a rectangle has its upper two vertices on the graph of and its lower two vertices on the -axis. what is the maximum possible area of the rectangle?

68% of the data falls between one standard deviation from the mean which is 13.2 and 19.6

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The empirical rule states that 68% of the data falls within one standard deviation, 95% within two standard deviation from the mean and 99.7% falls within three standard deviation from the mean.

Given a mean of 16.4 and a standard deviation of 3.2.

68% of the data falls one standard deviation from the mean = 16.4 ± 3.2 = (13.2, 19.6)

68% of the data falls between 13.2 and 19.6

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On solving the provided question we can say that the equation gives us  101.77 mi S; 63.59 mi W and S 39.4° W; 131.7 nautical miles

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.

The ship will have traveled 120 nautical miles in the six hours between noon and six o'clock using the formula distance = speed time distance (20 nm/h) (6 h).

The location of the ship will be in (S, W) coordinates.

[tex]120(cos(32), sin(32)) ≈ 120(0.848048, 0.529919) ≈ (101.77, 63.59)[/tex]

The ship will have traveled 101.77 miles south and 63.59 miles west.

83.59). The distance from port will be ...

[tex]d = √(101.77^2 +83.59^2) = 131.7\\ arctan(83.59/101.77) ≈ 39.4[/tex]

The bearing and distance are ...

S 39.4° W

131.7 nautical miles

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The probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck is 1/221.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

The probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck can be calculated as:

There is a total of 52 cards in a deck and 4 aces and 4 queen cards.

So, the probability is

4/52 * 4/51 = 1/221

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The correct option is Option A: (5h^2)^3 + (3k)^3

The total number of cubic units that the cube totally occupies is the definition of a cube's volume. A cube is a solid three-dimensional object with six square faces. Volume is simply the total amount of space an object takes up. A thing with a bigger volume would take up more room.

Total Volume = V₁ + V₂

V₁ = Volume of Cube 1

V₂ = Volume of Cube 2

Volume of Cube = (Side Length)³

V₁ = (5h²)³

V₂ = (3k)³

∴ Total Volume = (5h²)³ + (3k)³

And this cannot be simplified further.

Therefore, the correct option is Option A: (5h^2)^3 + (3k)^3

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Using the tangent side from trigonometric ratio, the angle of depression is 86.6 degrees

The angle created between the line of sight to a location below the horizontal line and the horizontal line of sight is known as the angle of depression.

The angle of depression that the balloon makes with the launch pad can be calculated using the trigonometric ratio.

Data;

Since we have the opposite and adjacent side, we can use the tangent of the angle to find the angle of depression.

tanθ = opposite / adjacent

substituting the values into the formula

tan θ = 10000 / 600

tan θ = 100 / 6

tan θ = 16.666

θ = tan⁻¹(16.666)

θ = 86.6°

The angle of depression is 86.6°

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The value of x in the expression 1 - (2/x²) = - x - 1 is  ± √2, 4.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, An expression 1 - (2/x²) = - x - 1.

- (2/x²) + x = 2.

Multiplying each term by x².

- 2 + x³ = 2x².

x³ - 2x² = 2.

x²(x - 2) = 2.

x² = 2 ⇒ x = ± √2 Or x - 2 = 2 ⇒ x = 4.

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Answer: all are congruent

Step-by-step explanation:

a. The pair of triangles are not congruent.

b. It is impossible to tell about congruency.

c. The pair of triangles are congruent.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

These triangles can be slides, rotated, flipped and turned to be looked identical.

a. The given triangles are not congruent.

The triangle has same measures but the side lengths are different.

So the pair of triangles are not congruent.

b. The given pair of triangles are might be congruent if they have side lengths same.

But in the given triangles the side lengths are not measured.

So it is impossible to tell.

c. The given pair of triangles have same measures and same side lengths.

By AAS rule the pair of triangles are congruent.

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Answer:

Total hours = (total time in seconds) / (3600 seconds in an hour)

Note: Remember to convert the result from seconds to hours.

It's important to mention that you need to know the value of t and y to be able to calculate the total time and the total hours.

If you have the values, you can substitute them in the equations above and get the answer.

Answer:

x = 5

Step-by-step explanation:

You are solving for a x that can, when plugged in, equate both given expressions. To do so, set each given expression equal to each other:

4x - 4 = 8x - 24

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 8x and add 4 to both sides of the equation:

4x (-8x) - 4 (+4) = 8x (-8x) - 24 (+4)

4x - 8x = -24 + 4

-4x = -20

Next, divide -4 from both sides of the equation:

(-4x)/-4 = (-20)/-4

x = -20/-4

x = 5

5 is your answer.

Check:

Plug in 5 for x in both given expressions:

4x - 4

4(5) - 4

= 20 - 4

= 16

-

8x - 24

8(5) - 24

= 40 - 24

= 16

~

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The profit of the insurance company is -20x, where x is the monthly premium.

Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating them. It is used to describe and analyze the relationship between numbers, variables, and operations. Algebra is used to solve equations and simplify expressions, and it is useful in a wide range of applications such as engineering, economics, and science. Algebra also helps us understand and explore abstract concepts such as equations, functions, and graphs. Algebraic thinking is a valuable skill that can help us to make sense of the world around us.

Let x = monthly premium

The insurance company's profit = (500,000 - 20x) - 500,000 = -20x

Therefore, the profit of the insurance company is -20x, where x is the monthly premium.

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Answer:

3.20

Step-by-step explanation:

Therefore , solution of unitary method problem The cost of the items purchased, the cost of shipping and handling, the cost of transit insurance.

The unitary approach is a method of problem solving that entails first calculating the percentage of a single set there is, then doubling that value to arrive at the solution. The unit technique, to put it simply, is used to extract a typical programming value from a given many. For instance, the price of 40 pens is 400 rupees ($1.01), meaning Rs. It's feasible that the method used to achieve this will be controlled in only one nation.

Here,

The finished goods kept in inventory are those that will be sold to clients.

All items that are owned by a business and kept for sale are included in the merchandise inventory.

a retail business:

purchases and sales of goods generate its net income.

It can also purchase goods from producers and market them to retailers.

It can also be a retailer or a wholesaler, purchasing goods from producers and selling them to clients.

The term "current asset" refers to merchandise inventory.

Therefore , The cost of the items purchased, the cost of shipping and handling, the cost of transit insurance, and the cost of storage are all included in the merchandise inventory account.

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The interpretation of the value, 29,864, in the quadratic regression equation is the initial loss incurred by the company. The correct option is therefore;

A quadratic regression equation is the equation of the parabola that corresponds of best fits the points of the dataset on the coordinate plane.

The points on the graph of the question, obtained from a similar question, posted online are;

Number of units [tex]{}[/tex]           Profits ($)

500 [tex]{}[/tex]                         -10000

1200  [tex]{}[/tex]                   3000

2500  [tex]{}[/tex]                   27000

3200  [tex]{}[/tex]                   40000

3600  [tex]{}[/tex]                   45000

4300  [tex]{}[/tex]                   47000

5000  [tex]{}[/tex]                   45000

6750  [tex]{}[/tex]                   20000

The polynomial regression equation that corresponds to the points in the above table, obtained with MS Excel is presented as follows;

y = -0.004·x² + 34.637·x - 29864

Where;

y = The profit made

x = Number of units

When the company produces 0 units, x = 0, we get;

The 29864 is therefore the loss of $29864, of the company when the company produces zero units.

The correct option is therefore;

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Answer:

t = 8

Step-by-step explanation:

8t - 2=62

8t =62+2

8t = 64

t = 64÷8

t = 8

Answer: t = 8

Step-by-step explanation:

In all, she purchased 1 book and 6 periodicals, taking into account the inequality.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, Angelina spent $23.65 on books and magazines when she went to chapters. She bought a total of 7 items. The books cost $5.95 each and the magazine cost $2.95 each.

Let "b" be the number of total book and "m" be the number of magazine she bought.

Inequality from the given data

m + b = 7

since, Angelina spent $23.65 on books and magazines

thus,

5.95 * b + 2.95 * m = 23.65

from equation 1

5.95b + 2.95(7 - b) = 23.65

5.95b + 20.65 - 2.95b = 23.65

3 b  = 3

b = 1

from any equation

m = 6

Therefore, she total bought 1 book and 6 magazines according the given inequality.

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Answer:

D)

That is the only one we can be certain with.

1st option is obviously incorrect

2nd option is wrong as it can also be two are negative one is positive

3rd option is wrong as it can also be one is negative two are positive

4th option is correct as u can't get negative values without a negative numberl.

Answer: Let's call the hourly rate of the first mechanic "r1" and the hourly rate of the second mechanic "r2".

We know that the total time they worked is 20 hours + 5 hours = 25 hours.

We also know that the sum of their hourly rates is $95 per hour, so:

r1 + r2 = $95

We can use this information along with the total amount they charged, $1150, to find out how much each mechanic charged. We know that the total amount charged is the product of the number of hours worked and the hourly rate. So we can use the following equation:

(20 hours * r1) + (5 hours * r2) = $1150

Now we can substitute the equation r1 + r2 = $95 into the above equation and solve for r1:

(20 hours * r1) + (5 hours * (95 - r1)) = $1150

20r1 + 475 - 5r1 = 1150

15r1 = 675

r1 = $45/hour

To find out the hourly rate of the second mechanic, we can use the equation r1 + r2 = $95

r2 = $95 - r1

r2 = $95 - $45

r2 = $50/hour

So the first mechanic charges $45 per hour and the second mechanic charges $50 per hour.

Step-by-step explanation:

If you attempt to solve an equation and the result is false, the problem has no solutions.

If both sides of a linear equation have unique constant values but the same variable term, then the problem has no solutions.

For instance, in the equation [tex]3x+8=1+3x[/tex],

the variable term is the same, [tex]3x[/tex], but the constant terms, 8 and 1, are on opposite sides of the equation. It, therefore, lacks solutions. Try the equation to determine why.

[tex]3x+8=1+3x\\8=1[/tex]

following mathematics, the term is not possible. so, here equation has no solutions. so how we can know that equation has no solution if mathematical inequality is wrong.

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======================================================

Explanation:

Check out the diagram below.

I've defined the following points:

Now focus on triangle ACF. This is an isosceles right triangle with legs of 0.5x each. The hypotenuse is the radius of the circle. Let R be that unknown radius.

The area of the circle is given to us. It is 56 square cm. Use this to find the value of R.

[tex]A = \pi*(\text{radius})^2\\\\56 = \pi*R^2\\\\R^2 = 56/\pi\\\\R = \sqrt{56/\pi}\\\\R = 4.22200825\\\\[/tex]

This value is approximate. I used the calculator's stored version of pi to get the most accuracy possible.

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

We now know the hypotenuse of triangle ACF.

Use Pythagoras (aka Pythagorean Theorem) to have the following steps:

[tex]a^2+b^2 = c^2\\\\(0.5\text{x})^2+(0.5\text{x})^2 = 4.22200825^2\\\\0.25\text{x}^2+0.25\text{x}^2 = 17.82535366\\\\0.5\text{x}^2 = 17.82535366\\\\\text{x}^2 = 17.82535366/0.5\\\\\text{x}^2 = 35.65070732\\\\\text{x} = \sqrt{35.65070732}\\\\\text{x} = 5.97082132708726\\\\\text{x} = 5.97\\\\[/tex]

With the exception of 0.5 and 0.25, each decimal value mentioned is approximate.

Keep in mind that rounding to 3 sig figs means that we're rounding to 2 decimal places. The units digit is 1 sig fig, and the 2 decimal places give a total of 1+2 = 3 sig figs.

In short, we're rounding to the nearest hundredth.

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

Check:

x = 5.97 is the square's side length.

It divides in half to get x/2 = 5.97/2 = 2.985 which gives each leg of triangle ACF.

Use a = 2.985 and b = 2.985 in the Pythagorean Theorem to find that c = 4.22142748 approximately. This is the approximate radius of the circle.

Use that radius to find the area of the circle.

A = pi*r^2

A = pi*(4.22142748)^2

A = 55.984594705958

A = 56.0

I'm rounding the area to 3 sig figs to keep consistent with the rounding done to x. We arrive at the circle area of 56 square cm, which helps confirm the answer is correct.

Answer:

Step-by-step explanation:

the sum of the interior angles in a triangle is 180°, take away the know angle and divide by 2, it's an isosceles triangle so 2 side and 2 equal angles

(180 - 134) : 2 =                         (remember PEMDAS)

46 : 2 =

23°

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

23 + 23 + 134 = 180°

Answer:

398.32

Step-by-step explanation:

647.82 - 249.50 = 398.32

On solving the provided question we can say that equation of pendulum traces an arc, s, that is roughly 4.61 inches long.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

6° = 6°  X [tex]\pi /180 = \pi /30[/tex]

s = r∅

s = 44 X  [tex]\pi /30[/tex]

s = 4.61

Hence, The pendulum traces an arc, s, that is roughly 4.61 inches long.

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Answer: X = [tex]\frac{1}{\sqrt{2} }[/tex]

Step-by-step explanation: Because the two angles are equal (You circled them, also 45 degs), and there is a right triangle, which means that the 90-degree angle's adjacent sides are equal, in this case, both sides equal to X.

Using the special triangle ratio ( 1, 1, [tex]\sqrt{2}[/tex]), in this case, the "2" is equal to [tex]\sqrt{2}[/tex] times [tex]\sqrt{2}[/tex], so you have to divide the "1" (X) by [tex]\sqrt{2}[/tex], you simply get [tex]\frac{1}{\sqrt{2} }[/tex].

Sorry for my bad english

On solving the provided question, we can say that  10% condition is met,

There are two separate random samples available.

selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.

There are two separate random samples available.

The 10% requirement is satisfied.

For both samples, 24, 26, 29, and 31 triumphs and failures are anticipated.

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The constant of proportionality for the proportional equation is 36.

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,
Box = b

Number of pencils in one box.

p = 36

Now,

The proportional equation for b and p.

p ∝ b

p = mb

where m is the constant of proportionality.

Now,

b = 1

p = 36

p = mb

36 = m x 1

m = 36

Thus,

The constant of proportionality is 36.

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Jerome will have $3261.93 after 4 years

The formula for compound interest is A = P(1 + r/n)^(nt)

where:

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for.

In this case, P = $3,000, n = 3, r =  2.1% = 0.021, t = 4 years. Thus:

A = P(1 + r/n)^(nt)

A = 3000(1 + 0.021/3)^(3×4)

A = 3000(1 + 0.021/3)^(12)

A = $3261.93

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Answer: (0, -1/3)

Step-by-step explanation: The answer is: (0, -1/3)

y=mx+b

Slope being "m"
And the y intercept being "b"

I think it's (0, -1/3)

......

..

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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Answer:

C

Step-by-step explanation:

807 is equal to 800 + 7, and 24 is equal to 20 + 4. Using the distributive property, we get 20(800) + 4(800) + 20(7) + 20(7)

Answer:

C

Step-by-step explanation:

Because 24*807 in distributive property is C