Which of the following represents the total area of the figure?
44 ft²
400 ft²
440 ft²
484 ft²​

Answer:

x=105

Step-by-step explanation:

The angles of a triangle add up to 180 degrees.

[tex]180 = 30 +45+x[/tex]

[tex]x=105[/tex]

The number of solutions that the system has is

One Solution

To solve the system algebraically, we can substitute the first equation into the second equation to eliminate one of the variables. We'll use y:

x=2y-5

7x-14y=10

Substitute x=2y-5 into 7x-14y=10:

7(2y-5)-14y=10

Expand the left side:

14y-35-14y=10

Combine like terms:

-35=10

Solve for y:

y = -7.5

Substitute y = -7.5 back into x=2y-5:

x = 2(-7.5) - 5

Solve for x:

x = -10

So the solution to the system of equations is (x, y) = (-10, -7.5).

Since there is one unique solution, the system has One Solution.

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In 30 minutes, the woman will travel 12.5 miles.

This is due to the fact that the rate (25 mph) times the time equals the distance traveled. Mathematically, this can be expressed as d = rt, where d represents the distance, r represents the rate (speed), and t represents the time. In this instance, the distance can be calculated as d = 12.5 miles by multiplying d = 25 mph by 30 minutes/60 minutes.

The distance between two points is measured in distance. The rate, or the amount of distance traveled per unit of time, is the speed at which a person or vehicle travels. The woman in the car is traveling at a rate of 25 miles per hour (mph).

In this instance, the time is. The formula d = rt can be used to determine the distance traveled by multiplying her rate by the time. Given the rate and duration of travel, this formula can be used to determine the distance traveled by any object or person.

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The only value that remains unchanged is the standard deviation.

The mean, median, range, and standard deviation will all change once the corrected weight is used to calculate the data. The mean is calculated by adding all the weights and dividing by the total number of horses. Therefore, the mean will be recalculated using the corrected weight of 1005 and the new value will be lower than the previous mean. The median is the midpoint of the data set, so it will also decrease with the updated weight. The range is the difference between the highest and lowest values, so it will also decrease with the corrected weight. Lastly, the standard deviation is a measure of the spread of the data and will also decrease when the corrected weight is used. Therefore, the only value that remains unchanged is the standard deviation.

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This statement is a description of basic concepts in probability theory.

An outcome of flipping a coin is heads, which can be assigned a probability of 0% or 100% depending on whether the coin lands heads or tails. In general, probabilities must be between 0% and 100% to ensure that a probability distribution is valid. The sum of all probabilities for all possible outcomes must also add up to 100%.

The ratio of the ways to succeed to all possible ways that something can occur is referred to as the probability of the event. This is the fundamental definition of probability.

Finally, to find out how many ways a multi-step process can be completed, you can use the concept of combinations or permutations. These are mathematical concepts used to count the number of possible arrangements or selections of items, given a certain set of conditions.

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If one of the three machines breaks down before starting the service, it would take the remaining two machines longer to meet the demand. If each machine can produce the same amount of material, it would take each machine 24 hours / 3 machines = 8 hours to perform the entire service.

So, with two machines working, it would take each machine 8 hours / 2 machines = 4 hours to complete the job. Thus, the total time to meet the demand would be 4 hours * 2 machines = 8 hours.

Customers have to wait for d) approximately 12 minutes if we do pool the employees.

This can be found by calculating the average waiting time per customer, which is the average service time divided by the average number of customers.

In this case, the average service time is 6 minutes (with a standard deviation of 3 minutes) and the average number of customers is 24. So, the average waiting time per customer is 6/24 = 0.25 hours = 15 minutes.

To ensure that customers do not have to wait any longer than necessary, it is best to have three separate lines for the three tellers. This way, customers are served in the order they arrive, rather than having to wait for one teller to serve all the customers.

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Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do note that this question requires the concept on Pythagoras' Theorem.

Work is defined as the product of force and distance, and can be calculated using the equation W = F * d, where W is work, F is force, and d is distance.

When lifting the whole log, the force required is equal to the weight of the log, and the distance over which the force is applied is the distance from the ground to the height of the shoulder.

When lifting one end of the log, the force required is still equal to the weight of the log, but the distance over which the force is applied is reduced. This is because the lever arm (the distance from the axis of rotation, which is the shoulder joint, to the point where the force is applied, which is the end of the log) is reduced.

So the equation for work done in lifting the whole log would be  W = m * g * h, where m is the mass of the log, g is the acceleration due to gravity, and h is the height from the ground to the shoulder. The equation for work done in lifting one end of the log would be W = (m/2) * g * h', where h' is the reduced height.

It can be seen that the work done in lifting one end of the log is equal to half the work done in lifting the whole log, because the force applied is the same, but the distance over which it is applied is reduced.

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The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given,  line containing the point (5, −3) and is parallel to: y = − 2/5x − 3/4

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

In our case Line is parallel to the Line y = − 2/5x − 3/4,

So the slope would be the same.

m = -2/5

Thus, the equation of the line:

y = -2/5x + b

Since the line passes through the point (5, -3)

-3 = -2/5 * 5 + b

b = -1

Thus the final equation of a line:

y = -2/5x - 1

Therefore, The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

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Answer:

Below

Step-by-step explanation:

Value will be original value * ( 1 + i)^n      i = decimal annual interest

                                                                      n = years

  Value = 300 ( 1 + .07)^10 = 590.15  (dollars ?)

The cardinalities:

n(A) = 3

n (B) = 1.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Let sets A and B be defined as follows.

A is the set of integers greater than or equal to -9 and less than or equal to - 3

Set A can be expressed as,

A = {n ≥ -9 or n ≤ -3}

And set B is given,

B = {1-29, -26, -23, 30}

Simplifying,

B = {-28, -26, -23, 30}

The cardinalities:

n(A) = 3

n (B) = 1.

Therefore, n(A) = 3 and n (B) = 1.

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The closest answer to the increase in the distance of the Olympic marathon is 1.50 miles. Hence the correct answer is option C.

In order to find the increase in the distance of the Olympic marathon, we will find the difference between the old distance (40 km) and the new distance (42 km) and then convert it to miles.

40 km - 42 km = -2 km

Converting -2 km to miles, we get:

-2 km x 1.6 miles/km = -3.2 miles

However, since the marathon was lengthened, the actual increase in the distance is:

-3.2 miles = 3.2 miles

Rounding to the nearest 0.25 miles, we get,

3.2 miles = 3.25 miles ≈ 3.25 miles

So the closest answer to the increase in the distance of the Olympic marathon is 1.50 miles.

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The complete question is -

In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)

A) 1.00

B) 1.25

C) 1.50

D) 1.75

Ted needs 47 + 53 = 100 inches of curved track to complete the missing parts of his model station layout.

First, we need to find the length of each arc. To do this, we'll use the formula:

arc length = circumference * central angle / 360

The circumference of a circle with radius 10 inches is 2 * pi * 10 = 20 * pi inches.

So, for the 75º sector:

arc length = 20 * pi * 75 / 360 = 15 * pi inches

And for the 85º sector:

arc length = 20 * pi * 85 / 360 = 17 * pi inches

Rounding pi to 3.14, we get:

arc length = 15 * 3.14 = 47.1 inches (rounded to 47 inches)

arc length = 17 * 3.14 = 53.4 inches (rounded to 53 inches)

So, Ted needs 47 + 53 = 100 inches of curved track to complete the missing parts of his model station layout.

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Rewrite expression in rational exponent form

[tex]a) \: \: \: \: \sqrt[5]{ (- 53) ^{4} } \\ b) \: \: \: \: \: \: \sqrt[4]{(110) {}^{7} } [/tex]

the rational exponent form :

a)

[tex] { - 53}^{ \frac{4}{5} } [/tex]

b)

[tex]110 { }^{ \frac{7}{4} } [/tex]

Exponential numbers are a form of mathematical abbreviation that allow us to write complex mathematical expressions more succinctly. An exponential number is a number that is repeatedly multiplied by itself.

Exponential is written with numbers and letters to the right of certain mathematical expressions called bases. While exponential numbers are often also called powers. Properties of exponential numbers

Exponential numbers have their own special properties as follows:

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Every year, 1800 units crossover point. The process focus is less expensive for volumes over 1800.

When all tax credits have been used up by a limited partnership and the limited partners are left with a tax burden, that moment is known as the crossover point.

When both projects have positive values, the crossover point is formed by the intersection of two IRR curves.

The weighted average cost of capital, also known as the crossover rate, is the rate of return at which the net present values (NPV) of two projects are equal.

The rate of return at which the net present value profiles of two projects cross each other is what this term denotes.

So, annual crossover sales are 1800 units.

Process emphasis is less expensive and less important for volumes under 1800 units; repeated manufacturing concentration is less expensive and less important for volumes exceeding 1800 units.

Fixed cost ÷ variable cost

$90000÷50 =$1800

$9,000÷5=$1800

Therefore, every year, 1800 units cross over. The process focus is less expensive for volumes over 1800.

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Correct question:

A product is currently made in a process-focused shop, where fixed costs are $9,000 per year and variable costs are $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacturing. The new process would have fixed costs of $90,000, and variable costs of $5. The cross over is at 1800 units annually. for volumes over 1800, the process focus is cheaper.

The coordinates of point H are (2 - 3, -4) = (-1, -4).

In mathematics, a graph is a visual representation of a relationship between two variables. It is usually represented as a set of points on a coordinate plane, where the horizontal axis represents one variable and the vertical axis represents the other variable. The points are plotted based on their corresponding values for the two variables, and a line or curve is drawn through the points to show the relationship between the two variables.

Graphs are often used to represent mathematical functions and equations, as they provide a quick and easy way to visualize the relationship between the input and output values. They can also be used to represent data in fields such as science, economics, and social sciences, where they provide a way to analyze and interpret data trends and patterns.

Graphs can be drawn by hand, using graph paper and a ruler, or they can be generated using software, such as spreadsheet programs, mathematical software, and graphing calculators. In addition to helping to visualize the relationship between two variables, graphs can also be used to estimate values, find maximum and minimum points, and make predictions.

The coordinates of point H can be determined by subtracting 3 from the x-coordinate of point G. Therefore, the coordinates of point H are (2 - 3, -4) = (-1, -4). So, point H is located 3 units to the left of point G on the x-axis.

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The value of arc x is solved to be 120 degrees

The Arc x is solved using the knowledge of linear pair

A linear pair of angles forms a straight line, and the two angles are said to be "linear" because they are next to each other and their measures add up to 180 degrees.

Applying this we have that

60 + x = 180

x = 180 - 60

x = 120 degrees

hence we can say that x is 120 degrees

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3a.) The number of calories at 24 minutes would be = 60 calories

3b.) The time at 280 calories = 42 minutes.

4a.) The height in feet after 4 minutes = 24 feet

4b.) The time when the height is 48 minutes = 8 mins.

There are two main graphs represented above which include the following details:

The first graph: Calories was plotted in y-axis against time in x-axis.

The second graph : Height was plotted in y-axis against time is X axis.

When an imaginary straight line is drawn from the origin of the graph, the following values can be derived:

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The parametric equations of a line can be determined using a point on the line and a direction vector. To find the parametric equation of a line that passes through a point A and is parallel to a direction vector b, we can use the following formula:

x = x0 + tbx

y = y0 + tby

z = z0 + tbz

where (x0, y0, z0) is the position vector of point A, (bx, by, bz) is the direction vector, and t is the parameter that varies along the line.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

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The die's color is noted and it is not replaced. This experiment is repeated four times. The probability that a green die is selected fewer than three times is 8/11.

A box contains six green dice, three red dice and three white dice.

Total dice = Green Dice + Red Dice + White Dice

Total dice = 6 + 3 + 3

Total dice = 12

The probability that a green die is selected fewer than three times = P(G'G'G'G') + P(G'G'G'G) + P(G'G'GG') + P(G'GG'G') + P(GG'G'G') + P(GGG'G') + P(GG'GG') + P(GG'G'G) + P(G'GGG') + P(G'GG'G) + P(G'G'GG)

Here G represents that the dice is green while G' represents as the dice is not green.

The probability that a green die is selected fewer than three times = 6/12×5/11×4/10×3/9 + 6/12×6/11×5/10×4/9 + 6/12×6/11×5/10×4/9 + 6/12×5/11×6/10×4/9 + 6/12×5/11×4/10×6/9 + 6/12×5/11×6/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9  + 6/12×5/11×6/10×5/9

The probability that a green die is selected fewer than three times = 360/11880 + 720/11880 + 720/11880 + 720/11880 + 720/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880

The probability that a green die is selected fewer than three times = 8640/11880

The probability that a green die is selected fewer than three times = 8/11

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Based on each given quadrilateral, we know that:

Rectangle ABCD has:

Rhombus FGHJ:

Square LMNO:

Let's discuss each quadrilateral we have:

ABCD is a rectangle; then:

DC = AB = 12

BD² = BC² + CD²

13² = BC² + 12²

169 = BC² + 144

BC² = 25

BC = 5

DE = 1/2 BD

DE = 1/2 (13)

DE = 6.5

∠DBA and ∠BDC are alternate interior angles and congruent, then:

∠DBA = ∠BDC = 35°

∠DBA = ∠BAC because triangle BAE is isosceles triangle.

∠BAC is the alternate interior angle of ∠DCA; then:

∠BAC = ∠DCA = 35°

∠DAB = ∠DAC + ∠BAC

90° = ∠DAC + 35°

∠DAC = 55°

Focus on triangle DEC:

∠DEC + ∠EDC + ∠ECD = 180°

∠DEC + 35° + 35° = 180°

∠DEC = 110°

Focus on triangle CEB:

∠CEB + ∠EBC + ∠CBE = 180°

∠CEB + 55° + 55° = 180°

∠CEB = 70°

FGHJ is a rhombus; then:

∠JGH = ∠FJH = 2∠FJG

∠JGH = ∠FJH = 2(60)

∠JGH = ∠FJH = 120°

Since FGHJ is a rhombus, then:

∠JGH + ∠JHG + ∠FGH + ∠JFG = 360°

120° + ∠JHG + 120° + ∠JGH = 360°

240° + 2∠JHG = 360°

2∠JHG = 120°

∠JHG = 60°

∠KFG = 1/2∠JHG

∠KFG = 1/2 (60)

∠KFG = 30°

GH = FG = 10

To find KG, we need to focus on triangle F.KG. Under the Sines Law:

KG / sin 30 = FG / sin 90 = F.K / sin 60

KG / √3/2 = 10 / 1 = F.K / 1/2

KG = 5

F.K = 5√3

FH = 2F.K

FH = 2(5√3)

FH = 10√3

LMNO is a square, then:

∠OMN = 45°

Please focus on triangle MNP. Under the Sines Law:

PM / sin 45 = MN / sin 90

PM / √2/2 = 8√2 / 1

PM = 8

LN = 2PM

LN = 2(8)

LN = 16

∠OPL = 90°

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72 cm²  

3 * ( 6+2+2) + 2 * (2 * 6) + 6 * 3

Answer: 5/6

Step-by-step explanation:

(4/9)/(8/5)=5/6

The expression which can be used to represent the given using the fewest possible terms is 2x + 2

The correct answer choice is option B.

(−5x − 12) + (14 + 7x)

open parenthesis

-5x - 12 + 14 + 7x

collect like terms

-5x + 7x - 12 + 14

2x + 2

In conclusion, 2x + 2 is the expression which represents the fewest possible terms of (−5x − 12) + (14 + 7x)

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Answer:

its C

Step-by-step explanation:

other guy wasn't reasonable and chose the actual shortest one possible instead of the one that made sense

Answer:

I think B

Step-by-step explanation:

sorry if I said wrong

There will be left 7.5 grams of the radioactive kind of neodymium after 44 days, with half life of 11 days.

Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.

Given that, a radioactive kind of neodymium have the half-life is 11 days, and with 120 grams

We need to find the remaining after 44 days,

The formula to calculate half life =

[tex]N(t) = N(1/2)^\frac{t}{t_{1/2} }[/tex]

N(t) = quantity of the substance remaining

N = initial quantity of the substance

t = time elapsed

t{1/2} = half life of the substance

N(t) = 120(1/2)⁴⁴/₁₁

= 120(1/2)⁴

= 120(1/16)

= 7.5

Hence, there will be left 7.5 grams of the radioactive kind of neodymium after 44 days, with half life of 11 days.

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If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, then the  proportional equation for p in terms of s is, p = $21 x s

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Let's call the selling price of each sweater "sp".

The store buys 15 sweaters for $90, so each sweater must cost

=$90 / 15

= $6

The store sells each sweater for

= $405 / 15

= $27,

so sp = $27

The total profit is equal to the selling price minus the buying price, so the equation for the total profit, p, in terms of the number of sweaters sold, s, is:

p = sp x s - $6 x s

We can simplify this equation to:

p = ($27 - $6) x s

p = $21 x s

So, the proportional equation for the total profit in dollars and cents when the store buys any number of sweaters, s, is:

p = $21 x s

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