An account earning interest at a rate of 4% compounded monthly has a principal of $ 500,000 . If no more deposits or withdrawals are made , how much money will be in the account after five years?

Answer:  Choice A

Step-by-step explanation:

1/8 = 0.125

That is a decimal that terminates after 3 decimal places (choice A)

The key features that f(x) and g(x) have in common are; A: Both f(x) and g(x) have the same domain of (∞, -∞).

We are given the functions as;

Polynomial function; f(x) = 2x² - 3x + 5

Exponential function; g(x) = 2ˣ - 5

In this question we must analyze the domain, range, x-intercepts and changing intervals:

The domain of both functions are a set of all real numbers with both functions continuous.

The range of both functions from the graph attached is;

Range of f(x) = (3.875, +∞)

Range of g(x) = (-5, +∞)

The x-intercepts of both functions are;

x-intercept for f(x) is non existent

x-intercept for g(x) is (2.322, 0)

From the attached graph;

f(x) increases over interval of (3.875, ∞)

g(x) increases over the interval of a set of real numbers

Looking at the given options, we can say that option A is the correct one

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The given equation, y = -4(x-3)² + 6, rewritten in standard form is y = -4x² + 24x - 30

From the question, we are to rewrite the given equation in standard form.

The given equation is

y = -4(x-3)² + 6

The standard form of a quadratic equation is

y = ax² + bx + c  

Now, we will express the given equation in the standard form of a quadratic equation.

y = -4(x - 3)² + 6

y = -4(x - 3)(x - 3) + 6

y = -4(x(x -3) -3(x - 3)) + 6

y = -4(x² - 3x - 3x + 9) + 6

y = -4x² + 12x + 12x - 36 + 6

y = -4x² + 24x - 30

Hence, the equation is y = -4x² + 24x - 30

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y = 1/4x + 1 is parallel to line a

-4x + y = -8 is neither parallel nor perpendicular to line a

4x + y = -3 is perpendicular to line a

From the question, we are to determine how the given equations compare to line a.

From the given information,

Line a is -x + 4y = 32

First, we will determine the slope of line a

To do this, we will compare the equation to the slope-intercept form of a line

The slope-intercept form of a line is

y = mx + b
Where m is the slope

and b is the y-intercept

Writing -x + 4y = 32 in the slope-intercept form

-x + 4y = 32

4y = x + 32

Divide through by

y = 1/4 x + 8

By comparison, the slope of line a is 1/4

NOTE: If two lines are parallel, their slopes will be equal

and

If two lines are perpendicular, their slopes will be the negative reciprocal of each other

Now, we will determine the slopes of each of the lines

For y = 1/4x + 1

By comparing with the slope-intercept form of a line, y = mx + b

The slope of the line is 1/4

Thus, the line is parallel to line a

For -4x+y=-8

Rewrite in the slope-intercept form of a line

-4x + y = -8

y = 4x - 8

By comparing with the slope-intercept form of a line, y = mx + b

The slope of the line is 4

4 is not equal to 1/4 and 4 is not the negative reciprocal of 1/4.

Thus, the line is neither parallel nor perpendicular to line a.

For 4x+y=-3

Rewrite in the slope-intercept form of a line

4x + y = -3

y = -4x - 3

By comparing with the slope-intercept of a line, y = mx + b

The slope of the line is -4

-4 is the negative reciprocal of 1/4.

Thus, the line is perpendicular to line a.

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Answer:

[tex]\huge\boxed{\sf x = 128\°}[/tex]

Step-by-step explanation:

x + 52° = 180 (Angles on a straight line add up to 180°)

Subtract 52 to both sides

x = 180 - 52

x = 128°

[tex]\rule[225]{225}{2}[/tex]

Answer:

X= 128°

Step-by-step explanation:

The angels on a straighlije add up to 180°

hence <DCA+ <BCA= <BCD

X+ 52°=180°

X=180°-53°

X=128°

The the smallest positive solution to the Trigonometry sin(5x)cos(9x) - cos(5x)sin(9x) = - 0.25 is x = 3.617degree

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles

sin(5x)cos(9x) - cos(5x)sin(9x) = -0.25

sin(5x)cos(5x + 4x) - cos(5x)sin(5x + 4x) = -0.25

-sin( 5x - 9x) = -0.25

-sin (9x -5x) = -0.25

sin ( 4x) = 0.25

Using the sine inverse

arcsin(0.25) = x = 0.25268 rad ≅ 14.47 degree

so dividing this angle by 4

x = 3.617degree

Therefore, the smallest positive solution to the Trigonometry is x = 3.617degree

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Answer: 45

Step-by-step explanation:

The total profit in all was [tex]1040-900=\$ 140[/tex].

The total profit per pizza was [tex](0.50)(8)=\$4[/tex].

This means they sold [tex]\frac{140}{4}=35[/tex] pizzas.

Adding this to the 10 pizzas held back, there were [tex]35+10=45[/tex] pizzas in the original order.

The quadratic function is y = 2x^2+3x-4.

Given:

The quadratic function y = ax² + bx + c whose graph passes through the given points.(-1,-5), (1,1),(-2,-2)

(-1,-5) passes.

y = ax^2+bx+c

-5 = a(-1)^2+b*-1+c

-5 = a-b+c

(1,1) passes.

1 = a*1^2+b*1+c

1 = a+b+c

(-2,-2) passes.

-2 = a(-2)^2+b*-2+c

-2 = 4a-2b+c

on solving three equations

a = 2 , b = 3 and c = -4

The quadratic equation is y = 2x^2+3x-4.

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Answer:

the III quadrate the x line (horizontal line) the number there is -4 on the y line (vertical line) -6 from the right side of the III quadrate

Answer: [tex]m\angle DE F=90^{\circ}[/tex]

Step-by-step explanation:

The slope of [tex]DE[/tex] is [tex]\frac{7-3}{5-4}=4[/tex].

The slope of [tex]EF[/tex] is [tex]\frac{3-2}{4-8}=-\frac{1}{4}[/tex].

Thus, [tex]DE \perp EF[/tex], meaning [tex]m\angle DE F=90^{\circ}[/tex].

The parametric equations for an object moving clockwise along the ellipse are x =  3 cos((2π/3) t) and y = 5 sin((2π/3) t)

Given: the equation of an ellipse x²/9 + y²/25 = 1

Beginning at (0,5) and requiring 3 seconds

The parametric equations representing an ellipse x²/a² + y²/b² = 1  are

x = a cos(t) and y = b sin(t)

where t is the parameter with values between [0, 2π]

If t represents time. Then, if a lap around the ellipse is completed in T seconds we have,

x = a cos((2π/T) t)

y = b sin((2π/T) t)

where 2π/T is the period of the motion.

Combining these results, therefore, we have the parametric equations:

x =  3 cos((2π/3) t)

y = 5 sin((2π/3) t)

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The number of pinto beans in the jar is 24

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent

let x be the number of pinto beans

white beans = x + 36

Total beans = 2x + 36

Total share = 2 + 5, which is 7

number of pinto beans(x) = 2/7 * (2x + 36)

x = 2/7 * (2x + 36)

By cross multiplying,

7x =2(2x + 36)

7x = 4x + 72

collect like terms

7x - 4x = 72

3x = 72

x = 72/3

x = 24

In conclusion, 24 pinto beans are in the jar.

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Answer: its answer b

Step-by-step explanation:

Answer:

-3x -12

Step-by-step explanation:

-6x +3x = -3x

-3-9 = -12

Answer:

1250 teenagers

Step-by-step explanation:

= 5000 * (1/4)

= 5000 * 0.25

= 1250

Answer:

[tex]\huge\boxed{\sf 1250 \ teenagers}[/tex]

Step-by-step explanation:

Total people = 5,000

= 25% of total people

Key: "of" means "to multiply" and total people = 5000

= 25% × 5000

Key: % means "out of 100"

[tex]\displaystyle =\frac{25}{100} \times 5000\\\\= 25 \times 50\\\\= 1250 \ teenagers\\\\\rule[225]{225}{2}[/tex]

The matrix formed after solving C-D is C-D = -4     8    10

                                                                              4   -12   -6

                                                                              1      2    4

What is Matrix in Mathematics?

A matrix is a rectangular array or table of numbers, symbols, or expressions that are organised in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns.

Solution:

Given That Matrix C = 1   7   5

                                    4   -7  0

                                    2   6   7

Also, Matrix D = 5   -1   -5

                          0    5   6

                          1     4    3

To Find: C-D

Since the order of both the matrices is 3 * 3

we can solve the problem

For this we will substract each element from Matrix C from its corresponding element in Matrix D

C-D = (1-5)   (7+1)   (5+5)

         (4-0)   (-7-5)   (0-6)

         (2-1)   (6-4)   (7-3)

C-D = -4     8    10

           4   -12   -6

           1      2    4

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Answer:

-10

Step-by-step explanation:

2(x+3)=x-4

2x+6=x-4

-x     -x

x+6=-4

  -6 -6

x=-10

Answer:

x = -10

Step-by-step explanation:

HOW TO SOLVE YOUR PROBLEM

1. Distribute

2(x + 3) = x - 4

2x + 6  = x - 4

2. Subtract 6 from both sides

2x + 6  = x -4

2x + 6 - 6 = x - 4 - 6

3. Simplify

Subtract the numbers:

2x + 6 - 6 = x - 4 - 6

2x = x - 4 - 6

Subtract the numbers:

2x = x - 4 - 6

2x = x - 10

4. Subtract x from both sides

2x = x - 10

2x - x = x - 10 - x

5. Simplify

Combine like terms:

2x - x = x - 10 - x

1x  = x - 10 - x

Multiply by 1:

1x = x - 10 - x

x = x - 10 - x

Combine like terms:

x = x - 10 - x

x = -10

Solution:

x = -10

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The solution of the absolute value equation is x=1/6.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

When |3x-1|- | 2x+5-(5-x)| = 0

When 3x-1 < 0 and 2x+5-(5-x) < 0

-(3x-1) - ( - ( 2x+5-(5-x) ) ) =0

on simplifying, variable cancels out, so no solution

When 3x-1 < 0 and 2x+5-(5-x) > 0

-(3x-1) - (  ( 2x+5-(5-x) ) ) =0

on simplifying, x=1/6

When 3x-1 >0 and 2x+5-(5-x) < 0

(3x-1) - ( - ( 2x+5-(5-x) ) ) =0

on simplifying, x=1/6

When 3x-1 >0 and 2x+5-(5-x) >0

(3x-1) - (  ( 2x+5-(5-x) ) ) =0

on simplifying, variable cancels out, so no solution

So, the solution is x=1/6

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Step-by-step explanation:

4x + 17 = 49

subtract 17 from both sides:

4x + 17 - 17 = 49 - 17

4x = 32

divide both sides by 4:

4x/4 = 32/4

x = 8

Answer:

1/3 cup

Step-by-step explanation:

A brownie recipe needs 1/2 cup of white sugar per batch if I only want to make 2/3 of a batch how much white sugar do I need?

1/2 * 2/3 = 2/6 = 1/3 cup

The function f ( x ) = y = 2 ( x + 5 )² - 6 is a one to one function

What is one to one function?

One to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets. It is also written as 1-1. In terms of function, it is stated as if f(x) = f(y) implies x = y, then function f is one to one.

The function, f(x), is a one to one function when one unique element from its domain will return each element of its range. This means that for every value of x, there will be a unique value of y or f(x).

f ( x₁ ) = f ( x₂ ) if and only if x₁ = x₂

Given data ,

Let the function be f ( x )

where f ( x ) = y

So , the equation will be

y =  2 ( x + 5 )² - 6

Now , on simplifying the equation , we get

y = 2 ( x² + 10x + 25 ) - 6

y = 2x² + 20x + 50 - 6

y = 2x² + 20x + 44

Therefore , the function is f ( x ) = y = 2x² + 20x + 44

Now , replace y with x , we get

f ( y ) = x = 2y² + 20 y + 44

And f ( x₁ ) = f ( x₂ )

So , the function is one to one function

Hence , The function f ( x ) = y = 2 ( x + 5 )² - 6 is a one to one function

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Answer:

375 minutes

Step-by-step explanation:

72 km = 90 mins. 32 km = 40 mins. how many mins = 300 km?

72/90 = 0.8

32/40 = 0.8

so:

300/x = 0.8

multiply both sides by x:

x(300/x) = 0.8(x)

300 = 0.8x

divide both sides by 0.8:

x = 375

Answer:

The blue dot is -19

Step-by-step explanation:

Since every 2 ticks are worth 6 (|-10|-|-4|=6), then one tick is worth 3.

We are going backward, so we can count backward.

We have to go down 3 ticks, so -10-3=-13; -13-3=-16; -16-3=-19.

The blue dot is -19

Answer: The blue dot equals to -19.

Step-by-step explanation:

On the number line, there are the numbers -10 & -4.

-7 would fit in the middle of them. That means the number line goes by minus 3.

Count -10 , -13, -16, then you get on the the blue dot which is -19.

Therefore, -19 is the answer.

Answer:

2p+32

Step-by-step explanation:

8(p+4)-6p

8(p)+8(4)-6p

8p+32-6p

8p-6p+32

2p+32

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Answer: 4.3 meters

Step-by-step explanation:

Let the angle opposite the 3-meter side be [tex]\alpha[/tex].

Using the Law of Sines,

[tex]\frac{\sin \alpha}{3}=\frac{\sin 25^{\circ}}{2}\\\\\sin \alpha=1.5 \sin 25^{\circ}\\\\\alpha=\arcsin(1.5 \sin 25^{\circ})[/tex]

Using the sum of the angles in a triangle, the angle opposite the side [tex]\ell[/tex] is [tex]155^{\circ}-\arcsin(1.5 \sin 25^{\circ})[/tex].

Using the Law of Sines,

[tex]\frac{\ell}{\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}=\frac{2}{\sin 25^{\circ}}\\\\\ell =\frac{2\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}{\sin 25^{\circ}}\\\\\ell \approx 4.3[/tex]

Answer:  The correct answer is 4.3

Step-by-step explanation:

This is an Obtuse Scalene Triangle

Side a = 2

Side b = 3

Side c = 4.26571

Angle ∠A = 25°

Angle ∠B = 39.34°

Angle ∠C = 115.66°

Area = 2.70415

Perimeter p = 9.26571

Semiperimeter s = 4.63285

Calculate c, ∠B, and ∠C based on given a, b, and ∠A.

∠B = arcsin(b·sin(A)/a)

= 0.68662 rad = 39.34°

∠C = 180° - A - B = 2.01864 rad = 115.66°

c = a·sin(C)/sin(A) = 4.26571 = 4.3

Answer: To make it very simple for ourselves, we can just divide 8 by 4.29. Our answer will then be 1.8648018648 or rounded to 1.86 servings per dollar.

Hope this helps.

The solution for f(3) in the function f(x) = 7x² - 2x is 57

From the question, we have the following equation that can be used in our computation:

F(X) = 7x2-2x

To make the equation legible, we need to rewrite it

So, we have the following representation

f(x) = 7x² - 2x

Also from the question, we have

f(3)

This means that the value of x is 3, and we calculate f(x) when x = 3

Substitute the known values in the above equation, so, we have the following representation

f(3) = 7x² - 2x

So, we have the following equation

f(3) = 7(3)² - 2(3)

There are constants to add or subtract to both sides of the equation

So, we have the following representation

f(3) = 57

Hence, the solution is 57

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Answer:

D. The sum of the angles is 90°.

Step-by-step explanation:

The definition of complementary angles is that their measures add to 90°.

Answer:

y - 4 = (32/3)x

Step-by-step explanation:

x-intercept: -3/8

y-intercept: 4

x-intercept: (-3/8, 0)

y-intercept: (0, 4)

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (4 - 0)/(0 - (-3/8)) = 4/(3/8) = 32/3

y - y_1 = m(x - x_1)

y - 4 = (32/3)x

The probability that the weight will be between 3183 and 4022 grams is; 0.9323

The formula for z-score is;

z-score = (x – μ) / σ

where;

x is sample mean

μ is population mean

σ is standard deviation

Now, we want to find the probability that the weight will be between 3183 and 4022 grams. This is;

P(3183 < X < 4022)

When X = 3183

z = (3183 - 3637)/227

z = -2

When X = 4022

z = (4022 - 3637)/227

z = 1.696

Using online probability between two z-scores calculator, we have;

P(-2 < x < 1.696) = 0.9323

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