Clue #8
In a group of middle school students:
.
●
●
.
21 students play tennis
16 students play soccer
19 students play volleyball
3 students play soccer & tennis
5 students play volleyball & tennis
4 students play volleyball & soccer
1 student plays all 3 sports
13 students do not play volleyball, tennis,
or soccer
Based on this information, what values are
missing from the Venn diagram shown?
Soccer
X
3
2
1
Z
Volleyball
Tennis
4
y
W

If a car was driving at a speed of 40 miles per hour and slams on its brakes the vehicle will produce a skid mark that measures around 64.2 feet.

Equation v = √(32fd), where f is the surface's coefficient of friction, relates the speed, v (in feet per second), to the length of the skid mark, d (in feet).

To begin, we may convert the car's starting speed from miles per hour to feet per second:

25 miles/hour × 5280 feet/mile / 3600 seconds/hour ≈ 36.7 feet/second

In order to solve for d, we may then enter the above numbers into the equation v = √(32fd):

36.7 = √(32 × 0.5 × d)

36.7² = 32 × 0.5 × d

d = (36.7²)/(32 × 0.5) ≈ 64.2 feet

As a result, the vehicle will produce a skid mark that measures around 64.2 feet.

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Answer:

Step-by-step explanation:

I gotchu.

Area is piR^2

= pi(70squared)

= 15393.804

Circumference is 2piR

= 2pi(70)

= 493.82

The area of the region bounded by the two lines is 19 square units.

The two lines intersect at the point where they have the same

y-coordinate, so we can set y=3x-6 equal to y=-2x+8 and solve for x:

3x - 6 = -2x + 8

5x = 14

x = 2.8

Therefore the two lines intersect at x=2.8, and the corresponding y-coordinate is y = 3(2.8) - 6 = 6.4.

We can find the coordinates of the two other corners of the region by setting x=0 and x=5:

x=0: y = 3(0) - 6 = -6

x=5: y = 3(5) - 6 = 13

So the other two points are (0, -6) and (5, 13).

We will use the Shoelace Theorem to find the area:

A = 1/2 * |(0 * 6.4) + (2.8 * 13) + (5 * -6) - (6.4 * 5) - (13 * 2.8) - (-6 * 0)|

A = 1/2 * |(0 * 6.4) + (37.4) + (30) - (32) - (36.4) - 0|

A = 1/2 * |37.4 + 30 - 32 - 36.4|

A = 1/2 * |38| = 19

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Answer:

Step-by-step explanation:

The evaluation of the possible graph and table in the question, which indicates proportional relationships are presented as follows;

Part A: The rate of change of a bushel of corn in the current year is; 8 dollars per bushel of corn

Part B: Tnhe price of a bushel of corn in the current year is three dollars ($3) more than the price in the previous year.

A proportional relationship is one in which the output variable of the relationship, is a multiple of the input variable and factor.

The points on the graph in the question, obtained from a similar question posted on the website are;

(0, 0), (3, 24), (6, 46), (9, 72), (12, 76), (15, 120), (18, 144)

Part A: The slope is the rate of change of the bushel of corn. Therefore, the rate of change for the current year can be found by finding the slope as follows;

The graph is a straight line graph, indicating a proportional relationship therefore, the slope of the graph is a constant, which can be found as follows;

Slope = (24 - 0)/(3 - 0) = 8

The rater of change of the bushel for the current year is; 8 dollars per bushel of corn

Part B: Whereby the values in the table for the number of bushels to the price of corn for the previous year can be presented as follows;

Number of Bushels [tex]{}[/tex]   Price of Corn (dollars)

2        [tex]{}[/tex]                            10

4        [tex]{}[/tex]                            20

6        [tex]{}[/tex]                            30

8        [tex]{}[/tex]                            40

The rate of change of the price for the previous year is therefore;

Rate of change = (20 - 10)/(4 - 2) = 5

The rate of change for the previous year is therefore 5 dollars per bushel

The price of a bushel in the current year is three more dollar than the price of a bushel in the previous year.

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The graph of the problem depicts the rate of the temperature change.

To graph temperature change, you can use a line graph. The horizontal axis represents time, while the vertical axis represents temperature. You plot points on the graph corresponding to the recorded temperature at specific times, and then connect the points to form a line.

The slope of the line represents the rate of temperature change, with a steep line indicating a rapid increase or decrease in temperature and a gentle slope indicating a slow change. The line graph helps to visually represent changes in temperature over time and can be used to analyze patterns and trends.

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At 8.5 per meter, the cost of tying lace around the tablecloth is $18.36.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Identity equations and conditional equations are the two types of equations. An identity holds true for all possible values of the variables. A conditional equation is valid only for certain values of the variables. An equation consists of two expressions joined by an equals sign ("=").

Here,

The perimeter of the table cloth is 4 times the length of one side, so it is 4 * 54 cm = 216 cm.

To convert from centimeters to meters, we divide by 100, so the perimeter is 216 cm / 100 = 2.16 meters.

At a rate of ₹8.5 per meter, the cost of putting lace around the table cloth is 2.16 meters * ₹8.5 per meter = ₹18.36.

The cost of putting lace around the table cloth at the rate of ₹8.5 per meter is $18.36.

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Answer:

The number of ways the 7 members of the student council can pose in a line for a yearbook photograph if the chair and vice-chair must be side by side is 6!.

To see why, consider the first 6 members as a group. They can be arranged in 6! ways, since they are interchangeable. Then, the chair and vice-chair must be positioned together in the first two spots, which is only one way. So, the total number of arrangements is 6! * 1 = 720 ways.

can give brainliest if this helps ;)

Answer:

1440

Step-by-step explanation:

We should first count the chair and vice-chair as one unit i.e. one person since they have to be seated together

This means there are 6 items effectively and these 6 items can be arranged in 6! ways

6! = 720 ways

But there is more....

The chair and vice-chair have to sit together but they can sit together in two different ways:
Chair can be on the left, vice-chair can be on the right

or

Chair can be on the right,  vice-chair can be on the left

So for each of the 6! combinations there are 2 ways of seating the chair and vice-chair together

Total number of ways = 6! x 2

= 720 x 2 = 1440

Answer im not sure frl but its ok

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

The probability that the chip drawn from urn II is red is 4/15. Let's call the event that the chip drawn from urn I and transferred to urn II is red "R1", and the event that the chip drawn from urn II is red "R2".

The probability of event R1 is 2/6 = 1/3.

Given that event R1 has occurred, the number of red chips in urn II becomes 4, and the number of total chips becomes 4+1=5. The probability of event R2 is 4/5 = 4/5.

The probability of both events occurring is (1/3) * (4/5) = 4/15.

So, the probability that the chip drawn from urn II is red is 4/15.

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Answer:

I. 11%
II. ₹ 1110 in interest over 3 years

Step-by-step explanation:

To solve for the interest rate and the total interest earned, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where A is the maturity amount, P is the principal, r is the interest rate, n is the number of times compounded per year, t is the time in years, and

Since we know the maturity amount (A = ₹ 10,110), the principal (P = 250 * 12 * 3 = 9,000), and the time (t = 3 years), we can rearrange the formula to solve for the interest rate:

r = n * ((A/P)^(1/nt) - 1)

We'll assume that the interest is compounded monthly, so n = 12. Then:

r = 12 * ((10110/9000)^(1/36) - 1)

r ≈ 0.11

So, the interest rate is approximately 11% per year.

To find the total interest earned, we can use the formula:

Interest = A - P

Interest = 10110 - 9000

Interest = 1110

So, Mr Sharma earned ₹ 1110 in interest over 3 years.

Answer:

x=1, y=3

Step-by-step explanation:

Answer:

x = 1, y = 3

Step-by-step explanation:

y = x + 2

y = -5x + 8

Using substitution:
x + 2 = -5x + 8

6x = 6
x = 1

y = 1 + 2
y = 3

The given assertion states that the sequence's nth element is -k² + (2n-3)k + 1.

Sequential is a derivative of the Latin word consecutus, which means "following closely" without a pause. Similar to those snowstorms, which occurred back-to-back each day for five months in a succession. Additionally, consecutive numbers progress in the correct sequence or follow one another. For instance, the numerals 5, 6, 7, 8, 9, and 10 follow one another.

Looking at the differences between consecutive terms, we have:

(k+2) - (-k²-k+1) = k²+3k+3 - (k+2) = k²+2k+1 = (k+1)²

(k²+3k+3) - (k+2) = k²+2k+1 = (k+1)²

(2k²+5k+4) - (k²+3k+3) = k²+2k+1 = (k+1)²

We can see that the differences between consecutive terms are all the same, which means that the sequence is an arithmetic sequence.

To find tₙ, we need to find the common difference d. From the differences above, we have:

d = (k+1)² - (k²+k-1) = 2k

So, the nth term of the sequence is given by:

tₙ = t₁ + (n-1)d

tₙ = (-k²-k+1) + (n-1)(2k)

tₙ = -k²-k+1 + 2nk - 2k

tₙ = -k² + (2n-3)k + 1

Therefore, the nth term of the sequence is -k² + (2n-3)k + 1.

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The ordered pairs of points on a graph is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The ordered pairs

The ordered pairs are represented as

A(0, 3), B(5, 8), C(9, 8), D(4, 3), E(9, 6), F(4, 1), G(0, 1)

Next, we create a plot of the ordered pairs

When this is done, we then connect the points

See attachment for the graph of the ordered pairs

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y coordinate of point p is 2.

Arrangement of reference lines or curves used to identify the location of points in space.

Using the section formula, if a point (x,y) divides the line joining the points

(x₁, y₁) and (x₂, y₂) in the ratio m:n then

(x, y)=(mx₂+nx₁/m+n, my₂+ny₁/m+n)

(x,y)=(3(1)+4(5)/7, 3(-2)+4(5)/7)

=(3+20/7, -6+20/7)

=(23/7, 14/7)

=(23/7, 2)

The y coordinate of point p is 2

Hence, y coordinate of point p is 2.

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Answer:

Step-by-step explanation:

Let's call the number of cans Reggie collected as "x".

According to the problem, Tanner collected 360 cans, which was 40% of what Reggie collected, so:

360 = 40/100 * x

To find the value of x, we can isolate x by dividing both sides by 40/100:

x = 360 * 100/40

x = 900

So Reggie collected 900 cans.

Answer:

900 cans

Step-by-step explanation:

We know

360 cans = 40%

We have to find 1% by taking

360 divided by 40 = 9 cans

How many cans did Reggie collect?

We take

9 x 100 = 900 cans

Answer:To find the number of students who want to be both a doctor and a social worker, we can use the Principle of Inclusion-Exclusion (PIE). This principle states that the total number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements in their intersection.

So, the number of students who want to be both a doctor and a social worker can be calculated as:

|Doctor ∩ Social worker| = |Doctor| + |Social worker| - |Doctor U Social worker|

|Doctor ∩ Social worker| = 40 + 20 - 65

|Doctor ∩ Social worker| = -5

However, this result is negative which is not possible, therefore, no students want to be both a doctor and a social worker.

To find the number of students who want to be both, we have to find the number of students who want to be both a doctor and a social worker which is 0 in this case.

Step-by-step explanation:

Answer:

7, 2, 3, 4, 8, 3

-------------------------

This is about the distributive property of multiplication and the product of exponents with same base.

When you multiply exponents with same base the powers add up:

The blanks are going to be:

Answer:

[tex]15m^{7}n^{2}-20m^3n^{4}+10m^{8}n^{3}[/tex]

Step-by-step explanation:

Given expression:

[tex]5m^3n\left(3m^4n-4n^3+2m^5n^2\right)[/tex]

Distribute:

[tex]5m^3n \cdot 3m^4n-5m^3n \cdot 4n^3+5m^3n \cdot 2m^5n^2[/tex]

Multiply the numbers:

[tex]15m^3nm^4n-20m^3nn^3+10m^3nm^5n^2[/tex]

Rearrange to collect like terms:

[tex]15m^4m^3nn-20m^3n^3n+10m^5m^3n^2n[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]15m^{4+3}n^{1+1}-20m^3n^{3+1}+10m^{5+3}n^{2+1}[/tex]

Therefore:

[tex]15m^{7}n^{2}-20m^3n^{4}+10m^{8}n^{3}[/tex]

Answer:

12

Step-by-step explanation:

[tex]\dfrac{x}{4} + 17 = 20\\\dfrac{x}{4} = 20 - 17\\\dfrac{x}{4} = 3\\x = 4 \cdot \;3 \\\\x = 12[/tex]

Answer:

x = 12

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ (x/4) + 17 = 20

Then the value of x will be,

→ (x/4) + 17 = 20

→ x/4 = 20 - 17

→ x/4 = 3

→ x = 3 × 4

→ [ x = 12 ]

Hence, the value of x is 12.

As per the mentioned distribution of cards, Clara has 2 baseball cards.

Let the number of baseball cards with Clara be x. So, number of baseball cards with Jeff will be 3x. Now, the baseball cards that Yolonda has is (3x + 7). We know their sum is 21, therefore, forming the equation now -

x + 3x + 3x + 7 = 21

Performing addition on Left Hand Side of the equation

7x + 7 = 21

Dividing the whole equation by 7

x + 1 = 3

Rewriting and solving the equation for x

x = 3 - 1

Performing division on Right Hand Side of the equation

x = 2

The number of baseball cards with Clara are 2.

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The artist reportedly got $225 or $275 for her paintings this week, depending on the statement provided.

We might, for instance, move to the city. Most likely, he will start classes again in the fall. If we could finish the job by tomorrow, that would be perfect. In the worst-case scenario, we would have to commence the project over.

Let x become the sum the artist got this week for her works in Part A.. The situation is represented by the absolute value equation:

|250 - x| = 25

Part B: To solve the equation, we can split it into two cases:

Case 1: 250 - x = 25

Solving for x, we get:

x = 250 - 25 = 225

Case 2: 250 - x = -25

Solving for x, we get:

x = 250 + 25 = 275

Therefore, the artist received either $225 or $275 for her prints this week.

Part C: The minimum amount the artist received is $225, which is $25 less than her goal of $250. The maximum amount the artist received is $275, which is $25 more than her goal of $250.

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Answer:

Step-by-step explanation:

x will be the original weight.

2x - 20 = 180

2x = 200

x = 100

Answer:

The equation is not true.

Step-by-step explanation:

Starting with the left side,

sin²(θ) - cos²(θ) = 1 - cos²(θ) - cos²(θ) = 1 - 2cos²(θ)

The right side,

2 sin²(θ) - 1 = 2(sin²(θ) - 0.5)

Thus, in general, sin²(θ) - cos²(θ) ≠ 2 sin²(θ) -1.

Answer:

To determine how many cakes Jahnay is making, we need to calculate the total weight of the ingredients for one cake and then divide the total amount of flour Jahnay is using by that amount.

First, let's calculate the total weight of ingredients for one cake:

150 g sugar + 120 g butter + 210 g flour + 2 eggs = 480 g

Next, let's divide the total amount of flour Jahnay is using by the total weight of ingredients for one cake:

840 g / 480 g = 1.75 cakes

So Jahnay is making 1.75 cakes.

The required orders are Kara served 12.5 orders, Harry served 22.5 orders, and Erin served 50 orders.

An equation that holds true for one or more values of the variable but holds false for other values of the variable is known as a conditional equation. In Hannah's example, the equation holds true for the value of x equal to 10, but not for other values, such as 1. The equation is a conditional equation as a result.

Let we consider the number of orders Kara served as x.

Then, Harry served x + 10 orders and Erin served 4x orders.

The total number of orders they served is x + x + 10 + 4x = 86 orders.

So, 6x + 10 = 86

6x = 76

x = 12.5

Kara served 12.5 orders, Harry served 22.5 orders, and Erin served 50 orders.

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Answer:

Step-by-step explanation:

Let the orders served by Kira be k.

Orders served by Henry= 10 less than Kira

                                       = k-10

Orders served by Erin= 4 times of Kira

                                   = 4k

Total orders served= 86

     Kira+Henry+Erin= 86

               k+k-10+4k= 86

                       6k-10= 86

                            6k= 86+10

                            6k= 96

                              k= 96/6

                              k= 16

Kira= k= 16

Henry= k-10= 16-10= 6

Erin= 4k= 4x16= 64

∴ Kira served 16 orders, Henry served 6 orders & Erin served 64 orders

The new diagram with a scale factor of 1 unit = 8 feet will look the same

as each new grid now represents 8 feet.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, A drawing represented by a scale factor of 1 unit = 4ft,

Where every grid unit represents 4 ft.

The new drawing model will look exactly the same as now each grid unit represents 8 feet.

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The number of seats in the front row can be represented as: s = x - (n - 1) * (2y / n - x) / (n - 1) = x - (2y - nx) / n

Let's call the number of seats in the first row "s". Then, the number of seats in the second row is s + d, the number of seats in the third row is s + 2d, and so on. The total number of seats in the theater can be represented as:

s + (s + d) + (s + 2d) + ... + (s + (n - 1)d) = y

Expanding this equation and combining like terms, we get:

ns + (d * (n - 1) * n) / 2 = y

Now that we have an equation for the total number of seats in terms of n, d, and y, we can use the number of seats in the last row to solve for s, the number of seats in the first row:

s + (n - 1)d = x

ns + (d * (n - 1) * n) / 2 = y

Solving for s in terms of n, x, and y:

s = x - (n - 1)d

ns + (d * (n - 1) * n) / 2 = y

Substituting this expression for s into the equation for the total number of seats:

(x - (n - 1)d) + (d * (n - 1) * n) / 2 = y

Expanding and solving for d:

x + (n - 1)d = 2y / n

d = (2y / n - x) / (n - 1)

Finally, substituting this expression for d back into the equation for s:

s = x - (n - 1) * (2y / n - x) / (n - 1)

So the number of seats in the front row can be represented as:

s = x - (n - 1) * (2y / n - x) / (n - 1)

= x - (2y - nx) / n

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The complete question is:

A theater has n rows of seats, and each row has d more seats than the row in front of it. There are x seats in the last (nth) row and a total of y seats in the entire theater. How many seats are in the front row of the theater? Write your answer in terms of n, x, and y.

The standard deviation of the average expenses of 200 patients who were hospitalized at RWJ Hospital in New Brunswick cannot be determined from the information provided. The average expenses of the sample is $4400, but the standard deviation of these expenses is not given.

The standard deviation is a measure of the variability or dispersion of the data in a set and is calculated using a complete dataset of the expenses of all 200 patients. Without this dataset, it is not possible to determine the standard deviation of the average expenses.

Option A, less than $400, Option B, at least $400, and Option C, between $0 and $400, are all based on assumptions about the standard deviation that cannot be made without a complete dataset of expenses.

In conclusion, the standard deviation of the average expenses of 200 patients who were hospitalized at RWJ Hospital in New Brunswick cannot be determined from the information provided and a complete dataset of expenses would be needed to make any assumptions about the standard deviation.

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Complete Question: A sample of 200 patients who were hospitalised at the rwj hospital in New Brunswick incurred $4400 on average in costs. The patients' average monthly costs have a standard deviation of

A. less than $400.

B. $400 or more.

C. from $0 to $400

D. Unable to determine D.

The volume of the cylinder is approximately 6058.73 cubic meters.

A cylinder is a three-dimensional geometric shape that is similar to a tube. It has two parallel bases that are circular in shape, and its lateral surface is a rectangle. The height of the cylinder is the distance between the two bases. The cylinder has a top base and a bottom base, and these are both circles with the same diameter. The volume of a cylinder can be found by multiplying the area of one of its circular bases by its height. The surface area of a cylinder can be found by adding up the areas of the two circular bases and the lateral surface. Cylinders are widely used in mathematics, engineering, and physics, and they play an important role in the study of various geometric and physical concepts.

Given the diameter of a cylinder is 34m and its height is 27m, we can find the volume of the cylinder using the formula:

Volume = π × (diameter / 2)² × height

Plugging in the values, we get:

Volume = 3.14 × (17 / 2)² × 27

Volume = 3.14 × (8.5)² × 27

Volume = 3.14 × 72.25 × 27

Volume = 6058.73 cubic meters

So, the volume of the cylinder is approximately 6058.73 cubic meters.

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Quinn will need 8 cups of sugar to make 16 pies based on the table that shows the ratio of pies and sugar.

What we know from the question:

3 pies = 1 ½ cups of sugar

5 pies = 2 ½ cups of sugar

9 pies = 4 ½ cups of sugar

16 pies = ?

To make it easier, the answer will be explained through sentence:

First, we find out how much sugar it takes to make one pie. Use one of the ratio provided above by dividing the pie amount with the sugar’s. For example, 3 divided by 1 ½ equals ½ .

Therefore, one pie would require only ½ cups of sugar. Crosscheck with the other ratio to make sure it is correct using the same method earlier.

Second, we find out how much sugar it takes to make 16 pies. Multiply the amount of pies with the amount of sugar. So 16 x ½ equals 8.

Here are the summary

1 pies = ½ cups of sugar

16 pies = 8 cups of sugar

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