Evan loaned $54,000 to a small business at 3.65% compounded semi-annually for 1 year and 9 months. How much would the business have to repay him at the end of the period?

Answer:

The answer is 7/2

Step-by-step explanation:

d=2r

7=2r

r=7/2

The surface area of Cone is 452.16 unit².

The surface area of a cone is equal to the curved surface area plus the area of the base: π r² + πlr

where r is the radius and l is the slant height.

Given:

Radius= 8 unit

height= 6 unit

slant height, l = √8²+6²= √64+36 =√100= 10units

So, the Surface area of Cone

= πr (l +r)

= 3.14 x 8 ( 10 + 8)

= 25.12 x 18

= 452.16 unit²

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The equation of the velocity is v(t) = 24t² - 24t - 288 and the time where velocity is equal to zero is t = -3 and t = 4.

Apart from integration, differentiation is one of the two key ideas in calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a process called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation.

The function for the velocity can be found by differentiating the equation for the motion for the particle.

s(t) = 8t³ - 12t² - 288t

v(t) = d/ dt s(t)

v(t) = 24t² - 24t - 288

Velocity is zero for:

v(t) = 0

24t² - 24t - 288 = 0

t² - t - 12 = 0

t² - 4t + 3t -12 = 0

t(t - 4) + 3(t - 4) = 0

(t + 3)(t - 4) = 0

t = -3 and

t = 4

Hence, the equation of the velocity is v(t) = 24t² - 24t - 288 and the time where velocity is equal to zero is t = -3 and t = 4.

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Answer:

You can use the fact that both the cars were travelling at the same speed so we can take them equal to some variable.

The speed of the cars was 0.8 miles per hour

How to form may you can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

How  to find the speed of the cars?

Supposing that both the cars were travelling with the speed

Let the first car travels  miles

then as second car travels 12 miles extra, thus, distance traveled by second car is  miles.

Using the formula for speed, we have:

For first car:

Distance traveled =  miles

Speed =

Time taken =

Thus,

For second car:

Distance traveled =  miles

Speed =

Time taken =

Thus,

So, we got system of 2 linear equations in two variables.

Using the expression for x from first equation and substituting it in second equation, we get

Substituting this value in first equation to get the value of x

Thus,

The speed of the cars was 0.8 miles per hour

Answer:

Rational

Step-by-step explanation:

You will always get a rational number when you add, subtract, multiply, or divide rational numbers with integers.

Hope it helps!

The value of x is 1.51.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]5^x[/tex] - 4 = 7

[tex]5^x[/tex] = 7 + 4

[tex]5^x[/tex] = 11

Taking logs on both sides.

log [tex]5^x[/tex] = log 11

x log 5 = log 11

x = log 11 / log 5

x = 1.04/0.69

x = 1.51

Thus,

x is 1.51.

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The solution is, he have after his birthday total cards 79 cards.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Gil got 4 packages of trading cards.

He already had 75 cards.

so,

he have after his birthday total cards = 75 +4

                                                              = 79 cards

Hence, The solution is, he have after his birthday total cards 79 cards.

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Answer:

Step-by-step explanation:

AB= 20

We need 32.65 W power to maintain the temperature at 197°C.

In order to discover the wattage to maintain a temperature of 197°C for the crystals, we need to start by substituting that value into the function:

T(x) = 0.1w² + 2.157w + 20

197 = 0.1w² + 2.157w + 20

and set the equation equal to zero by subtracting 197 from both sides:

0.1w² + 2.157w - 177 = 0

To solve this equation we make use of the quadratic formula, which in this case will be:

[tex]w = \frac{- b (+/-)\sqrt{b^{2}-4ac } }{2a}[/tex]

in this case:

a=0.1

b=2.157

c=-177

which come from the equation according to their position in the equation with the form ax²+bx+c = 0.

so we substitute them into the formula like this:

[tex]w = \frac{- 2.157(+/-)\sqrt{2.157^{2}-4*(0.1)*(-177) } }{2*0.1}[/tex]

w= -54.22W and w=32.65W

we use the positive answer since that means that the power is being input into the system, a negative answer would mean you are retrieving power from the system which would cool the system down.

So we need 32.65W power to maintain the temperature at 197°C.

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The volume common to the two spheres is V = 2 * (2/3) * pi * r^3 = (4/3) * pi * r^3.

The volume shared by two spheres with radii r and centers separated by r/2 can be calculated by using the volume of a sphere equation and subtracting the volumes of two smaller spheres cut out by the intersection of the larger spheres.

Assume that the two spheres are centered at (r/2,0,0) and (-r/2,0,0). Finding the points where it intersects with a plane perpendicular to the x-axis and passes through the x-axis at x = r/4.

This plane cuts the spheres at two points, and the smaller spheres have the same radius as the distance between these points.

The radius of these spheres can be found using the Pythagorean theorem:

r = sqrt(r^2 - (r/2)^2) = sqrt(3r^2/4)

The volume of each smaller sphere is given by:

V = (4/3) * pi * (r)^3 = (4/3) * pi * (sqrt(3r^2/4))^3 = (2/3) * pi * r^3

Therefore, the volume common to the two spheres is given by:

V = 2 * (2/3) * pi * r^3 = (4/3) * pi * r^3.

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There are 38,400 different ways for Xing to construct a banana split at this ice cream shop if he is allowed to choose between zero and three sprinkled toppings.

a) In order to construct a banana split, Xing needs to select 3 flavors of ice cream, 6 sauces, and 3 sprinkled toppings. Therefore, the formula for the number of ways to construct a banana split is (20 flavors)(6 sauces)(10 toppings)^3. When calculated, this number is 28,800. This means that there are 28,800 different ways for Xing to construct a banana split at this ice cream shop.

b) In this scenario, the formula for the number of ways to construct a banana split is (20 flavors)(6 sauces)(10 toppings)^0 + (20 flavors)(6 sauces)(10 toppings)^1 + (20 flavors)(6 sauces)(10 toppings)^2 + (20 flavors)(6 sauces)(10 toppings)^3. When calculated, this number is 38,400. This means that there are 38,400 different ways for Xing to construct a banana split at this ice cream shop, with the option to choose zero, one, two, or three sprinkled toppings.

Therefore, there are 38,400 different ways for Xing to construct a banana split at this ice cream shop if he is allowed to choose between zero and three sprinkled toppings.

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The market equilibrium on the graph is the point at the middle of the graph where supply and demand intersect.

The market equilibrium has the price of $ 6 and the quantity of 20 units.

The revenue at the equilibrium is $ 120.

The price floor would create a surplus.

The market equilibrium is described as the point where the supply and demand curves intersect. This point has the price of $ 6 and the quantity of 20 units as shown on the graph.

The revenue at this point is:

= 6 x 20

= $ 120

The price floor of $ 8 would mean that the minimum supply would be 30 units and the maximum demand would be 10 units which therefore creates a surplus.

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Option (b) is correct. The sample size was not sufficiently large.

The histogram that is shown at the end of the answer shows the results of the simulation. We can clearly see that there are different variations in the population size. There are various reasons which can cause the simulation not to be normal. The main reason for this if the sample size is not big enough. That is because a theory stated that when the sample size taken by a person or researcher is not large or insufficient for the alpha level as well as the analysis one chooses to do, it will limit the statistical power of the study.

Due to the above, we can say that the sample size is not big enough that's why the simulation of the sampling distribution is not approximately normal. So option (b) is correct.

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Your question was incomplete, your most probable question was stated below:
A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation.

Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

(a) The samples were not selected at random.

(b) The sample size was not sufficiently large.

(c) The population distribution was approximately normal.

(d) The samples were selected without replacement.
(e) The sample means were less than the population means.

The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed.

When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x² up by 3 units, the graph of the function f(x) = x² + 3 is obtained.

Given that the transformation of the coordinate is x,y ( x+2,y-3). Let the coordinate of the point be ( 2, 2 ).

The translation of the point will be:-

( 2 , 2 ) = ( 2 + 2 , 2 - 3 )

( 2 , 2 ) = ( 4 , -1 )

The graph of the translation of the point is attached with the answer below.

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Answer:

option B

Step-by-step explanation:

it's off and on 12345678910

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Therefore , the solution of the given problem of area comes out to be Formula for Square Area is = length * length.

Its surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.

Here,

To fill the blank space in the given problem is

Formula for Square Area

We are aware that Side Side equals the area of a square.

7 7 Equals 49 when the side length of 7 cm is substituted.

As a result, the square's area is 49 cm2.

Therefore , the solution of the given problem of area comes out to be Formula for Square Area is = length * length.

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A linear system is a set of linear equations that can be written in the form ax + by = c, where x and y are variables, a and b are coefficients, and c is a constant.

A linear system is considered homogeneous when all the equations in the system are equal to zero, i.e., they have a constant term of zero. For example, a homogeneous linear system could be:

a linear equation is represented as

2x + 3y = 0

4x - 5y = 0

In this example, both equations are homogeneous because the constant term is equal to zero.

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The formula for the tangent line to f(x) = ln(x) at x = 2 is 2y = x − 2.

We must first differentiate f(x).

The derivative of ln(x) is 1/x

The slope of the tangent at a point x = a on the function f(x) is given by evaluating f'(a).

Hence, the slope of the tangent is 1/x = 1/2

The function passes through,

(1/2, ln1)=(2, 0).

Now, we can use point slope form to find the equation of the tangent.

y − y1 = m( x− x1)

y − 0 = 1/2( x− 2 )

2y = x - 2

Thus, the equation of the tangent is 2y = x − 2.

The straight line that "just touches" the curve at a given position is known as the tangent line to a plane curve at that location. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

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The mean of the data is 4, the median is also 4. The range is 9, with an interquartile range of 2. The standard deviation is 2.14 and the skewness measure is 0.38, indicating a slight positive skew. No outliers are present.

(a) [tex]Mean = (7 + 2 + 6 + 4 + 9 + 4 + 1 + 4 + 2 + 4 + 5 + 2 + 3 + 5 + 2 + 0 + 6 + 7 + 4 + 2) / 20 = 4.[/tex]

[tex]Median = 4[/tex] (after sorting the data)

(b) First quartile (Q1) = 2 (after sorting the data and finding the median of  the lower half)

Third quartile (Q3) = 6 (after sorting the data and finding the median of the upper half)

(c) Range = 9 - 0 = 9

Interquartile Range (IQR) = Q3 - Q1 = 6 - 2 = 4

(d)[tex]Variance = ((7-4)^2 + (2-4)^2 + (6-4)^2 + (4-4)^2 + (9-4)^2 + (4-4)^2 + (1-4)^2 + (4-4)^2 + (2-4)^2 + (4-4)^2 + (5-4)^2 + (2-4)^2 + (3-4)^2 + (5-4)^2 + (2-4)^2 + (0-4)^2 + (6-4)^2 + (7-4)^2 + (4-4)^2 + (2-4)^2) / 20 = 9.05[/tex]

Standard deviation = √Variance = √9.05 = 3.01

(e) Skewness measure = 0. The data are symmetrically distributed (i.e., not skewed to the left or to the right)

(f) Lower limit = 4 - 3.01 x 1.5 = -1.51

Upper limit = 4 + 3.01 x 1.5 = 8.51

Data does not contain outliers as all values are within the lower and upper limits.

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the CPI to the nearest tenth in 1950 was 24.06.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, a bottle of dishwashing detergent cost $0.31 in 1950 and In 1970, a bottle of dishwashing detergent cost $0.50

Since CPI, Consumer Price Index measures the overall change in consumer prices based on a representative basket of goods and services over time.

The price of dishwashing detergent increased at the same rate as the CPI from 1950 to 1970.

So,

0.50 / 0.31 = CpI for 1970/ CPI for 1950

Since CPI in 1970 is 38.80

CPI in 1950 = 0.62 * 38.80

CPI in 1950 = 24.056

Therefore,  the CPI to the nearest tenth in 1950 was 24.06.

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Complete question:

In 1970, a bottle of dishwashing detergent cost $0.50. To answer each of the parts below, assume that the consumer price index (CPI) was 29.6 in 1960, 38.8 in 1970, and 82.4 in 1980.

If the price of dishwashing detergent increased at the same rate as the CPI from 1970 to 1980, how much did a bottle of dishwashing detergent cost in 1980? By how much did the price of a bottle of dishwashing detergent increase from 1970 to 1980?

Answer:

Step-by-step explanation:

A. The total cost after t hours can be represented by the linear equation C(t) = 50 + 190/4 * t, where C(t) is the total cost after t hours.

B. The electrician charges 190/4 = $47.5 per hour.

The correct answer is option C. In a research proposal, the Data Collection method discusses the types of scales to be used for data collection.

The Data Collection Method section of a research proposal is where the various scales for data collection are discussed. The types of scales (such as Likert scales, qualitative scales, etc.) and specific research instruments (such as surveys, interviews, questionnaires, or focus groups) typically are described in this section. that will be applied to the measurement of the variables. The target population and the definition of the sample size might also be discussed in the sample design section.

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[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{(~~ 4- (-2)~~)^2 + (~~ 3- (-2)~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 6)^2 + ( 5)^2} \implies \boxed{AB=\sqrt{ 61 }} \\\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill BC=\sqrt{(~~ 3- 4~~)^2 + (~~ 4- 3~~)^2}[/tex]

[tex]~\hfill BC=\sqrt{( -1)^2 + ( 1)^2} \implies \boxed{BC=\sqrt{ 2 }} \\\\\\ C(\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad A(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-2}) ~\hfill CA=\sqrt{(~~ -2- 3~~)^2 + (~~ -2- 4~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -5)^2 + (-6)^2} \implies \boxed{CA=\sqrt{ 61 }} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{two equal sides}}{\textit{\LARGE Isosceles}}~\hfill[/tex]

A simple path which visits all vertices can be found using a linear-time algorithm.

How to handle visited vertex is the issue.

The time complexity isn't really linear as you follow because of the many visits.

If not, the following straightforward example will show that your algorithm is flawed:

1 --> 2 -----------> 3 --> 4

       \         /

        --> 5 -->

After finding 1-2-3-4 in the initial search, the search returns to 2 and finds 1-2-5-3. Now that number 3 has been visited, the search halts and ultimately fails.

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Answer:

(9.25*0.03)+9.25=9.53

(9.53*0.16)+9.53=11.05

Sales tax was $0.28

Step-by-step explanation:

Answer:

B.0.85

C.85/100

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3

I really think it's option A because it's more than 90° and less than 180°

Answer:

A

Step-by-step explanation:

An obtuse triangle is a triangle in which one of the interior angles measures more than 90° degrees

formula for finding obtuse triangle is 1/2 *base*height

The expressions of the sale price is as follows:

Expression B: 0.8p

Expression D: p - 0.2p

The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price.

Therefore, the expression that represent the sale price in dollars of the items can be calculated as follows:

original price = p

Therefore, let's find the percent off the price.

price off = 20% of p

price off = 20 / 100 p

price off = 0.2p

Therefore,

sale price = p - 0.2p

sale price = 0.8p

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Answer:

It's 59 degrees