During the period 2000-2016, the average costs B (in dollars) for a new boat and the average costs H (in dollars) for a hovercraft can be modeled


by the following functions:


B = 30 +140 and H=-1012 +350 + 400


where t is the number of years since 2000


(a) How can the difference of the costs of a hovercraft and the costs of a boat be expressed? (4 points)


(b) About how much was the difference in the year 2010? (2 points)

These statistical measures help the researcher summarize, describe, and understand the data collected from the study participants.

As the researcher is describing the characteristics of the subjects, the appropriate statistical analysis would be descriptive statistics.

Descriptive statistics is a method that summarizes and describes the data collected in a study. It includes measures such as mean, median, mode, standard deviation, range, and frequency distribution.

These measures can provide a clear picture of the demographic data of the three groups of subjects and help in drawing meaningful conclusions.

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The z test statistic needed for this hypothesis test is 0.75 .

Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.

NOW,

sample proportion =  p = x / n = 0.23

Test statistics

z = ( p - p0 ) / \(\sqrt{ p0*(1-p0)}\) / n

= ( 0.23 - 0.20) /  \(\sqrt{ (0.20*0.80) / 100}\)

= 0.75

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Answer:

No

Step-by-step explanation:

Probability meaning: "the extent to which something is probable; the likelihood of something happening or being the case."

Probability only is a range from 1-100 %

Probability can also be written as a percentage, which is a number from 0 to 100 percent. ... The probability of a certain event occurring depends on how many possible outcomes the event has. If an event has only one possible outcome, the probability for this outcome is always 1 (or 100 percent).

(credits to scientific american)

Answer:

values in range

Step-by-step explanation:

Answer:

If Bryan can run 2 miles in 20 minutes, he can run 10 miles in 100 minutes.

Step-by-step explanation:

To determine the answer to this problem, we can first find how many minutes it takes Bryan to run one mile. Because it takes him twenty minutes to run two miles, it must take Bryan ten minutes to run one mile.

1 mile = 10 minutes

Multiply this by ten to find how many miles Bryan runs in 100 minutes.

10 miles = 100 minutes

Bryan can run 10 miles in 100 minutes.

Answer: 10 miles

Step-by-step explanation: They’re equivalent to the minutes. 20 minutes 2 miles, 40 minutes 4 miles and so on.

Step-by-step explanation:

by using Pythagoras law

ZY=√{45²-27²)=36

sin X=ZY/XY=36/45=0.8

Cos X=XZ/XY=27/45=0.6

Tan X= YZ/XZ=36/27=1.33

The lines are taken from the short story 'The Yellow Wallpaper'. The woman stops mentioning the wallpaper to others because she feels suspicious about it.

The short story summarizes a woman who is suffering from nervous depression and what happens when she comes in contact with wallpaper in her new house which she thinks is alive. Throughout the entire story, the narrator expresses how the woman feels, how she thinks the wallpaper is alive and that it can cause harm to her.

At first glance, she feels that it is ugly, and to get better she describes the entire house. She feels very disturbed when she sees the wallpaper in her bedroom and it makes her feel strange. She becomes so obsessed with the wallpaper to such an extent that she feels like it is the shape of a woman who is alive.

She becomes possessive and feels that the woman in the wallpaper is moving through the entire house so she starts biting and tearing the wallpaper to free the women trapped inside. The entire story mentions the mental health of the women.

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she left her computer open for 48 hours

Using expression, the following provides one explanation for why there are two ways to add up the symbols on the tablet.

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.

The hieroglyphic number system of ancient Egypt employed a decimal system with hieroglyphs to denote the powers of ten. It is challenging to give a precise response, though, without being able to see the precise symbols on the tablet.

It is feasible that there are two distinct ways to add the numbers represented by the symbols on the tablet, presuming that the tablet is employing a fundamental arithmetic operation like addition and that each symbol represents a different number.

Finding two different sets of integers that, when added together, yield the same answer is one way to approach this issue.

As an illustration, if the symbols stand for 2, 3, and 5, one technique to add them up would be:

2 + 3 + 5 = 10

They might also be added up as follows:

3 + 7 = 10

In this instance, the number 2 would be represented by the sign 2, and the number 5 by the symbol 3. This could be one reason for why the symbols on the tablet can be added in two different ways.

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No, they are not; rectangles only resemble one another if their side ratios are constant. A rectangle that is 2 x 7 and another that is 4 x 14 are two examples of two rectangles that are similar.

They are comparable because the ratio of the sides of the latter rectangle to the former is 2:1. A 2 x 6 and a 2 x 10 rectangle are not comparable to one another.

No, similarity maintains the length-to-length ratio. As a result, two rectangles with differing side ratios cannot be comparable.

In comparison, all squares have the same ratio and are similar (the length of the sides are equal).

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Answer:

A. The graph is nonlinear.

D. The graph is a function

E. The graph is increasing in two intervals.

Step-by-step explanation:

        We will review each answer choice to decide on our answer to this question.

✓ A. The graph is nonlinear.

             Since the graph has a change in it's rate of increase, it's nonlinear.

✗ B. The function increases at the same rate.

             As stated below, the rate increases after x = 2 so the function is not increasing at the same rate.

✗ C. The rate decreases after x = 2.

             No, the rate increases after x = 2.

✓ D. The graph is a function.

             Yes, there is only one output for every input, so this is a function.

✓ E. The graph is increasing in two intervals.

             The graph is only increasing in two intervals. These intervals change at x = 2.

Answer:

45° and 12

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

(8)

The polygon has n = 8, that is 8 exterior angles, thus

exterior angle = 360° ÷ 8 = 45°

(9)

The number of sides n is

n = 360 ÷ 30 = 12

Answer:

45° 12 sides

Step-by-step explanation:

1) Every polygons interior angles is equal to 180 times two less than the amount of sides it has (i.e 180•(4-2)=360:quadrilateral) So applying that here we have eight sides so 180(8-2)=1080. Now divide that by 8 to get the measure of one angle and subtract it from 180 to get the exterior angle 45°

2) if the exterior angle is 30° then the interior angle is 150°. For this part i guess and checked but you can refer to the equation above. (180(x-2)=y/150)

Answer:

Step-by-step explanation:

9.8 p = 10 hours

24 hours = ?

= 24 hours   (9.8p)

   10 hours

=23.92p

In a case whereby a ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the time the ball is thrown will it strike the​ ground at t = 2.5 or -3.5.

Height of building = 140 ft

Initial velocity, u = 16 ft/sec

the equation given is

h = -16t² -16t +140

h(t) = -16t² -16t +140

AT h(t) = 0 , We can divide by -2 and have

(8t² + 8t - 70) = 0

8t² + 8t - 70 = 0

Then if we solve with quadratic equation formula where  a=8, b=8, c=- 70 then the root will be -7/2 and 5/2 then  t = 2.5 or -3.5

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complete question;

A ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the height of the ball h in feet after t seconds is given by the equation h equals negative 16 t squared minus 16 t plus 140. how long after the ball is thrown will it strike the​ ground?

Using the Uniform Distribution and the Z- distribution, it is found that 1591 specimens should be tested.

Uniform Distribution: It refers to a type of probability distribution in which all outcomes are equally likely.

Z- Distribution: The standard normal distribution, also known as z distribution, is a special normal distribution where the mean is 0 and standard deviation is 01.

For an uniform distribution of bounds a & b the standard deviation is given by:  α = √ (b-a)²÷12

here, α= standard deviation.

in this problem, a = 45 and b = 750, thus the estimate is:

α = √(750-45)² ÷ 12

  = √497025 ÷ 12

  = 203.5

the margin of error of a Z confidence interval is given by:

                  M = z (α ÷√n)

where, z is the critical value

            α is the population Standard deviation

             n is the sample size.

Now, finding the critical value which is z with a p - value of (1+∝ )÷2, where ∝ is confidence level.

here, ∝ = 0.95, thus z with a p-value of (1+0.95)÷ 2 = 0.96

∴ z= 0.96

standard deviation estimates is 203.5.

now, we want sample for a margin of error of 10, then,

               M= z( α ÷ √n)

         ⇒ 10 = 1.96 ( 203.5 ÷ √n)

         ⇒ 10√n = 1.96 (203.5)

         ⇒ √n = 0.196 (203.5)

         ⇒ (√n)² = [0.196(203.5)]²

         ⇒ n = 1590.89

Round up the value 1590.89 by:

1591 specimen should be tested

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The options are analyzed as follows:

1: The overline 0.729 means:

This is a non- terminating recurring decimal hence it is rational.

2: The nuumber 0.0195347... is a non terminating and non recurring decimal hence it is irrational.

3. The number -12 is rational since it is an integer.

4.The number 4.565656... is a non terminating recurring decimal hence it is rational.

5. The number given by:

Since square root of 2 is irrational and 3 is rational the product is irrational.

Also the decimal is non terminating non recurring hence it is irratonal.

So the options 2 and 5 are irrational.

Step-by-step explanation:

\(( {x}^{2})(x + 3) - (x + 3)\)

\((x + 3)( {x}^{2} - 1) \)

\((x - 1)(x + 1)\)

\((x - 1)(x + 1)(x + 3)\)

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

(x+1) (x-1) (x+3)

Step-by-step explanation:

. .....................

The probability of red is 0.1724, given the following table.

The table provided is given in the form of a contingency table. It is used to display the relationship between two categorical variables or nominal data through frequency distribution. It is also referred to as a two-way frequency table.

The table has "Yes" and "No" categories in the rows and "Red" and "Blue" categories in the columns.

The probability of Red can be calculated using the formula;

P(Red) = (Frequency of Red) / (Total Frequency)

Using the values provided in the table

,P(Red) = 15/87P(Red) = 0.1724

Hence, the probability of red is 0.1724.

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Answer:

250

Step-by-step explanation:

We can approximate that the scientists counted \(\frac{18}{30}=\frac{3}{5}\) of the elk.

So, the best estimate of the elk population is \(150(5/3)=250\).

Answer:1,250

Step-by-step explanation:

Standard Error of the Mean (SEM) is the standard deviation of the sample statistic estimate of the population parameter. It is calculated using the formula:SEM = s / sqrt (n) where s is the standard deviation of the sample and n is the sample size.

The sample size in this case is n = 50.

The standard deviation of the population is s = 8. Therefore, the standard error of the mean (SEM) based on the general population parameters is:\(SEM = 8 / sqrt (50)SEM = 1.13\)The standard error of the mean (SEM) is 1.13 based on the general population parameters.

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The trigonometric values for a right triangle can be obtained through the measurements of the different sides,

this can be found in a triangle like this,

then, identify the measurements in the given triangle

then,

\(\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\\\ \textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(p=\log_2(x) \\\\[-0.35em] ~\dotfill\\\\ \log_2(x^2) \implies 2\log_2(x)\implies \boxed{2p} \\\\[-0.35em] ~\dotfill\\\\ \log_2(16x)\implies \log_2(16)+\log_2(x)\implies \log_2(2^4)+p\implies \boxed{4+p} \\\\[-0.35em] ~\dotfill\\\\ \log_8(x)\implies \cfrac{\log_2(x)}{\log_2(8)}\implies \cfrac{p}{\log_2(2^3)}\implies \boxed{\cfrac{p}{3}}\)

Answer:

\(\textsf{(a)} \quad 2p\)

\(\textsf{(b)} \quad 4+p\)

\(\textsf{(c)} \quad \dfrac{p}{3}\)

Step-by-step explanation:

Given:

\(\boxed{p=\log_2x}\)

\(\begin{aligned}&\textsf{Given}: \quad & \log_2x^2\\&\textsf{Apply log power law}: \quad & 2 \log_2 x\\&\textsf{Substitute value of $p$}: \quad & 2p\end{aligned}\)

\(\begin{aligned}&\textsf{Given}: \quad & \log_2(16x)\\&\textsf{Apply log product law}: \quad & \log_2(16)+\log_2x\\&\textsf{Rewrite $16$ as $2^4$}: \quad & \log_2(2)^4+\log_2x\\&\textsf{Apply log power law}: \quad & 4\log_22+\log_2x\\&\textsf{Apply log law $\log_aa=1$}: \quad & 4(1)+\log_2x\\&\textsf{Simplify and substitute value of $p$}: \quad & 4+p\end{aligned}\)

\(\begin{aligned}&\textsf{Given}: \quad & \log_8x\\\\&\textsf{Apply log change of base law}: \quad & \dfrac{\log_2x}{\log_28}\\\\&\textsf{Rewrite $8$ as $2^3$}: \quad & \dfrac{\log_2x}{\log_2(2)^3}\\\\&\textsf{Apply log power law}: \quad & \dfrac{\log_2x}{3\log_2(2)}\\\\&\textsf{Apply log law $\log_aa=1$}: \quad & \dfrac{\log_2x}{3(1)}\\\\&\textsf{Simplify and substitute value of $p$}: \quad & \dfrac{p}{3}\\\end{aligned}\)

\(\boxed{\begin{minipage}{7.3 cm}\underline{Log Laws}\\\\\begin{aligned}&\textsf{Product law}: \quad & \log_axy &=\log_ax + \log_ay\\\\&\textsf{Power law}: \quad & \log_ax^n &=n\log_ax\\\\&\textsf{Log law}: \quad & \log_aa &=1\\\\&\textsf{Change of Base}: \quad &\log_ba &=\dfrac{\log_xa}{\log_xb}\\\end{aligned}\end{minipage}}\)

The player would have turned over a red card on the first turn roughly 500 times.

Here, the solitaire player has played 1000 games,

Hence, we can assume that the player has turned over the first card 1000 times.

In a standard deck of 52 cards, 26 cards are red (13 hearts and 13 diamonds) and 26 cards are black (13 spades and 13 clubs).

So, The probability of turning over a red card on the first turn is,

⇒ 26/52

⇒ 1/2

So, if the player turned over the first card 1000 times, we can expect that the player turned over a red card on the first turn 1/2 of those times.

Therefore, the player would have turned over a red card on the first turn roughly 500 times.

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Answer:

3(3d+1)

9d+3

Step-by-step explanation:

The probability of A or B or C occurring is 0.54.

To find P(A or B or C), we need to use the principle of inclusion-exclusion.

P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)

Substituting the given probabilities:

P(A or B or C) = 0.35 + 0.23 + 0.18 - 0.13 - 0.03 - 0.07 + 0.01

P(A or B or C) = 0.54

Therefore, the probability of A or B or C occurring is 0.54.

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The approximate interest rate needed to turn $3,500 into $7,000 over 10 years is 9%. Correct answer is C.

The value of money increases over time with the help of compounding interest. If one puts in a principal amount in an account, the amount will increase over time as interest accrues. Let's use the future value formula for the calculation. Let’s assume that the interest rate needed to turn $3,500 into $7,000 over 10 years is x percent. P = $3,500 (principal)FV = $7,000 (future value)

N = 10 years (duration of the investment)Using the future value formula:

FV = P(1 + r/n)^(nt)where, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the duration of the investment in years.

Substituting the given values, we have: $7,000 = $3,500(1 + x/n)^(n × 10)We can solve for x by approximating the interest rate using each of the answer options given in the question until we find an answer that is close to $7,000. A calculator can also be used to calculate the compound interest for each option. If the interest rate is 7%, then the interest is compounded annually. Therefore, n = 1$7,000

= $3,500(1 + 0.07/1)^(1 × 10) If the interest rate is 10%, then the interest is compounded annually.

Therefore, n = 1$7,000 = $3,500(1 + 0.1/1)^(1 × 10)Thus, x ≈ 9.57%, greater than the required amount.

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By applying the algebra concept, we can conclude that the movie that Mario and his friend watched starting at 7 PM

The use of algebra in everyday life.

Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used for financial planning, traveling time calculation, and so on.

In the above problem, we can take some notes as follows:

Departure time (x) = 5:15 PM

Travel time (t) = 1 hour 20 minutes

Arrival time (y) = 25 minutes

If z is the playing time of the movie, then z can be expressed mathematically in the following way:

z = x + t + y

= 5:15 + 1 hour 20 minutes + 25 minutes

= 6:60 PM or generally written 7:00 PM

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Step-by-step explanation:

The side opposite to the 4 degree angle is 18 m

The side adjacent the 4 degree angle is x

tan(4) = opposite / adjacent

adjacent = opposite / (tan(4))

adjacent = 18 / tan(4)

adjacent = 257.41