Ryan is taking a survey to find out how many people prefer soda A over soda B. He surveyed 100 people and forty-nine preferred soda A. Seven percent had no preference for soda A or soda B. What percentage of peoples surveyed preferred soda B?

It will take 17 years and 10 months for the investment to grow to $4000.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P (1+r/n

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

Given:

Charmaine deposited $2000 into an account with a 3.9% annual interest rate, compounded quarterly.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.9/100

r = 0.039 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(4,000.00/2,000.00) / ( 4 × [ln(1 + 0.039/4)] )

t = ln(4,000.00/2,000.00) / ( 4 × [ln(1 + 0.00975)] )

t = 17.86 years

Hence, the time is 17 years and 10 months.

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Step-by-step explanation:

The limit of (sin(x)) / x as x approaches 0 is a well-known limit in calculus, known as the limit definition of the derivative of the sine function.

lim (x -> 0) (sin(x)) / x = 1

This limit can be proven using L'Hopital's rule or by considering the Taylor series expansion of the sine function about x = 0:

sin(x) = x - (x^3) / 6 + (x^5) / 120 + ...

As x approaches 0, the higher order terms in the Taylor series become arbitrarily small, and the expression (sin(x)) / x approaches 1. This shows that the limit of (sin(x)) / x as x approaches 0 is equal to 1.

The probability that the scholarship will be awarded to a senior given that it will not be awarded to a freshman is 2/9.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of students = 100

Freshman = 10

Sophomores = 325

Juniors = 30

Seniors = 20

Graduate students = 15

Now,

The probability that the scholarship will be awarded to a senior given that it will not be awarded to a freshman.

This means,

We will subtract the freshman from the total number of students.

So,

Total students = 100 - 10 = 90

Seniors = 20

And,

Probability = 20/90 = 2/9

Thus,

The probability that the scholarship will be awarded to a senior is 2/9.

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Answer:

A. 5 to 8
B. 13 to 8

Step-by-step explanation:

The solution is Option C.

The wholesale price of the sofa is given by the equation A = $ 1810.67

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the wholesale price of the sofa be A

Now , the sale price of the sofa = $ 2499.00

The percentage of markup in price = 38 %

So , the whole sale price A + percentage of markup of ( 38/10 )A = sale price of the sofa

Substituting the values in the equation , we get

( A + ( 38/100 )A ) = 2499

On simplifying the equation , we get

( 138/100 )A = 2499

Multiply by 100 on both sides of the equation , we get

138A = 249900

Divide by 138 on both sides of the equation , we get

A = $ 1810.87

Therefore , the wholesale price is $ 1810.87

Hence , the equation is A = $ 1810.87

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By using the relationship between quantities, the missing values in the table are:

A = 750

B = 1,250.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be represented by this mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in this 2-column table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 250/1

Therefore, a linear equation for this proportional relationship can be correctly written as follows:

y = kx

y = 250x

When x = 3, the value of A is given by:

y = 250(3) = 750.

When x = 5, the value of A is given by:

y = 250(5) = 1,250.

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The percentage of students that like chocolate chip the best is 50% percent.

Based on the information provided, the number of students that prefer chocolate chip flavor is 13. Using this number and the following formula, let's determine what percentage this number represents:

percentage = number of students x 100 / total of students

percentage = 13 x 100 / 50

percentage = 26%

This implies that the percentage of students who prefer chocolate chip flavor is 26% (twenty-six percent).

Note: This question is incomplete; here is the missing information:

Chocolate chip- 13

Vanilla- 25

Cookie Dough- 12

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B and E are both right angles.

C is an acute angle.

B and E are both 90⁰ as they are marked with a square on the angle. C is acute as it can not be larger than 90⁰ as angles in a triangle add up to 180⁰.

The value of cot(θ - π/2) is 1.52.

What are trigonometry ratios?

The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.

There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their respective angles using trigonometric ratios.

Given that tan θ = -1.52.

The given expression is

cot(θ - π/2)

= - cot(π/2 - θ)

Now applying the trigonometry identity cot(π/2 - θ) = tan θ:

= - tan θ

Now putting the value of tan θ = -1.52:

= - (-1.52)

= 1.52

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As a result, f(x-3) = x² - 6x + 13, as well as the simplified expression for f(x) = x² +4.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided.

Here,

To simplify the expression f(x-3), we need to substitute x-3 for x in the original expression f(x) = x² + 4.

So, f(x-3) = (x-3)² + 4

= x² - 6x + 9 + 4

= x² - 6x + 13

Therefore, f(x-3) = x² - 6x + 13 and also the simplified expression for f(x) = x² +4.

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Answer:

Step-by-step explanation:

In this case, the median would be a better measure of the center than the mean. The median is the value in the middle of a set of data when the values are arranged in order from least to greatest. In this case, there are 60 households, so the 31st household would be the median. Since 29 houses are worth $280,000 and one house is worth $2,500,000, the 31st house must be worth $315,000.

The mean, on the other hand, is calculated by adding up all the values and dividing by the number of values. The mean in this case would be significantly influenced by the one high-value household worth $2,500,000, leading to an estimate of the center that is much higher than the other values. In this situation, the median provides a better representation of the "typical" value among the majority of the households.

For equation B → 2A, the rate of reaction becomes:

-Δ[B]/Δt = (1/2) Δ[A]/Δt

Correct option: c

The rate of reaction may be defined as the change in concentration of any of the products or reactants per unit of time. The pace at which reactants change into products is known as the rate of reaction or reaction rate. It goes without saying that the pace at which chemical reactions take place varies greatly.

The given reaction is:

B → 2A

rate of reaction in terms of A:

rate = (1/2) d[A]/dt

rate of reaction in terms of B:

rate = -d[B]/dt

So,

rate = -d[B]/dt = (1/2) d[A]/dt

Correct option: c

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A permutation is a collection of things where the arrangement is important. In general, a permutation of a set in mathematics is the rearranging of its members into a sequence or linear order if the set already has an ordered structure.

A permutation is a grouping of items where the order is crucial.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.

The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

Contrasted with combinations, which are selections of a few members of a set independent of order, are permutations.

There are six permutations of the set "1, 2, 3," for instance, represented as tuples: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1).

Therefore, a permutation is a collection of things where the arrangement is important. In general, a permutation of a set in mathematics is the rearranging of its members into a sequence or linear order if the set already has an ordered structure.

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As h decreases, the value of (the change in x^2)/h increases, since 16h gets divided by a smaller value of h. For example, when h=0.1, (the change in x^2)/h = 16/0.1 = 160.

a. If h=1, then (the change in x^2)/h = 16/1 = 16

b. If h=0.1, then (the change in x^2)/h= 16/0.1 = 160

c. If h=0.01, then (the change in x^2)/h= 16/0.01 = 1600

d. If h=0.001, then (the change in x^2)/h= 16/0.001 = 16000

The change in x^2 refers to the difference in the value of x^2 when x is increased from 4 to 4+h. In other words, it is the difference between (4+h)^2 and 4^2. The change in x^2 is 16h, since (4+h)^2 = 16h + 4^2. To find (the change in x^2)/h, we simply divide 16h by h, which gives us 16. So, for each of the values of h given, when x is increased from 4 to 4+h, (the change in x^2)/h is 16. As h decreases, the value of (the change in x^2)/h increases, since 16h gets divided by a smaller value of h. For example, when h=0.1, (the change in x^2)/h = 16/0.1 = 160.

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The p-value for the test is  0.0062

To determine the p-value for Kara's hypothesis test, we need to calculate the test statistic and then find its corresponding p-value.

Let's start by calculating the sample mean and standard deviation of the given data:

Sample mean x = (46+43+41+48+51+51+52+42+51+54+40+53+46+46+46+39+47)/17 = 46.529

Sample standard deviation (s) = 4.547

We can use these values to calculate the t-statistic for the one-sample t-test:

t = (x - μ) / (s / sqrt(n))

where μ is the hypothesized population mean (50 hours), n is the sample size (17).

t = (46.529 - 50) / (4.547 / sqrt(17)) = -3.15

Using a t-distribution table with 16 degrees of freedom (n-1), we find that the p-value for a two-tailed test with a t-statistic of -3.15 is approximately  0.0062.

Therefore, the p-value for this hypothesis test is  0.0062

Since the p-value is less than the commonly used alpha level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the true mean work week for engineers in start-up companies is less than 50 hours.

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Answer:

look at the screenshot

Step-by-step explanation:

Water vapor is created when liquid water evaporates, and this water vapor then develops into clouds and falls back to earth as rain and snow.

Weather is the culmination of the present meteorological variables, such as temperature, wind speed and direction, precipitation amount and kind, weather is great hours, etc. The weather dictates a little window of time up over several days.

What you perceive outside when any given day is the weather. Therefore, for instance, it may be 20 ° with heavy snow or it could be 75 degrees and sunny. That is the climate. The average of the weather is the climate.

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The equation of the line is y = 4 and the y-coordinate of every point along this line is 4.

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y-axis, also known as the y -intercept.

Given that, we need to find an equation of a line passing through given points,

Considering two points, (-3, 4) and (1, 4)

We know that, the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by,

(y-y₁) = (y₂ - y₁ / x₂ - x₁)(x-x₁)

Here, (x₁, y₁) and (x₂, y₂) = (-3, 4) and (1, 4)

Therefore, the equation =

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

y-4 = 0

y = 4

Since, the slope is zero and y-intercept is 4 that mean, the line given is parallel to x-axis,

Hence, all the y coordinates will be 4.

Hence, the equation of the line is y = 4 and the y-coordinate of every point along this line is 4.

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Answer:

19/8

Step-by-step explanation:

[tex]a\frac{b}{c}=\frac{ac+b}{c}\\\\2\frac{3}{8}=\frac{2(8)+3}{8}=\frac{16+3}{8}=\frac{19}{8}[/tex]

Answer:

= 19/8

Step-by-step explanation:

2 = 16/

2 3/8 = 2+3/8 = 16/8 + 3/

= 19/

The correlation coefficient r is -0.7642

The equation of least square line is

y = -0.37x + 305.98

Correlation describes the strength of an association between two variables, and is completely symmetrical, the correlation between A and B is the same as the correlation between B and A.

Given,

Games won: 109,119,107,67,79,63,65,90

Batting average: 259,267,264,288,277,288,269,277

calculation is done by calculator and attached below.

Hence, Correlation coefficient is - 0.7642

Least square line:

y = -0.37x + 305.98

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From the Venn diagram, the values that come under set A are A = { h,p,d,t,x }.

The area of mathematical logic known as set theory examines sets, which are essentially collections of objects. Set theory is a branch of mathematics that primarily deals with objects that are pertinent to mathematics as a whole, despite the fact that any kind of object can be gathered into a set.

Given that the Venn diagram consists of the values for set A and set B. The values which come under set A of the Venn diagram can be written as below,

A = { h,p,d,t,x }.

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Discrete values are the data values which are quantitative and the number of values is finite or countable.

What is discrete data?

In a count involving integers, there are only a finite number of potential values. It is impossible to break this kind of data into separate components. Discrete data consists of discrete variables that are non-negative, finite, numerical, and countable.

We are given interval, discrete, categorical and continuous values.

Of these, we need to find that which type of data values are quantitative and the number of values is finite or countable.

Interval data is quantitative but not countable because interval can range from infinity to infinity.

Discrete data is both quantitative and countable.

Categorical data is qualitative and not quantitative.

Continuous data is quantitative but not finite.

Hence, discrete values are the data values which are quantitative and the number of values is finite or countable.

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If you purchase 200 shares for $70 a share ($14,000), and after a year the price falls to $60. the percentage return on your investment are:

27.21%,  49.11%, 78.57%.

If the margin requirement was 15%:

Total cost of the investment = $14,000 / (1 - 0.15)

Total cost of the investment = $16,471.43

After a year, Value of the investment =  200 * $60 = $12,000

Percentage return = ( $16,471.43 -12,000 ) / $16,471.43 * 100

Percentage return = 27.21%

If the margin requirement was 40%:

Total cost of the investment = $14,000 / (1 - 0.40)

Total cost of the investment  = $23,529.41

After a year, Value of the investment  =200 * $60 = $12,000

Percentage return = ( $23,529.41 -$12,000 ) / $23,529.41 * 100

Percentage return = 49.11%

If the margin requirement was 75%:

Total cost of the investment = $14,000 / (1 - 0.75)

Total cost of the investment = $56,000

After a year, the value of the investment = 200 * $60 = $12,000

Total cost of the investment =  ($56,000 - $12,000 ) / $56,000 * 100

Total cost of the investment = 78.57%.

Therefore  the percentage return on your investment are:

27.21%,  49.11%, 78.57%.

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The total surface area of the triangular pyramid is 936 cm²

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The surface area of the triangular prism is the sum of the individual area of the surface. Hence:

Surface area = (0.5 * 24 cm * 18 cm) + (0.5 * 24 cm * 18 cm) + (24 cm * 7 cm) + (18 cm * 7 cm) + (30 cm * 7 cm) = 936 cm²

The total surface area is 936 cm²

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Answer: Yes at x = 2.

Step-by-step explanation: There are two ways to do it. Graph the function or solve it. Since im on a computer solving would be easiest for me to explain. To find a point where the two lines meet, you should set the two equations equal to each other. When you solve by subtracting 1/2x on both sides, the result is 3/2x = 3. This means that x=2. When you graph you should see that when x =2 the answer is right.

Answer:

See below

Step-by-step explanation:

r = 4*2 = 8

q = 4√3

p = q = 4√3

s = √(4√3)^2 + (4√3)^2) = √96 = 4√6

The most accurate comment about the graph  data is: "China's steel production is increasing while its major competitors' production is declining."

Academics are using graphs to logically chart or graphically depict events or quantities. A graph point is a common way to depict how different things interact. The non-linear storage structure known as a graph is made up of nodes, also referred to as vertices, and lines. Glue ought to be used to connect the edges, also known as nodes , respectively.  (4.5).

Here,

The most accurate comment about the data is: "China's steel production is increasing while its major competitors' production is declining."

This is because the graph shows that China's steel production has been steadily increasing since the early 2000s, while the steel production of other major producers such as Japan, the United States, and Germany has been declining or stagnant. This trend is particularly evident after the global financial crisis of 2008-2009.

While it is true that Japan's steel production has increased and shows no signs of decreasing, this comment does not address the overall trend of declining steel production among major producers.

The other two comments are not accurate. The statement "By 2009, China’s tons of steel produced per US million ($) GDP was 50, about 10 tons less than Japan’s all-time high" is not supported by the graph, as there is no information about tons of steel produced per US million ($) GDP on the graph.

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The solution to the system of equations in this problem is given as follows:

(-5, 4).

The system of equations for this problem is defined as follows:

Applying linear combination, we can add the equations and remove the variable y, hence the solution for x of the system of equations is obtained as follows:

3x = -15.

x = -15/3

x = -5.

Then the solution for y is given as follows:

-5 - 4y = -21

4y = 16

y = 16/4

y = 4.

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Answer:

1.C

2.D

3.A

4.A

Step-by-step explanation:

1. The negative must be outside to be reflected across the Y axis. Also you can never find the square root of a negative number

2.Its D because when you move to the right, you subtract on the inside. doing it outside would move it down

3. As I said in "2" to move up or down you have to keep the number outside. In this case it was down 3 so -3 ouside of the square root.

4. This is a combination of the two so right 4 and 4 four translates to -4 on the inside and -4 on the outside.

Hope it helps!

Answer:

You would have to buy three raffle tickets to have a chance to receive all three pieces of merchandise.

Step-by-step explanation:

Each raffle ticket gives you a chance to win one of the three pieces of marching band merchandise: T-shirt, hat, or shorts. To have a chance of winning all three pieces, you would need to buy three separate raffle tickets, each with a chance to win a different piece of merchandise. This way, you would increase your chances of receiving all three pieces through the random selection process of the raffle.

If each raffle ticket has an equal chance to win any of the three pieces of merchandise, then you would have a 33% chance of winning any one piece of merchandise with each ticket you buy. To have a greater chance of winning all three pieces, you would need to buy multiple tickets.

For example, if you buy three tickets, the chance of winning all three pieces of merchandise would be (1/3) * (1/3) * (1/3) = 1/27. This means that you have a 1 in 27 chance of winning all three pieces of merchandise with three raffle tickets.

Answer:3 i d k

Step-by-step explanation: