The box plot below represents some data set. What percentage of the data values are less than 90?

The experimental probability of red is given as follows:

p = 0.68 = 68%.

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the experimental probability, we have that:

Hence the experimental probability is given as follows:

p = 34/50

p = 0.68 = 68%.

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1. The volume of the solid generated by rotating the region bounded by y = x([tex]e^x[/tex]), x = 0, x = 1, and y = 0 about the y-axis is approximately 1.305 cubic units.

2. The volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis is π (1 + ln(2)) cubic units.

1. To find the volume of the solid generated by rotating the region bounded by the curve y = x(e^x), x = 0, x = 1, and y = 0 about the y-axis, we can use the method of cylindrical shells.

The volume of a cylindrical shell is given by the formula:

dV = 2πx × f(x) × dx

Integrating this formula from x = 0 to x = 1 will give us the total volume of the solid.

So, let's set up the integral:

V = ∫[0,1] 2πx × (x(e^x)) dx

To solve this integral, we need to use integration by parts. Let's define u = x and dv = x(e^x) dx. Then, we can find du and v:

du = dx

v = ∫x(e^x) dx

Using integration by parts, we find:

v = x(e^x) - ∫e^x dx

= x(e^x) - e^x

Now, we can substitute these values back into the integral:

V = ∫[0,1] 2πx × (x(e^x) - e^x) dx

Expanding and simplifying:

V = ∫[0,1] 2π(x^2e^x - xe^x) dx

Integrating each term separately:

V = 2π ∫[0,1] (x^2e^x - xe^x) dx

= 2π [(x^2 - 2x + 2)e^x] |[0,1]

Evaluating the limits:

V = 2π [(1^2 - 2(1) + 2)e^1 - (0^2 - 2(0) + 2)e^0]

= 2π (1 - 2 + 2e - 2)

= 2π (2e - 3)

Therefore, the volume of the solid generated by rotating the region bounded by y = x(e^x), x = 0, x = 1, and y = 0 about the y-axis is 2π (2e - 3).

2. To find the volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis, we can use the method of cylindrical shells.

The volume can be calculated using the formula:

V = 2π ∫[a,b] x × f(x) dx,

where f(x) is the function representing the curve, and [a,b] is the interval of integration.

In this case, the interval of integration is [0,1], and the function f(x) = arctan(x).

So, the volume can be computed as:

V = 2π ∫[0,1] x × (arctan(x)) dx.

To evaluate this integral, we can use the technique of integration by parts. Let's define u = arctan(x) and dv = x dx. Then, we have du = (1 / (1 + x^2)) dx and v = (1/2)x^2.

Applying integration by parts:

V = 2π [(x^2 × arctan(x))/2 - ∫[0,1] (x^2 / (2(1 + x^2))) dx]

V = π [(x^2 × arctan(x)) - ∫[0,1] (x^2 / (1 + x^2)) dx].

To evaluate the integral on the right side, we can use the substitution method. Let's substitute u = 1 + x^2, then du = 2x dx. Rearranging for x^2:

x^2 = u - 1.

Substituting back into the integral:

V = π ∫[0,1] ((u - 1) / u) du

V = π ∫[0,1] (1 - (1/u)) du

V = π [u - ln(u)] |[0,1]

V = π [(1 + ln(2)) - (0 - ln(1))].

Simplifying further:

V = π (1 + ln(2)).

Therefore, the volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis is π (1 + ln(2)) cubic units.

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The expressions are simplified to;

1. 5x + 11

2. x - 11

3. x - 11y

4. 4x + 20

5. 5x² - y²

6. 5x² - 5y² - 5y

7. -12y²

8. 4x + 20

9. 4x - 20

10. 8x² - 20xy

To simply the algebraic expression, we have to expand the bracket, collect the like terms and then add or subtract them.

From the information given, we have that;

1. 3x + 5 + 2x + 6

collect and add like terms

5x + 11

2. 3x - 5 - 2x - 6

collect and add the like terms

x - 11

3. 3x - 5y - 2x - 6y

collect and add the like terms

x - 11y

4. 6x + 12 - 2x + 8

collect and add the like terms

4x + 20

5. 3x² + 5y² + 2x² - 6y²

collect and add the like terms

5x² - y²

6. 3x² - 5y² + 2x² - 6y

collect and add the like terms

5x² - 5y² - 5y

7. 6x³ - 10y³ + 4x³ - 12y²

collect and add the like terms

-12y²

8. 6(x + 2) - 2(x - 4)

expand the bracket

6x + 12 - 2x + 8

4x + 20

9. 6(x - 2) - 2(x + 4)

expand the bracket

6x - 12 - 2x - 8

4x - 20

10. 6x(x - 2y) + 2x(x - 4y)

expand the bracket

6x² - 12xy + 2x² - 8xy

8x² - 20xy

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Answer: 62°

Step-by-step explanation:

The Probability of randomly selecting a student who did not play lacrosse or tennis is 107/367.

The probability of randomly selecting a student who did not play lacrosse or tennis, we need to consider the number of students who did not participate in either activity.

Given that there are 367 students in total, 145 play lacrosse, 149 play tennis, and 34 play both sports. We can determine the number of students who did not play either sport by subtracting the students who played at least one of the sports from the total number of students.

Students who played at least one sport = Students who played lacrosse + Students who played tennis - Students who played both

= 145 + 149 - 34

= 260

Therefore, the number of students who did not play lacrosse or tennis is:

Total students - Students who played at least one sport

= 367 - 260

= 107

The probability of randomly selecting a student who did not play lacrosse or tennis is given by the ratio of the number of students who did not play either sport to the total number of students:

Probability = Number of students who did not play lacrosse or tennis / Total number of students

= 107 / 367

The fraction cannot be simplified further, so the probability of randomly selecting a student who did not play lacrosse or tennis is 107/367.

In conclusion, the probability of randomly selecting a student who did not play lacrosse or tennis is 107/367.

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Answer:

-5

Step-by-step explanation:

Looking at the slope, there are two points; (-1,3) and (0,-2).

[tex]m = \frac{y _{2} - y_{1}}{x_{2} - x_{1}} \\ = \ \frac{ - 2 - 3}{0 - (- 1)} \\ = \frac{ - 5}{1} \\ = - 5[/tex]

Answer:

The surface area of the larger pyramid is 16 times the surface area of the smaller pyramid.

Step-by-step explanation:

The student's error in the problem is during the solution of (x + 1)², as the correct result is x² + 2x + 1 instead of x² + 1x + 1.

The simplified expression is then given as follows:

g(x) = 2x² + 4x - 4.

The expression in the context of this problem is defined as follows:

g(x) = 2(x + 1)² - 6.

For the square of the addition, we have that:

(x + 1)² = (x + 1)(x + 1) = x² + x + x + 1 = x² + 2x + 1.

Hence the simplified expression is obtained applying the distributive property and then combining the like terms as follows:

g(x) = 2(x² + 2x + 1) - 6

g(x) = 2x² + 4x + 2 - 6

g(x) = 2x² + 4x - 4.

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37+20x = 850 equation represents how many more packs of shirts he needs.

Mr. Brooks already has 37 shirts in his office, so we start with the initial quantity he has.

The shirts are sold in packs of 20, so we can represent the number of packs he needs with the variable x.

Since each pack contains 20 shirts, the total number of shirts in the additional packs is 20x.

To find the total number of shirts Mr. Brooks needs, we add the initial quantity of 37 shirts to the number of shirts in the additional packs, which is 20x.

The sum of these quantities should equal 850 shirts, as stated in the problem.

Putting all of this together, we express the equation as:

37 + 20x = 850

Hence, 37 + 20x = 850 equation allows us to solve for x, representing the number of additional packs of shirts Mr. Brooks needs to reach a total of 850 shirts.

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Answer:

9 × (60-5) is 495

Step-by-step explanation:

To find a suitable property for the expression 9 × (60-5), we can simplify the expression first:

9 × (60-5) = 9 × 55

Now, let's evaluate this expression:

9 × 55 = 495

Therefore, a suitable property for the expression 9 × (60-5) is 495

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

Answer:

y = 4x + 4

Step-by-step explanation:

Intercepts at -1 ajd 4 with slope 4

Answer:

Let's start by assigning variables to the number of quarters, dimes, and pennies, respectively, in the pile. We can represent these variables as q, d, and p. Then we can set up two equations based on the information given:

0.25q + 0.1d + 0.01p = 1.07 (total value of coins is $1.07)

q + d + p = n (total number of coins is some integer n)

We want to find the values of q, d, and p that satisfy these equations and also make it impossible to make change for a dollar (i.e., there is no combination of these coins that add up to exactly $1.00).

To maximize the number of coins, we want to minimize the value of each coin. Since we are dealing with quarters, dimes, and pennies, we can start by assuming that there are no nickels in the pile (since a nickel is worth more than two pennies). In other words, we want to express 1.07 as a sum of quarters, dimes, and pennies using the fewest possible coins.

One way to do this is to start with as many quarters as possible, then add dimes until we get as close to $1.07 as we can without going over, and then fill in the rest with pennies. If we start with 4 quarters (which is the most we can have without making change for a dollar), we have $1.07 - $1.00 = $0.07 left to make up with dimes and pennies. We can add one dime (since 2 dimes would put us over $0.07), which leaves us with $0.07 - $0.10 = $0.03 to make up with pennies. We can use three pennies to make up the remaining $0.03.

So the solution is q = 4, d = 1, and p = 3. We can check that this satisfies the equations:

0.25(4) + 0.1(1) + 0.01(3) = 1.07

4 + 1 + 3 = 8

Therefore, there are 4 quarters, 1 dime, and 3 pennies in the pile, and this is the largest number of coins that can be used to make a total value of $1.07 without being able to make change for a dollar.

As for why $1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar, this is because any amount of money that is a multiple of $0.05 can be made up with nickels and pennies. For example, if we have $1.10, we can make change for a dollar with 2 dimes and 5 pennies, or with 1 nickel and 5 pennies. But if we have $1.15, we can make change for a dollar with 2 dimes and 5 pennies, or with 1 dime, 1 nickel, and 5 pennies. In other words, any amount of money between $1.05 and $1.20 can be made up with nickels, dimes, and pennies, so the largest amount of money we can have without being able to make change for a dollar is $1.19.

The solution is: Proved that, when BD and AC bisects each other, then AB|| CD.

Here, we have,

AB is congruent to CD by CPCTC or Corresponding Parts of Congruent Triangles are Congruent.

Triangles ABE and CDE are congruent by SAS postulate.

Therefore, angle B and angle D are congruent.

Note that the segment BD is a transversal line that cuts AB and CD, and angle B and angle D are alternate interior angles.

with a reason of :

Parallel lines cut by a transversal form congruent alternate interior angles.

The answer is :

XY || WZ ⇒ AB || CD

Hence, Proved that, when BD and AC bisects each other, then AB\\ CD.

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complete question:

Given BD and AC bisects each other. prove AB\\ CD

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3500\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 3500e^{0.12\cdot 5} \implies A=3500e^{0.6}\implies A \approx 6377.42[/tex]

The average change as a simplified mixed number would be,

⇒ 1 3/4

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The running back for the Bulldogs football team carried the ball 7 times for a total loss of 12 1/4 yards.

Now, The average change as a simplified mixed number would be,

⇒ (12 1/4) / 7

⇒ (49/4) / 7

⇒ (49 / 4×7)

⇒ 7/4

⇒ 1 3/4

Therefore, The average change is,

⇒ 1 3/4

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Answer:

8 : 343

Step-by-step explanation:

yah

The surface area of the pyramid is 96 ft²

The surface area of the square base prism is 552 ft²

The surface area of the cube is 216 ft²

The total surface area is 756 ft²

The surface area of the pyramid = A + 1/2 ps

where

A = base area

p = perimeter

s = slant height

Thus,

A = 6² = 36 ft²

p = 4(6) = 24 ft

s = √(3² + 4²)

  = √(9 + 16)

  = √25

   = 5 ft

Thus,

The surface area of the pyramid = 36 + (1/2 × 24 × 5) = 96 ft²

The surface area of the square base prism = 2a² + 4ah

where

a = side of the square base

h = height

Thus,

The surface area of the square base prism = 2(6)² + 4(6)(20) = 72 + 480 = 552 ft²

The surface area of the cube  = 6l² = 6 × 6² = 6 × 36 = 216 ft²

Total surface area = 96 + 552 + 216 = 864 - 36  - 36 - 36 = 756 ft²

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Complete Question

See attached image

Step-by-step explanation:

OUT of  35 spins   4 + 15 + 3  = 22   were blue or green or purple

 22/35 probability  = 63%

The translated figure by the transformation rule is added as an attachment

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

The figure (see attachment)

Where we have

Parent figure = red

Transformed figure = black

Also, we have:

Translate the figure 1 unit left and 3 units up.

This means that we shift the red figure left by 1 unit and we shift it up by 3 units

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Answer:

(7 x 2) x (2 x 2), or if you want the answer, it's 28

Step-by-step explanation:

You can break it down into (2 x 7) x (2 x 2)

First you o 7 x 2, which is 14, and then you do 14 x 2 which is 28.

Answer:

C

Step-by-step explanation:

By using PEMDAS, you evaluate the equations in parentheses first, then do multiplication, then finally add the final two numbers.

hello

the answer to the question is:

Arc = θ × r = θ × (π/180) × r = 60 × (π/180) × 5.4 = 1.8π

Answer:

5/14

Step-by-step explanation:

The total length of the line is LP = 2 + 8 + 10 + 4 = 24. LN = 2 + 8 = 10. LN/LP = 10/28 simplifies to 5/14

Answer: 5/12

Step-by-step explanation:

LP=2+8+10+4=10+10+4=20+4=24

LN=2+8=10

10/24=5/12

The average number of matches per box is 50.5.

To calculate the mean number of matches per box given the number of matches, we add all the values and divide the sum by the total number of values.

Here, we are given the number of matches per box. Therefore, we will add these values and divide the sum by the total number of values.

Hence,Mean = (47 + 48 + 49 + 50 + 51 + 52 + 53 + 54) / 8= 404 / 8= 50.5

Hence, the mean number of matches per box is 50.5.

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I’m sorry but I could not find a pdf version of the Envision volume 2 book for 5th grade online. However, I found some websites that have answer keys and lesson plans for the book. You can check them out by searching for the following queries:

I hope this helps you with your homework.

Explanation:

There are 10 letters listed.

We have 10 choices for the first slot, then 9 for the next, and so on until reaching 1 choice for the tenth slot. Multiply that countdown of values to get the final answer.

10*9*8*7*6*5*4*3*2*1 = 3628800

For more information, search out "factorials". A related idea is "permutations".

Let's assume the number of cookies Lily bought is represented by "C," and the number of brownies is represented by "B."

According to the problem, the cost of one cookie is $2, and the cost of one brownie is $3. Lily spent a total of $144.

We can set up two equations based on the given information:

C + B = 60 (equation 1, representing the total number of sweets)

2C + 3B = 144 (equation 2, representing the total cost in dollars)

To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.

From equation 1, we can rewrite it as C = 60 - B.

Now substitute this value of C in equation 2:

2(60 - B) + 3B = 144

Simplify the equation:

120 - 2B + 3B = 144

Combine like terms:

120 + B = 144

Subtract 120 from both sides:

B = 144 - 120

B = 24

Now substitute the value of B back into equation 1 to find C:

C + 24 = 60

C = 60 - 24

C = 36

Therefore, Lily bought 36 cookies and 24 brownies.

Answer: 13√2

Step-by-step explanation:

• 45-45-90 triangle follows that the hypotenuse will always be √2*leg(x)

• So, 26/2 = 13; multiply with √2 and square it for Pythagorean Theorem

• (13√2)^2 + (13√2)^2 = 676 ✅

• 26^2 = 676 ✅

• a^2 + b^2 = c^2