3 years ago, the residents of Planet X found a black hole leading to another galaxy. Since then, they have been leaving Planet X at a rate of 120 residents per year.
The following equation describes this situation:
\quad -120\cdot 3 = -360−120⋅3=−360minus, 120, dot, 3, equals, minus, 360
What does -360−360minus, 360 tell us?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
A total of 360360360 residents left Planet XXX in the past three years.

(Choice B)
B
360360360 residents left Planet XXX each year.

(Choice C)
C
None of the above

Answer:

The value of y is 4.

Step-by-step explanation:

Note the system of equation:

x + y = 24

5y = x

First, plug in 5y for x in the first equation:

x + y = 24

(5y) + y = 24

Simplify. Combine like terms. Like terms are terms that have the same amount of the same variable:

(5y + y) = 24

(6y) = 24

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Divide 6 from both sides of the equation:

(6y)/6 = (24)/6

y = 24/6 = 4

Now, plug in 4 for y in one of the given equations in the system of equation:

x + y = 24

x + (4) = 24

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 4 from both sides of the answer:

x + 4 = 24

x + 4 (-4) = 24 (-4)

x = 24 - 4

x = 20

x = 20 , y = 4

~

Check. Use the other equation. Plug in 4 for y, and 20 for x:

5y = x

5(4) = (20)

5 * 4 = 20

20 = 20 (True)

~

The value of y is 4.

Answer:

False,

Step-by-step explanation:

The set that contains no elements is the null set Ф.

Answer: True

Step-by-step explanation: Where all inclusive set comprises of a set of all elements, the purge set contains no elements of the subsets.

Answer:

10cm2

Step-by-step explanation:

Answer:

As AE and BD intersect:

As AB is parallel to ED:

Therefore, we can use SSS Similarity Theorem to find the lengths of the sides:

[tex]\sf \dfrac{AC}{EC}=\dfrac{BC}{DC}=\dfrac{AB}{ED}[/tex]

[tex]\implies \sf \dfrac{400}{1000}=\dfrac{300}{ED}[/tex]

[tex]\implies \sf 400 \cdot ED=300 \cdot 1000[/tex]

[tex]\implies \sf ED=\dfrac{300000}{400}=750[/tex]

**The length of BC and CD cannot be determined without knowing an angle**

Therefore, the remainder of the calculations are based on the assumption that ∠BAC and ∠DEC are 90°

If ∠BAC = 90° then BC can be calculated using Pythagoras' Theorem

⇒ AB² + AC² = BC²

⇒ 300² + 400² = BC²

⇒ BC² = 250000

⇒ BC = 500

Using the side ratios stated previously:

[tex]\sf \dfrac{AC}{EC}=\dfrac{BC}{DC}=\dfrac{AB}{ED}[/tex]

[tex]\implies \sf \dfrac{400}{1000}=\dfrac{500}{DC}[/tex]

[tex]\implies \sf 400 \cdot DC=500 \cdot 1000[/tex]

[tex]\implies \sf DC=\dfrac{500000}{400}=1250[/tex]

Therefore, the distance of each side is:

Assuming the sides are the solid lines marked with arrows only:

⇒ Total distance = AB + BC + DC + ED

                            = 300 + 500 + 1250 + 750

                            = 2800 m

Answer:

  (a)  sin⁻¹(√35/14)

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relations between sides and angles in a right triangle. Here, the given sides AB and AC are the side opposite angle C, and the hypotenuse (opposite right angle B). That means the relevant relation is ...

  Sin = Opposite/Hypotenuse

  sin(C) = AB/AC

__

For this problem, substituting values gives ...

  sin(C) = (3√5)/(6√7) = (1/2)√(5/7) = (1/2)(√35)/7 = (√35)/14

  C = arcsin((√35)/14)

_____

Additional comment

Choice B can be eliminated on the grounds that the fraction is not reduced to lowest terms. Choices C and D are eliminated because they assume a cosine relation is involved. That is, you can choose the correct answer based on SOH CAH TOA without concerning yourself with the details of the radical expression.

Using the uniform distribution, it is found that there is a 0.3608 = 36.08% probability that the male will lose between 19.41 and 23.74 percent of their body weight.

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

In this problem, male black bears will typically drop between 17 to 29 percent of their body weight, hence the bounds are a = 17 and b = 29.

The probability that the male will lose between 19.41 and 23.74 percent of their body weight is given by:

[tex]P(19.41 \leq X \leq 23.74) = \frac{23.74 - 19.41}{29 - 17} = 0.3608[/tex]

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answer :

[tex]C=\frac{265}{9}[/tex]

work:

[tex]F=85[/tex] °[tex]C[/tex]

[tex]F= 85[/tex] into [tex]C=\frac{5}{9}(F-32)[/tex]

[tex]C=\frac{5}{9}[/tex] x [tex](85-32)[/tex]

[tex]C=\frac{265}{9}[/tex]

Answer:

It would not

Step-by-step explanation:

(12-4)=4+1 would be 8=5

12-4=4+1 would also be 8=5

The number of the adult leaders will be 4

A Number of cub scouts in troop 584 is = 25 .As per the statement given in the question "The number of scouts is 5 more than five times the number of adult leaders"

Number of scouts = 5(Number of adults) + 5

Here number of scouts = 25

Therefore, the equation will become as

25 = 5(Number of adults) + 5

5(Number of adults) = 25 - 5

5(Number of adults) = 20

(Number of adults) = 20/5=4

Hence the number of the adult leaders will be 4

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Answer: Reflection followed by a translation

Step-by-step explanation:

     First, RST is reflected along the x-axis.

     Then, RST is translated one unit down into R'S'T' giving us what we're looking for.

Answer:

33.33....

Step-by-step explanation:

If 2/3 of them are men, then 1/3 are women. I/3=0.333....

To find the percent you multiply by 100 and get 33.3333 and you can write then however your system requests a repeating decimal.  

Answer:

50

Step-by-step explanation:

1/2 x base x height

In this problem: (It's times 2 because I split it up into 2 triangles.)

1/2 x 10 x 5 x 2 =

50

hope this helps

have a good day

2(1+4)2 x (9-6)3

4(5) x 3(3)

20 x 9

180

Answer:

56.5 ft

Step-by-step explanation:

See the attached figure which represents the explanation of the problem.

We need to find the length of the tree to which is the length of AD

From the graph ∠BAC = 90° and ∠ABD = 76°, AB = 18 ft

At ΔABD:

∠BAD = ∠BAC - ∠DAC = 90° - 4° = 86°

∠ADB = 180° - ( ∠BAD + ∠ABD) = 180 - (86+76) = 180 - 162 = 18°

Apply the sine rule at ΔABD

∴[tex]\frac{AB}{SinD} =\frac{AD}{sinB}[/tex]

∴ 18/sin 18 = AD/sin 76

∴ AD = 18 * (sin 76)/(sin 18) ≈ 56.5 (to the nearest tenth of a foot)

So, The length of the tree = 56.5 ft.

The answer is 56.5 ft

Answer:

7/8 (seven eighths)

Step-by-step explanation:

add the numerators (top numbers) together, to get 7. Leave the denominator (bottom number) alone, since they are the same. Think about it like you're adding two different parts of a whole.

you should get 7/8

hope this helps

Answer:

[tex]\sf A) \quad \dfrac{9}{100}[/tex]

Step-by-step explanation:

Given:

Total number of marbles = 3 + 4 + 2 + 1 = 10

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Probability of selecting a green marble on first pick:

[tex]\implies \sf P(green\:marble)=\dfrac{3}{10}[/tex]

Probability of selecting a green marble on second pick:

[tex]\implies \sf P(green\:marble)=\dfrac{3}{10}[/tex]

(as the 1st pick was replaced)

Therefore,

[tex]\implies \textsf{P(green marble) and P(green marble)} \sf =\dfrac{3}{10} \times \dfrac{3}{10}=\dfrac{9}{100}[/tex]

Answer:

5

Step-by-step explanation:

just calculated and got it

Answer:

15

Step-by-step explanation:

First, change it to multiplication and flip the second fraction

5/3×9/1

Then you multiply 5×9 and 3×1. This gets you 45/3

45/3 can be simplified down to 15 so the answer is 15

Answer:

the awnser is -3 11/24

Step-by-step explanation:

Don't know

-2 5/7

Yan po answer ko inadd ko po by fraction

[tex]\sf \large \boxed{110 ^\circ}[/tex]

If the equations are the same then the solution will be the same. Then the correct option is D.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear equations are given below.

-3x - 8 = 19 ...1

-3x - 2 = 25 ...2

Adding 6 on both sides in equation 1, then we have

-3x + 6 - 8 = 19 + 6

     -3x - 2 = 25

The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

If the equations are the same then the solution will be the same.

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Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = a * log_b (x - h) + k

(h,k) = (x,y)

h = shift right/left

k = shift up/down

Original Points of y = log_3

y = log_3 (x + 2)

h = -2 thus shift left.

Asymptote: x = -2
Domain: [-2 , +inf)

Range: (-inf , +inf)

Answer:

line will be horizontal running through (0,2)

Step-by-step explanation:

6,2
1,2
2-2/1-6 = 0/-5 = 0 slope. 2 = 0x6+b, 2=b. line will be y=b , y=2.

Answer:

Kayla gets $0.77 back, Heidi gets $9.02 back

Step-by-step explanation:

12 - 11.23 = 0.77 (how I got 12 is the $10 dollar bill and TWO $1 dollar bills)

20.25 - 11.23 = 9.02 (how I got 20.25 is the $20 dollar bill and the quarter which is worth $0.25)

Answer:

The price for ounce is: $0.25 and she bought 16 ounces of straberris

Step-by-step explanation:

If you have 16 ounces and its 4 dollars you do 4/16 to get 0.25

A

Step-by-step explanation:

hope it helps

A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.

Given that Farhan bought a bag and a wallet at a discount from a store, and he was given a discount of 30% for the bag, and for the wallet, a discount was also given, and he saved a total of $66.60, and he paid a total of $121.40 for the 2 items and paid $46.60 more for the bag than the wallet, to determine A) what was the price of the bag without discount, and B) what was the percentage discount given for the wallet, the following calculations must be performed:

Therefore, A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.

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Answer:A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.

Step-by-step explanation:

Answer:

104.65 m

Step-by-step explanation:

The plane with the smaller angle of depression is closer to the raft.

Taking the tan values of both planes :

Plane 1 (57°)

Plane 2 (48°)

Equate Equations 1 and 2 :

Taking the sin ratio to find distance :

Answer:

a

Step-by-step explanation: