suppose sin(A) = 2/5. use the trig identity sin^2(A)+cos^2(A)=1 to find cos(A) in quadrant I. show all steps and round to ten-thousandth

Answer:

The approximate radian measure of the angle. So we have 15 nine 0.6 degrees convert degrees to radiance. You have to multiply by pi over 1 80. So if we did that, that'd be 59.6 pi over 1 80. So if we want to know the approximate value, we're going to use the pi button on our calculator to figure out what 59.6 times pi is. That's approximately 187.2389, Divided by 1 80. So now I would divide that number by 180 and that gives me 1.04 radiance, 1.04 radiance is the answer.

Answer:

  x = 22

  BD = 20 units

Step-by-step explanation:

The formula for the area of a rhombus can be used with the given values to write an equation that can be solved for x and for BD.

The formula is ..

  A = 1/2(d1)(d2) . . . . where d1 and d2 are the lengths of the diagonals.

Using the given values, we have ...

  120 = 1/2(12)(x-2)

Dividing by 6, we find ...

  20 = x -2 = BD

  22 = x . . . . . . . . add 2

The value of x is 22.

The length of BD is 20.

Answer:

x=12

BD=10

Step-by-step explanation:

[tex]\begin{array}{cccccccccccc} &&&&&&&&&\downarrow &&\downarrow \\ value&\stackrel{1^3+1}{2}&&\stackrel{2^3+1}{9}&&\stackrel{3^3+1}{28}&&\stackrel{4^3 + 1}{65}&&\stackrel{5^3 + 1}{126}&&\stackrel{6^3 + 1}{217} \\\cline{1-12} term&1&&2&&3&&4&&5&&6 \end{array}[/tex]

The probability that the jackpot prize will be won in each of four consecutive draws is (1/60)⁴.

The number of consecutive draws needed will be, n = 233

Probability is the likelihood or chance of an event happening or not.

From the given question, the probability of the jackpot being won in any draw is 1/60.

The probability that the jackpot prize will be won in each of four consecutive draws will be:

1/60 * 1/60 * 1/60 * 1/60 = (1/60)⁴

b. The number of consecutive draws that needs to be made for there to be a greater than 98% chance that at least one jackpot prize will have been won is calculated as follows:

There is a 100% - 98% chance that that none has been won = 2% that none has been won.

Also, the probability of the jackpot not being won in a draw is = 1 1/60 = 59/60

The number of consecutive draws needed will be (59/60)ⁿ ≤ 0.02

Solving for n by taking logarithms of both sides:

n = 233

In conclusion, probability measures chances of an event occurring or not.

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Answer:

4/5 of the students would have protractors.

Step-by-step explanation:

The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].

According to the statement

we have given that the statement and we have to find the derivative of that term.

So, We know that the

The given equation is

[tex]g(t) = \int\limits^x_4 {e^{5t^{2} - 4t} } \, dt[/tex]

Now find the derivative of that term

We find the derivative of the given term is with the help of the FTC.

And then

[tex]\frac{dg(x) }{dt} = {e^{5x^{2} - 4x} } \, \frac{dx}{dx}[/tex]

Then the equation become is

[tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex]

So, this is the derivative of the given equation.

So, The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].

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Using the law of cosines, the ship turned 72 degrees northwest when it changed direction.

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 94, b = 119, c = 173.

Hence the internal angle C is found as follows:

c² = a² + b² - 2abcos(C)

173² = 94² + 119² - 2 x 94 x 119cos(C)

22327cos(C) = -6932

cos(C) = -6932/22327

C = arccos(-6932/22327)

C = 108º.

The turning angle is the outside angle, which is supplementary with C, hence:

T = 180 - C = 180 - 108 = 72º.

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Answer:

15:7

Step-by-step explanation:

you put the numbers in order first the number of on time trains to off time trains

The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).

Here, the given rectangular coordinate is (5, 5.3, 10.3).

Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.

We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.

We know, ρ² = (x²+y²+z²)

Therefore, ρ

= √(x²+y²+z²)

= √[(5)²+(5.3)²+(10.3)²]

= √(25+28.09+106.09)

= √(159.18)

= 12.62

Again, tan θ = (y/x)

Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°

Similarly, cos Φ = (z/ρ)

Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°

Here, the spherical coordinate is (ρ, θ, Φ).

Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).

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The roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987

Quadratic equations are equations that have a second degree and have the standard form of ax^2 + bx + c = 0, where a, b and c are constants and the variable a does not equal 0

The equation of the function is given as:

f(x) = x^2 - 93987

The above equation is a quadratic equation

Express the equation as a difference of two squares

f(x) = (x - √93987)(x + √93987)

Set the equation of the function to 0

(x - √93987)(x + √93987) = 0

Split the factors of the above function equation as follows

x - √93987 = 0 and x + √93987 = 0

Solve for x in the above equations

x = √93987 and x = -√93987

Hence, the roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987

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The total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.

External radius of the hollow cylinder = 10.5 cm

Internal radius of the hollow cylinder = 10.1 cm

Height of the hollow cylinder = 56 cm

Cost to Polish Outer Surface: 20 paisa/sq. cm.

Surface Area of Hollow Cylinder = Circumference [tex]*[/tex] height

Surface area of hollow cylinder = 2 π r h

= 2 π (10.5 cm) 56 cm

= π (21)(56)

= 3692.64 [tex]cm^2[/tex] (Using π ≈ 3.14 rounding to 2 digits)

Total Cost of metallic cylinder [tex]$= 3692.64 cm^2 * 20 paisa/cm^2[/tex]

= 73,852.8 paisa

= Rs. 738.58

Therefore, the total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.

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Answer:

47/100

Step-by-step explanation:

First you have to make the denominators equal.

4/10 * 10/10 = 40/100

40/100 + 7/100 = 47/100

The simplest form of the given expression ( x⁴ )⁸ exists x³².

Expression in Math exists described as the collection of numbers variables and functions by utilizing characters like addition, subtraction, multiplication, and division.

The given expression will be simplified as:-

( x⁴ )⁸ = x ⁴ ⁽⁸⁾

( x⁴ )⁸ = x ³²

Therefore the simplest form of the given expression exists as x³².

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Answer:

Yup Yup

Step-by-step explanation:

yessah

Inequalities help us to compare two unequal expressions. The given inequality x<8 can be written in the interval notation as x=(-∞,8).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways. They do not, however, intend to indicate any particular location. Instead, they serve as a concise approach to expressing an inequality or a set of inequalities.

The given inequality x<8 can be written in the interval notation as,

x = (-∞,8)

Hence, The given inequality x<8 can be written in the interval notation as x=(-∞,8).

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Answer:

Each number is increasing by [tex]\frac{1}{4}[/tex].  The next number would be 1 [tex]\frac{1}{4}[/tex] or [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

I am not sure what the question is.  I am wondering if they are asking how is the list growing or what would be the next number.

Each number is increasing by 1/4

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] To change [tex]\frac{1}{2}[/tex] to [tex]\frac{2}{4}[/tex]  you multiple the top and the bottom of [tex]\frac{1}{2}[/tex] by2 to get [tex]\frac{2}{4}[/tex]

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{4}[/tex] or 1

Answer:

b) It is false

480 Ways can the letters be arranged.

What is the meaning of probability ?

First letter can't be n or l

=   4! × [tex]5P_{3}[/tex]

=    24 × 5! /3!

=     24 × 5 × 4

=         480

Therefore, 480 ways can the letters be arranged.

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Answer: 480 ways

Step-by-step explanation:

Ileana  have to invest for 8 years :

Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.

The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.

Principal amount = $15,500

interest = $5,084

Time = ?

Rate = 4.1% simple interest

to find the simple interest :

                                         I = [tex]\frac{(p*t*r)}{100}[/tex]

       Then:

         Time = [tex]\frac{I*100}{P*R}[/tex]

                  = [tex]\frac{(5084*100)}{(15500*4.1)}[/tex]

                  = [tex]\frac{508400}{63,550}[/tex]

                  = 8 years

Ileana  have to invest for 8 years

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The ticket price which will maximize the student's council is: C. $3.10.

Price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.

Based on the information provided about Valley High School student council, we can logically deduce the following data:

Mathematically, the equation which model the profit is given by:

Profit = price × number of tickets sold

P(x) = (2 + 0.2x)(420 - 20x)

P(x) = 840 + 84x - 40x - 4x²

P(x) = -4x² + 44x + 840.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -44/2(-4)

Xmax = -44/-8.

Xmax = 5.5

Ticket price for maximum profit is given by:

Ticket price = 2 + 0.2x

Ticket price = 2 + 0.2(5.5)

Ticket price = $3.10.

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The rule of the translation that maps the rocket from position I to position 2 is 4 units right and 4 units up

The translation is added as an attachment

From the attached figure, we have the following corresponding coordinates:

Figure 1 = (0, 0)

Figure 2 = (4, 4)

The rule of translation is calculated as:

(x, y) = T<Figure 2 - Figure 1>

This gives

(x, y) = T<4 - 0, 4 - 0>

Evaluate

(x, y) = T<4, 4>

Hence, the rule of the translation that maps the rocket from position I to position 2 is 4 units right and 4 units up

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Complete question

In an animated film, a simple scene can be created by translating a figure against a still background. Write a rule for the translation that maps the rocket from position I to position 2.

Answer + Step-by-step explanation:

(a)

[tex]\overrightarrow{PQ} =a+\frac{3}{5} b[/tex]

(b)

we are given:

[tex]\left\vert \overrightarrow{RQ} \right\vert =\frac{3}{5} \left\vert \overrightarrow{OP} \right\vert[/tex]

Then

[tex]\left\vert \overrightarrow{WR} \right\vert =\frac{3}{5} \left\vert \overrightarrow{WO} \right\vert[/tex]

and we know that :

[tex]\overrightarrow{OW} = \overrightarrow{OR} + \overrightarrow{RW}[/tex]

Then

[tex]\overrightarrow{OW} = a +\frac{3}{5} \overrightarrow{OW}[/tex]

Then

[tex]\frac{2}{5} \overrightarrow{OW} = a[/tex]

Then

[tex]\overrightarrow{OW} = \frac{5}{2} a[/tex]

The mpg and hp is print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))

MPG is an abbreviation for 'miles-consistent with gallon and it is used to give you an indication of the fuel financial system of a vehicle or industrial vehicle. It helps you to work out how reasonably-priced or high-priced an automobile might be to run.

As for a new vehicle, an awesome MPG is around 50 to 60. Having this stepped forward gasoline economy facilitates minimizing going for walks fees and cheaper avenue tax due to decreased CO2 emissions. consistent with What car's featured blog, here are a number of the most gasoline-green automobiles in the marketplace nowadays.

The gas economic system of a car relates to the space traveled via an automobile and the quantity of fuel fed on. intake can be expressed in terms of the volume of gasoline to travel a distance, or the gap traveled according to the unit quantity of gasoline consumed.

The car has the “best” combination of mpg and hp, where mpg and hp must be given equal weight.

#sum the scaled values of mpg and hp and add a new column called combination

myCars$combination<-scale(myCars$hp)+scale(myCars$mpg)

#Which car has the best combination of mpg and hp?

print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))

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Answer:

t = 6162 years

Step-by-step explanation:

This equation takes the form of

We are given everything but the amount of C-14 at time t = 0.  But we can figure it out from the info we ARE given.  We are told that when the spear head is found it contains 54% of its original amount of C-14.  Notice we are dealing in percents.  If 54% remains when it is found, it started out with 100% of its amount.  That's our N value.  Filling in:

Our goal is to get that t down from the exponential position that it is currently in.  To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication.  So we take the natural log of both sides.  On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone.  Before that, though, we will simplify by dividing both sides by 54.  100/54 = 1.851851852.  So, altogether...

Simplifying by plugging the log of that number into our calculator, we get

.6161861395 = .0001t  and

t = 6161.8613

Rounding to the nearest year, t = 6162 years

Answer: 46.7 in/3

Step-by-step explanation:

Answer: line ZX is congruent to line VX (option 4)

Step-by-step explanation:

We already know <X is congruent to <X, we also know that line YX is congruent to line XW. Now all we need is one more line adjacent to X which is going to be ZX ad VX

Answer:

Step-by-step explanation:

x = time

y = elevation

At x = 0  ,  y  = 0

It takes the submarine 2 hours to make descent of 2100 ft

=> x = 2 , y  = - 2100

Slope = ( -2100 - 0)/(2 - 0)  =  -1050

y - 0 = -1050 ( x -0)

=> y = -1050x

1050x  + y = 0

represent the relationship between the submarine's elevation and time.

Step-by-step explanation:

Circumference = πd

= π × 12

= 37.6991

=38

Answer:38

Step-by-step explanation:

Yoshi should buy 3 flats.

To find how many flats Yoshi should buy:

Therefore, Yoshi should buy 3 flats.

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The unit rate of Mikayla and brie is 0.16 miles per minutes and 0.25 miles per minutes respectively.

Brie runs faster.

Mikayla

2 miles in 12 1/2 minutes

Unit rate = miles / minutes

= 2 ÷ 12 1/2

= 2 ÷ 25/2

= 2 × 2/25

= 4/25

= 0.16 miles per minutes

Brie

5 miles in 22 1/4 minutes

Unit rate = miles / minutes

= 5 ÷ 22 1/4

= 5 ÷ 89/4

= 5 × 4/89

= 20/89

= 0.25 miles per minutes

Lucy

4 4/5 pounds for $18.50

Unit rate = pounds / price

= 4 4/5 ÷ 18.50

= 24/5 ÷ 18.50

= 24/5 × 1/18.50

= 24/92.50

= $0.26 per pound

Sophie

3 1/2 pounds for $14.75

Unit rate = pounds / price

= 3 1/2 ÷ 14.75

= 7/2 ÷ 14.75

= 7/2 × 1/14.75

= 7/29.5

= $0.24 per pound

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Answer: D

Step-by-step explanation: a^2+b^2=c^2

so use y value for b2 and 6 square root 3 as a and check with it.