2. CJ and Torey each have a rectangular prism. The base of CJ’s prism is 4 cm by 7 cm and has a height of 12 cm. The base of Torey’s prism is 6 cm by 10 cm and has a height of 3 cm. Whose rectangular prism will require more material to construct?

Answer:

Step-by-step explanation:

Starting with the left-hand side (LHS) of the identity:

(cos x)(tan x + sin x cot x)

We can simplify using trigonometric identities. First, we can rewrite tan x as sin x/cos x and cot x as cos x/sin x:

(cos x)(sin x/cos x + sin x(cos x/sin x))

Simplifying, we get:

(sin x + cos2 x)/sin x

Next, we can multiply the numerator and denominator by the conjugate of sin x + cos2 x, which is sin x - cos2 x:

[(sin x + cos2 x)/(sin x + cos2 x)] * [(sin x - cos2 x)/(sin x - cos2 x)]

Expanding and simplifying, we get:

[(sin x)(sin x - cos2 x) + (cos2 x)(sin x - cos2 x)] / [(sin x)(sin x - cos2 x) + (cos2 x)(sin x + cos2 x)]

Simplifying further, we get:

(sin2 x - cos2 x + cos2 x sin x - cos4 x) / (sin2 x + cos2 x)

Using the identity sin2 x + cos2 x = 1 and simplifying, we get:

(sin x - cos2 x) / 1

Finally, using the identity cos2 x = 1 - sin2 x, we can simplify to:

(sin x - (1 - sin2 x)) / 1

Simplifying further, we get:

2 sin x - 1

So the left-hand side is equal to 2 sin x - 1.

Now, let's simplify the right-hand side (RHS) of the identity:

sin x + cos2 x

Using the identity cos2 x = 1 - sin2 x, we can rewrite the RHS as:

sin x + 1 - sin2 x

Simplifying further, we get:

1 - sin2 x + sin x

Finally, using the identity sin2 x + cos2 x = 1, we can rewrite as:

cos2 x + sin x

So the right-hand side is equal to cos2 x + sin x.

Since the left-hand side is equal to 2 sin x - 1 and the right-hand side is equal to cos2 x + sin x, the identity is not true in general. Therefore, the given identity does not hold true.

hope this helps

The angle that the pilot should turn in order to fly directly to the airport is given as follows:

x = 28.2º.

The three trigonometric ratios are defined as follows:

For the angle x, we have that:

Hence the angle is obtained applying the tangent as follows:

tan(x) = 105/196

x = arctan(105/196)

x = 28.2º.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

Answer: 3:20

Step-by-step explanation:

Answer:  She will be finished by 3:20.

Step-by-step explanation: The time at which she started = 1:40

Adding 1 hour 40 minutes to the given time = 1:40 + 1:00 = 2:40

Adding 20 minutes to it, time becomes = 3:00

Adding 20 more minutes (20+20 =40), final time = 3:20.

Internal Links: https://brainly.com/app/ask?q=Naylar+spent+1+hour+and+40+minutes+listening+to+music+on+her+headphones.+If+she+started+at+1%3A40%2C+what+time+was+it+when+she+finished%3F&skip=30769089&source=answer-box

The relationship between quart to ml is that 1 quart is equal to 946.6 mililitres.

Quart and ml both are the unit of volume. ml is abbreviated form of mililitres and the two units are related together. Here is how they are related -

1 quart is equal to 946.6 mililitres.

Thus, in this method we can simply relate and calculate the quart amount of liquid in mililitres. Let us interpret the above mentioned statement through example. For instance, we need to know the mililitres in 0.25 quart. Here is how we will solve this.

Quantity in mililitres = quantity in quart × amount of mililitres in one quart

Quantity of mentioned liquid in mililitres = 0.25 × 946.4

Performing multiplication on Right Hand Side of the equation

Quantity of mentioned liquid in mililitres = 236.6 mililitres

Learn more about unit conversion -

https://brainly.com/question/13016491

#SPJ4

According to the concept of unit conversion, 57 feet is equal to 1737.36 centimeters.

Unit conversion is an essential skill to have in science, engineering, and everyday life. It allows us to convert between different units of measurement and compare them easily.

To convert 57 feet to centimeters, we need to know the conversion factor between these two units. One foot is equal to 30.48 centimeters. So, we can multiply the given number of feet by this conversion factor to get the equivalent number of centimeters.

57 feet x 30.48 cm/ft = 1737.36 cm

In unit conversion, it is important to keep track of the units and make sure they cancel out correctly. In this case, the feet unit cancels out with the feet unit in the conversion factor, leaving us with only the centimeter unit.

To know more about unit conversion here.

https://brainly.com/question/19420601

#SPJ4

The volume of the triangular prism is 144 cm³.

What is the volume of the triangular prism?

We know that the volume of the prism = base area × Length of the prism. Therefore, the volume of the prism, in this case, is calculated using the same formula, Volume of triangular prism = (1/2) bh × L.

We have given:

b = 8cm,

h = 3 cm

l = 12 cm

So, the Volume of the triangular prism = (1/2) bh × L.

= (1/2) 8*3 × 12.

= 12 * 12

= 144

Hence, the volume of the triangular prism is 144 cm³.

To learn more about the volume of the triangular prism visit:

https://brainly.com/question/17421674

#SPJ1

The missing information in the table is $290,000 for Firm 1 and $18,562,433 for Firm 2

The premium of a bond can be calculated by taking the coupon rate and subtracting the yield, and then multiplying the result by the face value of the bond.

For Firm 1, the premium is given by (7.00% - 8.00%) × $300,000 = -$10,000.

The proceeds of Firm 1 can then be calculated by

=> $300,000 – $10,000 = $290,000.

For Firm 2, the yield and coupon rate that is as interest are both given as 3.00%. This means that the bond will be sold at par value, so the face value and proceeds of the bond will be the same.

The face value of Firm 2 can be calculated by taking the proceeds given and dividing by the bond’s yield.

Thus, Firm 2’s face value is given by $556,853 / 3.00% = $18,562,433.

To know more about interest here.

https://brainly.com/question/29335425

#SPJ4

Complete Question:

Complete the missing information in the table below. Assume that all bonds pay interest semiannually.

Do not use negative signs with answers.

Round percentages to one decimal place (ex. 0.0345 = 3.5%).

Round all other values to the nearest whole number.

Annual Years to Coupon  Issue

Yield Maturity Rate Face value Proceeds

Firm 1 8.00% 15 7.00% $300,000 $_______

Firm 2 3.00% 10 0.00% $_______ $556,853

The exponential equation can be written as y = 84.3(1.02)ˣ.

Exponential equations are equations where the independent variable, x is in the exponent.

Given that,

Sale in the first week after opening her shop = $86

After advertising her new shop on social media, her sales increased by 20% the following week and continued to increase at that rate.

Percentage increase each week = 20%

Exponential equation will be of the form,

y = a (b)ˣ

where a is the initial sale.

b is the increase in sale.

Initial sale = $86

Sale in the second week = $86 + (20% of $86)

                                         = 86 + (0.2 × 86)

                                         = 86 (1 + 0.2)

Sale in the third week = [86 (1 + 0.2)] + [0.2 × 86 (1 + 0.2)]

                                     = [86 (1 + 0.2)] [ 1 + 0.2]

                                     = 86 (1 + 0.2)²

This goes on.

So sale after x weeks = 86 (1 +0.2)ˣ⁻¹

                                    = 86 (1.02)ˣ⁻¹

                                    = 86 (1.02)ˣ (1.02)⁻¹

                                    = 84.3(1.02)ˣ

Hence the function can be modeled as 84.3(1.02)ˣ.

To learn more about Exponential Equations, click :

https://brainly.com/question/29506679

#SPJ1

Your question is incomplete. The complete question is given below.

Isabella recently opened her online candle shop, Spectacular Scents. Her sales in the first week were $86. After advertising her new shop on social media, her sales increased by 20% the following week and continued to increase at that rate.

Write an exponential equation in the form y = a (b)ˣ that can model Isabella's weekly sales, y , x weeks after opening her shop.

For the given graph we have:

Domain [-4, 7]

Range [-5, 7]

For a function y = f(x) we define the domain as the set of the inputs and the range as the set of the outputs.

To identify the domain on a graph we need to see the horizontal axis, here we can see that the graph starts at x = -4 and ends at x = 7, then the domain is [-4, 7]

For the rangewe need to look at the vertical axis, here we can see that it starts at y = -5 and ends at y = 7

Then the range is [-5, 7]

Learn more about domain and range:

https://brainly.com/question/10197594

#SPJ1

it will take them both 600 seconds to ice 35 cupcakes.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here,  Ann can ice a cupcake in 30 seconds,

Then, the total number of cupcakes iced by Ann is,

t/30 cupcakes

Similarly, If Sarah can ice a cupcake in 40 seconds,

Then, the total number of cupcakes iced by Sarah is

t/40 cupcakes,

Hence, For them to ice 35 cupcakes together, then;

t/30 +  t/40 = 35

where t is the times taken by both of them to ice 35cupcakes

40t+30t/1200 = 35

70t/1200 = 35

7t/120 = 35

t/120 = 5

t = 600

Thus, This shows that it will take them both 600seconds to ice 35 cupcakes.

Learn more about the mathematical expression visit:

brainly.com/question/1859123

#SPJ1

The rule for the graph of g is g(x) = -4(x^2-3). This graph is a vertical stretch by a factor of 4 and a reflection in the x-axis of the graph of f(x) = x^2-3.

No, the probability that a continuous random variable equals a certain value is zero does not imply that the probability of finding even or odd values is also zero.

The reason for this is that even and odd values are not specific points in the continuous probability distribution, but rather sets of points. For example, if we consider a uniform distribution over the interval [0, 1], the probability of any particular point in the interval is zero, including both even and odd values. However, the probability of finding an even value in the interval is 1/2, since half of the values in the interval are even. Similarly, the probability of finding an odd value is also 1/2. Therefore, the fact that the probability of a continuous random variable taking a certain value is zero does not imply anything about the probability of finding even or odd values.

Find out more about probability

brainly.com/question/15728622

#SPJ4

Answer:-1

Step-by-step explanation:

When you multiply exponents that have the same bases you add the exponent. You subtract the exponents when you divide.

x^9=x^y*x^10  the blank box is -1.

The value where the histogram balances when supported at that point is called the mode of the distribution.

The mode of distribution is the value that appears most frequently in the data set. It is often used as a measure of central tendency, along with the mean and median. The mode is especially useful when dealing with categorical or discrete data, where the possible values are limited and well-defined.

For example, the mode of a list of test scores might be the score that occurs most frequently, indicating the most common level of performance. In a histogram, the mode is the value where the distribution is highest, or where the histogram balances when supported at that point.

Learn more about histograms:

https://brainly.com/question/2962546

#SPJ4

The equation of the ellipse is equal to (x - 6)² / 49 + (y + 6)² / 36 = 1.

In this problem we must derive the equation of an ellipse based on information about the center, a vertex and a co-vertex thereof. The vertex represents the end of the major semiaxis that lies on the curve and co-vertex is the end of the minor semiaxis that lies on the curve. The major semiaxis is parallel with x-axis and the minor semiaxis is parallel with y-axis.

The standard form of the ellipse is shown below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

Now we proceed to derive the equation of the ellipse:

Major semiaxis:

A = (13, - 6) - (6, - 6)

A = (7, 0)

a = 7

Minor semiaxis:

B = (6, 0) - (6, - 6)

B = (0, 6)

b = 6

Equation of the elipse:

(x - 6)² / 49 + (y + 6)² / 36 = 1

To learn more on ellipses: https://brainly.com/question/20393030

#SPJ1

The probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

The tree diagram makes it easier to arrange and see all of the potential possibilities. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end. To determine when to multiply and when to add, use tree diagrams.

Let A be an event: the first ticket extracted was the 5.

Let B be an event: the second ticket is 2.

The probability for the following is given as:

P (B/ A) = 2/7

Hence. the probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

Not necessarily. It is true that if a function F is differentiable at a point A, then F must be continuous at A. This is one of the basic properties of differentiable functions.

However, the converse is not necessarily true. A function can be continuous at a point A without being differentiable at A. In fact, there are many examples of such functions, such as the absolute value function f(x) = |x| at x = 0, which is continuous but not differentiable at x = 0.

To see why a function can be continuous at a point A without being differentiable at A, let's consider the definition of continuity and differentiability.

A function F is continuous at a point A if and only if:

F(A) is defined.

The limit of F(x) as x approaches A exists.

The limit of F(x) as x approaches A is equal to F(A).

Therefore, we can conclude that if a function F is continuous at a point A, we cannot infer that F is differentiable at A.

To learn more about Differentiable functions please click on below link.

https://brainly.com/question/30079101

#SPJ4

Is it true if F is continuous at A then F is differentiable at A?

a. Line A represents Duncan's wages. b. We can determine this by equation of the line. Luke's equation of line has an additional constant and thus it starts from the point 30 above from the origin.

In mathematics, a variable is a symbol that designates a mathematical object (from the Latin variabilis, "changeable"). Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable.

A variety of issues are resolved by algebraic calculations that treat variables like explicit integers in a single computation. The quadratic formula, for instance, can be used to solve any quadratic equation by exchanging the variables in the quadratic formula for the numerical values of the coefficients in the equation.

Let us suppose number of hours worked = x.

Given that,

Duncan gets paid R8,50 per hour. His equation of line is:

D = 850x

Luke gets R30 and R450 per hour. His equation of line is:

L = 450x + 30

a. From the graph we see that line A represents Duncan's wages.

b. We can determine this by looking at the equation of the line. Luke's equation of line has an additional constant and thus it starts from the point 30 above from the origin.

c. For x = 2 hours.

L = 450(2) + 30

L = 900 + 30 = R930

d. For D = 1000:

1000 = 850x

x = 1.17 hours.

Learn more about equation of line here:

https://brainly.com/question/21511618

#SPJ1

The outcome of removing (2x-3)2 from 5x2 is therefore x2 + 12x - 9.

Therefore, it can be expressed as Minuend Subtrahend = Differential. As a result, the number being removed is known as Barely heard, and the number being deducted is known as Minuend. As a result, the amount that is being removed from is known as the minuend, and the number being deducted from is known as the subtrahend.

To answer this question, we need to expand (2x-3)² and then subtract it from 5x².

(2x-3)² means (2x-3) multiplied by itself:

(2x-3)² = (2x-3) × (2x-3)

The first term in the first parentheses can be multiplied by both terms in the second parentheses using the distributive property, and the second term in the first parentheses can be multiplied by both terms in the second parentheses using the distributive property:

(2x-3) × (2x-3) = 2x × (2x-3) - 3 × (2x-3)

Simplifying each of the two terms:

= 4x² - 6x - 6x + 9

= 4x² - 12x + 9

Now we can subtract this expression from 5x²:

5x² - (4x² - 12x + 9)

Distributing the negative sign:

5x² - 4x² + 12x - 9

Combining like terms:

x² + 12x - 9

Therefore, the result of subtracting (2x-3)² from 5x² is x² + 12x - 9.

To know more about Subtract visit:

https://brainly.com/question/28467694

#SPJ1

The chi-square goodness-of-fit test can provide important information about whether the observed data significantly deviates from the expected distribution, which categories or bins contribute to the deviation, and the overall goodness-of-fit of the data to the expected distribution.

The chi-square goodness-of-fit test is a statistical test used to determine if a sample of data comes from a population with a specific distribution. Specifically, the test compares the observed frequencies of data in different categories or bins with the expected frequencies of data in those categories based on a hypothesized distribution.

It can determine whether the observed data significantly deviates from the expected distribution. If the test results in a p-value less than the chosen level of significance, it indicates that the observed data significantly deviates from the expected distribution, and the null hypothesis (that the data follows the expected distribution) can be rejected.

It can identify which categories or bins contribute the most to any significant deviation. The test statistic and associated p-value can help to identify which categories or bins show significant differences between the observed and expected frequencies.

It can provide information on the overall goodness-of-fit of the data to the expected distribution. The test statistic provides a measure of the overall goodness-of-fit, with higher values indicating greater deviation from the expected distribution.

To learn more about  Chi-square test :

https://brainly.com/question/14082240

#SPJ4

Nominal data have no inherent order or ranking, while ordinal data have categories that have a natural order or ranking.

Nominal and ordinal are two sorts of information that are utilized in measurements and information examination. The primary distinction between them is in the idea of the information.

Nominal information are all out information where the qualities address discrete classes or gatherings, however there is no inborn request or positioning among them. Instances of ostensible information incorporate tones, orientation, conjugal status, or sorts of natural product.

Ordinal information, then again, have a characteristic request or positioning to their qualities. They are straight out information, yet the qualities address a particular request or progressive system. Instances of ordinal information incorporate degrees of training, grades, or rankings of sports groups.

To sum up, ostensible information are portrayed by classes that have no intrinsic request or positioning, while ordinal information have classifications that have a characteristic request or positioning.

To learn more about nominal and ordinal, refer:

https://brainly.com/question/2141495

#SPJ4

The percent discount for a student ticket is C. 40%

Percent Discount is a kind of discount that is offered on a product or service in the form of an amount per hundred.

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

Original price of the ticket = $50

Price of ticket on Monday = $35

Additional discount = $5

To determine the percentage discount, we make use of the following equation

Discount = 1 - (Price of ticket on Monday - Additional discount)/Original price of the ticket * 100%

Substitute the known values in the above equation, so, we have the following representation

Discount = 1 - (35 - 5)/50 * 100%

Evaluate

Discount = 40%

Hence, the percentage discount is 40%

Read more about Percent Discount at

https://brainly.com/question/27519306

#SPJ1

Answer:

Blue dot: (0,10)

red dot: (1,-9) or (2,-8)

Step-by-step explanation:

The equation is y=x-10

We can convert milliseconds to seconds using the formula 1 millisecond = 10⁻³ seconds.

The second is the unit of time. A millisecond is likewise a time unit, however it is a smaller unit.

We already know Milli is equivalent to 10⁻³.

As a consequence, we may use the unit conversion concept to describe the connection.

One millisecond is equivalent to 10⁻³ seconds.

For instance, 6 milliseconds is equal to 6 x 10⁻³ seconds.

As a result, we now have a standard formula for calculating the value of time in milliseconds to seconds and seconds to milliseconds.

To know more about unit conversion, visit,

brainly.com/question/13016491

#SPJ4

The rate of $18 an hour will be approximately  $157248  for a year .

In order to find how much $18 an hour is in a year,

We need to know how many hours are present in a year.

The number of weeks in 1 year is = 52 weeks ;

and 1 week consists of 168 hours , as 1 week has 7 days and 1 day has 24 hours .

So , 1 year (52 weeks) is = 52 × 168 = 8736 hours .

We get that 1 year consists of 8736 hours ,

Now , multiplying the number of hours by $18 ,

We get ,

⇒ 8736 × 18 = $157248 .

Therefore , $18 an hour will be $157248 for a year .

Learn more about Hours here

https://brainly.com/question/30218624

#SPJ4

Word problems

Simultaneous equation

4b + 3n = $23.50 x2

5b + 2n = $21.50 x3

We solve this equation using the elimination method. By removing necklaces, we can find the cost of a bracelet.

8b + 6n = $47 --- eqn 1

15b + 6n = $64.5 --- eqn 2

Subtract eqn 1 from eqn 2

7b = 17.5

1b = 17.5/7

1b = $2.50

Substitute the value of bracelet into eqn 1 to find the cost of 1 necklace

8(2.5) + 6n = $47

20 + 6n = $47

6n = 47 -20

6n = 27

1n = 27/6

1n = $4.5

1b + 1n = ?

2.50 + 4.50 = $7

To learn more about simultaneous equation, visit https://brainly.com/question/16763389

#SPJ1

Answer:

$4

Step-by-step explanation:

Binomial probability distribution of the given experiment is as follows 0.00902, 0.07056, 0.22073, 0.34524, 0.26999, 0.08446. its mean is 3.05 and standard deviation is 0.53196.

The binomial distribution is a type of probability distribution that models the probability of one of two outcomes given a set of parameters. It summarizes the number of trials with the same chance of producing the same result. The value of a binomial is determined by multiplying the number of independent trials by the number of successes.

Given : n = 5

            P = satisfied Americans = 61/100

            Q = 1 – P = 1 – 61/100 = 39/100

Binomial distribution formula   P(x) = ⁿCₓ . Pˣ . Qⁿ⁻ˣ

                                                ⁿCₓ = n!/ x! (n-x)!

a) Binomial table

P(x) = P(0) = ⁵C₀ . (61/100)⁰. (39/100)⁵ = 0.00902

P(x) = P(1) = ⁵C₁ . (61/100)¹ . (39/100)⁴  = 0.07056

P(x) =P(2) = ⁵C₂  . (61/100)² . (39/100)³ = 0.22073

P(x) = P(3) = ⁵C₃ . (61/100)³ . (39/100)² = 0.34524

P(x) = P(4) = ⁵C₄ . (61/100)⁴ . (39/100)¹ = 0.26999

P(x) = P(5) = ⁵C₅ . (61/100)⁵ . (39/100)⁰ = 0.08446

b) mean of binomial distribution = np

                                                     = 5 * 61/100

                                                     = 5 * 0.61

                                                     = 3.05

c) Standard deviation of binomial distribution = √nPQ

                                                                           =√5 * 0.61 * 0.39

                                                                            =  0.53196

To know more about standard deviation visit:

https://brainly.com/question/23907081

#SPJ1

The most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8) is a kite.

Option C is the correct answer.

A kite is a quadrilateral where the adjacent sides are equal which means there are two pairs of equal sides.

We have,

Quadrilateral ABCD:

A = (4, 4)

B = (5, 8)

C = (8, 8)

D = (8, 5)

Now,

A__________B

|                      |

|                      |
|                      |

D_________ C

We see the distance between the two points.

AB = √(8 - 4)² + (5 - 4)² = √(4² + 1) = √17

AD = √(5 - 4)² + (8 - 4)² = √(1² + 4²) = √17

AB = AD

BC = √(8 - 8)² + (8 - 5)² = √9 = 3

CD = √(5 - 8)² + (8 - 8)² = √9 = 3

BC = CD

AB and AC are adjacent sides.

CD and DB are adjacent sides.

So,

The quadrilateral ABCD is a kite.

Thus,

The quadrilateral ABCD is a kite.

Learn more about kite here:

https://brainly.com/question/17306509

#SPJ1