Complete the equation describing how x
and y are related.
X
-3
-2
-1
0
1
2
Y
24
16
8
0
-8
-16
y = [? ]x
Enter the answer that
belongs in [?].

Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

a: $145,912,000,000

b: 4.6 bn shares

c: $31.72/per share (divide in half)

The final amount in the retirement account in which the rate or return and the regular contributions change over time is $33,844.51.

To determine the final amount in the retirement account, we first compute the future value of the periodic deposits of $213 for 4 years, using an online finance calculator.

The future value of $213 deposited for 48 months is used as the present value of the investment for the next 4 years or 48 months.

Then, with the present value and the periodic deposits, the final amount (future value) of the retirement account is determined as follows:

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

PMT (Periodic Payment) = $213

Results:

FV = $11,067.40

Sum of all periodic payments = $10,224.00

Total Interest $843.40

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 7%

PV (Present Value) = $11,067.40

PMT (Periodic Payment) = $348

Results:

Final Value (FV) = $33,844.51

Sum of all periodic payments = $16,704.00

Total Interest = $6,073.11

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Answer: (-3^4^-7)^-3 can be expressed with positive exponents as (-1/3^4^7)^3.

Step-by-step explanation:

First, we need to evaluate the exponents of the expression from the highest power to the lowest power. Since the exponent of 7 is negative, we need to apply the rule that a negative exponent indicates a reciprocal. Therefore, we can rewrite the expression as (-3^4^-1/7)^-3.

Next, we can simplify the expression -1/7 by flipping it to 7^-1. Therefore, we now have (-3^4^7^-1)^-3.

We can now evaluate the exponent of 4, which gives us (-3^16384^-1)^-3.

Finally, we can simplify 16384^-1 by flipping it to 1/16384, which gives us (-1/3^1/16384)^3.

This expression can be written using only positive exponents as (-1/3^4^7)^3.

Answer: 3.1

Step-by-step explanation: they are giving you the diameter so you halve it then you multiply it my 3.14 (pi) then you round it to the nearest tenth which is the 1 so you look to the left and it's not bigger than 5 so you round down so it stays as a 1

Answer:

Step-by-step explanation:

The total investment done by Lydia when her total annual interest is $420 at 11% dividend and 14% interest is equal to $3360.

Total annual interest = $420

Half of the investment in stock paying = 11% dividend

Half of the investment in stock paying = 14% interest

Let x be the amount Lydia has invested in each stock.

Since she has half of her investments in each stock,

The following system of equations to represent the situation,

Total annual interest is $420.

This implies ,

0.11x + 0.14x = 420

And  total investment is,

x + x = 2x

Simplifying the first equation, we get,

⇒ 0.25x = 420

Dividing both sides by 0.25, we get,

⇒ x = 1680

So, Lydia has invested $1680 in each stock, for a total investment of,

⇒ 2x = 2(1680)

        = 3360

Therefore, Lydia has a total investment of $3360.

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Answer:

6.324555320336759

Step-by-step explanation:

To find a missing leg in a right triangle use Pythagorean Theorem.

a^2 + b^2 = c^2                        Substitution

6^2 + 2^2 = c^2                         Simplify

36 + 4 = c^2                               Simplify

40 = c^2                                     Simplify
6.324555320336759 = c

The new drug appears to reduce epileptic seizures since the rerandomized mean differences are close to the mean difference found between the two groups studied.

The rerandomized mean differences are:

1.2, 2.4, 1.8, 1.3, 2.1, 0.9, 1.5, 0.7, 2.1, and 2.3.

Several of these values are close to the observed mean difference of 1.8, which suggests that the observed difference could be due to chance alone.

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Answer:

Fred doesn't run

Step-by-step explanation:

Fred doesn't run, Fred likes to walk, you obviously don't know Fred enough to answer this question, so tell your teacher how you can get in touch with Fred for a better relationship

let's firstly convert the mixed fractions to improper fractions, then sum them up.

[tex]\stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{1\frac{3}{8}} \implies \cfrac{1\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{11}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}+\cfrac{11}{8}\implies \cfrac{(2)5~~ + ~~(1)11}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{10+11}{8}\implies \cfrac{21}{8}\implies 2\frac{5}{8}~miles[/tex]

The crime that is often alcohol related is domestic violence. That is option D.

Domestic violence is defined as an abusive relationship that exist between two or more individuals that are closely related by blood or marriage.

The causes of domestic violence include the following:

Therefore, alcohol intake can lead to domestic violence because it can cause the abusive partner to have a reduction in cognitive and physical functions that impair self-control, with the consequent effect of reducing the ability to resolve conflicts nonviolently.

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Answer:

Step-by-step explanation:

January, June, and July

are 3 months out of 12, which equals 1/4 (12 : 3 = 4),

1/4 equals 25% (100 : 4 = 25%)

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Tom traveled for 4 hours by train and 4 hours by plane, for a total trip time of 8 hours.

We have,

Let's call the number of hours Tom traveled by train t.

Since he traveled the same number of hours by plane, he also traveled for t hours at 275 mph.

The total distance he traveled is given by the sum of the distances traveled by train and by plane:

Distance by train = 50t

Distance by plane = 275t

Total distance = 1300

So we can set up the equation:

50t + 275t = 1300

Simplifying and solving for t, we get:

325t = 1300

t = 4

Therefore,

Tom traveled for 4 hours by train and 4 hours by plane, for a total trip time of 8 hours.

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The value of x in the intersecting secant and tangent lines is 40 degrees

From the question, we have the following parameters that can be used in our computation:

Intersecting secant and tangent lines

Using the theorem of intersecting secant and tangent lines, we have

x = 1/2 * difference of the arcs

Substitute the known values in the above equation, so, we have the following representation

x = 1/2 * (170 - 90)

Evaluate

x = 40 degrees

Hence, the value of x is 40

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Answer:

16

Step-by-step explanation:

2×2×2×2=16

So, the answer is 16.

Answer:

False. The product of two negative integers is a positive integer.

Answer:

2.25 units³

Hope this helps!

Step-by-step explanation:

The formula, base, and height are already given so all you have to do is multiply 2 with [tex]3\frac{3}{8}[/tex].

2 × [tex]\frac{9}{8}[/tex]  =  [tex]\frac{9}{4}[/tex]  =  2.25 units³

The evaluation of the function gives 16.

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To evaluate the  function f(x) =80/4x-3, we need to substitute the value of the input (i.e. x = 2). Thus:

f(x) = 80/(4x-3)

f(2) = 80/(4*2 - 3)

f(2) = 80/(8 - 3)

f(2) = 80/5

f(2) = 16

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The maximum value above is 46 at (2, 6). The production output goal which refers to the maximisation of profits relative to production is described by the objective function.

The production output goal which refers to the maximisation of profits relative to production is described by the objective function, which is a mathematical equation. The quantity of the final result is then calculated using the correlation between the variables. In other words, it's a formula that companies employ to meet their production and profitability objectives.

F = 5x + 6y

The coordinates of the feasible region are (0, 6), (1, 6.5) and (2, 6)

Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation

F(0, 6) = 5(0) + 6(6) = 36

F(1, 6.5) = 5(1) + 6(6.5) = 44

F(2, 6) = 5(2) + 6(6) = 46

The maximum value above is 46 at (2, 6)

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The lateral surface area of the cylinder is approximately 175.84 square meters.

We have,

The lateral surface area of a cylinder.

= 2πrh

where r is the radius of the base, h is the height of the cylinder, and π is approximately 3.14.

Now,

r = 2 m, h = 14 m

Substituting these values in the formula, we get:

Lateral surface area = 2πrh

= 2 x 3.14 x 2 x 14

= 175.84 m² (rounded to the nearest tenth)

Therefore,

The lateral surface area of the cylinder is approximately 175.84 square meters.

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The quantity of candy that Eric ate would be = 14/15

The quantity of Candy Kim had = 2⅓ pounds.

The quantity of Kims candy that Eric ate = 2/5

That is 2/5 of 2⅓.

The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15

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The probability that a random point on the AK line will be on the BE line is 0.5 or 50%, since the length of the BE line is 10 units and the length of the AK line is 20 units.

To find the probability that a random point on the AK line will be on the BE line, we need to determine the length of the BE line and the length of the AK line.

The BE line extends from point -5 to point 5, a distance of 5 - (-5) = 10 units.

The AK line extends from point -10 to point 10, a distance of 10 - (-10) = 20 units.

Therefore, the probability that a random point on the AK line will be on the BE line is

Length of BE line / Length of AK line = 10 / 20 = 0.5

So, the probability that a random point on the AK line will be on the BE line is 0.5 or 50%.

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Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

Answer:

P((1 + r)^4) = 1,300

P((1 + r)^7) = 1,525

-----------------------

(1 + r)^3 = 61/52, so r = .0547 = 5.47%

P(1.0547^4) = 1,300, so P = $1,050.78

According to the information, It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.

The situation is: two friends are having an argument because one of them forgot to invite the other to a party.

I can imagine that it must be really difficult for both of your friends right now. One of them might be feeling hurt and left out because they didn't get an invitation to the party, while the other might be feeling guilty and regretful for forgetting to invite them. It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.

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