prove the following identity:

The area of the given rectangle in simplest fraction form is: 81³/₅ m²

The formula for the area of a rectangle is expressed as:

A = L * W

Where:

A is Area

L is length

W is width

We are given the parameters:

Length = 12³/₄ meters = 51/4 meters

Width = 6.4 meters = 6²/₅ meters = 32/5 meters

Thus:

Area = 51/4 * 32/5

= 408/5 m²

= 81³/₅ m²

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Answer:

Step-by-step explanation:

Answer = 50.8 in^2 for surface area of the triangular prism

Step by step

A “net” is the figure laid out so you can see it broke down into smaller shape

Starting from the left we have 3 rectangles and two triangles

Area of rectangles = L x W

Area of triangles = 1/2bh

Solve

Rectangle #1 = 2 x 5 = 10 in^2

Rectangle #2 = 2 x 4 = 8 in^2

Rectangle #3 = 2 x 6.4 = 12.8 in^2

Triangle #1 = (1/2) (4) (5) = 10 in^2

Triangle #2 = (1/2) (4) (5) = 10 in^2

Add your figures together

10 + 8 + 12.8 + 10 + 10 = 50.8 in^2

see attachment for breakdown

Answer:

Step-by-step explanation:

Solve for the variable. Determine if there is one solution, infinitely many solutions, or no solution.

-6x – 12 = 5(-2x – 3)

Let's start by simplifying the right side of the equation:

5(-2x – 3) = -10x - 15

Substituting this back into the original equation, we get:

-6x - 12 = -10x - 15

Next, we can simplify this equation by adding 10x to both sides:

4x - 12 = -15

Finally, we can add 12 to both sides:

4x = -3

Dividing both sides by 4 gives us:

x = -3/4

Therefore, there is one solution, and x equals -3/4.

By evaluating the linear function in different values of x, we will get the complete table:

x         f(x)

-3         -6

-2         -16/3

0            -4

3             -2

6              0

Here we have a table of x and f(x) and we want to complete it, to do so, we only need to evaluate the function in different  values of x and then put that in the correspondent places.

if x = -2

f(-2) = (2/3)*-2 - 4

      = -4/3 - 4 = -4/3 - 12/3 = -16/3

if x = 0

f(0) = (2/3)*0 - 4 = -4

if x = 3

f(3) = (2/3)*3 - 4 = 2 - 4 = -2

if x = 6

f(6) = (2/3)*6 - 4 = 0

Then putting these in the table, we will get:

x         f(x)

-3         -6

-2         -16/3

0            -4

3             -2

6              0

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The length of the rectangular lot is 30m

The formula for calculating the perimeter of a rectangle is expressed as;

P =2(l + w)

Such that the parameters are;

From the information given, we have that;

Length = 5 + w

Now, substitute the values

110 = 2( 5 + w+ w)

collect the like terms

110 = 2(5 + 2w)

expand the bracket

110 = 10 + 4w

4w = 100

Divide both sides by the coefficient of w

w = 25

Then, the length = 30m

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By answering the presented question, we may conclude that Therefore, the solutions to the equation 3y² + 5y = 12 are y = -2/3 or y = 1, rounded to the nearest hundredth.

A statement proving the equality of two expressions is known as an equation. It can include variables, integers, and mathematical operations like addition, subtraction, multiplication, and division. It also incorporates mathematical symbols. In mathematics and science, equations are frequently used to illustrate connections between quantities. The equals sign (=) is typically used in equations to denote that the expressions on each side of the sign have the same value. For instance, the formula 2 + 3 = 5 demonstrates that the total of 2 and 3 equals 5. Equations can be solved to determine a variable's value or to determine if a certain value meets the connection that the equation describes.

3y² + 5y = 12

3y² + 5y - 12 = 0

y² + (5/3)y - 4 = 0

y² + (5/3)y + 25/36 - 25/36 - 4 = 0

(y + 5/6)² - 49/36 = 0

(y + 5/6)² = 49/36

y + 5/6 = ±(7/6)

y = (-5 ± 7)/6

y = -2/3 or y = 1

Therefore, the solutions to the equation 3y² + 5y = 12 are y = -2/3 or y = 1, rounded to the nearest hundredth.

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Answer:

The 99% confidence interval for the population proportion is between (0.4526, 0.4960). The interpretation is that we are 99% sure that the true proportion of adults who have started paying bills online in the last year is between these two values.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\dfrac{\pi (1-\pi )}{n} }[/tex]

In which

z is the z-score that has a p-value of [tex]1-\dfrac{\alpha }{2}[/tex].

For this problem, we have that:

In a survey of 2954 ​adults, 1401 say they have started paying bills online in the last year. This means that [tex]n=2954, \ p=\dfrac{1401}{2954} =0.4743[/tex]

99% confidence level

So [tex]\alpha =0.01[/tex], z is the value of Z that has a p-value of [tex]1-\dfrac{0.01}{2} =0.995[/tex], so [tex]Z=2.575[/tex].

The lower limit of this interval is:

[tex]\pi -z\sqrt{\dfrac{\pi (1-\pi)}{n} } =0.4743-2.575\sqrt{\dfrac{0.4743\times0.4408}{2954} } =0.4526[/tex]

The upper limit of this interval is:

[tex]\pi -z\sqrt{\dfrac{\pi (1-\pi)}{n} } =0.4743+2.575\sqrt{\dfrac{0.4743\times0.4408}{2954} } =0.4960[/tex]

The 99% confidence interval for the population proportion is between (0.4526, 0.4960). The interpretation is that we are 99% sure that the true proportion of adults who have started paying bills online in the last year is between these two values.

Answer:

To reflect a point over the x-axis, we need to negate the y-coordinate while keeping the x-coordinate the same.

The given point is located 5 units to the left and 6 units up from the origin. So its coordinates are (-5, 6).

To reflect this point over the x-axis, we negate the y-coordinate to get (−5, −6).

Therefore, the ordered pair that is a reflection over the x-axis for the given point is (−5, −6).

Answer:

b

Step-by-step explanation:

 -5, -6

The answer of the given question is the monthly payment necessary to amortize the loan is $923.98.

Principal refers to the original amount of money that is borrowed or invested, not including any interest or fees that may accrue over time. In the context of a loan, the principal is the amount that the borrower receives and is responsible for repaying to the lender over a specified period of time, usually with interest.

To calculate the monthly payment necessary to amortize the loan, we can use the following formula:

M = P * (r/12) * (1 + (r/12))ⁿ / ((1 + (r/12))ⁿ - 1)

where:

M = monthly payment

P = principal amount borrowed

r = annual interest rate

n = total number of monthly payments

Plugging in the values for the given loan, we get:

P = 140,000

r = 0.02375 (2.375% expressed as a decimal)

n = 15 years * 12 months/year = 180 months

M = 140,000 * (0.02375/12) * (1 + (0.02375/12))¹⁸⁰ / ((1 + (0.02375/12))¹⁸⁰ - 1)

M = 923.98

Therefore, the monthly payment necessary to amortize the loan is $923.98.

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The monthly payment necessary to amortize the loan is $928.52.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To calculate the monthly payment necessary to amortize a loan, we can use the formula:

P = (A * r) / (1 - (1 + r)^(-n))

Where:

P = Monthly payment

A = Loan amount

r = Monthly interest rate (annual interest rate / 12)

n = Total number of payments (number of years * 12)

Using the formula and plugging in the values from the problem:

A = 140,000

r = 0.02375/12 (2.375% annual interest rate divided by 12 months)

n = 15*12 = 180

P = (140,000 * (0.02375/12)) / (1 - (1 + (0.02375/12))^(-180))

P = $928.52 (rounded to the nearest cent)

Therefore, the monthly payment necessary to amortize the loan is $928.52.

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Theoretically, there is a probability of 23.1%, or about 0.231, chance that a face card will be drawn at random from a deck of playing cards.

Each of the four suits hearts, diamonds, clubs, and spades in a conventional deck of playing cards, which has 52 cards total, has 13 cards (Ace, 2-10, Jack, Queen, and King). Among these 52 cards, there are 12 face cards (Jacks, Queens, and Kings). So the number of face cards is 12, and the total number of cards is 52.

The probability of selecting a face card can be calculated by dividing the number of face cards by the total number of cards:

[tex]P_{face card}[/tex] = [tex]\frac{number of face cards}{total number of cards}[/tex]

= 12 / 52

= 3 / 13

≈ 0.231 or 23.1%

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The complete question is:

Find the theoretical probability of randomly selecting a face card​ (J, Q, or​ K) from a standard deck of playing cards

The probability that a worker selected at random makes between $350 and $450 is 68%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

We can start by standardizing the values of $350 and $450 using the formula:

z = (x - mu) / sigma

where x is the value we want to standardize, mu is the mean, and sigma is the standard deviation.

For $350, we have:

z = (350 - 400) / 50 = -1

For $450, we have:

z = (450 - 400) / 50 = 1

Now, we can use the z-score table or calculator to find the probability of a standard normal distribution between -1 and 1, which is approximately 68%.

Therefore, the probability that a worker selected at random makes between $350 and $450 is 68%.

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(a) The size of angle x will be 90°.

(b) The theorem that helped to solve this problem is, the angle between the tangent and the radius at a point on a circle is 90°.

What is a circle's radius?

The radius of a circular is the separation between any two points on its circumference. R or r is typically used to indicate it. This amount is significant in practically all formulae involving circles. A circle's radius may also be used to calculate its surface area and circumference. Circle circumference equals two.

What are diameter and radius?

The circle's center is where a straight line called the diameter lies. Half of the size makes up the radius. It originates with a point circle and finishes at the circle's center.

Due to the fact that the angle between the tangent and the radius at a point on a circle is 90°.

As a result, angle x = 90°.

(b)The circle theorem that allows the calculation of angle is:

The angle between the tangent and the radius at a point on a circle is 90°.

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Suppose a pharmaceutical company wants to do a study of the commissions of its sales force. the probability that a simple random sample of 50 members of the sales force will have commissions within $400 of the population mean is 0.5812, or 58.12%.

We can use the following formula to calculate the standard error of the mean:

Standard error = population standard deviation / sqrt(sample size)

In this case, the standard error is:

Standard error = 3500 / sqrt(50) = 494.9747

Next, we can calculate the z-score for a commission value that is $400 above the population mean as follows:

z = (X - mu) / standard error

where X is the commission value, mu is the population mean, and standard error is the standard error of the mean that we calculated above.

For X = $52,800, the z-score is:

z = (52800 - 52400) / 494.9747 = 0.808

Similarly, we can calculate the z-score for a commission value that is $400 below the population mean:

z = (X - mu) / standard error

For X = $52,000, the z-score is:

z = (52000 - 52400) / 494.9747 = -0.808

Using a standard normal distribution table or calculator, we can find the probability that a random sample of 50 members of the sales force will have commissions within $400 of the population mean:

P(-0.808 < Z < 0.808)

= P(Z < 0.808) - P(Z < -0.808)

= 0.7906 - 0.2094

= 0.5812

Therefore, the probability  is 0.5812, or 58.12%.

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Answer:

Step-by-step explanation:

The two true statements are:

Answer:

Step-by-step explanation:

It seems like you have provided the dimensions of a cylinder, not a cone. To calculate the volume of a cylinder with a diameter of 12 meters and a height of 2 meters, we can use the formula:

Volume = πr^2h

where r is the radius of the cylinder (half of the diameter). So first, we need to find the radius:

r = d/2 = 12/2 = 6 meters

Now we can plug in the values and calculate the volume:

Volume = π(6 meters)^2(2 meters)

Volume = π(36 square meters)(2 meters)

Volume = 72π cubic meters

Therefore, the volume of the cylinder is 72π cubic meters.

90 dL times L/dL equals 9 L

To understand why 90 dL times L/dL equals 90L, it's important to understand the units involved and how they cancel out.

First, dL stands for deciliter, which is a unit of volume equal to one-tenth of a liter.

L, on the other hand, stands for liter, which is a unit of volume equal to 1000 milliliters or one cubic decimeter.

So, 90 dL represents a volume of 90 deciliters, while L/dL represents a ratio of liters to deciliters.

Specifically, L/dL means "liters per deciliter," which is a way of expressing a conversion factor between liters and deciliters.

Multiplying 90 dL by L/dL involves multiplying 90 dL by the conversion factor of L/dL, which is 1 liter per 10 deciliters. The deciliter units cancel out, leaving only the liter units.

Therefore, we can rewrite the calculation as follows:

90 dL x (1 L/10 dL) = (90/10) L = 9 L

So, the result is 9 L, which is equivalent to 90 dL times L/dL.

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Three and one-half times one and two-thirds is equal to 35/6 or 5 5/6.

Given the statement in the question; "three and one-half times one and two-thirds"

First, we can be written as a fraction:

Three and one-half → 3 1/2 = 7/2

One and two-thirds → 1 2/3 = 5/3

So, we have:

(7/2) × (5/3)

To multiply these fractions, we multiply the numerators together and the denominators together:

( 7 × 5 ) / ( 2 × 6 )

35/6

5 5/6

Therefore, the simplified form is 35/6 or 5 5/6.

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Answer:

b = 93°

Step-by-step explanation:

We Know

A triangle sum is 180°.

We know two angles, one is 21.5° and the other is 65.5°.

Find angle b

We take

180 - (21.5 + 65.5) = 93°

So, b = 93°

The fοci οf the given ellipse are apprοximately (-0.65, 3) and (-3.35, 3).

An ellipse is a clοsed curve in a plane that is symmetric abοut twο intersecting perpendicular axes, called the majοr axis and the minοr axis.

The given equatiοn represents an ellipse centered at the pοint (-2, 3) with semi-majοr axis οf length 4 and semi-minοr axis οf length 3. Tο find the fοci, we can use the fοrmula [tex]\rm c = \sqrt{(a^2 - b^2)[/tex], where a is the length οf the semi-majοr axis and b is the length οf the semi-minοr axis.

In this case, a = 4 and b = 3, so:

[tex]\rm c = \sqrt{(4^2 - 3^2) }= \sqrt7[/tex]

The foci are located on the major axis of the ellipse, which is parallel to the x-axis and passes through the center (-2, 3).

Therefore, the coordinates of the foci are [tex](-2 + \sqrt7, 3)[/tex] and [tex](-2 - \sqrt7, 3)[/tex].

Hence, the foci of the given ellipse are approximately (-0.65, 3) and (-3.35, 3).

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Answer: B. y= 6x -4 and C. 12x -2y=-4

Step-by-step explanation:

I got it wrong on nearpod. but luckily nearpod shows you the correct answer after submitting the answer choices. So these are the actual answers.

Therefore , the solution of the given problem of angles comes out to be  the detour via Town P is approximately 3.05 km longer .

The largest and smallest walls of a skew are determined by the point at which the lines that make up its ends meet. At a junction, it's possible that two routes will cross. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.

Here,

We can determine the length of the road from B to P using the rule of cosines:

=> BP² = AB² + AP² - 2AB(AP)cos(20°)

=>  BP² = x² + 4² - 2x(4)cos(20°)

We can determine the length of the detour via town P by using the rule of cosines once more:

y² = AP² + BP² - 2(AP)(BP)cos(110°)

y² = 4^2 + BP² - 2(4)(BP)cos(110°)

y² = 16 + BP² + 8BP(0.342)

y² = 16 + x² + 16 - 8x(cos(20°))(0.342) + 8(4)(0.342)(BP)

y²= 32 + x² - 2.75x + 1.368BP

=> BP² = x²+ 4² - 2x(4)cos(20°)

=> BP² = x² + 16 - 8x(cos(20°))

=> BP² = sqrt(x² + 16 - 8x(cos(20°)))

=> y² = 32 + x²- 2.75x + 1.368(sqrt(x^2 + 16 - 8x(cos(20°))))

=>  y - x = √(y²) - x

=>  y - x = √(32 + x² - 2.75x + 1.368(√x² + 16 - 8x(cos(20°))))) - x

With the aid of a computer, we can determine that y - x is roughly 3.05 km.

Consequently, the detour via Town P is approximately 3.05 km longer .

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Simplified withοut using the absοlute symbοl, |x - (-12)| is equal tο -(x + 12) when x is less than -12.

Mathematical expressiοns with inequalities οn bοth sides are knοwn as inequalities. In an inequality, we cοmpare twο values as οppοsed tο equatiοns. In between, the equal sign is changed tο a less than (οr less than οr equal tο), greater than (οr greater than οr equal tο), οr nοt equal tο sign.

If x is less than -12, then x - (-12) = x + 12. Therefοre,

|x - (-12)| = |x + 12| = -(x + 12) (since x + 12 is negative when x is less than -12).

Sο, simplified withοut using the absοlute symbοl, |x - (-12)| is equal tο -(x + 12) when x is less than -12.

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the first five terms of the sequence are (1, 1, 2, 3, 5). Option (d) correctly identifies this as the answer.

The problem provides a recursive sequence defined by the formula an = an-2 + an-1, where a1 = 1 and a2 = 1. We are asked to find the first five terms of this sequence.

To find the second term, we can use the formula and substitute n = 3:

a3 = a1 + a2 = 1 + 1 = 2

To find the third term, we can use the formula and substitute n = 4:

a4 = a2 + a3 = 1 + 2 = 3

To find the fourth term, we can use the formula and substitute n = 5:

a5 = a3 + a4 = 2 + 3 = 5

To find the fifth term, we can use the formula and substitute n = 6:

a6 = a4 + a5 = 3 + 5 = 8

Finally, to find the sixth term, we can use the formula and substitute n = 7:

a7 = a5 + a6 = 5 + 8 = 13

Therefore, the first five terms of the sequence are (1, 1, 2, 3, 5). Option (d) correctly identifies this as the answer.

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Answer: Y=10

Step-by-step explanation: please label me brainiest if I'm right

I. From 2(-5), we obtain -10. Next, we have: 3 -10 7

This cannot be true because -10 is not between 3 and 7. there is no solution to this inequality.

Make use of the following steps to solve an inequality:

Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator.

Step 2 Combine like terms on both sides of the inequality to simplify.

Step 3 Get the unknown on one side and the integers on the other by adding or subtracting quantities.

ii. To begin, we must use the following set of operations to simplify -7(3+2):

-7(3+2) = -7(5) = -35

We now have:

-14 < -35 < 1

This is accurate since -35 is less than both -14 and 1, as well as less than 1. As a result, the interval is the answer to this inequality: (-35, 1)

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Using rules of exponents,

Miguel:

Law-1: Rule of the product of powers: When multiplying like bases, add the powers together.

Law-2: Power of powers rule: When increasing a power by another exponent, multiply all the powers together.

Gia:

Law-1: Power of powers rule: When increasing a power by another exponent, multiply all the powers together.

Law-2: Rule of the product of powers: When multiplying like bases, add the powers together.

The work of simplifying exponent-based assertions is made easier by exponent rules, often known as the "laws of exponents" or "properties of exponents." These rules can help simplify formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.

Here in the question:

We can see that in case of Miguel,

He first added the powers as the bases are same. Then he multiplied the powers together.

In case of Gia, it is vice versa:

Gia first multiplied the powers of the individual components and raised the powers accordingly.

Then further she added the powers of the like bases.

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Answer:

Step-by-step explanation:

We are given that Lisa's age plus Sean's age is 17 years and Sean is 11 years old .

We need to find the age of Lisa.

Let's assume age of Lisa be x years.

A/q Lisa's age plus Sean's age is 17

[tex] \longrightarrow \: x + Sean's \: age = 17 \\ \\ \longrightarrow \: x + 11 = 17 \\ \\ \longrightarrow \: x = 17 - 11 \\ \\ \longrightarrow \: x = 6 \\ \\ [/tex]

Hence, Lisa is 6 years old.