Allan needs to repay a $3000 loan. His bank offers personal loans at 9.5% per year, compounded monthly. Allan can afford to make monthly payments of $100. How long will it take him to repay the loan?

Answer: first one is 700

Step-by-step explanation:

These are just a few examples of real life situations where you might need to find the volume or surface area of a shape. There are many other situations where this knowledge is useful, including in scientific research, medical imaging, and many other fields.

In mathematics, volume is the amount of space occupied by an object or a shape. It is a measure of how much three-dimensional space an object or a shape takes up. Volume is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or cubic inches (in³).

Here,

There are many real life situations where you might need to find the volume or surface area of a shape. Here are some examples:

Packaging and Shipping: In order to package and ship products, companies need to know the volume and surface area of the products and their packaging. For example, a shipping company needs to know the volume and surface area of a package in order to determine how much space it will take up in a truck or airplane, and how much packaging material will be required.

Construction: Architects, engineers and builders need to know the volume and surface area of building materials such as concrete, steel, bricks, and insulation in order to estimate the amount of materials required for a project. They also need to know the volume of a space to determine the amount of materials required to fill it, such as the amount of concrete required to fill a foundation or the amount of insulation needed to insulate a room.

Cooking and Baking: When cooking or baking, you may need to measure the volume or surface area of a container or cooking vessel to ensure that the recipe will fit and cook or bake properly. For example, you might need to measure the volume of a baking dish to know how much batter to use, or measure the surface area of a frying pan to know how much oil is needed.

Gardening and Landscaping: In gardening and landscaping, you may need to know the volume of soil required to fill a raised bed or the surface area of a lawn in order to determine the amount of fertilizer or weed killer required.

Industrial Design: In industrial design, designers need to know the volume and surface area of products in order to determine the materials required for production and to ensure that the product will fit in its intended location. For example, a designer may need to know the volume and surface area of a water tank to determine its capacity and the amount of materials required to build it.

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Answer: V(x) = -5x^2 + 70x

Step-by-step explanation:

Let the length and width of the rectangular base be represented by x and y, respectively.

Since the perimeter of the rectangular base is 28 cm, we have:

2x + 2y = 28

x + y = 14

The height of the box is given as 5 cm.

The volume of the box is given by:

V = lwh = xy(5)

V = 5xy

We can solve for y in terms of x from the equation x + y = 14:

y = 14 - x

Substituting this into the equation for the volume, we get:

V = 5x(14 - x)

Simplifying:

V = 70x - 5x^2

Answer:   To find the time at which the temperature is maximum, we need to find the vertex of the quadratic function T(x) = -0.07x^2. Recall that the x-coordinate of the vertex of a quadratic function f(x) = ax^2 + bx + c is given by -b/2a. In this case, a = -0.07 and b = 0 (since there is no linear term), so the x-coordinate of the vertex is x = -b/2a = -0/(-0.14) = 0.

Since x is the number of hours after 6 a.m., the time corresponding to x = 0 is 6 a.m. Therefore, the temperature is a maximum at 6 a.m.

To find the maximum temperature, we evaluate T(0) = -0.07(0)^2 = 0. Therefore, the maximum temperature is 0 degrees Fahrenheit. Note that this result makes sense, since the quadratic function T(x) = -0.07x^2 is a downward-facing parabola, which means that the temperature decreases as the number of hours after 6 a.m. increases.

Step-by-step explanation:

Answer:

9⁴

Step-by-step explanation:

If I'm understanding what you're asking correctly, it would just be the answer above, which evaluates to 6561.

55 + 5x, because we substitute g(x) = 5 in f(x) and get the final function as f(g(x)) = 55 + 5x. option E

We are given two functions:

f(x) = 55 + x

g(x) = 5

We need to find the value of f(g(x)), which means we need to substitute g(x) in place of x in f(x).

f(g(x)) = f(5)

Therefore, we need to find f(5).

f(x) = 55 + x

f(5) = 55 + 5 = 60

So, the answer is E. 55 + 5x, because we substitute g(x) = 5 in f(x) and get the final function as f(g(x)) = 55 + 5x.

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Answer:

a)

 103

         |

       96 +

         |

       92 |     *  

         |    * *  

       88 +--*    

         | *      

       84 |        

         |*        

       80 +        

         |        

       79 |        

         |        

       72 +        

         |        

       70 |

         |

b)b. The range is the difference between the highest and lowest scores: 103 - 45 = 58.

The IQR is the interquartile range, which is the range of the middle 50% of the scores. To find it, we first need to find the first and third quartiles:

   The first quartile (Q1) is the median of the lower half of the scores, which are 45, 70, 72, 79, and 80. The median of this set is (72+79)/2 = 75.5.

   The third quartile (Q3) is the median of the upper half of the scores, which are 84, 87, 88, 92, and 96. The median of this set is (88+92)/2 = 90.

Therefore, the IQR is 90 - 75.5 = 14.5.

c)c. To find any outliers, we need to first define the "fences" of the box and whisker plot. The lower fence is Q1 - 1.5IQR = 75.5 - 1.514.5 = 53.25. The upper fence is Q3 + 1.5IQR = 90 + 1.514.5 = 112.75.

There is one score that is outside the fences: 103. Therefore, 103 is an outlier.

Step-by-step explanation:

The square of the binomial that represents the trinomial is [tex](0.1b+10c)^{2}[/tex], and the missing monomial is 10bc.

What is Trinomial ?

A trinomial is a polynomial that consists of three terms. In algebra, a term is a combination of a constant and one or more variables, multiplied together. A trinomial, therefore, is a polynomial that has three such terms.

To represent the trinomial 0.01[tex]b^{2}[/tex]+ ∗ +100[tex]c^{2}[/tex] as a square of a binomial, we need to find a monomial that can be added to it to form a perfect square trinomial.

To do this, we can take the square root of the first and last terms of the trinomial and multiply them together:

√(0.011[tex]b^{2}[/tex]) = 0.1b

√(100[tex]c^{2}[/tex]) = 10c

Multiplying these square roots together, we get:

0.1b * 10c = b * 1c * 10 = 10bc

So, the missing monomial is 10bc. Adding this monomial to the original trinomial gives us:

0.011[tex]b^{2}[/tex] + 10bc + 100[tex]c^{2}[/tex] =  [tex](0.1b+10c)^{2}[/tex],

Therefore, the square of the binomial that represents the trinomial is   [tex](0.1b+10c)^{2}[/tex], and the missing monomial is 10bc.

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Answer:

36hrs is 36/6.5=5.538 doubling periods. Initial population x0=100

Step-by-step explanation:

The rate of exponential growth of a bacterial culture is expressed as generation time, also the doubling time of the bacterial population. Generation time (G) is defined as the time (t) per generation (n = number of generations). Hence, G=t/n is the equation from which calculations of generation time (below) derive.

Answer:

9 gallons

Step-by-step explanation:

4 quarts = 1 gallon

12/4=3

3 + 6= 9

9 gallons

Answer:

2nd option

Step-by-step explanation:

After answering the presented question, we can conclude that As a equation result, 625 millilitres of pure fruit concentrate are required to generate 5 litres of cold drink.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

If we need to dilute the pure fruit concentrate with water in a 1:7 ratio, this means that we need 7 parts water for every 1 part concentrate.

As a result, in order to prepare 5 litres of cool drink, we will need:

0.625 litres of pure concentration = 1/8 x 5 litres

We multiply litres by 1000 to get millilitres:

625 millilitres of pure concentrate (0.625 x 1000).

As a result, 625 millilitres of pure fruit concentrate are required to generate 5 litres of cold drink.

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Answer:

B?

Step-by-step explanation:

Answer:

603.2 cubic inches

Step-by-step explanation:

First, we need to find the radius of the cone, which is half of the diameter:

radius = 12 inches / 2 = 6 inches

Next, we can use the formula to find the volume of a cone:

V = (1/3)πr^2h

where V is the volume, π is pi (approximately 3.14), r is the radius, and h is the height.

Substituting in the values we have:

V = (1/3)π(6 inches)^2(16 inches)

V = (1/3)π(36 square inches)(16 inches)

V = (1/3)π(576 cubic inches)

V = 192π cubic inches

Rounding to the nearest tenth, the volume of the cone is:

V ≈ 603.2 cubic inches

Hopes this helps

The top of the ladder is about 24.81 feet up the wall.

We can use the Pythagorean theorem to solve the problem and assume  the height up the wall that the top of the ladder reaches "x". Then, we have a right triangle with legs of 3 feet and x feet and a hypotenuse of 18 + 7 = 25 feet (the length of the ladder). So, we can write:

[tex]3^{2}[/tex] + [tex]x^{2}[/tex] = [tex]25^{2}[/tex]

9 + [tex]x^{2}[/tex] = 625

[tex]x^{2}[/tex] = 616

x = [tex]\sqrt{616}[/tex]

x ≈ 24.81 feet

According to Pythagoras's Theorem, the square of the length of a right-angled triangle's hypotenuse (the side that faces the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides) and this can be expressed mathematically as follows  [tex]c^{2}[/tex]= [tex]a^{2}[/tex] + [tex]b^{2}[/tex] where c is the hypotenuse's length and a and b are the lengths of the other two sides.

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Answer:
x > 53

30 + x > 83

Subtract 30 from both sides:

x > 53

Therefore, the solution is:

x > 53

DH is radius.

EG is a chord

FI line is tangent to the circle

H is the point of tangency

The point of tangency is the point where a tangent line touches a curve or a circle at a single point, without intersecting it. At this point, the tangent line is perpendicular to the curve or circle at that specific point. The point of tangency is important in calculus and geometry, as it is used to calculate derivatives and solve problems related to circles, curves, and other geometrical figures.

In the given circle,

DH is radius.

(As it passes through center of circle and touches its circumference)

EG is a chord

(It divides the circle into two parts)

FI line is tangent to the circle

(It touches the line externally)

H is the point of tangency

(It is a point where the tangent of circle and circle meets)

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Ok

so the math that we need to do for this problem will be:

Total number of families = 240

minus the ones that don't have any pets = 91

minus the families that do have dogs = 91

minus the families that do have cats = 70

add back the overlap of dogs and cats = 31

add back the overlap of dogs cats parakeets = 7

240 - 91 - 91 - 70 + 31 + 7

^ this math will give us the families that ONLY have parakeets

so I stand by what I said before that this is the math you would to do get the answer to your problem

therefore its 26 buddy

Step-by-step explanation:

[tex]n(p) only= \: n(p) - n(c n d np) \\ = 91 - 7 \\ = 84[/tex]

Answer:

The mass of a 5-year-old child is 20 kg. We can express this mass in scientific notation as:

2 x 10^1 kg

To find approximately how many times larger an elephant is than a 5-year-old child, we need to know the mass of an elephant. According to National Geographic, an average elephant can weigh between 2,700 and 6,000 kg. Assuming an average weight of 4,350 kg for an elephant, we can calculate the ratio of elephant mass to child mass as follows:

4,350 kg / 20 kg ≈ 218

Therefore, an elephant is approximately 218 times larger than a 5-year-old child in terms of mass.

To determine approximately how many water drops equal the mass of a child, we need to know the mass of a single water drop. This can vary depending on the size of the drop and the substance it is made of. However, for the purposes of estimation, we can assume that the mass of a water drop is approximately 0.05 grams.

The company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.

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 point at which the company starts to turn a profit, we need to find the value of x for which the revenue is greater than the cost of production.

The revenue function is R(x) = 7x, and the cost of production is C(x) = 13x + 132.

So, we need to solve the inequality:

R(x) > C(x)

7x > 13x + 132

Subtracting 13x from both sides, we get:

-6x > 132

Dividing both sides by -6 (and flipping the inequality because we're dividing by a negative number), we get:

x < -22

Therefore, the company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.

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Answer:

[tex]3(5w + 4) < 12w + 15[/tex]

[tex]15w + 12 < 12w + 15[/tex]

[tex]3w < 3[/tex]

[tex]w < 1[/tex]

A is the correct answer.

Answer:

Step-by-step explanation:

If 15 out of 50 students are twelve years old, we can estimate the proportion of twelve-year-olds in the whole school as follows:

Proportion of twelve-year-olds = 15/50

Simplifying this fraction by dividing both numerator and denominator by 5, we get:

Proportion of twelve-year-olds = 3/10

Similarly, if 20 out of 50 students are thirteen years old, we can estimate the proportion of thirteen-year-olds in the whole school as:

Proportion of thirteen-year-olds = 20/50

Simplifying this fraction by dividing both numerator and denominator by 10, we get:

Proportion of thirteen-year-olds = 2/5

Finally, if 15 out of 50 students are fourteen years old, we can estimate the proportion of fourteen-year-olds in the whole school as:

Proportion of fourteen-year-olds = 15/50

Simplifying this fraction by dividing both numerator and denominator by 5, we get:

Proportion of fourteen-year-olds = 3/10

Therefore, the best estimate of the proportion of students who are twelve, thirteen, and fourteen years old in the school, respectively, is:

3/10 are twelve years old

2/5 are thirteen years old

3/10 are fourteen years old

The equations for Sean's and Felisha's eggs when dropped from a height of 120 feet are given. By solving for t in each equation, it is found that Felisha's egg landed first by approximately 0.53 seconds.

To find the time it takes for each egg to hit the ground, we need to solve for t in each equation:

For Sean's egg:

f(t) = -16t² + 75t + 120

We want to find t when f(t) = 0 (i.e., when the egg hits the ground)

-16t² + 75t + 120 = 0

Divide both sides by -1 to simplify the equation:

16t² - 75t - 120 = 0

Using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = 16, b = -75, and c = -120.

t = (-(-75) ± √((-75)² - 4(16)(-120))) / 2(16)

t = (75 ± √(75² + 4(16)(120))) / 32

t = (75 ± √(7955)) / 32

We know that the egg cannot hit the ground in negative time, so we can discard the negative solution:

t = (75 + √(7955)) / 32

t ≈ 3.742 seconds

For Felisha's egg:

f(t) = -16t² + 55t + 120

We want to find t when f(t) = 0 (i.e., when the egg hits the ground)

-16t² + 55t + 120 = 0

Divide both sides by -1 to simplify the equation:

16t² - 55t - 120 = 0

Using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = 16, b = -55, and c = -120.

t = (-(-55) ± √((-55)² - 4(16)(-120))) / 2(16)

t = (55 ± √(55² + 4(16)(120))) / 32

t = (55 ± √(7649)) / 32

We know that the egg cannot hit the ground in negative time, so we can discard the negative solution:

t = (55 + √(7649)) / 32

t ≈ 3.212 seconds

Therefore, Felisha's egg landed first by:

3.742 - 3.212 ≈ 0.53 seconds (rounded to 3 decimal places).

Answer: Felisha's egg landed first by approximately 0.53 seconds.

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Complete question is in the image attached below

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations can be used to model a wide range of real-world situations, and they are an essential tool in many fields of study, including physics, engineering, and economics.

To solve for y, we need to isolate y on one side of the equation. We can do this by first distributing the 3 on the right-hand side:

24 = 3y + 18

Next, we can isolate 3y by subtracting 18 from both sides:

24 - 18 = 3y

6 = 3y

Finally, we can solve for y by dividing both sides by 3:

y = 2

Therefore, the solution to the equation 24 = 3(y + 6) is y = 2.

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For the first graph the two lines are parallel, that is they do not intersect. Thus, the system has no solution. For the second graph the y-intercept is 3 units.

The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations. There is only ever one solution to a linear equation with one variable. The one and only position at which LHS and RHS are equivalent upon substitution is the unique solution of a linear equation. When there are two simultaneous linear equations, the answer must be an ordered pair (x, y). The ordered pair will in this instance satisfy the set of equations.

For the first graph the two lines are parallel, that is they do not intersect. Thus, the system has no solution.

For the second graph the y-intercept is 3 units.

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Smithson will recognize the loss. So,the amount of loss will Smithson recognize on retirement of the liability is $309,248.85.

Profit or loss is the financial gain or loss resulting from the difference between revenue and expenses in a business or financial context.

Book value of ARL = Present value of estimated cash flows for ARL - Accumulated depreciation and amortization

PV = PMT x (1 - 1 / (1 + r)ⁿ) / r

The formula for weighted average is:

Weighted average = (Cash flow 1 x Probability 1) + (Cash flow 2 x Probability 2) + (Cash flow 3 x Probability 3)

PV = (700,000 x 0.25 x (1 - 1 / (1 + 0.08)⁵) / 0.08) + (750,000 x 0.4 x (1 - 1 / (1 + 0.08)⁵) / 0.08) + (850,000 x 0.35 x (1 - 1 / (1 + 0.08)⁵) / 0.08)

PV = $2,317,283.36

Since this is the end of the first year, the accumulated depreciation and amortization is simply the present value of the estimated cash flows for the first year:

Accumulated depreciation and amortization = (700,000 x 0.25 / (1 + 0.08)) + (750,000 x 0.4 / (1 + 0.08)) + (850,000 x 0.35 / (1 + 0.08))

Accumulated depreciation and amortization = $1,830,532.21

Finally, we can calculate the book value of the ARL at the end of one year:

Book value of ARL = Present value of estimated cash flows for ARL - Accumulated depreciation and amortization

Book value of ARL = $2,317,283.36 - $1,830,532.21

Book value of ARL = $486,751.15

Therefore, the book value of the asset retirement liability at the end of one year is $486,751.15.

Loss = Actual restoration costs - Book value of ARL

Loss = $796,000 - $486,751.15

Loss = $309,248.85

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Based on the given information, the value of y is 5.

What is a cyclic polygon?

A cyclic polygon is a polygon that can be inscribed inside a circle in such a way that all of its vertices lie on the circumference of the circle. In other words, a cyclic polygon is a polygon that can be circumscribed by a circle.

In a polygon with n sides, the sum of its interior angles is given by the formula: (n - 2) * 180 degrees. Since this polygon is inside a circle, it must be a cyclic polygon, which means that its opposite angles add up to 180 degrees.

We are given that the opposite angles are 23y and 13y, so we can write:

23y + 13y = 180

36y = 180

y = 5

Therefore, the value of y is 5.

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The probability that Julian lives in a house with a skylight or a fireplace is 35/57, which can be simplified to 5/8 in the lowest terms. So the answer is: 5/8.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To calculate the probability that Julian lives in a house with a skylight or a fireplace, we need to add the number of houses that have a skylight and the number of houses that have a fireplace, and then subtract the number of houses that have both a skylight and a fireplace, because we don't want to count those houses twice:

Number of houses with a skylight = 12

Number of houses with a fireplace = 28

Number of houses with both a skylight and a fireplace = 5

Number of houses with a skylight or a fireplace = (12 + 28) - 5 = 35

Therefore, the probability that Julian lives in a house with a skylight or a fireplace is 35/57, which can be simplified to 5/8 in the lowest terms.

So the answer is: 5/8.

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Answer:

117in

Step-by-step explanation: 9in x 13in=117in

So, Edward needs to use a round cast iron pan with a radius of 177 inches to have the same area as the rectangular pan. correct answer is (d).

To find the area of a circle, you need to know its radius (the distance from the center of the circle to any point on its perimeter). Once you know the radius, you can use the following formula:

[tex]Area = \pi * radius^2[/tex]

where π (pi) is a mathematical constant approximately equal to 3.14159.

So, to find the area of a circle, follow these steps:

Measure the radius of the circle.

Square the radius (multiply it by itself).

Multiply the squared radius by π.

Round your answer to the desired number of decimal places (usually 1 or 2).

The area of a 9-in. by 13-in. rectangular pan is:

Area = length x width = 9 in. x 13 in. = 117 in.²

So, the area of the rectangular pan is 117 in.².

To use a round cast iron pan with the same area, Edward needs to find the radius of the circle with an area of 117 in.²:

Area of a circle = πr²

[tex]= \pi r^2[/tex]

[tex]= 117 in.^2 /[/tex]

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the complete question: Edward's grandmother used to make him Pannukakku when he was little. He wants to surprise.

her by making it himself. The recipe he found requires a 9-in. by 13-in. rectangular pan.

Edward would like to use a round cast iron pan like his grandmother does.

What is the area of a 9-in. by 13-in. pan?

[tex](a) 22in^{2} \\(b)44in^{2} \\(c)108in^{2} \\(d)117in^{2}[/tex]

Y=2x+6

x=2y+6

2y=6-x/÷2

y=[tex]\frac{6-x}{2}[/tex]