Caitlin is painting her bedroom. She paints 42 square feet in 2/3 hour. At this rate, how many square feet can she paint in one hour?

Answer:

8

Step-by-step explanation:

For each different outcome of the spinner, there are 2 different outcomes of the coin flip.

4 × 2 = 8

Answer: 8

Elyse has the option of combination of 960 cities, or another to choose from. If Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.

Given,

Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent.

To determine how many options Elyse will have, we use permutations and combinations.

We can say that she has a choice of any of the eight cities in Asia for every ten cities in Europe. Similar to how she can select any of the 4 cities in Africa for every 8 cities in Asia. The same is true for Australia and Africa.

Elyse has a choice of a total:

10×8×4×3

960

Elyse has the option of combination of 960 cities, or another.

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The area of the circle is obtained as 78.50 square feet. The correct option is (A).

A circle is a geometric shape, all of which points are equidistant from a fixed point called as the Centre.

The Centre of the circle does not lie on it.

Given that,

The radius of the circle is 5 feet.

The expression for the area of the circle is given as πr².

Substitute the value of r and take π = 3.14 to obtain,

Area = πr²

        = 3.14 × 5²

        = 3.14 × 25

        = 78.50

Hence, the area of the circle with given radius is obtained as 78.50 square feet.

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Shyla pay $2380 to clean the area outside the rug.

What is steam clean?

To use a device that generates hot steam to clean (something).

Given:

Shayla’s family room measures 20 ft by 17 ft.

There is an area rug centered in the room, 3 ft away from each wall.

So, the remaining area of the room will be 17 ft by 14 ft.

Shayla wants to pay a company to steam clean just the area outside the rug.

The total area of the room outside the rug is

17 ft x 14 ft = 238 square feet.

The charge for one square foot is $10.

So, the charge for 238 square foot will be

238 x $10 = $2380.

Hence, Shyla pay $2380 to clean the area outside the rug.

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The evaluation of the table, equations, and graphs in the question are as follows;

First question;

Part A; The table does not represent a function

Part B; The value of f(300) is $123 represents the total cost for driving 300 miles

Second question;

Part A; The equation is; y = -2·x + 8

Part B; The graph can be obtained by finding the ordered pair of values for the first five hours and plotting the result on a graph, to form a straight line graph.

Third question;

Part A; The solution is; (2, -1)

Part B; Two solutions for f(x) are; (1.5, 0) and (0, 3)

Part C; The solution for the equation, g(x) = f(x) is the point (0, 3)

A function is rule, law or expression that maps the elements of one set A unto the elements of another set B such that each element of the set A maps unto exactly one element of the set B.

First question;

Part A: The value of x = 4 has two values of y = 2, and -2

The value of x = 9 has to values of output, y = 3 and -3

The function therefore is; y = f(x) = ±√x

The above function indicates that a value of x returns two values of y, which indicates that a vertical line drawn through the graph of the function f(x) = ±√x intersects the graph twice for values of x > 0, therefore, the equation, f(x) = ±√x, represented by the values in the table is not a function

Part B: The function for the total cost of driving a car is f(x) = 90 + 0.11·x

Where; f(x) = The total cost in dollars

x = The distance the car is driven in miles

Therefore, f(300) is obtained by plugging in x = 300 as follows;

f(300) = 90 + 0.11 × 300 = 123

The value of f(300) = $123

f(300) represents the total cost of driving the car for 300 miles

Second question set;

The velocity of the runner after one hour = 6 km/h

The velocity of the runner after three hours = 2 km/h

Part A:  The ordered pair of points of the function are; (1, 6) and (3, 2)

Making use of a linear model, we get;

Slope of the equation of the model, m = (2 - 6)/(3 - 1) = -2

The equation of the model is therefore; y - 6 = (-2) × (x - 1) = -2·x + 2

y = -2·x + 2 + 6

y = -2·x + 8

Where: y = The speed of the runner

x = The number of hours the runner has been running

Part B:

The graph of the equation can be plotted from the values of y obtained from the corresponding values of x for the first 5 hours as follows;

[tex]\begin{array}{|c|c|}x & y \\1 & 6 \\2 & 4\\3 & 2 \\4 & 0 \\5 & -2\\\end{bmatrix}[/tex]

Please find attached the graph of the velocity of the runner with time created using the above table of values found with MS Excel

Third Question;

Part A; The solution to pair of equation can be found from the point of intersection of their graphs

Therefore, the solution of the pair of equations represented by p(x) and f(x) is the point of intersection of the graph of f(x) and p(x), which is the point (2, -1)

Part B; Two solutions for the function f(x) can be obtained by the point of intersection of the x- and y-axis as follows;

The x-intercept of f(x) = (1.5, 0)

The y-intercept of f(x) = (0, 3)

Part C; The solution for g(x) = f(x), is the point of intersection of g(x) and f(x), which is the point (0, 3)

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Answer:

Slope is -1

Step-by-step explanation:

-5/5= -1

I am not sure if you want an explanation or just the answer, but I am willing to explain it if needed.

The approximate height of the kite from the ground will be 159 feet

The best angle to fly the kite = 45 degrees

Th length of the string = 225 feet

To find the height above the ground to the kite, we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

The angle θ = 45 degrees

The length of the hypotenuse = 225 feet

Substitute the values in the equation of sin θ

sin 45 = Opposite side / 225

Opposite side = 225 × sin 45

= 159 feet

Therefore, the height of the kite from the ground is 159 feet

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Answer:

Below

Step-by-step explanation:

Assuming a circular track

Outside track is 3 m 'thicker ' so the diameter is (44 + 3 + 3) = 50 m

Outside track circumference = pi * d =  pi * 50 = 50 pi m

  Inside track circumference = 44 pi

Outside 10 laps = .500 pi   KM     time = .5 pi  km / 4.5 km/hr = .3490658 hr

Inside 10 laps = .444 pi KM            time = .444 pi km / 4.5 km/hr = .309974

Difference = .039095 hr =2.35 minutes

Answer: for the first one, the one that says 7 x 5 = 5 x 7, as the blank is 7.

for the second one, 10 x 11 = 11 x 10, the blank is 10

for the third one, which is Julia's candy, draw 6 pieces of candy in each box and do 4 x 6, which is 24 pieces of candy [4 being the amount of bags].

for the fourth one, draw 5 pieces of candy in each box, then do 5 x 6 = 30.

for the fifth one, it is 4 x 6 = 6 x 4

for the final box, it is 5 x 6 = 6 x 5

Step-by-step explanation:

math

Answer: Hope this helps..

Step-by-step explanation:

7 * 5 - 5 = 30

10 * 11 - 11 = 99

For the candy questions the answers are:

Julia has 24 pieces of candy.

Tommy has 30 pieces of candy.

The equation for Julia is: 4 * 6 = 24

The equation for Tommy is: 5 * 6 = 30

By solving a linear equation, it can be calculated that

x = [tex]\frac{-3y + 5}{2}[/tex]

Option A is correct

What is a linear equation?

At first, it is important to know about algebraic expression.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Now we need to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Linear equation is a very important tool in mathematics

The given linear equation is

2x + 3y = 5

Now,

2x + 3y = 5

2x = -3y + 5

x = [tex]\frac{-3y + 5}{2}[/tex]

Option A is correct

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A line segment with a length of 1.5 and a midpoint of -0.5 is given below:

In the given question, we have to use the drawing tool to form the correct answer on the provided number line.

We have to draw a line segment with a length of 1.5 and a midpoint of -0.5.

As we know that;

Line section on a number line is referred to as a number line segment. A line segment varies from the a lines because a line continues infinitely in both directions, while a line segment is limited by end points. The shortest distance between any two points is a section of a line.

So a line segment with a length of 1.5 and a midpoint of -0.5 is given below:

A line segment a length of 1.5 and a midpoint of -0.5 is notify in the color of red in the graph below.

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Answer:

Isabella spent $1302.52 and Jesus spent $1740.99.

Step-by-step explanation:

In order to figure out how much each individual person spent, we need to write a mathematical equation to express this situation. An equation in math is a statement that relates two expressions that are equal in value, and can be used to solve for variables. A linear equation with one variable is often presented in is standard form, [tex]ax+b=0[/tex].

In this case, we can represent the amount that Isabella spent with the variable x. Since Jesus spent $438.47 more than Isabella, this amount can be represented with x + 438.47. We can set up our equation as follows:

[tex]x+(438.47+x)=3043.51[/tex]

*Note that the use of parentheses is not necessary but may be useful in making your work clearer!

To solve for x, we should combine like terms and then move the variables to one side and constants to the other. The variable can be isolated by subtracting 438.47 from 3043.51:

Now that we have the variable by itself, we can divide by 2 on both sides to solve for x.

As we defined, x equals the amount of money that Isabella spent, which is $1302.52. We can plug that number into x + 438.47 to get the amount that Jesus spent, which we calculate to be $1740.99.

Thus, Isabella spent $1302.52 and Jesus spent $1740.99.

To check our work, we can simply add up the two amounts to see if it totals to $3043.51:

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Answer:

20.69 m

Step-by-step explanation:

36/360 * 2πr = 13

r = 130/2π = 20.69 m

The approximate measures of the angles of ΔABC and the images formed by translation, reflection, and rotation of ΔABC, which are rigid transformations are;

   ΔABC [tex]{}[/tex]                 ΔA'B'C'                 ΔA''B''C''                     ΔA'''B'''C'''

∠A    =  [tex]{}[/tex]  22°           ∠A'  =  22°              ∠A'' = 22°                  ∠A'''  = 22°

∠B    = [tex]{}[/tex]   120°          ∠B'  =  120°            ∠B   = 120°                 ∠B'''  = 120°

∠C [tex]{}[/tex]   =    38°            ∠C'  = 38°              ∠C  =  38°                   ∠C'''  = 38°

A rigid transformation, also known as congruence transformation, in geometry, is one in which the length of the pre-image is preserved, such that the image and the pre-image have the same side lengths, and are therefore congruent.

The coordinates of the vertices of triangle ΔABC, obtained from a similar question online are;

A(-6, -1), B(-3, -3), C(-1, -2)

The lengths of the sides of triangle ΔABC are;

AB = √((-3 - (-6))² + (-3 - (-1))²) = √(13)

BC = √((-1 - (-3))² + (-2 - (-3))²) = √5

AC = √((-1 - (-6))² + (-2 - (-1))²) = √(26)

The law of cosines can be used to fined the measure of an angle of the triangle as follows;

Let a represent the side BC, let b represent the side AC, and let c represent the side AB, the formula for the law of cosines is presented as follows;

a² = b² + c² - 2·b·c·cos(A)

Where;

∠A = The angle at the vertex A

Therefore;

(√5)² = (√(26))² + (√(13))² - 2 × √(26) × √(13) × cos(A)

5 = 26 + 13 - 2 × √(26) × √(13) × cos(A)

cos(A) = (5 - (26 + 13))÷ (-2 × √(26) × √(13))

∠A = arccos((5 - (26 + 13))÷ (-2 × √(26) × √(13))) ≈ 22°

Similarly, we get:

cos(B) = (26 - (5 + 13))÷ (-2 × √(5) × √(13))

∠B = arccos((26 - (5 + 13))÷ (-2 × √(5) × √(13))) ≈ 120°

cos(C) = (13 - (26 + 5))÷ (-2 × √(5) × √(26))

∠C = arccos((13 - (26 + 5))÷ (-2 × √(5) × √(26))) ≈ 38°

The transformation from  ΔABC to ΔA'B'C', obtained from a similar question online, is a translation 5 units to the right and 2 units up

The transformation from ΔA'B'C' to ΔA''B''C'' is a reflection across the line y = -x

The transformation from ΔA''B''C'' to ΔA'''B'''C''' is a counterclockwise rotation by 270° about the origin

The translation, reflection, and rotation transformations are rigid transformations, such that the shape and sizes of the pre-images are preserved, and we get;

[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\Delta ABC &Measure & \Delta A'B'C' &Measure & \Delta A''B''C'' & Measure & \Delta A'''B'''C''' & Measure \\\angle ABC & 120^{\circ} & \angle A'B'C' & 120^{\circ} &\angle A''B''C'' &120^{\circ} &\angle A'''B'''C''' &120^{\circ} \\\angle ACB &38^{\circ} & \angle A'C'B' & 38^{\circ} &\angle A''C''B'' &38^{\circ} &\angle A'''C'''B''' &38^{\circ} \\\\end{bmatrix}[/tex]

[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\Delta ABC &Measure & \Delta A'B'C' &Measure & \Delta A''B''C'' & Measure & \Delta A'''B'''C''' & Measure \\\angle CAB & 22^{\circ} &\angle C'A'B' & 22^{\circ} &\angle C''A''B'' &22^{\circ} &\angle C'''A'''B''' &22^{\circ} \end{bmatrix}[/tex]

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The required probability is approximately 0.0228 that the diameter is greater than 85 millimeters.

The probability that the diameter of a selected bearing is greater than 85 millimeters can be found by calculating the z-score for 85 millimeters and then using the standard normal table to find the corresponding probability.

First, we need to standardize the value 85 millimeters by subtracting the mean diameter and dividing by the standard deviation:

z = (85 - 81) / (4 / sqrt(16)) = 4 / 2 = 2

Next, we can use the standard normal table to find the probability that a randomly selected bearing has a diameter greater than 85 millimeters.

Since the distribution is symmetric, we can find the probability that the diameter is less than 85 millimeters and then subtract this probability from 1 to find the probability that the diameter is greater than 85 millimeters. Looking up the z-score 2 in the standard normal table, we find that the probability that the diameter is less than 85 millimeters is approximately 0.9772.

Therefore, the probability that the diameter is greater than 85 millimeters is approximately 1 - 0.9772 = 0.0228.

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Answer:

0 muffins and 8 cookies

6 muffins and 4 cookies

Explain:

These are the only two combinations of muffins and cookies that Jordan could have sold to earn $24. If Jordan sold 0 muffins and 8 cookies, they would have earned $24 because 0 x $3 + 8 x $2 = $24. If Jordan sold 6 muffins and 4 cookies, they would have earned $24 because 6 x $3 + 4 x $2 = $24.

The graph equation has been plotted on the graph which crosses the points  (0, 10) and (20, 0) on the y and x axis.

Write the equation in the form y = MX + b to determine the slope m and the y-intercept.

This will allow you to graph the equation using the slope and y-intercept (0, b).

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, we have the equation:

8x+16y=160

Where:

x represents the short sleeves.

y represents the long sleeves.

Now, we need to plot the equation as follows:

(Refer to the graph attached below)

So, the equation crosses the points (0, 10) and (20, 0) on the y and x axis.

Therefore, the graph equation has been plotted on the graph which crosses the points  (0, 10) and (20, 0) on the y and x axis.

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1. For the given line segment if PQ = RS then it is proved that PR = QS .

2. From the given angles  if ∠1 is complement to ∠2 (∠1 + ∠2 = 90° )  then angle 1 is complement to angle 3.

As given in the question,

1. Given : PQ = RS

To prove : PR = QS

Proof:

PQ = RS ( given )

Add both the side QR we get,

PQ + QR = QR + RS

From the diagram, it is given P - Q - R - S are collinear points

PR = QS  ( PQ + QR = PR and QR + RS = QS)

Hence, PQ = RS implies that PR = QS.

2. Given: ∠1 is a complement of ∠2

∠2 ≅ ∠3

To prove : ∠1 is a complement of ∠3

proof: ∠1 is a complement of ∠2

⇒∠1 + ∠2 = 90°

⇒∠1 + ∠3 = 90° ( given ∠2 = ∠3 )

⇒∠1 is a complement of ∠3.

Hence, it is proved that ∠1 is a complement of ∠2 implies that ∠1 is a complement of ∠3.

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Answer:

5

Step-by-step explanation:

We have f(x) = 10x^3 and g(x) = 4x^(8/3) given. We need to find f/g, evaluating at x = 8. So how do we do this?

First, let's put our x value into the function f. f(8) = 10*8^3 = 5120.

Next, let's put our x value into the function g. g(8) = 4*8^(8/3) = 1024.

Now we just need to find f/g, which is just the result from our function f divided by our result from function g. This is f(8) / g(8). Substituting our solutions in, we have 5120/1024 = 5.

Answer:

5120/1024 = 5

Step-by-step explanation:

5120/1024 = 5

The polynomial of degree 3 in factored form is calculated and of the form: y = x(x + 3)(x - 10) + 210

Information given in the question include

degree 3

leading coefficient 1

x intercept (10, 0) and (-3, 0)

y intercept (0, -210)

The polynomial is written starting from the x intercept

x = 10, (x - 10)

x = -3, (x + 3)

(x + 10)(x - 10)

y = (x + 3)(x - 10)

for a polynomial of degree three and leading coefficient 1

y = x(x + 3)(x - 10)

for a y intercept (0, -210)

y = x(x + 3)(x - 10)

- 210 = 0

y = x(x + 3)(x - 10) + 210

The factored form of the polynomial is  y = x(x + 3)(x - 10) + 210

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The investment yields a greater return over a 10-year​ period if he invested 7.83​% compounded daily.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Suppose that you have ​$4000 to invest.

The total amount of the investment after 10 years in each case will be given as,

At = r = 7.83% compounded daily, then we have

[tex]\rm A = \ \$4,000 \times \left (1 + \dfrac{0.0783}{365} \right)^{10\times 365}[/tex]

A = $4,000 × (1.000214521)³⁶⁵⁰

A = $4,000 × 2.1878

A = $8,751.37

At = r = 7.9% compounded quarterly, then we have

[tex]\rm A = \ \$4,000 \times \left (1 + \dfrac{0.079}{4} \right)^{10\times 4}[/tex]

A = $4,000 × (1.01975)⁴⁰

A = $4,000 × 2.186

A = $8,745.98

The investment yields a greater return over a 10-year​ period if he invested 7.83​% compounded daily.

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For isosceles trapezoid PQRS the coordinates for point R are;; (a - b, c).

We are told that the following figure is an isosceles trapezoid. This tells us that the two non - parallel sides of the given trapezoid are equal.

A parallel side of the trapezoid lies on the x-axis, which tells us that the opposite side is a horizontal line parallel to the x-axis and that the y-coordinate remains the same for all point lie on that side.

Since the opposite side has vertex (b, c), therefore the y-coordinate for point R is c.

The non-vertical sides are equal. Since the horizontal distance between (0,0) and (b, c) is b, then it means that the horizontal distance between point R and (a, 0) is b. So, the x-coordinate of R is (a - b).

Therefore we conclude that the coordinates for point R are (a - b, c).

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Using mathematical operations, we know that the all-star players of Claremont are 2.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."

The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

So, we know that 25 players in 3 cities.

1 city has 12 players.

Another city has 11 players.

So, the number of players that the 3rd city will have:

12 + 11 + x = 25

23 + x = 25

x = 25 - 23

x = 2

Therefore, using mathematical operations, we know that the all-star players of Claremont are 2.

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Answer:

P/mh

Step-by-step explanation:

P = mgh  to solve for g  Divide both sides by mh

[tex]\frac{P}{mh}[/tex] = [tex]\frac{mgh}{mh}[/tex]    On the right side of the equation the m and h cancel out and you are left with

[tex]\frac{P}{mh }[/tex] = g

As two angles are Complementary Angles they sum up to 90.

So value of d is 10.

Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

60° + 30° in the figure below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,

The opposite of 30° is 60°.

The opposite of 60° is 30°.

Given;

24,(7d-4) are complementary angles

So, 24°+7d-4 =90°;

⇒7d-4=90-24;

⇒7d-4=66;

⇒7d=70;

⇒d=10.

As two angles are Complementary Angles they sum up to 90.

So value of d is 10.

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Answer:

Step-by-step explanation:

Yes, the lines are parallel.

so its d. trust me :)

The solution of the line is, (3, 2), (-1, 1), (1, 3/2), and the equation of the line is y = 1 / 4 x + 5 / 4, so options A, B, C, E, and F are correct.

A line is a shape with an infinite length but no width, depth, or curvature. Lines are one-dimensional objects even though they can exist in two, three, or higher-dimensional contexts.

Given:

The graph of linear equation,

As you can see from the graph the line has coordinates of (3, 2), (-1, 1), (1, 3/2).

Calculate the equation of the line by using the coordinates as shown below,

[tex]y - y_1 = [y_2 - y_1 / x_2 - x_1] (x- x_1)[/tex]

y - 1 = [1 - 2 / -1 - 3]  [x-(-1)]

y - 1 = -1 / (-4) (x + 1)

4y - 4  = x + 1

y = 1 / 4 x + 5 / 4

And line can have many solutions, as it can have more than two values.

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