How much would you be willing to pay today for an investment that would return $800 each year at the end of each of the next 6 years? Assume a discount rate of 4 percent.

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:

B?

Step-by-step explanation:

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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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 probability of picking a 7 and then picking a 7 is 8.33%.

Since we are not replacing the first card before drawing the second one, the probability of drawing a 7 on the first card is 1/4. After drawing the first card, there are three remaining cards, and only one of them is a 7. Therefore, the probability of drawing a 7 on the second card given that the first card was a 7 is 1/3.

Using the multiplication rule of probability, the probability of drawing a 7 on the first card and then drawing a 7 on the second card without replacement is

P(7 on the first card) x P(7 on the second card | 7 on the first card) = (1/4) x (1/3) = 1/12

P(7 on the first card and then a 7 on the second card) = 1/12 x 100% = 8.33%

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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 6

Step-by-step explanation:  A = 1/2 bh, 6 x 2 is 12 and 1/2 of 12 is 6

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: first one is 700

Step-by-step explanation:

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:

2nd option

Step-by-step explanation:

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:

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]

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.

Part (a)

Answers:

A' = (0, 2)

B' = (-1, -2)

C' = (-3, -2)

D' = (-4, -1)

Explanation:

Multiply each coordinate by 1/3.

For instance,

[tex]B(-3,-6) \to B( -3*(1/3), -6*(1/3) ) \to B \ '(-1, -2)[/tex]

====================================================

Part (b)

Answers:

A' = (-5, 5)

B' = (-8, -7)

C' = (-14, -7)

D' = (-17, -4)

Explanation:

Subtract 5 from the x coordinate. Subtract 1 from the y coordinate. This moves each point 5 units to the left and 1 unit down.

I'll show an example using point C.

[tex](\text{x},\text{y})\to(\text{x}-5,\text{y}-1)\\\\(-9,-6)\to(-9-5,-6-1)\\\\(-9,-6)\to(-14,-7)\\\\[/tex]

Therefore, C(-9,-6) moves to C ' (-14,-7)

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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Answer:
x > 53

30 + x > 83

Subtract 30 from both sides:

x > 53

Therefore, the solution is:

x > 53

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.

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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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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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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Triangle ABC's longest side is found as 4 units. Thus, Triangle DEF has a 100-times larger area than triangle ABC.

A ratio is a tool being used compare the sizes of two or more quantities with relation to one another in mathematics. By making amounts easier to understand, ratios enable us to evaluate and express quantities.

Given that both triangles remain similar, triangle DEF is 10 times larger than triangle ABC according to the ratio 1:10.

Thus, Triangle DEF has a 100-times larger area than triangle ABC.

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It asserts that if the sky is clear, then it is not possible for the plane to be on time.

In general, a hypothesis is a proposed explanation or tentative answer to a research question or problem. It is a statement that can be tested through investigation and analysis of data.

The statement "q -> ~p" can be interpreted as "If the sky is clear, then the plane is not on time."

This is a conditional statement, where q represents the hypothesis or condition ("the sky is clear") and ~p represents the conclusion or result ("the plane is not on time").

It asserts that if the sky is clear, then it is not possible for the plane to be on time.

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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: 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:

[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:

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

Y=2x+6

x=2y+6

2y=6-x/÷2

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

1. The two triangles are congruent, ASA criteria. angle H ≅ angle M, HY ≅ MN and EY ≅ AN using CPCT. 2. The two triangles are congruent, ASA criteria. AT ≅ AP, by CPCT. Angle T ≅ angle P. CT ≅ RP, by CPCT.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

1. For the given triangle HEY and triangle MAN we see that,

angle E ≅ angle A

angle Y ≅ angle N

and HE ≅ AM

Thus, the two triangles are congruent using the ASA criteria.

Also angle H ≅ angle M (CPCT)

HY ≅ MN

EY ≅ AN using CPCT.

2. For triangle CAT and PAR we have:

angle A ≅ angle A (vertically opposite angles)

Angle C ≅ angle R

AC ≅ AR

Thus, the two triangles are congruent using the ASA criteria.

Also, AT ≅ AP, by CPCT

Angle T ≅ angle P, by CPCT

CT ≅ RP, by CPCT.

3. For the triangles ACL and triangle ARS:

AC ≅ AR and angle 1 ≅ angle 2 (Given)

Also, angle A = angle A (Vertically opposite angle)

Thus, the two triangles are congruent using ASA criteria.

Now, angle 3 ≅ angle 4 using CPCT.

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