What is 3 to the 4th power

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

First one

Step-by-step explanation:

50 + 30 can be broken up into (10x5)+(10x3). You can simplify that into 10(5+3) because 10 x 5 =50 and 10x 3 = 30. :)

Answer:

10(5+3)

Step-by-step explanation:

If If you multiply 5 and 3 by 10 you'll get 50 + 30

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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Answer:

The 12.6 oz bottle

Step-by-step explanation:

0.19/oz for the 12.6 oz

0.21/oz for the 25.3 oz

The size is the better buy based on the unit price is 12.6 oz bottle if a certain shampoo is available in two sizes.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A certain shampoo is available in two sizes. A 12.6-ounce bottle costs $2.37. A 25.3-ounce bottle costs $5.24.

Let the unit price be x:

= 0.19/oz for the 12.6 oz

x = 0.21/oz for the 25.3 oz

Thus, the size is the better buy based on the unit price is 12.6 oz bottle if a certain shampoo is available in two sizes.

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Answer:

224

Step-by-step explanation:

360.-136.

Answer: 5

Step-by-step explanation:

Answer:

1 and 1/2 or 1.5

Step-by-step explanation:

3/8 × 4/1 = 3/2 = 1 and 1/2

Result in decimals: 1.5

Calculation steps:

3/8 × 4/1 = (3 × 4)/(8 × 1) = 12/8

12 ÷ 4 = 3

8 ÷ 4 = 2

= 3/2 = 1 and 1/2

The midpoint of the line segment is the average of the respective coordinates.

So the x-value of the midpoint if the average of the two individual x-coordinates.

    (-3.5 + 4)/2 = 0.5/2 = 0.25

And the y-value of the midpoint if the average of the two individual y-coordinates.

    (2 + (-2.5))/2 = -0.5/2 = -0.25

So, the midpoint is (0.25, -0.25) or (1/4, -1/4) or "C".

9514 1404 393

Answer:

  6(9v -7w)

Step-by-step explanation:

The greatest common factor of the two terms is 6. Any factor of 6 can be brought outside parentheses:

  54v -42w = 2(27v -21w) = 3(18v -14w) = 6(9v -7w)

Answer:

The coorect option is letter C

check your textbook for the remainder theorem, where it states that for a factor (x-5) of f(x) then the remainder will be 0, thus f(5) = 0, what the heck all that means?

well, it means that if we evaluate f(5) our result should be 0, so

\(\stackrel{factor}{(x-5)}\hspace{5em}f(5)=(5)^3-7(5)^2+(5)+a=0 \\\\\\ 0=(5)^3-7(5)^2+(5)+a\implies 0=125-175+10+a \\\\\\ 0=-40+a\implies \boxed{40=a}\)

The correct statement that F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

To determine whether the function shown in the table is exponential, we need to analyze the relationship between the x-values and y-values.

The table shows x-values that are increasing by a power of 2 (1, 2, 4, 8, 16, 32, 64) and y-values that are increasing by a constant rate of 1 (0, 1, 2, 3, 4, 5, 6).

The constant ratio between consecutive x-values indicates exponential growth or decay.

In this case, the function is growing exponentially because the y-values are increasing at a constant rate.

Based on this information, we can conclude that the function is exponential.

Therefore, we agree with statement F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

The other statements are incorrect because they do not accurately describe the relationship between the x-values and y-values in an exponential function.

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Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P \((x_0,y_0,z_0)\) is

\(z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\\)

Now the partial derivatives of f are

\(f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}\)

\(\\\\=\frac{1}{9-8}\)

= 1

Now

\(f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}\)

= -8

So, the tangent equation is

\(z - 0 = 1\times (x - 9) -8\times (y - 1)\)

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

The equation of the tangent plane is \(x-8y-z=1\)

An equation of the tangent plane to the given surface at the point \(P(x_0,y_0,z_0)\) is,

\(z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)\)

The function is,

\(z = ln(x-8y)\)

And the point is (9,1,0)

Now, calculating \(f_x,f_y\)

\(f_x(x,y)=\frac{1}{x-8y}\\ f_y(x,y)=\frac{x-8}{x-8y}\)

Now, substituting the given points into the above functions we get,

\(f_x(9,1)=\frac{1}{9-8(1)}=1\\ f_y(x,y)=\frac{-8}{9-8(1)}=-8\)

So, the equation of the tangent plane is,

\(z-0=1(x-9)-8(y-1)\\z=x-8y-1\\x-8y-z=1\)

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

As per the given data, to enable the drain pipe to carry 60 liters per second, there needs to be a 66.67% increase in the diameter of the drain pipe.

We must comprehend the link between the carrying capacity and the area of the pipe's cross-section in order to calculate the percentage increase in the drain pipe's diameter required to make it capable of carrying 60 litres per second.

The cross-sectional area of the pipe directly relates to its carrying capacity. This implies that the carrying capacity will grow if the cross-section's area increases.

Q ∝ A

Q1/A1 = Q2/A2

A2 = (Q2/Q1) * A1

A2 = (60/36) * A1

A2 = (5/3) * A1

Percentage increase = (A2 - A1)/A1 * 100

Percentage increase = [(5/3) * A1 - A1]/A1 * 100

Percentage increase = (2/3) * 100

Percentage increase = 66.67%

Thus, the answer is 66.67%.

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The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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Answer:the line x+y<10 has a negative slope and a positive y intercept

The line representing 20x+25y>200 is solid and the graph is shaded above line

The overlapping region contains the point (4,5)

Step-by-step explanation:

;)

Answer:

The answers are B, C, and E.

Step-by-step explanation:

I got it right on edge

Answer:

blank 1: 0.75b

black 2: 2/5p

The given quadrilateral can be named as ABCD, where A(0,-1), B(1,4), C(4,3), and D(3,-2). The area of the given quadrilateral ABCD is 17 square units.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

To find the area of this quadrilateral, we can use the formula:

Area = 1/2 * |(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) - (y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁)|

where (x₁,y₁), (x₂,y₂), (x₃,y₃), and (x₄,y₄) are the coordinates of the vertices of the quadrilateral in order.

Substituting the values, we get:

Area = 1/2 * |(04 + 13 + 4*(-2) + 3*(-1)) - (-11 - 44 - 3*3 - (-2)*0)|

Area = 1/2 * |(-8 - 26)|

Area = 1/2 * |-34|

Area = 17 square units

Therefore, the area of the given quadrilateral ABCD is 17 square units.

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Area of ΔQRS is 1/2×9×15×sin20° which is correct option (C)

Area of triangle is half the product of any two sides and the sine of the included angle.

Area = 1/2.ab.sinC

Area of ΔQRS = 1/2×9×15×sin∅

∵ ∅ = 20°

Area of ΔQRS = 1/2×9×15×sin20°

Hence, area of ΔQRS is 1/2×9×15×sin20°

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Answer:  8 x 7 = 56   7 x 8 = 56     56/8=7      56/7=8

Step-by-step explanation: the way that you do it you will the same numbers

Step-by-step explanation: 8: 1,8, 2,4,4,2 8,1

                                              7: 1,7,

                                              56: 1,56,7,8,8,7

Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

a) The distance of the stone above ground level at any time t is given by h(t) = 950 + 4.9t², where h(t) is measured in meters and t is measured in seconds.

b) It takes approximately 13.93 seconds for the stone to reach the ground.

c) The stone strikes the ground with a velocity of approximately 136.04 m/s.

d) It takes approximately 16.75 seconds for the stone thrown downward with a speed of 6 m/s to reach the ground.

When objects are dropped or thrown from a height, their speed and position can be determined using physics equations. In this problem, we will calculate the distance, time, and velocity of a stone dropped from a tower.

First, we need to determine the equation for the height of the stone above the ground at any given time t. We can use the formula:

h(t) = h0 + vt + 0.5at²

where h0 is the initial height, v is the initial velocity (which is zero for a dropped object), a is the acceleration due to gravity (g = 9.8 m/s^2), and t is the time since the stone was dropped.

Using the given values, we can plug in the numbers and simplify:

h(t) = 950 + 0t + 0.5(9.8)t²

h(t) = 950 + 4.9t²

To find the time it takes for the stone to reach the ground, we need to set h(t) = 0 and solve for t:

0 = 950 + 4.9t^2

t^2 = 193.88

t ≈ 13.93 seconds

To find the velocity at which the stone strikes the ground, we can use the formula:

v = v₀ + at

where v₀ is the initial velocity (which is zero for a dropped object) and a is the acceleration due to gravity (g = 9.8 m/s²). We can plug in the values for t and solve for v:

v = 0 + 9.8(13.93)

v ≈ 136.04 m/s

Finally, if the stone is thrown downward with a speed of 6 m/s, we can use the same formula for h(t) as before, but with an initial velocity of -6 m/s. We can then find the time it takes to reach the ground using the same method as before:

h(t) = 950 - 6t + 0.5(9.8)t²

0 = 950 - 6t + 4.9t²

t² - 1.22t - 193.88 = 0

t ≈ 16.75 seconds

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Answer: 20% of 90 = 18

Answer:

90%

Step-by-step explanation:

i hope this helps:)

Answer:

\( \boxed{ \bold{ \huge \boxed{ \sf{x = 18.5}}}}\)

Step-by-step explanation:

\( \sf{3(22 + 2) = 18 + 4(x - 5)}\)

Add the numbers : 22 and 2

⇒\( \sf{3 \times 24 = 18 + 4(x - 5)}\)

Multiply the numbers : 3 and 24

⇒\( \sf{72 = 18 + 4(x - 5) }\)

Distribute 4 through the parentheses

⇒\( \sf{72 = 18 + 4x - 20}\)

Calculate the difference

⇒\( \sf{72 = - 2 + 4x}\)

Swap the sides of the equation

⇒\( \sf{ - 2 + 4x = 72}\)

Move 2 to right hand side and change it's sign

⇒\( \sf{4x = 72 + 2}\)

Add the numbers : 72 and 2

⇒\( \sf{4x = 74}\)

Divide both sides of the equation by 4

⇒\( \sf{ \frac{4x}{4} = \frac{74}{4} }\)

Calculate

⇒\( \sf{x = 18.5}\)

Hope I helped!

Best regards!!

Answer:

x=18.5

Step-by-step explanation:

3(22+2) =18 + 4(x-5)

3(24) = 18 + 4(x-5)

72=18+4(x-5)

4(x-5)+18=72

4x-20+18=72

4x= 72-18+20

4x=72+2

4x=74

x=74/4

x=18.5

Answer:

I didn't really now but I did this to day

The height of the building that cast the shadow 98 feet will be 61.25 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building.

Let 'h' be the height of the building. Then the equation is given as,

h / (90 + 8) = 5 / 8

h / 98 = 5 / 8

h = 98 x 5 / 8

h = 12.25 x 5

h = 61.25 feet

The height of the building that cast the shadow 98 feet will be 61.25 feet.

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Answer:354

Step-by-step explanation:

35335345

Answer:

=2m−5n

Step-by-step explanation:

Let's simplify step-by-step.

m−(2m+5n−3m)

Distribute the Negative Sign:

=m+−1(2m+5n−3m)

=m+−1(2m)+−1(5n)+−1(−3m)

=m+−2m+−5n+3m

Combine Like Terms:

=m+−2m+−5n+3m

=(m+−2m+3m)+(−5n)

=2m+−5n