write a linear funtion f with f (-4)=2 and f (6)= -3 f(×)= ?
​

The investment οf $1,000 will be wοrth $1,225.04 after 3 years.

Cοmpοund interest is interest οn the principal amοunt οr lοan which is calculated accοrding tο the number οf cοmpοunds in οne year.

In this, the interest earned in each periοd is based οn the tοtal amοunt, which includes bοth the principal and the accumulated interest.

The fοrmula used fοr cοmpοund interest is

Here we have

The principal amοunt is $ 1000

The annual interest rate here is 7.5%  

The interest is cοmpounded annually.

The time periοd is 3 years  

Using the fοrmula,

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

A = 1,000 (1 + 0.075/1)⁽¹⁽³⁾⁾

= 1,000 (1.075)³

= $1,225.04  

Therefοre,

The investment of $1,000 will be wοrth $1,225.04 after 3 years.

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The number of solutions of the polynomial equation, 4x^(5)-8x^(4) +6x^(3)=0 is 5 and the solutions are x=0, x=3/2, and x=1.

The polynomial equation at hand is of degree 5, which means that the highest power of the variable present in any term is 5.

Therefore, we can infer that the equation can be written in the form of ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, where a, b, c, d, e, and f are constants and x is the variable. To solve this equation, we can try factoring it:

4x^(5)-8x^(4) +6x^(3)=0

2x^(3)(2x^(2)-4x+3)=0

2x^(3)(2x-3)(x-1)=0

The solutions are x=0, x=3/2, and x=1.

Therefore, the number of solutions of the polynomial equation is 5 and the solutions are x=0, x=3/2, and x=1.

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Two possible lengths of the bases of a trapezoid with a height of 1 foot and an area of 9 square feet are 6 feet and 12 feet, or 4 feet and 14 feet.

Let's denote the lengths of the two bases of the trapezoid as b1 and b2 (where b1 is the longer base), and the height as h = 1 foot. The formula for the area of a trapezoid is,

A = (b1 + b2) / 2 × h

Given that the area is 9 square feet, we can plug in the values and solve for one of the bases,

9 = (b1 + b2) / 2 × 1

9 = (b1 + b2) / 2

18 = b1 + b2

b2 = 18 - b1

We can substitute b2 in terms of b1 in the formula for the area to get:

9 = (b1 + (18 - b1)) / 2 × 1

9 = 18 / 2

9 = 9

This equation is true for any value of b1, which means that there are infinitely many possible trapezoids with a height of 1 foot and an area of 9 square feet. However, we can find two specific values of b1 that correspond to different trapezoids:

If we let b1 = 6 feet, then b2 = 18 - b1 = 12 feet. This trapezoid has bases of length 6 feet and 12 feet, and a height of 1 foot.

If we let b1 = 4 feet, then b2 = 18 - b1 = 14 feet. This trapezoid has bases of length 4 feet and 14 feet, and a height of 1 foot.

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Therefore, the retirement account must contain $2,758,686.58 when you retire in order to withdraw $4000 at the end of each quarter for 30 years.

To find the amount that the retirement account must contain when you retire, we can use the formula for the future value of an annuity due:

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

Where FV is the future value, PMT is the payment amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, PMT = $4000, r = 0.07, n = 4 (since the account is compounded quarterly), and t = 30.

Plugging these values into the formula, we get:

FV = 4000 * [(1 + 0.07/4)^(4*30) - 1] / (0.07/4) * (1 + 0.07/4)

FV = 4000 * [(1.0175)^120 - 1] / (0.0175) * (1.0175)

FV = 4000 * 11.9478 / 0.0175 * 1.0175

FV = $2,758,686.58

Therefore, the retirement account must contain $2,758,686.58 when you retire in order to withdraw $4000 at the end of each quarter for 30 years.

Round your final answer to the nearest cent, the retirement account must contain $2,758,686.58.

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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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We can rewrite y=[tex]5e^{-0.7t}[/tex] using the properties of exponents as follows:

y=[tex]5e^{-0.7t} =5(e^{-0.7)t} =5(\frac{1}{e^{0.7} })t[/tex]

We can recognize [tex]\frac{1}{e^{0.7} }[/tex] as a base for exponential function that can be written in the form 1 ±r We know that is an increasing function, so [tex]e^{0.7}[/tex]≥1

therefore [tex]\frac{1}{e^{0.7\\} }[/tex]≥1 which means we must use the form y=a[tex](1-r^){t}[/tex]

To find the percent rate of change, we can use the formula:

percent rate of change=|r|×100

So, the percent rate of change is:

=|0.503|×100

Rounding to the nearest tenth of a percent, we get a percent rate of change of approximately 50.3%.

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Statistically significant means that the relationship between two variables is likely to be real and not due to chance. If the p-value is lower than the predetermined threshold, usually 0.05, then the correlation is said to be statistically significant.

When a correlation between two variables is said to be statistically significant, it means that the relationship between the two variables is not due to chance or random error. In other words, the relationship is likely to be a real one and not just a coincidence.

Statistical significance is often determined by calculating a p-value, which is the probability of observing a relationship as strong as the one observed if there was no actual relationship between the variables. If the p-value is less than a predetermined threshold, usually 0.05, the relationship is considered to be statistically significant. This means that there is less than a 5% chance that the relationship observed is due to random error.

Therefore, It is usually determined by calculating a p-value, which measures the probability that the relationship between two variables is due to random chance.

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Local Minima is -1.

A. f has a local minimum at x = -1; the local minimum is -1.

To find the local minima of a function, we must identify any points at which the slope of the graph is equal to zero. In this graph, the slope of the graph is equal to zero at x = -1, indicating that f has a local minimum at x = -1. The value of the function at this point is -1, so the local minimum is -1.

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Answer:

No solution

Step-by-step explanation: no values of x

The total number of eggs in 7 dozens of eggs is 84 eggs

Word Problem is a sentence usually made up of a few sentences describing a scenario that needs to be solved through mathematics.

How to determine this

When a dozen mean a group of twelves things

When 1 dozen of an egg = 12 eggs

To get the total number of eggs in 7 dozens of eggs

Let x represent the total number of eggs

When 1 dozen = 12 eggs

7 dozens = x

x = 7 dozens * 12 eggs/1 dozen

x = 84 eggs/1

x = 84 eggs

Therefore, 84 eggs make 7 dozens of eggs

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From the given information provided, A is crest, B is wavelength, C is  trough, D is amplitude, E is equilibrium line in the transverse wave.

Amplitude: The maximum displacement of wave from its equilibrium position. In other words, it is the height of the wave measured from the midpoint (or equilibrium position) to the crest or trough.

Wavelength: The distance between two consecutive crests or troughs of a wave. It is usually denoted by Greek letter lambda (λ) and measured in meters.

Crest: The highest point or peak of a wave. It is the point on the wave with maximum positive displacement from the equilibrium position.

Trough: The lowest point of a wave. It is the point on the wave with maximum negative displacement from the equilibrium position.

Equilibrium: The position where there is no net force acting on an object. In the context of waves, the equilibrium position is the position where there is no displacement of the medium through which the wave is travelling.

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Answer:

Last answer choice: 4

Step-by-step explanation:

The set of inputs to the graphed function is he set of all x values for which the function has a defined value

Looking at the answer choices we see that the graph does not go the negative x region nor does it have a value for 0

So x = 4 is an input, and the resultant output y from the graph = 0

Answer

Last answer choice: 4

We're required to find the value of angle KTR.

It can easily be seen that angle KTR and angle BTF are vertically opposite angles.

[tex]\therefore \: \angle \: KTR= \angle \: BTF \: \\ \implies \: 4h + 160 = 3h + 156 \\ grouping \: the \: like \: terms \: at \: either \: sides \\ \implies \: 4h - 3h = 156 - 160 \\ \implies \: \boxed{h = - 4\degree}[/tex]

now ,

[tex]\angle \: KTR \: = 4h + 160 \\ \implies \: \angle \:KTR \: = 4( - 4) + 160 \\ \implies \: \angle \: KTR \: = - 16 + 160 \\ \implies \:\boxed{ \angle \:KTR = 144\degree}[/tex]

hope helpful! :)

P therefοre has a value οf 45/2 and x = -0.4.

A mathematical assertiοn that twο expressiοns are equivalent is knοwn as an equatiοn. It frequently includes οne οr mοre variables, which are unknοwable things with a wide range οf pοssible values. Finding the value οr values οf the variable that make the equatiοn true is the aim οf equatiοn sοlving. Mοst equatiοns take the fοrm: expressiοn is alsο expressiοn. Fοr instance, the fοrmula x + 2 = 5 states that the prοduct οf x and 2 is 5.

given

If the answer tο the equatiοn px² + 16x + 4 = 0 is x=-2/3, we can be cοnfident that we will οbtain an equivalence if we replace x = -2/3 in the fοrmula.

Adding x=-2/3 tο the sοlutiοn results in:

p(-2/3)² + 16(-2/3) + 4 = 0

Simplifying the phrase:

(4/9)p - (32/3) + 4 = 0

(4/9)p = (32/3) - 4

(4/9)p = (20/3)

By adding (9/4) tο bοth ends, we get:

p = (20/3) * (9/4)

p = 15

P therefοre has a value οf 45/2.

For x,

15x² + 16x + 4 = 0

3x(5x + 2) + 2(5x + 2)

(3x + 2)(5x + 2)

x = -2/3 and x = -0.4

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The expression that shows the number of laps Glenn swam during the week is 2 * 7 + 3(2) = 20.

A mathematical expression is a grouping of numbers, variables, and operations without the equal sign. It may be condensed or given a single value. On the other hand, an equation is a declaration that employs the equal sign to demonstrate the equality of two expressions. To get the value of the variable that makes an equation true, equations can be solved.

Given that, 2 laps every morning for 7 days:

2 * 7

3 laps with his friends one Tuesday and Thursday.

3(2)

Total laps = 2( 7) + 3(2) = 20

Hence, expression that shows the number of laps Glenn swam during the week is 2 * 7 + 3(2) = 20.

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Isabella and Jayla are thus separated by about 11.0 metres.

The Pythagorean Theorem states that the spaces on the right triangle (the side across from the right angle) of a right triangle, or, in common mathematical notation, a2 + b2, are equal to the spaces on the legs.

The Pythagoras formula can be used to resolve this issue. Let's call the distance between Isabella and Jayla "x". Then we have:

x² = (6.3)² + (9)²

Simplifying:

x² = 39.69 + 81

x² = 120.69

Taking the square root of both sides:

x ≈ 10.98

Rounding to the nearest tenth, we get:

x ≈ 11.0

Therefore, Isabella and Jayla are approximately 11.0 meters apart.

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Answer:

21 times

Step-by-step explanation:

3x21=62

The sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.

The sum of the perimeters of the three squares displayed on the computer monitor can be found by first finding the side length of each square, and then multiplying that side length by 4 to find the perimeter of each square. Finally, we add the perimeters of the three squares together to find the sum of the perimeters.

For the first square with an area of 112 cm^2, the side length is √112 cm, or 4√7 cm. The perimeter of this square is 4(4√7 cm) = 16√7 cm.

For the second square with an area of 28 cm^2, the side length is √28 cm, or 2√7 cm. The perimeter of this square is 4(2√7 cm) = 8√7 cm.

For the third square with an area of 63 cm^2, the side length is √63 cm, or 3√7 cm. The perimeter of this square is 4(3√7 cm) = 12√7 cm.

The sum of the perimeters of these three squares is 16√7 cm + 8√7 cm + 12√7 cm = 36√7 cm.

Therefore, the sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.

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Answer:

y= -1/3x+3

Step-by-step explanation:

we only need to look at the gradient as the gradient of both equations is not the same.

gradient= -1-0/12-9

= -1/3

hence, the answer is y= -1/3x+3

Answer:

8k - (5 + 2k) can be simplified by distributing the negative sign to the terms inside the parentheses:

8k - 5 - 2k

Then, we can combine like terms by adding the constants -5 and 8k:

6k - 5

Therefore, an equivalent expression to 8k - (5 + 2k) without parentheses is 6k - 5.

(B) 0.9%. We can use the formula for compound interest to find the value of the investment after 2 years:

A = P(1 + r/n)^(nt)

where A is the amount of money after the time period, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Plugging in the given values, we get:

A = 1000(1 + 0.018/2)^(2*2)

= 1000(1 + 0.009)^4

= 1000(1.009)^4

≈ 1083.02

So the investment is worth approximately $1083.02 after 2 years.

To find the interest rate per year, we can use the formula:

r = n[(A/P)^(1/nt) - 1]

Plugging in the values we know, we get:

r = 2[(1083.02/1000)^(1/(2*2)) - 1]

= 2[(1.08302)^(1/4) - 1]

≈ 0.9%

Therefore, the answer is (B) 0.9%.

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The rate at which the petrol was used in kilometers per liter is 10 km/L that means that for every litre of petrol used for driving, Peter's car could travel 10 kilometers.

Peter drove a thousand km and used 100 liters of petrol. To find the rate at which the petrol was utilized in kilometers consistent with liter, we divide the whole distance traveled via the quantity of petrol used.

The formulation for this is rate of petrol usage = overall distance traveled/quantity of petrol used.

Rate of petrol usage = total distance traveled/quantity of petrol used

Substituting the values we get,

= 1000 km / 100 L

= 10 km/L

This means that for every liter of petrol used, Peter was capable of travel 10 kilometers.

Thus, the rate at which the petrol was used in kilometers per liter is 10 km/L.

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Due to length restrictions, we kindly invite to read the explanation to see the lenghts of each 30-60-90 right triangles.

In this problem we find six cases of 30-60-90 right triangles, that is, right triangles whose inner angles have the following measures: 30°, 60°, 90°. The length of sides can be found by the following relationships:

Now we proceed to determine the missing length:

Case 1:

PV = 4 / (1 / 2)

PV = 8

VT = √3 · 4

VT = 4√3

Case 2:

PT = 2 / √3

PT = 2√3 / 3

PV = 2 / (√3 / 2)

PV = 4√3 / 3

Case 3:

PT = (1 / 2) · 3

PT = 3 / 2

VT = 3√3 / 2

Case 4:

PT = 7 / √3

PT = 7√3 / 3

PV = 7 / (√3 / 2)

PV = 14√3 / 3

Case 5:

VT = √3 · (1 / 2)

VT = √3 / 2

PV = (1 / 2) / (1 / 2)

PV = 1

Case 6:

PV = 100

PT = 50

VT = 50√3

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The line of reflection that produces Z′(10, 7) is y - axis.

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is a Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).

The rule for a reflection over the y -axis is (x, y) → (−x, y). We can write the reflection as -

Z(- 10, 7) → Z'(10, 7)

Therefore, the line of reflection that produces Z′(10, 7) is y - axis.

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The line of reflection that produces Z′(10, 7) is y - axis.

What is a triangle?

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is a Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).

The rule for a reflection over the y -axis is (x, y) → (−x, y). We can write the reflection as -

Z(- 10, 7) → Z'(10, 7)

Therefore, the line of reflection that produces Z′(10, 7) is y - axis.

The area of the shaded region which is a triangle will be 32 square inches.

Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

From the graph, the height of the triangle is given as,

2h = L

2h = 16 inches

h = 8 inches

And the base of the triangle is half of the base of the rectangle. Then we have

b = L / 2

b = 16 / 2

b = 8 inches

Then the area of the shaded region is given as,

A = 1/2 x 8 x 8

A = 32 square inches

The area of the shaded region which is a triangle will be 32 square inches.

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The area of the rectangle is 9 square units

First, we need to know the properties of a rectangle. They are;

From the diagram shown, we have that;

Length of the transformed shape(parallelogram to rectangle) = 3 units

Width = 3 units

The formula for the area of a rectangle is expressed as;

Area = lw

Substitute the values

Area = 3(3)

Area = 9 square units

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The book sold 38,100 copies in its first month of release. then approximately 537,324 copies have been sold to date.

What is the percentage?

A percentage is a ratio, fraction, or portion of a whole which is represented as 100.

Let "x" be the total number of copies sold to date.

According to the problem, 38,100 is 7.1% of x, which can be written as:

38,100 = 0.071x

To find x, we can solve for it by dividing both sides of the equation by 0.071:

x = 38,100 / 0.071

x = 537,323.94 (rounded to the nearest whole number)

Therefore, approximately 537,324 copies have been sold to date.

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The standard deviation of the sample is 24. Therefore the correct option is, option b. 24.


The variance of a sample is the square of the standard deviation. In other words, the standard deviation is the square root of the variance. Therefore, to find the standard deviation of the sample, we need to take the square root of the variance:
√576 = 24

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Like the variance, if the data points are close to the mean, there is a small variation whereas the data points are highly spread out from the mean, then it has a high variance.

So, the standard deviation of the sample of 169 observations and variance 576 equals 24. The correct option is b.

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