Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team?

WRONG ANSWER = REPORTED

Answers

Answer 1

Answer:

47/60

Step-by-step explanation:

You want to know the probability of a randomly selected student is on the honor roll or varsity team when 176 of 240 students are on the honor roll, 48 are on the varsity team, and 36 are on both.

One or the other

The probability of A or B is ...

P(A+B) = P(A) +P(B) - P(A·B)

The probability of interest is ...

P(honor roll + varsity) = P(honor roll) + P(varsity) - P(honor roll & varsity)

P(honor roll + varsity) = 176/240 +48/240 -36/240 = (176 +48 -36)/240

= 188/240 = 47/60

The probability of interest is 47/60.

Answer 2

[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]

[tex]\\[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]

Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team?

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]

The probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]

We can use the inclusion-exclusion principle to find the number of students who are on the honor roll or are members of the varsity team.

This principle states that:

[tex]\sf |A\cup B| = |A| + |B| − |A\cap B|[/tex]

where:

A and B are sets,|A| is the cardinality (number of elements) of set A, andA∩B is the intersection of sets A and B.

Using this principle, we can find that:

[tex]\begin{aligned}\sf |Honors\cup Varsity|& =\sf |Honors| + |Varsity| − |Honors\cap Varsity|\\& =\sf 176 + 48 - 36\\& =\sf\red{188}\end{aligned}[/tex]

Therefore, there are 188 students who are on the honor roll or are members of the varsity team.

The probability that a randomly selected student is on the honor roll or is a member of the varsity team is then:

[tex]\begin{aligned}\sf P(Honors\cup Varsity)& =\sf \dfrac{|Honors\cup Varsity|}{|Total|} \\ &=\sf \dfrac{188}{240} \\&=\boxed{\bold{\: \dfrac{47}{60}\:}}\end{aligned}[/tex]

Therefore, the probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex]

[tex]{===========================================}[/tex]

[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]

Related Questions

find the value of w.

Answers

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]

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.

Answers

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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how do you multiply 7(b-5)(b-4) step by step

Answers

To multiply 7(b-5)(b-4), you can follow these steps:

Start by distributing the 7 to the terms inside the parentheses:

7(b-5)(b-4) = 7 * b * (b-4) - 7 * 5 * (b-4)

Simplify each term using the distributive property:

= 7b^2 - 28b - 35b + 140

Combine like terms:

= 7b^2 - 63b + 140

So, the final answer is 7b^2 - 63b + 140.

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

Answers

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 )

Suppose (-2,4) is (x1,y1)
And (-1,-5) is (x2,y2)
Midpoint =(x1+x2/2, y1+y2/2)
=(-2-5/2,4-1/2)
=(-7/2,3/2)
=(-3.5,1.5)

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.

Answers

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.

Determine whether the graph of the equation is symmetric with respect to the

Answers

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

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.)

Answers

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.

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?

Answers

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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y = a(x _ 2)^2 _ 3. :)

Answers

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.

Vertex

The vertex is the low point on the curve. Its coordinates are (-2, -3).

Vertex form

The 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.

PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer: 1 and 5

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:

Answers

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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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?

Answers

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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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

Answers

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.

karen bought a baby stroller on sale for $301.75. the original price of the stroller was $335. what was the percent of the discount

Answers

Answer: 9.9% (rounded to the nearest tenth

Step-by-step explanation:

A trundle wheel is used measuring distances. The circumference of the wheel is exactly 1 m. Each time the wheel rotates through one complete turn a click sound is heard and a counter adds a meter to the total. What is the radius of this wheel?

Answers

Answer:

Step-by-step explanation:

[tex]C=2\pi r[/tex]

[tex]1=2\pi\time r[/tex]

[tex]r=\frac{1}{2\pi}[/tex] ( divided both sides of equation by [tex]2\pi[/tex])

[tex]r\approx 16cm[/tex]

The wheel's radius is approximately 16cm.

HELP GEOMETRY WORK!!!!!!!

Answers

Answer:6

Step-by-step explanation:

there is a law for that:

5*12=x*(x+4)

60=x*x+4x

x*x+4x-60=0

(x+2)*(x+2)-64=0

(x+2)(x+2)=8*8

x+2=8

x=6

Answer:6

Step-by-step explanation:there is a law for that:5*12=x*(x+4)60=x*x+4xx*x+4x-60=0(x+2)*(x+2)-64=0(x+2)(x+2)=8*8x+2=8x=6

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.

Answers

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:

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.

Answers

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 )

Help with this question

Answers

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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what fraction of 5 litres is 6800ml give answer as mixed number and lowest term

Answers

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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the empirical rule assumes that the distribution of data follows a normal curve. group startstrue or false

Answers

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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Alyssa started a savings account with an initial deposit of $1600. The account ears 4.12% interest
compounded quarterly.
(a) Write an exponential equation to represent the amount of money in the account after t years.
(b) Using this equation, calculate how much money will be in the account after 7 years, assuming Alyssa
makes no additional deposits or withdrawals. (Please round to the nearest cent)

Answers

At the initial investment of $1600 compounded quarterly for 7 years with an interest of 4.12%, the amount Alyssa will get is $2,131.72.

What is compounding?

The powerful investing principle of compounding entails generating returns on both your initial investment and returns you have already received.

You must reinvest your returns back into your account for compounding to take effect.

Consider an investment of $1,000 that yields a 6% return.

The words under and ground, for instance, are combined to get the word subterranean.

So, we know that:

Initial deposit: $1600

Interest: 4.12%

Compounded quarterly for 7 years.

Then, the amount after 7 years would be:

Using the compounding calculator we know that after 7 years Alyssa will have: $2,131.72

Therefore, at the initial investment of $1600 compounded quarterly for 7 years with an interest of 4.12%, the amount Alyssa will get is $2,131.72.

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Complete question:

Alyssa started a savings account with an initial deposit of $1600. The account earns 4.12% interest compounded quarterly for 7 years. Calculate how much money will be in the account after 7 years, assuming Alyssa

makes no additional deposits or withdrawals.

←
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.)

Answers

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

I need helppppppppppppppppp

Answers

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.

please help!!! due tomorrow
(1 and 3 done)

Answers

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 figures

Figure 1: