Mav is working two summer jobs, making
$15 per hour lifeguarding and making $10
per hour landscaping. In a given week, she
can work at most 12 total hours and must
earn no less than $140. If x represents the
number of hours lifeguarding and y
represents the number of hours
landscaping, write and solve a system of
inequalities graphically and determine
one possible solution.
Inequality 1: y ≥û
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
y
Inequality 2: y ≥û
0 1 2 3
4
5
switch shade
plot
6
switch shade
plot
7
8 9 10 11 12 13 14 15 16 17 18 19 20
Xx

Answer: 38.8°

Step-by-step explanation:

See the attached diagram:

From it we can tell that the tunnel forms a right triangle, with the length of a leg and the hypotenuse given. We can use the sine function to easily answer this, (letting θ be the angle we need to find)

sinθ = 52/83

.: θ = arcsin(52/83)

(Note: arcsin is the inverse of the sine function)

.: θ ≅ 38.8°

The ratio of the coordinate point on the line is  2 to 7.

The ratio of the coordinate point on the line is calculated as follows;

Let the coordinate points = (xp, yp)

Let the ratio of the line = a:b

xp = x₁  +  (a/(a+b) (x₂ - x₁)

yp = y₁  + (a/a+b) (y₂ - y₁)

-3 = -7 + ( a/a+b)(11 - - 7)

-3 = -7 + (a/a+b)(18)

-3(a + b)  = -7(a+b) + 18a

7(a + b ) - 3(a+b) = 18a

7a + 7b - 3a - 3b = 18a

4b = 14a

4/14 = a/b

2/7 = a/b

2 : 7 = a : b

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The set of parametric equations are

[tex]x=\sqrt{t}[/tex]

[tex]y=\sqrt{3+t[/tex]

A parametric equation uses a parameter, which is an independent variable (often represented by the notation t), and dependent variables, which are expressed as continuous functions of the parameter and are independent of other variables.

Using one or more independent variables known as parameters, a parametric equation defines a set of quantities as functions.

Given the equation:

[tex]x= \sqrt[]{y^{2}-3 }[/tex]

Let's find a set of parametric equation for the given equation given the parameter:

[tex]x = \sqrt{t}[/tex]

From the parameter:

[tex]x = \sqrt{t}[/tex]

Now, substitute [tex]\sqrt{t}[/tex] for x in the given equation:

[tex]x=\sqrt{y^2-3} \\\\\sqrt{t} = \sqrt{y^2 - 3} \\\\t=y^2-3\\\\y^2=3+t\\\\y=\sqrt{3+t}[/tex]

Therefore, the set of parametric equations is:

• [tex]x=\sqrt{t}[/tex]

• [tex]y=\sqrt{3+t}[/tex]

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The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.

Let h be the height of the cone and A be the base area of the cone.

Then the volume of the cone will be given as,

Volume = (1/3) × A × h

At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12 feet and is 10 feet tall.

The base area of the cone is given as,

A = π × (d/2)²

A = 3.14 × (12 / 2)²

A = 3.14 × 36

A = 113.04 square feet

Then the volume of the cone is given as,

V = 1/3 × 113.04 × 10

V = 376.8 cubic feet

The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.

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The upper quartile score on the final exam is 83.

Upper quartile, represented as Q₃, also known as third quartile is the value in a data set such that 75% of the points in the data set are below this value, after arranging in an ascending order.

Given data set is the scores for the final exam in an 8th grade math class.

58, 72, 74, 92, 84, 40, 74, 81, 76, 83.

First arrange the data in an ascending order.

40, 58, 72, 74, 74, 76, 81, 83, 84, 92.

Median is the middle element.

Median = (74 + 76) / 2 = 75

Upper quartile is the median of the second half.

Consider the second half.

76, 81, 83, 84, 92.

Median = 83

Third quartile = 83

Hence 83 is the upper quartile score on the final exam.

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Answer:

k is 2.5.

Step-by-step explanation:

To find the value of k, we can use the information given about points A and B to find the value of the parameters a and b. Since we know that the curve passes through A (1, 10) and B (4, 80), we can substitute these points into the equation y = ab^x to find the values of a and b.

Starting with point A:

10 = a * b^1

Next, using point B:

80 = a * b^4

We can now use these two equations to find the value of b:

10 = a * b^1

80 = a * b^4

Dividing the second equation by the first equation:

8 = b^3

Taking the cube root of both sides:

b = 2

We can now use either of the two equations to find the value of a:

10 = a * b^1

a = 10/2 = 5

Now that we have found the values of a and b, we can substitute the point C (-1, k) into the equation y = ab^x to find the value of k:

k = 5 * 2^(-1) = 5 * (1/2) = 2.5

So the value of k is 2.5.

Answer:

C

Step-by-step explanation:

The probability that he does not select a comedy is 12/23

If we assume that all the movies have the same probability of being randomly selected, then the probability of selecting a movie that is not a comedy is equal to the quotient between the number of movies that aren't comedies and the total number of movies.

There are:

3 action ones.

11 comiedies.

9 dramas

For a total of 23 movies, and 12 of them are not comedies, then:

P = 12/23

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The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches is approximately 34.4 inches, found using the Pythagorean theorem.

The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches can be calculated using the Pythagorean theorem, which states that the square of the sum of the squares of the lengths of the legs determines the length of the hypotenuse.

So, if we call the length of the hypotenuse "h", we have [tex]h^{2}[/tex] = [tex]20^2 + 28^2[/tex]

Solving for h:

[tex]h^2 = 20^2 + 28^2[/tex]

[tex]h^2[/tex] = 400 + 784

[tex]h^2[/tex] = 1184

h = [tex]\sqrt{1184}[/tex]

h ≈ 34.4 in.

So, the length of the hypotenuse is approximately 34.4 inches, rounded to the nearest tenth.

The Pythagorean theorem is a fundamental mathematical relationship that states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal tothe squared lengths of the two legs added together. In this case, the two legs have lengths of 20 inches and 28 inches, and the length of the hypotenuse can be found by solving for the square root of the total of the leg squares.

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Answer:

27 children.

Step-by-step explanation:

Let's call the number of children who chose apples x. Then, the number of children who chose bananas is 0.25x. The number of children who chose watermelon is 60 - x - 0.25x = 60 - 1.25x.

Since 30% of the children chose apples, we know that:

0.30 * 60 = x

So, x = 18, which means 18 children chose apples.

And since 25% of the children chose bananas, we know that:

0.25 * 60 = 0.25x = 15

So, 15 children chose bananas.

Finally, the number of children who chose watermelon is:

60 - 18 - 15 = 27 children.

Answer: A

Step-by-step explanation: This is how to solve: 3239 / (36 *365)

That's 0.246499239 kills per day, so none died

I hope this helped!

The equation to represent the situation where the oldest child is 7 years older than the youngest child, using x for the age of the youngest child and y for the age of the oldest child, is y = x + 7.

If we let x represent the age of the youngest child in a family, then we can say that the oldest child is 7 years older than the youngest child. We can represent the age of the oldest child using the expression "x + 7", because if we add 7 to the age of the youngest child, we get the age of the oldest child.

Therefore, we can write an equation to represent this situation by equating the age of the oldest child to the age of the youngest child plus 7. This can be written as:

x + 7 = Oldest child's age

where x is the age of the youngest child, and "Oldest child's age" represents the age of the oldest child in the family. This equation tells us that if we know the age of the youngest child, we can find the age of the oldest child by adding 7 to it.

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Answer:

a = 6 ft.

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

Given is an isosceles right triangle.

As per property of a such triangle, its hypotenuse is √2 times its leg.

That is:

Answer:

a = 6 ft

Step-by-step explanation:

We have to find,

→ The value of a in the diagram.

Formula we use,

=> Using Pythagoras theorem.

→ (Hyp)² = (Opp)² + (Base)²

Forming the equation,

→ (6√2)² = (a)² + (a)²

Now the value of a will be,

→ (6√2)² = (a)² + (a)²

→ (a)² + (a)² = (6√2)²

→ 2a² = 36 × 2

→ 2a² = 72

→ a² = 72 ÷ 2

→ a² = 36

→ a = √(36)

→ [ a = 6 ft ]

Hence, the value of a is 6 ft.

The value of x is given as follows:

x = 130º.

To obtain the value of x, we must consider the exterior angle theorem, which states that each interior angle is supplementary with it's interior angle, meaning that the sum of their measures is of 180º.

As the interior angle is of 50º, the measure of the exterior angle x is given as follows:

x = 180 - 50

x = 130º.

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Using the empirical rule, we can conclude that approximately 68% of American women have shoe sizes between 6.54 and 9.58.

Using the empirical rule, we can say that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

To find the percentage of American women who have shoe sizes between 6.54 and 9.58, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:

z1 = (6.54 - 8.06) / 1.52 = -1.00

z2 = (9.58 - 8.06) / 1.52 = 1.00

Now, we can use the empirical rule to find the percentage of women with shoe sizes between z = -1.00 and z = 1.00. Since this interval corresponds to one standard deviation from the mean, we know that approximately 68% of the data falls within this range.

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Answer:

Step-by-step explanation:

5. Diagram 2 shows a cylinder and a cuboid. Diagram 2 shows a cylinder and a cuboid. Fold / Use = 271 30 cm Find the value of x and give the correct answer to the multiple of two places. It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Answer / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Us

Answer:

-16x² + 10x - 14.

Step-by-step explanation:

To find the composition of two functions, (f g)(x), we first evaluate g(x) and then substitute the result into f(x).

So, let's first evaluate g(x):

g(x) = 8x² - 5x + 7

Next, substitute g(x) into f(x):

(f g)(x) = f(g(x)) = f(8x² - 5x + 7) = -2(8x² - 5x + 7) = -16x² + 10x - 14

Therefore, (f g)(x) = -16x² + 10x - 14.

To convert milligrams per liter (mg/L) to micrograms per fluid ounce (µg/fl oz), we can use the conversion factor of 29.5735.

This conversion factor takes into account the difference in volume between a liter and a fluid ounce.

1 fl oz = 29.5735 mL

1 L = 1000 mL

So, to convert from milligrams per liter to micrograms per fluid ounce, we divide by 29.5735 and multiply by 1000:

(mg/L) * 1000 / 29.5735 = (µg/fl oz)

Therefore, to convert a value x from milligrams per liter to micrograms per fluid ounce:

x (µg/fl oz) = x (mg/L) * 1000 / 29.5735

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The equation in standard form is x - 9y = -45.

The equation of a line in standard form is Ax + By = C, where x and y are variables and A, B and C are integers.

Given equation is y = 1/9 x + 5.

Here 1/9 is not an integer.

So multiplying the equation throughout by 9, we get,

9y = x + (5 × 9)

9y = x + 45

Subtracting both sides by x,

9y - x = 45

-x + 9y = 45

Multiplying throughout by -1,

x - 9y = -45, which is in standard form.

Hence the equation is x - 9y = -45 in standard form.

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The degree of a vertex represents the number of other actors or actresses that an actor or actress has worked with in movies.

The neighborhood of a vertex represents the set of actors or actresses that an actor or actress has worked with in movies.

Isolated vertices represent actors or actresses who have not worked with any other actors or actresses in any movie, while pendant vertices represent actors or actresses who have only appeared in one movie with another actor or actress in the Hollywood graph.

The Hollywood graph is an undirected graph because the relationship between actors and actresses is mutual.

Each vertex in this graph represents an actor or actress, and the degree of a vertex represents the number of other actors or actresses that they have worked with in movies. In other words, the degree of a vertex represents the number of edges that are connected to that vertex.

The neighborhood of a vertex in a graph refers to the set of all vertices that are adjacent to it. In the context of the Hollywood graph, the neighborhood of a vertex represents the set of actors or actresses that a particular actor or actress has worked with in movies.

An isolated vertex in a graph is a vertex that has no edges connected to it. In the context of the Hollywood graph, an isolated vertex represents an actor or actress who has not worked with any other actors or actresses in any movie.

A pendant vertex in a graph is a vertex that has only one edge connected to it. In the context of the Hollywood graph, a pendant vertex represents an actor or actress who has only appeared in one movie with another actor or actress in the Hollywood graph.

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The proportion i/k = 12 can be used to find the length of sides i and k if the perimeter is 12 units. To solve for the length of each side, the equation i + k = 12 is used, and then the two sides are divided by each other to get the proportion i/k = 12.

The proportion i/k = 12 can be used to find the length of sides i and k of a shape if the perimeter is 12 units. In order to solve for the length of each side, the equation i + k = 12 is used to determine the sum of the sides. The two sides are then divided by each other, resulting in the proportion i/k = 12. This proportion can then be used to find the length of sides i and k. For example, if the length of side i is 8, then the length of side k is 4. This can be determined by dividing 8 by 4, which results in the proportion i/k = 2. If the perimeter is 12 units, then the equation i + k = 12 can be used to determine that the length of side i is 6 and the length of side k is 6, since 6 + 6 = 12. The proportion i/k = 12 can then be used to confirm that the length of side i is 6 and the length of side k is 6.

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The complete question is

Which proportion can be used to find the length of sides ik if the perimeter is 12 units?

Answer: 96

The sum of the interior angles of a regular heptagon is equal to (n-2)180 degrees, where n is the number of sides of the polygon.

Since a regular heptagon has 7 sides, the sum of its interior angles is (7-2)180 = 720 degrees.

Therefore, the measure of each interior angle is 720 degrees / 7 = 104 degrees.

If the measure of an interior angle is (w + 8) degrees, then w + 8 = 104.

Solving for w, we get w = 96.

Answer:

Step-by-step explanation:

V≈62.83ft³

I hope it helped you out.

Answer: D. 6 cm

Step-by-step explanation:

V = 4/3πr^3

r = (3 V/4π)^1/3 = (3* 900/4*π)^1/3 = 5.98942

Answer:

Yes, 26

Step-by-step explanation:

78 miles ÷ 3 gallons = 26 mpg

The program to cost of each container and the total cost of producing all the containers is given below.

The program based on the information will be:

#include <iostream>

using namespace std;

int main() {

int r,h,c,n;

cout<<"Enter the base radius : ";

cin>>r;

cout<<"\nEnter the height : ";

cin>>h;

cout<<"\nEnter the cost per square cm : ";

cin>>c;

cout<<"\nEnter the number of containers : ";

cin>>n;

int s_area = (3.14*r*2)+(2*3.14*r*h);

int cost = c*s_area;

int t_cost = n*cost;

cout<<"\nCost of each container : "<<cost<<endl;

cout<<"Total cost : "<<t_cost<<endl;

}

Based on the above, we've created a program to take the radius of the base, the height of the container, the cost per square centimeter of the material cost.

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A manufacturer wishes to determine the cost of producing an open-top cylindrical container. The surface area of the container is the sum of the area of the circular base plus the area of the outside (the circumference of the base times the height of the container). Create C program to take the radius of the base, the height of the container, the cost per square centimeter of the material (cost), and the number of containers to be produced (quantity). Calculate the cost of each container and the total cost of producing all the containers.

Answer:

1) Vertical angles

2) Corresponding

3) Alternate exterior

4) Same-Side Interior

Step-by-step explanation: