Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:

A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Since the calculated F-value of 7.098 is greater than the critical value of 5.79, we reject the null hypothesis and conclude that the population variance of total sales during active price competition is higher than during duopoly and tacit collusion at the 5% level of significance.

For the above issue, the null and alternate hypotheses are as follows:

The population variations of total sales under duopoly, active price competition, and tacit cooperation are all identical.

In contrast to duopoly and implicit collusion, total sales population variance is larger under active price competition.

To test the null  hypothesis, we must use a two-tailed F- test with a 5 % threshold of significance. The ratio of the sample variances is used to determine the F- statistic.

F = s1² / s2²

Where:
s1² - Sample Variance (Active price competition)

s2² -  SAmple variance (Duopoy and Tacit collusion)


Since n1-1 = 3
and n2-1 = 6

F = 114.09 / 16.08
F = 7.098

Having derived same, we know that the critical values of F for a two-tailed test with 3 and 6 degrees of freedom at 5% level of significance are:

Critical Value (3) = 5.14
Critical Value (6) = 5.79

Therefore, since the F-value > Critical Value in both cases, we must reject the null hypothesis.

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The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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A fraction means division.

To find the decimal equivalent of a fraction, divide the top number by the bottom number.

Answer:  0.00435 If you do it by one.

                0.0087 if you do it by two. And-

                 0.01304 if you do it by three.

              I really hope this helps have a good day :))  (pls make brainliest im trying to each a goal!)

Step-by-step explanation:

Answer:

J. V = 12h cubic units

Step-by-step explanation:

Volume if a square pyramid = ⅓*a²*h

Where,

h = height = ?

a = edge = 6 in.

Plug in the values

Volume = ⅓*6²*h

V = ⅓*36*h

V = 12*h

V = 12h cubic units

Answer:

a=18 b=24

Step-by-step explanation:

We know that BC=25 and QR=30, the key term is that they are similar triangles. Therefore, BC: QR=25:30=5:6. Then BA:A=5:6=15:X

x=a=18

20:b=5:6

b=24

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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The spherical coordinates of the given rectangular coordinates are (10, 0, 60).

The cartesian coordinate or rectangular coordinates describes the location of a point in space using an ordered triple where each coordinate represents a distance. The spherical coordinate system describes the location of a point in space using an ordered triple where coordinate describes one distance and two angles. In the spherical coordinate system, a point is represented by the ordered triple (ρ, θ, φ).

The equations which are used to convert from rectangular coordinates to spherical coordinates are:

ρ^2=x^2+y^2+z^2

tan⁡〖θ= y/x〗

φ=arccos⁡〖z/√(x^2+y^2+z^2 )〗

The given rectangular coordinates are (5√3, 0, 5). Hence,

ρ^2=〖(5√3)〗^2+0^2+5^2 ≈ 100

ρ ≈ √100 ≈ 10

tan⁡〖θ= 0/(5√3)=0〗

θ=  tan^(-1)⁡0=0

φ=arccos⁡〖5/√(〖(5√3)〗^2+0^2+5^2 )〗= arccos 5/10=arccos⁡0.5 ≈ 60

Note:  The question is incomplete. The complete question probably is: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (*,*,*). (5√3, 0, 5)

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Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

If one triangle is the dilation of the other triangle, then they are similar

The addition of the angles in a triangle is equal to 180°

Triangle XYZ has angles measuring 53° and 23º, then the third angle measure:

53° + 23° + x = 180°

x = 180° - 53° - 23°

x = 104

AA similarity postulate states that If two angles in one triangle are congruent to two angles in another triangle, the two triangles are similar

In this case, the two triangles have only one angle in common, then the AA postulate is not satisfied, and the triangles are not similar nor dilated.

Triangle X'Y'Z' is not a dilation of Triangle XYZ. The ratios of the lengths of the corresponding sides are not equal because the triangles do not have three pairs of congruent angles.

Answer:

15 songs of 14 I am not sure

Answer:

Triangle 2

Step-by-step explanation:

a^2+b^2=c^2

6^2+8^2=10^2

36+64=100

100=100

The average rate of change is 20 over that interval. [-2,3]

1) h(x) =x²+3x+9 [-2, 3]

h(-2) = (-2)²+3(-2)+9

h(-2) = 4+6+9

h(-2)=7

h(3) =(3)² +3(3) +9

h(3) =9 +9 +9

h(3)= 27

The average rate of change =

27-7/3-2 = 20/1 = 20

So Average rate of change over the interval [-2,3] is 20

Answer:

it is on ed it is 30

Step-by-step explanation:

Answer:

30 minutes

Step-by-step explanation:

9514 1404 393

Answer:

  -3/2

Step-by-step explanation:

Points are marked 2 units apart on the x-axis. Between a given point and the one to its right, the y-value changes by -3. The slope is ...

  slope = rise/run = (change in y)/(change in x)

  slope = -3/2

Answer:

11.5%

Step-by-step explanation:

Let the number of smokers before ban = 100

Decrease in 1st month = 3% , of 100 = 3

Smokers after 1st month = 100 - 3 = 97

Decrease in 2nd month = 2%, of 97 = 1.94

Smokers after 2nd month = 97 - 1.94 =  95.06

Decrease in 3rd month = 5%, of 95.06 = 4.75

Smokers after 3rd month = 95.06 - 4.75 = 90.31

Decrease in 4th month = 2%, of 90.31 = 1.80

Smokers after 4th month = 90.31 - 1.80 = 88.51

[ (100 - 88.51) / 100 ] x 100 = (11.49 / 100) x 100

= 11.5%

Answer:

a

Step-by-step explanation:

Answer:

c. 4/7

Hopefully this helped!

-Lavender Vye

Answer:

53.1441%

Step-by-step explanation:

Assuming each event is independent of one another, the probability of catching the tennis ball three times in a row is

(0.81)^3 = (0.81)*(0.81)*(0.81) = 0.531441

This converts to 53.1441%

the probability that a golden retriever catches three tennis balls in mid-air is 53.1441%.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Assuming each event is independent of one another,

the probability of catching the tennis ball three times in a row is

(0.81)^3 = (0.81)*(0.81)*(0.81) = 0.531441

This converts to 53.1441%

hence, the probability that a golden retriever catches three tennis balls in mid-air is 53.1441%.

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Answer:

You have two brackets..divide them as

x-3=0 and x-2=0

so x=3, x=2

The solutions to the equation ( x – 3 )( x − 2 ) = 0 using factors equal to zero are x = 3 and x = 2.

To find the solutions to the equation ( x – 3 )( x − 2 ) = 0, we set each factor equal to zero and solve for x. This is because the product of two factors is equal to zero only if at least one of the factors is zero.

Setting ( x – 3 ) = 0:

x – 3 = 0

x = 3

Setting ( x − 2 ) = 0:

x − 2 = 0

x = 2

Therefore, the solutions to the equation ( x – 3 )( x − 2 ) = 0 are x = 3 and x = 2.

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According to the information, this number on an abacus would look like this: tens of a thousand = 10,000, units of a thousand = 6,000, hundreds = 500, tens = 10, and units = 6.

To illustrate this value on an abacus we must find the number of this operation as shown below:

Now we must express it in an abacus, then we must separate each number by classifying it in the type of units to which it corresponds as shown below:

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Answer:

tell mariam to ask the shop keeper

Step-by-step explanation:

Answer:

Correct

Step-by-step explanation:

This is correct because if you divide fourteen by one fourth the answer would be fifty-six teddy bears.

Answer:

D

Step-by-step explanation:

Base area = (leg 1 x leg 2)/2 = (9 x 12)/2 = 54 ft^2

Base perimeter = leg 1 + leg 2 + hypotenuse = 9 + 12 + 15 = 36 ft

LA= base perimeter x 24 = 36 x 24 = 864 ft^2

SA = 2 x base area + LA = 54 x 2 + 864 = 972 ft^2

The number of centilitres which is equivalent to 0.00005 liters as required to be expressed in standard form is; 5 × 10-² cL.

Recall that; it follows from metric systems that;

100 centilitres = 1 litres.

On this note, it follows from proportion that the number of centilitres present in 0.00005 litres as required is;

= 0.00005 × 100 centilitres

= 0.005 centilitres.

Ultimately, when expressed in standard form, it follows that the number of centilitres in 0.00005 liters is; 5 × 10-² cL.

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The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Answer:

59°

Explanation:

If you add the angles 99° from angle C in the top shape and add 22° on the bottom shape it will give you 121°. When you get this subtract it from 180°

180°-121°= 59°

So, it's 58°

You can check by adding 180°+121°+59° = 180°

Answer:

I think it 31

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

3+1=4

4+2=6

6+3=9

9+4=13

13+5=18

18+6=24

24+7=31

you start with one 3+1=4but everytime you add you add an extra 1

Answer:

67

Step-by-step explanation: Given the quadratic equation $z^2 + bz + c = 0$, Vieta's formulas tell us the sum of the roots is $-b$, and the product of the roots is $c$. Thus,

\[-b = (-7 + 2i) + (-7 - 2i) = -14,\]so $b = 14.$

Also,

\[c = (-7 + 2i)(-7 - 2i) = (-7)^2 - (2i)^2 = 49 + 4 = 53.\]Therefore, we have $b+c = \boxed{67}$.

There are many other solutions to this problem. You might have started with the factored form $(z - (-7 + 2i))(z - (-7 - 2i)),$ or even thought about the quadratic formula.

This is the aops answer :)

The required value of b+c is 39.

A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.

The standard form of a quadratic equation is ax² + bx + c = 0.

Where a, b and c are constants.

The given quadratic equation,

z² + bz + c = 0

Also, the roots of the equation are -7 + 2i and -7 - 2i.

The sum of the roots

b / 1=  -7 + 2i +  -7 - 2i

b= -14

The product of the root

c/1 = (-7 + 2i)(-7 - 2i ) = 49 - (2i)² = 49 - 4i² = 49 + 4 = 53

c = 53

The required value of b and c

b + c = 53 - 14 = 39

The value of b + c is 39.

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Answer: 3.2%

Step-by-step explanation: i searched it up