A triangular prism has an approximate surface area of 39.5 square feet. The sides of the equilateral triangular bases are one-third the length of the prism. What are the dimensions of the prism to the nearest foot?

The value of the function f(x) = 3x^2 - 2x + 1 at x = -1, will be 6

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Algebraic expressions are expressions that are made up of variables and constants. Any value can be assigned to a variable. The value of an expression changes depending on the values assigned to the variables it includes. There are an unlimited number of points on a number line.

To evaluate the function f(x) = 3x^2 - 2x + 1 at x = -1,

we simply substitute -1 for x in the expression:

f(-1) = 3(-1)^2 - 2(-1) + 1

= 3(1) + 2 + 1

= 6

Therefore, f(-1) = 6.

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Answer:

180 divided by 5 = 36

Step-by-step explanation:

Math skillz

The value of n when  y varies directly as x using proportion is 30.

The correct option is C.

We have  y varies directly as x.

and, y is 180 when x is n with y is n and x is 5.

So, using Proportion as

180/ n = n/ 5

n² = 900

Take Square root on both side we get

n =√900

n= 30

Thus, the value of n is 30.

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el hombre tenía 50 acciones.

La pregunta es, ¿cuántas acciones poseía el hombre si declararon un dividendo del 6% pagadero en acciones y tenía 50 acciones con un valor de $30 cada una?Para calcular cuántas acciones tenía el hombre,

se puede utilizar la siguiente fórmula:Dividendos = Número de acciones * Precio por acción * Tasa de dividendosDe esta fórmula,

podemos despejar el número de acciones. Así, tenemos:Número de acciones = Dividendos / (Precio por acción * Tasa de dividendos)De los datos del problema, se sabe que el hombre tenía 50 acciones con un valor de $30 cada una.

Además, la corporación declaró un dividendo del 6% pagadero en acciones. Por lo tanto, la tasa de dividendos es del 6%.Para resolver el problema, primero debemos calcular el valor del dividendo que se pagará en acciones.

Para ello, se debe multiplicar el valor de las acciones del hombre por la tasa de dividendos.

Así, tenemos:Valor del dividendo = 50 acciones * $30 * 0.06 = $90El valor del dividendo es de $90. Ahora, podemos sustituir este valor en la fórmula para calcular el número de acciones que tenía el hombre.

Así, tenemos:Número de acciones = $90 / ($30 * 0.06) = 50 accionesPor lo tanto,

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Answer:

choice c

Step-by-step explanation:

The selling price of the house is approximately $122,200.

To find the selling price of the house, we need to calculate the total amount paid over the 30-year period, including the down payment and monthly payments.

First, let's calculate the total amount paid in monthly installments. The total number of months in 30 years is \(30 years \times 12 months/year = 360\)months.

Using the formula for the future value of an ordinary annuity:

\(Future Value = Payment \times ((1 + r)^n - 1) / r\)

Where:

Payment = $525 (monthly payment)

r = 7.8% / 100 / 12 (monthly interest rate)

n = 360 (number of months)

Future Value = $525 * ((1 + 0.078/12)^360 - 1) / (0.078/12)

Future Value ≈ $525 * (1.0065^360 - 1) / (0.0065)

Future Value ≈ $525 * (2.208 - 1) / (0.0065)

Future Value ≈ $525 * 1.208 / 0.0065

Future Value ≈ $97,200

Next, let's add the down payment of $25,000 to the total amount paid in monthly installments:

Selling Price = Down Payment + Future Value

Selling Price = $25,000 + $97,200

Selling Price ≈ $122,200

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The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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Hope it helps.

Answer:

2.6

Step-by-step explanation:

To calculate the variance of a data set, we need to first find the mean (average) of the data set.

Mean = (7 + 3 + 9 + 5 + 7 + 5 + 6) / 7 = 6

Next, we need to subtract the mean from each data point and square the result:

(7 - 6)^2 = 1

(3 - 6)^2 = 9

(9 - 6)^2 = 9

(5 - 6)^2 = 1

(7 - 6)^2 = 1

(5 - 6)^2 = 1

(6 - 6)^2 = 0

Then, we need to find the average of these squared differences:

(1 + 9 + 9 + 1 + 1 + 1 + 0) / 7 = 2.57 (rounded to the nearest tenth)

Therefore, the variance of the data set is approximately 2.6.

the acorn falls approximately 12.15 meters (to the nearest tenth of a meter) in 2.25 seconds.

the natural force  that makes things fall to the ground when you drop them.

The given function is:

d(t) = (1/2)a\(t^2\)

where a = 4.8 m/\(s^2\) is the acceleration due to gravity.

To find the distance an acorn falls in 2.25 seconds,  t = 2.25 seconds  

d(2.25) = (1/2)(4.8)\((2.25)^2\)

= (1/2)(4.8)(5.0625)

= 12.15 meters (rounded to two decimal places)

Therefore, the acorn falls approximately 12.15 meters.

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Answer:

1/4

Step-by-step explanation:

First you add all of the marbles in the bag which is 16 marbles.  The fraction of red marbles to the total would be 4/16.  In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.

Answer:

The proof is done in the step-by-step explanation below.

Step-by-step explanation:

We are given the following identity:

\(\frac{\sin{A}\tan{A}}{1-\cos{A}}\)

And we have to show that this is equals to:

\(1 + \sec{A}\)

Multiplying numerator and denominator by the conjugate of the denominator:

\(\frac{\sin{A}\tan{A}}{1-\cos{A}} \times \frac{1+\cos{A}}{1+\cos{A}}\)

\(\frac{\sin{A}\tan{A}(1+\cos{A})}{1 - \cos^2{A}}\)

We use these following identities:

\(\sin^2{A} + \cos^2{A} = 1\)

So

\(1 - \cos^2{A} = \sin^2{A}\)

Also:

\(\tan{A} = \frac{\sin{A}}{\cos{A}}\)

Then

\(\frac{\sin{A}\sin{A}(1+\cos{A})}{\cos{A}\sin^2{A}}\)

\(\frac{\sin^2{A}(1+\cos{A})}{\cos{A}\sin^2{A}}\)

\(\frac{1 + \cos{A}}{\cos{A}}\)

\(\frac{1}{\cos{A}} + \frac{\cos{A}}{\cos{A}}\)

\(\frac{1}{\cos{A}} + 1\)

Since:

\(\sec{A} = \frac{1}{\cos{A}}\)

We have that:

\(1 + \sec{A}\)

Thus, the proof is done.

The solution set for the given inequality is 3<x<5.

The given inequality is 6<x+3<8.

In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.

Now, solve the given inequality:

6<x+3<8⇒6<x+3 and x+3<8

6-3<x ⇒3<x

x+3<8⇒x<5

Thus, 3<x<5.

Therefore, the solution set is 3<x<5.

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Inequality and graph the solution set and a number line, express the Solution set in interval notation is 3 < x < 5

6<x+3<8

\(6 < x+3\quad \mathrm{and}\quad \:x+3 < 8\)

\(\mathrm{If}\:a < u < b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u < b\)

\(\mathrm{Combine\:the\:intervals}\)

\(x > 3\quad \mathrm{and}\quad \:x < 5\)

\(3 < x < 5\)

Therefore the Inequality and graph of the solution set and a number line, express the Solution set in interval notation as 3 < x < 5.

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1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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Answer:

a.) P(HH|C)=2/5

Explanation:

Given following:

Solving steps:

\(\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}\)

\(\sf P(HH|C) = \dfrac{4 }{10}\)

\(\sf P(HH|C) = \dfrac{2 }{5}\)

Answer:

f=  x^2+4x−12 /x

Step-by-step explanation:

Step 1: Divide both sides by x.

fx /x  =  x^2+4x−12 /x

f=  x^2+4x−12 /x

Answer:

not rejecting the null hypothesis when it is false.

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis.

For making the error, it should not reject the null hypothesis at the time when it should be false.

It is the level where the probability of rejecting the null hypothesis at the time when the null hypothesis should be true. It is relevant for making the incorrect decision. Also, it is the statistical test that measured the probability of type 1 error.

Therefore, For making the error, it should not reject the null hypothesis at the time when it should be false.

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Answer:

m=-3/2

b=3

equation f(x) = -3/2x +3

Proportional

negative slope

Step-by-step explanation:

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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By using  double-declining balance method, The depreciation expense for the first year is $112,000 and the depreciation expense for the second year is $67,200.

Under the double-declining balance method, the annual depreciation expense is calculated by applying a depreciation rate that is double the straight-line rate to the remaining book value of the asset. The depreciation rate for each year is calculated as follows:

Depreciation rate = 2 / Useful life in years

In this case, the useful life of the trencher is 5 years, so the depreciation rate is:

Depreciation rate = 2 / 5 = 0.4 or 40%

At the start of the first year, the book value of the trencher is its cost of $280,000. Therefore, the depreciation expense for the first year is:

Depreciation expense for Year 1 = Depreciation rate x Book value at start of year 1

= 0.4 x $280,000

= $112,000

The book value of the trencher at the end of the first year is:

Book value at end of Year 1 = Cost - Accumulated depreciation

= $280,000 - $112,000

= $168,000

At the start of the second year, the book value of the trencher is $168,000. Therefore, the depreciation expense for the second year is:

Depreciation expense for Year 2 = Depreciation rate x Book value at start of year 2

= 0.4 x $168,000

= $67,200

Therefore, the depreciation expense for the first year is $112,000 and the depreciation expense for the second year is $67,200.

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____The given question is incomplete, the complete question is given below:

On April 1, Cyclone Co. purchases a trencher for $280,000. The machine is expected to last five years and have a salvage value of $40,000. Compute depreciation expense at December 31 for both the first year and second year assuming the company uses the double-declining-balance method. (Enter all amounts as positive values.)

The mathematical function that models Autumn's situation of saving $500 that she keeps at home and does not add to the savings is G(x) = 500 + 0x.

A mathematical function is an equation, expression, rule, or law defining the relationship between the independent variable and the dependent variable.

There are many types of mathematical function, including:

The amount that Autumn saved = $500

The amount that Autumn adds to the savings = $0

Let the number of periods that Autumn saves the above amount = x

G(x) = 500 + 0x

Thus, based on the linear function above, the amount that Autumn saved would remain $500 after many periods.

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Answer: $7142.86

Step-by-step explanation:

Let the amount to be invested in the bond be represented by y.

Based on this, the amount to be invested in the CD will be: = 50000 - y.

From the information given, yearly interest on bond is 12%, this will be:

= 12% × y = 0.12 × y = 0.12y

Also, interest on CD will be:

= 5% × (50000 - y)

= 0.05(50000 - y)

Then, the equation to get the amount to be invested in bond will be:

0.12y + 0.05(50000 - y) = 3000

0.12y + 2500 - 0.05y = 3000

0.12y - 0.05y = 3000 - 2500

0.07y = 500

y = 500/0.07

y = 7142.8571

y = 7142.86

The amount to be invested in bond will be $7142.86

Answer:

  D.  13

Step-by-step explanation:

The first step in evaluating a piecewise function at a particular point is to find the piece that includes the point.

For x = 0, the relevant domain specification is x ≤ 0, the one applicable to the third piece. That piece of the function definition tells you ...

  f(0) = 13

since the function has an absolute value means that we have to graph the positive and negative form, also that it has to be moves 3 units to the right, 1 unit up and has a scale factor of -2.

final function should look like this

The domain of the function is all. values in x that the function can take place in, in this case it means that the domain will be:

the range is all values of the images in x, in this case there is a maximun value which is 1, meaning that the range will be

the increasing interval will be when the values tend to get higher values on the y axis, and the decreasing interval will be the contrary, according to this:

Hey there!

Here is your answer:

The proper answer to this question is option B "false".

Reason:

To solve for y in the equations y + 1/3 = 5/6, subtract 1/3 from both sides of the equation. This statement is false. In order to solve this you have to divide 1/3 on both sides.

Therefore the answer is option B.

If you need anymore help feel free to ask me!

Hope this helps!

~Matthew

i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

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The solution to find the five number summary shown below.

When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

To find a five number summary we have follow:

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The correct option that indicates the quadrant that contains the translation of the shaded figure is the option B

B. III

A translation is a transformation in which the size, relative position of the points on the pre-image, are preserved but the location of the pre-image changes to obtain the image.

The shape of the shaded figure is an L-shape

The geometric figure in quadrant II and IV are a reflection of the shaded figure, across the y-axis and across the x-axis, respectively which is not a translation transformation.

The geometric figure in quadrant III can be obtained from the shaded figure by a translation 4 units to the left and 5 units downwards, which can be expressed as <-4, -5>, which is a translation transformation, therefore;

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The value of the ratios between column A and column B is A = 20 and B = 60.

Problems involving comparable forms or items can be resolved using proportions. Objects or forms that have the same shape but vary in size are said to be similar. We can establish a ratio between two similar shapes or items' equivalent sides or dimensions. According to the proportion, the two forms or items have the same ratio of their respective sides or dimensions. By manipulating the percentage and finding a solution for the unidentified dimension, algebra may be used to solve the issue.

Given that, the ratio of A : B is:

4 : 6 = 2 : 3

Thus, for A : 30 we have:

A / 30 = 2 / 3

A = 2/3(30)

A = 20

Now, for 40: B we have:

40/B = 2 / 3

B = 40(3) / 2

B = 60

Hence, the value of the ratios between column A and column B is A = 20 and B = 60.

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By using the box plot, the top 25 percent of the cars have a typical gas mileage of at least 30 miles per gallon.

To find the value of the typical gas mileage for the top 25 percent of cars, we need to look at the upper quartile (Q3) of the box plot. The upper quartile is the point that separates the highest 25 percent of the data from the lowest 75 percent.

In the box plot, the upper quartile (Q3) is represented by the top of the box (the horizontal line inside the box) and the vertical line extending from the top of the box (the "whisker" above the box). We can estimate the value of Q3 by looking at the scale on the vertical axis and reading off the approximate value at the top of the box and the end of the whisker.

Assuming the scale on the vertical axis is in miles per gallon, we can estimate that Q3 is around 30 miles per gallon. Therefore, we can conclude that the top 25 percent of the cars have a typical gas mileage of at least 30 miles per gallon.

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The value of x is 16 and the value of y is 24. The maximum profit is 309,000 dollars.

C(x,y) = 2x²-2xy+y²-9x-10y+11

R(x,y) = 7x+6y

Profit function P(x,y) = R(x,y) - C(x,y)

= 7x+6y - (2x²-2xy+y²-9x-10y+11)

= -2x²-y²+16x+16y+2xy-11

P(x) = -4x+16+2y

P(y) = -2y+16+2x

P(x) = 0

P(y) = 0

-4x+16+2y = 0

-2y+16+2x = 0

-2x+32 = 0

x = 16

y = 24

P(16,24) = 304

Hence the maximum profit is 304,000.

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