A table of values of linear function is shown below.Find the y-intercept and e of the functions graph, and find the equation for the function.

Answer:

237

Step-by-step explanation:

This is a system of equations.

The theater sold 364 adult and child tickets, so a + c = 364

They made a total of $1930. Each adult ticket was $6 & child tickets were $4. The second equation is 6a + 4c = 1930.

Let's line them up

a  +  c = 364

6a + 4c = 1930

Since we need to solve for the number of adult tickets, we want to get rid of the c variable. I'm going to multiply the entire first equation by -4 to do this. The second equation stays the same. Now, I have:

-4a - 4c = -1456

6a + 4c = 1930            Add them together

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

2a = 474                      Divide by 2 to solve for a

a = 237

There were 237 adult tickets sold

Answer:

4 lawns

Step-by-step explanation:

20/5

Answer:

13 is a prime number, not divisible by any number greater than 1 or less than 13. So the prime factorisation of 78 is: 78 = 2 ⋅ 3 ⋅ 13 This can also be represented by a factor tree:

Step-by-step explanation:

Answer:

78 = 2 ⋅ 3 ⋅ 13

Step-by-step explanation:

78  ends with an even digit, so is divisible by  2 and we find:  78 = 2 ⋅ 39

39  ends with an odd digit, so is not divisible by  2 .

The digits of  39  add up to a multiple of  3 , namely  3 + 9 = 12 . So we can tell that  39  is divisible by  3 : 39 = 3 ⋅ 13

13  is a prime number, not divisible by any number greater than  1  or less than  13 .

So the prime factorization of  

78  is:

78= 2 ⋅ 3 ⋅ 13

Answer:

n = -8

Step-by-step explanation:

Answer:

-8

here's the solution

5(n - 4) = -60

5n - 20 = -60

5n = -60+20

5n = -40

n = -40/5

n= -8

hope it helps

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Given:

L :35 meter

B:25 meter of a rectangle

Required:

How many meter of rail does Laika needs

Explanation:

we are going to multiply 25 by 2 and then going to multiply 35 by 2

Now we are going to add both these values

Required answer :

=120 meter

Answer:

Yes, they are correct

Step-by-step explanation:

The width of the interval is 9 − 5 = 4.  So the minimum possible value of the area is 4m, and the maximum possible value of the area is 4M.

a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.

In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.

Counting these numbers, we find that there are 17 students who obtained more than 45 marks.

b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.

In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.

Counting these numbers, we find that there are 15 students who obtained less than 45 marks.

c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.

In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.

Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.

d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.

Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45

           = 1912

Total number of students = 40

Average marks = Total marks / Total number of students

                 = 1912 / 40

                 = 47.8

Therefore, the average marks obtained by the students in the class is 47.8.

e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.

In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,

49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.

Counting these numbers, we find that there are 40 students who obtained more than the average marks.

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer:

  9x -4y = -44

Step-by-step explanation:

You want the equation of the line through (-4, 2) and perpendicular to the line through (-4, 6) and (5, 2).

The equation of a line through (h, k) and perpendicular to the line through (x1, y1) and (x2, y2) can be written as ...

  (x2 -x1)(x -h) +(y2 -y1)(y -k) = 0

Using the given points, this becomes ...

  (5 -(-4))(x -(-4)) +(2 -6)(y -2) = 0

  9(x +4) -4(y -2) = 0

Expanding this gives the general form equation:

  9x -4y +44 = 0

Subtracting the constant gives the standard form equation:

  9x -4y = -44

Answer:

Im stuck on this one as well lol

Step-by-step explanation:

Good luck

You find out the answer for this one? I'm stuck on it

Answer:

The solution to the system of equations

Hence, the value of q = -50

Step-by-step explanation:

Given the system of equations

\(\begin{bmatrix}-16p-2q=100\\ p-4q=200\end{bmatrix}\)

solving to determine the value of q

Multiply p − 4q = 200 by 16:      \(16p-64q=3200\)

\(\begin{bmatrix}-16p-2q=100\\ 16p-64q=3200\end{bmatrix}\)

so adding the equations

\(16p-64q=3200\)

\(+\)

\(\underline{-16p-2q=100}\)

\(-66q=3300\)

so

\(\begin{bmatrix}-16p-2q=100\\ -66q=3300\end{bmatrix}\)

solve -66q = 3300

\(-66q=3300\)

Divide both sides by -66

\(\frac{-66q}{-66}=\frac{3300}{-66}\)

\(q=-50\)

substituting q = -50 in −16p − 2q = 100

\(-16p-2\left(-50\right)=100\)

\(-16p+100=100\)

Subtract 100 from both sides

\(-16p+100-100=100-100\)

Simplify

\(-16p=0\)

Divide both sides by -16

\(\frac{-16p}{-16}=\frac{0}{-16}\)

\(p=0\)

Thus, the solution to the system of equations

Hence, the value of q = -50

First, we need to find the equations of the two dotted lines.

One of the lines is parallel to the x-axis and passes through the point (0, 2), then its equation is:

y = 2

The other line has a slope of 1 and intercepts the y-axis at the point (0,0). Using the slope-intercept form with m = 1 and b = 0, its equation is:

y = mx + b

y = 1*x + 0

y = x

Given that the shaded region is below both lines and the lines are not included in the solution, then we need to use a "<" sign in the inequalities. Finally, the system of inequalities is:

y < x

y < 2

The given equation y = 3x + 45 in form ax+by=c is 3x - y = - 45.

So,  y=3x+45 into ax+by=c form:

Therefore, the given equation in form ax+by=c is 3x - y = - 45.

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Answer:

1. 1 in 5

2. There are 5 colors it could land on, and orange is one of them.

3. 40 different combinations

4. There are 5 colors with 8 corresponding numbers. 5x8=40

Step-by-step explanation:

1) 20%

2) Assuming that on the spinner with color, every section has an equal share, then the probability of landing on orange is \(\frac{1}{5}\) or 20%. This is because, the orange section is one of the five equal sections, or \(\frac{1}{5}\) or the spinner. \(\frac{1}{5}\) in decimal form is 0.2, to convert to a percent, multiply by 100. Hence one gets, 20%.

3) 40

4) There are 5 sections on the spinner with color, hence 5 possible outcomes when one spins the spinner. On the black and white spinner, there are 8 sections, hence 8 possible outcomes when one spins the spinner. To find the total number of outcomes resulting from the two events, one must multiply the total outcomes from one event by the total outcome of the other event. When one does this, they get that there are 40 possible events.

Answer:

22/25

Step-by-step explanation:

Answer:

22/25

Step-by-step explanation:

addition

Answer: A and B

Step-by-step explanation:

Q isn’t a binomial since the pens are being selected without replacement and the sample size is more than 10% of the population size, so the trails are not independent.

A binomial random variable is such that can take either of two possibilities at the same time.

Samples R and S can be considered as binomial random variables

For a random variable to be considered a binomial random variable, the population must be at least ten times the sample size.

So, we have the following highlights

Container A

\(n =100\)

\(x = 5\)

Divide n by x

\(\frac nx = \frac{100}{5}\)

\(\frac nx = 20\)

This means that the population is 20 times the sample size.

Hence, R is a binomial random variable.

Container B

\(n =1000\)

\(x = 5\)

Divide n by x

\(\frac nx = \frac{1000}{5}\)

\(\frac nx = 200\)

This means that the population is 200 times the sample size.

Hence, S is a binomial random variable.

Container C

\(n =20\)

\(x = 5\)

Divide n by x

\(\frac nx = \frac{20}{5}\)

\(\frac nx = 4\)

This means that the population is 4 times the sample size.

Hence, Q is not a binomial random variable.

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The baker would need 47. 25 cups of floor

We need to know that proportion is a form of mathematical comparison with two equations made equal to each other.

From the information given, we have that;

baker used 33 3/4 cups of flour to make 15 batches of cookies

This is represented as;

Convert to improper fractions

135/4 cups = 15 batches of cookies

Then, x cups = 21 batches of cookies

cross multiply the values

15x = 708. 75

Divide both sides by the coefficient of x, we have ;

x = 708. 75/15

x = 47. 25 cups of floor

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Answer:

I believe the answer is the second one, please let me know if I am wrong.

Answer: 34,104

Step-by-step explanation:

i got the question right

Michael must contribute $7,849.55 quarterly during the first 12 years in order to achieve his retirement goals.

The idea that money now is worth more than the same amount of money in the future owing to the potential earning capacity of money over time is known as the time value of money, and it is a basic concept in finance. The notion behind the concept is that money may be invested to produce interest or other returns, and that over time, inflation and other variables affect how much money is worth.

Given that, the contributions are made for 12 years.

The future value is thus given by:

\(FV = P[((1+r)^n - 1)/r]\)

The number of periods are:

12*4 = 48 periods.

The interest rate per quarter is 8%/4 = 2%.

Substituting the values we have:

\(FV = P[((1+r)^n - 1)/r] \\\\=P[((1+0.02)^48 - 1)/0.02] \\\\= P[67.242]\)

Now, for present value of an annuity, we get:

\(PV = C[(1-(1+r)^-n)/r] \\\\= 10000[(1-(1+0.02)^-40)/0.02] \\\\=528,113.20\)

Setting the two values equal we have:

P[67.242] = 528,113.20

P = 7,849.55

Hence, Michael must contribute $7,849.55 quarterly during the first 12 years in order to achieve his retirement goals.

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The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

nearest 10= 18620

have a nice day

Answer:

18624 to the nearest ten= 18620