In ABC, BC = a = 16, AC = b = 10, and m<C = 22º. Which equation can you use to find the value of c = AB?
​

Answer:

Z = 0.87

Explanation:

Given the following data;

Sample 1:

n1 = 30

Mean, X = 2.36

Standard deviation, Ox = 0.96

Sample 2:

n2 = 60

Mean, Y = 2.19

Standard deviation, Oy = 0.66

The formula for test statistics for two population is;

[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]

Substituting the values, we have;

[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]

[tex]Z = \frac{0.17}{0.19488}[/tex]

Z = 0.8723

The test statistics to 2 d.p is 0.87

Therefore, Z = 0.87

Answer:

D: 9, 12, 15

Step-by-step explanation:

Okay, this one is a very simple and a not so hard question. I understand that teachers prefer kids to not lay out all the terms, but in this case, it won´t be horrible in doing so!

Were going to plug 6 into n, and that will make the formula look like,

F(6)=3(6)-9

18-9=9 so the 6th term is 9

Plug in 7=

F(7)=3(7)-9

21-9=12

The 7th term is 12

Plug in 8=

F(8)=3(8)-9

24-9=15  8th term is 15

That means terms 6, 7, and 8 are: 9, 12, 15

Answer:

D. 9, 12, 15

Answer:

72º

Step-by-step explanation:

Hey there!

Well the interior of a pentagon's angle is 108º,

so we do,

180 - 108 = 72º

Hope this helps :)

Answer:

72°

Step-by-step explanation:

→ First find the measure of all interior angle, utilise the formula (n-2) × 180° where n is the number of sides

(n-2) × 180° ⇔ (5-2) × 180° ⇔ 3 × 180° ⇔ 540°

→ 540° is the total sum of the angles in the pentagon, divide this by 5 to get one of the interior angles

540° ÷ 5 = 108°

→ Now, remember the fact that 1 interior + 1 exterior angle = 180°

180 - ( 1 interior angle ) → 180 - (108) = 72°

Answer:

c is 35

d is 13

Step-by-step explanation:

I multiplied both sides, and then simplified the equation.

( plz give me brainliest, that would be most appreciated! )

It seems like information is missing. If so, then please update.

When intersecting a plane and a line, there are two possibilities:

Answer:

surface area of sphere = 615.44mm²

volume of sphere = 523.33mm³

Step-by-step explanation:

S.A = 4πr²

4 × 3.14 × 7 × 7 = 615.44.

volume = 4πr³/3

4 × 3.14 ×5 × 5 × 5 ÷ 3 = 523.33

Answer:

Step-by-step explanation:

To calculate the horizontal distance d we use cosine

cos ∅ = adjacent / hypotenuse

From the question

d is the adjacent

the hypotenuse is 145m

So we have

cos 55 = d / 145

d = 145 cos 55

d = 83.16

d is 83.2 meters to 3 significant figures

Hope this helps you

Answer:

1225

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

C

Step-by-step explanation:

Answer:

  1

Step-by-step explanation:

Use the form for the factoring of the sum of cubes.

To make this easier to write, we'll use the substitutions ...

  a = sin(θ), b = cos(θ)

It looks like you may want to simplify ...

  (a³ +b³)/(a +b) +ab

  = ((a +b)(a² -ab +b²))/(a +b) +ab

The factors of (a+b) cancel. In this case, we know that a² +b² = 1, so this becomes ...

  = (1 -ab) +ab

  = 1

  [tex]\boxed{\dfrac{\sin^3{\theta}+\cos^3{\theta}}{\sin{\theta}+\cos{\theta}}+\sin{\theta}\cos{\theta}=1}[/tex]

Answer:?

Step-by-step explanation:

Answer:

[tex] 4\sqrt{3} [/tex]

[tex] \dfrac{5 - \sqrt{3}}{11} [/tex]

[tex] \dfrac{11(3 + \sqrt{5})}{8} [/tex]

Step-by-step explanation:

If you have a simple square root in the denominator, multiply the fraction by a fraction that is the root over the root.

[tex] \dfrac{12}{\sqrt{3}} = [/tex]

[tex] = \dfrac{12}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} [/tex]

[tex]= \dfrac{12\sqrt{3}}{\sqrt{3}\sqrt{3}}[/tex]

[tex] = \dfrac{12\sqrt{3}}{3} [/tex]

[tex] = 4\sqrt{3} [/tex]

If you have a denominator consisting of a rational number plus a root, multiply the fraction by a fraction that is the denominator over the denominator in which you change only the sign outside the root.

[tex] \dfrac{2}{5 + \sqrt{3}} = [/tex]

[tex] = \dfrac{2}{5 + \sqrt{3}} \times \dfrac{5 - \sqrt{3}}{5 - \sqrt{3}} [/tex]

[tex] = \dfrac{2(5 - \sqrt{3})}{(5 + \sqrt{3})(5 - \sqrt{3})} [/tex]

[tex] = \dfrac{2(5 - \sqrt{3})}{25 - 3} [/tex]

[tex] = \dfrac{2(5 - \sqrt{3})}{22} [/tex]

[tex] = \dfrac{5 - \sqrt{3}}{11} [/tex]

[tex] \dfrac{11}{6 - 2\sqrt{5}} = [/tex]

[tex] = \dfrac{11}{6 - 2\sqrt{5}} \times \dfrac{6 + 2\sqrt{5}}{6 + 2\sqrt{5}} [/tex]

[tex] = \dfrac{11(6 + 2\sqrt{5})}{(6 - 2\sqrt{5})(6 + 2\sqrt{5})} [/tex]

[tex]= \dfrac{22(3 + \sqrt{5})}{36 - 4 \times 5}[/tex]

[tex] = \dfrac{22(3 + \sqrt{5})}{36 - 20} [/tex]

[tex] = \dfrac{22(3 + \sqrt{5})}{16} [/tex]

[tex] = \dfrac{11(3 + \sqrt{5})}{8} [/tex]

Answer:

see attached

Step-by-step explanation:

Answer:

i think its 42.77... might be wrong tho

Step-by-step explanation:

being marked down by 60 percent means to multiply original number by 0.4

so we get 39.6

the multiply it by 1.08 to get 42.768

Answer:

See below.

Step-by-step explanation:

To find the marked down price, multiply the total by the percentage.

[tex]99*.6=59.4[/tex]

Next, subtract the amount from the total.

[tex]99-59.4=39.6[/tex]

Then, multiply to find the sales tax.

[tex]39.6*0.08=3.168[/tex]

[tex]39.6+3.168=42.768[/tex]

Answer: $42.77

Answer:

Step-by-step explanation:

i^{11}+i^{16}+i^{21}+i^{26}+i^{31}

[tex]=(i^{2} )^5i+(i^{2} )^8 +(i^{2} )^{10} i+(i^{2} )^{13}+(i^{2} )^{15} i\\=(-1)^5 i+(-1)^8+(-1)^{10} i+(-1)^{13} +(-1)^{15} i\\=- i+1+i-1-i\\=0- i[/tex]

Answer:

25 - 3x^5

Step-by-step explanation:

-2x^4+16+2x^4+9-3x^5

Combine like terms

-2x^4+2x^4+9+16-3x^5

0                 + 25 -3x^5

Answer:

3x^5-25

Step-by-step explanation:

you but the terms with the same power together and don't forget to add the signs that are in front of each terms when combining.

Answer:     .28

Step-by-step explanation:

.3+.42= .72

1-.72=.28

Answer:

0.28

Step-by-step explanation:

The sum of a list of probabilities = 1

Sum of given probabilities = 0.72

So, probability of getting pasta = 1-0.72 = 0.28

Hope this helps

Answer:

The data that we have is:

Price per item = $25

spending limit = $200

Now, if you sell x items, then your earnings will be:

E = $25*x

So if you sell two items, we have x = 2

E(2) = $25*2 = $50

But the maximum spending possible will be such that:

$25*x = $200

x = $200/$25 = 8

Then the equation is:

E(x) = $25*x

such that  0 ≤ x ≤ 8

Which means that you can sell any number of units between 0 and 8.

Answer:

Label is 3 by 8.5 inches which equals (3 * 8.5)

25.5 square inches

Step-by-step explanation:

The label covers about 47.10 square inches of the Pringles can.

To calculate the area of the label that covers the Pringles can, you need to find the surface area of a cylinder.

The formula for the surface area of a cylinder is:

Surface Area = 2πr(h + r)

where r is the radius of the circular base and h is the height of the cylinder.

Given that the diameter of the Pringles can is 3 inches, the radius (r) is half of that, which is 1.5 inches. The height (h) is 8.5 inches.

Now, plug in these values into the formula:

Surface Area = 2 * π * 1.5 * (8.5 + 1.5)

Surface Area ≈ 2 * 3.14 * 1.5 * 10

Surface Area ≈ 47.1 square inches

Rounded to the nearest hundredth, the label covers about 47.10 square inches of the Pringles can.

More on area can be found here: https://brainly.com/question/1631786

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Answer:

Increase.

Step-by-step explanation:

Let's say p=25.

50/25=2

If p decreased and we turned the 25 into a 2, then 50/2=25.

The answer increased.

I hope this is what you were looking for!! <3

Answer:

[tex]Area = 24.8 cm^2[/tex]

Step-by-step explanation:

Given

[tex]PQ = 4.9cm[/tex]

[tex]RQ = 11 cm[/tex]

[tex]<Q = 113\ degrees[/tex]

Required

Find the area of the triangle

When presented with a triangle where two sides are known and an angle between the two sides; The area is solved as follows;

[tex]Area = \frac{1}{2}ABSinC[/tex]

Where A and B are the two known sides and C is the angle between A and B

Having said that;

The area of the triangle is calculated as thus;

[tex]Area = \frac{1}{2} * RQ * PQ * SinQ[/tex]

[tex]Area = \frac{1}{2} * 11 * 4.9 * Sin113[/tex]

[tex]Sin113 = 0.9205[/tex]

Hence, the equation becomes

[tex]Area = \frac{1}{2} * 11 * 4.9 * 0.9205[/tex]

[tex]Area = \frac{11 * 4.9 * 0.9205}{2}[/tex]

[tex]Area = \frac{49.6152}{2}[/tex]

[tex]Area = 24.8076[/tex]

[tex]Area = 24.8 cm^2[/tex] --- Approximated

Answer: 4

Step-by-step explanation:

This problem can be represented as:

4+(3-3)

Parenthesis

4+(0)

Add

4

Hope it helps <3

Answer:

The equation wold simply be d+1 simplified and d-3+4 if not im not sure if this is what ur asking?

Step-by-step explanation:

Answer:

15 ,90 30 45.90,23,23,45,

0

,12,3,

Step-by-step explanation:

Step-by-step explanation:

1 is 9 ² - 1 + 3x

the rest are really blury

use a calculator

hope this helps

i would appreciate it if u can heart and like my answer and maybe even give it 5 stars or brainliest pls i beg u thx !!! : )

Answer:

a) More.

b) Less.

c) More.

Step-by-step explanation:

a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.

b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.

c) The same exact thing as part a.

Hope this helps!

Step-by-step explanation:

The figure above is a cube since all it's sides are equal

Volume of a cube = l³

where l is the length of one side

From the question

l = 5

So the volume of the cube is

Volume = 5³

Surface area of a cube = l²

= 5²

Hope this helps you

Answer:

D. 1, 3, 5, 15

Step-by-step explanation:

Factors are numbers that divide another number evenly, with no remainders.

15 ÷ 1 = 15

15 ÷ 3 = 5

15 ÷ 5 = 3

15 ÷ 10 = 1.5

15 ÷ 2 = 7.5

15 ÷ 15 = 1

The numbers that 15 divide evenly into are 1, 3, 5, and 15.

Hope that helps.

Answer:

The answer is below.

Step-by-step explanation:

PROVE √(1-〖cos〗^2 θ)/cosθ = tanθ

Now 1 - cos^2 θ = sin^2θ

So  √(1 - cos^2 θ) = sin θ

and  √(1 - cos^2 θ) / cos  θ

= sin θ / cos θ

= tan θ

Step-by-step explanation:

[tex]\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\tan\theta\\\\\text{We know:}\\(1)\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\(2)\tan x=\dfrac{\sin x}{\cos x}\\\\\text{For}\ \sqrt{1-\cos^2\theta}\ \text{use}\ (1):\\\\L_S=\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\dfrac{\sqrt{\sin^2\theta}}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta\ \ \ _{used (2)}\\\\R_S=\tan\theta\\\\L_S=R_S[/tex]

[tex]\text{Of course, this equality is not true for everyone values of}\ \theta.\\\\1^o.\ \cos\theta\neq0\to\theta\neq\dfrac{\pi}{2}+k\pi,\ k\in\mathbb{Z}\\\\2^o.\ \sqrt{\sin^2\theta}=|\sin\theta|,\ \text{therefore}\\\\\text{for}\ \theta\in[2k\pi;\ (2k+1)\pi],\ \sin\theta\geq0\to|\sin\theta|=\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta[/tex]

[tex]\text{for}\ \theta\in\bigg((2k-1)\pi;\ 2k\pi\bigg),\ \sin\theta<0\to|\sin\theta|=-\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{-\sin\theta}{\cos\theta}=-\tan\theta\neq\tan\theta[/tex]

[tex]\text{Conclusion:}\\\\\text{This equality is true for}\ \theta\in\left[2k\pi;\ \dfrac{\pi}{2}+2k\pi\right)\cup\left(\dfrac{\pi}{2}+2k\pi;\ \pi+2k\pi\right],\ k\in\mathbb{Z}[/tex]

Answer:

Consumption in the 20th year  = 82252 (nearest unit)

Step-by-step explanation:

Exponential growth problem.

Current consumption (year 0), P = 31000

growth rate, r = 5%

consumption in nth year

P(n) = P(1+r)^n

for the 20th year,

P(20) = P((1+r)^20) = 31000*1.05^20 = 82252.2 m^3  

(note: annual water consumption in a town is likely to be measured by m^3, please double check)

The required volume of water will be used at 82253 liters.

The annual water usage rate increase 5% annually with current usage is 31000 liters. After 20 years what will be the volume usage? To determine.

The function which is in format f(x) =a^x  where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here, the rate of volume of water usage increases exponentially by 5%, current usage  = 31000. So Usage for the 20th year,
= 31000(1+5%)^20
=31000(1.05)^20
= 82253 liters

Thus, The required volume of water will be used at 82253 liters.

learn more about exponential function here:

brainly.com/question/15352175

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Answer:

a   8

Step-by-step explanation:

You are given two sides and the included angle. Since you don't have any side and the opposite angle, you must use the law of cosines.

[tex] a^2 = b^2 + c^2 - 2bc\cos A [/tex]

[tex] a^2 = 5^2 + 11^2 - 2(5)(11)\cos 39^\circ [/tex]

[tex] a^2 = 25 + 121 - 110\cos 39^\circ [/tex]

[tex] a^2 = 60.51 [/tex]

[tex] a = 7.779 [/tex]

Answer: a = 8 cm

Answer:

The percentage that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8)  = 83.9≅ 84 percentage

Step-by-step explanation:

Step(i):-

Mean of the Population = 8.3 points

Standard deviation of the Population = 0.5 points

Let 'X' be the random variable in normal distribution

Let X = 6.8

[tex]Z = \frac{x-mean}{S.D} = \frac{6.8-8.3}{0.5} = -3[/tex]

Let X = 8.8

[tex]Z = \frac{x-mean}{S.D} = \frac{8.8-8.3}{0.5} = 1[/tex]

The probability that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8) = P(-3≤Z≤1)

                     = P(Z≤1)- P(Z≤-3)

                    =  0.5 + A(1) - ( 0.5 -A(-3))

                   = A(1) + A(3)       (∵A(-3)=A(3)

                  =  0.3413 +0.4986    (∵ From Normal table)

                 = 0.8399

Conclusion:-

The percentage that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8)  = 83.9≅ 84 percentage

Answer:

The answer is

Step-by-step explanation:

Area of a rectangle = length × width

let w be the width and l be the length

Area of rectangle = 247 ft²

width is 6 feet less than its length is

w = l - 6

247 = l( 1 - 6)

l² - 6l - 247 = 0

(l + 13) (l - 19) = 0

l + 13 = 0 l - 19 = 0

l = - 13 l = 19

Since the length should be positive

The length of the rectangle is

Hope this helps you

Answer:

Length of the rectangle, L = 19 ft

Step-by-step explanation:

Area of a rectangle = Length * Width

Area of the rectangle, A = 247 ft²

Let the length of the rectangle be L

The width of the rectangle = W

Since the width of the rectangle is 6 ft less that the length;

W = L - 6

A = L * W

247 = L * (L - 6)

247 = L² - 6L

L² - 6L - 247 = 0

By solving the quadratic equation above:

(L - 19)(L + 13) = 0

L - 19 = 0, L = 19

L + 13 = 0; L = -13

Since the length of a rectangle cannot be negative, L = 19 ft