A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books isA 1 / 21B 10 / 21C 11D 21 / 11

Answer:

The area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.

Step-by-step explanation:

A semicircle is a two-dimensional shape that is exactly half of a circle.

The area of a circle is given by the formula:

[tex]\sf A=\pi r^2[/tex]

where A is the area of the circle, and r is the radius of the circle.

The diameter of a circle is twice its radius.

Given the diameter of the semicircle is 28 cm, the radius is:

[tex]\sf r = \dfrac{28}{2} = 14 \; cm[/tex]

Substituting this into the formula for the area of a circle, we get:

[tex]\sf A = \pi(14)^2[/tex]

[tex]\sf A = 196 \pi[/tex]

Finally, divide this by two to get the area of the semicircle:

[tex]\sf Area\;of\;semicircle = \dfrac{1}{2} \cdot 196 \pi[/tex]

[tex]\sf Area\;of\;semicircle = 98 \pi\; cm^2[/tex]

So the area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.

The steps for the perpendicular bisector construction when ordered are :

Identify the two endpoints of the given segment AB and labeling them as A and B. This is important for the subsequent steps of the construction. Then draw two circles: one centered at A with a radius equal to the length of AB, and the other centered at B with a radius equal to the length of BA (which is the same as AB).

The two circles drawn in Step 2 intersect at two points. These points are labeled as C and D. Note that these points are equidistant from A and B, since they lie on the circles with radii AB and BA.

Finally, we draw a line through points C and D. This line is the perpendicular bisector of the segment AB, meaning it intersects AB at its midpoint and is perpendicular to AB.

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Step-by-step explanation:

try this option (see the attachment), answers are marked with red colour.

Initially, while maintaining the very same [tex]x-[/tex]coordinates, the negative reflect across the [tex]x-axis[/tex] modifies the signs of all locations' [tex]y-[/tex]coordinates.

A negative value is one that always has a value lower than zero and is denoted by the minus (-) symbol. In a number line, negative values are displayed just left of zero.

If a number is higher than zero, it is considered positive. Or less zero numbers are referred to as negative numbers. If a number is bigger than that or equal to zero, it is not negative. If a number falls below or equal to zero, it is non-positive.

This transforms Figure [tex]1[/tex] into a new figure with points [tex](-2, -5), (-2, -4), (-3, -4), (-3, -2), (-5, -2), (-5, -5)[/tex].

Next, the [tex]180^{0}[/tex] rotation about the origin swaps the signs of both [tex]x[/tex] and [tex]y[/tex] coordinates of each point. This results in the final figure with points [tex](2, -5), (2, -4), (3, -4), (3, -2), (5, -2), (5, -5)[/tex].

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Answer:

see step by step.

Step-by-step explanation:

The THEORETICALLY probability is 0.5000 (this is, 50% each one) since each one have equal chance of being in list A or List B, but this is still a random probability, so this is not the same that if you have 60 students, 30 of them are going to be in the list A and the other 30 in B.

The experimental result show:

[tex]P (ListA) = \frac{27}{60} =0.45[/tex]

[tex]P (ListB) = \frac{33}{60} =0.55[/tex]

This is 45% of being in list A and 55% of being in list B, notice these values are close the the experimental value (50%) but still are lightly higher or lower. Additionally notice if you add both of them you still have 100% (0.45+0.55=1.00)

Answer:

Notice the change in sample size.

Answer:

1. The expected mean for a sample of 150 women is 168.5 pounds.

2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.

3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.

4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.

5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.

6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.

The solution is given below. Notice the change in sample size.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.

so. we get,

1. The expected mean for a sample of 150 women is 168.5 pounds.

2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.

3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.

4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.

5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.

6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.

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Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to draw an angle that is 150}^{\circ}.[/tex]

[tex]\textsf{We will need a Protractor to draw this angle.}[/tex]

[tex]\large\underline{\textsf{To Draw an Angle with a Protractor;}}[/tex]

[tex]\textsf{First, notice a point at the bottom of the Protractor. This is where we will start.}[/tex]

[tex]\textsf{Draw a Straight Line from the point to the 0}^{\circ} \ \textsf{mark.}[/tex]

[tex]\textsf{Secondly, use a ruler to carefully draw a straight line towards the 150}^{\circ} \ \textsf{mark.}[/tex]

[tex]\textsf{Note that some Protractors may be different from others. Similar steps should apply.}[/tex]

[tex]\textsf{Refer to the picture. It represents what the angle should look like afterwards.}[/tex]

To do :-

Instruments required:-

Steps of construction:-

Hence angle ECB represents 150° .

Precaution:- do not change the arm length of the compass.

and we are done!

Answer:

16, 22, and 32.

Step-by-step explanation:

Set up a system of equations to represent the situation with 3 unknown.

x + y + z = 70

z = 2x

x = y - 6  →  y = x + 6

The second two equations are the y and z in terms of x, so substitute both into the first equation.

x + (x + 6) + 2x = 70

4x + 6 = 70

4x = 64

x = 16

Use this number to calculate the value of the other unknowns.

y = x + 6

y = 16 + 6

y = 22

Calculate z.

z = 2x

z = 2(16)

z = 32

So, the three numbers are 16, 22, and 32.

The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm

The sector area

The area of the sector is calculated as

Area = x/360 * πr²

Where

r² = 8² + 6²

So, we have

r² = 100

This means that

Area = 82/360 * π * 100

Evaluate

Area = 71.55

The triangle area

This is calculated as

Area = 0.5bh

So, we have

Area = 0.5 * 8 * 6

Evaluate

Area = 24

So, the area of the figure is

Figure = 24 + 71.55

Figure = 95.55

Hence, the area is 95.55

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The linear homogeneous constant-coefficient equation is y'' - 4y' + 2y = 0

A linear homogeneous constant-coefficient equation is of the form:

ay'' + by' + cy = 0

where a, b, and c are constants, and y is a function of x. The general solution of this equation can be written as:

[tex]y(x) = c_1e^{(r_1x)} + c_2e^{(r_2x)}[/tex]

where r₁ and r₂ are the roots of the characteristic equation:

ar² + br + c = 0

In our case, the general solution is given as:

y(x) = [tex]Ae^{2x}[/tex] + Bcos(2x) + Csin(2x)

To find the linear homogeneous constant-coefficient equation that has this general solution, we need to first write the general solution in the form:

[tex]y(x) = c_1e^{(r_1x)} + c_2e^{(r_2x)}[/tex]

where r₁ and r₂ are the roots of the characteristic equation. Comparing this form with the given general solution, we see that r₁ = 2, r₂ = 2i, and r3 = -2i.

Therefore, the characteristic equation is:

a(r-2)(r-2i)(r+2i) = 0

Expanding this equation, we get:

a(r³ - 2r²i - 2ri² + 4r² + 8i²r - 8i) = 0

Simplifying and grouping the real and imaginary terms, we get:

a(r³ - 4r) + 2a(r² + 4) = 0

Dividing by a, we get:

r³ - 4r + 2(r² + 4) = y'' - 4y' + 2y = 0

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Complete Question:

Find a linear homogeneous constant-coefficient equation with the given general solution

y(x)=Ae²ˣ+Bcos(2x)+Csin(2x)

Answer:

Where is the table?

Step-by-step explanation:

The function of tiles with no empty spaces is n(t) = t² + 2t, the function of tiles removed to create empty spaces is r(t) = t.

We have a sequence of tiles represented by the numbers 3, 8, and 15.

This sequence can be described as a quadratic sequence, which can be expressed using the formula

n(t) = at² + bt + c.

By substituting the values of the first three terms into this formula, we can find the values of a, b, and c.

a + b + c = 3

4a + 2b + c = 8

9a + 3b + c = 15

These values can also be determined by graphing the sequence. In this case, a = 1, b = 2, and c = 0.

Therefore, the quadratic sequence can be written as n(t) = t² + 2t.

The given sequence of tiles can be represented as a linear sequence in which the current term is equal to the number of spaces.

Therefore, the function r(t) can be defined as r(t) = t.

The given equation is expressed as:

A(t) = n(t) + r(t)

Therefore, substituting t² + 2t + t for A(t), we get:

A(t) = t² + 2t + t

Consequently, the function can be represented as

A(t) = t² + 3t

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The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]

An interactive widget in a graph is a tοοl that allοws the user tο manipulate different elements οf the graph using their mοuse οr tοuch screen.

Interactive widgets can be used tο explοre the behaviοr οf a functiοn οr dataset in a mοre dynamic and engaging way than a static graph.

Sοme cοmmοn examples οf interactive widgets in graphs include sliders, buttοns, checkbοxes, and drοpdοwn menus.

Here we have

y = -5 cοs (π/16 x) - 4    

Represents a periοdic functiοn with a cοsine wave shape that is shifted dοwnwards by 4 units.

The cοsine functiοn οscillates between -1 and 1, sο multiplying it by -5 stretches the wave vertically by a factοr οf 5 and reflects it acrοss the x-axis.

The cοefficient οf x, π/16, cοntrοls the periοd οf the functiοn, which is the distance between twο cοnsecutive peaks οr trοughs οf the wave.

Specifically, the periοd οf this functiοn is 32 units, since the cοsine functiοn has a periοd οf 2π and 2π/(π/16) = 32.

Therefοre,

The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]

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The height οf the cylinder is apprοximately 6.38 centimetres.

The cylinder's altitude is a perpendicular segment frοm the plane οf οne base tο the plane οf the οther, and the cylinder's height is the length οf the altitude. A cylinder's axis is the segment cοntaining the centres οf the twο bases.

The vοlume οf a right circular cylinder is calculated as fοllοws:

[tex]V = \pi r^2h[/tex]

where V is the vοlume, r is the radius οf the base, and h is the cylinder's height.

Substituting the fοllοwing values:

[tex]1280 = \pi(8^2)h[/tex]

Simplifying:

[tex]1280 = 64\pi h[/tex]

By dividing bοth sides by 64, we get:

[tex]h = 1280/(64\pi)[/tex]

Simplifying and rοunding tο the nearest twο decimal places:

h ≈ 6.38

As a result, the cylinder's height is apprοximately 6.38 centimetres.

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20. Took the quiz, and received a 100 percent.

Answer:

Step-by-step explanation:

To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:

n! ≈ (n/e)^n √(2πn)

where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.

Using this approximation, we can rewrite (n!)^(1/n) as:

(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)

Taking the limit as n approaches infinity, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)

Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:

lim [√(2πn)]^(1/n) = 1

For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:

lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1

Therefore, combining the two terms, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1

Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.

Answer:1

Step-by-step explanation:

The sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex], is convergent sequence because the limit of an exists, that is as n approaches infinity, so the sequence an approaches 1 ( finite value).

The sequence can be convergent if the limit is zero, or if the limit is finite. The divergent sequence is one whose limit is not finite. The limit can be found suing the limit properties or by simplification method, as applicable. We have, an sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex]. We have to check whether the sequence converges or diverges. Using limits, [tex]lim_ {n->\infty } a_n = lim_{n-> oo} e^{\frac{-8}{\sqrt{n}}} [/tex]

n approaches infinity, so square root of n approaches infinity,

= e⁻⁰

= 1/e⁰ = 1 ( finite )

Therefore, it is a convergent sequence.

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Answer:

  40.3%

Step-by-step explanation:

You want to know the percentage of a 62 gram allowance of fat is represented by a burger with 25 grams of fat.

The fraction can be converted to a percentage by multiplying by 100%.

  burger/allowance = (25 g)/(62 g) × 100% = 40.3%

King has 40.3% of his daily allowance for fat when he ate his burger.

According to the Venn diagram the value of [tex]n(A ^ C \cap B ^ C) = {3}[/tex] so the number of elements in that set is 1.

What is Venn diagram ?

A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. It is usually represented as a rectangle or a circle for each set and the overlapping areas between them, showing the common elements that belong to more than one set. Venn diagrams are widely used in mathematics, logic, statistics, and computer science to visualize the relationships between different sets and help solve problems related to set theory.

According to the question:
To solve this problem, we first need to understand the notation used.

n(A) denotes the set A and the numbers within the braces {} indicate the elements in set A. For example, n(A)={7,4,3,9} means that the set A contains 7, 4, 3, and 9.

n(AnB) denotes the intersection of sets A and B, i.e., the elements that are common to both A and B. For example, n(AnB)={4,3} means that the sets A and B have 4 and 3 in common.

^ denotes intersection of sets

cap denotes the intersection of sets

Now, we need to find the elements that are common to sets A and C, and sets B and C. We can do this by taking the intersection of A and C, and the intersection of B and C, and then taking the intersection of the two resulting sets.

[tex]n(A ^ C) = n(A \cap C) = {3,9}[/tex]

[tex]n(B ^ C) = n(B\cap C) = {3,5}[/tex]

Now, we take the intersection of [tex]n(A ^ C)[/tex] and [tex]n(B ^ C)[/tex]:

[tex]n(A ^ C \cap B ^ C) = {3}[/tex]

Therefore, the answer is 1.

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The probability that the computer generates a number between 1 and 4 is 4/11.

Since X has a uniform distribution, the probability of generating any number between 0 and 10 is equally likely. Therefore, the probability of generating a number between 1 and 4 is the same as the probability of generating a number between 0 and 4 minus the probability of generating 0

P(1 ≤ X ≤ 4) = P(X ≤ 4) - P(X = 0)

Since X has a uniform distribution, the probability of generating any specific number is 1/11. Therefore

P(X ≤ 4) = (4 + 1)/11 = 5/11

and

P(X = 0) = 1/11

So,

P(1 ≤ X ≤ 4) = (5/11) - (1/11) = 4/11

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I have solved the question in general, as the given question is incomplete,

The complete question is:

A random number generator generates numbers between 0 and 10. Let random variable X be the number generated. Suppose X has a uniform distribution. What is the probability that the computer generates a number between 1 and 4?

According to the solving the function the value of  h(-2) + g(-2) is 45.

function is a mathematical phrase, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are used frequently in mathematics and are crucial for constructing physical links in the sciences.

To find h(-2) + g(-2), we need to evaluate h(r) and g(r) when r = -2, and then add the results:

h(-2) = 11(-2)² - 6 = 44

g(-2) = (-2)² + 8(-2) + 9 = 1

So, h(-2) + g(-2) = 44 + 1 = 45.

Therefore, h(-2) + g(-2) = 45.

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Step-by-step explanation:

try this option, all the details are in the attachment.

To solve this problem, we can use Bayes' theorem. Let's define:

- A: two story home

- B: owning a computer

We want to find the probability of B given A, which we can write as P(B|A). Using Bayes' theorem, we have:

P(B|A) = P(A|B) * P(B) / P(A)

We know that 50% of two story homes own computers, so P(B) = 0.5. We also know that 75% of homes in Dawn's neighborhood are two story, so P(A) = 0.75.

To find P(A|B), we need to use the conditional probability formula:

P(A|B) = P(A and B) / P(B)

We don't have the probabilities for A and B happening together, but we know that:

P(A and B) = P(B|A) * P(A)

Substituting this into the conditional probability formula gives:

P(A|B) = (P(B|A) * P(A)) / P(B)

Putting all the values together, we get:

P(B|A) = (P(A|B) * P(B)) / P(A)

= ((P(B|A) * P(A)) / P(B)) * P(B) / P(A)

= (P(B and A) / P(B)) * P(B) / P(A)

= P(A and B) / P(B)

Substituting the values gives:

P(B|A) = (0.5 * 0.75) / 0.5

= 0.75

Therefore, the probability that a two story home in Dawn's neighborhood owns a computer is 0.75.

The length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

Since the area of the soap carvings is 300 square inches, we want the top of the bookcase to have the same area. Let's assume the length of the top of the bookcase is "l" and the width is "b". Then we have:

Area of top of bookcase = lb

We want this area to be equal to 300 square inches. Therefore, we can write:

lb = 300

We are solving for "b", so we can rearrange this equation to solve for "b":

b = 300/l

Since we don't know the value of "l", we can't solve for "b" exactly. However, we can approximate it by assuming a value for "l". Let's say we assume that "l" is 20 inches. Then we can calculate "b" as follows:

b = 300/20 = 15

So if the length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

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There is a $243,570 cap on the amount you may finance.

MentaI arithmetic, aIso known as "quick math," aIgebra, trigonometry, statistics, and probabiIity are some of the key mathematicaI concepts and abiIities needed in the financiaI sector. A fundamentaI knowIedge of these abiIities shouId be sufficient to quaIify you for the majority of finance occupations.

The highest home vaIue that may be financed is x.

$39,000 in avaiIabIe cash for a down payment

16% is the needed down payment percentage.

16% of the home's worth can be expressed as,

x × 16/100=$39,000

x=39,000/0.16

x=$243,570

We can then infer that the highest vaIue you couId finance is $243,570.

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The cube has 8 vertices. Exercise 21 states that for a polyhedron with V vertices, E edges, and F faces, the following equation holds:

V - E + F = 2

To use this equation to find the number of vertices of a cube with 12 edges and 6 faces, we first need to identify the values of E and F.

A cube has 12 edges, as given in the problem statement, and it has 6 faces since a cube has 6 square faces.

Substituting these values into the equation, we get:

V - 12 + 6 = 2

Simplifying this equation, we have:

V - 6 = 2

Adding 6 to both sides, we get:

V = 8

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Answer:

E

Step-by-step explanation:

Answer has to have a star, the object (star) needs to be on the right side, and the two colors cannot be the same as any of the rest in the set. So E?

Answer:

0.75

Step-by-step explanation:

0.4 = 0.40

Add 0.40 + 0.35 = 0.75

Answer: -1/6

Step-by-step explanation:

Put the equation into y = mx + b (slope) form.

3x + 18y = -486

18y = -3x - 486

y = -1/6x - 27

If the line is parallel to this line, the slope must be the same.

Answer:

Step-by-step explanation:

Let's call the number we're looking for "x".

The problem tells us that "if the sum of a number and eight is doubled, the result is seven less than the number", which can be translated into an equation:

2(x+8) = x-7

Now let's solve for x:

2x + 16 = x - 7

2x - x = -7 - 16

x = -23

Therefore, the number we're looking for is -23.