$1250 invested at 8% compounded annually for 2 years. Using compound interest

The figure on the left side shows the water level is at the 0.5 liter mark, ie half a liter.

1 liter = 1000 mL

0.5*1 liter = 0.5*1000 mL

0.5 liter = 500 mL

If you poured all the water into the jug on the right (without spilling), then the water level should reach the 500 mL mark. This is the small tickmark exactly halfway between the 400 and 600.

Answer:

Westbound = x;

Eastbourne = x-20;

So they will have the common rate: 360/2 = 180;

x+x-20 = 180

2x = 200;

x = 100;

So Eastbourne will be 100-20 = 80 miles per an hour;

Answer:

35i+13j

Step-by-step explanation:

Vector a = 9i+9j

Vector b = -4i+7j

We need to find the value of 3a-2b.

3a = 3(9i+9j) = 27i+27j

2b = 2(-4i+7j) = -8i+14j

3a-2b = 27i+27j-(-8i+14j)

= 27i+27j+8i-14j

= 35i+13j

Hence, the required vector is equal to 35i+13j.

Answer:

9x - 6

Hope this helps! <3

(If you need a step by step lmk)

Answer:

6x+3(x-2)

6x+3x-6

9x-6

Answer:

answer is  30

Step-by-step explanation:

10 times 3 = 30

Answer:

Ethan is 33 and Evan is 10.

Step-by-step explanation:

We are given that Ethan is 23 years older than Evan.

We are also given that the sum of their ages is 43.

We are told to find the ages of both Ethan and Evan.

First, create a system of equations.

\(\texttt{Let} \ x \ \texttt{be Ethan's age and} \ y \ \texttt{be Evan's age:}\\\\\displaystyle \left \{ {{x+y=43} \atop {23+y=x}} \right.\)

Then, substitute the value for x from the second equation into the first equation:

\(x+y=43\\\\(23+y)+y=43\\\\23+2y=43\\\\23-23+2y=43-23\\\\2y=20\\\\\displaystyle \frac{2y}{2} = \frac{20}{2}\\\\y = 10\)

Finally, substitute 10 as y into the second equation:

\(23+y=x\\\\23+10=x\\\\33=x\)

Therefore, Ethan is 33 and Evan is 10.

Answer:

use the formula 1/3×base area×height

Step-by-step explanation:

finding base area

6x6=36

now the volume formula for pyramid

1/3×36×7=84in²

hope that helped

Answer:

Lo averiguaste, lo siento, amigos míos, por haberlos ayudado. pero la respuesta es 456 $.

Step-by-step explanation:

Answer:

  $42

Step-by-step explanation:

You want the price with tax of a $35 pair of shoes subject to a 20% tax.

The tax is the cost of the shoes multiplied by the tax rate. The final price is the sum of the cost of the shoes and the tax:

  final price = price + price × tax rate

  final price = price × (1 + tax rate) = $35 × 1.20 = $42

The final price of the shoes is $42.

Answer:

42$

Step-by-step explanation:

tax increase will be

20% of 35$

= 20/100 × 35

= 7$

Final price = Old price + Tax

= 35 + 7

= 42$

The correct answer is:  
     [A]:  " ∡2 is supplementary to ∡3 " .

___________________

The other answer choices given—which are correct statements—only prove that " a || b " {that is:  "Line A" is parallel to "Line B".}

___________________

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8

B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2

From the question, we are to solve the given equations

The given equation is log₄(x² - 12x + 48) = 2

From one of the laws of logarithm, we have that

logₐ x = n ⇒ x = aⁿ

Thus,

log₄(x² - 12x + 48) = 2 becomes

(x² - 12x + 48) = 4²

x² - 12x + 48 = 16

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

Solve the quadratic equation

x² - 12x + 32 = 0

x² - 8x - 4x + 32 = 0

x(x - 8) -4(x - 8) = 0

(x - 4)(x - 8) = 0

x - 4 = 0 OR x - 8 = 0

x = 4 OR x = 8

B) 27^(4x-6) =(1/9)^(2x-7)

Solve for x

27^(4x-6) =(1/9)^(2x-7)

Express the bases in index form

3^3(4x-6) =(3)^-2(2x-7)

Equate the powers

3(4x - 6) = -2(2x - 7)

12x - 18 = -4x + 14

12x + 4x = 14 + 18

16x = 32

Divide both sides by 16

16x/16 = 32/16

x = 2

Hence, the value of x is 2

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The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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Answer:

must be 14

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

I took the test :)

Answer:

Slope: 6

Y-intercept: 0

Proportional

Step-by-step explanation:

The equation for this table is y = 6x + 0 or just y = 6x.

y         =            6x           +                0

y-value          slope (x-value)           y-intercept

Proportional because it crosses (0,0) on the graph.

Answer:

3/4 there are 4 lines indicating the numbers and it is on the 3rd.

Answer:

Step-by-step explanation

Okay so lets solve step by step/

15% can be written as a  fraction: 15/100

The of in the equation means multiplying.

15/100= 3/20

3/20*9= 270/20

27/2 is answer

We want to calculate different ways of having 8 apples and bananas. If x is the amount of bananas we have and y the amount of apples. It should happen that the sum of this two quantities is always 8. That is, we have the following equation

If we subtract x on both sides of the equation, we would get

This means that for every value of x that we give, we can find the value of y by simply subtracting the value of x from 8.

So, to find 3 different ways of having 8 apples and bananas, we simply find three different values for x, so we have three different values of y.

Let x=1. then y=8-1=7. So if we have 1 banana, we should have 7 apples.

Let x=2, then y=8-2=6. So if we have 2 bananas, we should have 6 apples.

Finally, let x=3, then y=8-3=5. So if we have 3 bananas, we should have 5 apples.

A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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Answer:

T = 12

Step-by-step explanation:

8t+1=97

We move all terms to the left:

8t+1-(97)=0

We add all the numbers together, and all the variables

8t-96=0

We move all terms containing t to the left, all other terms to the right

8t=96

t=96/8

t=12

Answer:

25 months

Step-by-step explanation:

if x is the months, your equation will be

70x = 50x + 500

20x = 500

x = 25

Answer: 1

Step-by-step explanation: 3/4=0.75~1

Answer:

72\(\sqrt{3}\) units²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

Here b = ST = a = 12 and h = RS

To calculate RS use the tangent ratio in the right triangle and the exact value

tan60° = \(\sqrt{3}\) , thus

tan60° = \(\frac{opposite}{adjacent}\) = \(\frac{RS}{ST}\) = \(\frac{RS}{12}\) = \(\sqrt{3}\) ( multiply both sides by 12 )

RS = 12\(\sqrt{3}\)

Thus

A = \(\frac{1}{2}\) × 12 × 12\(\sqrt{3}\) = 6 × 12\(\sqrt{3}\) = 72\(\sqrt{3}\) units²

Answer:

y' = 14x

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

y = 7x²

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:

A' = (-3, 3 + 3) = (-3, 6)

B' = (0, 7 + 3) = (0, 10)

C' = (-3, 0 + 3) = (-3, 3)

Therefore, the coordinates of the vertices for the image triangle A'B'C' are A'(-3, 6), B'(0, 10), and C'(-3, 3).

So the correct answer is: A′(−3, 6), B′(0, 10), C′(−3, 3).

Answer:

1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

1/2 is 6/12. 6/12 is close to 5/12 than the others.

Answer:

13,608

Step-by-step explanation:

If 7/10 of the runners were women, than 3/10 of the runners were men. 3/10 of 45,360 runners is 13,608.

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