events which can never occur together in probability theories then it is classified as? a. mutually exclusive events b. collectively exclusive events c. mutually exhaustive events d. none of these

Answer:

21/18 or 1 and 3/18

Step-by-step explanation:

6/9 = 12/18

3/6 = 9/18

12/18 + 9/18 = 21/18 or 1 3/18

Answer:

A stratified sample in this case can be selected as follows:

The rooms are divided by whether they overlook the ocean or the street, and 25 of each are selected.

The five most common classifications for sampling are listed as follows:

In this problem, the groups are given as follows:

50 rooms will be sampled, hence the number that is sampled from each group is given as follows:

50/2 = 25 rooms from each group.

The problem asks to describe a stratified sample for this situation.

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The amount that Sascha will receive in annual interest based on the information is $63.40.

From the information, Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond and the bond pays 6.34% annual interest.

In this case, it should be noted that the simple interest is calculated as:

Principal × Rate × Time

Principal = $1000

Time = 1 year

Rate = 6.34%

The interest will be:

= Principal × Rate × Time

= 1000 × 0.0634 × 1

= $63.40

The interest is $63.40.

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Answer:

Step-by-step explanation:

It would be D.

The measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.

We have been given the measure of each side of an equilateral triangle whose area is √3 cm².

Let the measure of each side would be "a"

We know that,

Area of an equilateral triangle = √3a² / 4

As per the question,

⇒ √3 cm²= √3a² / 4

⇒ √3a² = 4√3 / √3

⇒ a² = 4 = √4

⇒ a = 2 cm

Thus, the measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.

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Answer:

2 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

2 + [tex]\frac{3}{4}[/tex]

= 2 [tex]\frac{3}{4}[/tex] ← as a mixed number

The expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. Similarly, any tirigonometric equation can be convereted into other forms of trigonometric functions.

What is trigonometric functions?

Denoting the relation between a right-angled triangle's angle and sides are trigonometric functions, which are periodic functions.

Consider the given expression.

[tex]3-2tan^2x\\[/tex]

Now, substitute [tex]\frac{sinx}{cosx}[/tex] for [tex]tanx[/tex] as follows:

[tex]3-2tan^2x=3-2(\frac{sinx}{cosx})^2\\=3-2(\frac{sin^2x}{cos^2x})[/tex]

Now, all the terms are converted into cos x except the sin x terms in the numerator. Hence, using the relation between sin x and cos x. Substitute [tex]1-cos^2x[/tex] for [tex]sin^2x[/tex].

[tex]3-2tan^2x=3-2(\frac{1-cos^2x}{cos^2x})[/tex]

Now, all the terms are in cos x. Hence, the expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. In the similar way any function can be conveted into other trigonometric functions.

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Using the properties of compound interest we can calculate that Jacob will have $1485 more than Brandon in his account.

Brandon invested $7,900 at the rate of 6 1/8% compounded daily.

Principal = $7900

Time = 15 years

Rate = 6 1/8% = 49/8 %

Amount earned after n years:

[tex]A=P (1+\frac{r}{n})^{nt}[/tex]  

Now we will use these values to find the amount at the end of 15 years.

P = 7900

r = 0.06625

n = 365

t = 15

[tex]A=P (1+\frac{.06125}{365})^{15\times 365}[/tex]

or, A = 19797.104...

or, A ≈ 19797.1

Again, Jacob invested the same sum at compound interest monthly at

6 5/8% .

Amount earned after 15 years:

P = 7900

r = 6.125

n = 12

t = 15

[tex]A=P (1+\frac{.06625}{12})^{15\times 12}[/tex]

or, A = 21282.383..

or, A ≈ 21282.38

Amount earned by Jacob more than Brandon

= $21282.38 - $19797.1

= $148785.283..

≈ $1485

Hence Jacob will have $1485 more than Brandon in his account.

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Answer:

  Isiah is correct. The slope is about 0.344.

Step-by-step explanation:

Lyra and Isiah want the slope of the hypotenuse in a triangle with an angle of elevation of 19°.

The slope is the ratio of "rise" to "run". In a right triangle, that is the ratio "opposite"/"adjacent". This ratio is the tangent of the angle of elevation.

  tan(19°) ≈ 0.344

The slope is about 0.344. Isiah is correct.

Isiah knows Lyra is not correct because the slope in a triangle with a 45° angle is 1. Lyra' value of 2.675 is about right for an angle of 69.5°, much greater than either 45° or the given angle of 19°.

__

Additional comment

Unfortunately, the diagram is not drawn to scale. This is often the case with diagrams in geometry problems. The diagram here is misleading in that it seems to show a slope greater than 1 for a 19° angle.

Answer:

-1,4

Step-by-step explanation:

move the point to the left 7 times

All the improper fractions in mixed or whole numbers are as follows:

So, the given improper fractions in the mixed or whole numbers are:

Therefore, all the improper fractions in mixed or whole numbers are as follows:

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The number of balcony seats sold is 110

Finding Unknown quantity using Linear equation:

The linear equation is an equation that is used to find an unknown quantity or an unknown number. In this, we will represent the Uknown value with a variable like x, y, z, etc.  

Here we have

Tickets for a community theater cost $11 for each main-floor seat
and $6 for each balcony seat.

There are 400 seats on the main floor, which are sold out for the evening performance  

The total revenue from ticket sales was $5060.

Here we don't know the number of balcony seats.

Let us assume that number of balcony seats = x

Then total revenue = 400(11) + 6x = 5060

=> 4400 + 6x = 5060

=> 6x = 5060 - 4400

=> 6x = 660

=> x = 110  

Therefore,

The number of balcony seats sold = 110

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Using the linear function, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

In the given question,

Arianna is going to use a computer at an internet cafe.

The cafe charges an initial fee to use the computer and then an additional price per minute of usage.

Let C represent the total cost of using a computer for t minutes at the internet cafe.

We have to determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

The additional change per unit = Slope of the linear function

The linear function C(t) given as;

C(t)=mt+b...............(1)

where m=slope and b=vertical intercept

Then, Slope = change in C(t)/change in t

Slope = ∆C(t)/∆t

We taking he given two point to find the slope

C(t) = 9.90 for t=1

C(t) = 15.30 for t=7

∆C(t)=15.30-9.90

∆C(t)=5.40

∆t=7-1

∆t=6

So, The required slope=5.40/6

The required slope=0.9=m

Now finding the value of b.

As we know that,

C(t) = 9.90 for t=1

The equation using this should be

9.90=m×1+b

Now putting the value of m in this equation

9.90=0.9×1+b

9.90=0.9+b

Subtract 0.9 on both side, we get

b=9

Now finding the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

Putting the value in equation (1)

15.75=0.9t+9

Subtract 9 on both side

15.75-9=0.9t+9-9

0.9t=6.75

Divide by 0.9 on both side

0.9/0.9 t=6.75/0.9

t=7.5

Hence, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

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At b= 24 will complete the square in the expression x^2 + bx + 144.

What is perfect square trinomial?

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b^2 = 4ac has the form ax^2 + bx + c, it is said to be a perfect square. The formula for the perfect square trinomial is (ax)^2 + 2abx + b^2 = (ax + b)^2.

Consider the given expression

x^2 + bx + 144

For this type of expression [tex]b = 2\sqrt{c}[/tex] will complete the square.

Here, c = 144

√144 = 12

So, b√c = 2(12) = 24

The expression becomes,

x^2 + 24x + 144 = (x + 12)^2

This is the perfect square.

Hence, b = 24  will complete the square in the expression x^2 + bx + 144.

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The expression is 2z+0.67

From the question, we have

During the first year that she owned the stock, it decreased by 35%. During the second year the value of the stock decreased by 32%.

z-35%+z-32%

=z-7/20+z-8/25

=2z+0.67

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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Answer: -3/8 or -0.375

Step-by-step explanation:

you have to get similar denominators to simplify

so times 1/4 by 2 to get 2/8

and then just do 2/8 - 5/8 and you get the answer

After a counterclockwise 90° rotation, the coordinates of A'B'C' are:

So, the coordinates after the counterclockwise rotation of 90°:

After counterclockwise 90° rotation, coordinates of A'B'C' are:

(Refer to the graph attached below)

Therefore, after a counterclockwise 90° rotation, the coordinates of A'B'C' are:

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The solution of the double-ended inequality is -7/2 < x < -5/2

From the question, we are to solve the doubled ended inequality.

The given inequality is

2x - 5 < 4x + 2 < 2x -3

From the inequality, we can write that

2x - 5 < 4x + 2 and 4x + 2 < 2x - 3

Now, we will solve each of the inequalities separately

Solving 2x - 5 < 4x + 2

Add 5 to both sides

2x - 5 + 5 < 4x + 2 + 5

2x < 4x + 7

Subtract 4x from both sides

2x - 4x < 4x - 4x + 7

-2x < 7

Divide both sides by -2 and reverse the sign

x > -7/2

-7/2 < x

Solving 4x + 2 < 2x - 3

Subtract 2x from both sides of the equation

4x - 2x + 2 < 2x - 2x -3

2x + 2 < -3

Subtract 2 from both sides

2x + 2 -2 < -3 - 2

2x < -5

Divide both sides by 2

x < -5/2

Putting the two solutions together, we get

-7/2 < x and x < -5/2

-7/2 < x < -5/2

Hence, the solution is -7/2 < x < -5/2

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The table of solutions should be completed based on the given equation (y = 2x²) as follows:

x                    y_

-2                  8

-1                   2

0                   0

1                    2

2                   8

Also, a graph of the solution to the given equation is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would complete the table based on the given equation as follows:

When x = -2, the value of point y is given by:

y = 2x²

y = 2(-2)²

y = 2 × 4

y = 8

When x = -1, the value of point y is given by:

y = 2x²

y = 2(-1)²

y = 2 × 1

y = 2

When x = 0, the value of point y is given by:

y = 2x²

y = 2(0)²

y = 2 × 0

y = 0

When x = 1, the value of point y is given by:

y = 2x²

y = 2(1)²

y = 2 × 1

y = 2

When x = 2, the value of point y is given by:

y = 2x²

y = 2(2)²

y = 2 × 4

y = 8

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Elena will need 180 more bats

Let she bats  b more needs

Total bats =  110 + b

Base hits = 24 + 0.35 b

From the question, we have

( 24 + 0.35b) / (110 + b) = 0.300

24 + 0.35b = 33 + 0.3 b

0.05 b = 9

b = 9 / 0.05 = 180

Subtraction:

The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.

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The cost of an adult ticket is £17 and a child ticket is £9.

Let's assume 'a'  for an adult ticket and 'c' for a child ticket

The cost of tickets for the Smith family of 2 adults and 3 children is £61

Equating, [tex]2a+3c=61[/tex]

[tex]2a=61-3c[/tex]

Dividing by 2, [tex]a=30.5-1.5c[/tex]        (equation 1)

Now, the cost of tickets for the Jones family of three adults and five children is £96

Equating, [tex]3a+5c=96[/tex]                 (equation 2)

Using equation 1, [tex]3(30.5-1.5c)+5c=96[/tex]

[tex]91.5-4.5c+5c=96[/tex]

[tex]91.5+0.5c=96[/tex]

[tex]0.5c=96-91.5[/tex]

[tex]0.5c=4.5[/tex]

[tex]c = \frac{4.5}{0.5}[/tex]

[tex]c=9[/tex]

Similarly, putting the answer of equation 2 in equation 1

we get, [tex]a=30.5-1.5c[/tex]

[tex]a=30.5-1.5(9)[/tex]

[tex]a=17[/tex]

Therefore, adult tickets cost £17 and child tickets cost £9

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a)4

so it's seven factorial divided by 7-5 factorial

The phrase [tex]f (x)[/tex] denotes a formula with [tex]x[/tex] serving as its input variable. Not multiply f and x, though!

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable .

The x in [tex]f(x)[/tex] is referred to the argument of the function or simply the argument in function notation. Therefore, the response is just 2 if they ask for a argument and give you the equation [tex]f(2)[/tex].

Hence,  the phrase [tex]f (x)[/tex] represents a formula with [tex]x[/tex] serving as its input variable.

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Answer: 2y   or   2 x y

Step-by-step explanation:

2 times the minutes

therefor if carlos answers 4 calls, you would say 2 x 4 and you ranswer would be 8 minutes.

The value of x in the given figure is x = 22.56 m .

In the question ,

a figure is given where the measure of angle(C) = 70° and angle(A) = 30°

In the triangle ABC ,

By Angle Sum Property Of Triangle  

angleA + angleB + angleC = 180°

30° + angleB + 70° = 180°

angleB = 180° - 100°

angle(B) = 80°

By using Sine Law ,

a/Sin(A) = x/Sin(C)

From the figure ,

a = 12 m

we get ,

12/Sin(30°) = x/Sin(70°)

x = (Sin70° × 12)/Sin(30°)

x = 11.2763/0.5

x = 22.5526

x ≈ 22.56 m

Therefore , The value of x in the given figure is x = 22.56 m .

The given question is incomplete , the complete question is

Find the value of x in the given figure ?

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The final balance is $97,920.

Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.

Given this, The principal is $3000.

Interest rate = 4.8%

Time = 2 years We must find the final balance.

The end balance formula is

C = P[ 〖(1+r)〗^n – 1]

C = 3000[ 〖(1+4.8)〗^2 – 1]

C = 3000 [ 〖(5.8)〗^2 – 1]

C = 3000 [ 33.64 – 1]

C = 3000 ( 32.64)

C = 97,920

Therefore the ending balance is $97,920

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Answer:

  17 cm

Step-by-step explanation:

You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.

The relation between the side lengths in the right triangle is ...

  a² +b² = c²

Substituting the given relations, we have ...

  a² +(2a-1)² = (2a+1)²

  a² +4a² -4a +1 = 4a² +4a +1

  a² -8a = 0 . . . . . . write in standard form

  a(a -8) = 0 . . . . . . factor

  a = 0 or a = 8

We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...

  c = 2(8) +1 = 17

The hypotenuse is 17 cm.

__

Additional comment

You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.

In linear equation, 22.5 kilometer  is Shaq from his original starting point.

What is linear equation?

Shaq is he climbs up on the side of a mountain = 4 1/2 = 9/2

  then he climbs down = 5 kilometer

Shaq from his original starting point = 9/2 * 5

                                                          = 45/2 = 22.5 kilometer

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The correct option A, 266. 9 cm²;  total surface area of the cone given in figure is found as 266.9 sq cm.

For the given question.

Put values -

Total surface area = πr (h + r)

Total surface area = 3.14 x 5 (12 + 5)

Total surface area = 3.14 x 5 x 17

Total surface area = 266.9 sq cm.

Thus, total surface area of the cone given in figure is found as 266.9 sq cm.

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