WILL GIVE BRAINLIEST
You walk 10km North then turn and walk 5km East. What is your displacement from where you started? Show your work

The value of cos 2A/cos A-sin A = cos A + sin A is proved

cos 2A =  2cos²A - 1

= 2cos²A - (sin²A + cos²A)

= 2cos²A - sin²A - cos²A

= cos²A - sin²A

We need to prove that

cos 2A/cos A-sin A = cos A + sin A

L.H.S

cos 2A/cos A-sin A

= cos²A - sin²A/ cos A-sin A

= (cos A + sin A)(cos A-sin A)/ cos A-sin A

= cos A + sin A

R.H.S

LHS = RHS proved

Therefore, cos 2A/cos A-sin A = cos A + sin A is proved

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Answer:

- 18

Step-by-step explanation:

let the number be n then double the number is 2n and

2n + 32 = [tex]\frac{2}{9}[/tex] n

multiply through by 9 to clear the fraction

18n + 288 = 2n ( subtract 2n from both sides )

16n + 288 = 0 ( subtract 188 from both sides )

16n = - 288 ( divide both sides by 16 )

n = - 18

the original number is - 18

Using the geometric mean theorem,

[tex]\frac{y}{14.4}=\frac{14.4}{19.2} \\ \\ y=10.8[/tex]

Using Pythagoras on triangle [tex]ABD[/tex],

[tex]x=\sqrt{14.4^2+10.8^2}=18[/tex]

Triangles [tex]ABD[/tex] and [ted]CBD[/tex] are similar because corresponding angles are congruent and pairs of corresponding sides have proportional lengths.

To determine this, use the complementary angles.

The percent of error concerning Alton's estimated attendance and actual attendance at the band concert is 30%.

The percent of error is a measure showing how big an error is between the estimate and actual results.

The smaller the percent of error the closer the estimate is to the actual observations, and vice versa.

Actual Observed Value = 200

Expected Value = 260

Percentage of error = (Expected Value - Observed Value) ÷ Actual Value

= (260 - 200)/200

= 60/200

= 0.3

= 30%

Thus, we can conclude that Alton made a 30% error in his estimate of attendance at the band concert.

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Answer: 13

Step-by-step explanation:

20(.65) = 13

Hope that helps!

Answer:

m∠D = 54°

Step-by-step explanation:

The sum of the measures of the interior angles of a triangle is 180°.

The sum of the measures of an interior angle and its corresponding exterior angle is 180°.

With this knowledge, we can construct the equation:

50° + (3x + 18)° + (180 - (8 + 8x))° = 180°

and solve for x.

50° + (3x + 18)° + (180 - 8 - 8x)° = 180°

(50 + 18 + 180 - 8)° + (3x - 8x)° = 180°

240° - 5x° = 180°

5x° = 240° - 180°

5x° = 60°

x° = 12°

Now, we can solve for m∠D by plugging in the x value that we solved for.

m∠D = (3x + 18)°

m∠D = 3(12)° + 18°

m∠D = 36° + 18°

m∠D = 54°

Answer:

θ = 64.98310506 degrees (65 degrees rounded to unit)

Step-by-step explanation:

4.2 * tanθ = 9

4.2 * tanθ/ 4.2 = 9/4.2

tanθ = 2.142857

θ = arctan 2.142857

θ = 64.98310506

Step-by-step explanation:

using the SOH CAH TOA Rule,

tan 0=opp÷adj

tan 0=9÷4.2

tan 0=2.14

0=tan inverse of 2.14

The total number of hours that Jerry would work during a week to make at least $700.00 is 11 hours

information given in the query

The amount of Jerry's pay every week before taxes, J,

a function of the number of overtime hours that he works (the number of hours over 40), h

J = $493.60 + $18.51h

The given equation is an equation of linear function

considering the equation J = $493.60 + $18.51h, the number of hours that Jerry would work is gotten by substituting the value of $700.00 and solving for number of hours

J = $493.60 + $18.51h

700 = 493.60 + 18.5h

18.5h = 700 - 493.60

18.5h = 206.4

h = 11.16

h = 11 hours

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The amount of Tritium that bottle contains now will be 439,421.

Consider the function:

y = a (1 - r)ˣ

Where x is the number of times this decay occurs, a = initial amount, and r = fraction by which this decay occurs.

Tritium is a radioactive isotope of hydrogen that rots by around 5% each year. An enormous container of water that contained 856,000 tritium iotas stayed undisturbed for a very long time.

Then the amount of Tritium that bottle contains now will be given as,

y = 856,000 (1 - 0.05)¹³

Simplify the equation, then we have

y = 856,000 (1 - 0.05)¹³

y = 856,000 (0.95)¹³

y = 856,000 (0.51334)

y = 439,421

The amount of Tritium that bottle contains now will be 439,421.

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Answer: 1/6

Step-by-step explanation: Make all of the denominators the same. The least common multiple of 6 and 12 is 12. 1/6 gets multiplied by 2/2 to the equivalent fraction 2/12. 11/12 stays the same. 5/6 is multiplied by 2/2 to get 10/12. 10/12 stays the same. 1/6 is the smallest fraction so it is the closest to 0.

The 10 forms 1/8 can be written is as follows;

A fraction refers to a number which consists of a numerator and a denominator.

A numerator is the upper value of a fraction.

A denominator is the lower value of a fraction.

1 over 8 can be written in the following ways;

1/8

1 ÷ 8

1/2³

= 1 / 2×2×2

= 1/8

1/√64

= 1/8

[tex]{8}^{ - 1} [/tex]

= 1/8

1 : 8

= 1/8

[tex]{√64}^{ - 1} [/tex]

= 1/√64

= 1/8

[tex]{2}^{ - 3} [/tex]

= 1/2³

= 1/8

2/16

= 1/8

4 : 32

= 4/32

= 1/8

In conclusion, 1/8 can be written in different forms including using square root and ratios.

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The percentage of people over speeding on this road on purpose is 9%

Percent of people speeding on this road noticed the sign = Percentage of people who notice the speed limit at the beginning of the road - Percentage of people who notice the sign and follow the speed limit

= 84% - 75%

= 9%

In conclusion, the percentage of people who intentionally speed on purpose is 9%

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Answer:

Step-by-step explanation:

1.) -112*-7=784

784=v+4

2.)784-4=780

v=780

Answer:

v = 12

Step-by-step explanation:

-112 = -7v -28

7v = 112 - 28

7v = 84

7/7 v = 84/7

v = 12

Answer:

-2/5

Step-by-step explanation:

the slope is change in y over change in x

formula for slope is

(y2-y1)/(x2-x1), so if you input the coordinates, (10-(-2))/(-11-19) = 12/30 = 2/5

The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

What is an expression?

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

Given that;

The values are,

sin 18° = √(3 - √5) / 2√2

cos 18° = √ (5 + √5) / 2√2

Now,

Find the value of sin 3° as;

⇒ sin 3° = sin (18 - 15)°

   = sin 18° cos 15° - cos 18° sin 15°

   = √(3 - √5) / 2√2 × (√3 + 1) / 2√2  - √(5 + √5) / 2√2 × (√3-1)/2√2

   = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

Thus, The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

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a) The test statistic is: t = -1.11.

b) The p-value is: 0.1342.

c) The conclusion is that the null hypothesis is not rejected.

d) The final conclusion is that there is not sufficient evidence to conclude that the population mean is of 6.

The standard deviation for the population is unknown, only the sample standard deviation is known, hence the t-distribution is obtain the test statistic.

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the variables of the equation are given as follows:

For this problem, the values of these parameters are as follows:

[tex]\overline{x} = 5.83, \mu = 6, s = 2.11, n = 189[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{5.83 - 6}{\frac{2.11}{\sqrt{189}}}[/tex]

t = -1.11.

The p-value is obtained using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less a value, with 189 - 1 = 188 df and t = -1.11, hence it is of 0.1342.

Since the p-value is greater than the significance level of 0.10, it is found that:

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The number of downloads that were standard version were 560 songs.

The first step is to form a system of equations:

2.9s + 4.5h = 5629 equation 1

s + h = 1450  equation 2

Where:

Multiply equation 2 by 4.5:

4.5s + 4.5h = 6525 equation 3

Subtract equation 3 from equation 1:

896 = 1.6s

Divide both sides of the equation by 1.6:

s = 560

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The expression that Langston have written -24 +3.

Expression:

Expression refers the finite combination of symbols that is well-formed according to rules that depend on the context and it consists of numbers, mathematical operations etc.

Given,

Langston wrote an expression with a value of -21.

Here we need to find the expression that could Langston have written.

In order to find the correct expression we have to solve each and every one in the options,

When we take the first expression

-20 - (-1)

Which is equal to

=> -20 + 1

When we simplify it then we get

=> -19

Then the second one is simplified as,

=> -25 - 4 = -29

And the third one given the value of

=> -24 + 3

=> -21

Therefore, this one is the correct expression and this one is taken by Langston.

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Answer: 3x²(5x+y)

Step-by-step explanation:

15x³ + 3x²y​

Apply exponent rule: 15x²x+3x²y

Rewrite 15 as 5*3: 5*3x²x+3x²y

Factor out common terms 3x²: 3x²(5x+y)

Hope this helps!!! :)

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ 1 }{ -2 } \implies - \cfrac{1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{- \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{3}) \\\\\\ y-1=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}\implies y=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}+1\implies {\Large \begin{array}{llll} y=- \cfrac{1 }{ 2 }x+\cfrac{5}{2} \end{array}}[/tex]

The measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.

First, let us understand the types of angles formed by parallel and transversal lines:

Corresponding Angles — Corresponding angles are angles on the same side of a transversal that are either above or below the lines.

Alternate Interior Angles - Alternate interior angles are the pairs of interior angles on opposing sides of the transversal.

Alternate Exterior Angles - Alternate exterior angles are the pairs of exterior angles on opposing sides of the transversal.

Consecutive interior angles - Internal angles on the same side of a transversal are also known as consecutive interior angles, related angles, or co-interior angles.

We are given:

∠2 is 48 degrees and ∠3 is 62 degrees.

We need to find the ∠5.

From the given figure we can see that;

∠3 and ∠5 are alternate interior angles.

So, ∠3 = ∠5 = 62 degrees.

So, the measure of ∠5 is 62 degrees.

Thus, the measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.

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The exponential model for the lily pad colony is L(t) = A[tex](1+r)^{kt}[/tex] and the values of A=5 and k=1.2.

Over time, anything grows in quantity through an exponential growth process. When a quantity's rate of change over time (or derivative) is proportional to the quantity itself, this phenomenon takes place. A number that is increasing exponentially is referred to as a function, and the exponent, which stands for time, is the variable that represents time (in contrast to other types of growth, such as quadratic growth).

When a quantity decrements with time, it is considered to be experiencing exponential decay rather than a positive constant of proportionality. It is also known as geometric growth or geometric decay when the definition's discrete domain has equal intervals since the values of the function form a geometric progression.

Given, there are 5 lily pads that are found in a pond

And after 30 days, there are 16 lily pads in that pond

Here, a=5

r=(11-5)/5=1.2

f(x)=a(1+r)ˣ

f(x)=5(1+1.2)³⁰

From the above equation, A=5, and k=1.2

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Answer:

Step-by-step explanation:

smaller

larger

bigger

larger

The future value of the account in 3 years is $15,918.

What is a future value?

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

Here, we have

FV  =C×[ ((1+i)ⁿ −1)/i]

where:

C = cash flow per period

i = interest rate

n = number of payments

By applying the future value formula, we get

= ​$5,000×[ ((1+0.06)³ −1)/0.06 ]

= $5,000×3.1836

= $15,918

​Hence, the future value of the account in 3 years is $15,918.

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The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:

X = N(17.5)

Where μ = 17.5 and σ = 4

Since the distribution for X is normal then, the distribution for the sample mean  is given by:

X = N(17.5, σ/√n)

X =N(17.5.4/√50) = 0.566

We select a sample of n =50 people. And we want to find the following probability

P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )

And using the normal standard table or excel we find the probability:

P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92

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Step-by-step explanation:

3 consecutive even integer numbers :

x

x + 2

x + 4

their sum is the perimeter : 60 ft.

x + x + 2 + x + 4 = 60

3x + 6 = 60

3x = 54

x = 18

the shortest of the 3 sides is 18 ft.

and then we have the other 2 sides with 20 and 22 ft.