Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selections down to eleven mysteries and six nonfiction books. If she randomly chooses three books from her selections, what's the probability that they will all be mysteries? Enter a fraction or round your answer to 4 decimal places, if necessary.

The length of line FG is 16 units

The length of FG is equal to length GH that is to say

line FG = line GH

From the problem, we have that

FG = x  + 11

GH = 3x + 1

Equation both lines

x + 11 = 3x + 1

collecting like terms

11 - 1 = 3x - 1

10 = 2x

rearranging and isolating x

2x = 10

x = 5

The line FG = x + 11 = 5 + 11 = 16 units

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Based on the derivative, a function can cross the x-axis a certain number of times depending on the number of times the derivative changes sign.

A derivative is a mathematical tool that measures the rate of change of a function at a specific point. Specifically, it is the slope of the tangent line to the function at that point. The derivative can be used to determine where a function is increasing, decreasing, or reaching a maximum or minimum value.
When a function crosses the x-axis, it means that the y-value of the function is equal to zero. In order for a function to cross the x-axis, it must change sign from positive to negative or vice versa. This happens when the function passes through a maximum or minimum point.
If the derivative of the function is positive at a point, it means that the function is increasing at that point. If the derivative is negative, the function is decreasing. If the derivative is zero, it means that the function is neither increasing nor decreasing, and it could be at a maximum or minimum point.
Therefore, the number of times a function can cross the x-axis depends on the number of times the derivative changes sign. If the derivative changes sign twice, the function can cross the x-axis twice. However, if the derivative changes sign an odd number of times, the function can only cross the x-axis once.

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Answer:

(x - 15) ( x + 3)

Step-by-step explanation:

x² - 12x - 45

= x² - (15 - 3)x - 45

= x² - 15x + 3x - 45

= x(x - 15) + 3(x - 15)

= (x - 15) ( x + 3)

Answer:

D

Step-by-step explanation:

W/-15=D

\(-\frac{W}{15}\)=D

On solving the provided question we can say that - the removable discontinuity of f(x) located is -5

Discontinuous functions in graphs are those that have no connections to one another. Discontinuities come in three different flavors: removable, jump, and infinite.. If the left limit and the right limit of a function, f(x), are both different, then the function has a first-kind discontinuity at x = a. a characteristic that cannot be mathematically continuous. Continuous functions allow you to sketch without having to lift your pen. In such a case, the function is said to as discontinuous.

here,

f(x) = \(\frac{x+5}{x^2+3x-10}\)

\(x^2+3x-10\)

x(x+5) - 2(x+5)

(x+5 )(x-2 )

x = 2, -5

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The selection of the appropriate immune suppressant is made by healthcare professionals based on the specific needs of each patient.

The most commonly used immune suppressant in medical practice is a medication called "cyclosporine." Cyclosporine belongs to a class of drugs known as calcineurin inhibitors and is primarily used to prevent organ transplant rejection.

The activity of T-cells, which are a type of immune cell involved in the body's immune response.

Cyclosporine is also used in the treatment of various autoimmune diseases, such as rheumatoid arthritis and psoriasis, where the immune system mistakenly attacks the body's own tissues.

T-cell activity, cyclosporine helps to reduce the inflammatory response and prevent further damage to the affected organs or tissues.

It's important to note that there are several other immune suppressants available, and the choice of medication depends on the specific condition being treated, the patient's overall health, and individual factors.

A commonly used immune suppressants include corticosteroid methotrexate, azathioprine, mycophenolate mofetil, and tacrolimus.

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Complete question:

While studying the T- and B-cell immune suppressors, the nursing students learn that the most commonly used immune suppressant is what?

Answer:

The value of a mathematical expression is the result of the computation described by this expression when the variables and constants in it are assigned values. The value of a function, given the value(s) assigned to its argument(s), is the value assumed by the function for these argument values.

Step-by-step explanation:

Yes, the value of an expression does mean the answer.

The value of an expression is a variable that is assigned to a number.

Lets say we have 3n + 2 = 10.

"n" is the variable and we need to find the value of it.

In that kind of question, that is the answer for an expression.

But there are cases where we have the value and we need to solve with it. Then, the value would not be the answer.

Best of Luck!

Answer:

$146.66

Step-by-step explanation:

I bopped this into a percentage calculator and this is what I got

Answer:

1/3

Step-by-step explanation:

3÷6/1 is the same thing as 3÷6

and when reducing to the lowest term gives 1÷3 or 1/3

The equation for the profit is 16.85N + 550

Production costs include all direct and indirect costs incurred by businesses when producing a product or providing a service. Labor, raw materials, consumable manufacturing supplies, and general overhead are all examples of production costs.

The total cost incurred by a business to produce a specific quantity of a product or provide a service is referred to as the cost of production. Labor, raw materials, and consumable supplies are examples of production costs

Given that the total production cost C (in dollars) is given by the function C = 15.95N + 550,

where N is the number of books.

The total revenue earned (in dollars) from selling the books is given by the function R = 32.80N.

Therefore, profit will be:

= Revenue - Cost

= 32.80N - 15.95N + 550,

= 16.85N + 550

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We will prove two statements. First, every infinite decimal representing a rational number is recurring. Second, if a rational number is represented by a fraction in lowest terms as a/b, then the number of recurring digits in its decimal representation is less than b.

Statement 1: Every infinite decimal representing a rational number is recurring. Let's consider a rational number represented as a/b, where a and b are integers and b ≠ 0. The decimal representation of this rational number can be expressed as a quotient a/b in long division.

In long division, the remainder can have a maximum of b - 1 possible values because it ranges from 0 to b - 1. Since there are only b possible remainders, at least two remainders must be equal due to the pigeonhole principle. This means that at some point in the long division process, we encounter a repeated remainder. Once a repeated remainder is encountered, the long division process will continue in a repeating pattern. Therefore, the decimal representation becomes recurring, where the repeating pattern corresponds to the digits after the decimal point. Hence, every infinite decimal representing a rational number is recurring.

Statement 2: If a rational number is represented by a fraction in lowest terms as a/b, then the number of recurring digits in its decimal representation is less than b. Let's consider a rational number a/b in lowest terms, where a and b are integers and b ≠ 0. We know that the decimal representation of this rational number is recurring.

In the recurring part of the decimal representation, the repeating pattern can have a maximum length of b - 1. This is because if the repeating pattern has a length equal to or greater than b, we can simplify the fraction further, contradicting the assumption that it is in lowest terms. Therefore, the number of recurring digits in the decimal representation of a rational number a/b, in lowest terms, is less than b.

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Answer:

1/2 - Half of the numbers are odd

On solving the provide question, we can say that by unitary method each person get = 24/14 = 1.7142857143 pounds of beef

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

a group of = 24 people

equally shared  = 14 pounds of ground beef.

each person get = 24/14 = 1.7142857143 pounds of beef

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Answer: Let us assume that the radius of the circle is r where the corresponding sector area and arc length are 37.5sq. cm and 7.5cm. From the given arc length of 7.5cm, the subtended angle at the circle center theta radian can be Theta /2π =7.5/2πr or

Theta radian =7.5/r. For the radian, 7.5/r subtended angle sector area can be 7.5/r/2π^2 or 7.5/2πr*πr^2 or 7.5r/2. We already have given sector area as 37.5, then 7.5r/2=37.5, or r will be 37.5*2/7.5 which gives us 10.

Step-by-step explanation:

Let us assume that the radius of the circle is r where the corresponding sector area and arc length are 37.5sq. cm and 7.5cm

By the arc length of 7.5cm, the subtended angle at the circle center theta radian will be

Theta /2π =7.5/2πr or

Theta radian =7.5/r

For the 7.5/r radian subtended angle sector area is

7.5/r/2π^2 or 7.5/2πr*πr^2 or 7.5r/2

We have given the sector area 37.5, so now 7.7r/2=37.5, or

r=37.5*2/7.5=10cm

Answer:

D=-64

Step-by-step explanation:

-10(d+56)=80

d+56=8

d=8-56

d=-64

Step-by-step explanation:

The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,

\(\implies 2x -y +6=0\\\\\implies 2x + 3y -6=0\)

On subtracting the given equations we have,

\(\implies -y - 3y +6 -(-6) = 0 \\\\\implies -4y = -12 \\\\\implies y = -12/-4\\\\\implies y = 3 \)

Put this value in any equation , we have ,

\(\implies 2x -3 +6 =0\\\\\implies 2x = -3 \\\\\implies x =\dfrac{-3}{2} \\\\\implies x =-1.5 \)

Hence the lines will Intersect at ,

\(\implies\underline{\underline{ Point=(-1.5, 3)}}\)

for the first one x = 1/2 y-3" and y = 2 x + 6 and for the other one is x =  − 3 /2  y+ 3  and y= − 2 /3  x + 2

how i did this Step 1: Add -3y to both sides.

Step 2: Add 6 to both sides.

Step 3: Divide both sides by 2.

Answer:

i think its a

Step-by-step explanation:

Karla spent $1500 to make the shirt and will lose $150 if she sells only 90 t-shirts.

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let t represent the number of t-shirts she needs to sell in order to make a profit. Since:

t > 100 and the price is $15 per shirt, hence:

Money spent = $15 * 100 = $1500

Money lost in sell 90 shirts = (100 - 90) * 15 = $150

Karla spent $1500 to make the shirt and will lose $150 if she sells only 90 t-shirts.

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Answer: 1 / 8806

Step-by-step explanation: not no noticeable way of it being a mixed number.

Answer:

1 solution (x = 1.5)

Step-by-step explanation:

2x + 2 - 3x = 3x - 4

First, combine like terms

2 - x = 3x - 4

Add 4 to both sides

6 - x = 3x

Add x to both sides

6 = 4x

Divide both sides by 4

1.5 = x

If you're looking for all it's forms,

Exact form: \(\frac{3}{2}\) (or 3/2)

Decimal form: 1.5

Mixed Number form: \(1\frac{1}{2}\) (or 1 1/2)

OR

Two solutions because it's a quadratic equation:

1. x = -1/2 = -0.500

2. x = 2

​

The number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Suppose we want to choose 6 letters without replacement from 10 distinct letters.

Number of letters = 10

Number of letters need to select = 6

Order is important.

A number of ways:

C(10, 6) = 10!/(10-6)!

= 10!/(4)!

= 151200

Thus, the number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.

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VW = 6

hope it helps...!!!

Answer:  8y^2−30y+27

Step-by-step explanation:

FOIL!!

Answer:

y = 3/2  when x = 15

Step-by-step explanation:

y = k / √1+x  

2 = k / √1+8 = k/3  

k = 6  

y' = 6 / √1+15 = 6/4 = 3/2

Answer:

x = -9 also called undefined slope.

Step-by-step explanation:

And if the line is like this ____________ it is zero slope and the equation is the number that is passes through the y- intercept.

Hope this helps.

x = -9

Answer:

x=-9

I hope this is good enough:

Answer: the lines are neither parallel nor perpendicular.

To determine whether two lines are parallel, perpendicular, or neither, we need to calculate their slopes. The slope of a line is a measure of how steep the line is. It is calculated by dividing the difference in the y-coordinates of the two points by the difference in the x-coordinates.

For line 1, the slope is calculated as follows: (4-(-5))/(1-(-2)) = 9/3.

For line 2, the slope is calculated as follows: (4-6)/(6-0) = -2/6 = -1/3.

Since the slopes of the two lines are different, they are not parallel.

To determine whether two lines are perpendicular, we need to check if the product of their slopes is -1. The product of the slopes of line 1 and line 2 is (9/3)*(-1/3) = -3/9 = -1/3. Since this is not equal to -1, the lines are not perpendicular.

Therefore, the lines are neither parallel nor perpendicular.

Answer: perpendicular

Step-by-step explanation: Line 1 has the following points

(-2,5) and (1,4)

We know that the equation of a straight has the form

y=mx+c

m=gradient or the slope

c= where the graph crosses the y axis

let us label our points

let(x1, y1)=(-2, -5)

let (x2, y2)=(1, 4)

Does not matter the labelling of points

we now need to find the gradient or the slope

It is given by the following formula

m=(y2-y1)/(x2-x1)

substitute the values into formula

m=(4--5)/(1--5)=9/3=3

Reminder that two negatives facing each other gives a postive

m=3

We substitute this into our general equation of a straight line to get the following:

y=3x+c

We now to solve for c

and we can use any of the two co-ordinate points

lets use(1,4) this means x=1 and y=4

substitute into the above equations and solve for c

4=3*1+c

4=3+c

c=1

the equation for Line1 is y=3x+1

We now look at line2

(0,6) and (6,4)

let(x1, y1)=(0,6) and (x2, y2)=(6,4)

We following the same procedure as for the first line

we look for the gradient or slope m

m=(y2-y1)/x2-x1)

m=(4-6)/(6-0)=-2/6=-1/3

We then substitute this value into the general equation for a line

y=mx+c

y=-1/3x+c

we now need to solve for c

we can choose any of the co-ordinate points to substitute into the equation

say we choose(0,6) this means x=0 and y=6

y=-1/3x+c

6=-1/3 *0+c

6=0+c

c=6

we then get the equation for line 2 which is

y=-1/3x+6

Line 1 has a gradient of 3

Line2 has a gradient of -1/3

when we multiply the two together we get -1

therefore the two line are perpendicular to each other

m1*m2=-1

gradient of line  multiplied by the gradient of line 2 gives -1

perpendicular line

The specific heat of a substance can be calculated by using the formula q = m × c × ΔT

Specific heat is the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree Celsius

The specific heat of a substance can be calculated using the following formula:

q = m × c × ΔT

where:

q is the amount of heat energy transferred to or from the substance

m is the mass of the substance

c is the specific heat of the substance

ΔT is the change in temperature of the substance

To calculate the specific heat, we rearrange the equation as follows:

c = q / (m × ΔT)

To perform the calculation, you need to know the mass of the substance, the amount of heat energy transferred to or from the substance, and the change in temperature of the substance. You can then plug these values into the equation to find the specific heat. The units of specific heat are J/(kg*K) in SI units.

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The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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