppppppppp
Answer:
Step-by-step explanation:
You just need to finish your proof by
adding what you were intending to prove.
m∠ ABC is equal to the m∠GHI.
You are correct so far.
Justin ate 1/2 of a pizza and Dan ate 3/8th. In total, how much pizza did they eat?
Answer: They ate 7/8 of the pizza in total.
Find the midpoint of the line segment with end coordinates of:
(−2,−4) and (−1,−5)
Give coordinates as decimals where appropriate.
What is the answer
Answer:
(- 1.5, - 4.5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (- 2, - 4 ) and (x₂, y₂ ) = (- 1, - 5 ) , then
midpoint = ( [tex]\frac{-2-1}{2}[/tex] , [tex]\frac{-4-5}{2}[/tex] ) = ( [tex]\frac{-3}{2}[/tex] , [tex]\frac{-9}{2}[/tex] ) = (- 1.5, - 4.5 )
PLEASE HELP ILL GIVE BRAINLIEST
Answer: 1 and 5
Step-by-step explanation:
Help with this question
The billing period is 31 days, so the average daily balance is $1,437.73.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and understand relationships between variables. Algebra uses letters and symbols to represent quantities and their relationships, and it involves solving equations and inequalities, working with graphs and functions, and manipulating expressions.
Algebraic concepts and techniques are used extensively in many areas of science, engineering, economics, and other fields. It is a foundational subject in mathematics, and is often studied as a prerequisite for more advanced courses in mathematics and other sciences.
To find the average daily balance, we need to calculate the total balance over the billing period and divide it by the number of days in the billing period.
The total balance is:
10 days at $778.12 = $7,781.20
8 days at $1,876.00 = $15,008.00
3 days at $2,112.50 = $6,337.50
10 days at $1,544.31 = $15,443.10
Total balance = $44,569.80
The billing period is 31 days, so the average daily balance is:
$44,569.80 / 31 = $1,437.73
Rounding this to the nearest cent, we get an answer of $1,437.74, which is option C.
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The vertices of a rhombus are located at the coordinates (1, 3), (4, 7), (9, 7),
and (6, 3)
Find the length of the horizontal sides of the rhombus and its perimeter.
Answer: To find the length of the horizontal sides of the rhombus, we need to find the distance between points (1, 3) and (9, 7), which is the same as the distance between points (4, 7) and (6, 3).
Using the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(9 - 1)² + (7 - 3)²]
d = √[64 + 16]
d = √80
d ≈ 8.94
So the length of the horizontal sides of the rhombus is approximately 8.94 units.
To find the perimeter of the rhombus, we need to find the distance between all four vertices and add them up.
Using the distance formula:
d₁ = √[(4 - 1)² + (7 - 3)²] = √25 = 5
d₂ = √[(9 - 4)² + (7 - 7)²] = √25 = 5
d₃ = √[(6 - 9)² + (3 - 7)²] = √16 + 16 = √32 ≈ 5.66
d₄ = √[(1 - 6)² + (3 - 7)²] = √25 + 16 = √41 ≈ 6.40
Perimeter = d₁ + d₂ + d₃ + d₄ = 5 + 5 + 5.66 + 6.40 ≈ 22.06
So the perimeter of the rhombus is approximately 22.06 units.
Step-by-step explanation:
A potato manufacturer make a small bag that holds 2 pounds of potatoes. They want to make a bag for Costco that holds 20 pounds of potatoes. By approximately what factor will the surface area of the bag increase? Round to the nearest tenth.
factor:
The surface area of the larger bag will increase by a factor of approximately 10.
What is surface area?
The surface area of a three-dimensional object is the total area of all its faces. In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things. increase.
In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things.
This is because the surface area of a three-dimensional object is proportional to the square of its linear dimensions.
Since the linear dimensions of the larger bag are 10 times that of the smaller bag (20 pounds vs. 2 pounds), the surface area of the larger bag will be roughly [tex]10^{2 }= 100[/tex] times that of the smaller bag.
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y = a(x _ 2)^2 _ 3. :)
Answer:
y = (x +2)² -3
Step-by-step explanation:
You want the math operators that are needed to properly write the equation of the given parabola in vertex form.
VertexThe vertex is the low point on the curve. Its coordinates are (-2, -3).
Vertex formThe vertex form of the equation for a parabola is ...
y = a(x -h)² +k
You want the equation for (h, k) = (-2, -3). It is ...
y = a(x +2)² -3
The operators are plus (+) and minus (-).
Answer:
[tex]y = a(x+2)^2-3[/tex]
Explanation:
You are adding the 2 to move the whole function two times to the left and you are subtracting the 3 so that the minimum of the quadratic function is -3.
Complete the statement. In any given circle, the measure of a(n) Choose... is one-half the measure of the Choose..
Answer:
In any given circle, the measure of an inscribed angle is one-half the measure of the central angle that intercepts the same arc.
what fraction of 5 litres is 6800ml give answer as mixed number and lowest term
The fraction of 5 liters that is 6,800 ml is 8/5 or 1 3/5 in mixed number form, which represents one whole 5-liter container plus 3/5 of another 5-liter container.6800 ml is equivalent to 6.8 liters. To find the fraction of 5 liters that is 6.8 liters, we can divide 6.8 by 5:
6.8 / 5 = 1 3/5
Therefore, the fraction of 5 liters which is 6800 ml is 1 3/5, which is a mixed number. This means that the total volume of 6.8 liters is equivalent to one whole 5-liter container, plus 3/5 of another 5-liter container.
To convert this mixed number into a fraction, we can first multiply the whole number by the denominator of the fraction and add the numerator to get the improper fraction:
1 * 5 + 3 = 8
The improper fraction is 8/5. This means that 6.8 liters are equivalent to 8/5 of 5 liters.
To reduce the fraction to the lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 1:
8/5 = 8 ÷ 1 / 5 ÷ 1 = 8/5
A fraction is a mathematical representation of a part of a whole. It is written in the form of a numerator and a denominator separated by a horizontal line, where the numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole.
For example, the fraction 3/4 represents three parts out of a total of four parts. It can also be represented visually using a diagram such as a pie chart or a number line.
Fractions can be added, subtracted, multiplied, and divided, and can also be converted between different forms, such as mixed numbers, improper fractions, and decimals. They are commonly used in a variety of mathematical applications, such as in measurements, ratios, and proportions, as well as in everyday life situations, such as dividing a pizza into slices or calculating discounts on a sale.
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!!PLEASE HELPPP!! CHECK IF IM RIGHTTT
Answer:
You are correct
Step-by-step explanation:
please help!!! due tomorrow
(1 and 3 done)
The volumes of the figures are 728 cubic meters, 47.14 cubic yards, 1260 cubic centimeters, 5581.71 cubic inches and 860.07 cubic inches
Calculating the volumes of the figuresFigure 1:
The volume is calculated as
Volume = Product of dimensions/3
So, we have
Volume = 13 * 8 * 21/3
Volume = 728 cubic meters
Figure 2:
The volume is calculated as
Volume = πr²h
So, we have
Volume = 22/7 * 5² * 3/5
Volume = 47.14 cubic yards
Figure 3:
The volume is calculated as
Volume = Product of dimensions
So, we have
Volume = 14 * 18 * 5
Volume = 1260 cubic centimeters
Figure 4:
The volume is calculated as
Volume = 1/3πr²h
So, we have
Volume = 1/3 * 22/7 * 12² * 37
Volume = 5581.71 cubic inches
Figure 5:
The volume is calculated as
Volume = 1/3h(a² + b²)
So, we have
Volume = 1/3 * 13.3 * (16 * 6 + 14 * 7)
Volume = 860.07 cubic inches
Other dimensions are not clear
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find the value of w.
Answer:
w = 8
Step-by-step explanation:
[tex] \frac{24}{w + 4} = \frac{w + 4}{6} [/tex]
[tex] {(w + 4)}^{2} = 144[/tex]
[tex]w + 4 = 12[/tex]
[tex]w = 8[/tex]
the empirical rule assumes that the distribution of data follows a normal curve. group startstrue or false
The statement "The empirical rule assumes that the distribution of data follows a normal curve." is True.
The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This implies that the distribution of data follows a normal curve.
A normal distribution is a type of probability distribution that follows a symmetrical bell-shaped curve. It is also known as the Gaussian distribution and is a continuous probability distribution. The normal distribution is defined by its mean, which is the average of the values, and its standard deviation, which is a measure of the spread of the values from the mean.
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suppose your friends have the following ice cream flavor preferences: 70% of your friends like chocolate (c). the remaining do not like chocolate. 40% of your friends like sprinkles (s) topping. the remaining do not like sprinkles. 25% of your friends who like chocolate (c) also like sprinkles (s). of the friends who like sprinkles, what proportion of this group likes chocolate? (note: some answers are rounded to two decimal places.)
We can start by creating a table to organize the information:
Likes Chocolate (c) Does Not Like Chocolate (~c) Total
Likes Sprinkles (s) 0.25 0.40
Does Not Like Sprinkles (~s) 0.60
Total 0.70 0.30 1.00
We are given that 40% of friends like sprinkles, so we can fill in that cell of the table. We are also given that 25% of friends who like chocolate also like sprinkles, so we can fill in the cell for likes chocolate and likes sprinkles as 0.25.
To find the proportion of friends who like sprinkles and chocolate, we need to divide the number of friends who like both by the total number of friends who like sprinkles:
proportion = likes chocolate and sprinkles / likes sprinkles
proportion = 0.25 / 0.40
proportion = 0.625
So, approximately 62.5% of friends who like sprinkles also like chocolate.
Can someone please tell me how the answer is ‘A’ and not ‘B’? We were told that ‘A’ was the answer but I still don’t get how.
Thank you.
Step-by-step explanation:
As the speed increases the time required to travel a distance is lessened.
say you have to go 100 km
if you go 20 km /hr it will take 5 hr....butif you increase your speed
( x axis) to 50 km/ hr it will take less time ....ony 2 hours so the graph A is most representative (look at the positive portion of the graph of
y = 100/x )