at a school pep rally, a group of sophomore students organized a free raffle for prizes. they claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. the results do not seem that random to you. you think it is a little fishy that sophomores organized the raffle and also won the most prizes. your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. a. what are the expected frequencies of winners from each class? b. conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. report your chi square and p values.

Answer:

$57.50

Step-by-step explanation:

find 10% of 50 first, which is 5, because 5 × 10 = 50, then add $10 to the $50 beacause 50 × 0.2 = 10, next, remove 5%, to do this divide 10% by 2 to get $2.50, 60 - 2.5 = 57.5

The linear inequality y</5/2 x - 7 does not have any common solution set with the given inequality.

The solution sets of the linear inequality  are drawn in the graph attached below,

From the graph it is seen that the yellow part represents the inequality y≥-5/2 x - 3

And the green section of the graph represents the other inequality

y<-5/2 x - 7

As we can see in the graph that the two areas are separate. So there are no common points.

Again if we consider the two inequalities as two lines  y= -5/2 x - 3

and y = -5/2 x - 7 . we can see that they both have the same slopes of  -5/2 so they are parallel lines. so they will never intersect.

Therefore we can conclude that the inequality  y</5/2 x - 7 does not have any common solution set with the given inequality.

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Answer:

Step-by-step explanation:

Answer -

a) 50% or 1/2

Explanation -

12+12=24

therefore, 12/24 = 1/2 which is 50%

b) 46.43% or 13/28

Explanation -

15+13=28

therefore, 13/28 which is 46.6%

Answer:

The given expression in factored form is (x + 2)(x - 3).

If the expression is set to zero, the solutions x = -2 and x = 3 are the roots of the graph of the equation.

Step-by-step explanation:

To factor a quadratic in the form ax² + bx + c, begin by finding two numbers that multiply to ac and sum to b.

Given quadratic:

\(x^2-x-6\)

Therefore:

\(\implies ac=1 \cdot -6=-6\)

\(\implies b=-1\)

Two numbers that multiply to -6 and sum to -1 are -3 and 2.

Rewrite b as the sum of these two numbers:

\(\implies x^2-3x+2x-6\)

Factor the first two terms and the last two terms separately:

\(\implies x(x-3)+2(x-3)\)

Factor out the common term (x - 3):

\(\implies (x+2)(x-3)\)

If the given expression is a function, then:

\(f(x)=(x+2)(x-3)\)

To find the solutions of the function, set it to zero and apply the zero-product property:

\((x+2)=0 \implies x=-2\)

\((x-3)=0 \implies x=3\)

Therefore, the solutions of the equation are x = -2 and x = 3.

These are the roots (x-intercepts) of the graph of the function.

Given:-

To find:-

Answer:-

Given expression to us is ,

\(\implies x^2 - x - 6 \\\)

Here we can write " - x " as the sum of -3x and x .

So we can write the given expression as ,

\(\implies x^2 - 3x + 2x - 6\\\)

\(\implies x ( x - 3) + 2(x -3) \\\)

\(\implies (x+2)( x-3)\\\)

Hence the factored form of the expression is (x+2)(x-3) .

By zeroes we mean the values , which when put in the equation at the place of variable here x , the value of expression becomes zero .

For finding the zeroes, we need to equate the given expression with 0 as ,

\(\implies (x+2)(x-3) = 0 \\\)

Here we can two values of x as ,

\(\implies \underline{\underline{ x = -2 , 3 }}\\\)

This means when we put x = -2 or x = 3 in the given equation , the equation becomes 0 .

and we are done!

The solution of the division of 4 2/9 by the number 1 1/3 is

Mixed fractions are type of fractions which consist of a whole number part and a fractional part.

Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.

The given fractions are 4 2/9 and 1 1/3.

First we have to change the mixed fraction into improper fraction.

4 2/9 = (4 × 9 + 2) / 9 = 38/9

1 1/3 = (1 × 3 + 1) / 3 = 4/3

Dividing these,

4 2/9 ÷ 1 1/3 = 38/9 ÷ 4/3

                     = (38/9) × (3/4)

                     = 38 / (3 × 4)

                     = 19/6

                     = 3 1/6

Hence the solution of the division of the mixed fractions given is 3 1/6.

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Robert started his presentation with interesting statistics. this is an example of a Hook.

What should you concentrate on initially when you are getting ready to start a paper?

What exactly is a sample thesis statement?

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Answer:

Step-by-step explanation:

The simple interest formula is ...

  I = Prt . . . . . r is the interest rate, t is the number of years

Solving for P, we have ...

  P = I/(rt)

6 months is 1/2 year, so the principal is ...

  P = $4.38/(0.035×1/2) = $250.2857...

Rounded to the nearest dollar, the principal invested is $250.

__

Using the same approach, for 18 months, t = 18/12 = 3/2 = 1.5.

  P = $20.70/(0.023×1.5) = $600

The principal in Account B is $600.

__

First Month's Interest

Using the interest formula, the first month's interest in each account is ...

  A: I = 250×0.035×1/12 = $0.73

  B: I = 600×0.023×1/12 = $1.15

Account B earns more interest in the first month.

Answer:

Step-by-step explanation:

The first three terms of the arithmetic sequence for the number of words written are 10010, 9760, 9510. These have a common difference of 9760-10010 = -250. The first term and common difference can be used to make the explicit equation for the words written on the n-th day.

The explicit formula for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...

  \(a_n=a_1+d(n-1)\)

For first term a₁ = 10010 and common difference d = -250, the explicit rule is ...

  \(a_n=10010-250(n-1)\)

On day 14, n=14, and the number of words written is ...

  \(a_{14}=10010-250(14-1)\\\\a_{14}=10010-250(13)=10010-3250\\\\a_{14}=6760\)

The writer would write 6760 words on the 14th day.

Answer:

2071

Step-by-step explanation:

let t-16 then you multiple that by 4 and there is your answer 2071

Answer:

que

Step-by-step explanation:

no Tengo carnitas yo quero sopes

Answer:

y = x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, - 3 ) and (x₂, y₂ ) = (7, 8 )

m = \(\frac{8-(-3)}{7-(-4)}\) = \(\frac{8+3}{7+4}\) = \(\frac{11}{11}\) = 1 , then

y = x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (7, 8 ) , then

8 = 7 + c ⇒ c = 8 - 7 = 1

y = x + 1 ← equation of line

The standard deviation for the probability distribution is approximately 0.79, rounded to two decimal places.

To find the standard deviation for this probability distribution, we first need to find the mean.

The mean is given by:

μ = Σ(x * P(x))

where x is the number of burglaries and P(x) is the probability of x burglaries being reported in a given day.

\(μ = (0 * 0.53) + (1 * 0.35) + (2 * 0.10) + (3 * 0.02)μ = 0 + 0.35 + 0.20 + 0.06μ = 0.61\)

So the mean number of burglaries reported in a given day is 0.61.

To find the standard deviation, we use the formula:

\(σ = √(Σ[(x - μ)^2 * P(x)])\)

where σ is the standard deviation.

\(σ = √[((0 - 0.61)^2 * 0.53) + ((1 - 0.61)^2 * 0.35) + ((2 - 0.61)^2 * 0.10) + ((3 - 0.61)^2 * 0.02)]\\σ = √[(0.61^2 * 0.53) + (0.39^2 * 0.35) + (1.39^2 * 0.10) + (2.39^2 * 0.02)]\\σ = √[0.197969 + 0.053865 + 0.257199 + 0.113964]\\σ = √0.623997σ ≈ 0.79\)

Therefore, the standard deviation for the probability distribution is approximately 0.79, rounded to two decimal places.

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Answer:

1/3 of the pizza remains.

Step-by-step explanation:

Matthew eats 1/3 of 1/2 of the pizza, which is (1/3)*(1/2) = 1/6 of the pizza.  The amount of pizza left is

1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3

1/3 of the pizza remains.

Given:

The digit given is 1/2.

To find:

Check which expression has a value greater than 1/2.

Explanation:

To find which term is greater than 1/2, let's simplify each expression:

(A)

Which is less than 1/2.

(B)

Which is equal to 1/2.

(C)

Which is equal to 1/2.

(D)

Which is greater than 1/2.

Final answer:

Hence, the correct expression which has a value greater than 1/2 is:

Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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Answer:

no

Step-by-step explanation:

theres no common theme between the x and y variable

Answer:

7

Step-by-step explanation:

→ Write the equation

40x + 120 = 400

→ Minus 120 from both sides

40x = 280

→ Divide by 40 on both sides

x = 7

The number of breaking gigs that it takes him to have is $400 will be 7  breaking gigs.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Mr. Delgado gets paid $40 per breaking gig. If he has $120 saved. If he doesn't spend any money.

Then the number of breaking gigs that it takes him to have is $400 will be

40x + 120 = 400

Simplify the equation then we have

40x = 280

x = 280/40

x = 7

The number of breaking gigs that it takes him to have is $400 will be 7  breaking gigs.

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Answer:

28 dvds in 14 weeks

Step-by-step explanation:

4 dvds in two weeks

2 dvds in a week

14 weeks equal 28 dvds

Answer:

-6y² -1 + 6x - y

Step-by-step explanation:

-6y² + 4 + 4x – y + 2x – 2 – 3 ?

-6y²- 1 + 4x - y + 2x

-6y² -1 + 6x - y

Step-by-step explanation:

Remember that

\( \frac{dy}{dx} \)

is the gradient or slope function.

So we need to analyze the slope of each graph over given time.l and how it changes.

For the 1st graph, we have a linear function.

Remember the special properties for all linear functions:

The slope at any two points on the line is the same.

So this means our slope here must be constant.

And since our slope is negative, our dy/dx, function must be a constant function that is negative. So

The answer for the first graph is draw a horizontal line underneath the x axis.

For the 2nd graph, we have a slope that is decreasing, reaches 0 at the minimum, then increases even more.

We can draw a linear function that is increasing forever for our dy/dx.

For the 3rd graph, we are increasing , till we hit 0, then decrease until we hit 0, then forever increases.

Our dy/dx will be a parabola that passes through the x axis twice at two different points, facing upwards.

The first , second, and third graph is the dy/dx graphs shown respectively.

All these are examples of possible graphs. If you need more clarification, let me know

We can define the function f(x) as:

f(x) = 2x + b, where 2 ≤ b ≤ 39

To find the function f(x) that satisfies g(x) ≤ f(x) ≤ h(x) for -2 < x < 1, we need to consider the given functions g(x) and h(x) and determine the range of values that f(x) can take within that interval.

Given:

g(x) = sin(π/2(x+2)) + 3

h(x) = -14x^3 - 32x^2 - 94x + 3

To ensure that g(x) ≤ f(x) ≤ h(x) for -2 < x < 1, we can choose f(x) to be any function that lies between the values of g(x) and h(x) within that interval.

Let's consider a simple linear function that satisfies this condition. We can define f(x) as follows:

f(x) = mx + b

where m is the slope of the line and b is the y-intercept.

To determine the slope (m) and y-intercept (b) values, we need to consider the boundary points of the interval -2 < x < 1 and evaluate g(x) and h(x) at those points.

For x = -2:

g(-2) = sin(π/2(-2+2)) + 3 = sin(0) + 3 = 3

h(-2) = -14(-2)^3 - 32(-2)^2 - 94(-2) + 3 = -24 - 128 + 188 + 3 = 39

For x = 1:

g(1) = sin(π/2(1+2)) + 3 = sin(3π/2) + 3 = -1 + 3 = 2

h(1) = -14(1)^3 - 32(1)^2 - 94(1) + 3 = -14 - 32 - 94 + 3 = -137

So, within the interval -2 < x < 1, the range of values for f(x) should be between g(x) and h(x), which means the range of values for f(x) is 2 ≤ f(x) ≤ 39.

Therefore, we can define the function f(x) as:

f(x) = 2x + b, where 2 ≤ b ≤ 39

Note: This is just one possible function that satisfies the given condition. There could be other functions that also satisfy g(x) ≤ f(x) ≤ h(x) within the specified interval.

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Answer:

10 feet

Step-by-step explanation:

yeah

The row of the table that reveals the x-intercept of the function f is given as follows:

Second row.

A function has two intercepts, which are listed as follows:

The definition of each type of intercept is given as follows:

From the second row of the table, we have that when x = -4, f(x) = 0, hence the x-intercept of the function is of x = -4.

The y-intercept is of y = -16, as from the fourth row, when x = 0, y assumes a value of 16.

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Answer: 56

Step-by-step explanation:

Given that :

Marbles in bag are only red and blue ;

Probability of randomly choosing a red = 2/7

Number of red marbles in bag = 16

The total Number of marbles =?

P(choosing a red marble) = required outcome / Total possible outcomes

Required outcome = number of red marbles

Total possible outcomes = total number of blue and red marbles

Total number of blue and red marbles = x

P(choosing a red marble) = required outcome / Total possible outcomes

2/7 = 16 / x

Cross multiply

2x = 16 * 7

2x = 112

x = 112 / 2

x = 56 marbles

Total number of marbles = 56

Answer:

1

Step-by-step explanation:

because the numerical coefficient of these variables is one

so

v3=1×1×1=1

v=1

v=1×1×1×1=1

The probability that a randomly chosen subject comples more than the expected number of puzzles in the five minute is equals to the 0.40. So, option (b) is right one.

We have a Random variables X denotes the number of puzzles complete by random choosen subject. The above table contains probability distribution of random variable X. The expected number of puzzles in the 5-minutes period while listening to smoothing music is calculated by following formula, \(E(x) = \sum x_i p(x_i)\)

= 1(0.2) + 2(0.4) + 3(0.3) + 4(0.1)

= 0.2+ 0.8+ 0.9+ 0.4

= 2.3

Now, the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music, that is possible value values of X are 1,2,3,4 but for X > 2.3 only 3 and 4. So, P(X>2.3)= P(X=3) + P(X=4)

=0.30+ 0.10=0.40

Hence, required value is 0.40.

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Complete question:

The above table complete the question

what is the probability that a randomly chosen subject comples more than the expected number of puzzles in the five minute period while losing music

a. 0.1

b. 0.4

c. 0.8

d. 1

e. Cannot be determined

Answer:

150 minutes

Step-by-step explanation:

30 × 5 = 150 minutes