16) The Audio Outlet purchased 75 CDs, gave away 5 in a contest, and sold the rest at 3 times their

purchase price. If the store's total profit was $2025, how much did the store selleach CD for?

The statement "if a > √n and b > √n, then n ≠ ab" is saying that if two positive integers, a and b, are both greater than the square root of another positive integer n, then the product of a and b is not equal to n. This statement can be proven by contradiction.

Suppose the opposite is true, and that n = ab, where a and b are positive integers such that a > √n and b > √n. Then, because n = ab, we have n/a = b and n/b = a. But because both a and b are greater than the square root of n, we have √n < a and √n < b. This leads to a contradiction, because it means that n/a = b > √n, but √n is the largest possible value of b such that b < n/a.

Thus, we have proven that if a > √n and b > √n, then n cannot equal ab, and our original statement is true.

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The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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Answer:

224

Step-by-step explanation:

Answer:

   b.

It's too short. Write at least 20 characters to explain it well



Answer:

x<-3

Step-by-step explanation:

Let's do this step by step:

1) isolate 4x : 4x<-6-6

2) so then we get : 4x<-12

3) isolate x :  x< -12/4

WHICH GETS YOU TO: x<-3

Answer:

4x + 6 < -6 = x < −3

The value of x = -2 or greater

The correct option is (C) The graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Option (C) gives a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.

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Answer:

see photo

be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.

Step-by-step explanation:

Plato/Edmentum

Answer:

First one: 114

Second one: 64

Step-by-step explanation:

For the first one, you can break apart the shapes to a square and a rectangle

The square is 7 x 7 (12 - 5 = 7)

The rectangle is 13 x 5

The square is 49

The rectangle is 65

Add them together

The first one is 114

For the second one you can break it apart to a triangle and a rectangle

The rectangle is 4 x 12

The triangle is 0.5 * 8 * 4   [8 is 12 - 4 (base)]

The rectangle is 48

The triangle is 16

Add them together

48 + 16 = 64

The second one is 64

To determine the number of $5 raffle tickets and $1.50 raffle tickets sold, we can solve the system of equations: 1.5x + 5y = 1152 and x = 4y - 2. The equation x = 4y - 2 can be used to determine the number of $1.50 raffle tickets sold, and the equation 1.5x + 5y = 1152 can be used to determine the number of $5 raffle tickets sold. Therefore, 416 $1.50 raffle tickets were sold.

We have a system of equations:

1.5x + 5y = 1152 ---(1)

x = 4y - 2 ---(2)

To find the number of $5 raffle tickets sold, we can use equation (2) and substitute it into equation (1):

1.5(4y - 2) + 5y = 1152

6y - 3 + 5y = 1152

11y = 1155

y = 105

So, 105 $5 raffle tickets were sold.

To find the number of $1.50 raffle tickets sold, we can substitute the value of y into equation (2):

x = 4(105) - 2

x = 418 - 2

x = 416

Therefore, 416 $1.50 raffle tickets were sold.

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Step-by-step explanation:

let me know if u need any more help! ^^

Answer:

7x²-2x-12,  -6x² +11x-4,  -12x⁵+14x³-2x²+10x ,  -10x⁷y²  

Step-by-step explanation:

Q1.  (5x²-3x-2)-(-2x²-x+10)

    =5x²-3x-2+2x²+x-10

     =7x²-2x-12

Q2.  ( -3x+4)(2x-1)

expand bracket

     -3x(2x-1)+4(2x-1)                 ( a+b )( a+b )=a²+2ab+b²

     -6x²+3x+8x-4  

    -6x² +11x-4  

 Q3.   -2x(6x⁴-7x²+x-5)

         -12x⁵+14x³-2x²+10x                         ∵ aⁿ x aˣ =aⁿ⁺ˣ

 Q4.   (12x⁴ )    (-5/6)x³y²  = -10x⁷y²  

The rate of change in the submarine's elevation is given by 7.87 feet per second approximately.

Given that the initial depth of the submarine = 198 feet

The final depth of the submarine = 316 feet.

The submarine takes 15 seconds to reach the final depth to initial depth.

The elevation of the submarine = (316-198) = 118 feet

So the rate of change = 118/15 = 7.87 feet/second (approximately)

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Answers:

===================================================

Explanation:

x = Erin's true speed

Her true speed x is within 2 mph of 56 mph.

This means the interval for x is \(56-2 \le \text{x} \le 56+2\) which simplifies to \(54 \le \text{x} \le 58\)

She could be going as slow as 54 mph, or as fast as 58 mph, or something in between.

The expression |x-56| measures the distance from x to 56 on the number line. Recall absolute value is used to ensure the distance isn't negative.

We want this distance to be within 2 units, i.e. we want the distance to be 2 or smaller.

\(\text{distance on number line} \le 2\\\\|\text{x}-56| \le 2\)

----------------

Here's what the steps look like to solve that absolute value inequality

\(|\text{x}-56| \le 2\\\\-2 \le \text{x}-56 \le 2\\\\-2+56 \le \text{x}-56+56 \le 2+56\\\\54 \le \text{x} \le 58\\\\\)

For the second step, we use the rule that |x| < k is the same as -k < x < k where k is some positive number.

In the third step, I added 56 to all three sides to isolate x fully.

Answer:

C. it doesn't have to

Step-by-step explanation:

you could limit your intake of social media ( as daunting as that task may seem) or avoid things you're aware affect your mental health; be in control and it doesn't have to hurt you as much?

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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Thhe ratio of the planter's length to width is 4. Length : Width = 4 : 1

We are given that the ratio of the planter's width to height is 4. Mathematically, this can be expressed as:

w/h = 4

Substituting the expressions for w and h, we have:

(42 - 2x)/(18 - 2x) = 4

Let's solve the equation to find the exact value.

First, cross-multiply:

(42 - 2x) * 1 = (18 - 2x) * 4

42 - 2x = 72 - 8x

6x = 30

x = 5

Now we can substitute x = 5 into the expression (42 - 2x)/(18 - 2x):

(42 - 2(5))/(18 - 2(5)) = 32/8 = 4

Therefore, the ratio of the planter's length to width is 4. Length : Width = 4 : 1

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Answer:

384m

Step-by-step explanation:

24 x 4 = 96

96 x 4 = 384

Answer:

the real answer is 96

Step-by-step explanation:

Answer:

studyyy that is allll

Step-by-step explanation:

study

Answer:

360°

Step-by-step explanation:

It kind of seems like a trick question, but as far as I'm concerned, it's more or less the same question as the 1st one you answered.

Answer:

It should be 60 degrees

Step-by-step explanation:

Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

Answer:

7 in

Step-by-step explanation:

Answer:

a = 7 in

Step-by-step explanation:

\(Area = \frac{a+b}{2} \times h\\\\26.25 = \frac{a + 10.5}{2} \times 3\\\\26.25 \times 2 = (a+ 10.5) \times 3\\\\52.5 = (A + 10.5) \times 3\\\\\frac{52.5}{3} = a + 10.5\\\\17.5 = a + 10.5\\\\a = 17.5 - 10.5 = 7\)

The equation of the tangent line for the function `g(x) = 9/x` at `x = 3` is `y = -x + 6`.

The function is `g(x) = 9/x`.

The equation of a tangent line to the curve `y = f(x)` at the point `x = a` is: `y - f(a) = f'(a)(x - a)`.

To find the equation of the tangent line for the function `g(x) = 9/x` at `x = 3`, we need to find `f(3)` and `f'(3)`.

Here, `f(x) = 9/x`.

Therefore, `f(3) = 9/3 = 3`.To find `f'(x)`, differentiate `f(x) = 9/x` with respect to `x`.

Then, `f'(x) = -9/x²`. Therefore, `f'(3) = -9/3² = -1`.

Thus, the equation of the tangent line at `x = 3` is `y - 3 = -1(x - 3)`.

Simplify: `y - 3 = -x + 3`. Then, `y = -x + 6`.

Thus, the equation of the tangent line for the function `g(x) = 9/x` at `x = 3` is `y = -x + 6`.

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Donna could order 24 different ice cream desserts.

Since Donna must order a size, flavor, and topping, there are 3 choices for each of those.

Using the multiplication rule of counting (also known as the fundamental counting principle), the number of ways Donna can order an ice cream dessert is found by multiplying the number of choices for each category.

Therefore, the number of different ice cream desserts Donna can order is:3 (sizes) × 8 (flavors) × 1 (topping) = 24So, Donna can order 24 different ice cream desserts.

Summary:Donna can order 24 different ice cream desserts by multiplying the number of choices for each category (size, flavor, and topping). Therefore, 3 (sizes) × 8 (flavors) × 1 (topping) = 24.

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Answer:

11,56,57

Step-by-step explanation:

11 56 57 do not represent the sides of a right triangle

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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Step-by-step explanation:

explanation:

Divide the number to be factored by the prime numbers in turn. Test that result is a natural number. If so, it is a prime factor. Continue until the factorisation is complete.

Answer:

125.

Given:

Step-by-step explanation:

As given in the question that the ratio is already given,

therefore,

1. The ratio of tourist of to locals

the ratio of tourist to local is 4:5

\(\frac{tourist}{locals}\)=\(\frac{4}{5}\)

2. Attendance of locals at the opening

here are 100 tourist at the opening

\(\frac{100}{locals} =\frac{4}{5}\)

locals= 125

locals are 125 in attendance.

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125 is the attendance of locals

The ratio of tourists to locals is 4:5

Tourists / Locals = 4 / 5

There are 100 tourists at the opening of the new museum

100 / locals = 4/5

locals = 500/4

locals = 125

The attendance of locals is 125.

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Answer:

Density (ρ) = 0.1875 gram/cubic centimeter

Step-by-step explanation:

Steps:

p=m/v, 3/16

Answer:

The answer is 18 hours

Step-by-step explanation:

3 hours x 6 days

3x6 = 18

Answer:770000

Step-by-step explanation:

That how much they made

Answer:

€8988.75

Step-by-step My bad that's not the answer