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Using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.

So, a number of adults and children who purchased the tickets:

Now, the equation can be:

Now, the second equation will be:

43.85a + 15.95c = 338.85

Now, substitute a = 9 - c in equation (2) as follows:

Hence:

Then:

Therefore, using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.

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Given the functions:

By definition, (f+g)(x) is equivalent to:

Finally, using the expressions for f and g:

1) Gathering the data

E (5,1.5) Circumcenter

H (4.3,2.3) incenter

I (3.6, 2.6) is the centroid.

2) Examining the figure we can see point C and B as the vertices of the

triangle, to find the radius let's use the distance formula between point E and C

E(5, 1.5) and C(3,5)

Since the radius is a line segment from the origin to the circumference then the distance BC = radius of the circumscribed triangle

Radius = 2.28

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Given,

The points which the line passes, (x₁, y₁) = (7, 6)

Slope of the line, m = 0

We have to find the equation of the line:

We know that,

y - y₁ = m(x - x₁)

So,

y - 6 = 0(x - 7)

y - 6 = 0

y = 6

That is,

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

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Answer:

C

Explanation:

Given:

Volume of a cylinder (V) = 4pi cubic units

To find:

Base area(A) and height(h)

Recall that the volume of a cylinder(A) is usually given as;

So let's go ahead and try each of the options and see which gives us 4pi on the left-hand side as we have on the right-hand side for Volume.

For option A;

We have that A = 1 and h = 2, so we'll have;

For option B;

We have A = 2pi and h = 1, so we'll have;

For option C;

We have A = 2pi and h = 2, so we'll have;

We can see from the above that option C is the right option.

ANSWER:

A. 15%

STEP-BY-STEP EXPLANATION:

We can determine the percentage using the following formula:

Therefore, the correct answer is A. 15%

The value of the car after 5 years is $13,500 and the value of the car after 9 years is $10,500.

According to the question,

We have the following information:

The value of the car is given by V(x) where x is the number of years.

V(x) = -1500x + 21,000

(a) Now, to find the value of car after 5 years, we will put 5 in place of x in the given expression:

V(5) = -1500*5+21000

V(5) = -7500+21000

V(5) = $13,500

(b) Now, to find the value of car after 9 years, we will put 9 in place of x in the given expression:

V(9) = -1500*9+21000

V(9) = -10500+21000

V(9) = $10,500

(c) When V(12) = 3000 then it means that the value of the car after 12 years is $3000.

Hence, the value of car after 5 years and 9 years is $13,500 and $10,500 respectively.

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To answer this question we will use the following property of sets:

(a) Since Ash has 153 cards in his collection (without any duplicates), Brock has 207 cards in his collection (also without any duplicates) and they have 91 cards in common, then:

Simplifying the above result we get:

(b) Expressing the above result using set notations:

Answer:

(a) There are 269 unique cards in between them.

(b)

Answer:

I believe the answer is g(x)=x+10

Step-by-step explanation:

it moves 4 units to the right making it positive, adding to the previous 6 units, making it move 10 units to the right

Given:

Required:

To determine the possibilities for the nature of the roots of the given equation.

Explanation:

(A)

Mean Value Theorem

Supposing that f(x) is a continuous function that satisfies the conditions below:

0. f(x) ,is continuous in [a,b]

1. f(x) ,is differentiable in (a,b)

Then there exists a number c, s.t. a < c < b and

However, there is a special case called Rolle's theorem which states that any real-valued differentiable function that attains equal values at two distinct points, meaning f(a) = f(b), then there exists at least one c within a < c < b such that f'(c) = 0.

As in our case there is no R(t) that repeats or is equal to other R(t), then there is no time in which R'(t) = 0 between 0 < t < 8 based on the information given.

Answer: No because of the Mean Value Theorem and Rolle's Theorem (that is not met).

Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.​

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

A=11,000

t=8 years

n=12

r=4.5%=0.045

substitute in the formula above

therefore

the answer is

We have to solve the equation.

We have 2 unknowns and one equation, so we can only express one in function of the other.

We already have x in function of y, so we will now express y in function of x:

Answer:

y = -x/8 + 9/8

Given

The expression is given as

Explanation

To find x, add the expression.

Answer

Hence the value of x is 8.

[tex]4x + 3x = 56\\7x = 56\\x = 56/7\\x = 8[/tex]

The answer is X=8

Step 1: Concept

You are going to apply the slope formula to find the slope of the line through each coordinate.

Step 2: Slope formula

The theorem that justifies why triangle ABC is congruent to triangle CDA is the: SAS.

The SAS theorem states that if we can show that two triangles have a pair of corresponding congruent included angles, and two pairs of corresponding sides that are also congruent to each other, then we can prove that both triangles are congruent to each other.

The triangles, ABC and CDA have:

Two pair of corresponding sides that are congruent to each other, which are AB ≅ BC, and AC ≅ CA.

A pair of corresponding included angles, which is angle 1 ≅ angle 2.

Based on the above known information, we can conclude that triangle ABC is congruent to triangle CDA by SAS theorem.

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Answer:

Substitute x = -8 into f(x).

f(-8) = 3(-8)² - 5(-8) + 20

= 3(64) + 40 + 20

= 192 + 60

= 252

Answer:

Explanation:

What we want to answer in this question is simply, the area of the room that will be painted blue if he decides he would paint exactly have the room blue

So, we need to simply get the area of the room and divide this by half

Mathematically, the area of a rectangle is the product of its two sides

Thus, we have it that the area of the room is:

Now, to get the area painted blue, we divide this by 2 as follows or multiply by 1/2

We have this as:

First, we need to know the ratio of boys to girls in Mrs. Navarro's class. There are 16 boys and 20 girls. The ratio would be 16:20.

From this given, we can choose from the options which rations are equivalent to our given ratio.

8 to 10 is a ratio that is equivalent from our given. If we scale are ratio by 2, we can get 8:10.

5:4, 8:18, and 5 to 9, however, are NOT equivalent to 16:20.

4:5 is equivalent. We just need to scale 16:20 by 4, and we will get 4:5.

10:8 is another ratio that is NOT equivalent to 16:20.

*Scaling ratios are similar to finding the lowest terms of fractions.

Solution

Using the Slope formula written above;

Therefore, the missing co-ordinate r is 5.

The first three terms of the sequence defined by the formula; Un=5n-2n³ as in the task content are; 3, -6 and -39 respectively.

It follows from the task content that the first three terms of the sequence defined by the formula be determined.

On this note, it follows that the first three terms are at; n = 1, n = 2 and n = 3 respectively.

Hence we have;

Hence, the first three terms are; 3, -6 and -39.

The first three terms of the sequence are as listed above.

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We were told that the distance from the Old North Church in Boston to Charlestown is approximately 1,410 meters.

Given that the speed of light is approximately 3 x 10 to the power of 8 meters per second and

speed = distance/time

It means that the number of seconds it took for the light to be visible in Charlestown is also the time it took the light to travel through 1410 meters

Therefore,

time = distance/speed

time = 1410/3 * 10 ^8 = 0.0000047 seconds

time = 4.7 * 10^-6 seconds

From the information available;

The population is 52% and the sample size is 7. The probability that exactly 4 of them use smartphones (if 7 adults are randomly selected) would be calculated by using the formula given;

We shall insert the values as follows;

Rounded to four decimal places, this becomes;

ANSWER:

The probability of selecting exactly 4 smartphone users is 0.2830

(-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5 as it's definition states "a relationship between two expressions or values that are not equal to each other".

A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b. a ≤ b means that a is less than or equal to b. a ≥ b means that a is greater than or equal to b.

When using interval notation, we first write the set's leftmost number, then a comma, and finally its rightmost number. Depending on whether those two numbers are a part of the set, we then enclose the pair in parentheses or square brackets (sometimes we use one parenthesis and one bracket!).

Here,

3x+4≤5

3x≤1

x≤1/3

(-∞,1/3]

As it's definition states "a relationship between two expressions or values that are not equal to each other" (-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5.

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First let's see how many hours are in a year:

We found that 1 year has 8769 hours, then if we lived 1,000,000 hours, we have to divide it by 8760 to know the number of years lived:

therefore, you would have lived 114.15 years

The minimum number of goals scored is 0 and maximum number of goals scored is 7. The range is equal to difference between maximum number of goals and minimum number of goals.

Determine the range for the goals scored.

So answer is 7.

Answer:

25/18 - 20

155/36 - 62

25/8 - 45

Step-by-step explanation:

In mathematical logic, the Law of Detachment says that if the following two statements are true:

( 1 ) If p, then q.

( 2 ) p

Then we can derive a third true statement:

( 3 ) q.

In our question, we have

( 1 ) If 0º< A <90º, then A is an acute angle.

( 2 ) The measure of A is 58º.

Then, from the first statement, we can affirm

( 3 ) A is an acute angle.

SOLUTION

Write out the given point

The equation of the line passing through the point above will be obtain by following the steps

Step1: Obtain the slope of the line

Substituting the values we have

Step 2: Obtain the y- intercept

The y-intercept is the point where the graph touch the y, axis

Steps 3; use the slope intercept rule

Hence

The equation in slope intercept form is

y = - 3/4 x + 6