In 2016 there were approximately 7,040 college and university libraries in the United States. A survey found that 65% of those libraries participated in an electronic "book-sharing" program. Based on this information, how many college and university libraries participated in the electronic "book-sharing" program in 2016?

Answer: -2

Step-by-step explanation:

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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To construct a table of values for the equation \( x=y+2 \) for integral values of \( y \) from -2 to +6, we can substitute each value of \( y \) into the equation and solve for \( x \).

Here is the completed table of values:

\[
\begin{array}{|c|c|}
\hline
\text{Value of } y & \text{Value of } x \\
\hline
-2 & -2+2=-0 \\
-1 & -1+2=1 \\
0 & 0+2=2 \\
1 & 1+2=3 \\
2 & 2+2=4 \\
3 & 3+2=5 \\
4 & 4+2=6 \\
5 & 5+2=7 \\
6 & 6+2=8 \\
\hline
\end{array}
\]

we substituted the values of \( y \) from -2 to +6 into the equation \( x=y+2 \) and obtained the corresponding values of \( x \) to complete the table. This shows the relationship between \( x \) and \( y \) for the given equation.

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The total volume of the composite object is 838.095

From the question, we have the following parameters that can be used in our computation:

The composite object

The volume is calculated as

Volume = Cylinder + Cube

The Cylinder and the Cube have the same dimensions

So, we have

V = 4/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 4/3 * 22/7 * 5² * 8

Evaluate

V = 838.095

Hence, the total volume of the composite object is 838.095

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Answer:

Answer is a.multiplication.

Step-by-step explanation:

I hope it's helpful!

Before we begin analyzing the question we were asked, we need to compute the probabilities of getting the individual numbers on the spinner out of a total of 12 slots.

Probability of getting a 1:

There is only a single value of 1, therefore the probability of getting a 1 is:

Probability of getting a 2:

There are double values of 2, therefore the probability of getting a 2 is:

Probability of getting a 3:

There are triple values of 3, therefore the probability of getting a 3 is:

Probability of getting a 4:

There are double values of 4, therefore the probability of getting a 4 is:

Probability of getting a 5:

There are 4 values of 5, therefore the probability of getting a 5 is:

Now that we know the probabilities of getting the individual numbers we can proceed to solving the questions asked.

A number less than 3 or a 5:

The only numbers less than 3 are: 1 and 2.

Since the spinner is spun just once, it means that, if we are to get a number less than 3, then we get either 1 OR 2.

The probability for getting a 1 OR a 2 is:

But the question goes on and says in the same trial, what is the possibility of also getting a 5.

This means we can rephrase the question as:

Probability of getting 1 OR 2 OR 5.

Therefore, to fully answer the first question, we say:

The probability of getting a number less than 3 or a 5 is 7/12

Now for the next question;

Spin Even number and then number greater than 3:

To get an even number you can have only: 2 and 4

The question says you spin twice and asks for the probability in which the first number is even. This means the first number is Either 2 OR 4 not both.

We can compute this probability as:

The question also says the second number is a number greater than 3. The only numbers greater than 3 are: 4 and 5.

The second number can be Either 4 OR 5

We can compute this probability as:

Now that we have both probabilities for the first spin and the second spin, we can therefore calculate for when you get:

Even number AND Number greater than 3

Therefore the probability of getting Even number and number greater than 3 is: 1/6

The final answer is:

#1: 7/12

#2: 1/6

Answer:

Step-by-step explanation:

$2400 in labor

Answer:

38-c

Step-by-step explanation:

We know that the answer is 38-c because any piece of candy that Hanson gives away will be subtracted from the amount that he started out with.

Answer:

9/28 and 32.1%

Step-by-step explanation:

So the sample space consists of all products for (5 * 1, 5 * 2, 5 * 3.... and the same thing for 6, 7, and 8)

This gives you the sample space: {5, 10, 15, 20, 25, 30, 6, 12, 18, 24, 30, 36, 7, 14, 21, 28, 35, 42, 8, 16, 24, 32, 40, 48}.

The size of the sample space is 4 * 6, since for each number (5, 6, 7, 8), there are 6 products (the dice have six numbers). This means the sample space has 24 combinations, you can also verify this by manually counting the sample space.

Now filtering the sample space so you only get a product that is 28 or higher you get: {30, 30, 36, 28, 35, 42, 32, 40, 48} which has 9 possible combinations that have a product greater than or equal to 28. Divide this by the entire sample space and you get a probability of: 9/28, which in decimal form is approximately: \(0.3214\). Multiplying this by 100 gives you: \(32.1\)%

Just plug -2 into x

f(-2) = 2(-2)^2 + 4(-2) + 5

Simplify the right side

f(-2) = 8 - 8 + 5

Combine like terms

f(-2) = 5

The proof of the identity cos²x(1 + tan²x) = 1 is complete using the mentioned rules.

Hi! I'd be happy to help you complete the proof of the identity cos²x(1 + tan²x) = 1 using the given terms.

1. Statement: cos²x(1 + tan²x) = cosx (sec²x)
  Rule: Identity (using the identity tan²x = sec²x - 1)

2. Statement: cosx (sec²x) = cosx (1 + cos²x)
  Rule: Identity (using the identity sec²x = 1/cos²x)

3. Statement: cosx (1 + cos²x) = cos²x + cos⁴x
  Rule: Distributive Property (cosx * 1 + cosx * cos²x)

4. Statement: cos²x + cos⁴x = 1
  Rule: Pythagorean Identity (since cos²x + sin²x = 1, we substitute sin²x with 1 - cos²x and simplify)

So, the proof of the identity cos²x(1 + tan²x) = 1 is complete using the mentioned rules.

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Answer:

Step-by-step explanation:

Comment

This uses the cosine Law for line length.

Formula

a^2 = b^2 + c^2 - 2*b*c*sin(A)

Givens

a  = 5

b = 7

c = 10

Solution

5^2 = 7^2 + 10^2 - 2*7*10*cos(A)

25 = 49 + 100 - 140*cos(A)                  Combine the right side

25 = 149 - 140 * cos(A)                         Subtract 149 from both sides

25 - 149 = - 140*cos(A)                    

-124 = -140 * cos(A)                               Divide both sides by -140

-124/-140 = cos(A)

Cos(A) = 0.8857                                   Take the inverse Cos of both sides

A = cos-1(0.8857)

Answer

A = 27.66 degrees

Answer:

I think the asnwer A or B !!

Step-by-step explanation:

The standard error of the sample mean is 1.21.

Given;

Suppose a diet regimen for men results in an average weight loss of between 13. 4 and 18. 3 pounds, according to a 95% confidence interval. These findings were based on a group of 42 men who were classified as overweight at the beginning of the four-month trial.

A 95% confidence interval for a population mean is (13.4, 18.3)

Upper limit = 18.3

Lower limit = 13.4

Since population SD is unknown, this interval is constructed using the t distribution.

n = 42

c = 0.95

∴ α = 1 - c = 1 - 0.95 = 0.05

α/2 = 0.025

Also, d.f = n - 1 = 42 - 1 = 41

∴ ta/2.d.f =  ta/2.n-1  =  t0.025,41  =  2.02 . . . . use t table

Now,

The margin of error = (Upper limit - Lower limit)/2

                                 = (18.3 - 13.4)/2

                                 = 2.45

But,

Margin of error = ta/2.d.f-  * (s / \sqrt{} n)

Margin of error = ta/2.d.f-  * Standard error

2.45 = 2.02 * Standard error

Standard error = 1.2129

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Answer: y + 11

Step-by-step explanation:

             1. Combine like terms

                =4+y+7

                 =(y)+(4+7)

                 =y+11

Answer:

y + 11

Step-by-step explanation:

4 + y + 7

y + 4 + 7

y + (4 + 7)

y + 11

I hope this helps you :)

Answer:

\(\frac{y}{2}\)

Step-by-step explanation:

n is doubled: 2n

y added: 2n + y

divided by 2: n + \(\frac{y}{2}\)

n subtracted -> final resutl: \(\frac{y}{2}\)

Answer:

hi

Step-by-step explanation:

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The area of the composite figure is 58. 71 square units.

It is important to note that the area of the composite figure is given as;

Area of a rectangle + area of a semi circle

The formula for area of a rectangle is expressed as;

Area = lw

Where;

Now, let's substitute the values, we have;

Area = 6 × 9

Area = 54 square units

The formula for area of a semicircle is expressed as;

Area = πr²/2

Where;

Given diameter = 6, radius = 6/2 = 3

Substitute the value

Area = 3. 14(3)/2

Area = 4. 71 square units

But area of the composite figure = 54 + 4. 71 = 58. 71 square units.

Hence, the area is 58. 71 square units.

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The true statement is the range for Week 1 equals the range for Week 2.

A dot plot is a graph that is used to show the frequency of a data set using dots. Range is the difference between the highest and lowest values of a set of observations

Range = highest value - lowest value

Range of the first dot plot : 89 - 62 = 27

Range of the second dot plot : 89 - 62 = 27

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Answer:

y=1/4x+4

Step-by-step explanation:

because the slope is 1/4

so k=1/4

y=1/4x+b

put the point into the equation

so

6=1/4*8+b

so

b=4

20,000

Thankyou :)

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By the principle of mathematical induction, we will show that the algorithm to compute the sum of the cubes of the first n positive integers returns the correct value for every positive integer input.

To prove that the algorithm to compute the sum of the cubes of the first n positive integers returns the correct value for every positive integer input using induction, we will need to show two things:

1. Base case: The algorithm returns the correct value for n = 1.

Base case: When n = 1, the algorithm returns 1^3, which is the correct value for the sum of the cubes of the first positive integer. Therefore, the base case is true.

2. Inductive step: Assume that the algorithm returns the correct value for some positive integer k, and show that it also returns the correct value for k + 1.

Inductive step: Assume that the algorithm returns the correct value for some positive integer k, i.e., SumCube(k) returns 1^3 + 2^3 + ... + k^3.

We need to show that the algorithm also returns the correct value for k + 1, i.e., SumCube(k + 1) returns 1^3 + 2^3 + ... + (k + 1)^3.

Using the recursive definition of the algorithm, we have:

SumCube(k + 1) = (k + 1)^3 + SumCube(k)

By the induction hypothesis, we know that SumCube(k) returns the correct value, so we can substitute it into the above equation to get:

SumCube(k + 1) = (k + 1)^3 + (1^3 + 2^3 + ... + k^3)

Expanding (k + 1)^3, we get:

SumCube(k + 1) = k^3 + 3k^2 + 3k + 1 + (1^3 + 2^3 + ... + k^3)

Simplifying the right-hand side, we get:

SumCube(k + 1) = 1^3 + 2^3 + ... + k^3 + (k^3 + 3k^2 + 3k + 1)

We recognize the last term as (k + 1)^3, so we can substitute it in to get:

SumCube(k + 1) = 1^3 + 2^3 + ... + k^3 + (k + 1)^3

which is the correct value for the sum of the cubes of the first (k + 1) positive integers. Therefore, the inductive step is true.

By the principle of mathematical induction, we have shown that the algorithm to compute the sum of the cubes of the first n positive integers returns the correct value for every positive integer input.

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The equation of the graph of the quadratic function is the option;

y = (x + 1)²

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The shape of the graph indicates that the graph is a quadratic function

The x and y-intercepts of the function are;

x-intercept = (0, -1)

y-intercept = (0, 1)

The x-intercept indicates that when x = -1, y = 0

The y-intercept indicates that when y = 1, x = 0

The number of x-intercepts, which is one, indicates that the possible number of solutions is one and therefore, the function is a perfect square of the form; y = (x + 1)²

The above function can be obtained from the standard form of the quadratic equation; f(x) = a·(x - h)² + k

(h, k) = The coordinates of the vertex

a = The leading coefficient

The vertex of the graph is; (-1, 0)

Therefore;

h = -1, and k = 0

f(x) = y = a·(x - (-1))² + 0 = a·(x + 1)²

y = a·(x + 1)²

When y = 1, x = 0, therefore;

y = a·(0 + 1)² = 1

a = 1/1 = 1

a = 1

y = a·(x + 1)² = 1 × (x + 1)² = (x + 1)²

y = (x + 1)²

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Answer:

Step-by-step explanation:

Write in slope-intercept form,

y=mx + b. − mowing, week, 20, 450

Answer:

Point N and point K

Step-by-step explanation:

The steeper a line is in the graph, the greater the value of the slope of the line would be, and also, the farther it would be from 0. On the other hand, the more gentle and less sloppy a line is, the smaller the value of the slope is, and also, the closer it is to 0.

From the graph given, there are possible set of points in a line that have a gentle line slope.

The first is, points N and K. The slope of this line is ⅑.

The second is, points P and L. The slope of this line is ⅙.

From the two above lines, the one with a slope closest to 0 is the line that runs through points N and K. ⅑ is closer to 0 than ⅙.

The radius of the pond is approximately 33.5 feet if he is 45 feet from the edge of the pond and 65 feet from the point of tangency.

Let's consider the scenario. We have an alligator laying out next to a perfectly circular pond. The alligator is 45 feet from the edge of the pond and 65 feet from the point of tangency.

To find the radius of the pond, we can create a right triangle using the alligator, the point of tangency, and the center of the pond. The line connecting the alligator to the point of tangency is perpendicular to the radius of the pond.

We can use the Pythagorean theorem to solve for the radius. The hypotenuse of the right triangle is the distance between the alligator and the point of tangency, which is 65 feet. One of the legs is the radius of the pond, and the other leg is the distance between the alligator and the edge of the pond, which is 45 feet.

Applying the Pythagorean theorem:

r^2 + 45^2 = 65^2

r^2 + 2025 = 4225

r^2 = 4225 - 2025

r^2 = 2200

Taking the square root of both sides:

r ≈ √2200

r ≈ 46.9

Rounding to the nearest tenth:

r ≈ 33.5

The radius of the pond is approximately 33.5 feet.

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Answer:

Choice 1

Step-by-step explanation:

Answer:

x<-1 and Number 1

Step-by-step explanation:

:)