The linear graph shows the possible combinations of cakes and pies a club must sell to meet their fundraising goal. What is the domain of the graph? A) {x: 0 < x < 40} B) {x: 0 ≤ x ≤ 40} C) {x: 0 < x < 20} D) {x: 0 ≤ x ≤ 20}

a)Using the chi-square distribution table, the critical value is 12.592 using Hypothesis.

b)The value of chi-square statistic for the sample is 16.042, given that

(a)Chi-square test

The Null Hypothesis H₀ : Myers-Briggs preference type is independent of area of study.

Alternative Hypothesis H₁ : Myers-Briggs preference type is dependent of area of study.

Test statistic is χ² = ∑ ((Oi - Ei)² / Ei)

Expected frequencies:To compute the expected frequencies of the data we use the formula:

Eij = (row total i * column total j) / n where

i is the row number and j is the column number.

To find the value of chi-square statistic, the following table is necessary:

Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519

We obtain the expected frequencies by the above formula, and these are listed in the table below.

Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 51.55 23.43 21.03 96
EN 86.71 39.56 27.73 154
IS 50.14 22.88 20.97 115
ES 82.61 37.13 32.27 154
Column total 271 123 125 519

The expected frequencies are computed by multiplying the row total and column total and dividing by the grand total, n.

Here, we have four rows and three columns.

Thus, the degrees of freedom are df = (4 - 1)(3 - 1) = 6 at the 0.05 level of significance.

Since we have four rows and three columns, the number of degrees of freedom will be 6.

Using the chi-square distribution table, the critical value is 12.592.

Since 16.04 > 12.592,

we reject the null hypothesis and conclude that Myers-Briggs preference type is dependent of area of study.

(b) Value of chi-square statisticThe formula to compute the chi-square statistic is

χ² = ∑ ((Oi - Ei)² / Ei) where Oi is the observed frequency and Ei is the expected frequency.

Calculating the chi-square statistic, we have

χ² = ((66 - 51.55)² / 51.55) + ((11 - 23.43)² / 23.43) + ... + ((43 - 32.27)² / 32.27)

  = 16.042 (rounded to three decimal places).

The value of chi-square statistic for the sample is 16.042.

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Answer:

1/4 of an hour is 15 minutes

Step-by-step explanation:

Answer: 1/4 of an hr

Step-by-step explanation:

15/60 is 1/4

The general solution to the initial value problem is:

y(t) = y_c(t) + y_p(t)

= 8 cos(√7t) + cos(√7t)

To solve the initial value problem using the method of undetermined coefficients, we assume a particular solution of the form:

y_p(t) = A sin(√7t) + B cos(√7t)

where A and B are constants to be determined.

Taking the first and second derivatives of y_p(t), we have:

y'_p(t) = A√7 cos(√7t) - B√7 sin(√7t)

y''_p(t) = -A(√7)^2 sin(√7t) - B(√7)^2 cos(√7t)

Substituting these derivatives back into the differential equation, we get:

(-A(√7)^2 sin(√7t) - B(√7)^2 cos(√7t)) + 7(A sin(√7t) + B cos(√7t)) = 7 sin(√7t)

Simplifying, we have:

(-A(√7)^2 + 7A) sin(√7t) + (-B(√7)^2 + 7B) cos(√7t) = 7 sin(√7t)

To satisfy this equation for all t, the coefficients of sin(√7t) and cos(√7t) must be equal to the corresponding coefficients on the right side.

Therefore, we have the following system of equations:

-A(√7)^2 + 7A = 0 (coefficient of sin(√7t))

-B(√7)^2 + 7B = 7 (coefficient of cos(√7t))

Solving these equations, we find:

A = 0

B = 1

So, the particular solution is:

y_p(t) = cos(√7t)

To find the general solution, we need to find the complementary solution by solving the homogeneous equation:

y'' + 7y = 0

The characteristic equation is:

r^2 + 7 = 0

Solving this quadratic equation, we find two complex roots:

r₁ = √7i

r₂ = -√7i

The complementary solution is then:

y_c(t) = C₁ cos(√7t) + C₂ sin(√7t)

where C₁ and C₂ are constants to be determined.

Using the initial conditions y(0) = 8 and y'(0) = √7, we can substitute these values into the general solution and solve for C₁ and C₂.

y(0) = C₁ cos(0) + C₂ sin(0) = C₁ = 8

y'(0) = -C₁√7 sin(0) + C₂√7 cos(0) = C₂√7 = √7

Therefore, C₁ = 8 and C₂ = 1.

The general solution to the initial value problem is:

y(t) = y_c(t) + y_p(t)

= 8 cos(√7t) + cos(√7t)

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Since s = Σ(xi - x) / n is the sample variance therefore,

Option (a) x/r is correct.

To find the maximum likelihood estimate of β,

We need to maximize the likelihood function L(β) with respect to β.

The likelihood function for a negative binomial distribution with parameters β and r, given n observations with mean x, is,

⇒ L(β) = (Γ(r+n)/Γ(r)n!)  (β^r / (β+x)^r+n) ∏([tex]x_i[/tex]+x)/(([tex]x_i[/tex]+β)^r+1

where Γ is the function and ∏ denotes the product over all n observations xi.

Taking the natural logarithm of the likelihood function, we get,

⇒ ln L(β) = ln(Γ(r+n)) - ln(Γ(r)) - ln(n!) + r ln(β) - (r+n) ln(β+x) + Σ ln(xi+x) - Σ ln(xi+β) - (r+1)Σ ln(xi+x)

To find the maximum likelihood estimate of β,

we take the derivative of ln L(β) with respect to β,

set it equal to zero, and solve for β,

⇒ d/dβ ln L(β) = r/β - (r+n)/(β+x) + Σ 1/(xi+β) - (r+1)Σ 1/(xi+x) = 0

We can solve this equation numerically using iterative  methods, but we can also simplify it by using the fact that when the derivative of a function equals zero, the function is at a maximum or minimum.

Multiplying both sides of the equation by β(β+x), we get.

⇒ r(β+x) - (r+n)β + β(β+x)Σ 1/(xi+β) - (β+x)(r+1)Σ 1/(xi+x) = 0

Simplifying and solving for β, we get,

⇒ β = x(r+n-1) / (Σ 1/(xi+β) - (r+1)Σ 1/(xi+x))

We can use an iterative method to solve for β, starting with an initial estimate of β and updating it until convergence.

One common method is to use the Newton-Raphson algorithm.

After some algebraic manipulations,

we can show that the maximum likelihood estimate of β is,

⇒ B =  x(r / s - 1)

Here s = Σ( - x) / n is the sample variance of the n observations. Therefore, the correct option is (a) x/r.

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Answer:

5ft^3

Step-by-step explanation:

The formula for volume is length × width × height.

so you multiply 1×2×2.5, which equals 5

Answer:

a = 7. b = 24, c = 25. This is a Pythagorean triple

Step-by-step explanation:

Answer:

Science students

Step-by-step explanation:

Answer:

it does not form a triangle

Step-by-step explanation:

brainliest give me pls pls pls

Answer:

It forms a obtuse triangle

Step-by-step explanation:

Because two sides are the same.

After considering the given data we conclude that the total number of 4-element subsets that can be generated is 70.

To evaluate the number of 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}, we can apply the combination formula:
[tex]nCr = n! / r!(n-r)![/tex]
Here,
n = maximum count of elements in the set
r = total count of elements we want to choose.
For the given case, n = 8 (since there are 8 elements in the set) and r = 4 (since we want to choose 4-element subsets).
Placing in these values, we get:
[tex]nCr = 8! / 4!(8-4)! = 8! / 4!4![/tex]
[tex]= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70[/tex]
Hence, creation of 70, 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}.
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Answer:

66.93 in^3

Step-by-step explanation:

Volume = πr^2h

=> V = 22/7*(1.9)^2*5.9 = 66.93 in^3

Answer:

1.3 times 10 to the 25th power

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

Hi! The answer to your question is 1.3 x [tex]10^{25}[/tex]

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

Answer:

50

Step-by-step explanation:

if im thinking right

im SOO sorrYYy if its wrong

Answer:

<

Step-by-step explanation:

-6 is lower than  -1. you can make a little line and count backwards from 0. -1 is closer to 0 than -6 is, therefore -1 being bigger and the sign being <

Answer:

60

Step-by-step explanation:

half of 2/5 is 1/5 so half of 24 is 12.

since 12  is 1/5 of the number multiply 12 by 5 and you get 60.

The whole number will be 60 whose two fifths will be 24.

Given, Two fifths of a number is 24.

Writing in form of equation,

Let the whole number be x.

So, two fifth of x is 24.

[tex]\frac{2}{5} of x = 24[/tex]

[tex]\frac{2}{5} \times x = 24[/tex]

Apply cross multiplication,

[tex]x = \frac{24 \times 5}{2}[/tex]

x = 60.

Therefore the whole number is 60.

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Answer:

a. 19 Questions

b. No, Collins grade was 81%, or B-minus :(

Step-by-step explanation:

There are 21 questions in total on the test. Collin wants a 90 percent at least. If you multiply 21 by 90 percent (as below), you will get 18.9

[tex]21 * .9\\=18.9[/tex]

Of course, you can't get 18.9 questions right (unless you're teacher gives .9 extra points lol, So we need to round UP to a whole number (don't round down because it'll give you a number lower than what 90 percent would equate to.

And, Collin got 17 questions right. That's equivalent to 81 percent of 21 (as below).

[tex]17 / 21\\=.8095[/tex]

This rounds to about 81%, meaning Collin did not reach his goal :(. Oh well, he'll just have to try harder next time!

Have a nice day, fam.

Answer:    5x-3

Step-by-step explanation:

3x+ 2x +2-5

5x        -3

PowerBroker provided a solution to the security issue at ABC Co. by removing admin rights, improving application security, and addressing network security and data protection concerns.

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Answer:

arc length d = ∫ √(1 + (dy/dx)²) dx

y = 228 - x²/57

dy/dx = -2x / 57

(dy/dx)² = (2x/57)²

Upper limit for integration:

y = 0 = 228 - x²/57

yields x = 114

d = ∫ √(1 + (2x/57)²) dx for 0 ≤ x ≤ 114 = 264.9 m

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

(-5) - (-2) = (-3)

hope it helps

Answer:

there is a three degree difference between san Diego and Los Angeles

Answer:

D

Step-by-step explanation:

Answer:

Zero.

Step-by-step explanation:

The minimum value  is where the function touches the x axis , at y = 0.

Answer:

this took hella long to do but it's B

Answer:

The Scale Factor is 1/4.

Step-by-step explanation:

if you multiply each side (of figure A) by 1/4, the product matches with figure B's corresponding sides. for example, 56 to 14, 28 to 7, and 64 to 16.

the scale factor is just how much a chosen shape is multiplied by to get the next shape.

to get bigger shapes into a smaller shape, multiply the sides by fractions like we did this problem.

Using the Chain Rule to dw/dt. w = ln [tex]\sqrt{2a}.gifx^{2} + y^{2} + z^{2}[/tex], x = 4 sin t, y = 7 cos t, z = 9 tan t the expression will give us the final result for dw/dt.

To find dw/dt using the Chain Rule,

we'll start by expressing w as a composition of functions and then differentiate it step by step.

Given:

w = ln[tex](\sqrt{} (x^2 + y^2 + z^2))[/tex], where x = 4 sin(t), y = 7 cos(t), and z = 9 tan(t).

We'll first substitute the values of x, y, and z into the expression for w:

w = ln[tex](\sqrt{} ((4 sin(t))^2[/tex] + [tex](7 cos(t))^2[/tex] + [tex](9 tan(t))^2))[/tex]

Next, we'll differentiate w with respect to t using the Chain Rule.

The Chain Rule states that if we have a composite function f(g(t)),

its derivative is given by f'(g(t)) ×g'(t).

In our case, f(u) = ln[tex](\sqrt{u}[/tex] and g(t) represents the expressions within the square root.

Applying the Chain Rule, we have:

dw/dt = [tex](1/\sqrt{} (x^2 + y^2 + z^2))[/tex] × (2xdx/dt + 2ydy/dt + 2z×dz/dt)

Substituting the expressions for x, y, and z, we get:

dw/dt = (1/[tex]\sqrt{} ((4 sin(t))^2 + (7 cos(t))^2[/tex]+[tex](9 tan(t))^2))[/tex] ×(2(4 sin(t))(cos(t)) + 2(7 cos(t))(-sin(t)) + [tex]2(9 tan(t))(sec^2(t)))[/tex]

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Answer:

That one

Step-by-step explanation:

It's kinda obvious if you look at the choices.

Answer:

8+14

Step-by-step explanation:

Answer: C

So I was right, I guess.

The correct answer is that 13 students who spend more than 12 hours a week on screens were surveyed.

The provided data represents the number of students based on their screen time and whether their grade average is above or below 80.

To find the total number of students who spend more than 12 hours a week on screens, we need to look at the "Screen Time" category that corresponds to "more than 12 hours" and sum up the corresponding counts.

Looking at the data:

Screen Time:

less than 4 hours: 6 students

4-8 hours: 15 students

8-12 hours: 9 students

more than 12 hours: 13 students

If we consider only the "more than 12 hours" category, we find that there were 13 students.

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Answer:  C

Step-by-step explanation:

Answer:

I believe this is the answer  9/(5 + 8x)