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Answer

• Exponential model

Explanation

The exponential model equation can be given by:

where C is the initial value, r is the rate of growth and t is the time.

We can get the initial value by evaluating in the table when t = 0. In this case the value A(0) = 13.60. Then our equation is:

Now we have to get r by choosing any point and solving for r. For example, (3, 26.56). By replacing the values and solving we get:

Thus, our rate is 0.25, and we can add it to our equation:

Finally, we evaluate t = 8:

the three integers are 215, 12 and 153

Explanation:

Let the three integers = x, y, and z

x + y + z = 380 ....equation 1

The sum of the first and second integers exceeds the third by 74:

x + y - 74 = z

x + y - z = 74 ....equation 2

The third integer is 62 less than the first:

x - 62 = z ...equation 3

subtract equation 2 from 1:

x -x + y - y + z - (-z) = 380 - 74

0 + 0 + z+ z = 306

2z = 306

z = 306/2

z = 153

Insert the value of z in equation 3:

x - 62 = 153

x = 153 + 62

x = 215

Insert the value of x and z in equation 1:

215 + y + 153 = 380

368 + y = 380

y = 380 - 368

y = 12

Hence, the three integers are 215, 12 and 153

Cos a = adjacent side / hypotenuse

Where:

a= angle = 37°

adjacent side = 20

Hypotenuse = x (the longest side , AC)

Replacing:

Cos (37)=20/ x (option B)

Let p be the number of pavilion seats and l be the number of lawn seats. Since there were sold 1400 tickets, we can write

and since the total money was $32000, we can write

Then,we have the following system of equations

Solving by elimination method.

By multiplying the first equation by -30, we have an equivalent system of equation

By adding these equations, we get

then, l is given by

Now, we can substitute this result into the equation p+l=1400 and obtain

which gives

Then, How many tickets of each type were sold? 400 for pavilion seats and 1000 for lawn seats

How many pavilion seats were sold? 400 tickets

To complete the table you evaluate the equation by the given value of x to find the corresponding value of y:

To put those (x,y) points in the plane;

the frist coordinate x is the number of units you move to the left (if x is negative) or to the right (if x is positive)

the second coordinate y is the number of units you move down (if y is negative) or up (if y is positive)

Then, using the points (0,4), (4,8), (8,12), (12,16) and (16,20) you get the next graph for y=x+4:

ANSWER

1987 and 1995

EXPLANATION

The revenue is modeled by:

To find the years that the revenue was $722 million, we have to solve for x when R is 722.

That is:

We can split the absolute value equation into two different equations because the term in the absolute value is equal to both the positive and the negative of the term on the other side of the equality.

That is:

Solve for x in both:

That is to say 7 and 15 years after 1980.

Therefore, in the years 1987 and 1995, the revenue was $722 million.

If two litters of soda cost $2.50;

Then, a dollar would buy;

a) f(0) = -1

b) f(1) = 1

c) f(4) = 7

d) f(5) = 121

Explanation:

. Since for every value between -2 (excluded) and 4 (included)

~ 0 , 1 and 4

You have to use the first equation

=> f(0) = 2 * 0 - 1 = -1

=> f(1) = 2 * 1 - 1 = 1

=> f(4) = 2 * 4 - 1 = 7

. For values between 4 (exclude) and 5(included)

~ 5

You have to use the second equation

=> f(5) = 5^3 - 4 = 121

Answer:

14 units

Explanation:

If quadrilaterals HGEF and DCAB are similar, then the ratio of some corresponding sides is:

Substitute the given side lengths:

The measurement of line EG is 14 units.

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following system of equations:

We solve by elimination:

Now, replacing z in (4):

Then, replacing z and x in (1):

As the triangle AEF has 2 angles with the same measure, triangle AEF is isosceles.

If B is the midpoint of AC, this means that point B divides the line AC exactly into 2 equal parts AB and BC, therefore,

Answer A

Thus, if AB = 28, BC = 28 too.

Answer B: Therefore, AC = 56

The solution is (x,y) = (0,2)

The expression is simplified to negative 23 over 14 times j plus negative 1 over 15. Option C

An algebraic expression can be defined as an expression mostly consisting of variables, coefficients, terms, constants and factors.

Such expressions are also known to be composed or made up of some mathematical or arithmetic operations, which includes;

From the information given, we have that;

Substitute the values

- 1/7j + 2/5 - 3/2j - 7/15

collect like terms

- 1/7j - 3/2j + 2/5 - 7/15

-2j - 21j /14 + 6  7 /15

-23j/14 + -1/15

Hence, the correct option is negative 23 over 14 times j plus negative 1 over 15

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As per given by the question,

There are given that a table of x and f(x).

Now,

The genral for of the equation is,

Then,

For the value of x and f(x).

Substitute 0 for x and -2 for f(x).

So,

Now,

For the value of b,

Substitute 1 for x and -1/3 for f(x),

So,

Now,

Put the value of a in above result.

So,

Now,

Put the value of a and b in the general form of f(x).

Hence, the exponential function is ,

The cost of an order is proportional to the number of tickets if the relation between them is constant.

Then, if we order 1 ticket the cost will be $7 + $3 = $10

And if we order 2 tickets, the cost will be $7*2 + $3 = $17

So, the relation between cost and the number of tickets is:

For 1 ticket = $10 / 1 ticket = 10

For 2 tickets = $17/ 2 tickets = 8.5

Since 10 and 8.5 are different, the cost of an order is not proportional to the number of tickets ordered.

Answer: they are not proportional

So first of all we should write the three equations in slope-intercept form. This will make the problem easier to solve. Remember that the slope-interception form of an equation of a line looks like this:

Where m is known as the slope and b the y-intercept. The next step is to rewrite the second and third equation since the first equation is already in slope-intercept form. Its slope is 4 and its y-intercept is -1.

So let's rewrite equation (ii). We can begin with substracting 4 from both sides of the equation:

Then we can divide both sides by 8:

So its slope is -1/4 and its y-intercept is -1/2.

For equation (iii) we can add 8x at both sides:

Then we can divide both sides by 2:

Then its slope is 4 and its y-intercept is -1. As you can see this equation is equal to equation (i).

In summary, the three equations in slope-intercept form are:

It's important to write them in this form because when trying to figure out if two lines are parallel or perpendicular we have to look at their slopes:

- Two lines are parallel to each other if they have the same slope (independently of their y-intercept).

- Two lines are perpendicular to each other when the slope of one of them is the inverse of the other multiplied by -1. What does this mean? If a line has a slope m then a perpendicular line will have a slope:

Now that we know how to find if two lines are parallel or perpendicular we can find the answers to question 4.

So for part (a) we must find the pairs of parallel lines. As I stated before we have to look for those lines with the same slope. As you can see, only lines (i) and (iii) have the same slope (4) so the answer to part (a) is: Lines (i) and (iii) are parallel to each other.

For part (b) we have to look for perpendicular lines. (i) and (iii) are parallel so they can't be perpendicular. Their slopes are equal to 4 so any line perpendicular to them must have a slope equal to:

Which is the slope of line (ii). Then the answer to part (b) is that lines (i) and (ii) are perpendicular to each other as well as lines (ii) and (iii).

Given

An independent third party found the cost of a basic car repair service for a local magazine.

The mean cost is $217.00 with a standard deviation of $11.40.

To find: The repair costs which would be considered an “unusual” cost.

Explanation:

It is given that, the mean is 217.00, and the standard deviation is 11.40.

Consider, the distribution as a Normal distribution.

Then, the first range is defined as,

And, the second range is defined as,

Hence, the answer is option a) 192.53 since it does not belongs to the above ranges.

Since we know the ratio is 2:1, then to find the number of students who like iced tea we convert the ratio to a fraction:

this means that one of two students preferred iced tea.

To find the number of students who prefer iced tea we multiply the total number of students by the fraction, then:

Since we can't have a fraction of a student, we conclude that 19 students prefer iced tea and 20 prefer lemonade.

In the given equations, the value of variables are:

So, solving for variables:

(A) 1/5a = -2:

(B) 8 + b = 7.8:

(C) -0.5 = -2c:

Therefore, in the given equations, the value of variables are:

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We need to remember that when two variables are in an inverse relationship, we have that, for example:

In this case, we have an inverse relationship, and we have that when x = 1, y = 12.

Therefore, we have that the correct relationship is:

In this relationship, if we have that x = 1, then, we have that y = 12:

Therefore, the correct option is the second option: y = 12/x.

Answer:

y=4/3x+3

Step-by-step explanation:

we know that slope intercept form is y=mx+b, where m is the slope and b is the y intercept

for 4x-3y=9, we have to isolate y

we subtract 4x to both sides to get

-3y=-4x+9

to get y alone, we divide both sides by -3

y=4/3x+3

Answer:

Y=4/3x-3

Step-by-step explanation:

Y=4/3x-3

the other guy had the right idea but the two negatives make a positive!

Option C

Points: A, B, C, D

Line segments: AB, AD, AC, DC, BC

The question requires us to find how many ways we can select 6 children from a total of 46.

The formula for combinations is given as follows;

Where n = total number of children, and r = number of children to be selected. The combination now becomes;

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equations

STEP 2: Define the point that is the solution for the given functions on the graph

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

STEP 3: Determine the solution for the system of equations

It can be seen from the image below that the two lines intersect at the origin and hence they are given as the solutions to the given system of equations.

Hence, the solutions are:

Answer:

5.124

Explanation:

Given the following sides

AB = 6.5cm

BC = 4.0cm

Required

AC

Using the pythagoras theorem;

AB^2 = AC^2 + BC^2

6.5^2 = AC^2 + 4^2

42.25 = AC^2 + 16

AC^2 = 42.25 - 16

AC^2 = 26.25

AC = \sqrt{26.25}

AC = 5.124

Hence the actual length of AC to 3dp is 5.124

Solution:

If A is true, B is true, and C is true, then:

we can conclude that the correct answer is:

TRUE

Problem

144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?​

Solution

for this case we can do the following proportional rule:

4/144 = x/100

And solving for x we got:

x= 100 (4/144)= 2.77

So between 2 and 3 grape fruits are expected