question 31 pts a fair six-sided die is tossed 300 times. find the expected value of the sample mean of the values obtained in these 300 tosses (write it up to first decimal place).

To find maximum value and minimum value in a set we have to use ven diagram from set theory.

Here we are taking an example?

Let A and B be 2 sets having elements 4 and 7 respectively. Then write the maximum number of elements that A∪B can have.

Let us assume that:

Number of elements of A is equal to n (A).

Number of elements of B is equal to n (B).

Number of elements of A∩B is equal to n (A∩B).

Now, the formula for the elements of A U B is as follows:

n(A∪B)=n(A)+n(B)−n(A∩B)

It is given in the question that, number of elements in set A is equal to 4 and number of elements in set B is equal to 7. So, we can write:

n (A) = 4, n (B) = 7

n (A∩B): the number of elements which are common in both the sets A and B.

We have to find the maximum number of elements which are in n(A∪B). So, the maximum of n(A∪B) is when n(A∩B) is minimum and the minimum of n(A∩B) is 0.

n(A∪B)=n(A)+n(B)−n(A∩B)⇒n(A∪B)=4+7−0⇒n(A∪B)=11

Hence, the maximum number of elements in A∪B is 11.

Note: You might be wondering, why for maximizing the n (A∪B) we have to minimize n (A∩B) and why the minimum value of n (A∩B) is 0.

In the formula for n (A∪B),

n(A∪B)=n(A)+n(B)−n(A∩B)

L.H.S will be maximized when in the R.H.S; the term after minus sign will be minimized. Hence, n (A∩B) must be minimized.

The minimum possible value of n (A∩B) is 0 means that the elements in the set A and B are such that there is not a single element is common in both the sets. And it could be possible that we have two sets and the sets have no element in common.

When no elements is common in both the sets, the n (A∩B) is ∅.

The set which has no element in it is called a null set or an empty set.

By this we can find maximum and minimum value in a set.

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Answer:

90000

Step-by-step explanation:

90 times 1000

= 90 × 1000

= 90000

Answer:9000

Step-by-step explanation:

The equation of the straight line passing through the point (1/2, 0) and parallel to the line y = 3x + 1 is y = 3x - ½ with slope m1 = 3 and m2 = 3.

Given line is y = 3x + 1

We need to find equation of line parallel to this line

Let us consider the equation of line as y = mx + c

We know that two lines are parallel if they have same slope i.e. m1 = m2

Here m1 = 3

So slope of required line m2 = 3

We need to find the value of c

Let us take a point (x1, y1) common to both lines

We know that (1/2, 0) is common to both lines

So x1 = 1/2, y1 = 0

Substituting these values in y = mx + c

0 = 3(1/2) + c

=> c = -1/2

Hence the equation of straight line passing through the point (1/2, 0) and parallel to the line y = 3x + 1 is y = 3x - 1/2.

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The solution to the given expression -5 5/8 + 3 1/2 is -2 1/8.

Given the expression in the question;

-5 5/8 + 3 1/2

First, convert the mixed fraction into an improper fraction.

-(5×8 + 5)/8 + (3×2 + 1)/2

-(40 + 5)/8 + (6 + 1)/2

-(45)/8 + (7)/2

-45/8 + 7/2

Now, write 7/2 as fraction with common denominator as -45/8 by multiplying by 4/4

-45/8 + ( 7/2 × 4/4 )

-45/8 + ( 28/8 )

-45/8 + 28/8

Next, combine the numerators over common denominators

( -45 + 28 )/8

( -17 )/8

Covert back to mixed fraction

-2 1/8

Therefore, the result of the summation of the expression is -2 1/8

Option C is the correct answer.

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By using the concept of permutation and combination, it can be calculated that

Number of ways of selecting two scoop ice cream if order matters = 600

Number of ways of selecting two scoop ice cream  = 300 ways

What is permutation and combination?

Permutation is the process of arranging some of the objects taken where the order of the selection matters.

Combination is the process of selection of items from a group of objects where the order of selection does not matter.

Here,

The concept of permutation and combination is used

Number of flavors of ice cream an ice cream parlor offers = 25

Here, order matters

For the first scoop, there are 25 choices

For the second scoop, there are 24 choices

Number of ways of selecting two scoop ice cream if order matters =

                                                                                                            25 [tex]\times[/tex] 24

                                                                                                           = 600

If no flavors are repeated,

Number of ways of selecting two scoop ice cream = [tex]{25 \choose 2}[/tex] = 300 ways

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Answer: 45.563

Step-by-step explanation:

The 6th term of the geometric progression is given by a₆ = 729 / 16

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the 6th term of the geometric progression be a₆

Now , the first term of the GP is a₁ = 6

Let the second term of the GP be a₂ = 9

So , the common ratio of the GP is r = second term / first term

Substituting the values in the equation , we get

The common ratio r = 9/6 = 3/2

Now , the 6th term of the geometric progression a₆ = arⁿ⁻¹

On simplifying the equation , we get

The 6th term of the geometric progression a₆ = 6 ( 3/2 )⁵

The 6th term of the geometric progression a₆ = 6 ( 243 / 32 )

The 6th term of the geometric progression a₆ = 729 / 16

Hence , the 6th term of the GP is 729/16

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Answer:

A:(4,12)

B: In image

C. Yes, it does because it shows that the two lines intersect at the same point.

Step-by-step explanation:

-Hope this helped & Happy Holidays!

The explanatory variable is the player's weight and the response variable is the player's 40-yard dash when 40-yard dash more slowly than lighter players.

Given that,

Football instructors who oversaw summer sessions noted that heavier players often ran the 40-yard dash more slowly than lighter players.

We have to find what are the relationship's explanatory variable and response variable.

We know that,

We must determine what is causing the player's slower times.

The players' slower times are a result of their added weight.

So,

The player's weight is the explanatory variable, while their 40-yard dash time is the response variable.

Therefore, The explanatory variable is the player's weight and the response variable is the player's 40-yard dash when 40-yard dash more slowly than lighter players.

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Answer: It would be -48

Step-by-step explanation: Hope it helps:)

The remainder of 5x³ + 7x +57 over x+2  is 3.

What is expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Given expressions are 5x³ + 7x +57 and x+2.

Remainder theorem: According to the remainder theorem, the remainder equals f(a) when a polynomial, p(x), is divided by (x - a).

Assume that P(x) = 5x³ + 7x +57.

Equate x + 2 to zero and find the value of x:

x + 2 = 0

x = -2

Putting x = -2 in the polynomial P(x) = 5x³ + 7x +57:

P(-2) = 5(-2)³ + 7(-2) +57

P(-2) = 5(-8) + 7(-2) +57

P(-2) = -40 - 14 +57

P(-2) = 3

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Salma can therefore rent the vehicle for a maximum of 5 days and go 275 miles. When A rental car company charges $22. 50 per day to rent a car and $0. 10 for every mile driven. Salma wants to rent a car, knowing that: she plans to drive 275 miles. She has at most $140 to spend.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given

Although your question is incomplete, you might be referring to the following in its entirety: Renting a car from a rental car agency costs $22.50 per day plus $0.10 every mile driven. Salma wants to rent a car because she knows she will go 275 kilometres. She can only spend up to $140. The number of days Salma can rent the car for while staying within her budget can be calculated by writing and solving an inequality.

The formula that solves this issue is:

Let x represent how many days Salma can afford to rent the automobile for.

Inequality

22.5x + 0.10(275) ≤ 140

22.5x + 2.75 ≤ 140

22.5x ≤ 140 - 2.75

22.5x ≤ 137.25

x ≤ 5

automobile rental on a daily basis get x <= 5

Salma can therefore rent the vehicle for a maximum of 5 days and go 275 miles.

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Answer:

B

Step-by-step explanation:

The best interpretation of this slope is A. On average, each 1-centimeter increase in foot length was associated with a 5.89-centimeter increase in shoulder height.

The elephants of Kruger would need to be continuously culled until the habitats began to recover, at which point the reduced population numbers would need to be maintained until the vegetation had recovered to a near-climax state in order to determine that number.

The average change in the response (y) variable that is associated with a change of one unit in the explanatory (x) variable is shown by the slope of the regression line.

In this instance, the slope represents the average change in shoulder height caused by an increase in foot length of one centimeter.

Slope = ∆Y/∆X = change in Y per unit change in X = 5.89

thus, The average increase in shoulder height was 5.89 centimeters for every 1-centimeter increase in foot length.

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(complete questions)

Baruti, a ranger in kruger national park in south africa, collected data about the elephant population in the park. She compared the foot lengths of the elephants and their shoulder height (both in centimeters) and created the following scatterplot and regression line. The fitted line has a slope of 5. 895. 895, point, 89. What is the best interpretation of this slope?.

A. On average, each 1 centimeter increase in foot length was associated with a 5.89 centimeter increase in shoulder height.

B. On average, each 1 centimeter increase in shoulder height was associated with a 5.89 centimeter increase in foot length.

C. We would predict an elephant with a foot length of 0 centimeters to have a shoulder height of 5.89 centimeters.

D. We would predict an elephant with a foot length of 0 centimeters to have a shoulder height of 0 centimeters.

Jacob has a tree growing in his yard. if the tree grows 9.5 feet per year, 9.5 inches  does it grow in a month.

From the question, we have

Tree grows 9.5 feet per year

9.5 feet = 114 inches

Tree grows in one month = 114/12

= 9.5 inches

Divide:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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Using the formula of surface area to calculate the height and using the formula for volume , The answer is 24.98 [tex]cm^{3}[/tex] .

A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.

The required formula are :

[tex]SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})[/tex]  (Surface Area)

[tex]V = \pi r^{2} \frac {h}{3}[/tex] (Volume)

radius = 3 cm

Area= 66 [tex]cm^{2}[/tex]

[tex]SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})[/tex]

h = 2.65 cm

[tex]V = \pi r^{2} \frac {h}{3} = \pi * 3^{2} * \frac {2.65}{3}[/tex]

=24.98 [tex]cm^{3}[/tex]

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If the value of the variable 'x' is 12. Then the measure of the angle ∠B will be 118°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

In triangle ΔABC, ∠B = (12x − 26)°, and the measure of the exterior angle to ∠B is (7x − 22)°.

The sum of the interior and exterior angles will be 180°. Then the equation is given as,

(12x − 26)° + (7x − 22)° = 180°

12x - 26 + 7x - 22 = 180

19x - 48 = 180

19x = 228

x = 12

Then the measure of the angle ∠B will be given as,

∠B = 12 (12) - 26

∠B = 144 - 26

∠B = 118°

If the value of the variable 'x' is 12. Then the measure of the angle ∠B will be 118°.

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Answer:

118

Step-by-step explanation:

(12x - 26)

12x - 26 + 7x - 22 = 180

12x  + 7x + 26 - 22 = 180 (add 26 and 22 together)

19 - 48

180 + 48

228/19 = 12

(12x(12) - 26)

12 x 12 = 144 - 26 = 118

118 is your answer deer (lol corny joke)

There is 4 bottles in each of the packs when Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3 packs of bottled drinks, plus 11 single bottles. Jillian purchased 5 packs, plus 3 singles. Andre and Jillian discovered that they had purchased the same number of bottles

The bottles in each of the packs can be calculate as follows:

Expressions that indicate the total number of bottles purchased

The formula 3p + 11 can be used to express how many bottles André purchased.

The formula that can be used to express how many bottles Jillian purchased is 5p + 3

Where:

P is the number of bottles in the purchased packs.

Counting how many bottles are in the pack

The expressions of Andre and Jillian would be equal if they each had the same number of bottles.

3p + 11 = 5p + 3

Take the subsequent actions to find the value of p:

Combine related words

5p - 3p = 11 - 3

2p = 8

Subtract 2 from both sides of the equation.

p = 4

Your question is incomplete but most probably your full question was

Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3 packs of bottled drinks, plus 11 single bottles. Jillian purchased 5 packs, plus 3 singles. Andre and Jillian discovered that they had purchased the same number of bottles. How many bottles were in each of the packs? (All of the packs have the same number of bottles.)

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The required sample size of the given problem with a margin of error of at most 0.01 in a 99% confidence interval is 16590.

A margin of error is a factual estimation that records for the distinction among genuine and extended brings about an irregular overview test. In less complex terms, the margin of error you to measure the degree of unconventionality in information and exploration results.

Let p be the population proportion of cyanobacteria.

Given : E = 0.01

Critical value for 99% confidence interval : z = 2.576

If Ian does not want to rely on previous knowledge , then we assume p=0.5 because the largest standard error is at p=0.5.

Now, the required sample size = n

⇒0.5(1 - 0.5)([tex]\frac{2.576}{0.01}[/tex])^2

⇒ 0.25(257.6)^2

⇒ 0.25(66357.76)

⇒ 16589.44 ≈≈ 16590

Thus, the size of sample is 16590.

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First we find number of passengers on each train.

4752/3 = 1584

Each train has 1584 passengers and 8 cars.

To find passengers per car, divide 1584 by 8.

198

Hope this helps :)

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- Jeron

The permutation combination of license plate is 35152000.

Numbers can be 10 digits (0, 1, 2, …, 9) and 26 letters (A, B, C, ..., Z).

Repetition is allowed, leaving 26 next choices for each letter used and 10 next choices for each digit used.

Therefore, according to the multiplication principle, the total number of different letter permutations.

26× 26 × 26 = 17576

and the total number of digit permutation: 10 × 10 × 10 = 1000

now,  they can be in any order:

⁶C₃ = 6!/(6−3)!3!

We have to consider 20 different combinations of positions.

So the total number of different license plates possible by the multiplication principle is

17576 × 1000 × 20 = 351520000

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Answer:

Z= -3

Step-by-step explanation:

-6z-3z=27

-9z=27

/-9.   /-9

z= -3

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The equation of the line is [tex]2x+y=1[/tex] passing through the points [tex](-1,3)[/tex] and [tex](2,3)[/tex]

The general equation can be written as [tex]y=mx+c[/tex]

where m is the slope and c is the intercept

The equation of a line passing through the points [tex](x_{1,} y_{1})[/tex] and [tex](x_{2,} y_{2})[/tex]

slope [tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

The equation is [tex]y-y_{1} =m(x-x_{1} )..........(1)[/tex]

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\m=\frac{-3-3}{2-(-1)} \\m=\frac{-6}{3} \\m=-2[/tex]

Put this value in 1 equation

[tex]y-3=-2(x+1)\\y-3=-2x-2\\y=-2x+1\\2x+y=1[/tex]

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Answer:

Step-by-step explanation:

If Joseph earns 252.50 working 35 hours, that means his hourly rate is $7.50.  If he works 8 hours, he will multiple the hourly rate, 7.50 x 8 = 60.

Answer:

7.5

Step-by-step explanation:

perimeter = 4 × side

√120 = 4s

s = (√120)/4

A = s²

A = [(√120)/4]²

A = 120/16

A = 7.5

The leftmost three digits of nn would be 816.

Solution:

The two-digit perfect squares are $16, 25, 36, 49, 64, 81$. We try making a sequence starting with each one:

The largest is 81649, so our answer is [816].

The leftmost three digits of nn would be 816.

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To draw a dilation with a scale factor 1/2 , multiple every coordinates of pre-image with 1/2 and join the obtained points

A dilation is a transformation that alters the size of an image.

There is a centre and a scale factor in all dilations. The centre serves as the dilation's reference point (like the vanishing point in a perspective drawing)

The scale factor indicates how much the figure expands or contracts. A scale factor is usually denoted by the letter "k," and it is always greater than zero.

To draw a dilation with a scale factor of 1/2, follow these steps:

Step 1: Determine the scale factor and the dilation centre.

Step 2: Identify an image vertex. Draw a line through one of the image's vertices from the center of dilation.

Step 3: Find the horizontal distance and the vertical distance between the center of dilation and the vertex.

To find the horizontal and vertical distances from the centre of dilation to a new vertex, multiply the distances by the scale factor 1/2.

Step 4: Determine the new horizontal and vertical distances from the centre of dilation. Make a point plot.

Step 5: Join the new vertices together to create the dilated image.

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Answer:

cos S = 3/4

sin T = 3/4

Step-by-step explanation:

cos S = adj/hyp = 3/4

sin T = opp/hyp = 3/4

cos S and sin T are the sine and cosine of complementary angles arnd are equal.

Answer:

D=74

D solution 8.60233

Step-by-step explanation: