Please helpppppppppppp

[tex]\dfrac{15 + 10i}{1 + 2i}=\\\\\dfrac{(15 + 10i)(1-2i)}{(1 + 2i)(1-2i)}=\\\\\dfrac{15-30i+10i+20}{1+4}=\\\\\dfrac{35-20i}{5}=\\\\7-4i[/tex]

Answer:

7-4i

Step-by-step explanation:

Multiplying the numerator and denominator by $1-2i$ gives

\begin{align*}

\frac{15+10i}{1+2i} &= \frac{15+10i}{1+2i}\cdot\frac{1-2i}{1-2i}\\

&= \frac{(15+10i)(1-2i)}{1^2 + 2^2} \\

&= \frac{5(3 + 2i)(1 - 2i)}{5} \\

&= (3 + 2i)(1 - 2i) \\

&= 3 + 2i - 6i - 4i^2 \\

&= 3 + 2i - 6i + 4 \\

&= \boxed{7 - 4i}.

Answer:

4096/15,625

Step-by-step explanation:

The reason is because the power is distributed individually within the fraction. Since the fraction is already fully simplified, 4096/15625 multiplied by itself is also simplified.

Thus the answer is 4096/15,625 = (4^6)/(5^6)

Answer: 0.1457

Step-by-step explanation:

Let p be the population proportion.

Given: The proportion of Americans who are afraid to fly is 0.10.

i.e. p= 0.10

Sample size : n= 1100

Sample proportion of Americans who are afraid to fly =[tex]\hat{p}=\dfrac{121}{1100}=0.11[/tex]

We assume that the population is normally distributed

Now, the probability that the sample proportion is more than 0.11:

[tex]P(\hat{p}>0.11)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.11-0.10}{\sqrt{\dfrac{0.10(0.90)}{1100}}})\\\\=P(z>\dfrac{0.01}{0.0090453})\ \ \ [\because z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}} ]\\\\=P(z>1.1055)\\\\=1-P(z\leq1.055)\\\\=1-0.8543=0.1457\ \ \ [\text{using z-table}][/tex]

Hence, the probability that the sample proportion is more than 0.11 = 0.1457

Answer:

[tex]\huge\boxed{x=7\dfrac{23}{25}}[/tex]

Step-by-step explanation:

[tex]x\div3\dfrac{3}{10}=2\dfrac{2}{5}\\\\\text{convert the mixed number to the impropper fraction}\\\\3\dfrac{3}{10}=\dfrac{3\cdot10+3}{10}=\dfrac{33}{10}\\\\2\dfrac{2}{5}=\dfrac{2\cdot5+2}{5}=\dfrac{12}{5}\\\\x\div\dfrac{33}{10}=\dfrac{12}{5}\\\\x\times\dfrac{10}{33}=\dfrac{12}{5}\qquad\text{multiply both sides by}\ \dfrac{33}{10}\\\\x\times\dfrac{10\!\!\!\!\!\diagup}{33\!\!\!\!\!\diagup}\times\dfrac{33\!\!\!\!\!\diagup}{10\!\!\!\!\!\diagup}=\dfrac{12}{5}\times\dfrac{33}{10}\\\\x=\dfrac{396}{50}[/tex]

[tex]x=\dfrac{198}{25}\\\\x=\dfrac{175+23}{25}\\\\x=\dfrac{175}{25}+\dfrac{23}{25}\\\\x=7\dfrac{23}{25}[/tex]

Answer:

[tex] f = 10.7 [/tex]

Step-by-step explanation:

Given ∆DEF,

<F = 36°

DF = e = 15

EF = d = 6

DE = f = ?

f can be found using the Law of Cosine as shown below:

[tex] f^2 = d^2 + e^2 - 2(d)(e)*cos(F) [/tex]

Plug in your values:

[tex] f^2 = 6^2 + 15^2 - 2(6)(15)*cos(36) [/tex]

Evaluate:

[tex] f^2 = 36 + 225 - 180*0.809 [/tex]

[tex] f^2 = 261 - 145.62 [/tex]

[tex] f^2 = 115.38 [/tex]

[tex] f = 10.74 [/tex]

[tex] f = 10.7 [/tex] (to nearest tenth)

Answer:

second option

Step-by-step explanation:

The range is all of the y values. In this scenario, the y values are the number of sit-ups per minute. We can eliminate the first and third options because they're talking about x when we want y. Additionally, we can eliminate the last option because that is all of the x values, therefore, the answer is the second option.

Answer:

[tex]\boxed{\mathrm{B}}[/tex]

Step-by-step explanation:

The range of a function is the set of all possible output values [tex]F(x)[/tex].

Options A and C are wrong because they talk about the input value x.

The output values are the number of sit-ups.

Option D talks about the ages (input).

Answer:

0.72

Step-by-step explanation:

hope i helped

pls mark brainliest im trying to level up

Answer:

0.719 rounded to the nearest hundredth is 0.720

Step-by-step explanation:

9 is more than 5, so you round up, and the next hundredth is 2, so you get 0.720.

Hope this helps!!!  Brainliest would be appreciated

Answer:

(x,y) = Any point on the line

m = the slope of the line

(x₁, y₁) = A given point on the line

Step-by-step explanation:

the equation of a straight line is;

y = mx + c

where;

x and y are any point on the line

m is the slope of the line

c is the intercept on the y axis

And a given point on (x,y) can be written as (x₁, y₁)

Therefore, for the case above;

(x,y) = Any point on the line

m = the slope of the line

(x₁, y₁) = A given point on the line

Answer:

1) a+b(x)+a+(y)

b) a+b(x)-a-b(y)

2)p-q(r)-p-q(s)

b)r-2r(s)+r-2t(t)

Step-by-step explanation:

1) ax+bx+ay+by

a+b(x)+a+b(y)

b) ax+bx-ay-by

a+b(x)-a-b(y)

2) pr-ps+qr-qs

pr+qr-ps-qs

p+q(r)-p-q(s)

b) rs-2rs+rt-2t^2

r-2r(s)+r-2t(t)

Hope this helps ;) ❤❤❤

Answer:

Step-by-step explanation:

a)Use distributive property

ax + bx + ay + by = x(a + b) + y(a + b)

                            = (a + b) (x + y)

b) ax + bx - ay - by = x(a + b) - y (a +b)

                              = (a +b) (x - y)

2)

a) pr - ps + qr - qs =  p (r - s) + q( r - s)

                             = (r -s )( p + q)

Answer:

[tex] Area = 2,031ft^2 [/tex]

Total weight of gravel on the roof = [tex] 24,372 pounds [/tex]

Step-by-step Explanation:

The area Adams planned to cover with gravel can be divided into 3 rectangles as shown in the diagram attached.

We would have 3 rectangles. See the attachment below to check out how we arrive at the dimensions of the 3 rectangles.

Area of rectangle = L*W

Area to be covered by gravel = area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Area to be covered with gravel = [tex] (30*17) + (13*9) + (52*27) [/tex]

[tex] Area = (30*17) + (13*9) + (52*27) = 2,031ft^2 [/tex]

Total weight of gravel on the roof = 12 pounds per square foot multiplied by total area of the roof to be covered = [tex] 12 * 2031 = 24,372 pounds [/tex]

Answer:

2031 and 16925

Step-by-step explanation:

Answer:

The owner needs 195 meters of wire

Step-by-step explanation:

If the lot is squared shaped, then its area is given by the formula:

[tex]Area =x^2[/tex]

where x is the side of the square. Then considering the value they provide for the surface, each side must be of length:

[tex]x^2=\frac{4225}{16} \,m^2\\x=\sqrt{\frac{4225}{16}} \,\,m\\x=16.25\,\,m[/tex]

Then the perimeter around this square lot is four times that side length:

Perimeter = 4 (16.25 m) = 65 m

and since the owner wants three rows of wire, the total length of wire needed is:

3 (65 m) = 195 m

Answer:

Step-by-Step Explanation:

Perimeter = 75

Sides:

2x + 3

3x + 4

2x - 9

75 = 2x + 3 + 3x + 4 + 2x - 9

2x + 3 + 3x + 4 + 2x - 9  = 7x - 2

75 = 7x - 2

75 = 7x - 2

+2        +2

77 = 7x

77 = 7x

/7     /7

2x + 3 = 2(11) + 3 = 22 + 3 = 25

3x + 4 = 3(11) + 4 = 33 + 4 = 37

2x - 9 = 2(11) - 9 = 22 - 9 = 13

Answer:

Graph (B)

Step-by-step explanation:

For x < 3,

An arrow starting with a hollow circle at x = 3 and heading towards 0 will represent the given inequality on a number line.

Similarly, x ≥ 5,

An arrow starting with a dark circle at x = 5 and heading towards 12 will represent the given inequality on a number line.

When we combine these inequalities on a number line, Graph (B) will be the answer.

Answer:

The function is:

y = 150*x

where y is the number of calories consumed, and x is the number of pieces of candy consumed.

Now, the domain of a function is the possible values of x that you can input in the function.

For this particular case you can have:

x = 0 (no pieces candy)

x = 1 (one piece of candy)

x = 2 (two pieces of candy)

Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.

So we only use x = whole numbers.

Then the domain of the function is equal to all the natural numbers plus the zero, or:

D = {x ∈ N ∪ {0}}

"x belongs to the union between the set of the natural numbers and the zero"

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The domain of a function is the input values of the function for which it exists.

Given the expression that relates the number of calories you consume after eating x pieces of candy as shown:

y = 150x

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The function is also discrete because the number of candies can be counted. Note that the domain of all discrete functions is countable.

Learn more about discrete function here:

https://brainly.com/question/25050804

Answer:

The correct answers are B, C ,E

Step-by-step explanation:

The correct options are a, c and e

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that, the solution of 15 greater-than-or-equal-to 22 + x

1) The first one is correct because the statement is x greater-than-or-equal-to negative 7. And 22+(-7) is = to 15. This means that in order to get a number below 15 by adding 22 and 15, we need a number that is lower than -7.

2) The second one is incorrect because it is the opposite of the first one. As the first one was correct, this statement is implying the complete opposite as the first one.

3) The third one is correct because we are using greater than or equal to; this means the circle would be closed.

4) The fourth option is incorrect because we need x to be lower than -7, not higher.

5) The fifth option is also correct.

Hence, the correct options are is a, c, e.

For more references on inequality, click;

https://brainly.com/question/28823603

#SPJ2

Answer:

n = 108

Step-by-step explanation:

Radius of the given circle = 9 in.

If this circle is dilated by a scale factor of 6, radius of the dilated circle will be

= 6 × 9

= 54 in.

Circumference of a circle is determined by the formula,

Circumference = 2πr

Where r = radius of the circle

By substituting the value of 'r' in the formula,

Circumference = 2π(54)                          

                         = 108π

By comparing it with circumference = nπ

Value of n = 108

Answer:

4.2 miles per/hour

Step-by-step explanation:

we know

speed  total distance covered/ total time taken to cover that distance.

Time from 9:00 Am to 11:30 Am is 2 hours 30 minutes

time = 2 1/2 hours = 5/2 hours

for distance\

By 11:30 AM, he was 13 miles from the start.

so he covered a total distance of 12 miles

At 9:00 AM, a person running a race was 2 1/2 miles from the start

until 9 am he had already ran 2 1/2 miles = 5/2 miles

since we have to take distance travelled from 9 to 11 :30 Am

we need to subtract distance travel until 9 am from total distance traveled until 11:30 pm

Distance travlled from 9:11:30 am = distance traveled from start till 11:30AM -  distance traveled from start till 9 AM

Distance traveled from 9:11:30 am =  13 - 5/2 = (26-5)/2 = 21/2

Thus, speed = 21/2 / 5/2 = 21/5 = 4 1/5 miles/hour = 4.2 miles/hour

Thus, he was running with 4.2 miles per/hour.

Answer:

y = -3x + 6

Step-by-step explanation:

Any line perpendicular to

y = (1/3)x + 4

has a slope of -1/(1/3) = -3

and equation

y = -3x + b  .................(1)

If the line has an x intercept of 2 at (0,2), then

0 = -3(2) + b

solving

b = 6

By substituting b=6 into (1), the line required

y = -3x + 6

Answer:

y = -3x + 2

Step-by-step explanation:

y= [tex]\frac{1}{3}x +4[/tex]

Slope [tex]m_{1}=\frac{1}{3}[/tex]

slope of the perpendicular line [tex]m_{2}[/tex] = [tex]\frac{-1}{m_{1}}[/tex] = [tex]\frac{-1}{\frac{1}{3}}=-1*\frac{3}{1}=-3\\[/tex]

b= 2

Slope intercept form of required line: y = mx + b

y = -3x + 2

Answer:

The exact values of sinθ = -7/√58.

The exact value of  secθ = -√58/3 and

The exact value of tanθ = 7/3

Step-by-step explanation:

Given that a point on the terminal side is of an angle is (x,y) and we are given (-3, -7). So x = -3 and y = -7. The length of its terminal side is given by r = √(x² + y²) = √((-3)² + (-7)²) = √(9 + 49) = √58

We know that sinθ = y/r.

So, sinθ = y/r = -7/√58

We know that secθ = 1/cosθ = 1/x/r = r/x

So, secθ = r/x = √58/-3 = -√58/3

We know that tanθ = y/x.

So, tanθ = y/x = -7/-3 = 7/3

So, the exact values of sinθ = -7/√58.

The exact value of  secθ = -√58/3 and

The exact value of tanθ = 7/3

Answer:

Option B.

Step-by-step explanation:

According to the question, the data provided is as follows

[tex]H_o : p_1 - p_2 = 0\ (p_1 = p_2)\\\\ H_\alpha : p_1 - p_2 < 0\ (p_1 < p_2)[/tex]

Based on the above information,

The type ii error is the error in which there is an acceptance of a non rejection with respect to the wrong null hypothesis. The type I error refers to the error in which there is a rejection of a correct null hypothesis and the type II refers that error in which it explains the failure of rejection with respect to null hypothesis that in real also it is wrong  

So , the type II error is option B as we dont create any difference also the proportion is very less

Answer:

The last option

Step-by-step explanation:

The centroid is the point that is equidistant from all the vertices, not the incenter. Furthermore, the incenter is formed by finding the point of concurrency (intersection) of the angle bisectors.

Step-by-step explanation:

[tex]( {x}^{2})(x + 3) - (x + 3)[/tex]

[tex](x + 3)( {x}^{2} - 1) [/tex]

[tex](x - 1)(x + 1)[/tex]

[tex](x - 1)(x + 1)(x + 3)[/tex]

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

(x+1) (x-1) (x+3)

Step-by-step explanation:

. .....................

Answer:

[tex]\large \boxed{\sf \ \ y=(x+5)^2+5 \ \ }[/tex]

Step-by-step explanation:

Hello, please find my work below.

[tex]y=x^2+10x+30\\\\\text{*** We can notice that ***}\\\\\text{*** } x^2+10x = x^2+2\cdot 5 \cdot x=(x+5)^2-5^2=(x+5)^2-25\\\\y=x^2+10x+30=(x+5)^2-25+30=(x+5)^2+5\\\\[/tex]

a = 1

h = -5

k = 5

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: 20cm

Step-by-step explanation:

The perimeter of a rectangle can be calculated as 2(l+w)

2(6+4)

2(10)

20

Hope it helps, and if you want more info on perimeter, just ask <3

Answer:

20 cm

Step-by-step explanation:

Use folmula P=2(l+w)

Answer:

This question is unanwserable without the "Spider Tool" If you would like to revise it i'd be happy to help

Step-by-step explanation:

But the units are degrees

Answer:

Associative Property.

Step-by-step explanation:

The Associative Property is the property that says that (a + b) + c = a + (b + c).

Hope this helps!

Answer:

Associate Property

Step-by-step explanation:

I found my answer at baba com

Answer:

your answer is k

Step-by-step explanation:

not all the isosceles triangles are similar

Answer: Resultant force = 114.96 pounds at angle 81.76°

Answer: magnitude = 114.96 lbs, direction =  88.21°

Step-by-step explanation:

Vector A: 150 lbs at  40°

Vector B: 100 lbs at 170°

Slide Vector B onto Vector A so you have a head to tail connection.

Calculate the angle between the vectors (50°).

Use Law of Cosines to find the magnitude of the resultant vector.

Use Law of Sines to find the direction of the resultant vector.

Law of Cosines:  c² = a² + b² - 2ab cos θ

Given: a = 150, b = 100, C = 50°

c² = (100)² + (150)² - 2(100)(150) cos 50°

c = 114.96

Law of Sines:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c}\\\\\text{Given: a=150, c=114.96, C=50}^o\\\\\\\dfrac{\sin A}{150}=\dfrac{\sin 50^o}{114.96}\\\\\\\sin A=\dfrac{150\sin 50^o}{114.96}\\\\\\A=\sin^{-1}\bigg(\dfrac{150\sin 50^o}{114.96}\bigg)\\\\\\A=88.21^o[/tex]