Perform the indicated operation numbers be sure to express your answer in reduced form

We know that for any number of mutually exclusive events, we have the formula:

In this case, we have that P(A)=0.60 and P(B)=0.30, then:

Therefore, P(A or B) =0.90

If we know the confidence interval for the proportion, the point estimate will be at the center of this interval.

Then, we can calculate the point estimate p as the average between the boundaries of the interval:

The margin of error can be calculated, knowing the interval, as half the difference between the upper boundary and the lower boundary of the interval:

The margin of error is 0.04. This margin of error is also the absolute difference between any boundary of the interval and the point estimate.

If the town's population is 31,526, the best estimate for the number of people who

would support the bike lanes is to use the point estimate as the proportion:

Answer:

a) The point estimate is p=0.61

b) The margin of error is MOE = 0.04

c) The best estimate is X=19231

Explanation

Step 1

convet the mixed numbers into simple fractions

remember

then

Step 2

now, make the sum to find the total amount

I hope this helps you

ANSWER

• (g o f)(x) = ,16x² + 24x + 9

• B., the domain of g o f is all real numbers

EXPLANATION

The composition is,

This means that, to find the composition, we have to replace x with f(x) in the function g(x),

Now, replace f(x) with its expression,

We can expand this binomial squared to write it in standard form. The composition is,

As we can see, this is a polynomial function. Therefore, the domain is all real numbers.

Given:-

If a person travels 3.5 miles in 30 minutes.

To find their speed in miles per hour.

So now we solve using the formula,

Substituting the known values. we get,

Now we solve for speed. so we get,

So the required speed is 7miles/hr.

Johann uses 42 +7 to represent the number of players who are on teams.

Explain what 42÷7 means.

_______________________________

42 +7 = the number of players who are on teams

42 = he number of players who are on teams minus 7

42 players

________________________

Dividing by 7 (the number of player per group)

Each team has 7 players

_____________

The area, in square inches, of the painted face of the brick is; 144 in²

The area of a square is given by;

A = L²

where;

L is the length of the side of the square

The sides of a square all have the same length, and as such we just need to find the length of one side.

The length of the side of the square here is the distance between two vertices, which can be calculated as

L = √[(x₂ - x₁)² + (y₂ - y₁)²]

However, to avoid long process, since it is a square, we can use subtraction of coordinates to get the side length which is gotten by using the first 3 coordinates;

Horizontal length = (6 + 6) = 12

Thus;

Area = L² = 12² = 144 in²

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To solve the exercise it is easier to convert all the given points to decimals. So,

Then,

*The point closest to the benchmark 1 is at 0.9.

*The point closest to the benchmark 0 is 0.1.

*Ordering these points from least to greatest you have:

SOLUTION:

Step 1:

In this question, we are given the following:

Suppose that you decide to buy a car for $32,635, including taxes and license fees.

You saved $9,000 for a down payment and can get a four-year car loan at 6.31%.

Find the monthly payment and the total interest for the loan.

Step 2:

In this question, we are given:

Cost of the car = $ 32, 635

Down payment = $ 9000

Principal on the Car loan = $ ( 32,635 - 9,000 ) = $ 23, 635

Rate = 6. 31%

Using the PMI Formulae, we have that:

Solution:

Given:

To find the product, we multiply the terms in the second parentheses by each term in the first parentheses.

Thus, we have

Hence, the product of the complex numbers is

The correct option is B

Coterminal angles are different angles that have the same terminal side.

A positive angle has one turn more around so it has a measure of 100°+360° = 460°.

A negative angle will have a measure that is represented in clockwise rotation and be equal to 100° - 360° = -260°.

We can sketch an angle of measure 100°, a positive coterminal angle and a negative coterminal angle as:

As given by the question

There are given that the point

Now,

First, break the point

So,

According to the above point, there are showing 3 in the denominator

So, between 0 and 1 divide 3 parts in the number line

Then,

[tex]\huge\red{\mid{\underline{\overline{\textbf{EQUATION AND ANSWER}}}\mid}}[/tex]

_________________

Let's solve this equation using rates,

Unit Rate - A unit rate means a rate for one of something.

Cross Multiplication - In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.

_________________

Now that we understand the definition we can further solve this equation

[tex]\large\red{\mid{\underline{\overline{\textbf{Values}}}\mid}}[/tex]

[tex]165[/tex] [tex]km[/tex] ⇒ [tex]1.5[/tex] [tex]hr[/tex]

[tex]x\\[/tex] [tex]km[/tex] ⇒ [tex]2.2[/tex] [tex]hr[/tex]

Now we will use cross-multiplication to solve this equation

[tex]\large\red{\mid{\underline{\overline{\textbf{Equtation}}}\mid}}[/tex]

[tex]165 \cdot 2.2\\x\cdot1.5[/tex]

Once solving this equation we get

[tex]1.5x=363[/tex] [tex]km[/tex]

Divide both sides by [tex]1.5[/tex]

[tex]x=242[/tex] [tex]km[/tex]

[tex]\large\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}[/tex]

The train would've traveled a total of 242 km in 2.2 hours.

Since the tax on the room is given by the function:

T(x)=0.06x+45

And x(cost in dollars of the room) is given= $120, you just have to subtitue x=120 on the function

T(120)=0.06(120)+4.5

T(120)=7.2+4.5

T(120)=11.7

So, the tax in dollars would be $11.7

y=3x+1 (1)

y=5x-3 (2)

To solve this system, we can use the equalize method:

3x+1=5x-3

3+1=5x-3x

4=2x

x=4/2

x=2

Now, substitung x=2 in y=3x+1

y=3(2)+1

y=6+1

y=7

Then, the solution to this system of equation would be: (2, 7)

We can formulate an expression for the surface area of the attic like this:

The area of a triangle is given by the following formula:

Where b is the base and h is the height of the triangle.

The area of a rectangle is given by the following formula:

Where w is the width and l is the length of the rectangle.

In this case, the attic has three rectangular faces, all of them have a width of 45 ft. two of them have a length of 25 ft and one has a width of 40 ft, then we can calculate the areas of these faces like this:

By summing up these areas, we get the area of the rectangular faces:

From this expression, we can factor 45 to get:

For the two triangular faces, their height equals 15 ft and the length of the bases equals 40 ft, then their areas are:

By summing them up, we get the area of the triangular faces:

By summing the area of the rectangular faces and the area of the triangular faces, we get the expression to calculate the total surface area of the attic, like this:

Then, the net Linda draw is correct. The first term of Linda's expression 45(40+25+25) is correct. The second term of Linda's equation missing a factor of 2. The surface area of Linda's attic is 4650 square feet

Hangalakani leaves his work for home at 3.30 PM .

Hangalakani starts his work at 7.30 am.

He works for 6.5 hours.

He then takes a lunch break for 1 hour .

He then takes tea break for about 30 minutes = 0.5  hour

Total time spent at work = 6.5 + 1 + 0. 5 = 8 hours.

So if he starts work at 7.30 then he will end at

7.30 am + 8 hours  = 3.30 pm in the afternoon .

Now the manager says that they need 246 bags while Hangalakani calculated they need 245.37 bags of cement.

The manager is correct because bags of cement are not sold as a part or decimal .  The number of bags that can be bought must be a whole number.

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Answer:

n = 24

Explanation:

The initial expression is:

n + 7 = 31

So, to solve the equation, we need to subtract 7 from both sides:

n + 7 - 7 = 31 - 7

n = 24

Therefore, the solution is n = 24

The exponential equation given is,

Given the points

Therefore, the values for k and b will be resolved graphically.

Let us now plot the graph using a graphical calculator

From the graph,

Final answers

a) The mean of the data set is 4.61

The median of the data set is 4.35

The mode of the data set is 1.9

b) Sample standard deviation is 2.58

Coefficient of Variation is 55.96

Range is 6.7

Given,

The data set;

1.9, 2.8, 5.7, 4.8, 1.9, 8.6, 3.9, 7.3

a) We have to find the mean, median and mode

Order the data first;

1.9, 1.9, 2.8, 3.9, 4.8, 5.7, 7.3, 8.6

Now,

The data is of even number, so;

Median = [(n/2) + (n/2 + 1)] / 2

Here,

n/2 = 8/2 = 4th term

n/2 + 1 = 5th term

Then,

Median = (3.9 + 4.8) / 2 = 8.7/2 = 4.35

The mode of the given data is 1.9

Here it is the formula to calculate it:

x = √(∑(xi - x)²/n-1))

sₓ = √(46.85/7) ≈ 2.58

CV is the quotient between sample Standard deviation over Mean and it is used to make comparisons.

CV = sₓ/x × 100 = 2.58/4.61 x 100 = 55.96

The difference between the highest and the lowest value of this sample

8.6 - 1.9=6.7

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Given:

a function is given as h(x) = -2x + 9

Find:

we have to evaluate the function at x = -2 , 0 and 5.

Explanation:

when x = -2

h(-2) = -2(-2) + 9 = 4 + 9 = 13

when x = 0

h(0) = -2(0) + 9 = 0 + 9 = 9

when x = 5

h(5) = -2(5) + 9 = - 10 + 9 = -1

Therefore, the values of given function h(x) are 13, 9 , -1 at x = -2, 0 , 5 respectively.

To find the constant of proportionality of the equation y = rx, from the values of the given table, just calculate the quotient r = y/x, where x and y can be any pair of values of the table.

For x = 3 and y = 30:

r = 30/3

r = 10

Hence, the constant of proportionality is

r = 10

a) in term

b)subtraction

c) N/A

d) 4

Explanation

a term is a single mathematical expression , it can be a number, a variable or a combination, the terms are separated by the symbols + or -

for example:

in

there are 3 expression , so

Step 1

check the expression

it has only a term ( a fractions)

so

a)the number of terms is : 1

Step 2

b)first thing to do to term 1

PEMDAS means the order of operations for mathematical expressions involving more than one operation. It stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.so

we need to P ( break the parenthesis)

to do that,

do the SUBTRACTION

Step 3

c) as there is not term 2

N/A

Step 4

simplify the expression: folloing the PEMDAS order

so

d) 4

i hope this helps you

The expression represents the number of COVID deaths since March 1 2020 minus 100,000 deaths.

GIven data :

The coordinates of ferris wheel is, (2,7).

The coordinates of exit is (4,0).

they have given exactly half way so let us use the midpoint formula,

the mid point formula is,

take the coordinates as

let us subsitute in eqiuation (1),

thus the coordinates of parking spot is (3,3.5).

Answer

Option 1 is correct.

The triangle is an isosceles triangle.

Explanation

Noting that the sum of angles in a triangle is 180°.

We can solve for each of the angles in this triangle to obtain the type of triangle it is.

The angles of the triangle are 2x, (3x - 15) and (7x + 15)

2x + 3x - 15 + 7x + 15 = 180°

2x + 3x + 7x - 15 + 15 = 180°

12x = 180°

Divide both sides by 12

(12x/12) = (180°/12)

x = 15°

We can then solve for the measures of the three angles now

2x = 2 (15°) = 30°

3x - 15 = 3 (15°) - 15° = 45° - 15° = 30°

7x + 15 = 7 (15°) + 15° = 105° + 15° = 120°

So, the angles of the triangle are 30°, 30° and 120°

A tringle that has two of its angles equal to each other is called an isosceles triangle.

Hope this Helps!!!

Given data:

The x-intercepts given are 4 and -2.

Substitute 0 for y in the first option.

Substitute 0 for y in the second option.

Substitute 0 for y in the third option.

Substitute 0 for y inlast option.

Thus, option (D) is correct.

a) the cost of the house is 96000 and the down paidment is the 20% so we can use a rule of 3 to solve it so:

so the equation will be:

b) her income is $4000 so the 28% will be:

so the equation will be:

c) the equation that models a loan is:

So we replace the princeiple and find monthly paidment.

d)The total monthly paidment will be:

SOo the answer is NO she can't afort to buy this house

The factors are 1 , -1 twice and 3

Here, we want to find the rational roots of;

We can start here by trying out simple numbers if we cannot factorize the polynomial at a go

The given polynomial here can be factorized

We can express it as;

So what we have here is to simply equate individual linear factor to zero

Thus, we have the factors as;

1 , -1 twice and 3

Let's begin by identifying key information given to us:

51.2% = 51.2/100