1
James purchases a rare coin for $450. The coin appreciates at a rate of 1.2% each year. How much will the coin be worth after 25 years?

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: 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:

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.

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:

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:

I can't seem to work out the other two, sorry

Step-by-step explanation:

1. -> c. because there are 10 letters in total and there are 4 vowels, so it would be 4/10, then we'd simplify by 2, and I gives us 2/5

4. -> g. because there are 10 letters so it's 10/10 which gives us 1

Answer:

CEFG

Step-by-step explanation:

1. P = 4/10 = 2/5

2. P= (4/10)(4/10)=16/100=4/25

3. P= (4/10)(3/9) = 12/90 = 2/15

4. P = 12/12 = 1

Hope this helps

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:

( 18.4, 4.6 )

Step-by-step explanation:

2x - 6y  = 14

Add 6y to both sides

2x = 6y + 14

divide both sides by 2

             x = (3y + 7)

Substitute this ^ for x in the othe equation

4 (3y + y) - y = 9

distribute the 4

12y + 4y - y = 9

combine like terms

15y = 9

divide both sides by 15

y = 4.6

Now substitute this value for y in the equation we previously substituted .to find the value of x

x = 3 (4.6) + 4.6

x = 13.8 + 4.6

x = 18.4

Hope this makes sense and was helpful!

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:

d

Step-by-step explanation:

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:

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:

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:

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:

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:

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

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

Answer:  It breaks up into 864+216

Reason:

x = some positive real number

The ratio 4:1 scales up to 4x:1x, so we have two parts one is 4x and the other is 1x. Those two parts add up to 1080

4x+1x = 1080

5x = 1080

x = 1080/5

x = 216

We can then find 4x = 4*216 = 864

As a check: 864+216 = 1080, so the answer is confirmed.

Answer:

0.965 to the nearest thousand.

Step-by-step explanation:

This is a binomial probability distribution.

Prob(getting no 3's) = (5/6)^5 = 0.4019

Prob(getting  1 * 3 )   = 5C1(1/6)(5/6)^4 = 0.4019

Prob (getting 2 3's ) = 5C2(1/6)^2(5/6)^3 = 0.1608

So required probability = 2 * 0.4019 + 0.1608

= 0.9646

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:

21000

Step-by-step explanation:

2745 -> 3000

6.9 -> 7

3000 x 7 =

21000

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:

a

Step-by-step explanation:

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

4(5) x 3(3)

20 x 9

180

Answer:

10 duh

Step-by-step explanation:

The value of x will be equal to 3 for the given expression.

The fraction is defined as the division of the whole part into an equal number of parts.

Given expression is solved as:-

[tex]\dfrac{\dfrac{3}{4} }{\dfrac{6}{x}} = \dfrac{3}{8}[/tex]

[tex]\dfrac{3}{4}\times \dfrac{x}{6}=\dfrac{3}{8}[/tex]

[tex]\dfrac{x}{8}=\dfrac{3}{8}[/tex]

x = 3

The value of x will be equal to 3 for the given expression.

Therefore the value of x will be equal to 3 for the given expression.

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Answer:

Step-by-step explanation:

→Perimeter (P)  = 2×(L+W)              Perimeter = 48m

But Length = 2 × Width

∴ P = 2×( 2W + W)

       = 2×(3W)

  48 = 6W

Divide both sides by 6

          [tex]\frac{48}{6}[/tex] = [tex]\frac{6}{6}[/tex] W

∴Width (W) = 8m  

→This means Length = 2W

                                = 2×8m

                             L = 16m

→Area of a rectangle = L × W

                               = 8m × 16m

     ∴ Area of the rectangular field= [tex]128m^{2}[/tex]