y(x + x - y) ; when x = 5 and y = 3

The sine of an acute angle is less than one because it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio is always less than one.

To what does sin equate?

In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.

It's also the same reason why the cosine of an acute angle is always less than one because it is the ratio of the adjacent side of the angle to the hypotenuse.

It's important to note that this is only true for acute angles, angles smaller than 90 degrees.

For obtuse angles, greater than 90 degrees, the sine and cosine values are greater than one.

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Answer:

picture is missing.

Step-by-step explanation:

picture is missing

The area of the base of the triangular prism in square centimeters is 14.6 square centimeters.

In Mathematics, a triangular prism can be defined as a geometric shape (figure) with five (5) faces in total. Generally speaking, a triangular prism comprises two (2) triangular bases and three (3) rectangular lateral faces.

Mathematically, the volume of a triangular prism is calculated by using this formula:

Volume = base area × height of the prism.

365 = base area × 25

Base area = 365/25

Base area = 14.6 square centimeters.

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Answer:

n/4 - 3 OR 1/4n - 3

Step-by-step explanation:

First, let's assign a variable to Emily's number.  Let is be x.

Now all we have to do is go through the problem step by step.

"She finds 1/4 of the number..."

There are two ways you can do this.  You can either multiply n by 1/4 (1/4n), or you can divide by 4 (dividing by four is the same as finding 1/4 of a number).  For this example let's divide by four

n/4

"...and then subtracts 3."

All we have to do is subtract 3 from n/4

n/4 - 3

REMEMBER: like I said, there are two possible options.  You can either have n/4 or 1/4n. They mean the same thing

Answer:

1/4n - 3

Step-by-step explanation:

Answer: $1296

Step-by-step explanation:

Surface area of s sphere = 4πx r^2

Diameter = 1/2 radius

Surface area = 4π x 12^2

= 1809.56 cm^2 = 18.096 m^2

Material required = 71.62 x 18.096

= $1296

Answer:

$13

Step-by-step explanation:

First step is to convert cm to metres (24cm/100=0.24m)

therefore diameter is now 0.24

SA= 4π^r2      r=d/2=0.24m/2= 0.12m

SA= 4π^(0.12)^2= 0.1809...m^2

So since the surface area of this basketball is 0.1809..m^2, we then must calculate how much it will cost for the material to cover for one basketball. (this is why converting is important because you can end up with the wrong price/answer)

$71.62/1m^2 =0.1809..m^2 =$12.96

They want it in nearest DOLLAR  so final answer is $13 to make one basketball

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Answer:

y = 1000 x .30 (+ 1000)

Step-by-step explanation:

since it grows by 30%, you multiply .30 (the decimal version of 30%) and 1000 (your initial amount) to find how much it grows. Then you add $1000 at the very end, because that is how much you started with.

The required equation is b = 1000 × 0.7^t where b is the amount after 't' years.

"It is statement which consists of equal symbol between two mathematical expressions."

"It is the ratio that can be expressed as a fraction of 100. "

"f(t) = a(1 + r)^t, where 'a' is the initial value, r is the growth rate and t is time period

For given example,

"A" invest  $1000 in a friend's new business.

Value of the investment growing at a rate of 30%

30 percent = 30/100

                  = 0.3

So, the growth rate (r) = 0.3

a = 1000 dollars

Using the formula of exponential growth the amount in business after 't' years would be,

b = 1000 (1 - 0.3)^t

b = 1000 × 0.7^t

Therefore, the required equation is b = 1000 × 0.7^t

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Answer:

Step-by-step explanation:

30% mark represents:

So

The difference is:

Answer:

25 students

Step-by-step explanation:

Step-by-step explanation:

A parenthesis is used when the number next to it is NOT part of the solution set

   like :   all numbers up to but not including 3 .    

  Parens are always next to  infinity  when it is part of the solution set .

  A bracket is used when the number next to it is included in the solution set.

Answer:

\(\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx = \frac{e^\bigg{\frac{1}{4}}}{8} - \frac{e^\bigg{\frac{1}{9}}}{8}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

Integrals

Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]:                                     \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

U-Substitution

eˣ Integration:                                                                                                         \(\displaystyle \int {e^u} \, dx = e^u + C\)

Step-by-step explanation:

Step 1: Define

\(\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx\)

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Step 3: Integrate Pt. 2

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

The ratio between the hour hand and the second hand in a clock is 1:120.

1.1 A clock's ratio between the hour and minute hands can be calculated by looking at how both hands move over a certain amount of time.

In a 12-hour simple clock, the hour hand finishes a full upset (360 degrees) in 12 hours, while the moment hand finishes a full upheaval in an hour. We must compare the angular displacement covered by each hand over the same time period in order to calculate the ratio between the hour and minute hands.

Let's say that after "t" minutes, we want to figure out the ratio.

In 12 hours, the hour hand rotates 360 degrees, or 720 minutes (12 hours x 60 minutes/hour). The hour hand's angular displacement after "t" minutes can therefore be calculated as follows:

Hour hand angular displacement = (360 degrees divided by 720 minutes) x t In a similar fashion, the minute hand rotates 360 degrees every 60 minutes. As a result, the following formula can be used to determine the minute hand's angular displacement after "t" minutes:

Minute hand angular displacement = (360 degrees divided by 60 minutes) x t To determine the ratio, divide the hour hand's angular displacement by the minute hand's angular displacement:

The final formula is: Ratio = (Angular displacement of hour hand) / (Angular displacement of minute hand). By incorporating the respective equations,

The hour hand in a clock is 1:1 because the ratio is equal to ((360 degrees / 720 minutes) x t) / (360 degrees / 60 minutes) x t) = (360 / 720) / (360 / 60) = 1/2.

1.2 A clock's minute hand and second hand's ratio can be determined by taking into account how they move over a given amount of time.

Explanation:

In a clock, the second-hand goes through a full revolution in 60 seconds, while the minute hand goes through a full revolution (360 degrees) in 60 minutes. We must compare their angular displacements over the same time period in order to calculate the ratio between the minute and second hands.

Let's say that after "t" seconds, we want to figure out the ratio.

60 minutes divided by 60 seconds per minute sees the minute hand rotate 360 degrees or 3600 seconds. Therefore, the following formula can be used to determine the minute hand's angular displacement after "t" seconds:

The second hand rotates 360 degrees in 60 seconds, so the minute hand's angular displacement is equal to (360 degrees divided by 3600 seconds) x t. As a result, the following formula can be used to determine the second hand's angular displacement after "t" seconds:

Second hand angular displacement = (360 degrees divided by 60 seconds) x t To determine the ratio, divide the second hand angular displacement by the minute hand:

The final formula is: Ratio = (Angular displacement of minute hand) / (Angular displacement of second hand). By incorporating the respective equations,

((360 degrees / 3600 seconds) x t) / ((360 degrees / 60 seconds) x t) = (360 / 3600) / (360 / 60) = 1/10; consequently, the clock's minute hand to second hand ratio is 1:10.

1.3 A clock's hour hand and second hand's ratio can be determined by taking into account how they move over a given amount of time.

Explanation:

In a clock, the hour hand completes a 360-degree revolution in 12 hours, while the second hand takes 60 seconds to do the same. We must compare their angular displacements over the same time period in order to calculate the ratio between the hour hand and the second hand.

Let's say that after "t" seconds, we want to figure out the ratio.

In 12 hours, the hour hand rotates 360 degrees, or 43,200 seconds (12 hours x 60 minutes/hour x 60 seconds/minute). As a result, the hour hand's angular displacement after "t" seconds can be calculated as follows:

The hour hand's angular displacement is equal to (360 degrees divided by 43,200 seconds) x t. The second hand also rotates 360 degrees in 60 seconds. As a result, the following formula can be used to determine the second hand's angular displacement after "t" seconds:

Second hand angular displacement = (360 degrees divided by 60 seconds) x t To determine the ratio, divide the hour hand's angular displacement by the second hand's angular displacement:

The final formula is: Ratio = (Angular displacement of hour hand) / (Angular displacement of second hand). By incorporating the respective equations,

The hour hand in a clock is 1:120 because the ratio is equal to ((360 degrees / 43,200 seconds) x t) / (360 degrees / 60 seconds) x t) = (360 / 43,200) / (360 / 60) = 1/120.

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Answer:

430 km

Step-by-step explanation:

If they traveled 350 km by bus and biked 80 km more than they were bused, then,

Traveled by bus, Y = 350 km

Traveled by bike, X = 350 + 80 = 430 km

Hope this will help. Please mark me brainliest if it helps.

Answer:

Step-by-step explanation:

(5/6)(5/6) (-5/6)(5/6)

(5/6)(-5/6) (-5/6)(-5/6)  they  are they same but  you can also change them  and they will  still be the  same just backwords

Hope that helps

Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

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Hey there!

“The quotient of y and 27”

When you hear the word “quotient” think of the word “Division”, so basically we’re DIVIDING y from 27.

Your y-value is unknown so we can’t do anything to it.

Answer: y ÷ 2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The total number of hours Josh worked during the week is 44.7 hours.

We first need to calculate his regular pay by dividing his weekly gross earnings by his hourly rate:

$487.29 / $10.95 = 44.7 hours

Since the company pays time-and-a-half for any hours worked exceeding 40 in one week, we need to determine if Josh worked more than 40 hours during the week. If he did, we'll calculate his overtime pay by multiplying his regular pay by 1.5.

If Josh worked 44.7 hours, then he worked 44.7 - 40 = 4.7 hours of overtime.

His overtime pay would be 4.7 hours * $10.95 * 1.5 = $81.48

His regular pay would be 40 hours * $10.95 = $438.00

So his total weekly pay would be $438.00 + $81.48 = $519.48

The total number of hours Josh worked during the week is 44.7 hours.

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Answer:

  34 square feet

Step-by-step explanation:

The net is a useful tool for computing surface area. It often must be divided into sections whose areas must be added to give the required total.

Here, it can be convenient to divide the net into a central vertical rectangle that is 4 ft wide and (1.5 +2 +1.5 +2) = 7 ft high. Then there will be 2 "wings" that are each rectangles 2 ft by 1.5 ft.

Since the area of a rectangle is the product of its length and width, the total area using the above decomposition is ...

  A = (4 ft)(7 ft) +2(2 ft)(1.5 ft) = 28 ft² +6 ft²

  A = 34 ft²

Answer:

Step-by-step explanation:

In conclusion, it can be argued that Abby Sunderland was too young to sail solo. Despite her ambitious and determined nature, her lack of experience and maturity put her at a significant risk during her solo sailing journey. The fact that she had to be rescued twice during her attempt highlights the dangers of attempting such a feat at such a young age. While it is admirable to have the courage to pursue one's dreams, it is important to consider the potential consequences and weigh them against the potential benefits. In this case, it can be argued that the risks far outweighed the potential rewards.

The derivative  of y with respect to x is -2.

To find \(\frac{dy}{dx}\), we first need to express y and x in terms of a common variable, which we choose to be t.

Given x = t^2, we can differentiate both sides with respect to t using the chain rule to obtain:

\(\frac{dx}{dt}\) = 2t

Solving for t, we get:

t = (1/2) \(\frac{dx}{dt}\)

Substituting this value of t into the equation y = 8 - 2t, we get:

y = 8 - 2((1/2) \(\frac{dx}{dt}\))

Simplifying, we get:

y = 8 -\(\frac{dx}{dt}\)

Differentiating both sides with respect to x using the chain rule, we get:

\(\frac{dy}{dx}\) = d/dx(8 - \(\frac{dx}{dt}\))

Using the chain rule again, we have:

\(\frac{dy}{dx}\) = -    \(\frac{d(dx/dx)/dt }\)

Since \(\frac{dx}{dt}\) = 2t, we can substitute this to obtain:

\(\frac{dy}{dx}\) = -\(\frac{d2t}{dt}\)

Taking the derivative of 2t with respect to t, we get:

\(\frac{dy}{dx}\) = -2

Therefore, the derivative of y with respect to x is -2.

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Step-by-step explanation:

the distributive property is 6(1+5), the greatest common factor is 6

Answer:

6(1+5)

Step-by-step explanation:

khan told me

The area of a circle in polar coordinates can be calculated as an integral, where r = 4sinθ is  2π.

The region encircled by a circle with radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

We know that the area of a polar curve can be calculated using the formula:

A = ½ ∫ [f(θ)]² dθ

where f(θ) is the radial function.

In this case, the radial function is r = 4 sin θ. Substituting this into the formula, we get:

A = ½ ∫ [4 sin θ]²dθ

= ½ ∫ 16 sin² θ dθ

= ½ [8θ - 4 sin 2θ] from 0 to π/2

= 2π

Therefore, the area of the circle r = 4 sin θ is 2π.

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Answer:

a = -2  

Step-by-step explanation:

Ok, so for parallel lines you need to make slopes for both the lines equal. So for line y = x + 4 the slope is 1. (slope is the coefficent infront of the x value while in y=mx+b form. To make the other line have a slope of 1 a needs to be a number as so that 2a+5 = 1

2a+5 = 1

2a = 1 - 5

a = -4/2

a = -2  

The item that is not an item in the income statement is b. Furniture & Fixture as it is considered a fixed asset and is reported on the balance sheet instead.

The income statement, also known as the profit and loss statement, provides a summary of a company's revenues, expenses, gains, and losses over a specific period. It helps to assess the financial performance of a business. The income statement typically includes various items such as revenues, cost of goods sold, operating expenses, interest income or expense, and other gains or losses.

a. Discount allowed is a revenue item that represents the discounts given to customers as an incentive for early payment or other reasons. It is usually reported as a deduction from sales revenue.

c. Furniture & Fixture is not typically included in the income statement. Instead, it is considered a non-operating or non-recurring item and is generally classified as a fixed asset on the balance sheet. Fixed assets represent long-term investments made by a company for its operations.

d. Discount received is also not an item in the income statement. It represents the discounts received by a company from its suppliers for early payment or other reasons. Similar to discount allowed, it is usually reported as a deduction from the respective expense account.

In summary, b. Furniture & Fixture is the item that is not included in the income statement. It is considered a fixed asset and is reported on the balance sheet instead.

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Answer:

22

Step-by-step explanation:

The centroid divides a median in two parts that have this ratio = 1/3 and 2/3

In particular the part between the vertex and the centroid is 2/3 of the median.

So we have:

XN = (33 * 2)/3 = 22

Answer:

1. option c

2. option b

3. option b

Step-by-step explanation:

1 . option C

Square of longer side = sum of squares of other side

a)

5, 6 , 11

\(121 = 25 + 36\\does\ not \ satisfy\)

b)

9, 12, 16

\(256 = 144 + 81\\Does\ not \ satisfy\)

c)

7, 24, 25

\(625 = 576 + 49\\Does\ satisfy\)

d)

12, 20, 25

\(625 = 400 + 144\\does \ not \ satisfy\)

2. Option B

Square of longer side = sum of squares of other side

15 ² = 8 ² + r²

225 = 64 + r²

161 = r²

r = 12.688

r = 13ft

3 . Option b

To find length  of AB,  Use distance formula

\(AB = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2}\)

    \(= \sqrt{(14-3)^2 + (6-1)^2}\\\\=\sqrt{11^2 + 5^2}\\\\=\sqrt{121 + 25}\\\\= \sqrt{146} \\= 12 \ ft\)

Answer:

A or B i hope this helps! sorry

Step-by-step explanation:

Answer:

option a is the correct answer.

Step-by-step explanation:

-3 × 5 = - 15

x² × x = x³

y × y² = y³

-3x² × x = -3x³

y × y = y²

positive integers × negative integers = negative integers ( - )

hope this answer will help u

a.  The sample size must be at least 8 to have a 95% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60. b. The sample size must be at least 22 to have a 99% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

a. The formula for finding the width of a confidence interval is:
Width of confidence interval = 2 × Zα/2 × σ/√n

where Zα/2 is the Z-score for the desired level of confidence.

For 95% confidence level, Zα/2 = 1.96.

Width of 95% confidence interval = 60σ = 30Zα/2 = 1.96

Substituting the given values in the formula:60 = 2 × 1.96 × 30/√nn = (2 × 1.96 × 30/60)²n = 7.84≈ 8

Therefore, the sample size must be at least 8 to have a 95% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

b. For a 99% confidence level, Zα/2 = 2.576

Width of 99% confidence interval = 60σ = 30Zα/2 = 2.576

Substituting the given values in the formula:

60 = 2 × 2.576 × 30/√nn = (2 × 2.576 × 30/60)²n = 21.16≈ 22

Therefore, the sample size must be at least 22 to have a 99% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

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Answer:

Step-by-step explanation:

Box a = 4 + 10 + 2 = 16

Box b = 15 - (7+4) =  4

Box c = 10 + 4 + 6 = 20

Question 1

4 + 4 = 8

Question 2

21/50 = 0.42

Question 3

9/50 = 0.18 = 18%