F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23

Answer:

  C)  549 km²

Step-by-step explanation:

The area of the regular pentagon is given by ...

  A = (1/2)Pa

where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.

The lateral area is the product of the perimeter and the height:

  LA = Ph

Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...

  total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)

  = (45 km)(6 km +6.2 km) = 549 km^2

Answer:

[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex]

Step-by-step explanation:

We are given the graph of r = cos( θ ) + sin( 2θ ) so that we are being asked to determine the integral. Remember that [tex]\:r=cos\left(\theta \right)+sin\left(2\theta \right)[/tex] can also be rewritten as [tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex].

Let's apply the functional rule [tex]\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex],

[tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex] = [tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex]

At the same time [tex]\int \cos \left(\theta \right)d\theta \right=\sin \left(\theta \right)[/tex] = [tex]sin( \theta \right ))[/tex], and [tex]\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]-\frac{1}{2}\cos \left(2\theta \right)[/tex]. Let's substitute,

[tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \right)[/tex]

And adding a constant C, we receive our final solution.

[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex] - this is our integral

Answer:

x = 17/5

y = -2/5

Step-by-step explanation:

2x + 2y = 6

3x - 2y = 11

sum both equations results

5x + 0 = 17

x = 17/5

2x + 2y = 6

2*17/5 + 2y = 6

34/5 + 2y = 6

2y = 6 - 34/5

2y = 30/5 - 34/5

2y = -4/5

y = (-4/5)/2

y = -2/5

verify:

3x - 2y = 11

3*17/5 - 2*-2/5 = 11

51/5 + 4/5 = 55/5

51 + 4 = 55

[tex] \Large{ \boxed{ \bold{ \color{lightgreen}{Solution:}}}}[/tex]

So, Let's solve this question by using cartesian plane.

Well, What is cartesian plane?

A - A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. 

━━━━━━━━━━━━━━━━━━━━

Answer:

a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication

Step-by-step explanation:

a) This expression can be solved by using the Compatibility of Equality with Addition, that is:

1) [tex]3+x = 27[/tex] Given

2) [tex]x+3 = 27[/tex] Commutative property

3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition

4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property

5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction

6) [tex]x=24[/tex] Modulative property/Subtraction/Result.

b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:

1) [tex]\frac{x}{6} = 5[/tex] Given

2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division

3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication

4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property

5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse

6) [tex]x = 30[/tex] Modulative property/Result

Answer:

3 + x = 27

✔ subtraction property of equality with 3

x over 6  = 5

✔ multiplication property of equality with 6

Answer:

87 mph

Step-by-step explanation:

Total distance needed is 120 mi + 300 mi and that is 420 mi.

Driving at 65 mph means that it would take

420 / 65 hours to reach his destination.

6.46 hours .

at the first phase, he drove at 40 mph for 120 mi, this means that it took him

120 / 40 hours to complete the journey.

3 hours.

the total time needed for the whole journey is 6.46 hours, and he already spent 3 hours in the first phase. To keep up with the 6.46 hours required, in the second phase, he has to drive at a speed of

6.46 - 3 hours = 3.46 hours.

300 mi / 3.46 hours => 86.71 mph approximately 87 mph

Therefore, he needs to drive at not more than 87 mph to keep up with the journey while not breaking his speed limit

Answer:

2 * (x + 2) = 50

Step-by-step explanation:

Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.

Answer:

A)0.126775 B)0.000004325376 C) 0.07548

Step-by-step explanation:

Given the following :

A.) a. n = 15, p = 0.4, find P(4 successes)

a = number of trials p=probability of success

P(4 successes) = P(x = 4)

USING:

nCx * p^x * (1-p)^(n-x)

15C4 * 0.4^4 * (1-0.4)^(15-4)

1365 * 0.0256 * 0.00362797056

= 0.126775

B)

b. n = 12, p = 0.2, find P(2 failures),

P(2 failures) = P(12 - 2) = p(10 success)

USING:

nCx * p^x * (1-p)^(n-x)

12C10 * 0.2^10 * (1-0.2)^(12-10)

66 * 0.0000001024 * 0.64

= 0.000004325376

C) n = 20, p = 0.05, find P(at least 3 successes)

P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)

To avoid complicated calculations, we can use the online binomial probability distribution calculator :

P(X≥ 3) = 0.07548

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find GV

To find GV we use cosine

cos∅ = adjacent / hypotenuse

From the question

GV is the adjacent

GC is the hypotenuse

So we have

GC = 55°

GV = 55 cos 37

GV = 43.92495

We have the final answer as

Hope this helps you

Answer:

F /T = Z

Step-by-step explanation:

F/Z=T

Multiply each side by Z

F/Z *Z=T*Z

F = ZT

Divide each side by T

F /T = ZT/T

F /T = Z

Answer:

[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]

Step-by-step explanation:

[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]

False!

The answer is: False.

Whomever stated the answer is "true" is wrong.

Answer:

Step-by-step explanation:

x + 30 + 25 = 180

x + 55 = 180

x = 125

y + 125 = 180

y = 55

Answer:

-36

Step-by-step explanation:

3*12=36

she is going down (negative) so, it is -36

not sure if this is what you are asking for, if not try this

0-12-12-12=-36

Answer:

Yes

Step-by-step explanation:

you would do 2(5x-10) + 2(8x+4)= 26x-12

Answer:

26x - 12

Step-by-step explanation:

The perimeter is the sum of all the exterior sides of a figure.

Here, we have a parallelogram, and its sides are 5x - 10, 8x + 4, 5x - 10, and 8x + 4. Adding these, we get:

(5x - 10) + (8x + 4) + (5x - 10) + (8x + 4) = 26x - 12

Thus, the answer is 26x - 12. Note that since the problem doesn't give a value for x, this cannot be simplified further.

~ an aesthetics lover

Answer:

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Step-by-step explanation:

Let be [tex]f(m, b) = m\cdot b - m^{2}[/tex], if [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex], the value of the expression:

[tex]f(3.48,96.52) = (3.48)\cdot (96.52)-3.48^{2}[/tex]

[tex]f(3.48,96.52) = 323.779[/tex]

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Answer:

y = 700x - 400

Step-by-step explanation:

A negative number represents an altitude below sea level.

Beginning: -400

y = mx + b

y = mx - 400

In 2 hours the altitude was now 1000 m.

1000 m - (400 m) = 1400 m

The altitude went up 1400 m in 2 hours. The rate of change is

1400/2 m/h = 700 m/h

The rate of change is the slope.

y = 700x - 400

Answer:

The graph answer is below :)

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

-8+(-15) means that you are subtracting 15 from -8. So you end up with -8-15=-23.

Answer:

W = 9 * g

Step-by-step explanation:

W/9 = g

W = 9 * g

The expression W/9 = g can be written as W = 9g after cross multiplication.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

W/9 = g

To solve for W

Make subject as W:

W = 9g

By cross multiplication.

Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.

Learn more about the expression here:

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Answer:

(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.

Answer:

No

Step-by-step explanation:

The square root of 65 is irrational.

It is not a rational number because 65 is not a perfect square.

The square root of 65 is 8.06225775...

The square root of 65 is not a rational number.

65 is not a perfect square which means it's impossible to

find a whole number times itself to give us 65.

On a calculator if you type in the square root of 65,

you will get an infinite decimal number.

The decimal values never end and never have same repeated pattern.

Answer:

(a) P(E∪F)= 0.8

(b) P(Ec)= 0.4

(c) P(Fc)= 0.7

(d) P(Ec∩F)= 0.8

Step-by-step explanation:

(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.

If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:

P(A∪B) = P(A) + P(B) - P(A∩B)

In this case:

P(E∪F)= P(E) + P(F) - P(E∩F)

Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1

P(E∪F)= 0.6 + 0.3 - 0.1

P(E∪F)= 0.8

(b)  The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A.  The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is  P (Ac) = 1- P (A)

In this case: P(Ec)= 1 - P(E)

Then: P(Ec)= 1 - 0.6

P(Ec)= 0.4

(c) In this case: P(Fc)= 1 - P(F)

Then: P(Fc)= 1 - 0.3

P(Fc)= 0.7

(d)  The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.

As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:

P(Ec intersection F) + P(E intersection F) = P(F)

P(Ec intersection F) + 0.1 = 0.3

P(Ec intersection F)= 0.2

Being:

P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)

you get:

P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)

So:

P(Ec∩F)= 0.4 + 0.3 - 0.2

P(Ec∩F)= 0.8

Answer:

a ≈ 1.59

b ≈ 6.69

Step-by-step explanation:

Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

Step 1: Find c using Law of Sines

[tex]\frac{6}{sin58} =\frac{c}{sin13}[/tex]

[tex]c = sin13(\frac{6}{sin58})[/tex]

c = 1.59154

Step 2: Find a using Law of Sines

[tex]\frac{6}{sin58} =\frac{a}{sin109}[/tex]

[tex]a = sin109(\frac{6}{sin58} )[/tex]

a = 6.68961

Answer:

1) the domain is all real numbers

2) the range is

[tex]y \geqslant 3[/tex]

Answer:

red

Step-by-step explanation:

Since the bag contains more red marbles than any other color, you are most likely to pick a red marble

The required value of the tanФ is given as -3/4. C option is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Tan(180 - Ф) = -tanФ = perpendicular / base

From figure,  perpendicular= 12 and  base = 16
-tanФ = 12 / 16
tanФ = -3/4

Thus, the required value of the tanФ is given as -3/4. C option is correct.

Learn more about trigonometry equations here:

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Answer:

Exoected age is 15.49 years

Step-by-step explanation:

Expected age

= E(x)

= sum (p(i)*i)

= 13*0.01+14*0.23+15*0.26+16*0.28+17*0.20+18*0.02

= 15.49

Answer:

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]

Step-by-step explanation:

Given that;

the winning chance of a weekly local lottery = [tex]\dfrac{1}{10^6}[/tex]

= [tex]\dfrac{1}{1000000}[/tex]

The probability of losing = 1 - probability of winning (winning chance)

The probability of losing = [tex]1- \dfrac{1}{1000000}[/tex]

The probability of losing =[tex]\dfrac{999999}{1000000}[/tex]

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{1}{10^6} )^0 ( \dfrac{999999}{1000000})^x[/tex]

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]

Answer:

R: {y∈R | -1 ≤ y ≤ 5}

Step-by-step explanation:

the lowest point is -1 and the highest point is 5.

Answer: 3.41x10^3

Step-by-step explanation:

At the beginning of the year, we have:

R = 6.2x10 rats.

And we know that, in one year, each rat produces:

O = 5.5x10 offsprins.

Then each one of the 6.2x10 initial rats will produce 5.5x10 offsprings in one year, then after one year we have a total of:

(6.2x10)*(5.5x10) = (6.2*5.5)x(10*10) = 34.1x10^2

and we can write:

34.1 = 3.41x10

then: 34.1x10^2 = 3.41x10^3

So after one year, the average number of rats is:  3.41x10^3