A triangle has side lengths of (6.2v+5.4w) centimeters, (5.2v - 6.7x) centimeters, and (2.1x - 5.3w) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?​

Answer:

Step-by-step explanation:

For this kind of problem, all you need to know is one formula:

The Distance Formula

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

in this case,

[tex]x_2=1[/tex], [tex]x_1=0[/tex], [tex]y_2=-3[/tex], [tex]y_1=-10[/tex]

[tex]D = \sqrt{(1-0)^2+(-3--10)^2}[/tex]

[tex]D = \sqrt{1^2+7^2}\\D = \sqrt{1+49}[/tex]

[tex]D = \sqrt{50}\\D = \sqrt{25*2} D = 5\sqrt{2}[/tex]

The resulting values of the given operations are listed below.

Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.

Given are various operations.

(1) 235,654 ÷ 10000

When dividing a number with any powers of 10, we will shift the decimal point from right to left up to the number of zeroes in the given power of 10.

Here 10,000 contains 4 zeroes.

235,654 can be written as 235,654.00.

Shift the decimal point 4 places from left to right.

235,654 ÷ 10000 = 23.5654 ≈ 23.57 rounded to two decimal places.

(2) 895,21 x 100

When multiplying a number with any powers of 10, we will shift the decimal point from left to right up to the number of zeroes in the given power of 10.

895,21 x 100 = 89521.00 x 100 = 895,2100

(3) 1307 in words is one thousand three hundred and seven.

(4) 1307 in expanded form.

1307 = (1 × 1000) + (3 × 100) + (0 × 10) + (7 × 1)

        = 1000 + 300 + 0 + 7

(5) 1307 + 13 = 1320

(6) In roman numerals, 1000 is M, 100 is C and 10 is X.

1320 = (1 × 1000) + (3 × 100) + (2 × 10) + (0 × 1)

        = M CCC XX

1320 in roman numerals is MCCCXX.

Hence all the operations are found.

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Answer:

a. The amount borrowed is $95,000. The annual interest rate is 5%. The number of payments per year is 12 (monthly payments). The loan term in years is 25, and the payment amount is $450.

b. The loan requires a total of 25 x 12 = 300 payments over the full term.

To calculate the total amount paid over the full term of the loan, we can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + r)^-n) / r]

Where PV is the present value (the amount borrowed), PMT is the payment amount, r is the monthly interest rate (5% / 12 = 0.004167), and n is the total number of payments (300).

Plugging in the values, we get:PV = $95,000

PMT = $450

r = 0.004167

n = 300PV = $450 x [(1 - (1 + 0.004167)^-300) / 0.004167] = $144,781.92

Therefore, the total amount paid over the full term of the loan is $144,781.92.

Answer: Shown in screenshot.

Step-by-step explanation: First, let's start at 7. We are adding 2 to seven, so we move to the right two places. When we do so, we get to 9. So, 9 is the answer.

This answer will probably get taken down like SO MANY of my answers for no reason when literally WRONG answers stay on the website.

9 is the answer .When using a number line and you need to add you go to the right or forward

The values of the missing entries are given below:

x  2  1  3  5  0

y  0  1  1   9  4

Given:

y= x^2 - 4x + 4

= (x-2)^2

Thus, when y= 0, (x-2)^2 =0

x =2 (substitute y=0 into the equation)

When x= 1,  y = (1-2)^2 = 1

When y =1, (x-2)^2 =1, x-2 ± 1

x= 3, or x=1 (choose 3)

when x= 5, y= (5-2)^2 = 3^2 =9

when x = 0,  y= (0-2)^2 = 2^2 = 4

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Answer:

The correct statement is (B), You can safely carry out the test if your sample size is large and there are no outliers.

Step-by-step explanation:

Step 1: Given Information

A one-sample test about a population mean using a significance level.

Next,  OR Step 2

To identify the correct statement:

(a) False, because if a distribution is moderately skewed, then you can still carry out the test if the sample size is large ( or more).

(b) True, because if the sample size is larger ( or more) and there are no outliers, then you can still safely carry out the test.

(c) False, the sample size should be large ( or more) since the distribution is moderately skewed.

(d) False, the one-sample  test can only be used if the population standard deviation is unknown. You apply the onesample  test if the population standard deviation is known.

(e) False, -procedures are not robust, because they are heavily influenced by outliers.

Thus the answer to your problem is, B.

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Using arithmetic operations the individual would save approximately 76.36 gallons of gas per year by switching to a hybrid car for their commute.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Let's first calculate the annual distance driven by the individual to work.

Use arithmetic operation of multiplication.

Annual distance driven = 60 miles/week x 50 weeks/year = 3000 miles/year

Now, let's calculate how much gas the individual would use for their commute in their current car.

Use arithmetic operation of division.

Gas used in current car = (Annual distance driven) / (Miles per gallon of current car)

Gas used in current car = 3000 miles/year / 22 miles/gallon = 136.36 gallons/year

Next, let's calculate how much gas the individual would use for their commute in a hybrid car.

Use arithmetic operation of division.

Gas used in hybrid car = (Annual distance driven) / (Miles per gallon of hybrid car)

Gas used in hybrid car = 3000 miles/year / 50 miles/gallon = 60 gallons/year

Finally, let's calculate how much gas the individual would save by switching to a hybrid car.

Use arithmetic operation of subtraction.

Gas saved = Gas used in current car - Gas used in hybrid car

Gas saved = 136.36 gallons/year - 60 gallons/year = 76.36 gallons/year

Therefore, the amount of gas value saved is 76.36 gallons of gas per year.

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An individual has been driving a passenger vehicle to work, averaging 60 miles a week in a car that averages 22 miles per gallon. The individual plans to purchase a hybrid vehicle that averages 50 miles per gallon. If the individual drives to work 50 weeks a year, how much gas will they save if they switch to a hybrid vehicle for their commute?

The value of the transformed function after a vertical stretch in the y direction is h ( x ) = k ( | x | - 3 ) , where k is the scale factor

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = ( | x | - 3 )   be equation (1)

Now , when the function is stretched in the y direction , we get

Vertical stretch by a factor k: y = k × f(x)

On simplifying , we get

Let the transformed function be represented as h ( x )

where the value of h ( x ) is

Let the scale factor of stretching be k

h ( x ) = k ( | x | - 3 )

Hence , the transformed function is h ( x ) = k ( | x | - 3 )

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Answer:

length =7 breadth =2

Step-by-step explanation:

l x b = 14, so l= 14/b

2(l+b) =18 , l+b =9

14/b+b=9

[tex]b^ {2}[/tex] -9b+14=0

[tex]b^ {2}[/tex] -7b-2b+14=0

(b-7)(b-2) =0

b= 7 or 2

The arc length of PR: 16/3π unit. This can be solved by using the formulas of circle.

A circle is a form made up of all points on a plane that are at a specific distance from the centre point. In other words, it is the path a moving point in a plane takes to travel around a curve while maintaining a constant distance from another point. The group of points in a plane that are all equally far from one another is known as a circle. The radius and the centre both refer to the distance from the centre. The diameter is defined as the radius divided by two. A circle's angle of subtraction from its centre is a complete angle, which is equal to or radians.

In circle Z, m∠PZR = 2/3π

radius = 8 unit

length of the arc PR:

= 2/3π × 8

= 16/3 π unit

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Answer:

Step-by-step explanation:

Let's call the regular price of the stereo "x".

The stereo is sold at a 10% discount, which means the selling price is 90% of the regular price:

Selling price after discount = 0.9x

Then, a 10% tax is added to the selling price, so the final sale price is:

Final sale price = (1 + 0.1)(0.9x) = 1.1(0.9x) = 0.99x + 0.1(0.9x) = 0.99x + 0.09x = 1.08x

We are given that the final sale price is $589.05, so we can set up the equation:

1.08x = 589.05

Solving for x, we get:

x = 589.05 ÷ 1.08

x = 545.83 (rounded to the nearest cent)

Therefore, the regular price of the stereo was $545.83.

Answer:

The ordered pair that is a solution is (2, 10)

Step-by-step explanation:

2x + 6 = 4x + 2  Subtract 2x from both sides

2x - 2x + 6 = 4x - 2x + 2

6 = 2x + 2  Subtract 2 from both sides

6 - 2 = 2x + 2 -2

4 = 2x  Divide both sides by 2

2 = x

Substitute 2 for x in either of the two original equations.

y = 2x + 6

y = 2(2) + 6

y = 4 + 6

y = 10

The ordered pair that is a solution is (2, 10)

Answer:

PQ is 35.6 units.

Step-by-step explanation:

From the problem, we can see that the smaller quatilateral is 4x smaller than the bigger one. We can multiply 8.9 by 4 to get 35.6 units.

The kind of evidence geologists use to make geological timelines of events in Earth's history is the fossil remains.

A geological timeline shows a calendar of events in Earth's history.

To develop geological timelines, scientists understudy physical objects or structures on the Earth.  These objects or structures enable them to prove a phenomenon of interest.

Generally, the best form of evidence for the study of the history of life on earth is fossils, as they give clues about geological events and past climates, including the ages of rocks.

Other kinds of evidence for developing geological timelines include the following:

Thus, fossils provide the best kind of evidence for geological timelines.

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M'(11, -8), L'(13, -8), K'(13, -10) and J'(11, -10) are the coordinates of the vertices after a reflection over the line x = 4

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The coordinates of the quadrilateral MLJK are M(7, -8), L(9, -8), K(9, -10)

and J(7,-10)

Now we have to find the  coordinates of the vertices after a reflection over the line x = 4

We need to find the coordinates of the vertices after reflecting over the line x = 4, we just need to flip the x-coordinate of each vertex across the line.

M(7, -8)--->M'(7+4, -8)

=M'(11, -8)

L(9, -8)--->L'(9+4, -8)

=L'(13, -8)

K(9, -10)--->K'(9+4, -10)

=K'(13, -10)

J(7,-10)--->J'(7+4, -10)

=J'(11, -10)

Hence, M'(11, -8), L'(13, -8), K'(13, -10) and J'(11, -10) are the coordinates of the vertices after a reflection over the line x = 4

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We kindly invite to see the image attached below to know the representation of the parabola according to its features.

A parabola is the graphic representation of any quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. An alternative presentation is the vertex form:

y - k = C · (x - h)²

Where:

The procedure to sketch the parabola according to its features is described below:

Step 1 - Determine the y-intercept:

y = 6 · 0² - 17 · 0 + 12

y = 12

Step 2 - Determine the x-intercepts.

6 · x² - 17 · x + 12 = 0

6 · [x² - (17 / 6) · x + 2] = 0

6 · (x - 3 / 2) · (x - 4 / 3) = 0

x = 3 / 2 or x = 4 / 3

Step 3 - Determine the coordinates of the vertex:

y = 6 · x² - 17 · x + 12

y = 6 · [x² - (17 / 6) · x + 2]

y + 6 · (1 / 144) = 6 · [x² - (17 / 6) · x + 2 + 1 / 144]

y + 1 / 24 = 6 · [x² - (17 / 6) · x + 289 / 144]

y + 1 / 24 = 6 · (x - 17 / 12)²

(h, k) = (17 / 12, - 1 / 24)

Steps 4 & 5 - Add the points on Cartesian plane and match the resulting curve.

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The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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The probability that the basketball player makes 0 shots out of 3 is 0.343, or 34.3%. This can be calculated by using the binomial probability formula.

To calculate the probability of any outcome of a binomial experiment, use the formula: P(x) = nCx * px * (1-p)n-x, where n is the number of trials, x is the number of successes, and p is the probability of success in any one trial.

The Binomial Probability formula is

In this case, n = 3, x = 0, p = 0.39, and (1-p) = 0.61. Plugging these values into the formula, we get

P(x) = 3C0 * [tex]0.39^0[/tex] * 0.61³

= 0.343.

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Square root of 8 plus square root of 1 equal 3.82842712

Algebraic integers

The square roots of an integer are algebraic integers —more specifically quadratic integers. The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors.

⇒ 3.8 rounded.

⇒ = 3.82842712

Hence, Square root of 8 plus square root of 1 equal 3.82842712

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Answer:
The perimeter of the picture frame is 44 inches.

Step-by-step explanation:
The formula for the perimeter of a rectangle is:

Perimeter = 2 x (length + width)

In this case, the length of the picture frame is 14 inches and the width is 8 inches. Substituting these values into the formula, we get:

Perimeter = 2 x (14 + 8) = 2 x 22 = 44 inches

Therefore, the perimeter of the picture frame is 44 inches.


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The solution of the trigonometric equation for θ is given as follows:

θ = 80º.

The trigonometric equation for this problem is defined as follows:

sin(θ - 70) = cos(θ).

When two angles are complementary, that is, the sum of their measures is of 90º, we have that the sine of one angle is equals to the cosine of the other angle.

The angles for this problem are given as follows:

As the sine of one is equals to the cosine of the other, they are complementary, hence the angle θ is obtained as follows:

θ - 70 + θ = 90

2θ = 160

θ = 160/2

θ = 80.

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The solution to the expression 9•6 is 54

From the question, we have the following parameters that can be used in our computation:

9•6 divided by long division

The above expression is a product expression

This means that it cannot be evaluated using long division

When the expression is evaluated. we have

9 * 6 = 54

Hence, the solution is 54

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The composite function (fg)(0) has a value of -4

From the question, we have the following parameters that can be used in our computation:

The graph

Also, we have

(fg)(0)

The notation (fg)(x) represents the composite function of two functions f(x) and g(x), where one function is applied to the result of the other function.

The formula for (fg)(x) is:

(fg)(x) = f(g(x))

So, we have

(fg)(0) = f(g(0))

This gives

(fg)(0) = f(3)

(fg)(0) = -4

Hence, the value is -4

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Answer:

1. volume= 135

2. prism volume in cubic feet is: 21

3. surface area is 294 ft^2

4. surface area is 430 ft^2

The mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
To calculate the mean, variance, and standard deviation of the ages of the 12 students, we first need to find the sum of the ages:

Sum = 16 + 17 + 18 + (16/0.5) + 17 + 18 + 19 + 17 + 17 + 13 + (17/2/2) + 16

= 16 + 17 + 18 + 32 + 17 + 18 + 19 + 17 + 17 + 13 + 4.25 + 16

= 204.25

Mean = Sum / Number of students = 204.25 / 12 ≈ 17.02 years

To calculate the variance, we need to subtract the mean from each age, square the differences, add up the squares, and divide by the number of students minus one:

Variance = [ (16 - 17.02)² + (17 - 17.02)² + ... + (16 - 17.02)² ] / (12 - 1)

= [ 0.16 + 1.96 + ... + 0.16 ] / 11

= 37.41

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = √(Variance) ≈ 6.117

Therefore, the mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.

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Answer:

x = 40

Step-by-step explanation:

Alternate exterior angles are congruent (equal).

2x + 16 = 96   Subtract 16 from both sides

2x + 16 -16 = 96 - 16

2x = 80  Divide both sides by 2

x = 40

Answer:

x=40

Step-by-step explanation:

A variable in mathematics is a number that can change depending on the issue. Several mathematical statements and equations use the generic letters x, y, and z. In other words, a variable is a symbol that stands for an unknowable numeric value. Say that x Plus 5 equals 10. The "x" variable is used here.

The variable "model of car driven" is qualitative because it is an attribute characteristic. Qualitative variables are those that are not numerical in nature but rather represent characteristics or categories that can be observed or measured through attributes. In this case, the model of the car driven is a type of attribute that describes the make and model of the car, such as Honda Civic, Toyota Corolla, etc.

Therefore, option B is the correct answer.

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Optiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

A qualitative variable is a type οf variable in statistics that describes a characteristic οr quality οf an οbject οr phenοmenοn. It is alsο called a categοrical variable, and it can be nοminal οr οrdinal. Nοminal variables have categοries that have nο inherent οrder, while οrdinal variables have categοries with a natural οrder οr ranking.

The variable "Mοdel οf car driven" is qualitative because it is an attribute characteristic. Qualitative variables are variables that are nοt numerical in nature but are based οn attributes οr characteristics. In this case, the mοdel οf the car driven is a categοrical variable that describes a particular characteristic οf the car, such as its make οr mοdel. This variable cannοt be measured quantitatively οr numerically, but rather it can be categοrized based οn specific attributes οr features.

Therefοre, οptiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

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The program to find the divisible values gives the number of multiples of 2 between 3 and 8 inclusive is 3

To check if an integer is divisible by x, you could divide it by x and check if the remainder is 0.

If the remainder is 0, then the integer is divisible by x and therefore is a multiple of x.

We can use this concept to find the number of multiples of x between low and high inclusive.

If low is 3, high is 8, and x is 2, then we can check if each number between 3 and 8 is divisible by 2.

3 is not divisible by 2, so it is not a multiple of 2.

4, however, is divisible by 2, so it is a multiple of 2.

5 is not divisible by 2, so it is not a multiple of 2.

6, however, is divisible by 2, so it is a multiple of 2.

Then 7 is not divisible by 2, so it is not a multiple of 2. 8 is divisible by 2, so it is a multiple of 2.

Therefore, the number of multiples of 2 between 3 and 8 inclusive is 3 (4, 6, and 8).

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Answer:

This scenario describes a business combination in which Alfonso Inc. acquired 100% ownership of BelAire Company on January 1, 2020, using both cash and common stock as consideration. The combination is a statutory merger, meaning that BelAire is dissolved as a legal corporation and its assets and liabilities are assigned to a new reporting unit.

To record this business combination, Alfonso would need to perform a detailed analysis of the fair values of the assets and liabilities of BelAire as of the acquisition date, and allocate the total consideration paid (i.e., $387,500 in cash plus the fair value of 100,000 shares of Alfonso's common stock) to those assets and liabilities based on their fair values.

Assuming that the fair values of the assets and liabilities of BelAire on the acquisition date were as follows:

Assets:

Cash: $50,000

Accounts receivable: $100,000

Inventory: $150,000

Property, plant, and equipment: $400,000

Goodwill: $200,000

Liabilities:

Accounts payable: $75,000

Long-term debt: $250,000

The total fair value of BelAire's net assets is ($50,000 + $100,000 + $150,000 + $400,000 + $200,000) - ($75,000 + $250,000) = $575,000.

The allocation of the consideration paid would be as follows:

Cash paid: $387,500

Fair value of 100,000 shares of Alfonso's common stock: 100,000 shares x $15 per share = $1,500,000

Total consideration paid: $1,887,500

Allocation of consideration:

Cash: $50,000 / $575,000 x $1,887,500 = $164,348

Accounts receivable: $100,000 / $575,000 x $1,887,500 = $328,261

Inventory: $150,000 / $575,000 x $1,887,500 = $492,174

Property, plant, and equipment: $400,000 / $575,000 x $1,887,500 = $1,310,870

Goodwill: $200,000 / $575,000 x $1,887,500 = $657,391

Accounts payable: $75,000 / $575,000 x $1,887,500 = $246,739

Long-term debt: $250,000 / $575,000 x $1,887,500 = $818,478

The entry to record the acquisition would be:

Debit Property, plant, and equipment: $1,310,870

Debit Goodwill: $657,391

Debit Cash: $164,348

Debit Accounts receivable: $328,261

Debit Inventory: $492,174

Credit Accounts payable: $246,739

Credit Long-term debt: $818,478

Credit Cash: $387,500

Credit Common stock: $1,500,000

This entry records the allocation of the total consideration paid to the assets and liabilities acquired, as well as the issuance of Alfonso's common stock to BelAire's shareholders.