Use the compound interest formula to compute the total amount accumulated and the interest earned.
​$3000 for 3 years at ​%4 compounded semiannually.

The amount in the account is ____.
(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Mean absolute deviation is the variation in a data set and is the average distance between each value and mean.

It is calculated by finding the difference between each data value and mean and then finding average of that.

So, let data set be x1,x2,x3,x4...xN.

mean of the data set is [tex]\bar{x}[/tex].

then mean absolute deviation will be

[tex]M.A.D=\sum\limits^N_{n=0}\frac{ {x_n-\bar{x}}}{N}[/tex]

Thus, mean absolute deviation shows how much the data vary in the data set.

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Answer:

612.5

Step-by-step explanation:

Area is the length times the width

a = 70x35

a = 2450  Divide this number by 4

612.5

Answer:

x > -5

Make a number line.  Put a circle on the number line at -5 and then darken an arrow on the number line going to the right of -5

Step-by-step explanation:

-8-8(2x-4) > -5(4x -5) -21  Distribute the -8 and -5

-8 - 16x + 32 > -20x +25 -21  Combine like terms

-16x + 24 > -20x +4  Add 20x to both sides

4x + 24 > 4  Subtract 24 from both sides

4x > -20  Divide both sides by 4

x > -5

The inequality that represents the number and type of shots the player needs to win the title is -

x + 2y ≥ 28

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have A basketball player in a game who makes [x] free throws worth 1 point and [y] free throws worth 2 point baskets. The player needs to score at least 28 points to win the scoring title.

The inequality that represents the number and type of shots the player needs to win the title is -

x + 2y ≥ 28

Therefore, the inequality that represents the number and type of shots the player needs to win the title is -

x + 2y ≥ 28

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The amount invested in the account that yields 10% simple interest is $1,000.

The amount invested in the account that yields 7% simple interest is $9,000.

The first step is to form a system of equations using the information provided in the question:

a + b = $10,000 equation 1

0.1a + 0.07b = 730 equation 2

Where:

a = amount invested in the account that yields 10% simple interest

b =  amount invested in the account that yields 7% simple interest

The elimination method would be used to solve the equations

Multiply equation 1 by 0.1

0.1a + 0.1b = 1000 equation 3

Subtract equation 2 from equation 3

0.03b = $270

Divide both sides of the equation by 0.03

b = $270 / 0.03

b = 9,000

Substitute for b in equation 1

a + 9,000 = 10,000

a = 10,000 - 9,000

a = 1000

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The exact value of sin(θ) given that cos(θ) = -2√5/5 is √5/5

The given trigonometry ratio is

cos(θ) = -2√5/5

By the trigonometry ratio, we have

sin²(θ) + cos²(θ) = 1

Substitute cos(θ) = -2√5/5 into the above equation

So, we have the following representation

sin²(θ) + (-2√5/5)² = 1

Evaluate the exponent

sin²(θ) + 4/5 = 1

Subtract 4/5 from both sides

This gives

sin²(θ) = 1/5

Take the square root of both sides

√sin²(θ) = √1/5

Evaluate the square root

sin(θ) = ±1/√5

Sin is positive in quadrant II

So, we have

sin(θ) = 1/√5

Rationalize

sin(θ) = 1/√5 * √5/√5

This gives

sin(θ) = √5/5

This gives the value of sin(θ)

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Based on the figures that we are provided, we can see that Kadisha has walked 10 miles already and is yet to walk 14 miles.

The total distance Kadisha has to walk is 24 miles

The distance she has walked is represented in the ratio as 5

The distance she has left to work is 7

5x + 7x = 24

12x = 24

x = 2

Therefore, the distance that Kadisha has walked is

5 × 2 = 10 miles

The distance she is yet to walk is

7 × 2 =14 miles

When represented as a ratio, 10/14 is the same as 5/7, so the answer is proven to be correct.

Complete Question:

A hiking trail is 24 miles from start to finish. There are two rest areas located along the trail. a. The first rest area is located such that the ratio of the distance from the start of the trail to the rest area and the distance from the rest area to the end of the trail is 2:9. To the nearest hundredth of a mile, how far is the first rest area from the starting point of the trail? b. Kadisha claims that the distance she has walked and the distance she has left to walk has a ratio of 5:7. How many miles has Kadisha walked?

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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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Using the substitution method, the solution to the system of equations is: x = -4 and y = 12.

To solve a system of equations using the substitution method, find the value of one of the variables in one equation, then substitute it in the second equation and solve to find the value of the second variable.

Given the equations:

x + y = 8 --> eqn. 1

y = -3x --> eqn. 2

Substitute -3x for y into equation 1:

x + (-3x) = 8

x - 3x = 8

-2x = 8

-2x/-2 = 8/-2

x = -4

Substitute x = -4 into equation 2:

y = -3(-4)

y = 12

The solution is, x = -4 and y = 12.

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Answer:

Step-by-step explanation:

there is no question?

Answer:

v = 4

Step-by-step explanation:

[tex]collect \: like \: terms \: \\ 7v - 4v - v + 4v = 7 + 7 + 10\\ 3v - v + 4v = 14 + 10\\ \\ 2v + 4v = 24 \\ 6v = 24 \\ v = 4[/tex]

Step-by-step explanation:

81 3/8 ÷ 9 2/5

81*8+3 = 651

651/8

9 2/5 = 9*5+2=47

47/5

651/8 ÷ 47/5 =

651/8 * 5/47 = 3255/376 =

8.65691489362

The acceleration when the car comes to a full stop is 20.76 meters per square second.

Here we have the velocity function:

v(t) = -3t^2 + 18t + 9

To find the acceleration we need to differentiate with respect to the variable t, so we will get the acceleration:

a(t) = 2*(-3)*t + 1*18

a(t) = - 6*t + 18

Now, the car will come to a stop when the velocity is equal to zero, so we need to solve:

-3t^2 + 18t + 9 = 0

Dividing all by -3 we get:

(-3t^2 + 18t + 9)/-3 = 0

t^2 - 6t - 3 = 0

The solutions are:

[tex]t = \frac{6 \pm \sqrt{(-6)^2 - 4*1*-3} }{2*1} \\\\t = \frac{6 \pm 6.92}{2}[/tex]

We only care for the positive solution:

t = (6 + 6.92)/2 = 6.46

The acceleration at that time is:

a(6.46) =  - 6*6.46 + 18 = -20.76

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(I suggest using desmos graphing calculator for the future.)

(0,5) and (4,0) or the one in the left upper corner. Hope this helps.

Answer:

  (x, y) = {(-2, -3), (2, 5)}

Step-by-step explanation:

You want to solve the system of equations y=x²+2x-3 and y=2x+1.

The two expressions for y can be equated, and the resulting equation put in standard form.

  x² +2x -3 = 2x +1

  x² -4 = 0 . . . . . . . . . . subtract (2x+1)

  (x -2)(x +2) = 0 . . . . . factor

Values of x that make the factors zero are 2 and -2.

Corresponding values of y are ...

  y = 2x +1 = 2(2) +1 = 5

  y = 2(-2) +1 = -3

Solutions are ...

The probability of rolling a 3 first time and a number greater than 4 thre second time is 1/18

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain. An example of a certain event is tomorrow being Friday if today is Thursday. This is definitely going to happen.

The possible outcomes of a fair die are : 1, 2, 3, 4, 5, 6. which is 6 in all

the required outcome for obtaining a 3 = 3 which is 1 outcome

the required outcome for obtaining a number greater than 4 : 5, 6. which is 2 outcomes.

probability of getting 3 first time = 1/6

probability of getting a number greater than 4 = 2/6 ( lowest term = 1/3)

Probability of rolling a 3 first time and a number greater than 4 second time is  = 1/6 x 1/3 = 1/18

In conclusion, probability of obtaining a 3 and a number greater than 4 is 1/18.

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5 inches

I just randomly guessed

The angle x will be 34°.

From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.

Supplementary angles are those which always sum to to 180°.

For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.

similarly ∠ROP + ∠RQP = 180°

∠RQP = 180° - ∠ROP

∠ROP is given to us 146°

After putting it in the equation above we get ∠RQP = 34°

Therefore x comes out to be 34°.

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Answer:

[tex] \sqrt[2]{15} = 7.5[/tex]

Answer:

48

Step-by-step explanation:

multiply by 4 to make x whole number

-32+x=16

+32 to isolate x

x=16+32

add for answer

x=48

Using the Pythagorean Theorem, the approximately length of ladder is 20.6 feet

As we know Michael is standing on roof of his house.

He stands 5 feet away from his house

The ladder touches the point 20 feet above the ground and where the Michael standing

In this order we have to find the approximately length of ladder

From this question we can clearly figure out that in this question we have:

Perpendicular= 20 feet

Base = 5 feet

So as we can understand that we have to use Pythagorean Theorem

Pythagorean Theorem:

(Hypotenuse)^2 = (Perpendicular)^2+(Base)^2

(Hypotenuse)^2 = (20)^2+(5)^2

(Hypotenuse)^2 = 400+25

(Hypotenuse)^2 = 425

Hypotenuse=square root(425)

Hypotenuse=20.6 feet

Hence, the approximately length of ladder is 20.6 feet

So the option C is correct.

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The acceleration of the car three seconds before it comes to a stop is  -2.76 m/s² (Letter B).

Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.

In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.

For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x

The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you  should solve this quadratic function:

Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]

[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]

[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]

[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]

Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].

The acceleration can be found from the derivative of the velocity function. See below.

a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]

a(t)= -6*[tex]2\sqrt{3}[/tex]t+18

a(t)= [tex]-12\sqrt{3}[/tex]t+18

a(t)=-2.76

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Answer:

x=-1,x=3/5

Step-by-step explanation:

Those are the two values of x

Answer:

Step 1:subtract 5 from both sides

step 2: divide both sides by two

final answer: c= p-5/2

Answer:

Step 1: Subtract 5 from both sides.

Step 2: Divide 2 from both sides.

Final answer: C= p-5 / 2

Step-by-step explanation:

The average rate of change = 1.59 ≈ 2

The average rate of change can be calculated by

1) The first one = [tex]\frac{3 + 0}{2}[/tex] = 1.5

2 ) the second can also be solved by ; 8 + 2/ 2 = 5

3 ) the third one will be 20 + 6 / 2 = 13

4) 8.5

5) 12.5

To calculate the average rate of change

we will first add all the distance

Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51

The total time = 2 + 6 + 9 +15 = 32

Thus the average rate of change = 51 / 32 = 1.59

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The degree and number of unique zeros of f(x) = (x – 5)(x + 3)(x – 1)² is:

Degree: 4; number of unique zeros: 3.

The end behavior of the polynomial is:

As x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞.

The degree of the polynomial function is given by the sum of the multiplicities of the roots.

These roots are given as follows:

Hence the degree is:

1 + 1 + 2 = 4.

The unique zeros are the roots, hence there are three unique zeros, which is the same number of linear factors of the function.

The end behavior is the limit of the function as x goes to negative infinity and to positive infinite, hence:

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