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3 years ago

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In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts Co

llege, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The calculated value for the test statistic equals:_______.
a. 0.01
b. 0.75
c. 4.29
d. 4.38

1 answer:

Vera_Pavlovna [14]3 years ago

7 0

B. 0.75 is the answer for this equation

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seropon [69]

Answer:

Second option

Third option

Fourth option

Step-by-step explanation:

We have the following quadratic function

$f(x) =(x-1)(x+7)$

Use the distributive property to multiply the expression

$f(x) =x^2+7x-x-7$

$f(x) =x^2+6x-7$

For a function of the form $f (x) = ax ^ 2 + bx + c$ the x coordinate of the vertex is:

$x =-\frac{b}{2a}$

Then in this case the coordinate of the vertex is:

$x =-\frac{6}{2(1)}$

$x =-3$

To obtain the y coordinate of the vertex we evaluate the function at $x = -3$

$f(-3) =(-3)^2+6(-3)-7$

$f(-3) =9-18-7$

$f(-3) =-16$

Then the vertex is: (-3, -16)

We can see in the graph that the zeros of the function are x=1 and x=-7

Then the function is decreasing from -∞ to -3 and then it is increasing from -3 to ∞

The function is positive for $x$ and $x> 1$

The correct answers are:

Second option

Third option

Fourth option

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3 years ago

What is the value of b in the equation (y Superscript b Baseline) Superscript 4 Baseline = StartFraction 1 Over y Superscript 24

shusha [124]

The value of b is -6.

Explanation:

The expression is $\left(y^{b}\right)^{4}=\frac{1}{y^{24}}$

To determine the value of b, we shall solve the expression.

Applying exponent rule, $\left(a^{b}\right)^{c}=a^{b c}$ , we get,

$y^{4b}=\frac{1}{y^{24}}$

Applying exponent rule, $\frac{1}{a^{b}}=a^{-b}$ , we have,

$y^{4b}=y^{-24}$

The expression is of the form, $a^{f(x)}=a^{g(x)}$ then $f(x)=g(x)$

Applying this rule, we get,

$4b=-24$

Dividing both sides by 4, we have,

$b=-6$

Hence, the value of b is -6.

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3 years ago

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Degger [83]

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3 years ago

1. Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4)) 2. Let f(x) = 5x^2 - 5. What is f(f(x))? 3. Let f(g(x)) = 3x + 3 a

ludmilkaskok [199]

Answer:

1. f(g(4)) - g(f(4)) = -6

2. f(f(x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g(4) = -9

Step-by-step explanation:

1.

First we need to find f(4) and g(4):

f(4) = 4 + 3 = 7

g(4) = 3*4 + 5 = 17

Then, we find g(f(4)) = g(7):

g(7) = 3*7 + 5 = 26

And we find f(g(4)) = f(17):

f(17) = 17 + 3 = 20

so f(g(4)) - g(f(4)) = 20 - 26 = -6

2.

To find f(f(x)), we use the value of f(x) for every x in f(x):

f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5

f(f(x)) = 125x^4 - 250x^2 + 120

3.

To find f(g(x)), we use the value of g(x) for every x in f(x):

f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 -> a = 3 and b = -3

a + b = 3 - 3 = 0

4.

If we assume g(x) = ax + b, we have:

g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = -4 -> a = -2

-3a + b = 5

6 + b = 5 -> b = -1

g(x) = -2x - 1

g(4) = -2*4 - 1 = -9

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3 years ago

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Kryger [21]

Answer:

No because 21 is close to it.

Step-by-step explanation:

To be considered an outlier, it would need to be a farther distance such as the distance from 28 to 21.

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3 years ago

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