Simplify the expression to a+bi form: (10+10i)+(-7+3i)

Answer:

16.06 ft

Step-by-step explanation:

The figure is attached below.

In triangle ACB:

[tex]tan(41)=\frac{x}{y} \\x=ytan(41)[/tex]

In triangle ADB:

[tex]tan(25)=\frac{x}{y+10} \\(y+10)tan(41)=x[/tex]

Therefore equating both equations gives:

[tex]ytan(41) = (y+10)tan(25)\\ytan(41) = ytan(25)+10tan(25)\\ytan(41)-ytan(25)=10tan(25)\\y(tan(41)-tan(25))=10tan(25)\\y=\frac{10tan(25)}{(tan(41)-tan(25)} =11.5715ft[/tex]

Therefore x = 11.5715*tan(41) = 10.06 ft

The distance of the jot air balloon to ground = 10.06 + 6 = 16.06 ft

Answer:

0.6

Step-by-step explanation:

Given that the spinner has 5 equal sections numbered 1 to 5.

Multiples of 2 in 1 to 5 are: {2,4}

Number less than  than 3 are:{1,2}

Since we are required to find the probability of the spinner stopping on a number that is a multiple of 2 or is less than 3, we take the union of both sets.

{2,4} [tex]\cup[/tex] {1,2} ={1,2,4}

Number of Outcomes=3

Therefore,

Probability of the spinner stopping on a number that is a multiple of 2 or is less than 3  [tex]=\dfrac{3}{5}=0.6[/tex]

Answer:

.667

Step-by-step explanation:

4/6 = 2/3 = .667

The probability that it is a 5 or an even number is 5/6 or 0.834 if

you roll a six-sided die.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Number of total outcomes = 6

P(5) = 1/6

P(even) = 4/6

The probability that it is a 5 or an even number:

P = 1/6 + 4/6 = 5/6

P = 0.834

Thus, the probability that it is a 5 or an even number is 5/6 or 0.834 if

you roll a six-sided die.

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Answer:

31

Step-by-step explanation:

63-32=31

Answer:

the answer is 3:5

Step-by-step explanation:

Total number of jobs for the interview = 15

number of job offers received by Gabby = 6

number of jobs not offered = 15 - 6 = 9

therefore, the relationship will be 9:15

                                                           3:5

Answer:

y=1

x=2/5

Step-by-step explanation:

1=-5x+3

-2=-5x

x=2/5

Answer:

x = 2/5

Step-by-step explanation:

-5*2/5+3=1

x is 2/5

Answer:

920 ft^2

Step-by-step explanation:

area of triangles: base x height / 2 (2)

8 x 15 / 2

= 60 x 2

= 120

area of rectangular base: length x width

15 x 20 = 300

area of sloped rectangle: length x width

17 x 20 = 340

area of rectangle: length x width

8 x 20 = 160

Total: 120 + 300 + 340 + 160

=920 ft^2

Answer:

920 ft²

Step-by-step explanation:

2 triangles + 3 rectangles

2(½×15×8) + 20(17+8+15)

120 + 800

920

Answer:

36

Step-by-step explanation:

Answer:

x ≈ 370

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

Answer:

1/7

Step-by-step explanation:

divide 6/42

Answer:

138.248cm²

Step-by-step explanation:

Surface area=2πrh + 2πr²

Surface area=2x3.142x2x9+ 2x3.142x2²

Surface area=113.112+25.136

Surface area=138.248cm²

Answer:

Answer:

138.248cm²

Step-by-step explanation:

Surface area=2πrh + 2πr²

Surface area=2x3.142x2x9+ 2x3.142x2²

Surface area=113.112+25.136

Surface area=138.248cm²

"credit goes to unknown76th"

Step-by-step explanation:

Answer:

[tex] D= 375 - (-150) m = 375m +150 m= 525 m[/tex]

So then the distance between the submarine and the airplace is 525 m

Step-by-step explanation:

For this case we know that the submarine is 150 m below the sea level and the airplane is 375 m above the sea level and we want to find the difference between the heights and we got:

[tex] D= 375 - (-150) m = 375m +150 m= 525 m[/tex]

So then the distance between the submarine and the airplace is 525 m

Answer:

I think the correct answer is 27 so option c. :)

Answer:

22/28 = 11/14

Step-by-step explanation:

no of socks other than blue = 22

total no of socks = 28

so probability= 22/28 = 11/14

Answer:

22

Step-by-step explanation:

8 black 6 blue and 14 white is equal to 28

and if 6 are blue the rest are not so 6-28=22

Answer:

1

Step-by-step explanation:

Solve. Remember to follow PEMDAS.

PEMDAS  is the order of operation, and =

Parenthesis

Exponent (& Roots)

Multiplication

Division

Addition

Subtraction

First, divide 54 with -6:

54/(-6) = -9

Next, combine the terms.

10 + (-9) = 10 - 9 = 1

1 is your answer.

~

Answer:

1. $0.99

2. $1.98

Step-by-step explanation:

1. From the question we have

Cost of box = $2.48

Selling price = $1.49

That is the box is discounted from $2.48 to $1.49

Therefore, amount saved = $2.48 - $1.49 = $0.99

2. The amount saved from buying a second box is hence;

2 × $0.99 = $1.98

Hence, as the number of boxes bought increases, the amount saved increases

Answer:

The answers to both questions are

1. You save $0.99 on the box when it is purchased on sale

This is calculated by subtracting on-sale price from pre-sale price:

$2.48-$1.49 = $0.99

2. Total amount saved when a second box is purchased on-sale price is derived by multiplying the amount saved on-sale purchase by two:

$0.99 x 2 (boxes)

$0.99 x 2 = $1.98

Cheers!

We have been given that in ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. We are asked to find the length of r to the nearest 10th of an inch.

We will use law of sines to solve for side r.

[tex]\frac{a}{\text{Sin}(a)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are corresponding sides to angles A, B and C respectively.

Let us find measure of angle S using angle sum property of triangles.

[tex]\angle R+\angle S+\angle T=180^{\circ}[/tex]

[tex]\angle R+123^{\circ}+28^{\circ}=180^{\circ}[/tex]

[tex]\angle R+151^{\circ}=180^{\circ}[/tex]

[tex]\angle R+151^{\circ}-151^{\circ}=180^{\circ}-151^{\circ}[/tex]

[tex]\angle R=29^{\circ}[/tex]

[tex]\frac{r}{\text{sin}(R)}=\frac{s}{\text{sin}(S)}[/tex]

[tex]\frac{r}{\text{sin}(29^{\circ})}=\frac{93}{\text{sin}(123^{\circ})}[/tex]

[tex]\frac{r}{\text{sin}(29^{\circ})}\cdot \text{sin}(29^{\circ})=\frac{93}{\text{sin}(123^{\circ})}\cdot \text{sin}(29^{\circ})[/tex]

[tex]r=\frac{93}{0.838670567945}\cdot (0.484809620246)[/tex]

[tex]r=110.889786233799179\cdot (0.484809620246)[/tex]

[tex]r=53.7604351[/tex]

Upon rounding to nearest tenth, we will get:

[tex]r\approx 53.8[/tex]

Therefore, the length of r is approximately 53.8 inches.

Look at the attached picture

Hope it will be helpful to you ...

The range of the number given is given as (12, 32) while the mean of the given number is 17.14.

Given that,
The list of the number is given as 12, 13, 19, 16,32, 15, and 13.
The range of the number and mean of the given numbers is to be determined.

Range, it is the set of values that come out to an outcome for a certain mathematical operation.

The mean of the values is the ratio of the total sum of values to the number of values.

Here,
Rearrange the number in ascending order,
12, 13, 13, 15, 16, 19, 32

The range of the list is given as,
Range = [12, 32]

Mean of the numbers = [12 + 13 + 13 + 15 + 16 + 19 + 32] / 7
Mean =  17.14

Thus, the range of the number given is given as (12, 32) while the mean of the given number is 17.14.

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Answer:

Cosine is Adj/Hyp

a simple trick i use when doing these kind of problems is first finding the sides. If you only know the Hypotenuse then you multiply that with the cos(x) or whatever angle it is. If you only know Adjacent then you divide the adjacent with the Cos(x) and you get the answer

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Firstly, to answer this question, we need to calculate the change in elevation.

Let’s just think of the question as, the distance from the foot of the mountain to the top is 4,418 meters. Now we have climbers starting at a height of 2,550 meters. We now need to know the difference or the distance to which they have climbed.

To calculate this is quite straightforward, all we need do is to subtract the starting point from the end position.

Mathematically that would be 4,418 - 2,550 = 1,868 meters

Now our answer need be in foot. we have a conversion system given in the question already.

1 foot = 0.3048 meters

x foot = 1,868 meters

x = 1,868/0.3048

x = 6,128.6 feet which is approximately 6,129 feet

Answer:

8

Step-by-step explanation:

Vanillas percentage is 26%

26% of 50 is 13

Chocolates percentage is 42%

42% of 50 is 21

21-13=8

Using proportions, it is found that 8 more of Ursula’s classmates chose chocolate than chose vanilla.

In total, there are 50 students.

[tex]0.42(50) = 21[/tex]

That is, 21 choose chocolate.

The sum is 100%, hence the percentage that choose vanilla is:

[tex]x + 14 + 18 + 42 = 100[/tex]

[tex]x = 100 - 74[/tex]

[tex]x = 26[/tex]

26%, out of 50, hence:

[tex]0.26(50) = 13[/tex]

13 choose vanilla.

21 - 13 = 8.

8 more of Ursula’s classmates chose chocolate than chose vanilla.

To learn more about proportions, you can check https://brainly.com/question/24372153

Answer:

(5yz)^2(x^2z^3)

(25y^2z^2)(x^2z^3)

25x^2y^2z^5

Step-by-step explanation:

Answer:

The median is NOT the same thing as a quartile.

The median is a measure of center.

Answer:

She uses [tex]\frac{1}{12}[/tex] of the sheet of paper to make the flower.

Step-by-step explanation:

She cuts 1/2 of a piece of paper.

Of what was cut, she used 1/6 to make a piece.

What fraction of the sheet of paper does she use to make the flower?

A sixth of one half. So

[tex]\frac{1}{6}*\frac{1}{2} = \frac{1}{12}[/tex]

She uses [tex]\frac{1}{12}[/tex] of the sheet of paper to make the flower.

Answer:

Complementary

Step-by-step explanation:

When 2 things are complementary, they take up all given space.

When it's unlikely, it isn't all probability

Independent means they don't affect each other.

Disjoint means mutually exclusive.

Answer:

-1.3

Step-by-step explanation:

Answer:

-2-(-0.7)

= -2-(-0.7)

= -2 + 0.7

= -1.3

Step-by-step explanation:

minus into minus is plus

-2 is greater so we are going to put "-" sign

and get the aswer by adding

to pu this in number line just estimate the closest whole number on line and and also check the mines integers left is minus and right is plus side thanks

pleas mark me as brainliest i told every thing in detail