Your retirement account earns 7%, compounded quarterly. How much must the account contain when you retire if you want to withdraw $4000 at the end of each quarter for 30 years? ANSWER: _______dollars Round your final answer to the nearest cent. Note: This is almost identical to example 3 (only the payment amount is different), so check out the example 3 video if you need help.
__________

The solution to the given system of equations is x = 2.67 and y = 5.

The given system of equations can be solved by adding the two equations together.


3x + 4y = 20
-6x - 8y = -38


Adding the two equations together, we get:

-3x - 4y = -18


Subtracting 3x from both sides, we get:

-4y = -20
y = 5


Substituting the value of y in either of the given equations, we get:

3x + 4(5) = 20
3x = 8
x = 8/3

x = 2.67

After solving system of equations is x = 2.67 and y = 5.

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Answer:

The surface area of the new prism increased by less than a scale factor of two.

Step-by-step explanation:

original prism:  S.A. = SA of 4 sides + Top + Bottom = 4(9x6) + 2 (3x6) = 252

scaled up prism:  SA = 4(18x6) + 2(3x6) = 468

height = 2(9) = 18

468/252 = 1.857 < 2

Step-by-step explanation:

so u could see that the yellow cab that will take Emma to airport is much more cheaper even though the entry price is a bit expensive .

Answer:

136cm²

Step-by-step explanation:

explanation in the screenshot

The probabilities are given as follows:

The probabilities are different, as the theoretical probability is higher.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

Out of 20 tosses, 4 resulted in heads, hence the experimental probability is given as follows:

p = 4/20

p = 1/5.

A coin is equally as likely to be heads or tails, hence the theoretical probability is given as follows:

p = 1/2.

Over a large number of trials, it is expected that the two probabilities assume close values, but for a small number of trials such as 20 it is expected for there to be differences.

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No, the inverse of a quadratic function is not a linear function.

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. The graph of a quadratic function is a parabola, which is a curved line.

The inverse of a function is a function that "undoes" the original function. In other words, if f(x) = y, then the inverse function, f^(-1)(x), would be such that f^(-1)(y) = x. The graph of the inverse of a function is a reflection of the original function across the line y = x.

Since the graph of a quadratic function is a parabola, the graph of its inverse would also be a parabola, but reflected across the line y = x. This means that the inverse of a quadratic function is also a quadratic function, not a linear function.

It is important to note that the inverse of a quadratic function may not be a function, as it may not pass the vertical line test. In this case, restrictions would need to be applied to the domain and range in order for the inverse to be a function. However, even with these restrictions, the inverse of a quadratic function would still not be a linear function.

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Answer:
To calculate the time at which they flash together we need to find the least common multiple of 3 and 8.

Multiples of 3 =

3 x 1 = 3​

3 x 2 = 6​

3 x 3 = 9​

3 x 4 = 12​

3 x 5 = 15​

3 x 6 = 18​

3 x 7 = 21​

3 x 8 = 24​

3 x 9 =27​

3 x 10 = 30

Multiples of 8 =

8 x 1 = 8​

8 x 2 = 16​

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40​

8 x 6 = 48

8 x 7 = 56​

8 x 8 = 64​

8 x 9 =72​

8 x 10 = 80

So LCM of 3 and 8 = 24

So both the lights will flash next at 7:24

Step-by-step explanation:

The probability distribution function of Y = |X| is given by:

P(Y ≤ y) = P(|X| ≤ y) = P(-y ≤ X ≤ y)

Since X ~ N(0, 2), we can use the standard normal distribution to find the probability;

P(Y ≤ y) = P(Z ≤ y/√2) - P(Z ≤ -y/√2)

where Z is a standard normal random variable.

To find E(|X|), we can use the formula:

E(|X|) = √(2/π) * σ

where σ is the standard deviation of X. Since X ~ N(0, 2), σ = √2, so:

E(|X|) = √(2/π) * √2 = √(4/π)

To find Var(|X|), we can use the formula:

Var(|X|) = E(X^2) - E(|X|)^2

Since X ~ N(0, 2), E(X^2) = σ^2 = 2. And we already found E(|X|) = √(4/π), so:

Var(|X|) = 2 - (4/π) = (2π - 4)/π

Therefore, the probability distribution function of Y = |X| is P(Y ≤ y) = P(Z ≤ y/√2) - P(Z ≤ -y/√2), the expected value of |X| is E(|X|) = √(4/π), and the variance of |X| is Var(|X|) = (2π - 4)/π.

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The probability of the sum of the two numbers being even can be calculated using the formula for the probability of independent events.
The formula for the probability of independent events is: P(A and B) = P(A) x P(B
In this case, A represents the first die and B represents the second die.

To calculate the probability of the sum being even, we need to consider the possible outcomes for each die that would result in an even sum.
For the first die, there are three possible outcomes that would result in an even sum: 1, 3, and 5. The probability of any of these outcomes occurring is 3/6, or 1/2.
For the second die, there are also three possible outcomes that would result in an even sum: 2, 4, and 6. The probability of any of these outcomes occurring is also 3/6, or 1/2.
Using the formula for the probability of independent events, we can calculate the probability of the sum being even:
P(A and B) = P(A) x P(B) = (1/2) x (1/2) = 1/4

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Therefore , the solution of the given problem of unitary method comes out to be in a group of 15, we would anticipate that 5 pupils would choose a candy.

To finish a job using the unitary method, divide the lengths of just this minute subsection by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait. There are changes and unanswered issues (mathematics, algebra).

Here,

There are a total of 12 sweets in the bag: 5 + 1 + 2 + 4 candies. Given that there are 4 gold-wrapped candies out of a total of 12, the chance of choosing one during any given draw is 4/12 = 1/3.

. Therefore, regardless of how many draws have been conducted before, the chance of choosing a gold-wrapped treat is always 1/3.

In a class of 15 pupils, the predicted proportion of students who would choose a gold-wrapped treat would be:

Expected number of gold-wrapped candies = (1/3) * (number of draws) * (probability of choosing gold-wrapped candy on one draw) = 5

Therefore, in a group of 15, we would anticipate that 5 pupils would choose a candy that was wrapped in gold.

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Answer:

The answer is -4

Step-by-step explanation:

The slot of the line can be calculated using the formula : y2 - y1/ x2 - x1.

So, you would plug in the values making the equation 5 - (-7)/ -1 - 2 and solve.

The circumference of the circle is approximately 31.4 cm to the nearest tenth.

Use this formula to get a circle's circumference:

C = 2πr

where C is the circumference, pi (roughly 3.14), is a mathematical constant, and r is the circle's radius.

If you have the diameter of the circle, you can find the radius by dividing the diameter by 2.

Once you have the radius, you can plug it into the formula to find the circumference.

For example, if the radius is 5 cm:

C = 2πr

C = 2 x 3.14 x 5

C = 31.4

So the circumference of the circle is approximately 31.4 cm to the nearest tenth.

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Answer:

To find the coordinates of the root of the equation y = 3 + 2x - x^2, we need to find the values of x where y = 0 (because the root is the point where the function intersects the x-axis). So we can set y equal to 0 and solve for x:

0 = 3 + 2x - x^2

Rearranging, we get:

x^2 - 2x - 3 = 0

We can factor the quadratic equation by finding two numbers that add up to -2 and multiply to -3. These numbers are -3 and 1, so we can write:

(x - 3)(x + 1) = 0

This equation is true when either x - 3 = 0 or x + 1 = 0. So the roots of the equation are:

x = 3 or x = -1

Therefore, the coordinates of the roots of the equation y = 3 + 2x - x^2 are (3, 0) and (-1, 0).

Answer:

12345,13345,14345,15345,16345

Step-by-step explanation:

A linear function is a polynomial function with a degree of 1, and a degree 4 polynomial function is a polynomial function with a degree of 4. The leading coefficient of a polynomial function is the coefficient of the term with the highest degree. The y-intercept of a graph is the point where the graph crosses the y-axis.

To create the linear function, h(x), we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept can not be 0, we can choose a value for b that is not 0. For example, b = 2. We can also choose a value for m that is not 0, so that h(x) is not a horizontal or vertical line. For example, m = 3. Therefore, h(x) = 3x + 2.

To create the degree 4 polynomial function, P(x), we can use the factored form: P(x) = a(x - r1)(x - r2)(x - r3)(x - r4), where a is the leading coefficient, and r1, r2, r3, and r4 are the zeros of the function. Since the leading coefficient can not be |1|, we can choose a value for a that is not 1 or -1. For example, a = 2. Since one of the factors must be repeated 2 times, we can choose a value for r1 and set r2 equal to r1. For example, r1 = 1 and r2 = 1. Since one of the zeros must be a fraction, we can choose a value for r3 that is a fraction. For example, r3 = 1/2. Since the zeros should have a mix of positive and negative numbers, we can choose a value for r4 that is negative. For example, r4 = -2. Therefore, P(x) = 2(x - 1)(x - 1)(x - 1/2)(x + 2).

To find the points of intersection between h(x) and P(x), we can set h(x) equal to P(x) and solve for x:
3x + 2 = 2(x - 1)(x - 1)(x - 1/2)(x + 2)
This equation can be solved algebraically by expanding the right-hand side and rearranging the terms to form a degree 4 polynomial equation. Then, we can use the Rational Root Theorem and synthetic division to find the possible rational roots of the equation. Once we find the rational roots, we can use them to factor the equation and find the remaining roots. The x-coordinates of the points of intersection are the roots of the equation.

To determine the intervals when h(x)≥P(x), we can use the points of intersection and the signs of h(x) and P(x) on either side of the points of intersection. If h(x) is greater than or equal to P(x) on an interval, then the graph of h(x) is above or coincident with the graph of P(x) on that interval. We can use a sign chart or a graph to determine the intervals when h(x)≥P(x).

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Answer:

(x+4)^2=4

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

This is an example of a biased sample, because the sample was not chosen at random from the entire population. It is possible that certain groups of people were more likely to have their names drawn from the hat, such as people who were sitting near the person doing the drawing.

To predict how many guests at the party have blonde hair, we can use the proportion of people in the sample who had blonde hair (3 out of 8), and apply it to the entire population of 200 guests:

(3/8) x 200 = 75

Therefore, we can predict that approximately 75 guests at the party have blonde hair.

Answer:

1. Unbiased sample

2. 75

The system of linear equations will be 2x+3y=8,  4x+6y=15.

Which mathematical equation is the most challenging?

A mathematics issue have baffled the finest scientists in the world for decades. The Diophantine equation x3+y3+z3=k, where k is the sum of all of the numbers from 1 to 100, is sometimes referred to as the "sum of three cubes."

What is an equation's most basic form?

The lowest corresponding fraction of the integer is its simplest form. How to determine the simplest form: Look for shared components in the denominator and numerator. Verify if a fractional integer includes a prime number.

For example:

2x+3y=8

4x+6y=15

Part C:

Using the example above,

2x+3y=8

4x+6y=15

If we multiply the first equation by , we get:

4x+6y=16

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In a statistical test, the goal is to determine whether the null hypothesis (H0) is true or false based on the observed data. In this case, the null hypothesis is that the difference between the two population means (????T and ????????) is equal to zero, and the alternative hypothesis (H1) is that the difference is greater than zero.

The investigator initially compares the observed probability (Pobs) with the significance level (????) to make her decision. If Pobs is less than ????, then the null hypothesis is rejected, and if Pobs is greater than ????, then the null hypothesis is not rejected.

If the investigator had instead compared the observed test statistic (tobs) with the critical value (tcrit), she would have made the same decision. This is because the critical value is determined based on the significance level, and the test statistic is determined based on the observed data. If the test statistic is greater than the critical value, then the null hypothesis is rejected, and if the test statistic is less than the critical value, then the null hypothesis is not rejected.

Since the decision to reject or not reject the null hypothesis is based on the same criteria (whether the observed value is greater than or less than a predetermined value), the decision would be the same whether the investigator compares Pobs with ???? or tobs with tcrit.

In conclusion, the investigator would have made the same decision had she compared tobs with tcrit instead of Pobs with ???? because both methods are based on the same criteria for rejecting or not rejecting the null hypothesis.

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Answer:

35%

Step-by-step explanation:

26/40 = 0.65
1-0.65=35

The values of the x in all triangles are:

1) x = 15. (2) x = 8. (3) x = 3. (4) x = 11.95. (5) x = √-5. (6) x = √104.

The Pythagorean theorem consists of a formula a²+b²=c² which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent).

1) In this triangle:

Adjacent = 9mi

Opposite = 12 mi

Hypotaneous = x

so, x² =  (9)² + (12)²

x = √81 + 144

x = 15.

2) In this triangle:

Adjacent = x

Opposite = 6 in

Hypotaneous = 10 in

so, (10)² =  (x)² + (6)²

√100 - 36 = x

x = 8.

3) In this triangle:

Adjacent = x

Opposite = 4 ft

Hypotaneous = 5 ft

so, (5)² =  (x)² + (4)²

√25 - 16 = x

x = 3.

4) In this triangle:

Adjacent = x

Opposite = 5 yard

Hypotaneous = 13 yard

so, (13)² =  (5)² + (x)²

√168 - 25 = x

x = 11.95.

5) In this triangle:

Adjacent = x

Opposite = √13 mi

Hypotaneous = 2√2 mi

so, (2√2 )² =  (√13)² + (x)²

8 - 13 = x

x = √-5.

6)  In this triangle:

Adjacent = 13 yd

Opposite = √65 yd

Hypotaneous = x

so, (x)² =  (13)² + (√65 )²

169 - 65 = x

x = √104.

Hence, The values of the x in all triangles are:

1) x = 15. (2) x = 8. (3) x = 3. (4) x = 11.95. (5) x = √-5. (6) x = √104.

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Answer:

60

Step-by-step explanation:

Colton is 60 because Polly is 21 and plus 39 is 60.

The pair of expressions which represents the price of an order that was originally x dollars are x - 0.15x and 0.85x

Percentage discount = 15%

Original price of an order = x dollars

New price = Original price of an order - (Percentage discount × Original price of an order)

= x - (15% of x)

= x - 0.15x

= 0.85x

Therefore, x - 0.15x and 0.85x are the expressions which represent the price of an order that was originally x dollars

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Using prοperties οf quadrilaterals, The line segment in the image that cοrrespοnds tο BC¯¯¯¯¯ in the pre-image is the line segment FG¯¯¯¯¯.

A pοlygοn with fοur sides and fοur vertices is called a quadrilateral (cοrners). It is a twο-dimensiοnal οbject that is flat and can take οn a number οf fοrms.

We knοw that matching sides οf the pre-image and image are identical in length since a reflectiοn maintains the size and shape οf the figure.

Since a reflectiοn preserves the shape and size οf the figure, we knοw that cοrrespοnding sides οf the pre-image and image are equal in length.

Therefοre, the line segment in the image that cοrrespοnds tο BC¯¯¯¯¯ in the pre-image is the line segment FG¯¯¯¯¯.

Tο see why, imagine fοlding the figure alοng the line οf reflectiοn sο that the pre-image and image cοincide. In this fοlded pοsitiοn, the cοrrespοnding sides οf the twο quadrilaterals will be οn tοp οf each οther. In particular, side BC¯¯¯¯¯ οf the pre-image will be οn tοp οf side FG¯¯¯¯¯ οf the image, cοnfirming that FG¯¯¯¯¯ cοrrespοnds tο BC¯¯¯¯¯ in the pre-image.

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B' is the reflection of the x-axis at position B(1,3) (1,-3) as a consequence of B (1, 3) being reflected over the x-axis.

A coordinate is a group of integers used to describe a point's location in space in mathematics. Cartesian coordinates are the most widely used form of coordinates. They are made up of an ordered pair of numbers (x, y) that represent a point's horizontal and vertical distances from a constant point of reference known as the origin. The y-coordinate indicates the point's vertical distance from the origin, while the x-coordinate represents the point's horizontal distance from it.

given

The x-coordinate remains constant while the sign of the y-coordinate varies when a point is reflected over the x-axis.

Therefore, we only need to alter the sign of the y-coordinate of B in order to determine the reflection B' of the point B(1,3) over the x-axis.

B' is the reflection of the x-axis at position B(1,3) (1,-3) as a consequence of B (1, 3) being reflected over the x-axis.

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figure 1: length of sides are, 5[tex]\sqrt{2}[/tex] and 5

figure 2: height is 8[tex]\sqrt{3}[/tex] and base is 8

A triangle, with three sides, three angles, and three vertices, is one of the most fundamental and straightforward shapes in geometry. Any of the three sides and angles of a triangle can have various measurements. Depending on their angle dimensions and side lengths, triangles can be classified into various categories.

Equilateral triangles, for instance, are triangles with three equal sides and three equal 60-degree angles.

Right triangles, on the other hand, have one 90-degree angle, and the side opposite the right angle is known as the hypotenuse, with the other two sides called legs.

Isosceles triangles, whose two sides and angles are equal.

The values of figure 1: the angles are 45° 90° and 45° So, we can use right angle triangle and isosceles triangle rules in figure therefor, the base is 5[tex]\sqrt{2}[/tex] and other side is same as the another side which is 5.

Check the solution from the figure.

figure 2: height is 8[tex]\sqrt{3}[/tex] and base is 8

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Answer:

Step-by-step explanation:

It is given that ,

tanA=3/4 , [tex]\pi < A < \frac{3\pi }{2}[/tex]

so , angle are in 3rd Quadrant .

cosB = -15/17 ,[tex]\frac{\pi}{2} < B < \pi[/tex]

So, angle B are in 2nd Quadrant

We use Compound formula of tan(A+B)

[tex]tan(A+B) = \frac{tanA + tanB}{1- tanAtanB}[/tex]         ..........(1)

To use this formula , we need to find the value of tanA and tanB.

tanA = 3/4   ........ given

cos B =-15/17

Using Identity ,

[tex]sin^{2}B + cos^{2}B=1[/tex]

put the value of cosB

[tex]sin^{2}B + (-\frac{15}{17})=1\\ sin^{2}B = 1 - \frac{225}{289} \\sin^{2}B = \frac{64}{289} \\sinB = \frac{8}{17}[/tex]

we know that ,

tanB = sinB/cosB

put the value of sinB and CosB

[tex]tanB = \frac{\frac{8}{17} }{-\frac{15}{17}} \\tanB = - \frac{8}{15}[/tex]

[tex]tanB = -(-\frac{8}{15}) \\tanB = \frac{8}{15}[/tex]the value of tan in 2nd quadrant are negative .

We find the value of tanB and next we put the value of tanA and tanB in

equation(1)

[tex]tan(A+B) = \frac{tanA + tanB}{1- tanAtanB}\\tan(A+B) = \frac{\frac{3}{4}+\frac{8}{15}}{1 - \frac{3}{4}\frac{8}{15} } \\tan(A+B) = \frac{\frac{77}{60} }{1 - \frac{24}{60} } \\tan(A+B) = \frac{\frac{77}{60} }{\frac{36}{60} } }\\tan(A+B) = \frac{77}{36}[/tex]

Hopeful,this answer will help you!

If any wrong in this answer please let me know

A company will make a profit of 63.9%

Here, the cost of making pins = £1.10

the number of pins = 1000

Using unitary method, the total cost for making 1000 pins would be,

= Cost of each pin × Number of pins

= 1.10 × 1000

= £1110

Now we find the number of pins that sold in charities.

35 percent of pins in charities.

Using percentage formula, we find 35% of total number of pins.

= 35% of 1000

= (35/100) × 1000

= 350 pins

This means that 350 pins were sold in charities.

So, the number of pins left = 1000 - 350

                                          = 650 pins

Out of these remaining pins, 60% are sold at £3. 00 each

So, the number of pins sold at £3.00:

= 60% of 650

= (60/100) × 650

= 390

And the selling price of these 390 pins would be:

= 390 × £3.00

= £1170                           .................(1)

40% of 650 pins were sold at £5. 00 for 2

So, using percentage formula the number of pins sold at £5.00 for 2 would be:

= 40% of 650

= (40/100) × 650

= 260

These 260 pins were sold in pairs for £5.

Therefore, number of pairs sold

= 260/2

= 130 pairs

The selling price of these 130 pairs of pins would be,

= 130 × 5.00

= £650                    ...............(2)

Therefore, from (1) and (2) the total selling price would be,

= £1170 + £650

= £1820

So, the Profit would be:

= Selling price - Cost price

= 1820 - 1110

= £710

Now using  we find the profit percentage:

= Profit × 100 / Total cost price

= 710 × 100 / 1110

= 63.9%

Therefore, the required percentage profit = 63.9%

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All of the functions have a constant rate of change since they are linear functions with a slope (rate of change) that is equal to the coefficient of the independent variable. Therefore, all functions have a constant rate of change of their slope.

Option A: y = 6(2) = 12 has a slope of 6, which means it increases by 6 for every unit increase in x.

Option B: y = 2(3) = 6 has a slope of 2, which means it increases by 2 for every unit increase in x.

Option C: y = 3(4) = 12 has a slope of 3, which means it increases by 3 for every unit increase in x.

Option D: y = 4(2) = 8 has a slope of 4, which means it increases by 4 for every unit increase in x.

Therefore, option A has the most rapid rate of change with a slope of 6.

Answer:

the ans the last person gave is very correct

20c2 + 10c = {c | c ≠ 0}

The sets for these two rational expressions are as follows:


22x + 11 x2 – 3x – 10 = {x | x ≠ 1/2}


1 – 2c = {c | c ≠ 1/2}


20c2 + 10c = {c | c ≠ 0}


To simplify the expressions, use the following steps:


1. Factor out the greatest common factor (GCF) if one exists.


2. Simplify the numerator and denominator separately.


3. Combine the numerator and denominator.

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