A graduate student is performing a study on a new antidepressant. The drug is supposed to reduce depression, but the graduate student realizes that it may do nothing or even increase depression, so she decides to formulate nondirectional hypotheses and conduct a two-tailed test. First, she uses mu_general population to denote the average score on the depression inventory for the population of all depressed people, and mu_antidepressant to denote the average score on the depression inventory for the population of depressed people who take the new antidepressant. She knows that the average score for all depressed people is mu_general population = 25, with a standard deviation of sigma = 6. The graduate student identifies the null and alternative hypotheses as: H_0: mu_antidepressant = mu_general population H_1: mu_antidepressant notequalto mu_general population The sample of 36 depressed people who tried out the new antidepressant scored an average of 23.3. Since the graduate student knows the standard deviation of the scores on the depression inventory for the population of people who are depressed, she intends to use a hypothesis test that uses the z-score of the sample mean as the test statistic (also known as the z test). First, she wants to make sure all the required assumptions are satisfied. Which of the following conditions is not a required assumption for the z test?
The scores on the depression inventory follow a normal distribution or the sample size is large (at least 30).
The standard deviation of the scores on the depression inventory is the same for those who take the antidepressant and those who don't.
Each observation is independent of every other observation.
The sample size must be very large.
Members of the sample are selected randomly.
Use the Distributions tool to find the critical region for alpha = .05. The critical z-scores (the values for z-scores that separate the tails from the main body of the distribution, forming the critical regions) are_______
Calculate the z statistic, and use the Distributions tool to evaluate the null hypothesis. The z statistic is______ The z statistic_______ lie in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is______ .

Answer:

Your answer would be B: 30 ft squared

Step-by-step explanation:

Find the area of the circle: 5.5 (radius) multiply it by itself then multiply that by 3.14 which gets you 94.985. Now find the area of the square which is 8*8 = 64. Subtract 64 from 94.985 and your answer will be 30.985. The questions asks for the approximate (estimate), so the closest one would be 30 ft squared

Answer: hello your question is incomplete below is the complete question

The Two vectors;  A = 5i + 6j +7k and B = 3i -8j +2k.

answer;

angle = 102°

Step-by-step explanation:

multiplying the vectors

A.B = |A| * |B|* cosθ

hence : Cosθ = (Ai*Bi )+ (Aj*Bj) + ( Ak*Bk/ (√A^2 *√B^2 )

                       = 15 - 48 + 14 /(√25+26+29) * (√9+64+4)

                      = -0.206448454

θ = cos^-1 ( -0.206448454) = 101.9° ≈ 102°

Answer: y = 1/8x+1

y=mx+b is slope intercept form

given m = 1/8 and a point we can find b by plugging in what we have

1=1/8(8)+b

1=1b

b=1

So then we know m = 1/8 and b = 1

y=1/8x+1 is the answer

Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).

To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.

One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.

Using the distance formula, we get:

\(\sqrt{(x-1)^{2} +(y-1)^{2} }\) = 5

Simplifying and squaring both sides, we get:

(x-1)^2 + (y-2)^2 = 25

Expanding the left side and simplifying, we get:

\(x^{2}\) - 2x + \(y^{2}\) - 4y + 20 = 0

Completing the square for x and y, we get:

\((x-1)^{2}\)  + \((y-1)^{2}\)  = \(6^{2}\)

This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.

Using this method, we can find several possible locations of the other vertices of the square. Three of them are:

(7, 2), (-5, 2), (1, 8)

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Answer:

(6.3*10³) ÷ (1.8*10⁵)

6.3*10³ = 0.063*10⁵

then:

(6,3*10³) ÷ (1.8*10⁵) = (0.063*10⁵) ÷ (1.8*10⁵)

= 0.063/1.8

= 0.035

0.035 = 3.5 *10⁻² = 35*10⁻³

Answer:

n = 26

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable  

n.

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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The solution of the composite function fog(x) = 3x + 3 at x > 2.

Let the two function f(x) and g(x) generate a new function h(x) using an operation.

The operation is composition of functions and h(x) is a composite function.

We have three piecewise function.

First we have to show that,

the composite function,

fog(x) at x > 2.

For that,

g(x) at x > 2 is,

g(x) = 3x.

Now, f(g(x)),

= f(3x)

= 3x + 3 at x > 2.

Therefore, the function is fog(x) = 3x + 3.

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The complete question:

Find the fog(x) at x > 2

Solution :

Let x be student will be left handed

P = 0.09

Using the normal approximation to binomial distribution,

a). n = 108,

    μ = np = 9.72

    \($\sigma = \sqrt{np(1-p)}$\)

       \($=\sqrt{8.8452}$\)

       = 2.9741

Required probability,

P(x=8) = P(7.5 < x < 8.5)

\($=P\left(\frac{7.5-9.72}{2.9741}< \frac{x-\mu}{\sigma}< \frac{8.5-9.72}{2.9741}\right)$\)

\($=P(-0.75 < z < -0.41)$\)

Using z table,

= P(z<-0.41)-P(z<-0.75)

= 0.3409-0.2266

= 0.1143

b). P(x=12) = P(11.5 < x < 12.5)

\($=P\left(\frac{11.5-9.72}{2.9741}< \frac{x-\mu}{\sigma}< \frac{12.5-9.72}{2.9741}\right)$\)

\($=P(0.60 < z < 0.94)$\)

Using z table,

= P(z< 0.94)-P(z< 0.60)

= 0.8294 - 0.7257

= 0.1006

Answer:

-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

the y intercept is the point on the graph where the line crosses the x axis

Answer:

To find the scale factor, locate two corresponding sides, one on each figure. Write the ratio of one length to the other to find the scale factor from one figure to the other. In this example, the scale factor from the blue figure to the red figure is 1.6 : 3.2, or 1 : 2.

Step-by-step explanation:

Answer:

80

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

A

Therefore , the solution of the given problem of probability comes out to be AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

(a) The voting box contains a total of seven slips, four of which are for candidate A and three for candidate B. Thus, there are 35 events that can occur from 7 choose 4 (or 7 choose 3) options.

Each vote can be represented by a letter, with A standing for a vote for candidate A and B for candidate B, so that all outcomes can be listed. These are the potential results:

AAAA

AAAB

AABA

ABAA

BAAA

AABB

ABAB

BABA

BBAA

ABBB

BABB

BBAB

BBBA

(b)

For instance, the following results could occur if the slips were removed in the following order:

A (1 vote for contender A) (1 vote for candidate A)

AA (2 ballots for candidate A) (2 votes for candidate A)

AAB (2 ballots for candidate A, 1 vote for candidate B) (2 votes for candidate A, 1 vote for candidate B)

AAAB (3 ballots for candidate A, 1 vote for candidate B) (3 votes for candidate A, 1 vote for candidate B)

AAAAB (4 ballots for candidate A, 1 vote for candidate B) (4 votes for candidate A, 1 vote for candidate B)

AAAABB (4 ballots for candidate A, 2 votes for candidate B) (4 votes for candidate A, 2 votes for candidate B)

AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

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Answer:

can u help me with my answer

Step-by-step explanation:

1x1 the answer is a

Answer:

4

Step-by-step explanation:

(3+5+6+2+4) / 5 = ?

(20) / 5 = 4

Answer:

\(y=-\frac{5}{2}x-16\)

Step-by-step explanation:

Slope intercept form is a way of expressing a line in the format;

\(y=mx+b\)

Where (m) is the slope of the line, and (b) is the y-intercept. One can solve for (b) by substituting in a point on the line and using inverse operations to solve.

\(y=mx+b\\\\m=-\frac{5}{2}\\\\y=-\frac{5}{2}x+b\)

Substitute in point (-6, -1)

\(-1=-\frac{5}{2}(-6)+b\\\\-1=15+b\\\\-15\\\\-16=b\)

\(y=-\frac{5}{2}x-16\)

Answer:

a = b = 1 , c = - 8

Step-by-step explanation:

ax² + bx + c = y

( - 5 )² a - 5b + c = 12

c = - 8

3² a + 3b + c = 4

25a - 5b - 8 = 12 ⇔ 25a - 5b = 20 ⇔ 5a - b = 4 ........ (1)

9a + 3b - 8 = 4 ⇔ 9a + 3b = 12 ⇔ 3a + b = 4 .......... (2)

(1) + (2)

8a = 8 ; a = 1

b = 1

y = x² + x - 8

Answer:

D. G is closer to the axis, and f is closer to the y-axis.

Step-by-step explanation:

I calculated it logically

Answer:

a = 0

b = 8

c = 53

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

8r + 62 - 7 = 2

Step 2: Rewrite

Step 3: Identify Variables

a = 0

b = 8

c = 53

Answer:

x = 15

Step-by-step explanation:

Step 1: Write out equation

1/4x - 7/4 = 2

Step 2: Add 7/4 to both sides

1/4x = 15/4

Step 3: Divide both sides by 1/4

x = 15

Answer:

4 1/2

Step-by-step explanation:Because 2x2 =4 and 2x1/4 = 1/2 so it is 4 1/2

Answer:

x = -8

Step-by-step explanation:

Step 1: Write equation

1/2x + 13 = 9

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

1/2(-8) + 13 = 9

-4 + 13 = 9

9 = 9

Answer:

-8

Step-by-step explanation:

you use inverse operation

meaning opposite signs

subtract -13 from 13 cross it out

subtract 13 from 9

you get 1/2x=-4

divide 1/2 on both sides

-4 divided by 1/2 =-8

We have to remember that in one-to-one functions each element of the domain maps to a different element in the range.

When we have a bijection we have that each element in the set A, for example, corresponds to exactly one element of B, and vice versa.

When we have a bijection, we also have an inverse function.

Then, we have that:

To find the inverse, we have to interchange the variables:

Now, we have:

And we need to solve for y:

1. Add 13 to both sides of the equation:

2. Divide both sides by -2:

Then, we have that:

We can check this if we make a composition between the two functions (then we will get x as a result).

Then, we have that the result for this composition is equal to x. Thus:

We also have that:

We have that h(4) = 3, then h^(-1)(3) = 4 or

In summary, we have:

Answer:

1/3a

Step-by-step explanation:

\( \frac{(a - 3)}{15a} \times \frac{5}{(a - 3)} = \frac{5}{15a} = \frac{1}{3a} \)

Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

Answer:

-11/20 or -0.55

Step-by-step explanation:

1/5 = 4/20

3/4 = 15/20

4/20 - 15/20 = -11/20

Answer:

- 11/20

or

-0.55

Step-by-step explanation:

PLZ MRAK ME BRAINLIEST

Degree of a term is the exponents of a variable , if a term have two variables then the degree of a term is the sum of the exponents of the variables.

Degree of a term:

The degree of an individual term of a polynomial is the exponent of its variable.

Examples:

1) \(2x^3\)

here exponent of variable x is 3.

so the degree  = 3

2) \(5x^5y^4\)

sum of exponent of variables x and y is = 5+4 = 9

so the degree = 9

3) \(x^2y^3\)

sum of exponent of variables x and y is = 2+3 = 5

so the degree = 5

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Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.