3.The following are real data from Santa Clara County, CA. As of a
certain time, there had been a total of 3,059 documented cases of
AIDS in the county. They were grouped into the following categories:

Homosexual IV Drug User* Heterosexual Contact Other
Female 0 70 136 49
Male 2,146 463 60 135

Suppose a person with AIDS in Santa Clara County is randomly
selected.
(i) Find P (Person is female). (2 Marks)
(ii) Find P (Person has a risk factor heterosexual contact). (2 Marks)
(iii) Find P (Person is female OR has a risk factor of IV drug user (2 Marks)
(iv) Find P (Person is female AND has a risk factor of homosexual) (2 Marks)
(v) Find P (Person is male AND has a risk factor of IV drug user) (2 Marks)
(vi) Find P (Person is female GIVEN person got the disease from
heterosexual contact) (2 Marks)
(v)Construct a Venn diagram. Make one group females and
the other group heterosexual contact. (3 Marks)

A 95% confidence interval for the difference of the meantime that the customers stayed for lunch and for dinner the correct option is option a (3.35, 16.65).

Given:

The number of random customers n1 = 25

The number of random customers n2 = 30

x1 = 45, x2 = 55

σx1 = 10, σx2 = 15

Zα12 = Z0.025 = 1.96

95% confidence interval,

= {(x2-x1) ± Zα12 [(σx1)^2/n1 + (σx2)^2/n2]^0.5}

= {(55-45)  ± 1.96 [\(10^{2}\)/25 + \(15^{2}\)/30]^0.5}

= {10 ± 1.96(4 + 7.5)^0.5}

= {10 ± 1.96(11.5^0.5)}

= {10 ± 1.96(3.3911)}

= {10 ± 6.6466}

=> (10-6.6466, 10 + 6.6466)

=> (3.35, 16.65)

So, the correct option is a (3.35, 16.65) for the difference of the meantime.

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The size of the largest interior angle of the field is 69.86°

The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

Given that, a triangular field has boundaries of lengths 170m, 195m and 210m, we need to find the size of the largest interior angle of the field,

We know that, angle opposite to the largest side is largest,

Therefore,

The largest angle is opposite is 210 m side, (say c)

Using the cosine rule,

210² = 170²+195²-2(170)(195)cosC

CosC = 170²+195²-210² / 2(170)(195)

CosC = 22825 / 66300

CosC = 0.344268477

C = 69.86°

Hence, the size of the largest interior angle of the field is 69.86°

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Answer:

1. = 2/3

2. = 5/7

3. = 2/3

Step-by-step explanation:

divide by 4 for 1

divide by 2 for 2

divide by 2 for 3

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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The insurance company would pay a total of $101,000 for the medical expenses resulting from the accident.

In this scenario, Sally's car insurance policy has coverage limits of 100/300/50. These numbers represent the maximum amount the insurance company will pay for different types of damages in an accident. Let's break down what these numbers mean in the context of the collision.

The first number, 100, represents the maximum amount (in thousands of dollars) that Sally's insurance company will pay for bodily injury per person. Since Sally sustained $150,000 in injuries and her passenger sustained $1,000 in injuries, the insurance company will cover Sally's medical expenses up to the policy limit, which is $100,000.

The second number, 300, represents the maximum amount (in thousands of dollars) the insurance company will pay for bodily injury per accident. In this case, both Sally and her passenger were injured, so the insurance company will cover their combined medical expenses up to the policy limit, which is $300,000.

The third number, 50, represents the maximum amount (in thousands of dollars) the insurance company will pay for property damage per accident. However, since the question only mentions injuries and not property damage, we can disregard this number for now.

Therefore, the total medical expenses the insurance company would pay for this accident would be $100,000 for Sally's injuries and $1,000 for her passenger's injuries, totaling $101,000.

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Answer:

B

Step-by-step explanation:

x + 3y = 2 → (1)

4x - 3y = 23 → (2)

adding (1) and (2) term by term will eliminate y

(x + 4x) + (3y - 3y) = 2 +  23

5x + 0 = 25

5x = 25 ( divide both sides by 5 )

x = 5

Answer:

It's a rectangular prism :)

Step-by-step explanation:

Well I automatically know this because,

it can't be a triangle since the left and right corners aren't angled with 3 sides like a triangle

It can't be a square pyramid because that would mean it is the shape of a triangle when folded with a square base

It can't be a cube because cubes have sides equal in length, while this shape when folded is long in length and short in width

So the answer is a rectangular prism! Rectangles have long lengths and short widths and if this shape is folded from 2D to 3D that makes it a prism.

Hope this helps! Have a meowgical day :)))

Rectangular prism shape can be created by the given net.

A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices.

A square pyramid is a three-dimensional geometric shape that has a square base and four triangular sides that are joined at a vertex. It is a polyhedron (pentahedron) with five faces. A square pyramid consists of a square base and four triangles connected to a vertex. Its base is a square and the side faces are triangles with a common vertex.

A cube is a 3D solid object with six square faces and all the sides of a cube are of the same length. It is also known as a regular hexahedron and is one of the five platonic solids. The shape consists of six square faces, eight vertices, and twelve edges. The length, breadth, and height are of the same measurement in a cube since the 3D figure is a square that has all sides of the same length

A rectangular prism is a prism whose bases (the top face and the bottom face) are also rectangles. It has 6 faces in all, out of which there are 3 pairs of identical opposite faces, i.e., all the opposite faces are identical in a rectangular prism. It has three dimensions, length, width, and height.

A rectangular prism has 6 faces, 12 edges (sides) and 8 vertices (corners). In the 12 edges, 3 edges intersect to form right angles at each vertex.

According to the question

We can observe that the net consists of 6 faces, out of which there are 3 pairs of identical opposite faces.

A rectangular prism is a prism whose bases (the top face and the bottom face) are also rectangles. It has 6 faces in all, out of which there are 3 pairs of identical opposite faces, i.e., all the opposite faces are identical in a rectangular prism. It has three dimensions, length, width, and height.

We can say that the given net is of rectangular prism.

Option D is correct.

Thus, rectangular prism shape can be created by the given net.

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Step-by-step explanation: answer: 108

270

\(270 \times \frac{60}{100} \)

\(27 \times 6 = 162\)

270=60%

60% =162

40% = not going

270 students - 60% 162= 108

→108 students are not going

Answer:

270 students - 60% 162= 108

Step-by-step explanation:

Part A:

Let's focus on the following two lines of Jillian's procedure:

As we can see, she added the 3 and the 7. However, in an arithmetic operation the multiplication takes priority over the addition, and as a result she should have multiplied the 3 and the 16 first before doing the addition.

Part B:

Let's work on simplifying the expression in a similar manner as it was done in the example:

Now, because of the PEMDAS criteria, we do the multiplication first:

Hence, these lines are perpendicular to each other.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Draw the graph by using the given equation is

(24)

line \(a: y = 5x - 6\)

line \(b: x + 5y = 5\)

Graph is of the form:-

(25)

line \(a: 2x = y = 10\)

line \(b: -6x - 3y = 3\)

line \(c: x - 2y = 8\)

Graph is of the form:-

Hence, these lines are perpendicular to each other.

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(a) 45 tens is equal to 450. :- True

(b) 12.3 is equal to 123 ones. :- True

(c) 80 tens is greater than 6 hundreds. :- True

(d) 43,200 is less than 50 thousands. :- True

(e) 60 hundreds = 6,000 :- True

Consider the first statement,

45 tens are equal to 450

So, 45 tens mean 45 times 10 is written as:

45 × 10 = 450

Hence, it's true.

Consider the second statement,

12.3 is equal to 123 ones.

Now, 123 ones is equal to 123 times 1.

123 × 1 = 123

Hence, the statement is true.

Consider the third statement,

80 tens is greater than 6 hundreds.

Now 80 tens = 80 × 10 = 800

Now, 6 hundreds = 6 × 100 = 600

Now, 800 > 600

Hence, the statement is true.

Consider the fourth statement.

43,200 is less than 50 thousands.

Now, 50 thousands = 50 × 1000 = 50,000

We know,

50,000 > 43,200

Therefore, the statement is true.

Consider the fifth statement,

60 hundreds = 6000

Now, 60 hundreds = 60 × 100 = 6000

Therefore, the statement is true.

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3x + 2y = 5 ,, slope and y intercept: \(-\frac{3}{2}\)

3y - x = 9 ,, slope and y intercept: \(\frac{1}{3}\)

hope this helps!

Answer:

800

Step-by-step explanation:

Check out the attached photo

The number of proper subsets of Z = 255.

Subsets are a subset of the mathematical idea known as Sets. A set is a group of items or components that are enclosed in curly braces, such as "a,b,c,d." Set B is said to be a subset of A if set A is a collection of even numbers and set B contains the numbers 2, 4, and 6. B is designated as BA and A is the superset of B.

The number of proper subsets can be calculated by the formula 2 raise ti the power n where n represents the number of elements in the set

Here, n = 8

thus \(2^{n} = 2^{8}\)

which is equal to 256

However since one of the subsets of Z is itself it is not a proper subset

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Mean must be set to 491.775 ml in order for 95% probability.

A normal distribution in statistics is defined as the type of continuous probability distribution where the datas are arranged in a symmetrical bell shaped graph.

Given that,

Probability that the bottle is not underfilled = 95% = 0.95

That is, the probability that the bottle is filled = 0.95

Half liter = 500 ml

z = (x - μ) / σ

We know that the z value for 95% probability is 1.645 below the mean.

So substituting,

1.645 = (500 - μ) / 5

500 - μ = 1.645 × 5

500 - μ = 8.225

μ = 500 - 8.225

μ = 491.775

Hence the mean is 491.775 ml.

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The complete question is as given below.

The amount of fill in a half liter soft drink bottle is normally distributed. The process has a std. deviation of 5 ml. The mean is adjustable.

Where should the mean be set to ensure a 95 percent probability that a half-liter bottle will not be underfilled? (round your answer to 2 decimal places.)

Answer:

Kendall is 24 and Jamal is 15.

Step-by-step explanation:

39 - 9 = 30

30 ÷ 2 = 15

15 is Jamal's age.

15 + 9 = 24

24 is Kendall's age.

A sample size of 176 tenth graders would be needed in order to estimate the fraction of students with reading skills at or below the eighth grade level at a 99% confidence level having an error of at most 0.03.

To calculate the sample size required for estimating the fraction of tenth graders with reading skills at or below the eighth grade level, we can use the formula for sample size estimation for proportions;

n = (ZZ × p × (1 - p)) / (EE)

where; n = sample size

Z = Z-score corresponding to the desired confidence level (in this case, the Z-score for a 99% confidence level, which is approximately 2.626)

p = estimated population proportion (in this case, 0.22)

E = desired margin of error (in this case, 0.03)

Plugging in the given values;

n = (2.6262.626 × 0.22 × (1 - 0.22)) / (0.030.03)

n = 0.15774 / 0.0009

n ≈ 175.27

Since we need to round up to the next integer, the sample size required would be 176.

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Answer:

26) 70

27) 12.86 sec

28) 350 feet

Step-by-step explanation:

26) Given points A(0, 0) and B(16, 1120)

slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

\(=\frac{1120-0}{16-0}\\ \\=\frac{1120}{16}\\ \\=70\)

slope = 70

27) eq of a line is :

y = mx + c

y = 70x + c

Since the line passes through A(0,0) substituting the points in the equation,

0 = 70(0) + c

⇒ c = 0

eq of line: y = 70x

given distance is 900 ft

y = distance and x = time

⇒ y = 900

sun in eq,

900 = 70x

⇒ x = 900/70

⇒ x = 12.86

28) time is 5 sec

⇒ x = 5

sub in eq

y = 70(5)

⇒ y = 350

Answer:

\(1. \: ans \: is \: c. \: the \: hinge\)

\(2. \: the \: ans \: is \:b . \: knee \: and \: elbow\)

\(3. \: ans \: is \: b. \: hypodermis - dermis \\ - epidermis.\)

The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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Answer:

95.73%

Step-by-step explanation:

Given data:

mean μ= 95

standard deviation, σ = 11

to calculate, the probability that a randomly selected firm will earn less than 114 million dollars;

Use normal distribution formula

\(P(X<114)=P(Z<\frac{X-\mu}{\sigma} )\)

Substitute the required values in the above equation;

\(P(X<114)=P(Z<\frac{114-95}{11} )\\P(X<114)=P(Z<1.7272)\\P(X<114)=0.9573\)

Therefore, the probability that a randomly selected firm will earn less than 114 million dollars = 95.73%

Check the picture below.

\((x+18)(18)=(24+16)(16)\implies 18x+324=640 \\\\\\ 18x=316\implies x=\cfrac{316}{18}\implies x=\cfrac{158}{9}\implies x=17\frac{5}{9}\)

We know that the roots are

We can express these roots as factors.

If we use the distributive property, we can find the equation.

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

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The calculated measure of t from the given equation is 15 degrees

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

10

to

25°

When expressed properly, we have

10° + t° = 25°

Evaluate the like terms

So, we have

t° = 15°

Hence, the value of t° is 25°

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Answer:

it will be choice 3

Step-by-step explanation:

as if you bend each shape of each of them the only choice that will give you a pyramide with a omitted side

P(s) indicates that the triangle's perimeter is 60 units, and A value of s = 20 makes the equation true.

An closed path that surrounds, distinguishes, or encompasses a multiple shape or a three-dimensional length is referred to as a boundary. The perimeter of an ellipse or circle refers to its outermost area. Geometric perimeter calculation have several practical uses. The perimeter of a form is its edge's radius. Discover how to determine the perimeter by adding the dimensions of the sides of myriad guises. You can always find the perimeter of a shape by multiplying its side lengths. The perimeter of an object is the space around it. At my house, a closed garden is one illustration. The perimeter of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.

given

The equilateral triangle's perimeter is represented by 60 in the equation p(s) = 60.

Plug in 60 as p(s) and do an s-solve to determine the value of s that makes the equation p(s) = 60 true.

p(s) = 3s

60 = 3s

20 = s

Therefore, the equation will be true for s = 20.

P(s) indicates that the triangle's perimeter is 60 units, and A value of s = 20 makes the equation true.

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The complete question is :-

Function p gives the perimeter of an equilateral triangle of side length s. It is represented by the equation p(s)=3x

a. What does P(s)=60 mean in this situation?

b. Find a value of s to make the equation P(s) = 60 true.

The unit rate for Option A is $4.4 per pound of gummy bears.

The unit rate for each option is a mathematical expression that compares two quantities of different measures by dividing one quantity by the other.

The unit rate is used to determine how much an item costs per unit of measure.

To find the unit rate for each option, we can use the following formula: Unit rate = price ÷ weight Option A: $15.40 for 3.5 lbs of gummy bears Unit rate = 15.40 ÷ 3.5Unit rate = $4.4 per pound of gummy bears.

Therefore, the unit rate for Option A is $4.4 per pound of gummy bears.

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Here is the complete question given below:

The unit rate for each option. 9. Option A: $15.40 for 3.5 lbs of gummy bears. $7.65 for 1.8 Ibs of gummy bears.