You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 245 yards due west from your position and takes a bearing on the cabin of N 22.6°E. How far are you from the cabin? answer asap and ill give you a pat on the back

Answer:

k = [tex]\frac{980a}{b}[/tex]

Step-by-step explanation:

Fisherman noticed a stretch in the spring = 'b' centimetres

Weight of the fish = a kilograms

If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,

F = kΔx

Where k = spring constant

Δx = stretch in the spring

F = weight applied

F = mg

Here 'm' = mass of the fish

g = gravitational constant

F = a(9.8)

  = 9.8a

Δx = b centimetres = 0.01b meters

Therefore, 9.8a = k(0.01b)

k = [tex]\frac{9.8a}{0.01b}[/tex]

k = [tex]\frac{980a}{b}[/tex]

Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]

Answer: m = - 2200

Step-by-step explanation: Slope of a line is a number which describes the steepness and direction of a linear graph. It is represented by the letter m.

The year a car is bought and its price means:

f(0) = 31,500

Five years later, the price is $20,500, i.e.:

f(5) = 20,500

With these two pairs of value, slope is calculated as:

[tex]m = \frac{y-y_{0}}{x-x_{0}}[/tex]

[tex]m = \frac{20500-31500}{5-0}[/tex]

[tex]m = \frac{- 1100}{5}[/tex]

m = - 2200

The slope of the depreciation line is m = -2200 and it is negative because the line decreases along time.

Answer:

1.    [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]

2.   [tex]cos(60)[/tex]

3.   [tex]cos(60) = \frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]cos(\alpha - \beta )[/tex]

[tex]cos(79)cos(19) + sin(79)sin(19)[/tex]

Solving for [tex]\alpha[/tex] and [tex]\beta[/tex]

In trigonometry;

[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]

Equate the above expression to [tex]cos(79)cos(19) + sin(79)sin(19)[/tex]

[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex] and [tex]cos(\alpha - \beta ) = cos(79)cos(19) + sin(79)sin(19)[/tex]

By comparison

[tex]cos\alpha\ cos\beta + sin\alpha\ sin\beta = cos(79)cos(19) + sin(79)sin(19)[/tex]

Compare expression on the right hand side to the left hand side

[tex]cos\alpha\ cos\beta = cos(79)cos(19) \\\\ sin\alpha\ sin\beta = sin(79)sin(19)[/tex]

This implies that

[tex]cos\alpha\ = cos(79)\\cos\beta = cos(19) \\\\ and\\\\sin\alpha\ = sin(79)\\sin\beta = sin(19)[/tex]

By further comparison

[tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]

Substitute [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex] in [tex]cos(\alpha - \beta )[/tex]

[tex]cos(\alpha - \beta ) = cos(79 - 19)[/tex]

[tex]cos(\alpha - \beta ) = cos(60)[/tex]

Hence, the expression is [tex]cos(60)[/tex]

Solving for the exact values;

Express [tex]cos(60)[/tex] as a difference of angles

[tex]cos(60) = cos(90 - 30)[/tex]

Recall that [tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]

So;

[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex]

------------------------------------------------------------------------------------

In trigonometry;

[tex]cos(90) = 0[/tex]; [tex]cos(30) = \frac{\sqrt{3}}{{2}}[/tex]; [tex]sin(90) = 1[/tex]; [tex]sin(30) = \frac{1}{2}[/tex];

---------------------------------------------------------------------------

[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex] becomes

[tex]cos(90- 30 ) = 0 * \frac{\sqrt{3}}{2} + 1 * \frac{1}{2}[/tex]

[tex]cos(90- 30 ) = 0 + \frac{1}{2}[/tex]

[tex]cos(90- 30 ) = \frac{1}{2}[/tex]

Hence;

[tex]cos(60) = \frac{1}{2}[/tex]

Answer:

[tex]\boxed{195}[/tex]

Step-by-step explanation:

The fruit flies grows geometrically.

[tex]125=80k^2[/tex]

Find the value of k.

[tex]\sqrt{\frac{125}{80} } =k[/tex]

[tex]1.25=k[/tex]

[tex]P=80(1.25)^t[/tex]

[tex]t[/tex] is number of days.

[tex]P=80(1.25)^4[/tex]

[tex]P=195[/tex]

Step-by-step explanation:

im sorry but i need more info or a picture or something to actually anwser the question...

Answer:A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root. Example: √36 = 6 (because 6 x 6 = 36)

Answer:

A and E

Step-by-step explanation:

If the answer was A, it would translate to:

I have done some stuff.

If the answer was D, it would translate to:

I have some stuff.

Both of the sentences are grammatically correct, so A and E are the answers.

Incorrect:

B. - I's do some stuff - doesn't make sense

C. - I's doing some stuff - doesn't make sense

D. - I's did some stuff - doesn't make sense

Answer: C. Interest will be charged

Step-by-step explanation:

Answer:

Step-by-step explanation:

Interest will be charged is your answer!

Answer:

-3.5 meters per second

Step-by-step explanation:

Take the distance and divide by the time

-17.5 meters/ 5 seconds

-3.5 meters per second

Answer:

-3.5 m/s

Step-by-step explanation:

Rate of the anchor =  [tex]\frac{distance}{time}[/tex]

[tex]\frac{-17.5}{5}[/tex]

-3.5 meters per second.

Answer:

x=10/3

Step-by-step explanation:

isolate the variable

Answer:

1. x = 4

2. x = 10/3

Step-by-step explanation:

1. 3x - 5 = 3 + x

3x - x = 3 + 5

2x = 8

x = 4

2. x/2 + 5/9 = 2x/3

(x/2 + 5/9) * 18 = (2x/3) * 18

9x + 10 = 12x

10 = 12x - 9x

10 = 3x

x = 10/3

Answer:

5/(1/3)

Step-by-step explanation:

She has 5 granola bars and gives 1/3 of one to each of her friends. To find how many friends she can give it to, divide 5 by 1/3. You would get a total of 15 friends that you can give granola bars to. The question is asking for an expression so the expression would be 5/(1/3) or 5*3

Answer:

1/3 x = 5

x=15

Step-by-step explanation:

You’re multiplying 1/3 times the number of friends (x), and then multiplying both sides by the reciprocal to solve for x

Answer:

100

Step-by-step explanation:

height = constant/ width

Taking the point (5,20)

where 5 is the width and 20 is the height

20 = constant/ 5

Multiply each side by 5

5*20 = constant

100 = constant

Answer:

This is called an Inductive reasoning.

Step-by-step explanation:

It is a logical process in which a number of premises all believed true combine to come up with specific conclusions. This is a generalisation based on observations.

Hope it helps.

Answer:

13 2/5

Step-by-step explanation:

a = 2 and b = -3

so the question asks whats.... a^3 - b^3/5

First we plug in the values of a and b

(2)^3 - (-3)^3 /5

Now we solve the ones in paranthesis first

(2)^3 = 8 because 2×2×2 and

-(-3)^3 forget about the - outside the parenthesis so

(-3)^3 = (-27) because (-3)×(-3)×(-3)

now we put it back together

8 -(-27)/5

the two minus become plus so

8 + 27/5

Now we solve it like fractions

8 and 27/5

simplify

13 and 2/5

Hope that helps!

Answer:

The daily rate is $33 and the per mile rate is $0.35

Step-by-step explanation:

4x + 440y = 286

3x + 190y = 165.5

We can solve this systems of equations by multiplying the second statement by [tex]-\frac{4}{3}[/tex] to try and eliminate the x variable.

4x + 440y = 286

-4x - [tex]\frac{760}{3}[/tex]y = -220[tex]\frac{2}{3}[/tex]

[tex]\frac{560}{3}[/tex] y= [tex]\frac{196}{3}[/tex]

560y = 196

y = 0.35

So, the rate per mile is 0.35. Now, with this info, let's find the daily rate by plugging it into the equation.

[tex]4x + 440\cdot0.35 = 286\\4x + 154 = 286\\4x = 132\\x = 33[/tex]

So, the daily rate is $33 and the mile rate is $0.35.

Hope this helped!

Answer:

the daily fee =33 dollars

and the mileage charge.=0.35

let d: be daily fee and m for mileage

cost of rental =(d*number of days)+ (m*number of mileage)

her first trip: 4d+440m=286

her second trip: 3d+190m=165.5

solve by addition and elimination

4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286

3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)

12d+1320m=858

12d+760m=662

subtract two equation to eliminate d

12d+1320m-12d-760m=858-662

560m=196

m=7/20=0.35 for on mileage

d: 4d+440m=286

4d=286-440(0.35)

d=(286-154)/4 33 dollars

Answer:

45

Step-by-step explanation:

Both angles (2x+45) and x together form a straight angle which measures 180 degrees.

Together should make you think of adding the angle measurements.

So we have that (2x+45)+x should be 180 degrees.

The equation we want to solve is:

(2x+45)+x=180

2x+45+x=180

(2x+x)+45=180

3x+45=180

3x=180-45

3x=135

x=135/3

x=45

Let's confirm that x is 45.

(2x+45) with x=45:

(2*45+45)

(3*45)

135

So (2x+45)+x at x=45 gives us:

135+45

180

Answer has been confirmed.

Answer:

[tex]\boxed{x = 45}[/tex]

Step-by-step explanation:

=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)

=> [tex]3x+45 = 180[/tex]

Subtracting 45 to both sides

=> 3x = 180-45

=> 3x = 135

Dividing both sides by 3

=> x = 45

Answer:

Step-by-step explanation:

In a pictogram, data can be arranged as follows:

Answer:

[tex] y = 3 [/tex]

Step-by-step explanation:

Given the above right angled triangle, we would use a trigonometric ratio formula to find y.

Given angle = 30°

Hypotenuse = 6

Opposite side = y

Solve for y using the trigonometric ratio formula as follows:

[tex] sin(X) = \frac{opposite}{hypotenuse} [/tex]

[tex] sin(30) = \frac{y}{6} [/tex]

Multiply both sides by 6

[tex] sin(30)*6 = \frac{y}{6}*6 [/tex]

[tex] 0.5*6 = y [/tex]

[tex] 3 = y [/tex]

[tex] y = 3 [/tex]

Answer:

56 number of ways

Step-by-step explanation:

This question is a combination question since it involves selection.

Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

If a manager receives 8 applications for a specific position and wants to narrow it down to 5, the number of ways he can do this is 8C5

8C5 = 8!/(8-5)!5!

= 8!/3!5!

= 8*7*6*5!/3*2*5!

= 8*7*6/3*2

= 8*7

= 56 number of ways.

This means that the manager can rank 5 applications in 56 number of ways

The number of ways that can she rank 5 applications should be 6720.

Since A manager receives 8 applications for a specific position. She wants to narrow it down to 5.

So here we do apply the permutation here:

[tex]= 8!\div 5!3! \times 5!\div 0!\\\\= 8\times 7\times 6\times 5\times 4[/tex]

= 6720

Hence, The number of ways that can she rank 5 applications should be 6720.

Learn more about ways here: https://brainly.com/question/18988173

Answer:

C. [tex] \frac{343}{18} pie [/tex]

Step-by-step explanation:

Given a circle of:

Radius (r) = 14

Measure of minor arc = 115°

We are required to find the length of DGE = length of major arc.

Length of arc is given as 2πr(θ/360)

Measure of the major arc DGE (θ) = 360 - 115 = 245°

Length of major arc DGE = [tex] 2*pie*14*\frac{245}{360} [/tex]

[tex] = 28*pie*\frac{49}{72} [/tex]

[tex] = \frac{28*49}{72} pie [/tex]

[tex] = \frac{7*49}{18} pie [/tex]

[tex] = \frac{343}{18} pie [/tex]

Length of arc DGE =

[tex] \frac{343}{18} pie [/tex]

Answer:

[tex]6-8cos2x+2cos4x[/tex]

Step-by-step explanation:

We are given that

[tex]16sin^4 x[/tex]

We can write the given expression as

[tex]16(sin^2x \times sin^2 x)[/tex]

[tex]16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})[/tex]

By using the formula

[tex]sin^2\theta=\frac{1-cos2\theta}{2}[/tex]

[tex]4(1-cos2x)^2[/tex]

[tex]4(1-2cos2x+cos^2(2x)[/tex]

Using the identity

[tex](a-b)^2=a^2+b^2-2ab[/tex]

[tex]4(1-2cos2x+\frac{1+cos4x}{2})[/tex]

[tex]4-8cos2x+2+2cos4x[/tex]

[tex]6-8cos2x+2cos4x[/tex]

This is required expression.

Answer:

Sum of money = $600

Step-by-step explanation:

X = sum of money

Simple interest means that its the same percentage of interest for a given number of years.

The interest per annum is 5% for 3 years, so 5% x 3 = 15%

15% = 0.15 (as a decimal)

Now, we can put this into an equation:

0.15x = 90

x = 90 / 0.15

x = 600.

sum of money invested = $600

Answer:

No solutions.

Step-by-step explanation:

You will only have solutions when the two lines meet. But since the slopes are the same, the two lines are parallel. Since the y-intercepts are different, that means that the two slopes will never intersect, which means that there are no solutions.

Hope this helps!

Answer: no solution

Step-by-step explanation: When lines have the same slope, the graphs of the two lines are parallel which means they never intersect.

Let's look at an example.

Below, you will see two equations.

Both of the lines have a slope of 1.

So, they must be parallel which means they don't cross.

So there is no solution.

Answer:

see explanation

Step-by-step explanation:

differentiate using the power rule.

[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus

[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1

x = 5 → 2(5) - 1 = 10 - 1 = 9

To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero

2x - 1 = 0 , then

2x = 1 and

x = [tex]\frac{1}{2}[/tex]

Answer:

it opens up

goes up 4 but doesn't move left or right

Answer:

6/4

Step-by-step explanation:

Answer:

6/4

Step-by-step explanation:

There are 6 brooms to 4 mops.

So you would write it that way as a fraction, but you could also write it like 6:4 or 6 to 4.

Answer:

123 domestic stamps

89 foreign stamps

Step-by-step explanation:

Answer:

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

Which equation represents the total number of stamps Malik collected?  

✔ x + y = 212

Which equation represents the difference in the number of foreign and domestic stamps Malik collected?  

✔ x – y = 34

Which system of linear equations represents the situation?  

✔ x – y = 34 and x + y = 212

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

This system of equations models the given information for both stamp types.

x – y = 34

x + y = 212

Solve the system of equations.  

How many foreign stamps does Malik have?

✔ 89  foreign stamps

How many domestic stamps does Malik have?

✔ 123 domestic stamps

Step-by-step explanation:

its right on 2021 edge! :) hope this helps

Answer:

Inequality:  [tex]1558 + 60 x \geq 2158[/tex]

Number of Weeks:  [tex]x \geq 10[/tex]

Step-by-step explanation:

Given

[tex]Initial\ Savings = \$1558[/tex]

[tex]Amount\ Needed = \$2158[/tex]

[tex]Additional\ Savings = \$60\ weekly[/tex]

Required

Represent this using an inequality

Represent the number of weeks as x;

This implies that, She'll save $60 * x in x weeks

Her total savings after x weeks would be

[tex]Initial\ Savings + 60 * x[/tex]

From the question, we understand that she needs at least 2158;

Mathematically, this can be represented as (greater than or equal to 2158)

[tex]\geq 2158[/tex]

Bringing the two expressions together;

[tex]Initial\ Savings + 60 * x \geq 2158[/tex]

Substitute 1558 for Initial Savings

[tex]1558 + 60 * x \geq 2158[/tex]

[tex]1558 + 60 x \geq 2158[/tex]

Hence, the inequality that represents the situation is [tex]1558 + 60 x \geq 2158[/tex]

Solving further for x (number of weeks)

[tex]1558 + 60 x \geq 2158[/tex]

Subtract 1558 from both sides

[tex]1558- 1558 + 60 x \geq 2158 - 1558[/tex]

[tex]60x \geq 600[/tex]

Divide both sides by 60

[tex]\frac{60x}{60} \geq \frac{600}{60}[/tex]

[tex]x \geq 10[/tex]

This means that she needs to save $60 for at least 10 weeks

Answer:

Its the first one

Step-by-step explanation:

I just did it lol

Answer:

They will find 69 viruses in 8 hours.

Step-by-step explanation:

The number of viruses after t hours is given by the following equation:

[tex]V(t) = V(0)(1-r)^{t}[/tex]

In which V(0) is the initial number of viruses and r is the decay rate, as a decimal.

They start with 500 viruses

This means that [tex]V(0) = 500[/tex]

Decay rate of 22% per hour.

This means that [tex]r = 0.22[/tex]

So

[tex]V(t) = V(0)(1-r)^{t}[/tex]

[tex]V(t) = 500(1-0.22)^{t}[/tex]

[tex]V(t) = 500(0.78)^{t}[/tex]

How many viruses will they find in 8 hours?

This is V(8).

[tex]V(t) = 500(0.78)^{t}[/tex]

[tex]V(8) = 500(0.78)^{8}[/tex]

[tex]V(8) = 68.51[/tex]

Rounding to the nearest whole number

They will find 69 viruses in 8 hours.

Answer:

The researchers will find 86 viruses.

Step-by-step explanation:

Identify the value of each variable in the formula. Be sure to put the percent in decimal form. Be sure the units match—the rate is per hour and the time is in hours.

A =?

A0 =  500

R= -0.22/hour

t= 8 hours

Substitute the values in the formula.

A= A0e^rt

A= 500e^-0.22x8

Compute the amount.

A ≈ 86.02

Round to the nearest whole number.

A ≈ 86

Answer:

See below.

Step-by-step explanation:

So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.

Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.

Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.

Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:

In other words, we will have:

[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.

Let's determine n first. We know that f(0)=64, thus:

[tex]f(0)=64=4(-2)^3\cdot n[/tex]

[tex]64=-32n, n=-2[/tex]

Now, let's expand:

Expand:

[tex]f(x)=(x+4)(x^2-4x+4)(x-2)(-2)[/tex]

[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]

[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]

[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]

This is the simplest it can get.