In what year will the two quantities be​ equal?

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

Answer: 1 To find the sampling distribution of the sample mean, we need to use the Central Limit Theorem. According to the Central Limit Theorem, for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

In this case, the population has a normal distribution with a mean of 87 minutes and a standard deviation of 22 minutes. Since the sample size is large (25), we can assume that the sampling distribution of the sample mean will be approximately normally distributed with the same mean but a smaller standard deviation.

To calculate the standard deviation of the sampling distribution (also known as the standard error), we divide the population standard deviation by the square root of the sample size:

Standard Error = Population Standard Deviation / √(Sample Size)

Standard Error = 22 / √(25)

Standard Error = 22 / 5

Standard Error = 4.4 minutes

Therefore, the sampling distribution of the sample mean has a mean of 87 minutes (same as the population mean) and a standard deviation of 4.4 minutes.

3 To determine the sample size needed to achieve a desired margin of error and confidence level, we can use the formula:

Sample Size = (Z-score)^2 * (p * (1 - p)) / (E^2)

In this case, the desired margin of error is 3% (0.03) and the confidence level is 90%, which corresponds to a Z-score of 1.645.

Sample Size = (1.645)^2 * (0.5 * (1 - 0.5)) / (0.03^2)

Sample Size = 2.705 * 0.25 / 0.0009

Sample Size = 6.762 / 0.0009

Sample Size = 7513.33

Therefore, approximately 7514 students should be surveyed to achieve a 90% confidence level with a margin of error of 3%.

5. To test the hypothesis about the population mean lifetime of batteries, we can perform a one-sample t-test.

Null hypothesis (H0): The population mean lifetime of batteries is 50 hours.

Alternative hypothesis (H1): The population mean lifetime of batteries is not 50 hours.

We are given that the sample mean lifetime for a sample of nine batteries was 48.2 hours. The population standard deviation is 3 hours.

Using a significance level of 0.01, we can calculate the t-value and compare it to the critical t-value from the t-distribution with (n-1) degrees of freedom.

t-value = (Sample Mean - Population Mean) / (Sample Standard Deviation / √n)

t-value = (48.2 - 50) / (3 / √9)

t-value = -1.8 / (3 / 3)

t-value = -1.8

With a significance level of 0.01 and (n-1) degrees of freedom (n-1 = 9-1 = 8), the critical t-value is approximately ±2.896.

Since the calculated t-value (-1.8) does not exceed the critical t-value of ±2.896, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population mean lifetime of batteries is significantly different from 50 hours at the 0.01 level of significance.

6.To test the hypothesis about the proportion of customers who cannot distinguish the wine producer's product, we can perform a one-sample proportion test.

Null hypothesis (H0): The proportion of customers who cannot distinguish the product is 0.09 or less.

Alternative hypothesis (H1): The

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

84 = 3 x 28

56 = 2 x 28

Minimum number of square plot, each square is 28 x 28

the number is 3 x 2 = 6

The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.

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Maci and 2 appointments and Logan had 3 appointments.

The linear equation that represents the total amount earned by Maci is:

Total amount earned = (amount per appointment x number of appointments)  + tips

$170 = ($60 x a) + $50

$170 = $60a + $50

$170 - $50 = $60a

$120 = $60a

a = $120 / $60

a = 2

The linear equation that represents the total amount earned by Logan is:

Profit = total revenue - total cost

Profit = (fee per appointment  x number of appointments) + amount received in tips - (rental fee x number of appointments)

$235 = ($75 x a) + $40 - ($10 x a)

$235 = $75a + $40 - $10a

$235 = $65a + $40

$235 - $40 = $65a

$195 = $65a

a = $195 / 65

a = 3

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The current market price for the bond is $870 the yield to maturity is 14.13%

The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)

knowing that:

the formula is:

\(P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n\)

Putting the values:

\($870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13\)

Using the math we find that the percentage is  approximately 14.13%;

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Step-by-step explanation:

those are 4 and 5s I swear

Answer:

\(\frac{3x+7}{x+2}\)

Step-by-step explanation:

Given the following question:

\(\frac{(x+4)(3x+7)}{(x+4)(x+2) }\)

In order to simplify the expression given we can only cancel the common factor which is four.

\(\frac{(x+4)(3x+7)}{(x+4)(x+2) }\)
\(cf=(x+4)\)
\(\frac{x+4}{x+4}\)
\(=\frac{3x+7}{x+2}\)

Cannot be simplified further due to it not having any more common factors. Your answer is "3x + 7 / x + 2."

Hope this helps.

Answer:

( 3x+7 ) / ( x+2 )

Step-by-step explanation:

\frac{(x+4)(3x+7)}{(x+4)(x+2)}

When you set up the equation like a fraction, you can now cancel out like terms. (x+4) is in the denominator- as well as the numerator. They are the same in parentheses. So you can cancel. Once that's done, you'll be left with

\frac{3x+7}{x+2}

You cant simplify any further because there are no more (like groups) aka (common factors)

( 3x+7 ) / ( x+2 )

Answer:

b. f(3.5) = 52

Hope this helps!

The number of lights L that are on after t minutes of the stage shows is,

A. L = (1/2)t + 10.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, When the show starts, 10 lights are on which is a constant in out function.

Every 30 seconds or (1/2) a minute 1 more light comes on.

∴  The function best models the number of lights that are on after t minutes of the stage shows is,

L = (1/2)t + 10.

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Answer:

21

Step-by-step explanation:

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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My own multi-step combination problem is given below:

To solve this problem, Amanda  need to use the formula for combinations and it is:

nCr = n! / (r! x (n-r)!)

where:

n = total number of items to select from

r is the number of items to select.

First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:

5C3

=  5! / (3! x (5-3)!)

= 10

Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be

4C2

= 4! / (2! x  (4-2)!)

= 6

Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:

3C2

= 3! / (2! x  (3-2)!)

= 3

To have the total number of dinner menus, we have to multiply these three numbers together:

= 10 x 6 x 3

= 180

Therefore, one can say that Amanda have 180 different dinner menus that she can be create.

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Answer:

Step-by-step explanation:

solve for a from the given equation: 7a - 6 = a² + 4

a² - 7a + 10 = 0

the equation can be solved using quadratic equation: ax² + bx + c = 0

x₁,₂ = - b ± √(b² - 4ac)

                2a

where a = 1

           b = -7

           c = 10

now, plug in values into the formula:

a₁,₂ = - (-7) ± √(-7² - 4(1)10)

                  2(1)

a₁   = 7 + 3   = 10  =  5

            2          2

a₂   = 7 - 3   = 4  =  2

           2          2

therefore, the answer to the equation is:

a = 5 ;  a = 2

Answer:

The time taken for the upward motion is 1 second. The same time is taken for the downward motion

It reaches a maximum height of 4.9 meters.

Step-by-step explanation:

The equation of motion is:

\(x(t) = -4.9t^{2} + 9.8t\)

Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.

Vertex of a quadratic equation:

Quadratic equation in the format \(x(t) = at^{2} + bt + c\)

The vertex is the point \((t_{v}, x(t_{v}))\), in which

\(t_{v} = -\frac{b}{2a}\)

In this question:

\(x(t) = -4.9t^{2} + 9.8t\)

So \(a = -4.9, b = 9.8\)

Vertex:

\(t_{v} = -\frac{9.8}{2*(-4.9)} = 1\)

The time taken for the upward motion is 1 second.

\(x(t_{v}) = x(1) = 9.8*1 - 4.9*(1)^{2} = 4.9\)

It reaches a maximum height of 4.9 meters.

Downward motion:

From the vertex to the ground.

The ground is t when x = 0. So

\(-4.9t^{2} + 9.8t = 0\)

\(4.9t^{2} - 9.8t = 0\)

\(4.9t(t - 2) = 0\)

\(4.9t = 0\)

\(t = 0\)

Or

\(t - 2 = 0\)

\(t = 2\)

It reaches the ground when t = 2 seconds.

The downward motion started at the vertex, when t = 1.

So the duration of the downward motion is 2 - 1 = 1 second.

Hey there!

Solve for x :

x = 6 ✅

3x - 2 = 16

>> Add 2 to both sides :

3x - 2 + 2 = 16 + 2

3x = 18

>> Divide each side by 3 :

3x / 3 = 18 / 3

x = 6

▪️Let's verify :

3(6) - 2 ⇔18 - 2 ⇔ 16

Therefore, your answer is x = 6

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3x−2=16

Add 2 to both sides.

3x=16+2

Add 16 and 2 to get 18.

3x=18

Divide both sides by 3.

x = 18 /3

Divide 18 by 3 to get 6.

x = 6 ===> Answer

Let x = 6

3×6−2=16

18-2= 16

16 = 16

Checked ✅

Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

Answer:

\( \frac{1}{8} \)

Step-by-step explanation:

The total amount of cards is 8, and the stack have 4 even numbers, so the probability is

4/8 Simplify it and

1/2

Now, there are just 6 cars bigger than 6, so:

2/8. Simplify it

1/4

Now you have to multiply the two values:

1/2×1/4 = 1/8

The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than \($\frac{4500}{22}\)=204.545

\($$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$\)

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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hello

the question here is a given quadratic equation and we're required to use quadratic formula to solve it.

now, to solve this, let's bring out quadratic formula first

now from our equation given, we can easily identify a, b and c.

next we plug in the variables into the equation and solve

Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

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Answer:

(0,-3)

Step-by-step explanation:

Answer: The second number goes on your X axis and the first number goes on your Y axis .

Step-by-step explanation:

(0,0)=Y,X

Answer:

44.44

Step-by-step explanation:

Answer:

9kg

Step-by-step explanation:

Because it is said that Polly's mass is 3kg but, Barney's mass is 3 times more kg than Polly.

So we multiply 3 (Polly's mass) multiplied by 3(cuz it is said three times more). So 3*3 = 9kg

let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so

\(\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}\)

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

Using central angle theorem,

The measure of the arc BC = 110°.

An angle with its vertex in the middle of the circle it creates with its two radii is said to be central.

Here in the question,

As per the central angle theorem:

(2x -30) ° + x° = 180°

⇒ 2x - 30 + x = 180

⇒ 3x - 30 = 180

Adding 30 on both sides:

⇒ 3x = 180 + 30

⇒ 3x = 210

Dividing both sides by 3.

⇒ x = 70°

Now BC = 2x-30

= 2 × 70 -30

= 140 - 30

= 110°

Therefore, the measure of BC = 110°.

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The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.

To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:

Area = (1/2) * a * b * sin(C),

where a and b are the lengths of the two sides adjacent to the given angle C.

In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:

c² = a² + b² - 2ab * cos(C),

where C is the angle opposite side c. Rearranging the formula, we have:

b² = a² + c² - 2ac * cos(C),

b² = 86² + 37² - 2 * 86 * 37 * cos(128°).

By substituting the given values and calculating, we find b ≈ 63.8.

Now, we can calculate the area using the formula:

Area = (1/2) * a * b * sin(C),

Area = (1/2) * 86 * 63.8 * sin(128°).

By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.

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