a) It is known that in a sports club, there are 1000 registered members.
60% of members play Tennis, 50% of members play Cricket,
70% of members play Football, 20% of members play Tennis and Cricket,
40% of members play Cricket and Football and 30% of members play Football and Tennis.
If someone claimed that 20% of members play all the three sports,
what is your opinion and why?
[Use inclusion and exclusion principle to provide your opinion]

The equation of the graph of the function g(x) is A. g(x) = (x - 2)²

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

f(x) = x²

Also, we have the given graph

From the graph, we can see that the graph f(x) is shifted right y 2 units

This means that

g(x) = f(x - 2)

So, we have

g(x) = (x - 2)²

Hence, the equation is (a) g(x) = (x - 2)²

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The option that  correctly describes the graph of the relationship is; D: A line that goes through (0, 0) and (4.5, 13.5)

The formula for the slope between two coordinates is;

Slope = (y₂ - y₁)/(x₂ - x₁)

Let us take two coordinates from the table which are;

(2.4, 7.2) and (4.5, 13.5)

Thus;

Slope = (13.5 - 7.2)/(4.5 - 2.4)

Slope = 3

Now, looking at the options, the first 3 cannot be correct because they have mixed up x-coordinate values with y-coordinate values.

Let us check the last option which is a line that goes through (0, 0) and (4.5, 13.5). Thus;

Slope = (13.5 - 0)/(4.5 - 0)

Slope = 13.5/4.5

Slope = 3

Thus, we conclude that it is correct.

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The price before tax of the books at Barnes and Noble would be 44$ - 25.1$ = 18.9$ if you use your coupon.

The price before tax of the books at Target would be 35$ - 51.1$ = -16.1$ if you use your Red card discount. However, the final price of the books cannot be negative, so the price before tax of the books at Target would be 35$ if you use your Red card discount.

Using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

So, we have a random sample of 20 people.

n = 20

And we also know that 25% of Americans identify themselves as republicans.

Then the number of republicans in 20 people would be:

20/100 * 25

.2 * 25

5

Therefore, using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.

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Mean = 95.125

Variance = 198.90625

Standard deviation = 14.06,

Confidence interval = 95.125 +/- 3.45

To find the 95% confidence interval of the mean score for all bowlers in this league, we need to first calculate the sample mean and sample standard deviation of the given data set.

The sample mean is calculated as follows:

mean = 95.125

The sample standard deviation is calculated as follows:

First, we need to calculate the variance of the data set, which is done by taking the sum of the squared differences between each score and the mean, and dividing by the sample size minus 1:

variance = 198.90625

The sample standard deviation is then the square root of the variance:

standard deviation = sqrt(198.90625)

standard deviation = 14.06

Now that we have the sample mean and sample standard deviation, we can use these values to calculate the 95% confidence interval of the mean score for all bowlers in this league.

We can use the following formula to calculate the confidence interval:

confidence interval = mean +/- (1.96 * (standard deviation / sqrt(sample size)))

Substituting in the values we calculated above, we get:

confidence interval = 95.125 +/- (1.96 * (14.06 / sqrt(40)))

Hence , confidence interval = 95.125 +/- 3.45

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Answer:

(90.78, 98.22)

Step-by-step explanation:

A 95% confidence interval for μ is (x¯−zα/2σn‾√,x¯+zα/2σn‾√). Here, α=0.05, σ=12, and n=40. Use Excel to calculate the 95% confidence interval.1. Open Excel, enter the given data in column A, and find the sample mean, x¯, using the AVERAGE function. Thus, the sample mean is x¯=94.5.2. Click on any empty cell, enter =CONFIDENCE.NORM(0.05,12,40), and press ENTER.3. The answer rounded to two decimal places is zα/2σn‾√≈3.72. The confidence interval for the population mean has a lower limit of 94.5−3.72=90.78 and an upper limit of 94.5+3.72=98.22.Thus, the 95% confidence interval for μ is (90.78, 98.22).

According to question,

Given data,

A hospital director is told that 54% of the emergency room visitors are insured.

A sample of 120 patients  found that 60 were insured.

We know that,

To determine the percentage,

we have to divide the value by the total value and then multiply the resultant by 100,

Percentage formula

Is /of=%?100

Or

Part/whole=%/100

With the help of formula,

Part/sample of patient=%/100

60×100/120=50%

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The value of variable x in the equation is x = -3y + 5/ 2

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, the equation 2x + 3y = 5 can be solved for x as follows:

We have to make x the subject of the formula in the equation.

Subject of the formula is the variable which is expressed in terms of other variables involved in the formula.

Hence,

2x + 3y = 5

subtract 3y from both sides of the equation

2x + 3y = 5

2x + 3y  - 3y = 5 - 3y

2x = 5 - 3y

divide both sides by 2

Therefore,

x = 5 - 3y / 2

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The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.

The Three Kinds of Probability

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency.

Formula used to find probability

The probability is often defined as the proportion of positive outcomes to all outcomes in the sample space. It is written as, the likelihood of an event

P(E) = (Number of favorable outcomes) ÷ (Sample space).

As die is rolled 4 times ,

X≈ binomial(4, 1/6)

P(X=r) = nCr (p)^r (q)^(n-r)

P(X = 1) = 4C1 × (1/6)^1 × (5/6)^3

           = 4 × 1/6 × (5/6)^3

∴P(X = 1) = 0.257

The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.

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The interest rate required to grow the investment to $13,400.00 would be = 35%

Simple interest is the amount of money that is received for a particular period of time due to an investment made to an account.

The principal amount = $4,000.00

The time for investment = 25 months = 2 years

The simple interest = 13,400 - 4000= $9400

The rate (R) = X

The formula for simple interest=

p×t×r/100

9400= 13,400× 2×r/100

Make R the subject of formula;

R = 9400×100/13400×2

R = 940000/ 26800

R= 35%

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Number of ways total inventory of 32 batteries  be distributed among the 8 different types - 15257889504

The number of possible arrangements for a given set is determined mathematically, and this process is known as permutation. The term "permutation" simply refers to the variety of possible arrangements or orders. The positioning of the permutations matters a lot.

Number of ways total inventory of 32 batteries  be distributed among the 8 different types -

39!/30! 7! = 39X38X37X36X35X34X33X32X31 / 7X6X5X4X3X2X1

= 15257889504

Number of ways total inventory of 32 batteries  be distributed among the 8 different types, in inventory must include A76 - 35! / 28! 7!

= 35X34X33X32X31X30X29 / 7X6X5X4X3X2X1 = 6714520

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Answer:

D) 48

Step-by-step explanation:

Let s = Scott

Let j - James

s = 5

s + 43 = j  Substitute 5 for s

5 + 43 = j

48 = j

The steps to construct a cumulative frequency distribution table are mentioned above.

Given is to construct a cumulative frequency distribution table.

Since the data is not given, we can write the steps to construct a frequency distribution table. The steps to create a cumulative frequency distribution table are mentioned below -

Therefore, the steps to construct a cumulative frequency distribution table are mentioned above.

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Answer:

Based on the information provided, it does not seem like this game is fair. Since region 1 and region 2 are the same size, each player has an equal chance of winning, but since region 3 is significantly larger than the other regions, neither player has a high chance of winning. This means that one player could potentially win multiple times in a row just by luck, without the other player having a chance to catch up. In order for the game to be considered fair, the relative sizes of the regions should be such that each player has a roughly equal chance of winning.

Answer:

yes. they both have ⅓ chance of winning

Step-by-step explanation:

Answer:

it might be 4

Step-by-step explanation:

that's all I have

All vectors of the form(a, b, a - 2b) is a subspace of R³. So, the correct option is option(D).

If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if

Now, check the options and find out the option which satisfy the subspace conditions.

A) All the vectors are of form (0, a,a²)

let (0,1,1) = u and v=(0,2,4) and both are belongs to { 0, a,a² : a∈R }, (0,0,0)∈ {0, a,a² : a∈R }.

u + v = (0,1,1) + (0,2,4) = (0,3, 5) not belongs to

{ 0, a,a² : a∈R }. So, this is not correct option.

B) Here, (0,0,0) does not belongs to

{0, a, a+2 : a∈R } because if a= 0 then a+2 =/ 0 .

So, it is also not subspace.

C) All vectors of the form (a, b, 2)

The third tuple is 2 which never be equal to zero. Hence, (0,0,0) does not belongs to (a, b, 2) and it is not form subspace.

D) All vectors of the form (a, b, a - 2b)

When a = 0 , b = 0 => (0,0,0) ∈(a, b, a - 2b)

let u = ( a1, b1 , a1- 2b1) and v = ( a₂, b₂ , a₂ - 2b₂)

and α∈R

u + v = ( a₁, b₁ , a₁- 2b₁ ) + ( a₂, b₂ , a₂ - 2b₂)

= ( a₁ +a₂ , b₁+b₂ , a₁+a₂ -2(b₁ - b₂)) €(a, b, a - 2b)

αu = α(a₁ , b₁ , a₁- 2b₁)

=( αa₁ , αb₁ , α(a₁ - 2b₁))∈(a, b, a - 2b)

both the conditions are satisfied, so it is Subspace of R³.

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Step-by-step explanation:

she made shots = 34%of 54

=50*34/100

=17

he made 17 shots

following algorithms correctly updates the values, If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.

The game records the highest and lowest scores that were earned. This indicates that the game already has the highest and lowest score stored in its memory.

Now, if a new score, num, is achieved, the game must compare num with the minimum and maximum scores in order to update the minimum and maximum scores. The minimum score is updated to the score, num if the most recent score, num, is lower than the minimum score.

Additionally, the maximum score is updated to the score, num if the most recent score, num, is higher than the maximum score.

Complete Question :

A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?

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Answer: Measure less 90 degrees

Step-by-step explanation: Less than 90 degrees measure acute angle. 90 degrees in right corner. Obtuse corners are larger than 90 degrees

Answer: 13 + 6√5

Step-by-step explanation: None

The required inequality expressions are 7x + 7y ≤ 49 and x + 2y ≤ 13 an the graph has been plotted with clarity.

The expression for inequality can be written by taking the suitable sign for the given problem and then relating the variable part to the constant terms.

(a) Suppose the number of short film and full movie are x and y respectively.

Then, the inequality expression for the given case can be written as follows,

The inequality for money raised is,

7x + 7y ≤ 49

And, the inequality for script writing is,

x + 2y ≤ 13

(b) These inequalities can be graphed as follows,

Hence, for the given case the required system of inequalities is 7x + 7y ≤ 49 and x + 2y ≤ 13 and the graph for the solution is drawn properly.

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The tangent AB is for circle in figure (a).The correct option is (a).

For a given circle there can only be one tangent at one point.

The tangent and the circle has only one point in common.

The tangent to a circle is always perpendicular to the radius at that point.

The tangent drawn to a circle is always at right angle to the radius at that point.

The given figures are examined one by one as follows,

(a) The sides of the triangle are given as 5, 12 and 13.

And, 13² = 5² + 12²

Which implies it is a right triangle by Pythagoras theorem.

(b) The sides of the triangle are given as 4, 10 and 11.

And, 11² ≠ 10² + 4²

Which implies it is not a right triangle by Pythagoras theorem.

(c) The sides of the triangle are given as 18, 25 and 18.

And, 25² ≠ 18² + 18²

Which implies it is not a right triangle by Pythagoras theorem.

Thus, only for figure (a) the criteria for the tangent satisfies.

Hence, the line segment AB is tangent to the circle given in figure (a).

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The slope of y = 7x - 10 is 7 while the y-intercept is -10 thus it has a high slope but a lower y-intercept so option (D) is correct.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A linear function with slope m and y-intercept c is given as y = mx + c.

Compare the given function y = 7x - 10

Slope m  = 10

y-intercept = -10

Hence "Y = 7x - 10 has a slope of 7 and a y-intercept of -10, meaning it has a high slope but a low y-intercept".

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Step-by-step explanation:

To make the equation AFGHACBD true, the value of y must be 7, and the value of z must be 32-1=31.

Here is how the equation works out:

2z + 14 = 2 * 31 + 14 = 68

2y + 35 = 2 * 7 + 35 = 49

68 + 2 = 70

70 > 49

49 + 7y = 49 + 7 * 7 = 98

98 > 70

70 + 32 - 1 = 70 + 31 = 101

101 > 98

98 + 2y + 35 = 98 + 2 * 7 + 35 = 146

146 > 101

So, the values of y and z that make the equation AFGHACBD true are y=7 and z=31.

Answer:

11325

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[a+l]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $l$ is the last term.\\\phantom{ww}$\bullet$ $n$ is the number of terms.\\\end{minipage}}[/tex]

A positive integer is a whole number that is greater than zero.

Therefore:

Substitute the values into the formula to find the sum of the first 150 positive integers:

[tex]\implies S_{150}=\dfrac{1}{2}(150)\left[1+150\right][/tex]

[tex]\implies S_{150}=75 \cdot 151[/tex]

[tex]\implies S_{150}=11325[/tex]

Therefore , the answer to this problem is that  y-coordinate for the solution is option a) y = -8

A number, a variable, or a mix of both are used in an expression coupled with specific operation symbols. An equal sign is used to denote the division of two expressions that make up an equation.

Here,

6x + y = -32 and

y = x - 4

=> 6x +( x - 4) = -32

=>7x -4=-32

=>7x =-28

=> x = -4

Thus,

y = -4 - 4 = -8

Therefore , the  y-coordinate comes out to be y = -8

Thus, the correct option in the following option is option a)y=-8.

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Answer:

The value of the correlation coefficient is 0.87, which means there is a strong, positive association between discharge and speed. A positive correlation means that as one variable increases, the other variable also increases. In this case, as the discharge of the Colorado River increases, the speed of the river also increases. The strength of the association is indicated by the magnitude of the correlation coefficient, which ranges from -1 to 1. A value of 0.87 is considered a strong positive correlation, indicating that there is a strong relationship between the two variables.

Answer:

30 oz

Step-by-step explanation:

x = size of original cup

x - (0.10)x = 27 oz

(0.90)x = 27 oz

x = 27 / 0.90 = 30 oz

Emerson actually hit the ball 32% of times at bat.

What is percentage ?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Since in Game 1, Emerson struck out 30 times in 90 times at bat;

in Game 2, he struck out 40 times in 120 times at bat;

in Game 3, Emerson struck out 42 times in 140 times at bat;

To determine what percentage of times at bat did Emerson actually hit the ball, the following calculation must be performed:

(30 + 40 + 42) / (90 + 120 + 140) = X

112/350 = X

0.32 = X

Therefore, Emerson actually hit the ball 32% of times at bat.

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Using combination we get  20475 teams can made up of 3 girls and 2 boys and 37128  teams can be selected with at least 3 girls.

Since this is just a team of 5 children,

we have   no of girls = 15

No of boys = 10

teams made up of 3 girls and 2 boys

girls out of 3 girls can be selected in  ¹⁵C₃ ways and

2 boys out of 10 boys can be selected in  ¹⁰C₂  ways.

[tex]\implies[/tex] ¹⁵C₃ X  ¹⁰C₂

= 455*45 =20475 Ways

Teams can be selected with at least 3 girls

It is the probability of at least 3 girls which means P(3 girls,2 boys) or P(4 girls,1 boy) or P(5 girls, 0 boys)

[tex]\implies[/tex] ¹⁵C₃ X  ¹⁰C₂  + ¹⁵C₄ X  ¹⁰C₁ + ¹⁵C₅ X  ¹⁰C₀

= 455 * 45 +1365*10+3003*1

=20475 +13650 +3003

=37128 ways

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