A balloon floats 18.5 kilometers east
and then 24.6 kilometers north.
What is the angle of the
balloon's resultant vector?
Hint: Draw a vector diagram.
[?]°
Round your answer to the nearest tenth.

Answer:

4.4

Step-by-step explanation:

The sum of the probabilities of all possible outcomes is 1.

As the die is loaded so that the number 4 occurs 3/10 of the time, and the other numbers occur with equal frequency, then the probability of numbers 1, 2, 3, 5, 6, 7 and 8 being rolled is 1/10.

Create a probability distribution table for X, where X is the score on the loaded 8-sided die:

[tex]\begin{array}{ | c | c | c | c | c | c | c | c | c |}\cline{1-9}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\cline{1-9} & & & & & & & &\\ \text{P}(X=x) & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{3}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10}\\& & & & & & & &\\\cline{1-9}\end{array}[/tex]

Add a product row and a totals column:

[tex]\begin{array}{ | c | c | c | c | c | c | c | c | c | c |}\cline{1-10}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 &\text{Total} \\ \cline{1-10} &&&&&&&&& \\ \text{P}(X=x) & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{3}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & 1\\ &&&&&&&&&\\ \cline{1-10} &&&&&&&&&\\\text{Product} & \frac{1}{10} & \frac{2}{10} & \frac{3}{10} & \frac{12}{10} & \frac{5}{10} & \frac{6}{10} & \frac{7}{10} & \frac{8}{10} & \frac{44}{10} \\ &&&&&&&&&\\\cline{1-10}\end{array}[/tex]

(The Product is row is the product of the score on the die and its probability).

The expected value (EV) is the sum of the product of each outcome and its probability.  

Therefore, the expected value (EV) of this die is 44/10 = 4.4

Answer:

Hence, 0.0000087 can be expressed as [tex]$8.71 \times 10^{-6}$[/tex].

Step-by-step explanation:

- Given 0.00000871

- Move the decimal point so that the factor is greater than or equal to 1 but less than 10 .

- Then count n and write no. as product with a power of 10 .

Step 1 of 1

Consider 0.00000871,

8.71

Decimal has moved 6 places to right.

The power will be negative as the original no. is less than 1 .

[tex]$$\begin{array}{r}8.71 \times 10^{-6} \\0.0000087=8.71 \times 10^{-6}\end{array}$$[/tex]

Answer:

its answer is 36

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8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]

11. The value of x is 4

From the question, we are to simplify the give expression

The given expression is

[tex]y^{3}\sqrt[5]{32x^{4} } - 7\sqrt[5]{x^{4}y^{15} }[/tex]

[tex]y^{3} (32x^{4} )^{\frac{1}{5} } - 7(x^{4}y^{15} )^{\frac{1}{5}[/tex]

[tex]y^{3} \times 32^{\frac{1}{5} } x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{\frac{15}{5}}[/tex]

[tex]y^{3} \times 2^{5 \times} ^{\frac{1}{5} } \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]

[tex]y^{3} \times 2 \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]

[tex]2 x^{\frac{4}{5} } y^{3} - 7 x^{\frac{4}{5}}y^{3}[/tex]

[tex]= - 5 x^{\frac{4}{5}}y^{3}[/tex]

11. [tex]\frac{1}{2}(5x+7 )^{\frac{2}{3} } =\frac{9}{2}[/tex]

Multiply both sides by 2

[tex]2 \times \frac{1}{2}(5x+7 )^{\frac{2}{3} } =2 \times \frac{9}{2}[/tex]

[tex](5x+7 )^{\frac{2}{3} } =9[/tex]

Multiply both sides by a power of 3/2

[tex](5x+7 )^{\frac{2}{3} \times {\frac{3}{2} } } =9^{\frac{3}{2} }[/tex]

[tex](5x+7 )=3^{2 \times} ^{\frac{3}{2} }[/tex]

[tex]5x+7 =3^{3}[/tex]

[tex]5x+7 =27[/tex]

[tex]5x =27-7[/tex]

[tex]5x = 20[/tex]

[tex]x = \frac{20}{5}[/tex]

x = 4

Hence,

8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]

11. The value of x is 4

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The length of each side of the base of the pyramid is 14 cm

From the question, we are to determine the length of each side of the base of the pyramid

The volume of a square-based pyramid is given by

V = 1/3(b²h)

Where V is the volume

b is the length of the base

and h is the height

From the given information,

V = 392 cm³

h = 6 cm

Putting the parameters into the equation, we get

392 = 1/3(b²× 6)

392 = b² ×2

b² = 392/2

b² = 196

b = √196

b = 14 cm

Hence, the length of each side of the base of the pyramid is 14 cm

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Since both the given triangles are equilateral, their interior angles are each measure 60°.

Consider triangles ADC and BEC.

We have:

According to above, two sides and the included angle of triangles ADC and BEC are congruent by ASA.

Therefore AD = BE as corresponding sides of congruent triangles, hence proved.

The solution to the inequality 2x + 5y < 25, y < 3x-2 and 5x - 7y < 14 is the dark triangular region shown in the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality shows the non equal comparison of two or more numbers and variables.

The solution to the inequality 2x + 5y < 25, y < 3x-2 and 5x - 7y < 14 is the dark triangular region shown in the graph.

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Answer:

-50

Explanation:

At sea level would be 0 so anything above would be a positive number and anything below a negative number.

The maximum value of allowable emissions in the year 2031 is equal to 3,502.

In order to determine the maximum value of allowable emissions in the year 2031, we would use an exponential function which also relates to compound interest as follows:

A = P(1 - r)^t

For the time, we have:

Time, t = 2031 - 2022

Time, t = 9

Substituting the given parameters into the formula, we have;

A = 4,200(1 - 0.02)^9

A = 4,200(0.98)^9

A = 4,200 × 0.8338

A = 3501.7 ≈ 3,502.

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The first five terms of the sequence will be 3, 6, 11, 18, 27. Then the correct option is C.

A sequence is a list of elements that have been ordered sequentially, such that members come either before or after.

The equation will be given below.

[tex]\rm a_n = n^2+2[/tex]

Then the first five terms of the sequence will be

For n = 1, we have

a₁ = 1² + 2

a₁ = 3

For n = 2, we have

a₂ = 2² + 2

a₂ = 6

For n =3, we have

a₃ = 3² + 2

a₃ = 11

For n = 4, we have

a₄ = 4² + 2

a₄ = 18

For n = 5, we have

a₅ = 5² + 2

a₅ = 27

Then the sequence will be 3, 6, 11, 18, 27.

Then the correct option is C.

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If the population can be shown to be decreasing in size, then the lambda would be positive while the r would be negative.

When the population is decreasing, the rate would be negative because the population is shrinking. This is why r - which is rate - will be negative.

Lambda on the other hand will be positive to show that the population started from a higher value and is now decreasing.

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Answer:

(b) 25 muffins

(c) 38 muffins

Step-by-step explanation:

Given:

Forming system of linear equations:

muffins (m) + cookies (c) = 200 treats

1.60m + 0.80c = $200

Solve by Substitution:

m + c = 200

1.6m + 0.8c = 200

using m + c = 200, solve for m by subtracting c:

m + c - c = 200 - c

m = 200 - c

we can now plug in m tot he second equation,

1.6(200 - c) + 0.8c = 200

320 - 0.8c = 200

320 - 320 - 0.8c = 200 - 320

-0.8c = -120

-0.8c/-0.8 = -120/-0.8

c = 150

plug c back in to find m,

m = 200 - c

m = 200 - 150

m = 50

(b) if you buy 200 cookies, then how many muffins?

we use this equation as we want to stay in the price limit: 1.6m + 0.8c = 200

c = 200 so 1.6m + 0.8(200) = 200

1.6m + 0.8(200) = 200

1.6m + 160 = 200

1.6m = 200 - 160

1.6m = 40

1.6m/1.6 = 40/1.6

m = 25

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Answer:

the answer is false .

Step-by-step explanation:

Answer:

8+16+2=28

Step-by-step explanation:

Answer:

210 yd²

Step-by-step explanation:

If we rotate the shape we get a right angle triangle with a hypotenuse of 29 yd :

The area of a right angle triangle is given by the formula :

A = [tex]\frac{ab}{2}[/tex]

Substituting the 2 values given in diagram gives us :

A = [tex]\frac{(20)(21) }{2}[/tex] = 420÷2 = 210

Our units will be yd² as we are dealing with area

Part 1

The gradient of the line is [tex]\frac{11-1}{-3-2}=-2[/tex], so the equation is [tex]y=-2x+5[/tex].

This means the system is

[tex]y=-2x+5\\\\y=ax^2 +b[/tex]

Part 2

Substituting in the coordinates (-3,11) and (2,1) into the equation of the parabola,

[tex]11=9a+b\\\\1=4a+b[/tex]

Subtracting the equations, we get 10=5a, and thus a = 2

Substituting a = 2 back into the system, we get b = -7

Part 3

The equation of the parabola is [tex]y=2x^2 - 7[/tex], and the turning point is at [tex]x=0[/tex]. Therefore, the value of y is -7

The value of the given algebraic expression is -63/8.

To evaluate an algebraic expression, we substitute the values of the variables in the expression, and then follow the rules of solving a numeral expression.

In the question, we are asked to evaluate the algebraic expression:

{(3a - b)/2c} + {(3a - c)/(c - b)}, given the values of a = 3, b = -2, and c = -4.

To evaluate the expression {(3a - b)/2c} + {(3a - c)/(c - b)}, given the values a = 3, b = -2, and c = -4, we substitute these values in the expression and solve as follows:

{(3(3) - (-2))/2(-4)} + {(3(3) - (-4))/((-4) - (-2))}

= {(9 + 2)/(-8)} + {(9 + 4)/(-4 + 2)}

= {-(11/8)} + {-(13)(2)}

= -(11/8) - (13/2)

= -(11/8) - (52/8)

= -(63/8).

Thus, the value of the given algebraic expression is -63/8.

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Answer:

104m²

Step-by-step explanation:

we can find the area of a trapezoid from its bases and height in the following formula:

[tex]A=\frac{a + b}{2}h[/tex]

where...

A: area

a: one base

b: other base

h: height

here, we can see that our two bases are 9 and 17, and that our height is 8.

Now, let's plug these values into our formula:

a: 9

b: 17

h: 8

[tex]A=\frac{a + b}{2}h[/tex]

[tex]A=\frac{9 + 17}{2}8[/tex]

Now, we can simplify:

[tex]A=\frac{9 + 17}{2}8[/tex]

[tex]A=\frac{26}{2}8[/tex]

A = 13 · 8

A = 104

so, the area of this trapezoid is 104m²

(note: we write area as squared / in square units)

hope this helps! have a lovely day :)

Answer:

0.4

Step-by-step explanation:

4/3(1.5/5)

4/3(0.3)

1.33333333333(0.3)

0.4

The solution to the given product is:

-6i*(6 - 2i) = -12 - 36i

Here we want to solve:

-6i*(6 - 2i)

Here the thing that you need to remember is that i² = -1.

Expanding the product, we get:

-6i*(6 - 2i) = (-6i)*6  + (-6i)*(-2i)

               = -36i + (6i)*(2i) = -36i + 12i² = -36i - 12

Then we conclude:

-6i*(6 - 2i) = -12 - 36i

That is the solution to the given expression.

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Answer:

D

Step-by-step explanation:

The domain is the x value which in this case would be the hours of training

Answer:

5.5x+7.146 (the six is repeating)

Step-by-step explanation:

Answer:

5.5x + 7.25

Step-by-step explanation:

5.5(x+6.5)-(x+9.5)-(19-x)              Convert the fractions to decimal

5.5x+35.75 -x - 9.5 - 19 +x         Expand

(5.5x - x + x) +(35.75 - 9.5 - 19)  Group like terms

5.5x + 7.25                                 Combine like terms

Answer:

0.2

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

1 divided by 5 = 0.2

Answer:

31°

Step-by-step explanation:

Given Angle EFG = Angle EFH + Angle HFG (based on the diagram)

[tex]2x+52 = 21 + (x+31)\\2x+52 = 21+x+31\\2x+52=x+52\\2x-x+52=52\\x+52=52\\x=52-52\\x=0[/tex]

From here we can see the value of x is non-existent.

Substitute x to find Angle HFG.

x+31 = 0 + 31 = 31°

Using proportions, it is found that the family would spend $36.75 on clothing.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The family has a budget of $525, and spends 7% of it in clothing, hence the amount is given by:

A = 0.07 x 525 = $36.75.

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There are 120 6-digit numbers that can be formed

The digits are given as:

0,1,3,5,7 and 9

Since the number must be divisible by 10.

Then the number must end in 0

The other 5 digits can take any of the 0,1,3,5,7.

So, the number of combination is:

Count = 5! * 1

Expand

Count = 5 * 4 * 3 *2 * 1 * 1

Evaluate

Count = 120

Hence, there are 120 6-digit numbers that can be formed

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This are also referred to as exponential sequence.  The common ratio if r > 0 is 2

This are also referred to as exponential sequence. Given the following sequence

(7-2x),9,(5x+17)

If they are in geometric progression, hence;

9/7-2x = 5x+17/9

Cross multiply

7-2x(5x+17) = 9(9)

Expand

35x+119-10x²-34x = 81

-10x²+x+119-81=0
10x²-x-38 = 0

Factorize

10x²-20x +19x-38 = 0

10x(x-2)+19(x-2)= 0

x - 2 = 0

x = 2

Hence the common ratio if r > 0 is 2

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The mean of the data about researcher counting of seconds each by stander helps a stranger struggling to pick up a heavy box fan varying amounts of time is 11.67 seconds.

Given if a researcher counting how many seconds each by stander helps a stranger struggling to pick up a heavy box fan varying amounts of time but is 10 seconds and 15 seconds equally as much in the data. all the restaurant under 10 seconds.

We have to calculate mean of the data.

Mean is the sum of numbers divided by total numbers included.

Mean=∑X/n

where n is the numbers.

Mean =(10+15+10)/3

=35/3

=11.67

Hence mean of the data about researcher's counting is 11.67.

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Part 1

By the inscribed angle theorem, arc PA measures 62 degrees.

Part 2

Angles inscribed in the same arc are congruent, so angle PRA measures 31 degrees.

Part 3

Diameters form semicircles, and the arc of a semicircle measures 180 degrees, so arc PAR measures 180 degrees.

Part 4

Subtracting arc PA from arc PAR, we get arc AR measures 118 degrees.

The cost of covering the triangular prism wedge in silver is: $108.

Surface area = (s1 + s2 + s3)L + bh.

Given the following:

Plug in the values into the formula

Surface area of the triangular prism metal wedge = (10 + 8 + 6)0.5 + (6)(8)

Surface area of the triangular prism metal wedge = 72 cm²

Cost of covering = 72/2 × 3 = $108

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