Which are simplified forms of the expression sec^2 theta sin 2theta? Select all that apply.
There are two answers.

a) 2 cot theta
b) 2-sec^2 theta
c) 2 tan theta
d) sec^2 theta-1
e) (sin2 theta) / (cos^2 theta)

Answer:

Brad picked 130 apples. Andy picked 45 apples. Krystal picked 115 apples.

Step-by-step explanation:

B = 2Y                A = Y - 20            K = Y + 50        B + A + K + Y = 355

130 = 2(65)        45 = 65 - 20        115 = 65 + 50     130 + 45 = 115 + 65 = 355

130 = 130           45 = 45                115 = 115      

If this answer is correct, please make me Brainliest!

Answer:

316

Step-by-step explanation:

The question has a little problem:

"the probability that they chose the same book is m n for relatively prime positive integers m and n. Compute 100m + n."

The correct sentence:

the probability that they chose the same book is "m/n" for relatively prime positive integers m and n.

Total number of books = 4

We have:

Number of 200page book = 1

Number of 400page book = 1

Number of 600page book = 1

Number of 800page book = 1

Probability of picking same book:

Velma read page 122 of her book Daphne read page 304 of her book

If it is same book, it must contain atleast 400page.

Therefore, 400page, 600page and 800 page would be considered in the probability.

Pr(one 400page) = 1/4

Pr(picking two 400page) = 1/4 * 1/4 = 1/16

Pr(one 600page) = 1/4

Pr(picking two 600page) = 1/4 * 1/4 = 1/16

Pr(one 800page) = 1/4

Pr(picking two 800page) = 1/4 * 1/4 = 1/16

Pr(picking same book page)=

Pr(picking two 400page) or Pr(picking two 600page) or Pr(picking two 800page)

= Pr(picking two 400page) + Pr(picking two 600page) + Pr(picking two 800page) = 1/16+ 1/16+ 1/16

Pr(picking same book page)= 3/16

This answer satisfies the probability as m/n for relatively prime positive integers m and n.

Two numbers are said to be relatively prime integers if the only positive integer that divides both of them is 1. It means the numerator and denominator of the fraction have been reduced to the lowest form.

m/n = 3/16

m = 3, n= 16

100m + n = 100(3) + 16

= 316

Answer:

100m+n = 6425

Step-by-step explanation:

Let X be the book Velma picks and Y the book that Daphne picks. Note that X and Y are independent and identically distributed, so for computations, i will just focus on X for now.

Lets denote with A, B, C and D the books with 200, 400, 600 and 800 pages respectively.

Note that, without any restriction P(X=A) = P(X=B) = P(X=C) = P(X=D) = 1/4. However, if we also add the condition that R = 122, where R is the page picked, we will need to apply the Bayes formula. For example,[tex]P(X=A|R=122) = \frac{P(R = 122|X=A)*P(X=A)}{P(R=122)}[/tex]

P(X=A) is 1/4 as we know, and the probability P(R=122|X=A) is basically the probability of pick a specific page from the book of 200 pages long, which is 1/200 (Note however, that if he had that R were greater than 200, then the result would be 0).

We still need to compute P(R=122), which will be needed in every conditional probability we will calcultate. In order to compute P(R=122) we will use the Theorem of Total Probability, in other words, we will divide the event R=122 in disjoint conditions cover all possible putcomes. In this case, we will divide on wheather X=A,  X=B, X=C or X=D.

[tex]P(R=122) = P(R=122 | X=A)*P(X=A) + P(R=122|X=B)*P(X=B)+P(R=122|X=C)*P(X=C)+P(R=122|X=D)*P(X=D) = 1/200 * 1/4 + 1/400*1/4 + 1/600*1/4+1/800*1/4 = 1/4*(12/2400 + 6/2400 + 4/2400 + 3/2400) = 1/384[/tex]

Thus, P(R=122) = 1/396

With this in mind, we obtain that

[tex]P(X=A|R=122) = \frac{\frac{1}{200}*\frac{1}{4}}{\frac{1}{396}} = \frac{384}{800} = \frac{12}{25}[/tex]

In a similar way, we can calculate the different values that X can take given that R = 122. The computation is exactly the same except that for example P(R=122|X=B), is 1/400 and not 1/200 because B has 400 pages.

[tex]P(X=B|R=122) = \frac{\frac{1}{400}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{1600} = \frac{6}{25}[/tex]

[tex]P(X=C|R=122) = \frac{\frac{1}{600}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{2400} = \frac{4}{25}[/tex]

[tex]P(X=D|R=122) = \frac{\frac{1}{800}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{3200} = \frac{3}{25}[/tex]

We can make the same computations to calculate the probability of Y = A,B,C or D, given that R=304. However, P(Y=A|R=304) will be 0 because A only has 200 pages (similarly, P(R=304|Y=A) = 0, R=304 and Y=A are not compatible events). First, lets compute the probability that R is 304.

[tex]P(R=304) = P(R=304|Y=A)*P(Y=A)+P(R=304|Y=B)*P(Y=B)+P(R=304|Y=C)*P(Y=C)+P(R=304|Y=D)*P(Y=D) = 0+1/400*1/4+1/600*1/4+1/800*1/4 = 13/9600[/tex]

Thus, P(R=304) = 13/9600. Now, lets compute each of the conditional probabilities

[tex] P(Y=A|R=304) = 0[/tex] (as we stated before)

[tex]P(Y=B|R=304) = \frac{\frac{1}{400}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{1600*13} = \frac{6}{13}[/tex]

[tex]P(Y=C|R=304) = \frac{\frac{1}{600}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{2400*13} = \frac{4}{13}[/tex]

[tex]P(Y=D|R=304) = \frac{\frac{1}{800}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{3200*13} = \frac{3}{13}[/tex]

We want P(X=Y) given that [tex] R_x = 122 [/tex] and [tex] R_y = 304 [/tex] (we put a subindex to specify which R goes to each variable). We will remove the conditionals to ease computations, but keep in mind that we are using them. For X to be equal to Y there are 3 possibilities: X=Y=B, X=Y=C and X=Y=D (remember that Y cant be A given that [tex] R_y = 304). Using independence, we can split the probability into a multiplication.

[tex] P(X=Y=B) = P(X=B|R=122)*P(Y=B|R=304) = \frac{6}{25} * \frac{6}{13} = \frac{36}{325} [/tex]

[tex] P(X=Y=C) = P(X=C|R=122)*P(Y=C|R=304) = \frac{4}{25}*\frac{4}{13} = \frac{16}{325} [/tex]

[tex] P(X=Y=D) = P(X=D|R=122)*P(Y=D|R=304) = \frac{3}{25}*\frac{3}{13} = \frac{9}{325} [/tex]

Therefore

[tex] P(X=Y) = \frac{36}{325} + \frac{16}{325} + \frac{9}{325} = \frac{61}{325} [/tex]

61 is prime and 325 = 25*13, thus, they are coprime. Therefore, we conclude that m = 61, n = 325, and thus, 100m+n = 6425.

Answer:

260 text

Step-by-step explanation:

First you're gonna want to subtract 17.50 form 56.50 and get 39.00 left over for text messages.

dividing 39 by .15 ([tex]\frac{39}{0.15}[/tex]) gives you 260

he can send 260 text per billing period

Answer:

She can sen a MAXIMUM of 260 texts

Step-by-step explanation

so lets start with the info we know

Her limit - $56.50

a flat rate (constant) - $17.50

and how much is cost PER text - $0.15

so we can make an inequality

56.50 ≤ .15x + 17.50

first, we would take away the constant

56.50-17.50 = 39

39 ≤ .15x

divide by .15

39/.15

leaving us with

260≤ X

Answer:    the answer is 1.00

Step-by-step explanation:   4/4 as a decimal is 1.00 because if you have four parts out of 4 then  it makes a whole so it is 1.00

a

The solution is 1.00

The value of the equation is A = 1.00

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

The value of n = ( 4/4 )

A = ( 4/4 )   be equation (1)

On simplifying the equation , we get

The value of A = 1

The value of A in decimal form is A = 1.00

Therefore , the value of A is 1.00

Hence , the value of the equation is A = 1.00

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Answer:

1) first two (A & B)

2. -1,533

Step-by-step explanation:

Sum to infinity is finite when

-1 < r < 1

Option 1: r = -¼

Option 2: r = 27/81 = ⅓

Option 3: r = 3/2

Option 4: r = 17.75/7.1 = 2.5

a = -3

r = -6/-3 = 2

S9 = -3 × (2⁹ - 1)/(2 - 1)

= -1533

Answer:

6.4%

Step-by-step explanation:

Answer:

6.4%

Step-by-step explanation:

Answer:

Niles and Bob were traveling for 6 hours.

Step-by-step explanation:

The speed or rate at which an object is moving can be computed using the formula:

[tex]s=\frac{d}{t}[/tex]

Here:

s = speed

d = distance traveled

t = time taken

It is provided that Niles and Bob sailed at the same time for the same length of time.

Speed of Niles sailboat is, s₁ = 6 mph.

Distance traveled by Niles' sailboat is, d₁ = 36 miles.

Speed of Bob's sailboat is, s₂ = 16 mph.

Distance traveled by Bob's sailboat is, d₂ = 96 miles.

It took both Niles and Bob the same time to travel the respective distance.

Compute the time it took Niles to travel 36 miles at 6 mph speed as follows:

[tex]t_{1}=\frac{d_{1}}{s_{1}}[/tex]

   [tex]=\frac{36}{6}\\=6[/tex]

It took Niles 6 hours to travel 36 miles at 6 mph speed.

Compute the time it took Bob to travel 96 miles at 16 mph speed as follows:

[tex]t_{2}=\frac{d_{2}}{s_{2}}[/tex]

   [tex]=\frac{96}{16}\\=6[/tex]

It took Bob 6 hours to travel 96 miles at 16 mph speed.

Thus, Niles and Bob were traveling for 6 hours.

Answer:

  $14.10

Step-by-step explanation:

To have 30 bulbs, Maura can buy 10 packages of 3 at $5.37 each, for a total of $53.70. Or, she can buy 15 packages of 2 at $4.52 each, for a total of $67.80.

Buying in packages of 3, Maura saves $67.80 -53.70 = $14.10.

Answer:

∠ ABC ≈ 137.9°

Step-by-step explanation:

Using the Cosine rule in Δ ABC

cos B = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]

with a = 89, b = 144, c = 65

cos B = [tex]\frac{89^2+65^2-144^2}{2(89)(65)}[/tex] = [tex]\frac{7921+4225-20736}{11570}[/tex] = [tex]\frac{-8590}{11570}[/tex] , thus

B = [tex]cos^{-1}[/tex] ( - [tex]\frac{8590}{11570}[/tex] ) ≈ 137.9° ( to the nearest tenth )

Answer:

where are your answers?

I need all the question to answer becbecause it seems it is incomplète.

Step-by-step explanation:

however, Reflection in algèbre is something that changes place or position but it never changes its size. for example you can flippe a triangle's position and it will remind the same but it just changes place or position .

I hope this helps .

Answer:

A B E

Step-by-step explanation:

Answer:

They'll build 66 cars in those conditions.

Step-by-step explanation:

In this case we can use a compounded rule of three to solve the problem. We need to set it up as shown bellow:

160 workers -> 32 cars -> 2 hours

220 workers -> x cars -> 3 hours

If the number of workers rise, then we expect the number of cars to rise aswel, so they're directly proportional. If the number of hours worked increase we can expect the number of cars to increase aswell, so they're directly proportional. We can now set the fractions:

(160*2)/(220*3) = 32/x

320/660 = 32/x

x = (32*660/320) = 66 cars

They'll build 66 cars in those conditions.

Final answer:

To find the number of cars that 220 workers can produce in 3 hours, we can use the joint variation equation and the given information. By solving for the constant of variation, we can substitute the new values to find the answer.

Explanation:

To solve this problem, we can set up a joint variation equation:

cars = k * workers * time

Given that 160 workers can produce 32 cars in 2 hours, we can substitute these values into the equation:

32 = k * 160 * 2

Solving for k, we find that k = 0.1.

Now, we can use this value of k to find the number of cars that 220 workers can produce in 3 hours:

cars = 0.1 * 220 * 3

cars = 66

Therefore, 220 workers can produce 66 cars in 3 hours.

Answer:

cant

Step-by-step explanation:

Answer:

Correct answer:  x = 217

Step-by-step explanation:

Given:

N = 350 customers

62%  made additional purchases

x = ?  the number of customers that is made additional purchases

Solution is:

x = (62 / 100) · 350 = 217

x = 217

God is with you!!!

Step-by-step explanation:

Given

it is a right angled triangle so

with reference angle x

hypotenuse (h) = 12

base (b) = 5

Now

cos x = b / h

cos x = 5 / 12

x = cos ^-1 ( 5/12)

Therefore x = 65.4°

Hope it will help :)

Answer:

Step-by-step explanation:

The side length of a cube with a volume of 64 mm^3 is found by taking the cube root of the volume, which is 4 mm.

To find the side length of a cube with a given volume, you apply the formula for the volume of a cube, which is V = s3, where V is the volume and s is the side length of the cube. Since the volume of the cube is given as 64 mm3, you need to take the cube root of 64 to find the side length.

The steps are as follows:

Substitute the value into the formula: V = s^3, so 64 mm3 = s3.

Undo the cube by applying the cube root: s = ∛64 mm3, which simplifies to s = 4 mm.

Therefore, the side length of the cube is 4 mm.

Answer:

a= 11rad6/2

Step-by-step explanation:

sin45=a/11rad3

Answer:

Price decrease = 24 %

Step-by-step explanation:

Given:

Initial price of the 60 inch television = $ 1050

Final price of the same television = $ 798

We have to find by what percent did the price of the television decrease.

Let the percent decrease be "x".

Formula to be used:

⇒ [tex]Percent\ decrease =\frac{(Initial\ price) - (Final\ price)}{Initial\ price}\times 100[/tex]

Using the above formula:

And plugging the values.

⇒ [tex]\%\ decrease =\frac{(Initial\ price) - (Final\ price)}{Initial\ price}\times 100[/tex]

⇒ [tex]\%\ decrease =\frac{(1050) - (798)}{1050}\times 100[/tex]

⇒ [tex]\%\ decrease =\frac{252}{1050}\times 100[/tex]

⇒ [tex]\%\ decrease =0.24\times 100[/tex]

⇒ [tex]\%\ decrease =24[/tex]

By 24 percent did the price of the television decreases.

Final answer:

Susie was 20 meters behind Andy when he reached the finish line in the 100-meter race.

Explanation:

To determine how many meters Susie was behind Andy at the moment Andy reached the finish line during the 100-meter race, let's consider the information given:

Andy finished the race.

Blaise was 10 meters behind Andy at that moment.

Susie was 10 meters behind Blaise when Blaise finished the race.

When Blaise reached the finish line, Andy would have already finished since Blaise was behind by 10 meters. However, at the moment Andy finished, Susie was also behind Blaise, who was 10 meters from finishing. Hence, Susie was 10 meters (the distance Blaise was behind Andy) + 10 meters (the distance Susie was behind Blaise at her finish) = 20 meters behind Andy when he finished the race.

In conclusion, Susie was 20 meters behind Andy when Andy reached the finish line.

Answer:

rearrange them properly to get

x-y=7

-3x+y=12

( by elimination method)

x-y = 7

-3x+y=

(x+ –3x) + (–y+y) = (7+12)

-2x+0= 19

x= -9.5

from eqn(i)

x-y=7

-9.5 - y=7

-y=16.5

y= -16.5

Answer:

15(2a - 2)= 5(a2 - 1)

The simplified form of the given equation is 5a²-30a-31=0.

The given equation is 15/(a²-1)=5/(2a-2).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

By cross-multiplying we get,

15/(a²-1)=5/(2a-2)

⇒ 15(2a-2)=5(a²-1)

⇒ 30a-30=5a²-1

⇒ 5a²-30a-31=0

Therefore, the simplified form of the given equation is 5a²-30a-31=0.

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Answer: 34.25

Step-by-step explanation:

Answer:

34.3 the real answer is 34.25 but rounded it is 34.3

Answer:

R(t)=401−10t

Step-by-step explanation:

Given the data, there appears to be a negative linear relationship between time and radius as the balloon deflates. This suggests a model of the form R(t) = a - bt best fits the data.

The subject matter here is a Mathematical topic related to model fitting - a statistical method that estimates the relationship between variables. In this case, the variables are Time (t) and radius (R). From the given data, it seems that the radius is reducing as the time increases, which likely indicates a negative linear relationship.

We can also observe that the data points reduce at a constant rate (e.g., it goes down by 50 cm every 5 seconds initially), which further supports the idea of a linear model.

Therefore, considering this rate of change and the mathematical relationship between the variables, a linear model of the form R(t) = a - bt (where a is the initial radius and b is the rate of decrease) would likely be the best option.

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Answer:

B = 612.2 ft

Step-by-step explanation:

Solution:-

- The elevation of person, H = 235 ft

- The angle of depression, θ = 21°

- We will sketch a right angle triangle with Height (H), and Base (B) : the boat's distance to the edge of the cliff and the angle (θ) between B and the direct line of sight distance.

- We will use trigonometric ratios to determine the distance between boat and the edge of the cliff, using tangent function.

                             tan ( θ ) = H / B

                             B = H / tan ( θ )

                             B = 235 / tan ( 21 )

                             B = 612.2 ft    

Answer:

The distance of the boat from the edge of the cliff is 655.75 ft

Distance of the boat from the base of the cliff is 251.72 ft

Step-by-step explanation:

Height of person above sea level = 235 ft

Angle of depression of sight to the boat from the person = 21°

Therefore, based on similar angle between person and angle of depression and the boat with angle of elevation we have,

Angle of elevation of the location of the person as sighted from the boat θ = 21°

Distance from the edge of the cliff of the boat is then given by;

[tex]Sin\theta = \frac{Opposite \, side \, to\, angle}{Hypothenus\, side \, of\, triangle} = \frac{Height\, of\, person\, above \, ses \, level}{Distance\, of\, boat\, from \, edge\, of \, cliff}[/tex]

[tex]Sin21 =\frac{235}{Distance\, of\, boat\, from \, edge\, of \, cliff}[/tex]

[tex]Distance\, of\, boat\, from \, edge\, of \, cliff=\frac{235}{Sin21 } = \frac{235}{0.358} = 655.75 \, ft[/tex]

Distance of the boat from the base of the cliff is given by

[tex]Distance\, of\, boat\, from \, base\, of \, cliff=\frac{235}{cos21 } = \frac{235}{0.934} = 251.72 \, ft[/tex].

You can construct a pie chart by calculating the percentage each item contributes to the total in your table. Each percentage point represents a slice of the pie, with the size of the slice proportional to the percentage of the total.

In a pie graph, each slice of the pie represents a share of the total, or a percentage. For example, 50% would be half of the pie and 20% would be one-fifth of the pie. The pie graphs allow you to get a feel for the relative size of the different historical data sets.

To create your pie chart based on your table, you will want to find the percentage of the total that each holiday destination in your table represents. Once you've calculated these percentages, you can begin creating your pie chart. Each slice of your pie will correlate to a holiday destination, with the size of the slice representative of the percentage of people that chose that destination.

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Given:

Given that the triangle.

Let the length of the side a be 10 cm.

Let the length of the side b be 13 cm.

Let the measure of ∠C is 105°

We need to determine the area of the triangle.

Area of the triangle:

The area of the triangle can be determined using the formula,

[tex]A=\frac{1}{2} a b \ sin \ c[/tex]

Substituting a = 10, b = 13 and ∠C = 105°, we get;

[tex]A=\frac{1}{2}(10)(13) \ sin \ 105[/tex]

Simplifying, we get;

[tex]A=\frac{1}{2}(10)(13)(0.966)[/tex]

[tex]A=\frac{1}{2}(125.58)[/tex]

[tex]A=62.79 \ cm^2[/tex]

Rounding off to 1 decimal place, we have;

[tex]A=62.8 \ cm^2[/tex]

Thus, the area of the triangle is 62.8 cm²

The area of the triangle is 65 square centimeters when rounded to one decimal place.

To find the area of a triangle, you can use the formula:

[tex]Area = (\frac{1}{2} ) \times base \times height[/tex]

In this case, you have a base of 13 cm and a height of 10 cm. Plug these values into the formula:

[tex]Area =(\frac{1}{2} ) \times 13 cm \times 10 cm[/tex]

[tex]Area = (\frac{1}{2}) \times 130 cm^2[/tex]

Now, calculate the area:

[tex]Area = 65 cm^2[/tex]

So, the area of the triangle is 65 square centimeters when rounded to one decimal place.

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Answer:

f(13) = 44

Step-by-step explanation:

f(13) = 3 (13) +5 = 39 + 5= 44

Answer:

g(5) = 120

Step-by-step explanation:

g(x) = x^3 - 5;

Let x=5

g(5) = 5^3 -5

       = 125 -5

       = 120

Answer:

g(5) = 120

Step-by-step explanation:

We want to find g(x) when x is equal to 5, so we can substitute 5 in for x.

g(x) = x^3 - 5

g(5) = 5^3 - 5

Solve the exponent

g(5) = 125-5

Subtract

g(5) = 120

Answer:

H0:p=0.41

Step-by-step explanation:

The null hypothesis always contain equality i.e. (=) sign. The null hypothesis contains the statement regarding population parameter. Here, the claim about population proportion is mentioned in the statement that 10 p.m. newscast of local CBS reaches 41% of viewers. So, the null hypothesis would be

Null hypothesis:H0: p=0.41.

Answer:

7^ 30

Step-by-step explanation:

We know that a^b^c = a^ (b*c)

7^6^5 = 7^(6*5) = 7^ 30

Answer:

7^6= 117,649

(117,649)^5= 2.25 if you're estimating

2.253934029x10^25