What is the conjugate of 3+3i?

Answer:

A

Step-by-step explanation:

We can use the trigonometric ratios. Recall that sine is the ratio of the opposite side to the hypotenuse:

[tex]\displaystyle \sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side with respect to ∠C is 24 and the hypotenuse is 26.

Hence:

[tex]\displaystyle \sin(C)=\frac{24}{26}=\frac{12}{13}[/tex]

Our answer is A.

Answer:

(a)[tex]D(t)=\dfrac{50000}{1.9t+9}[/tex]

(b)[tex]D'(115)=-1.8355[/tex]

Step-by-step explanation:

The demand function for a product is given by :

[tex]D(p)=\dfrac{50000}{p}[/tex]

Price, p is a function of time given by [tex]p=1.9t+9[/tex], where t is in days.

(a)We want to find the demand as a function of time t.

[tex]\text{If } D(p)=\dfrac{50000}{p},$ and p=1.9t+9\\Then:\\D(t)=\dfrac{50000}{1.9t+9}[/tex]

(b)Rate of change of the quantity demanded when t=115 days.

[tex]\text{If } D(t)=\dfrac{50000}{1.9t+9}[/tex]

[tex]\dfrac{\mathrm{d}}{\mathrm{d}t}\left[\dfrac{50000}{\frac{19t}{10}+9}\right]}}=50000\cdot \dfrac{\mathrm{d}}{\mathrm{d}t}\left[\dfrac{1}{\frac{19t}{10}+9}\right]}[/tex]

[tex]=-50000\cdot\dfrac{d}{dt} \dfrac{\left[\frac{19t}{10}+9\right]}{\left(\frac{19t}{10}+9\right)^2}}}[/tex]

[tex]=\dfrac{-50000(1.9\frac{d}{dt}t+\frac{d}{dt}9)}{\left(\frac{19t}{10}+9\right)^2}}}[/tex]

[tex]=-\dfrac{95000}{\left(\frac{19t}{10}+9\right)^2}\\$Simplify/rewrite to obtain:$\\\\D'(t)=-\dfrac{9500000}{\left(19t+90\right)^2}[/tex]

Therefore, when t=115 days

[tex]D'(115)=-\dfrac{9500000}{\left(19(115)+90\right)^2}\\D'(115)=-1.8355[/tex]

Answer:

Center, radius, chord, diameter... are Words related to circle

Answer:

See below in bold.

Step-by-step explanation:

We can write the equation as

y = a(x - 28)(x + 28)   as -28 and 28  ( +/- 1/2 * 56) are the zeros of the equation

y has coordinates (0, 32) at the top of the parabola so

32 = a(0 - 28)(0 + 28)

32 = a * (-28*28)

32 = -784 a

a = 32 / -784

a = -0.04082

So the equation is y = -0.04082(x - 28)(x + 28)

y = -0.04082x^2 + 32

The second part  is found by first finding the value of x corresponding to  y = 22

22 = -0.04082x^2 + 32

-0.04082x^2 = -10

x^2 = 245

x = 15.7 inches.

This is the distance from the centre of the door:

The distance from the edge = 28 - 15.7

= 12,3 inches.

Answer:

100 possible extensions

Step-by-step explanation:

we can calculated how many possible extensions they have to try using the rule of multiplication as:

___1_____*___10_____*___10_____*____1____ = 100

1st digit        2nd digit        3rd digit         4th digit

You know that the 1st and 4th digits of the extension are 5. it means that you just have 1 option for these places. On the other hand, you don't remember nothing about the 2nd and 3rd digit, it means that there are 10 possibles digits (from 0 to 9) for each digit.

So, There are 100 possibles extensions in which the 5 is the first and last digit.

Answer:

41

Step-by-step explanation:

[tex]24*2-7=\\48-7=\\41[/tex]

Answer:

-10

Step-by-step explanation:

Use the Order of Operations - PEMDAS

Do what is in parentheses first - (4-2) = 2

Next multiply 3 and 4 = 12

Last, perform 2 - 12; which equals -10

Answer:

(4, 3)

Step-by-step explanation:

Use the midpoint formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]

Answer:

20 4/5

Step-by-step explanation:

13/5 times 8/1

104/5

which is simplify

to 20 4/5\

hope this helps

Answer:

0.6%

Step-by-step explanation:

We have a standard deck of 52 playing cards, which is made up of 13 cards of each type (hearts, diamonds, spades, clubs)

Therefore there are one nine hearts, one nine diamonds, one nine spades and one nine clubs, that is to say that in total there are 4. Therefore the probability of drawing a nine is:

4/52

In the second card it is the same, an eight, that is, there are 4 eight cards, but there is already one less card in the whole deck, since it is not replaced, therefore the probability is:

4/51

So the final probability would be:

(4/52) * (4/51) = 0.006

Which means that the probability of the event is 0.6%

Answer:

Height of tank = 50cm

Step-by-step explanation:

Volume of water from tank that the water is 10cm down is 84000cm³

Length = 60cm

Width = 35cm

Height of water = x

Volume = length* width* height

Volume= 84000cm³

84000 = 60*35*x

84000= 2100x

84000/2100= x

40 = x

Height of water= 40cm

Height of tank I = height of water+ 10cm

Height of tank= 40+10= 50cm

Height of tank = 50cm

Answer:

225º or 3.926991 radians

Step-by-step explanation:

The area of the complete circle would be π×radius²: 3.14×8²=200.96

The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.

[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).

There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.

We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.

Answer:

225º

Step-by-step explanation:

Answer:

  [tex]\dfrac{x^2+8x+16}{x-1}[/tex]

Step-by-step explanation:

In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...

  [tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]

Answer:

The 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two means is:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

It is provided that:

[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]

The critical value of z for 90% confidence level is,

z = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

    [tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]

Thus, the 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Answer:

a=b

Step-by-step explanation:

When the denominator is zero, the expression is undefined

a-b=0

a=b

Answer:

[tex] 211600 = 225000 -k*6700[/tex]

[tex] k = \frac{225000-211600}{6700}= 2[/tex]

[tex] 238400 = 225000 +k*6700[/tex]

[tex] k = \frac{238400-225000}{6700}= 2[/tex]

So then the % expected would be:

[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]

So then the answer would be 75%

Step-by-step explanation:

For this case we have the following info given:

[tex] \mu = 225000[/tex] represent the true mean

[tex]\sigma =6700[/tex] represent the true deviation

And for this case we want to find the minimum percentage of sold homes between $211,600 and $238,400.

From the chebysev theorem we know that we have [tex]1 -\frac{1}{k^2}[/tex] % of values within [tex]\mu \pm k\sigma[/tex] if we use this formula and the limit given we have:

[tex] 211600 = 225000 -k*6700[/tex]

[tex] k = \frac{225000-211600}{6700}= 2[/tex]

[tex] 238400 = 225000 +k*6700[/tex]

[tex] k = \frac{238400-225000}{6700}= 2[/tex]

So then the % expected would be:

[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]

So then the answer would be 75%

Answer:

infinite solutions

Step-by-step explanation:

it means that all x are solution of this equation as 6=6 is always true

[tex]\displaystyle\bf\\\textbf{At any translation of a quadrilateral the sides remain the same,}\\\\\textbf{the angles remain the same.}\\\\\textbf{It turns out that the quadrilateral remains the same.}\\\\P_{A'B'C'D'}=P_{ABCD}=AB+BC+CD+DA=\\\\~~~~~~~~~~~~~~=2.2+4.5+6.1+1.4=\boxed{\bf14.2}[/tex]

Answer:

Volume of liquid which freezes to ice is 1620. 37 .

Expression to find this is 108x/100 = 1750

Step-by-step explanation:

Let the volume of liquid be x cubic inches

It is  given that volume of liquid increases by 8% when it freezes to ice

increase in volume of x  x cubic inches liquid = 8% of x = 8/100 * x = 8x/100

Total volume of ice = initial volume of liquid + increase in volume when it freezes to ice  = x + 8x/100 = (100x + 8x)/100 = 108x/100

Given that total volume of liquid which freezes is 1750

Thus,

108x/100 = 1750

108x = 1750*100

x = 1750*100/108 = 1620. 37

Volume of liquid which freezes to ice is 1620. 37 .

Expression to find this is 108x/100 = 1750

Answer:

44.93% probability that the person will need to wait at least 7 minutes total

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional probability:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes

This means that [tex]m = 5, \mu = \frac{1}{5} = 0.2[/tex]

Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total

Event A: Waits at least 3 minutes.

Event B: Waits at least 7 minutes.

Probability of waiting at least 3 minutes:

[tex]P(A) = P(X > 3) = e^{-0.2*3} = 0.5488[/tex]

Intersection:

The intersection between waiting at least 3 minutes and at least 7 minutes is waiting at least 7 minutes. So

[tex]P(A \cap B) = P(X > 7) = e^{-0.2*7} = 0.2466[/tex]

What is the probability that the person will need to wait at least 7 minutes total

[tex]P(B|A) = \frac{0.2466}{0.5488} = 0.4493[/tex]

44.93% probability that the person will need to wait at least 7 minutes total

Answer:

96 degrees

Step-by-step explanation:

Since x is half of 168, its angle measure is 84 degrees. Since x and y are a linear pair, their angle measures must add to 180 degrees, meaning that:

y+84=180

y=180-84=96

Hope this helps!

Answer:

The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).

Step-by-step explanation:

We want to calculate the bounds of a 95% confidence interval of the difference between proportions.

For a 95% CI, the critical value for z is z=1.96.

The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.

[tex]p_1=X_1/n_1=494/1000=0.494[/tex]

The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.

[tex]p_2=X_2/n_2=552/1000=0.552[/tex]

The difference between proportions is (p1-p2)=-0.058.

[tex]p_d=p_1-p_2=0.494-0.552=-0.058[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022[/tex]

Then, the margin of error is:

[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014[/tex]

The 95% confidence interval for the difference between proportions is (-0.102, -0.014).

Answer:

Step-by-step explanation:

This is a poisson distribution. Let x be a random representing the number of calls in a given time interval.

a) the expected number of calls in one hour is the same as the mean score in 60 minutes. Thus,

Mean score = 60/2 = 30 calls

b) The interval of interest is 5 minutes.

µ = 5/2 = 2.5

We want to determine P(x = 3)

Using the Poisson probability calculator,

P(x = 3) = 0.21

c) µ = 5/2 = 2.5

We want to determine P(x = 0)

Using the Poisson probability calculator,

P(x = 0) = 0.08

Answer:

AC = 11 cm , CB = 22 cm

Step-by-step explanation:

let AC = x then BC = 2x , then

AC + BC = 33, that is

x + 2x = 33

3x = 33 ( divide both sides by 3 )

x = 11

Thus

AC = x = 11 cm and CB = 2x = 2 × 11 = 22 cm

Answer:

Step-by-step explanation:

given a field of the form F = (P(x,y),Q(x,y) and a simple closed curve positively oriented, then

[tex]\int_{C} F \cdot dr = \int_A \frac{dQ}{dx} - \frac{dP}{dy} dA[/tex] where A is the area of the region enclosed by C.

In this case, by the description we can assume that C starts at (0,0). Then it goes the point (pi,0) on the path giben by y = sin(x) and then return to (0,0) along the straigth line that connects both points. Note that in this way, the interior the region enclosed by C is always on the right side of the point. This means that the curve is negatively oriented. Consider the path C' given by going from (0,0) to (pi,0) in a straight line and the going from (pi,0) to (0,0) over the curve y = sin(x). This path is positively oriented and we have that

[tex] \int_{C} F\cdot dr = - \int_{C'} F\cdot dr[/tex]

We use the green theorem applied to the path C'. Taking [tex] P = x+4y^3, Q = 4x^2+y[/tex] we get

[tex] \int_{C'} F\cdot dr = \int_{A} 8x-12y^2dA[/tex]

A is the region enclosed by the curves y =sin(x) and the x axis between the points (0,0) and (pi,0). So, we can describe this region as follows

[tex]0\leq x \leq \pi, 0\leq y \leq \sin(x)[/tex]

This gives use the integral

[tex] \int_{A} 8x-12y^2dA = \int_{0}^{\pi}\int_{0}^{\sin(x)} 8x-12y^2 dydx[/tex]

Integrating accordingly, we get that [tex]\int_{C'} F\cdot dr = 8\pi - \frac{16}{3}[/tex]

So

[tex] \int_{C} F cdot dr = - (8\pi - \frac{16}{3}) = \frac{16}{3} - 8\pi [/tex]

Answer: 18 cm

Step-by-step explanation:

We know the circumference formula is C=2πr. Since our circumference is given in terms of π, we can easily figure out what the radius is.

36π=2πr                   [divide both sides by π to cancel out]

36=2r                        [divide both sides by 2]

r=18 cm

Answer:

18cm

Step-by-step explanation:

because i found it lol

Answer:

It is vertically stretched by a factor of 200 and shifted 10 units right

Step-by-step explanation:

Suppose we have a function f(x).

a*f(x), a > 1, is vertically stretching f(x) a units. Otherwise, if a < 1, we are vertically compressing f(x) by a units.

f(x - a) is shifting f(x) a units to the right.

f(x + a) is shifting f(x) a units to the left.

In this question:

Initially: [tex]f(x) = \frac{1}{x}[/tex]

Then, first we shift, end up with:

[tex]f(x+10) = \frac{1}{x + 10}[/tex]

f was shifted 10 units to the left.

Finally,

[tex]200f(x+10) = \frac{200}{x + 100}[/tex]

It was vertically stretched by a factor of 200.

So the correct answer is:

It is vertically stretched by a factor of 200 and shifted 10 units right

Answer:

the answer is D

Step-by-step explanation:

Step-by-step explanation:

40 x $10.12/hr = $404.80

5 x $15.18/hr = $ 75.90

over time = $10.12 + $5.06 ( half of $10.12) = $15.18/hr

$404.80 + $75.90 = $480.70/weekly pay

assuming she works 52 weeks a year

$480.70 × 52 weeks = $24,996.40/yr

Answer:

Raspberry: 30%

Strawberry: 15%

Apple: 20%

Lemon: 35%

Step-by-step explanation:

18 + 9 + 12 + 21 = 60 (there are 60 gummy worms)

18 out of 60 = 30%

9 out of 60 = 15%

12 out of 60 = 20%

21 out of 60 = 35%

Please mark Brainliest

Hope this helps

Answer:

Raspberry Worms: 30%

Strawberry Worms: 15%

Apple Worms: 20%

Lemon Worms: 35%

Step-by-step explanation:

Raspberry Worms: [tex]\frac{18}{18+9+12+21}=\frac{18}{60}=\frac{30}{100}[/tex] or 30%

Strawberry Worms: [tex]\frac{9}{18+9+12+21}=\frac{9}{60} =\frac{15}{100}[/tex] or 15%

Apple Worms: [tex]\frac{12}{18+9+12+21} =\frac{12}{60} =\frac{20}{100}[/tex] or 20%

Lemon Worms: [tex]\frac{21}{18+9+12+21} =\frac{21}{60} =\frac{35}{100}[/tex] or 35%