Scott borrowed money from the bank for repairs at an 8% interest rate, At the end of 1 year, he owed a total of $7992 in principal and interest. How much money did he borrow? a) Write the model first b) solve the equation.

The standard equation of parabola that has focus (5, 0) and directrix x = -5 is y² = 20x.

We have,

focus of the parabola is (5, 0).

Directrix x = -5

The standard equation of parabola,

(y - k)² = 4 p (x  - h)

where Vertex = (h, k)

So, (h, k)

= ((x coordinate of focus + directrix)/2 , 0)

= ((5 - 5)/2, 0)

= (0, 0)

and, p = distance from focus to the vertex = 5 - 0 = 5

Thus, The required equation of parabola,

(y - 0)² = 4 × 5(x - 0)

y² = 20x

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The average return for Stock A over the 5-year period is -6.2%.

The returns for each year are 0%, -18%, -14%, 10%, and -9%. Adding these returns together gives us (-18) + (-14) + 10 + (-9) = -31%.

Next, we divide the sum by the number of years, which is 5.

∴  \(\frac{-31}{5}\)= -6.2%.

Hence, the average return for Stock A over the 5-year period is -6.2%. This means that, on average, the stock experienced a 6.2% decrease in value each year during this period.

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The required probability of the coin landing tails up at least two times is 15/16.

Given that,
A fair coin is flipped seven times. what is the probability of the coin landing tails up at least two times is to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
In the given question,
let's approach inverse operation,
The probability of all tails  = 1 / 2^7 because there is only one way to flip these coins and get no heads.
The probability of getting 1 head = 7 /2^7
Adding both the probability = 8 / 2^7
Probability of the coin landing tails up at least two times = 1 - 8/2^7
                                                                                     = 1 - 8 / 128
                                                                                     = 120 / 128
                                                                                     = 15 / 16

Thus, the required probability of the coin landing tails up at least two times is 15/16.

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Tyler charges $8 for an adult ticket.

It is given that Tyler charges $t for adult tickets and $5 for child tickets.

No. of tickets sold by him on Monday is 12 child tickets and 9 adult tickets.

No. of tickets sold by him on Tuesday is 20 child tickets and 4 adult tickets.

Therefore,

Tyler earned $12 X 5 + $9 X t on Monday

= $9t + $60

Tyler earned $20 X 5 + $4 X t on Tuesday

= $4t + $100

According to the problem, the earnings on both the days are same. Hence we get the linear equation as follows

9t + 60 =  4t + 100

bringing all the variables, i.e t's to LHS and constants to RHS we get

9t - 4t = 100 - 60

or, 5t = 40

Bringing 5 to RHS we get

t = 40/5

or, t = 8

Therefore, t = $8

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2.8x+8.7

Step-by-step explanation:

-2.1x+3.7+5+4.9x

=2.8x+8.7

Answer:

5

Step-by-step explanation:

20/4 = 5

Answer:

-14

Step-by-step explanation:

2- (7+5 - (-4))      ---- add 7 and 5

2 - (12 - (-4))       ----- subtract -4 from 12

2 - 16

= -14

We will use PEMDAS to solve this equation.

2-[7+5-(-4)]

2-[12-(-4)]

2-[16] You can remove the brackets at this point, if you want.

-14

Answer: -14

Answer: 150 <= x < 250

Step-by-step explanation:

A number, x, rounded to 1 significant figure is 200

Write down the error interval for x

Rounding x to 1 significant figure means that all subsequent digits after the first is rounded down to zero(0) (if the immediate number after the first is digit 5 or more, it is rounded to 1 and added to the first digit).

Answer:

The square root of 7250 is 85.15

Step-by-step explanation:

\({ \boxed{ \sf{7250}}} \\ ↓ \div 2 \\ { \boxed{ \sf{3625}}} \\ ↓ \div 5 \\ { \boxed{ \sf{725}}} \\ ↓ \div 5 \\ { \boxed{ \sf{145}}} \\ ↓ \div 5 \\ { \boxed{ \sf{29}}}\)

Find square roots of divisors:

\({ \sf{ = \sqrt{2} \times \sqrt{5 \times 5 \times 5} \times \sqrt{29} }} \\ = { \sf{ \sqrt{2} \times \sqrt{125} \times \sqrt{29} }} \\ = { \sf{85.15}}\)

\({ \underline{ \sf{ \blue{christ \:† \: alone }}}}\)

The value of x is 8

The theorems of triangle are the rules that governs solving mathematical problems. Part of this theorem is a theorem that states that: The line joining the midpoint of the two sides of a triangle is parallel to the base.

Therefore ;

If we represent a side by y, using similar triangle,

y/2y = x+8/(3x+8)

1/2 = x+8/(3x+8)

3x +8 = 2(x+8)

3x +8 = 2x +16

collect like terms

3x-2x = 16-8

x = 8

therefore the value of x is 8

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Answer:

line b

Step-by-step explanation:

go up 4 and over 3 on line b

Debbie can buy a maximum of 4 t-shirts with the remaining $38 after purchasing the $22 jeans.

To determine the greatest number of t-shirts Debbie can buy, we need to find out how much money she will have left after purchasing the pair of jeans. Debbie has $60 to spend and the jeans cost $22. Therefore, she will have $60 - $22 = $38 left to spend on t-shirts.

Each t-shirt costs $8, so we divide the remaining amount by the cost per t-shirt: $38 / $8 = 4.75.

Since Debbie cannot buy a fraction of a t-shirt, we round down the decimal value to the nearest whole number. Therefore, Debbie can buy a maximum of 4 t-shirts with the remaining $38.

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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

45 ft i think im not sure sorry if im wrong

Step-by-step explanation:

An equation which can be used to solve the given system of equations is 3x⁵ - 5x³ + 2x² - 10x + 4 = 4x⁴ + 6x³ - 11.

Given the following data:

y = 3x⁵ - 5x³ + 2x² - 10x + 4

y = 4x⁴ + 6x³ - 11

A system of equations can be defined an algebraic equation that only has two (2) variables and can be solved simultaneoulsy.

Equating the given equations, we have:

y = y

3x⁵ - 5x³ + 2x² - 10x + 4 = 4x⁴ + 6x³ - 11

3x⁵ - 5x³ + 2x² - 10x + 4 - (4x⁴ + 6x³ - 11) = 0

3x⁵ - 5x³ + 2x² - 10x + 4 - 4x⁴ - 6x³ + 11 = 0

3x⁵ - 5x³ + 2x² - 10x + 4 - 4x⁴ - 6x³ + 11 = 0

3x⁵ - 4x⁴ - 11x³ + 2x² - 10x + 15 = 0

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Working

Q=k÷p

0•25=k÷2(cross multiply)

0•50=k or k=0•50

Answer

Q=0•50÷2

The function g is defined by:

g(u) = - (1/lambda) * ln(1 - u) for 0 < u < 1.

The random variable X = g(U) has the exponential (lambda) distribution.

(i) To create a random variable X that has cdf F, and you have a number picked uniformly on (0,1), you should do the following:

Let U be a uniform (0,1) random variable. To construct a random variable X=F^(-1)(U) so that X has the cdf F, take the inverse of the cdf F, denoted as F^(-1), and apply it to the uniformly distributed random variable U.

(ii) To find the function g for an exponential distribution with parameter lambda, you should set F as the exponential cdf, which is given by:

F(x) = 1 - e^(-lambda * x)

Now, you can find the inverse function F^(-1)(u):

1. Set u = F(x): u = 1 - e^(-lambda * x)
2. Solve for x: x = - (1/lambda) * ln(1 - u)

So, the function g is defined by g(u) = - (1/lambda) * ln(1 - u) for 0 < u < 1. The random variable X = g(U) has the exponential (lambda) distribution.

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Answer:

They Don't

Step-by-step explanation:

Answer:

GJ = 16

Step-by-step explanation:

The little vertical lines you see indicate that both GH and HJ have same magnitude. Therefore, GH = HJ. If GH = 8 then HJ = 8 as well.

Therefore, GJ = GH + HJ = 8 + 8 = 16 units.

According to the problem, a 1/3 cup of beans is equivalent to 4 servings. To know the number of cups of beans for 28 servings, we just have to use the rule of three.

Answer:

there is your answer hope that helps

Answer: (-2,-2)

Step-by-step explanation:

Start at finding the y-intercept(-3) then do rise over run with -2x

Rise over run is count up/down then left/right

The compound inequality describes the possible lengths for the third side, x is -4< c< 14.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as a trigon. Every triangle has three sides and three angles, with some of them being the same.

A triangle with A, B, and C vertices is symbolized by ΔABC

The Triangle Inequality Theorem states that given two triangle side lengths, the length of the third side must be greater than the difference and less than the sum of the two provided sides. The third side c of a triangle must be the same as the first two sides a and b:

(a - b) < c < (a + b)

As a result, let a = 5 and b = 9

(5-9) <c (5+9)

-4< c< 14

As a result, the third side of the triangle must follow the inequality, which is -4< c <14

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Answer:

It would be positive, zero, negative, and undefined (the first answer).

Hope this helps!

Point estimate from the sample is 0.985, margin error is 0.003.

Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.

(a) To calculate point estimate or sample mean :

Point estimate is the mid point of the confidence interval.

Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.

Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985

(b) Margin error is the one half of the total width of the interval.

Margin error = (0.988 - 0.982) / 2 = 0.003

(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.

Hence the point estimate and margin error are 0.985 and 0.003 respectively.

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The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Answer:

I think the answer is c = 25/4

Step-by-step explanation:

The value of a³+b³+c³ - 3abc is approximately 22910.68.

Given equations: a²+b²+c²=40, ab+bc+ca=12

To find: a³+b³+c³ - 3abc

Using the identity (a+b+c)(\(a^2+b^2+c^2-ab-bc-ca\)) = \(a^3+b^3+c^3-3abc,\) we can rewrite the expression as:

\(a^2+b^2+c^2-ab-bc-ca\)= (a+b+c)(\(a^2+b^2+c^2-ab-bc-ca\))

Substituting the given values into the above equation, we get:

\(a^3+b^3+c^3-3abc = (a+b+c)(40-12)\)

\(a^3+b^3+c^3-3abc = 28(a+b+c)\)

To find a+b+c, we can use the equation derived from the given equations: (\(a^2+b^2+c^2)^2 = 12^2 + 2abc(a+b+c)\)

Solving for abc(a+b+c), we get: abc(a+b+c) = 783

Substituting this value in the equation for\(a^3+b^3+c^3-3abc,\) we get:

\(a^3+b^3+c^3-3abc = 28(783/(a+b+c))\)

To find a+b+c, we can solve the equation derived earlier:

40^2 = 144 + 2abc(a+b+c)

\(a+b+c = (40^2 - 144)/1566\)

Substituting this value in the equation for\(a^3+b^3+c^3-3abc\), we get:

\(a^3+b^3+c^3-3abc ≈ 22910.68\)

Therefore, the value of a³+b³+c³ - 3abc is approximately 22910.68.

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