When he was born, Cooper's
grandparents put $2,000 in a college
fund. The fund earns interest at 2.1%
compounded annually. Yesterday was
Cooper's 18th birthday. How much money
is in the account now?
A $2,907.32
C $2,756.00
B $2,838.96
D$2,698.18

Answer:

u = - [tex]\frac{t}{rs}[/tex]

Step-by-step explanation:

Given

t = - rsu ( multiply both sides by - 1 )

- t = rsu ( divide both sides by rs )

- [tex]\frac{t}{rs}[/tex] = u

To find u in terms of r, s, and t given the equation t = -rsu, divide both sides by -rs to get u = -t / (rs).

To solve for u in terms of r, s, and t using the given equation t = -rsu, we need to isolate u. We do this by dividing both sides of the equation by -rs, which gives us u = -t / (rs). This shows that u is inversely proportional to the product of r and s, and directly proportional to -t.

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They finish when their covered distance is equal to 5 kilometers. For Alice:

t/4 = 5

t = 5*4 = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 5²

2t = 25 + 1

t = 26/2

t = 13 minutes

c. They are side by side when they have covered the same distance, that is:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16*(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using quadratic formula:

[tex]t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]

[tex]t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)} [/tex]

[tex]t = \frac{32 \pm 30.98}{2} [/tex]

[tex]t_1 = \frac{32 + 30.98}{2} [/tex]

[tex]t_1 = 31.49 [/tex]

[tex]t_2 = \frac{32 - 30.98}{2} [/tex]

[tex]t_2 = 0.51 [/tex]

Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.

Answer:

a) Alice starts first, b) Briana gets the finish line first, c) [tex]t \approx 0.509\,min[/tex]

Step-by-step explanation:

a) Alice starts first, since binomial inside the squared root is equal to zero when [tex]t = \frac{1}{2}\,min[/tex], whereas Alice begins at [tex]t = 0\,min[/tex].

b) The instant when each competitor reach finish line is:

Alice

[tex]5\,km = \frac{t}{4}[/tex]

[tex]t = 20\,min[/tex]

Briana

[tex]5\,km = \sqrt{2\cdot t - 1}[/tex]

[tex]25\,km^{2} = 2\cdot t - 1[/tex]

[tex]t = 13\,min[/tex]

Briana gets the finish line first.

c) Alice and Briana are side by side when [tex]a(t) = b(t)[/tex]. Then:

[tex]\frac{t}{4} = \sqrt{2\cdot t - 1}[/tex]

[tex]\frac{t^{2}}{16} = 2\cdot t - 1[/tex]

[tex]t^{2} - 32\cdot t + 16 = 0[/tex]

The roots of the second order polynomial are:

[tex]t_{1} \approx 31.492\,min[/tex] and [tex]t_{2} \approx 0.509\,min[/tex]

Just the second roots makes sense, as they must be side by side at one instant before getting the finish line.

Answer:

y=6/-5x+1.4

Step-by-step explanation:

3--3 over -3-2 would equal 6 over -5

Answer:

P(A and B) = P(A) + P(B) - P(A or B)

                 = 0.6 + 0.45 - 0.66

                 = 0.39

The value of P(A AND B), given the probabilities of P(A), P(B), and P(A OR B),  is found to be 0.39.  

To find the probability of both events A and B occurring, we use the formula for the probability of the union of two events, which is P(A OR B) = P(A) + P(B) \'96 P(A AND B). We rearrange this formula to find P(A AND B) by subtracting P(A) and P(B) from P(A OR B):

P(A AND B) = P(A) + P(B) \'96 P(A OR B)

Substituting the given values:

P(A AND B) = 0.6 + 0.45 \'96 0.66 = 0.39

So, the probability of A and B occurring together, P(A AND B), is 0.39, which rounds to the nearest thousandth as required.

Answer:

26s

Step-by-step explanation:

4 x 3 s + 7 x 2 s

12s + 14s = 26s

Answer:

26 s

Step-by-step explanation:

[tex]4 \ast3s + 7 \ast2s \\ = 12s + 14s \\ = 26s[/tex]

Answer:

y≥ 5+5/3x

Step-by-step explanation:

5x-3y≤-15

-5x .     -5x

-3y≤-15 -5x

/-3 .     /-3 .(flip inequality when dividing or multiplying by a negative number)

y≥ 5+5/3x

Answer:

ok if its 3^4 then the answers are

the second one

the forth

and the fifth

Step-by-step explanation:

3^4 is (3)(3)(3)(3) so that equals 81 and the terminology is 3 to the power of 4

Answer: A or C (i think A because its not including)

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

because yes

Answer: 2

Explanation: To solve this problem, it's important to understand that we don't need to graph the line but we can use our slope formula. One method you could use is the graphing method which requires you to plot the points but I will be showing you the slope formula.

[tex]m =\frac{ ^{y}2 - ^{y}1 }{x^{2} - x^{1} }[/tex]

We take our second y minus our first y

which in this case is 12 - 4

over our second x minus our first x

which in this case is 6 - 2.

So 12 - 4 over 6 - 2 simplifies to 8/4.

Notice that our slope can

be simplified one step further.

So 8/4 reduces to 2.

So the slope of the line that passes through these points is 2.

Answer:

1/18

Step-by-step explanation:

1/3 divided by 6 = 1/3 x 1/6

You can multiply by the reciprocal of a number instead of dividing

1/3 x 1/6 = 1/18

Answer: The answer is 1/18

Step-by-step explanation: starting with 1/3 breaking into 1/6

e-s-s: 1/3 / 1/6 = 1/3 . 1/6 = 1/18

Answer:

[tex]\huge\boxed{28\ and\ 7}[/tex]

Step-by-step explanation:

[tex]x-\text{the bigger number}\\(x-21)-\text{the smaller number}\\35-\text{the sum of numbers}\\x+(x-21)-\text{the sum of numbers}\\\\\text{The equation:}\\\\x+x-21=35\qquad\text{add 21 to both sides}\\\\x+x-21+21=35+21\\\\2x=56\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{56}{2}\\\\x=28\to x-21=28-21=7[/tex]

Answer:

28+7= 35

28 and 7 are the numbers

Answer:

4 and 10

Step-by-step explanation:

To solve this problem, we need to find all the numbers between 1 and 13 that have a sum of 14. The list is shown below:

1 + 13,   2 + 12,   3 + 11,   4 + 10,   5 + 9,   6 + 8,   7 + 7

Now we must figure out which set of numbers include one number that is 2/5 of the value of the other. We can do that by turning the sets of numbers into fractions as shown below:

[tex]\frac{1}{13}\neq \frac{2}{5}[/tex]

[tex]\frac{2}{12}\neq \frac{2}{5}[/tex]

[tex]\frac{3}{11}\neq \frac{2}{5}[/tex]

[tex]\frac{4}{10}= \frac{2}{5}[/tex]    (answer)

[tex]\frac{5}{9}\neq \frac{2}{5}[/tex]

[tex]\frac{6}{8}\neq \frac{2}{5}[/tex]

[tex]\frac{7}{7}\neq \frac{2}{5}[/tex]

The first number is 4, and the second number is 10, and their sum is indeed 14, as given in the problem.

Let's call the first number "x" and the second number "y." According to the information given:

The sum of the two numbers is 14, so we can write the equation:

x + y = 14

The first number (x) is 2/5 of the second number (y), which can be expressed as:

x = (2/5)y

Now, we can solve this system of equations using substitution. First, we'll substitute the expression for x from the second equation into the first equation:

(2/5)y + y = 14

To make the equation easier to solve, we can get rid of the fraction by multiplying both sides of the equation by 5 (the denominator of 2/5):

5(2/5)y + 5y = 5 * 14

This simplifies to:

2y + 5y = 70

Now, combine like terms:

7y = 70

To solve for y, divide both sides by 7:

y = 70 / 7

y = 10

Now that we've found the value of y, we can find the value of x using the second equation:

x = (2/5)y

x = (2/5) * 10

x = 4

So, the two numbers are:

x = 4

y = 10

for such more question on first number

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the answer is 1/8

Look at the attached picture⤴⤴

Hope this will help u.....✔

Answer:35%

Step-by-step explanation:

The percentage decrease in the value of the book is 35%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Cost of the book = £19.80

Selling price of the book = £12.87

The percentage decrease in the value of the book.

= (19.80 - 12.87)/19.80 x 100

= 6.93/19.80 x 100

= 35%

Thus,

The percentage decrease is 35%.

Learn more about percentages here:

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Answer:

C

Step-by-step explanation:

The line crosses the y-axis at 3, and has a slope of -1/5. You can use the formula y=mx+b where m represents the slope and b is the point at which the line crosses the y-axis.

Answer:

The answer would be B or 3 1/16.

Step-by-step explanation:

Answer:

114.5 in³

Step-by-step explanation:

Volume of cone:

⅓ × 3.14 × 8² × 12

= 803.84 cm³

Volume of hemisphere:

⅔ × 3.14 × 8³

= 1071.786667 cm³

Total = 803.84 + 1071.786667

= 1875.626667 cm³

1 cm = 0.393701 inches

1 cm³ = 0.393701³ inches

Volume in in³:

1875.786667/0.393701³

= 114.4579471 in³

Answer:

3 stone necklaces

Step-by-step explanation:

so theres 5 designs and 3 stones you can only have 1 stone with one if your looking to put one on each necklace there will be three with one stone and two without

Answer: The answer for that would be 325

Step-by-step explanation:

Answer:

175 servings

Step-by-step explanation:

So you wanna find the remaining 35%.

35*500=17500

17500/100= 175

Answer:

C

By substuting x=- 3 the answer will be negative

Answer:

1. 5

2. 66/25

3. -7.2

4. 25/24

Answer:

5a) The number of red blocks increases by one every time while the blue one stays the same.

5b) The number of blue blocks increases by one every time while the red one stays the same.

Step-by-step explanation:

I don't really know how to explain this. The best way for you to understand this concept is to google algebraic expressions for pattern rules.

Answer:

B, 36 degrees

Step-by-step explanation:

Because AB and CB are congruent, so are arcs AB and CB. Therefore, 3x+12=6x-12

24=3x

x=8

3x+12=3(8)+12=24+12=36 degrees, or answer choice B. Hope this helps!

Answer:

i think its 2.7 or 1.7 iriririeieire

Answer:

V =343 cm^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = 7^3

V =343 cm^3

Answer:

Since the range of the original function is limited to y  6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

The answer is the statement Since the range of the original function is limited to y > 6, the domain of the inverse function is x ≥ 6.

The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.

The positive slope definition tells us that a line with a positive slope is one where the right side of the line is higher than the left side of the line.

So, by the definition given above, we see that

if the range of the original function is limited to y > 6, the domain of the inverse function is x >= 6.

Learn more about the domain of inverse functions on:

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Answer:

Step-by-step explanation:

hello :

f(n)=f(n-1)+2

means : f(n)-f(n-1)=2

this is the arithmetic seq when the common dif is d= 2  and the first term is : 9

the n-ieme term is : f(n)  = f(1) +(n-1)d

f(n) =9+2(n-1)

f(n) = 2n+7

so : f(5) = 2(5)+7 = 17

Final answer:

The value of f(5) is determined by consecutively applying the given recursive relation, f(n) = f(n-1) + 2, starting from the initial condition f(1) = 9. After applying this process four times, we find that f(5) is 17.

Explanation:

f(1) = 9

f(n) = f(n-1) + 2

To find the value of f(5), we can use the recursive formula provided:
f(2) = f(1) + 2 = 9 + 2 = 11
f(3) = f(2) + 2 = 11 + 2 = 13
f(4) = f(3) + 2 = 13 + 2 = 15
f(5) = f(4) + 2 = 15 + 2 = 17

Answer:

3

Step-by-step explanation:

You find rise/run.

The rise is (5-(-7)), which is 12

The run is (1-(-3)), which is 4

12/4 = 3

Answer:

3     hope this helps!   pic below    :)

Step-by-step explanation:

y = 3x + 2

Answer:

24.5

Step-by-step explanation:

When you round it you get 25. (sorry if im wrong) :(