Dominic's two daughters both want to take gymnastics this year. It costs $87 per month per child. How much does Dominic need to budget for a year ( 12 months) of gymnastics for both daughters? Do not include the dollar sign in your answer

The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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The reference angle for the angle with the measure 2x/3 is 54⁰

You should understand that a reference angle is the acute angle to a given angle.

The given angle is 2x/3

We should understand that since the angle has the variable x

= x + 2x/3 = 90⁰

Simplifying the fraction to have

(3x+2x)/3 = 90

Cross and multiply we have 5x=270⁰

Making x the subject

x= 270/5

x=54⁰

Therefore, the reference angle with the measure 2x/3 is = 54⁰

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

Step-by-step explanation:

No picture. But a function must satisfy the vertical line test. Which means that each value of x has only one value for y. If a graph shows two values for y for a single value of x it is not a function.

Answer:

455554444444555556555555554444

Based on the information provided, the missing number would be number 6.

When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.

In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.

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Let's factor out

\(\\ \rm\Rrightarrow 64m^2-9n^2\)

\(\\ \rm\Rrightarrow (8m)^2-(3n)^2\)

\(\\ \rm\Rrightarrow (8m-3n)(8m+3n)\)

Done

The dimensions of Mrs. Hinson's driveway are (8m -3n)unit ×  (8m + 3n) units.

Thus, the dimensions of the area are  (8m -3n)unit ×  (8m + 3n) units.

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The formula for the geometric sequence above is Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

In geometric sequence, the general formula of geometric sequence is:

Tₙ= ar⁽ⁿ⁻¹⁾

Information:

Tₙ = the n-th term

a = first term

r = ratio

n = the number of terms

In the question above,

a= 5

r= T2/T1=-15/5=-3 (This is the ratio)

Substitute the value of a and r to the formula of Tₙ:

Tₙ= ar⁽ⁿ⁻¹⁾

Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

So the formula of Tₙ for the sequence above is Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

In the above formula there is a ratio of geometric sequences. In a geometric sequence, two successive terms have the same ratio. Comparisons to geometric sequences are referred to as ratios (r). This is where the quotient of adjacent terms will be obtained.

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Answer:I think it Is the second

Step-by-step explanation:

Answer:

it is 17.5

Step-by-step explanation:

you add 6.2 and 11.3 equal 17.5

Answer:

≈ 681.38 ft^2 when pi≈ 3.14

Step-by-step explanation:

2(3.14)(6.2^2)+(3.14)(12.4)(11.3)

241.4032+439.9768≈ 681.38

Answer:

\((x,y) = (5,15)\)

Step-by-step explanation:

Given

\(Nickels = x\)

\(Pennies = y\)

Minimum of 20 coins means:

\(x + y \ge 20\)

A nickel worth $0.05

A penny worth $0.01

So, the worth can be represented as:

\(0.05x + 0.01y \le 0.40\)

See attachment for graph

From the attachment, the solution is:

\((x,y) = (5,15)\)

A square root function that is represented by the graph include the following: A. f(x) = √(4x + 8).

In Mathematics and Geometry, a square root function can be defined as a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

Therefore, the required square root function is given by;

f(x) = √(4x + 8)

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Answer:

a) The probability that in​ tonight's game the basketball player misses for the first time on his sixth attempt is 0.0311 = 3.11%.

b) The probability that in​ tonight's game the basketball player makes his first basket on his fifth shot is 0.0154 = 1.54%.

c) The probability that in​ tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936 = 93.6%.

Step-by-step explanation:

For each shot, there are only two possible outcomes. Either the player makes it, or he does not. The probability of making a shot is independent of other shots. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

A basketball player has made 60​% of his foul shots during the season.

This means that \(p = 0.6\)

a) Misses for the first time on his sixth attempt

Makes the first five, which is P(X = 5) when n = 5.

Misses the sixth, with probability = 1-0.6 = 0.4.

So

\(p = 0.4P(X = 5)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(p = 0.4P(X = 5) = 0.4*(C_{5,5}.(0.6)^{5}.(0.4)^{0}) = 0.0311\)

The probability that in​ tonight's game the basketball player misses for the first time on his sixth attempt is 0.0311 = 3.11%.

b) Makes his first basket on his fifth shot

Misses the first four, which is P(X = 0) when n = 4.

Makes the fifth, with a probability of 0.6.

So

So

\(p = 0.6P(X = 0)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(p = 0.6P(X = 0) = 0.6*(C_{4,0}.(0.6)^{0}.(0.4)^{4}) = 0.0154\)

The probability that in​ tonight's game the basketball player makes his first basket on his fifth shot is 0.0154 = 1.54%.

c) Makes his first basket on one of his first 3 shots

Either he makes his first basket on one of his first 3 shots, or he misses all of them. The sum of these probabilities is decimal 1.

Misses the first three:

P(X = 0) when n = 3. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{3,0}.(0.6)^{0}.(0.4)^{3} = 0.064\)

Makes on one of his first three:

1 - 0.064 = 0.936

The probability that in​ tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936 = 93.6%.

Answer:

Step-by-step explanation:

The probability that the basket player made a foul shot is 60% which is 0.60

Then the probability of good shot is 1 - 0.60 = 0.40

P = 0.40

a) the probability that the basket player misses for the first time on his sixth attempt ​is

P (first time on his sixth attempt) = (1 - P)⁵ (P)

= (1 - 0.4)⁵(0.4)

= (0.6)⁵(0.4)

= 0.07776 * 0.4

= 0.031104

≅ 0.0311

The probability that​  the basketball player misses for the first time on his sixth attempt is 0.0311

b) P(first basket on his fifth shot) = (1 - P)³ (P)

= (1 - 0.4)⁴(0.4)

= (0.60)⁴(0.4)

= 0.0518

c) The probability of making his first basket in first shot is 0.6

and the  probability of making his first basket in second shot is

0.6 * 0.4 = 0.24

the  probability of making his first basket in third shot is

0.6 * 0.4² = 0.096

So, the probability that the player makes his first basket on one of his first 3 shots is

= 0.6 + 0.24 + 0.096

= 0.936

Thus, the probability that in​ tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936

The probability that a randomly selected driver in the 20-24 age bracket will be in a car crash during the next year is 0.86%.

It is unlikely for a driver in that age bracket to be involved in a car crash during a year

The resulting probability of 0.0086 is relatively low.

The approximate probability can be calculated by dividing the number of drivers who were in a car crash in the last year by the total number of drivers in the 20-24 age bracket:

Probability = Number of drivers in a car crash / Total number of drivers in the age bracket

Probability = 3/350

Probability ≈ 0.0086

Part 2

Since the probability is less than 0.05, it is unlikely for a driver in that age bracket to be involved in a car crash during a year.

Part 3

While any car accident can be a concern, the resulting probability of 0.0086 is relatively low.

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Answer:

Step-by-step explanation:

.9357

The statement correctly describes the perpendicular bisector construction below The construction of JK to bisect GH: Option D is the correct answer

The term perpendicular bisector refers to the line that divides another line into two equal parts, making an angle of 90 degrees. The term is made up of two words, perpendicular and bisector.

Perpendicular refers to angle 90 degrees, while the bisector refers to dividing into two equal parts.

In the picture, the main line is GH while JK is the line constructed to bisect the main line

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I think that the anwser is probably 10.6

Answer:

40 sq units

Step-by-step explanation:

\(5x + 10y = 8\\\Rightarrow y=\dfrac{8-5x}{10}\\\Rightarrow y=-\dfrac{1}{2}x+\dfrac{2}{5}\)

Slope of \(L_2\) is \(m_2\)

\(m_1m_2=-1\\\Rightarrow m_2=-\dfrac{1}{m_1}\\\Rightarrow m_2=-\dfrac{1}{-\dfrac{1}{2}}\\\Rightarrow m_2=2\)

\(L_2\) passes through point \((8,6)\)

\(y-6=2(x-8)\\\Rightarrow y=2x-16+6\\\Rightarrow y=2x-10\)

Point at x axis where \(L_2\) intersects is

\(0=2x-10\\\Rightarrow x=\dfrac{10}{2}\\\Rightarrow x=5\)

Point \(A\) of the triangle will be \((5,0)\)

\(L_2\) intersects line \(x=-3\). The point is

\(y=2\times(-3)-10\\\Rightarrow y=-6-10\\\Rightarrow y=-16\)

The points of the triangle are \(A(5,0), O(0,0), B(-3,-16)\)

Area of triangle is given by

\(A=\dfrac{|A_x(B_y-O_y)+B_x(A_y-O_y)+O_x(A_y-B_y)|}{2}\\\Rightarrow A=\dfrac{|5(-16-0)+-3(0-0)+0(0-(-16))|}{2}\\\Rightarrow A=40\ \text{sq units}\)

The area of the triangle is 40 sq units.

Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.

Mary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.

Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.

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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.

The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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The quadratic equation that describes the function is  

f(x) = x² + 4x + 1

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the table that describes the quadratic function h(x) as follows -

{x}                h{x}

−3               −2

−2               −3

−1                −2

0                  1

1                   6

2                  13

3                  22

The quadratic equation is of the form given -

y = ax² + bx + c

For the point (0, 1), we can write -

1 = c                                                      ..... Eq{1}

For the point (1, 6), we can write -

6 = a + b + 1

a + b = 5                                               ...... Eq{2}

For the point (2, 13), we can write -

13 = 4a + 2b + 1

4a + 2b = 12                                               ...... Eq{3}

From Eq{2}, we can write -

a = 5 - b

So, the equation 3 can be written as -

4(5 - b) + 2b = 12

20 - 4b + 2b = 12

20 - 2b = 12

2b = 8

b = 4                                    ...... Eq{4}

then

a = 1                                ...... Eq{5}

So, we can write the quadratic equation as -

f(x) = x² + 4x + 1

Therefore, the quadratic equation that describes the function is  

f(x) = x² + 4x + 1

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Answer:

She sold 5.775 kilograms of pears at the farmer's market.

Step-by-step explanation:

Let's first determine the information that the question gives us, and what we need to find.

Given:

The farmer sold 7.7 kilograms of apples and pears

1/4 of the weight is apples

The rest of the weight is pears

Find:

Kilograms of pears that the farmer sold

Start by finding the fraction of the whole weight that was pears...

\(1-\frac{1}{4}=\frac{4}{4}-\frac{1}{4}=\frac{3}{4}\)

Now, find 3/4 of 7.7...

\(\frac{3}{4}(7.7)=\frac{23.1}{4}=5.775\ kg\)

She sold 5.775 kilograms of pears at the farmer's market.

The function used to estimate the revenue is:

R(x)= 79 x where R(x) is the revenue and x is the number of rooms booked.

Therefore, since the Domain of the function is the set of x-values that can be used to provide a valid result, that means that the set of possible number of rooms booked is the Domain.

That is any whole number between 0 and 220 (the maximum number of rooms that could be booked)

This coincides with the third answer listed.

Ray stayed for 25 minutes on the trampoline

Information from the question

The total cost of his session was $35

He had to pay a $5 entrance fee and $1.20 for every minute he was on the trampoline

How many minutes was Ray on the trampoline = ?

The information may be represented mathematically in the form

$35 = $5 + $1.20x

let x represent the number of minute on the trampoline

solving for x

$35 = $5 + $1.20x

$1.20x = $35 - $5

$1.20x = $30

x = $30 / $1.20

x = 25 minutes

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Answer:

The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 1, b = -1, and c = -1. So:

x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)

x = (1 ± sqrt(5)) / 2

Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.

Given:

The number of cellular phones = 2,700

For the number of persons = 1,000

So, to find the number of phones per person, we will divide 2,700 by 1,000

so, the answer will be:

So, the answer is:

The number of phones person is 2 7/10

{x| x is a natural number less than 7} ={1. 2. 3. 4. 5, 6}. The statement is true.

What is a natural number?

Natural numbers are all positive numbers that range from 1 to infinity and are consequently a part of the number system. Natural numbers are frequently referred to be counting numbers because they don't contain zero or negative numbers. They are a subset of real numbers that only contains positive integers and excludes all other types of numbers, such as negative, zero, fractional, and decimal.

It is in set builder form of set represenation.

A set consists of elements represented inside flower brackets { }.

Read as x such that x belongs to natural numbers less than 7.

Natural numbers starts from 1,2,3 .... to infinity.

Natural numbers less than 7 means

1,2,3,4,5,6

Represented in set as

{1,2,3,4,5,6}

Hence the statement is true.

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Answer:

4

Step-by-step explanation: