Evaluate the expression 2^5

In the given scenario ladder is 6.52 feet long.

Given that,

The angle between ground and ladder = 62 degree

The distance of ladder from ground and ladder = 3 feet

We have to find the length of  ladder.

Since we know that,

The trigonometric ratio

cosθ = adjacent/ Hypotenuse

Here we have,

Adjacent =  3 feet

Hypotenuse = length of ladder

Thus to find the length of ladder we have to find the value of hypotenuse.

Therefore,

⇒ cos62 = 3/ Hypotenuse

⇒    0.46 = 3/ Hypotenuse

⇒ Hypotenuse =  3/0.46

                          = 6.52

Thus,

length of ladder  = 6.52 feet.

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Answer:

It is C I am good at math

Step-by-step explanation:

Answer:

y= -2x+2

Step-by-step explanation:

Answer:

I believe one solution

Step-by-step explanation:

One line

Complete Question:

You plant an 8-inch spruce tree that grows 4 inches per year and a 14-inch hemlock tree that grows 6 inches per year.

The initial heights are shown.

Write a system of linear equations that represents this situation.

Answer:

\(s(x) = 8 + 4x\)

\(h(x) = 14 + 6x\)

Step-by-step explanation:

Given

Spruce Tree (s):

\(Initial\ Height = 8\)

\(Growth = 4\) (yearly)

Hemlock Tree (h):

\(Initial\ Height = 14\)

\(Growth = 6\) (yearly)

Required

Represent as system of linear equations

Let the number of years be x.

In both cases, the equation can be formed using:

\(Equation = Initial\ Height + Growth * x\)

For Spruce Tree (s):

\(s(x) = 8 + 4 * x\)

\(s(x) = 8 + 4x\)

For Hemlock Tree (h):

\(h(x) = 14 + 6 * x\)

\(h(x) = 14 + 6x\)

Hence, the equations are \(s(x) = 8 + 4x\) and \(h(x) = 14 + 6x\)

Using Euler integration, the next values of x and y can be determined as follows:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Euler integration is a numerical method used to approximate solutions to differential equations. It is based on the concept of dividing the interval into small steps and using the derivative at each step to calculate the next value. In this case, we are given the current values of x=2, y=8, and y'=9, with a step size of delta_X=5.

To determine the next values of x and y, we use the following formulas:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Substituting the given values into the formulas, we have:

x_next = 2 + 5 = 7

y_next = 8 + 5 * 9 = 53

Therefore, the updated values of x and y using Euler integration are x=7 and y=53.

It's important to note that Euler integration provides an approximate solution and the accuracy depends on the chosen step size. Smaller step sizes generally lead to more accurate results. Other numerical methods, such as Runge-Kutta methods, may provide more accurate approximations.

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a) Bearing from A to B is 253°.

b) Bearing from B to A is 287°.

What is a bearing?

A bearing is an angle measured clockwise from north in mathematics. Typically, bearings are expressed as a three-figure bearing.

a)

The bearing of 73° and the co-interior angle formed must total 180°. The counter-clockwise angle from B to A is 107°.

However a bearing must always be measured clockwise from north. 107° is counter-clockwise from north.

The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.

To work the bearing, subtract 107° from 360°.

360° – 107° = 253° and so, the bearing of A from B is 253°.

b)

The bearing of 107° and the co-interior angle formed must total 180°. The counter-clockwise angle from A to B is 73°.

However a bearing must always be measured clockwise from north. 73° is counter-clockwise from north.

The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.

To work the bearing, subtract 73° from 360°.

360° – 73° = 287° and so, the bearing of B from A is 287°.

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Answer:

1.8

Step-by-step explanation:

1.2p - 2q

Let p = 3.5 and q = 1.2

1.2 ( 3.5) - 2(1.2)

Multiply

4.2 - 2.4

Subtract

1.8

Answer:

The slope of the line is 4/2, or 2.

The equation of the line is y + 1 = 2(x − 1)

The expression that is equivalent to the given expression, 8x + 4, is 4(2x +1)

From the question, we are to determine the expression that is equivalent to the given expression.

The given expression is:

8x + 4

To determine the expression that is equivalent to the given expression, we will factorize the given expression.

First, we will determine the Greatest common factor (GCF) of the terms in the expression.

The terms in the expression are 8x and 4

The GCF of 8x and 4 is 4

Thus,

We can factor the expression as shown below:

8x + 4

4(2x + 1)

Hence, the expression is 4(2x + 1)

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Answer:

8

Step-by-step explanation:

If you plug in the answers it will give you 9x6= 54 which is wrong and 9x7=63 and 9x9=81 but 9x8=72.

Answer:

C   length = 8

Step-by-step explanation:

Area of Rectangle = lw

A = lw    Substitute l = (2x + 4) ; w = 9

72 = (2x + 4)9

72 = 18x + 36

36 =        -36

36 = 18x

36/18 = x

 2 = x

 Substitute into l = 2x + 4 ; l = 2(2) + 4; l = 4 + 4 ; l = 8

The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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Answer:

The ratio of the distance of Pluto and the earth to the Sun is 40.

Time taken by light to travel from Sun to Pluto is 5.3 hours.

Step-by-step explanation:

Distance between Earth an Sun = 93,000,000 miles

Time from Sun to Earth = 8 minutes

Distance beteen Pluto and Sun = 3.7 x 10^9 miles

The ratio of the distance between Pluto and Sun to the Earth and Sun is

\(\frac{3.7\times 10^9}{93000000}\\\\=39.8 =40\)

Now let the time taken by the light to move from Sun to Pluto is t.

\(\frac{93000000}{8}=\frac{3.7\times 10^9}{t}\\\\t =318.28 minutes = 5.3 hours\)

x = 0

hope this helps

Answer:

2.1

Step-by-step explanation:

+3.28 each side

add 5.8 and 2.4= 8.2

-8.2 from 9

0.8x=1.68

divide by 0.8

Work Shown:

a = change in distance = 492-300 = 192 miles

b = change in time = 12 weeks

c = a/b = rate of change of distance over time = speed of growth

c = (192 miles)/(12 weeks)

c = (192/12) miles per week

c = 16 miles per week

In other words, each time a week goes by, Ryan has walked another 16 miles.

For a related math concept, check out the slope formula. The slope represents the rate of change. It's useful for graphing linear equations.

Answer:

Step-by-step explanation:

Total members in the choir = 24 + 36 = 60

a) Percentage of men = \(\frac{24}{60}*100\)

                                 = 4 * 10  = 40%

b) Percentage of women = 60%

c) Number of men =24 + 10 = 34 men

Number of women = 36 + 10 = 46

Total = 34 + 46 = 80

Percentage of men = \(\frac{34}{80}*100= 42.5\)%

Percentage of women = (100 - 42.5)% = 57.5%

Answer:

a]

% of men = 24/60 × 100

% of men = 4/10 × 100

% of men = 4 × 10

% of men = 40%

b]

% of women = 36/60 × 100

% of women = 6/10 × 100

% of women = 6 × 10

% of women = 60%

c]

Men = 24 + 10 = 34

Women = 36 + 10 = 46

Total = 34 + 46 = 80

% of men = 34/80 × 100 = 42.5

% of women = (100 - 42.5) = 57.5 %

\( \\ \)

The expression, (5 > 57 % 8), evaluates to false.

To determine if the expression (5 > 57 % 8) evaluates to true or false, we need to first calculate the value of 57 % 8.

Step 1: Calculate 57 % 8, which represents the remainder when 57 is divided by 8.
57 % 8 = 1

Step 2: Compare 5 and the result from Step 1 using the '>' operator.
5 > 1

Step 3: Determine if the comparison in Step 2 is true or false.
Since 5 is greater than 1, the expression evaluates to true.

So, the expression (5 > 57 % 8) evaluates to true.

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Quantity of gasoline that Jonathan use cutting the grass is 24,000 milliliters

To calculate the amount of gasoline Jonathan used cutting the grass, we need to find the difference between the initial amount of gasoline and the amount of gasoline left in the tank after mowing the grass.

The initial amount of gasoline is 45 liters, and the amount of gasoline left in the tank is 21 liters

So, the amount of gasoline Jonathan used is

45 - 21 = 24 liters

However, we are asked to express the amount of gasoline used in milliliters. To do this, we can use a conversion factor that relates liters to milliliters.

There are 1000 milliliters in one liter, so we can multiply the amount of gasoline used in liters by 1000 to get the equivalent amount in milliliters.

Therefore, the amount of gasoline Jonathan used cutting the grass is

24 liters x 1000 ml/liter = 24,000 milliliters

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Answer:

Option B = 108 cm

Step-by-step explanation:

Please refer the figure attached

As the given figure have four 90° angles,

AB = CH

BC = AH

So, AB = 30 cm , CH = 30 cm

BC = 15 cm, AH = 15 cm

Already given ED = FG = 5 cm, EF = 11 cm

Working note : As, AB = CH = 30 cm

CH = CD + 3cm + GH

30 = CD + 3cm + GH

CD + GH = 27 cm

Perimeter is the overall measure of the boundary of the given figure, ie

AB + BC + CD + DE + EF + FG + GH + AH

= 30 + 15 + CD + 5 + 11 + 5 + GH + 15

= CD + GH + 81

= 27 + 81

Perimeter = 108 cm

True. in an assignment a(:) = b, the number of elements in a and b must be the same.

In MATLAB, the assignment statement a(:) = b is used to assign the elements of b to the elements of a in a column-wise fashion. For this to work, the number of elements in a and b must be the same. If the number of elements in b is less than that of a, then the remaining elements of a will retain their previous values. If the number of elements in b is greater than that of a, then an error will occur.

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The student will answer every item that is a multiple of 4 correctly, and every item that is a multiple of 3 will be incorrect.

On a true-false test of 100 items, every fourth item is true, and the rest of the items are false. Thus, there will be 100/4 = 25 correct answers. There are a total of 33 items that are multiples of 3, and the student answers them all wrong. Therefore, the student will answer 100-33 = 67 items correctly. Every item that is a multiple of 4 will be answered correctly by the student because every fourth item is true, and the student marks all true items correctly.

As a result, the student will have 25 correct answers because 100/4 = 25. The rest of the items, which are not multiples of 4, will be answered correctly by the student because they are true, and the student marks all true items correctly. The student will correctly answer 100-33 = 67 items because there are a total of 100 items and 33 multiples of 3 in the exam.

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The length of each side of the rug is (2x + 7) inches, and the side length of the purple square is x inches.

The area of the orange band in the square rug can be found by subtracting the area of the purple square from the total area of the rug. The side length of the purple square is given as x inches. Therefore, the length of each side of the rug is (x + 7 + x) inches.

Simplifying this expression, we get 2x + 7 as the length of the side of the rug.

Therefore, the area of the rug is (2x + 7)² square inches.

The area of the purple square is x² square inches.

Therefore, the area of the orange band is: (2x + 7)² - x² square inches. This simplifies to (4x² + 28x + 49 - x²) square inches, which is equal to 3x² + 28x + 49 square inches.

Thus, the area of the orange band is 3x² + 28x + 49 square inches.

Therefore, the area of the orange band is given by the expression 3x² + 28x + 49 square inches.

In conclusion, to find the area of the orange band, we subtract the area of the purple square from the area of the rug. The length of each side of the rug is (2x + 7) inches, and the side length of the purple square is x inches.

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Answer:

greater than

hope this helps! <3

The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

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Answer:

2

Step-by-step explanation:

4/2=2

Answer:

here is your answer = 56.7m

The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

Here,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

The velocity of a particle = \(\frac{d r(t)}{dt}\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

The acceleration of a particle = \(\frac{d^{2} r(t)}{dt^{2} }\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(\frac{d^{2} r(t)}{dt^{2} }= 2j\)

The speed of a particle = \(| \frac{d r(t)}{dt}| = |v(t)|\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(|v(t)|=\sqrt{1 + 4t^{2} }\)

Hence, The velocity of a particle = \(i + 2t j\)

The acceleration of a particle = \(2 j\)

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

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Answer:

114

Step-by-step explanation:

those angles are supplementary meaning that they will add up to 180. 180-66=114 so x=114