Isaac saves 20% on a hard drive that costs $110 but must pay 6% sales tax. What is the total amount that he must pay at the store?
A. $93.28
B. $88.00
C. $106.00
D. $140.80
E. None of the above

The future value and interest earned when compounded semiannually are $13,576.14 and $4,871.58 respectively.

The future value and interest earned when compounded continuously are $13,651.47 and $4,946.91 respectively.

Compound interest is mathematically expressed as;

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

Given the data in the question;

a) Determine the accrued amount and interest when compounded semiannually ( n = 2 )

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

A = 8704.56(1 + 0.05/2)^( 2× 9 )

A = 8704.56(1 + 0.025)¹⁸

A = 8704.56(1.025)¹⁸

A = 8704.56(1.025)¹⁸

A = $13,576.14

Note that; A = Principal + Interest.

Interest = $13,576.14 - $8704.56 = $4,871.58

b) Determine the accrued amount and interest when compounded continuously.

A = P × e^(r × t)

A = 8704.56 × e^(0.05 × 9)

A = 8704.56 × e^0.45

A = $13,651.47

Note that; A = Principal + Interest.

Interest = $13,651.47 - $8704.56 = $4,946.91

The future value and interest earned when compounded semiannually are $13,576.14 and $4,871.58 respectively.

The future value and interest earned when compounded continuously are $13,651.47 and $4,946.91 respectively.

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probability that a randomly chosen colony diameter is greater than or equal to 10 =P(10<X<12)+P(12<X<14)

=0.14+0.02 = 0.16

Probability is basically how likely something is to happen. Whenever we're uncertain around the outcome of an occasion, ready to talk approximately the probabilities of certain outcomes—how likely they are. The analysis of occasions administered by probability is called statistics.

Probability may be a measure of the probability of an event to occur. Numerous events cannot be predicted with add up to certainty. Able to predict as it were the chance of an occasion to happen i.e. how likely they are to happen, using it.

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By finding the positive root of the quadratic equation, we conclude that the rock will hit the ground 7 seconds after it is thrown.

We know that a rock is thrown from a cliff whose height is 224 ft. And the equation that models the height of the rock as is the quadratic equation:

h(t) = -16t² + 80t + 224

The rock will reach the ground when its height is equal to zero, so what we need to find is the positive root of the quadratic equation, so what we need to solve is:

-16t² + 80t + 224 = 0

Solving it we get:

t = (-80 ± √(80² - 4*(-16)*224)/(2*-16)

t = (-80 ± 144)/(-32)

The positive solution is:

t = (-80 - 144)/(-32) = 7

This means that the rock will hit the ground 7 seconds after it is thrown.

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The given statement is False. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.

Euclidean geometry a mathematical system in which we study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid.

Parallel Postulate is one of the five postulates of Euclidean geometry. It is Euclid's fifth postulate which states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.

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An angle is a figure formed by two rays with a common initial point called a of the angle.

What does a math angle mean?

What is type of angle ?

What is acute angle?

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The coordinate of another point will be (a/2,y) where y can be any value.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

An isosceles triangle is a triangle whose two sides are equal.

Let's say AB = AC

So,

Distance associate to AB = Distance associate to AC

(x- 0)² + (y - 0)² = (x - a)² + (y - 0)²

x² + y² = (x - a)² + y²

x = a/2

So the coordinate of the third vertex is (a/2,y)

Hence "The coordinate of another point will be (a/2,y) where y can be any value".

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Answer: x=2/3

Step-by-step explanation:

Just like polynomials and other expressions, you can perform basic arithmetic operations on rational expressions: addition, subtraction, multiplication, and division. A rational expression is a fraction whose numerator and the denominator is a polynomial. If f is a logical expression, then we can write f in the form of p/q, where p and q are polynomials.

Solution:

To find the restriction on a variable in the denominator, we Set the denominator equal to zero. Then we solve for X

So,

X+1 = 0

X = -1

X-4 = 0

X = 4

When we put the X= -1 or X= 4, we get 0 in the denominator, so these are restrictions variables

= (x2+4x+3)/(x2-3x-4)

= (x+1) (x+3)/(x+1) (x-4)

Now cancel the common factor (x+1)

= x+3x-4

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An equation that could be used to represent the context if a represents the number of miles in the taxi ride is ​1.70 + 1.75a = 17.45

We are given;

Base pick up fee = $1.70

Additional taxi fee per mile covered = $1.75

Total taxi fare = $17.45

Now, if we assume that a represents the number of miles in the taxi ride, then we can form the equation to represent the given scenario above as;

1.70 + 1.75a = 17.45

We conclude that an equation that could be used to represent the context if a represents the number of miles in the taxi ride is ​1.70 + 1.75a = 17.45

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Answer:

A shipping box is in the shape of a cube. What is the volume of the shipping box if the length of one side of the box is 4m24n4

The quotient of 117 divided by 9 is 13.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

The answer thus got is called the quotient.

We have to divide 117 by 9.

Division algorithm states that,

Dividend = (Divisor × quotient) + Remainder

Remainder will be 0 if divisor is a factor of dividend.

Here dividend = 117 and divisor = 9

We know that 90 is a multiple of 9, where 90 = 9 × 10.

Remainder is 117 - 90 = 27

27 = 9 × 3

Hence 117 = 90 + 27 = (9 × 10 ) + (9 × 3) = 9 (10 + 3) = 9 × 13

So 117 / 9 = 13

Hence the quotient is 13.

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So we are provided with the equation,

x2 + 10x + 40 = 5

To simplify it, we will first reorder the terms,

40 + 10x + x2 = 5

Now we will solve the equation to find the value of the unknown variable that we declared here as x.

40 + 10x + x2 = 5

Solving for variable 'x.'

40 + -5 + 10x + x2 = 5 + -5

We will combine similar terms; the variables and the constants.

40 + -5 = 35

35 + 10x + x2 = 5 + -5

Combine the like terms again:

5 + -5 = 0

35 + 10x + x2 = 0

Adding -35 on both sides

35 + 10x + -35 + x2 = 0 + -35

35 + -35 + 10x + x2 = 0 + -35

35 + -35 = 0

0 + 10x + x2 = 0 + -35

10x + x2 = 0 + -35

0 + -35 = -35

10x + x2 = -35

The x term is 10x.

Take half its coefficient (5) to make it a perfect square.

Square it (25) and add it to both sides.

10x + 25 + x2 = -35 + 25

25 + 10x + x2 = -35 + 25

-35 + 25 = -10

25 + 10x + x2 = -10

Perfect square on the left side:

(x + 5) (x + 5) = -10

We can see that the Square root of the right side can’t be calculated.

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Answer:

473085 is the answer

Step-by-step explanation:

Hope it helps you

to get the equation of any straight line, we simply need two points off of it, let's use the points from the table in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 3 }\implies -1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\LARGE \begin{array}{llll} y=-x+6 \end{array}}[/tex]

The answer is 4. The generalized equation is y = f(x). So when the coordinate of x is 4, value of y is 2

Graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9).

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

The coordinate plane comprises a horizontal line (x-axis) and a vertical line (y-axis), and it is divided into four quadrants named using roman numbers (I, II, III and IV).

The different points in a graph have coordinates written as ordered pairs (pairs of numbers within parentheses separated by a comma). The first number in an ordered pair (x, y) represents the value of x, and the second one represents the value of y for a given point.

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Answer:

Step-by-step explanation:

t = number of trees per 3 oranges

3t = 15

3t/3 = 15/3

    t = 5 trees

Answer:

14ft 8in by 12ft 10in

The simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3)  is 12x - 63.

According to the given question.

We have an expression 3[2(x - 3) + 2] + 5(x - 3).

To simplify the above expression we will use the distributive law and add and subtract the like terms.

Therefore,

3[2(x - 3) + 2] + 5(x - 3)        

= 3[2x - 6 + 5x - 15]      (distributive rule)

= 3[7x - 21]             (adding the like terms)

= 21x - 63

Therefore, the simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3)  is 12x - 63.

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Answer:

2

Since the numbers after the decimal are above 500 , thereby rounding it to nearest whole number is 2.

Answer:

its option C: x = 3

Step-by-step explanation:

The distance between the cars, x = 3 miles

The equation representing two cars traveling in opposite directions is given by, 8x-12 = 4x,

where 'x' is the distance (in miles) between the cars.

We need to find 'x'.

The equation given is a linear equation in x. So we will solve for 'x'.

8x-12 = 4x

⇒ 8x-4x = 12

⇒ 4x = 12

⇒ x = 12/4

⇒ x = 3

So the distance between the cars = 3 miles

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Answer:

The answer is A because both equations are true

[tex] a) \: {x}^{3} - 2 = {1}^{3} - 2 \\ = 1 - 2 \\ = - 1 \\ \\ b) \: {x}^{2} + 4 = {1}^{2} + 4 \\ = 1 + 4 \\ = 5 \\ \\ [/tex]

The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.

The given arithmetic series is 10+7+4+ . . .

The summation notion of given series is ∑10-3n , here n starts from 0.

The sum of arithmetic series can be written as,

[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]

n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.

We have, n=5, [tex]a_{1}[/tex] = 10

To calculate sum of arithmetic series, we need to find [tex]a_{5}[/tex] .

[tex]a_{5} = a_{1} + (n-1)d[/tex]

d = -3 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get

[tex]a_{5}[/tex] = 10 + (5-1)(-3)

[tex]a_{5}[/tex] = 10-12 =-2

On substituting values in sum of arithmetic series formula, we get

[tex]S_{5}[/tex] = (5(10 + (-2)))/2 = 20

The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.

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Answer:

40 psi

Step-by-step explanation:

We can see that the relationship is linear with pressure increasing by 5 psi for every extra 15 feet depth

The data is given from depth of 40 feet

At 40 feet, pressure = 10 psi  

At 55 feet, pressure = 15 psi

At 70 feet pressure = 20 psi

We have to use 40 as the base depth since there are no measurements less than that value. So relative depth is d - 40 and since for every 15', there is an increase of 5psi, the relative increase in pressure  per 15' is [tex]= \dfrac{d-40}{15}\cdot 5[/tex]

But the base pressure is 10psi not 0 so we have to add 10 to this equation to get the absolute psi

So the equation that connects depth (d) and pressure (p) is:

[tex]p = \dfrac{d - 40}{15}\cdot 5 + 10\\\\\textrm{At 130' depth},\\p = \dfrac{130-40}{15}\cdot 5 + 10\\= \dfrac{90}{15}\cdot 5 + 10\\\\= 30 + 10 = 40 psi\\[/tex]

If we plot these values, we can see they fit a straight line with slope = 1/3 and y-intercept = -10/3

Hope that helps

Using substitution method, the solution of the given system of equations is (-3,0)

A system of equation can be solved using:

The given system of equations:

4y - 6 = 2x   ............   (1)

y - 3x = 9  .............. (2)

We need to find the solution using substitution method.

In equation (2), add 3x to both sides:

y - 3x + 3x = 9 + 3x

y =  9 + 3x   ........ (3)

Substitute y =  9 + 3x into equation (1):

4y - 6 = 2x

4.(9 + 3x) - 6 = 2x

36 + 12x - 6 = 2x

12x - 2x = 6 - 36

10x = -30

   x = -3

Substitute back x = -3 into equation (3)

y =  9 + 3x

  = 9 + 3.(-3)

  = 9 + (-9) = 0

Hence, the solution is (-3, 0)

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Answer:

dbc

Step-by-step explanation:

thats the only one that is obtuse

Answer:

49π in²

Step-by-step explanation:

Formula for Area of a Circle: A = πr²

The image shows the radius (r) = 7in

A = πr² → A = π(7)²→ A = π(49)

A = 153.94 in²

Step-by-step explanation:

Area of circle with radius of r is given by:

[tex] a = \pi {r}^{2} \\ a = 49\pi {(in)}^{2} \\ or \: \: a = 153.9 \: {(in)}^{2} [/tex]

Answer: #11? y^2-14 #12 m^2-64

Step-by-step explanation:

- For the second question you apply the same steps to #12 to get m^2-64

Answers:

14 rides: 52

and

r rides: 3r + 10

Step-by-step explanation:

3(14) + 10

52

[tex]4x-2=-12\\\\4x=-10\\\\\frac{4x}{4} =\frac{-10}{4} \\\\x=\boxed{-\frac{5}{2} }[/tex]

The smallest integer is 1 and solution is (₋1)

Given, the inequality is 2x ₋ 8 ≥ ₋11

The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. A statement that two things are not equal is what is meant by the word "inequality." It's possible for one of the items to be more than, smaller than, equal to, or equal to the other things.

now add 8 on both sides.

2x ₋ 8 ₊ 8 ≥ ₋11 ₊ 8

2x ≥ ₋3

dividing both sides by 2.

2x/2 ≥ ₋3/2

⇒ x ≥ ₋3/2

₋3/2 is not an integer.

hence the smallest integer value of x is 1, and solution is (₋1)

Hence we get the integer value as 1.

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