Determine whether the relation defines a function, and give the domain and range.{(-8, 7),(4.7).(-9, 1);

Answers in bold

[tex]\begin{array}{|c|c|} \cline{1-2}k & P(X = k)\\\cline{1-2}0 & \boldsymbol{0}\\\cline{1-2}1 & \boldsymbol{0}\\\cline{1-2}2 & \boldsymbol{0.04}\\\cline{1-2}3 & \boldsymbol{0.18}\\\cline{1-2}4 & \boldsymbol{0.41}\\\cline{1-2}5 & \boldsymbol{0.37}\\\cline{1-2}\end{array}[/tex]

Note: The P(x) values for k = 0 and k = 1 are not actually zero, but they are small enough that they round to 0 when rounding to two decimal places.

=======================================================

Explanation:

I used a spreadsheet to compute the values in bold.

The specific command is called BINOMDIST

The template is BINOMDIST(k,n,p,0)

Let me know if you have any questions about how to use that function in a spreadsheet.

Also, I used the function called ROUND to round each value to 2 decimal places.

Example calculation

=ROUND(BINOMDIST(4,5,0.82,0),2)

This calculates the result of 0.41 and it corresponds to the value k = 4

Don't forget about the equal sign up front when computing these commands in the spreadsheet. Otherwise, it'll stay as text form.

-------------------

If you want to use a TI83 or TI84 calculator, then press the button labeled "2nd". Then press the button labeled "VARS". Scroll down until you reach "binompdf".

The template is binompdf(n,p,k)

So for example, type in binompdf(5,0.82,4) to get the P(X) value for k = 4

If you aren't able to access a spreadsheet or a TI83/84 calculator, then search out "binomial distribution calculator" and there are plenty of free ones to pick from.

In my opinion, a spreadsheet is the best option since the given data is already in tabular form. Also, many real world situations and careers use spreadsheets everyday.

3xy-5x+9y-45

Step-by-step explanation:

Step by Step Solution

STEP1:STEP2:Pulling out like terms

 2.1     Pull out like factors :

   3y - 15  =   3 • (y - 5) 

Equation at the end of step2: (x • (3y - 5)) + 9 • (y - 5) STEP3:Equation at the end of step 3 x • (3y - 5) + 9 • (y - 5) STEP4:Trying to factor a multi variable polynomial

 4.1       Split       3xy-5x+9y-45 

 4.1       Split       3xy-5x+9y-45 

             into two 2-term polynomials

             -5x+3xy   and    +9y-45

             This partition did not result in a factorization. We'll try another one:

             3xy-5x   and    +9y-45

             This partition did not result in a factorization. We'll try another one:

             3xy+9y   and    -5x-45

             This partition did not result in a factorization. We'll try another one:

             3xy-45   and    +9y-5x

             This partition did not result in a factorization. We'll try another one:

             -45+3xy   and    +9y-5x

             This partition did not result in a factorization. We'll try 

By identifying the first values of each point in the graph, we saw that the domain of the relationship is:

D: {-3, -1, 1, 3, 6}

A relation can be defined by a set of points (x, y), where the values of x are the values in the domain and the values of y are the values in the range.

Here we have the graph of a relation, and we can see the points:

(-3, 3)(-1, -1)(1, 2)(3, 0)(6, -2)

The domain of the graphed relationship will be the set of the first values of each of these points, then we can see that the domain is:

D: {-3, -1, 1, 3, 6}

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Answer:

A - $4060

B - 32 copies

Step-by-step explanation:

A -

P = 1900 + 90c

P = 1900 + 90(24)

P = 1900 + 2160

P = 4060

Total if Ann sold 24 copies: $4060

B -

1900 + 90c = 4780

90c = 4780 - 1900

90c = 2880

c = 32

Total copies: 32

Problem

Solution

For this case we can find the remain angle with this operation:

180 -39-90= 51º

And then we can use the sines law and we can do this:

And solving for x we got:

x= 14*sin(39)/sin (90) = 14*sin 39= 8.81

The money was invested for 8.60 years

Given:

Amount in the savings account = $2750

Amount invested = $2000

rate = 4.36% = 0.0436

To find:

the time it took to invest the money to obtain the amount in the account

The investment was done using simple interest. So to get the time, we will apply simple interest formula

Answer:

indetermination

Step-by-step explanation:

Hope this helps

The price will increase if number of students increase

By multiplying the  number of students with cost

Number of students varies in this example

The expression shown for trip amount is c = 10+13x.

The cost for 10 students is 140

The cost for 17 students is 231

Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.

1). The price will increase if number of students increase.

2). By multiplying the  number of students with cost.

3). Number of students varies in this example.

4). Let the number of students

Then total amount(c) of the trip is given by

c = 10+13x  ------ equation (1)

5). Put x = 10 in equation (1)

c = 10+13(10)

c = 140

6).  Put x = 17 in equation (1)

c = 10+13(17)

c = 231

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Answer:

(-7, 5) is correct.

Step-by-step explanation:

[tex]2x + 3y = 1[/tex]

[tex] - 2x - y = 9[/tex]

Add these two equations, and then solve for y.

[tex]2y = 10[/tex]

[tex]y = 5[/tex]

Substitute this value of y into 2x + 3y = 1, and solve for x.

[tex]2x + 3(5) = 1[/tex]

[tex]2x + 15 = 1[/tex]

[tex]2x = - 14[/tex]

[tex]x = - 7[/tex]

So (-7, 5) is the correct solution.

Step 1:

Question 1.1

Arrive time = 7:30

Departure time = 17:00

h (9:30) > 7

Garage B is cheaper

Question 1.2

Arrive time = 8:23

Departure time = 10:53

The time spent by issac and his friends is between 2 < h < 4

Since h = 2:30

Answer R11.00

Question 1.3

Karabo uses Garage B

Time spent is 4 < h < 6

The logarithm of the number 6.5 is log(6.5) = 0.8129

This is the number that represents the power by which a fixed number known as the base must be raised to result in another number.

The number is given as

6.5

The logarithm of the number is then represented as

log(6.5)

There are several ways to calculate the logarithm of the number

Some of which are:

In this case, the only way is by using a calculator

Using a calculator, we have

log(6.5) = 0.8129

Hence, the logarithm of 6.5 is 0.8129

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Fraction - A,C,D is the incorrect option that means 18 >17 is the correct option B

Equivalent fractions with the same denominator should be used to compare fractions with different denominators. Comparing fractions: If the denominators are the same, the numerators can be compared. The greater fraction is the one with a larger numerator.

Now, comparing the fraction,

first of all write the fraction in simplest form then cross multiplication.

1.   [tex]\frac{29}{35} < \frac{20}{30}[/tex]

[tex]\frac{29}{35} < \frac{2}{3}[/tex]

87 < 70

This option is wrong.

2.    [tex]\frac{18}{34} > \frac{16}{32}[/tex]

[tex]\frac{9}{17} > \frac{1}{2}[/tex]

18 >17

This option is correct.

3.    [tex]\frac{14}{21} > \frac{17}{24}[/tex]

[tex]\frac{2}{3} > \frac{17}{24}[/tex]

48 > 51

This option is wrong.

4.   [tex]\frac{20}{15} < \frac{28}{23}[/tex]

[tex]\frac{4}{3} < \frac{28}{23}[/tex]

92 < 84

This option is wrong.

Hence, option b is correct.
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The perimeter is 54 inches

The area is 108 square inches

The perimeter of the triangle is:

15 in + 15 in + 24 in

= 54 in

The area is:

(1/2)(24)(9)

= 108 sq. in

Given:

Given the equation

Required: Point at which the equation crosses the y axis.

Explanation:

At y -axis, the value of x is zero. Substitute 0 for x in the equation of y.

So, the point at which the equation cross the y-axis is (0, 5).

Final Answer: The point at which the equation cross the y-axis is (0, 5).

The number of horse is 1, goat is 2 and sheep is 3 a man has.

The problem we are dealing with is related to the linear equation which is referred to as the algebraic condition where each term has an exponent of 1 and when this condition is graphed, it continuously comes about in a straight line.

Now w consider x to be the number of sheep, y to be the  number of  goats, and z to be the number of horses the man owns.

the actual equation for the total number of animals he owns  is :

x+ y+ z

according to the first condition:

that all sheep bar three, means

y+ z=3

similarly, for the other condition, it will be

x+ z=4   and x+ y=5

Now we adding the three  equations:

y + z +x +z +x +y=5+4 +3

2(x+y+z)=12

x+y+z=6........equation(1)

As x + y = 5

Put this in equation in (1), we get

x+y+z = 6

5 + z = 6

z = 1

x + z = 4

x + y + z = 6

y + 4 = 6

y = 2

Now we know

x + y + z = 6

x + 1 + 1 = 6

x = 4

So simplifying the other equation  we get, that the number of horse is 1, goat is 2, and sheep is 4.

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Answer:

y = 1/6x + 1

Step-by-step explanation:

Add 2x to both sides of the equation.

12y = 12 + 2x

Divide each term in 12y = 12 + 2x by 12 and simplify.

y = 1 + x/6

Write in y=mx+b form.

y = 1/6x + 1

The critical value (tα/2) for a 95% confidence interval for the sample size 15 is 2.009.

We have to find the critical value tα/2 for 95% confidence interval, we are given the sample size.

First we will find the alpha value to get the critical value.

=100%-95%

=1-0.95

=0.05

α=0.05

α/2=0.05/2

α/2=0.025

degrees of freedom(df)= n-1=15-1=14

We will use degrees of freedom and α/2 values to find the critical value that is tα/2.

By using the t table we get the critical value  of tα/2=2.009.

Therefore, the critical value for 95% confidence interval with sample size of 15 is 2.009.

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Answer:

7 hours

Step-by-step explanation:

25x + 25 = 200.

25x = 175

175/25 = 7.

Answer:

25 + 35h = 200

and

h = 5

(5 hours)

Step-by-step explanation:

you have 200.

costs:

35 per hour

and

25 fee

h will represent the total hours spent renting a boat

25 + 35h = 200

now we will do inverse operations

subtract 25 from both sides

35h = 175

now divide both sides by 35

h = 5

ANSWER

EXPLANATION

Given:

Desired Outcome:

1. Domain

2. Range

Determine the domain of the function

Note: We want to include only input values that do not require the denominator to be 0 when there is a denominator. As a result, we'll set the numerator to 0 and solve for x.

We'll now remove 4 from the domain. All of the answers are real numbers x > 4 or x < 4. We will also use Union notation to combine the two sets.

That is:

Determine the range of the function

Set x to 4 to find y

We'll also remove 3 from the range. All of the answers are real numbers y > 3 or y < 3. We will also use Union notation to combine the two sets.

That is:

Answer:

7,002

Step-by-step explanation:

The product is the answer of a multiplication problem. You just have to multiply the numbers by using the techniques to solve it. Hope this helps!

Solution

- The probability of him getting 1 queston correctly given tahat there is only one correct option out of 4 optins,

- Since here are questions, it implies that there are multiplye trials the student has.

The final amount after 3 years compounded semi-annually is $3709.20

To solve this problem, we simply need to use compound interest formula which is given as

[tex]A = p(1 + \frac{r}{n})^n^t[/tex]

where

Lets substitute the values into the formula and solve

[tex]A = p(1 + \frac{r}{n})^n^t\\A = 3000(1 + \frac{0.072}{2})^2^*^3\\ A = 3709.20[/tex]

The amount accrued 3 years from now is $3709.20

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A sequence is a series that follows the sum general rule. The sum of the given sequence  ∑(n=1 to 4) [tex]u_{n}[/tex] is {u₁ + u₂ + u₃ + u₄ + u₅}.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

As per the given series,  ∑(n=1 to 4) [tex]u_{n}[/tex]

The sign ∑ is used to sum the terms of the series in the given interval.

Given that n = 1 to 4

Substiute n = 1 into  [tex]u_{n}[/tex] ⇒ u₁

Substiute n = 2 into  [tex]u_{n}[/tex] ⇒ u₂

Substiute n = 3 into  [tex]u_{n}[/tex] ⇒ u₃

Substiute n = 4 into  [tex]u_{n}[/tex] ⇒ u₄

So, the sum is {u₁ + u₂ + u₃ + u₄ + u₅}.

Hence "A sequence is a series that follows the sum general rule. The sum of the given sequence  ∑(n=1 to 4)".

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Answer:

She worked for 4 hours and made 16 shirts (work below)

Step-by-step explanation:

let h = number of hours worked

and s = number of shirts made :]

28h+2s = 144

4h = s

28h+8h=144

h=4, s=16

:]

Let n represent the number of nights

Cost to travel to Bali:

The cost of flight is constant so we simply add it to the cost of hostel per night times the number of nights

Cost to travel to Paris:

We can divide the given figure into different rectangular faces:

Faces 1 and 3 have the same measure, also 2 and 4, and faces 5 and 6.

Faces 1 and 3 have the following dimensions: L=100cm W=50cm.

Faces 2 and 4 have the following dimensions: L=100cm W=35cm.

Faces 5 and 6 have the following dimensions: L=50cm W=35cm.

The surface area of a rectangular face is given by:

Thus, the surface areas of the given faces are:

The surface area of the net is the addition of all of these surface areas:

Given:

Required:

To find the probability that the dart land will be in the shaded region.

Explanation:

Area of the circle is given by the formula:

Where r = radius

Thus the area of the circular region

The area of the square is given by the formula:

Thus the area of the given square

The probability of an event is given by the formula:

The probability that the dart land will be in the shaded region

Thus probability

Final answer:

Thus the probability that the dart land will be in the shaded region is 0.349.

Answer:

Five times the quantity x plus four equals x minus y.

Step-by-step explanation:

Probably the most confusing part is that parenthesis are pronounced "the quantity"

Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour.

The modelled equation representing the above scenerio is -

y = 3.5 + 1.75x

where (x) represents the number of hours for which the car is parked.

Maximum amount with Jose = $19.25

Therefore -

3.5 + 1.75x ≤ 19.25

1.75x ≤ 15.75

x ≤ 9 hours       [Maximum time]

Minimum amount with Jose = $12.25

3.5 + 1.75x ≥ 12.25

1.75x ≥ 8.75

x ≥ 5 hours               [Minimum time]

Therefore, Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.

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If Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years

The deposited amount = $500

The simple interest = 7.5%

The interest she earned = $225

Then the final amount = The deposited amount + The interest she earned

= 500+225

= $725

The equation of simple interest

A = P(1+rt)

Where A is the final amount

P is the initial amount

r is the interest rate

t is the time period

725 = 500(1+(7.5/100)×t)

(1+0.075t) = 1.45

0.075t = 0.45

t = 0.45/0.075

t = 6 years

Hence, if Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years

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