Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t, in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.

The average velocity during [1,2] time period is 6cm/s.

This looks like an exercise that's building toward the idea of a derivative.

These calculations are done best with a calculator, but here's how the first interval is used:

Average velocity = (position at 2 - a position at 1) / (2 - 1)

It's really distance divided by time!

Position at t = 2: 4sin(2[tex]\pi[/tex])+3cos(2[tex]\pi[/tex])=4(0)+3(1)=3

Position at t = 1: 4sin([tex]\pi[/tex])+3cos([tex]\pi[/tex])=4(0)+3(-1)=-3

So over the interval [1, 2], the average velocity is [tex]\frac{3-(-3)}{2-1} =\frac{6}{1} =6[/tex]

∴ Average velocity=6cm/s

I used a spreadsheet to calculate the average velocity over the other intervals and a couple of shorter ones, too.  (See attached image.)

As these intervals get shorter (the right endpoint is approaching 1), the average velocity gets closer and closer to the instantaneous velocity. An estimate would be -12.6.

To know more about Average velocity:

https://brainly.com/question/4854083

#SPJ4

Since the probability that a player gets a hit on any given at bat is independent of the other at bats, we can find the probability that Mark has fewer than 3 hits in his next 6 at bats by simply multiplying the probability of getting a hit on each at bat. Since Mark has a probability of 0.155 of getting a hit on any given at bat, he has a probability of (0.155)^3 of getting exactly 3 hits in his next 6 at bats. Therefore, the probability that he has fewer than 3 hits in his next 6 at bats is 1 - (0.155)^3  approx 0.76

Answer:

The probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.

Step-by-step explanation:

A batting average is the number of hits a player has divided by the number of times they have been at bat. In this case, Mark has a batting average of 0.155, which means that he has hit 0.155 of the times he has been at bat.

To find the probability that Mark will have fewer than 3 hits in his next 6 at bats, we can use the binomial probability formula. The formula for binomial probability is:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where "n" is the number of trials, "x" is the number of successes, "p" is the probability of success on a single trial, and "1-p" is the probability of failure on a single trial.

In this case, the number of trials is 6, the number of successes is 3, and the probability of success on a single trial is 0.155. Plugging these values into the formula, we get:

P(3) = (6 choose 3) * 0.155^3 * (1-0.155)^(6-3)

To calculate the probability that Mark will have fewer than 3 hits in his next 6 at bats, we need to sum the probabilities of 0, 1, and 2 hits. We can use the binomial probability formula to calculate the probability of each of these outcomes, and then add them together to find the total probability.

For 0 hits, the probability is:

P(0) = (6 choose 0) * 0.155^0 * (1-0.155)^(6-0) = 0.009

For 1 hit, the probability is:

P(1) = (6 choose 1) * 0.155^1 * (1-0.155)^(6-1) = 0.054

For 2 hits, the probability is:

P(2) = (6 choose 2) * 0.155^2 * (1-0.155)^(6-2) = 0.141

Adding these probabilities together, we get the total probability that Mark will have fewer than 3 hits in his next 6 at bats:

P(0 or 1 or 2) = 0.009 + 0.054 + 0.141 = 0.204

Therefore, the probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.

Answer: Fred will be 3(x-5) years old in 8 years, which is 3x-15 years old.

We know that x-1=3x-15, so x=16.

Fred is 16 years old now.

Step-by-step explanation:

Fred's age four years ago was (x - 5), Fred will be (x+7) years old in 8 years. Fred is currently eight years old.    

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Given that Fred is (x-1) years old

i) Fred age 4 years ago

Subtract 4 years from the present age

x -1  - 4

x - 5

So, Fred's age 4 years ago is  (x - 5)  

ii) Add 8 years to the present age  

(x-1) + 8

(x+7)

So, Fred's age after 8 years from now is (x+7) years      

iii) By the given statement

⇒ (x+7)  = 4 [ x - 5 ]

We can then solve for x by expanding the right side of the equation:

⇒ x + 7 = 4x - 20

Then, we can combine like terms to get:

⇒ 4x - x = 20 + 7

⇒ 3x = 27

⇒  x = 9

Fred's present age = (x-1) = 9 - 1 = 8 years

Thus, Fred's current age is 8 years.  

Learn more about the equations here:

brainly.com/question/10413253

#SPJ2

The question seems to be incomplete the correct question would be:

Fred is (x-1) years old now How old: (1) was he 4 years ago. (ii) will he be 8 years from now? (ii) is he now, if his age in 8 years time will be three times his age 4 years ago?​

A 90% confidence interval places the true mean normal body temperature between 98.14269 and 98.35577.

library(UsingR)

attach(normtemp)

print(normtemp)

hist(normtemp$temperature)

shapiro.test(normtemp$temperature)

qqnorm(normtemp$temperature)

qqline(normtemp$temperature)

We can observe that the data follows a normal distribution from the histogram and q plot.

The points in the q plot fall on a straight line and correspond to a normal distribution.

P-value = 0.2332, P>0.05, from the Shapiro test

hence, we fail to reject null htpothesis.

On accepting the null hypothesis we get to know that the data follows normal distribution.

The output for the given code will be ,

data: normtemp$temperature

t = 1527.9, df = 129, p-value < 2.2e-16

alternative hypothesis: true mean ≠0

90 percent confidence interval:

98.14269 98.35577

sample estimates:

mean of x

98.24923

Therefore , we can conclude that ,

The true mean normal body temperature is believed to be between 98.14269 and 98.35577 with a 90% confidence interval.

98.6 is not included in the 90% confidence interval.

To learn more about  confidence interval

brainly.com/question/27630001

#SPJ4

a) The variables are;

d = the number of hours walking his neighbor's dog.

c = the number of hours washing cars

b) The system of inequalities are;

6c + 7.5d ≥ 75

d + c ≤ 15

c) The two possible combinations are; (5, 10) and (10, 5)

d) Yes it will be sufficient

We are told that;

Tom is going to walk his neighbors dog for $6 an hour. Thus;

Money from walking neighbor's dog = $6 per hour

Money from car wash = $7.5 per hour

Total Number of hours of work not more than 15 hours

a) Let d represent the number of hours walking his neighbor's dog.

Let c represent the number of hours washing cars

b) Thus, money from walking neighbor's dog = 6c

Money from car wash = 7.5d

Therefore;

Total money saved = 6c + 7.5d

Since total number of hours of work is not more than 15 hours, then we have the inequality;

d + c ≤ 15

Tom needs to make at least $75 to cover prom expenses and so we have the inequality as;

6c + 7.5d ≥ 75

The system of inequalities represents this solution are;

6c + 7.5d ≥ 75

d + c ≤ 15

From the graph, the shaded part in between both lines provides the possible number of hours which we have as possibly; (5, 10) and (10, 5)

If he works 10 hours washing neighbors dogs and 3 hours on the cars, he will earn;

6(3) + 7.5(10) = $84

This is sufficient.

Read more about system of equations at; https://brainly.com/question/13729904

#SPJ1

The graph of y = f(x) is graphed. The end behavior of f(x) is as x → ∅ f(x) → -∅ and x → -∅ , f(x) → - ∅

The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f. In other words, if we look at the right end of the x-axis (as x approaches +∅) and the left end of the x-axis (as x approaches ∅), the end behavior of a function represents the trend of the graph. Look at the polynomial function's leading term to identify its end behavior. The leading term will dominate the graph since it has the largest power and will thus increase much more quickly than the other terms as x gets very large or very small.

Given,

Graph of y = f(x)

End behavior of f(x) is:

as x → ∅ f(x) → -∅ and x → -∅ , f(x) → - ∅

To learn more about end behavior, visit:

https://brainly.com/question/27514660

#SPJ1

The quantity of 30% acid content and 10% acid content used is 0.15 liters and 1.35 liters respectively

Let

x + y = 1.5

0.3x + 0.1y = 1.5 × 0.12

0.3x + 0.1y = 0.18

x + y = 1.5

0.3x + 0.1y = 0.18

From (1)

x = 1.5 - y

Substitute into (2)

0.3x + 0.1y = 0.18

0.3(1.5 - y) + 0.1y = 0.18

0.45 - 0.3y + 0.1y = 0.18

- 0.3y + 0.1y = 0.18 - 0.45

-0.2y = -0.27

divide both sides by -0.2

y = -0.27 / -0.2

y = 1.35

Substitute into (1)

x + y = 1.5

x + 1.35 = 1.5

x = 1.5 - 1.35

x = 0.15

Therefore, 0.15 30% acid content and 1.35 10% acid content is needed.

Read more on simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

To prove that a^3+b^3 is bigger or equal to ¼, we can use mathematical induction. This involves two steps:

To begin, let's consider the base case where a and b are equal to 0. In this case, a^3+b^3 is equal to 0^3+0^3, which is 0. Since 0 is greater than or equal to ¼, the statement is true for the base case.

Next, we can assume that the statement is true for some arbitrary values of a and b (i.e., the inductive hypothesis). That is, we can assume that a^3+b^3 is bigger or equal to ¼.

To complete the proof, we need to show that a^3+(b+1)^3 is also bigger or equal to ¼. To do this, we can use the fact that (a+1)^3 = a^3+3a^2+3a+1. Since the inductive hypothesis states that a^3+b^3 is bigger or equal to ¼, we can say that a^3+(b+1)^3 = a^3+b^3+3a^2+3a+1 is also bigger or equal to ¼.

Therefore, by mathematical induction, we have shown that a^3+b^3 is bigger or equal to ¼ for all values of a and b.

Answer: 3(x+y)+4=8

simplified:  3x+3y=4

Step-by-step explanation:

three times x (the first number) & y (the second number) & 4. Which means +4. is 8. which means =8

3(x+y)+4=8

Answer:

A) 60,480 cubic inches

B) 87 Fish

C) $155.73

Step-by-step explanation:

This will be long.

1) 5ft x 4ft x 3ft can be rewritten as 60in x 28in x 36 in.

      This will get you 60,480in^3 or 60,480 cubic inches.

2) We take that 60,480 in^3 and divide it by the 690 needed per fish.

       60,480 / 690 = 87.65. Since we need to make sure we can't go over, that gives us 87 fish.

3) We take that 87, and multiply it by 1.79

        87 x 1.79 = $155.73

Step 1: We need to test the given hypothesis.

We can take x1- x2 to represent the difference between the jumping and relaxed times.

[tex]H0: u1 = u2\\H1: u1 \neq u2[/tex]

Step 2: Simplification

We need to find the mean and standard deviation of both samples.

[tex]u1 = 32.375, s1 = 9.620477\\u2 = 30.625, s2 = 8.331309[/tex]

The differences between the jumping and relaxed times are calculated:

[tex]5, 7, 2, 1, -2, 2, 2, -3[/tex]

The number of differences is ∑(8, i-1) = [tex](d_{i} - \alpha ) ^{2}[/tex] = 75.5

Standard deviation differences are:

[tex]\sqrt{\frac{75.5}{7} }[/tex] = 3.284

The standard error is SE = 1.161

Using this, we can find the value of the test statistic t:

[tex]t = \frac{u1 - u2}{SE}[/tex] = 1.507

Using this and the graph, we get that the p value is 0.17554.

Therefore, since p-value is greater than α = 0.05, we cannot reject the hypothesis H0, and we can conclude that it is insufficient evidence to conclude that the average difference is not zero.

Since p-value is greater than α = 0.05, we cannot reject the hypothesis H0, and we can conclude that it is insufficient evidence to conclude that the average difference is not zero.

To learn more about hypothesis testing,

brainly.com/question/29996729

#SPJ4

The order of the distances, from least to greatest, is given by the following option:

D. 40, 675/16, 586/13, square root of 2,111, 10 square root of 27.

To order the distances, we have to find them all in the same format.

For this problem, I will use the decimal format for all the distances, meaning that:

Then the decimal distances are given as follows:

Then option D orders the distances correctly.

The problem is given by the image shown at the end of the answer.

More can be learned about the conversion of fraction to decimal at https://brainly.com/question/13635105

#SPJ1

Yes, knowing the value of b, the slope of the regression line, allows us to predict the correlation coefficient value with accuracy.

Regression and correlation techniques can be used to establish links between variables.

Every day, we refer to any form of association as a "correlation," using that word.

To determine whether or if there is a relationship between the variables under investigation, correlation analysis is used.

Although regression illustrates how the variables are related,

Correlation and regression analysis can be shown graphically using scatter plots.

According to the question,

If we know the value of the slopes of the regression line say byx and bxy

We can Calculate the value of Correlation coefficient by using the relation

=> r = √(byx × bxy)

Hence , Yes We can accurately guess the value of correlation when slope of regression line is given

To know more about Regression and Correlation here

https://brainly.com/question/29820584

#SPJ4

Answer: y=6x

Step-by-step explanation: You have to find the relationship between x and y. For this, 1 (x) times 6 = 6 (y). 2 (x) times 6 = 12 (y). This pattern will repeat in this table for eternity, so the relationship is y=6x.

Total service charges is 23.45 when Alan Booker's service fees included a basic charge is 6.95.

Given that,

Alan Booker's service fees included a basic charge, the payment of eight bills, the replacement of a lost card, and four atm transactions—two in-network and two out-of-network.

We have to find the total service charges.

We know that,

Alan borker

Basic charge is 6.95

Bill payments is 3×0.5= 1.5

Card replacement is 5

ATM Transactions

National is 2×2 =4

Out of network is 2×3 =6

Total service charges is 23.45

Therefore, Total service charges is 23.45 when Alan Booker's service fees included a basic charge is 6.95.

To learn more about service visit: https://brainly.com/question/15127644

#SPJ4

As per the constant of proportionality, the electric held at the point 7 as a result of a point charge at the origin is К.

What is meant by constant of proportionality?

In math, constant of proportionality refers the ratio that relates two given values in what is known as a proportional relationship.

Here we have given that electric  charge produces a vector field called the electric field, which represents the force on a unit positive charge placed at the point. Two positive or two negative charges repel one another, whereas two charges of opposite sign attract one another. The divergence of Ē is proportional to the density of the electric charge.

Here we need to find the positive constant of proportionality The electric held at the point.

As per the definition of the constant of proportionality, we have identified the following values from the given question,

Here we know that the two positive or two negative charges repel one another, whereas two charges of opposite sign attract one another.

And the divergence of Ē is proportional to the density of the electric charge.

So, based on these details, the point 7 as a result of a point charge at the origin is К.

To know more about Constant of proportionality here,

https://brainly.com/question/29126727

#SPJ4

Transversion is known as point mutation in DNA.

Transversion is a term used in molecular biology. It refers to a point mutation in DNA in which a single (two ring) purine (A or G) is changed for a (one ring) pyrimidine (T or C), or vice versa. A transversion can be spontaneous, or it can be caused by ionizing radiation or alkylating agents. It can only be reversed by a spontaneous reversion.

So, here 5'AGCCTAC3' we can replace (A or G) with (T or C)

So, the answer should be :

5'ATCCTAC3'

Here we have replaced G with T and other things are same

To know more about DNA follow the given link :

https://brainly.com/question/8806489

The full question will be like this

Assume that a wild-type sequence is 5'AGCCTAC3'. Indicate the sequence that might be produced by a transversion. Which of the following sequences might be produced by a transversion?

A) 5'AGTCTAC3'

B) 5'AGCCGCCGCCGCCTAC3'

C) 5'AGCCCAC3'

D) 5'ATCCTAC3'

#SPJ4

The point of intersection of the equations C = 100t + 5000 and C = 75t + 7000 represents the  the point in time where the cost of installing either will be the same.

Linear equations are equations where the right hand side and left hand side involves expressions with one or more variables for which the highest degree of the variable being 1.

We have two linear equations given,

C = 100t + 5000 and C = 75t + 7000.

The point of intersection of these linear equations will be when both the equations are equal.

100t + 5000 = 75t + 7000

100t - 75t = 7000 - 5000

25t = 2000

t = 2000/25

t = 80

This is the point in time where the cost of installing either will be the same, that is after 80 months.

Cost of installing = (100 × 80 ) + 5000 = 13,000

Or                         = (75 × 80) + 7000 = 13000

Hence the point of intersection of these equations represent the point in time where the cost of installing either will be the same.

To learn more about Linear Equations, click :

https://brainly.com/question/12412488

#SPJ1

The statement contained within FST that agrees with the statement that the research participant is an active partner in the endeavor is: We can only know women's experiences by paying attention to women's own interpretations of these experiences.

FST stands for Food Science and Technology. It is scientific journal reviewed by peers. It acknowledges all the branches of science and technology that deal with packaging and engineering of foods and food products.

Research is the detailed and in-depth study of any subject that includes discovering facts about it as well as inventing new facts. It includes learning from the existing facts and generating new knowledge.

Therefore, the research is the only detailed way for FST.

To know more about research, refer: brainly.com/question/29783805

#SPJ4

The total number of hours [h] that it will take to try the possible combinations are → h = {(x/40) - 2} + 1.

Given is that a thief tried 80 combinations to open the safe lock the

first hour, then 40 every hour after that.

Assume that their are total of [x] possible combinations for the lock. Then we can write the expression for the total number of hours [h] that it will take to try the possible combinations as -

x = 80 + 40(h - 1)

(x - 80) = 40(h - 1)

(h - 1) = (x - 80)/40

(h - 1) = {(x/40) - 2}

h = {(x/40) - 2} + 1

Therefore, the total number of hours [h] that it will take to try the possible combinations are → h = {(x/40) - 2} + 1.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ1

The answer is B & D

Answer:

Step-by-step explanation:

i'd say the 2nd one and the last one

Because the 2nd one is a straight line that is pointing up showing that it's increasing.

And the last one because the line is going up meaning it's increasing

The chance that the average of the draws will be in the range 73 to 77 is 0.6826 when the average ticket value per box is 75, while the standard deviation is 10.

Given that,

The average ticket value per box is 75, while the standard deviation is 10. With replacement from this box, 25 random draws are conducted in total.

We have to find the chance that the average of the draws will be in the range 73 to 77.

We know that,

Take

μ=75,σ=10

X₁=73, X₂=77

We need to compute P(73≤X≤77)

The corresponding p-values are calculated by using control limit theorem

Z=X-μ/σ

Z₁=73-75/10=-2/10=-1/5

Z₂=77-75/10=2/10=1/5

We get,

P(73≤X≤77)

P(-1/5≤z≤1/5)

P(z≤1/5)-P(z≤-1/5)

0.6826

Therefore, the chance that the average of the draws will be in the range 73 to 77 is 0.6826 when the average ticket value per box is 75, while the standard deviation is 10.

To learn more about average visit: https://brainly.com/question/15397049

#SPJ4

The population of a country increases by 31 years approximately.

differentiation:

To differentiate is to identify the differences between things, and to discriminate among them. There are a number of simple rules which can be used to allow us to differentiate many functions easily.

If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x".

Let population =x, at time t years.

Given  [tex]\frac{dx}{dt} \alpha X[/tex]

⇒  [tex]\frac{dx}{dt}=Kx[/tex]

where k is a constant of proportionality

 or  [tex]\frac{dx}{x} =Kdt[/tex].  Integrating, we get lnx=kt+lnc

⇒  [tex]\frac{x}{c}=e^{Kt}[/tex] or [tex]X=ce^{kt}[/tex]

If initially, i.e., when time t=0,x=x0 then xo=ce^0=c

[tex]X-Xoe^{kt}[/tex]

Given X=2Xo t=20 then,

[tex]2Xo=Xoe^{20k} \\\\= > 2=e^{20k} \\[/tex]

ln2=20k---(1)

To find t, when t triples X=3Xo

[tex]3Xo=Xoe^{kt} \\\\3=e^{kt}[/tex]

ln3=kt(2)---(2)

Dividing equation (2) by (1) then

[tex]\frac{t}{20} =\frac{ln3}{ln2}[/tex]

 or

[tex]t=20*\frac{ln3}{ln2}[/tex]

t=20*1.5849

t=31 years (approx)

To know more about differentiation:

https://brainly.com/question/954654

#SPJ4

In case whereby Afia bought shoes that were on sale for 30% off the regular price and Afia saved  $12` the regular price of the shoe is  $40.

It should be noted that the Regular price  can be described as the price at which the goods or services are openly and actively sold  with the producer or  supplier to the public  with repect to the continuing basis for a substantial period of time.

The amount of savings can be divided by the percentage off to find the

Since the sale for 30% off the regular price, then regular price.

(12/0.30) = 40

hence the regular price was $40

Learn more about price at:

https://brainly.com/question/26044784

#SPJ1

Answer:

Step-by-step explanation:

nCr = n! / r!(n-r)!

n=46

r=6

=46!/6!(46-6)!

=46!/[6!(40)!]

=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)

Cancel out 40!

=46*45*44*43*42*41/(6*5*4*3*2*1)

=6744109680/720

=9366819

Possible different selection 9366819

Answer:

both of them are incorrect so the answer is no

Step-by-step explanation:

If the value of y grater than 6 or equal to 6 it should be 6 or above but in (6,2) the value of y is 2 and x=6 so the value of y is less than 6

and in (-2,5) the value of x is -2 and y=5 , again the value of y is not above 6 so the answer is no for both.

Answer:

n = 6

Step-by-step explanation:

(5 x [tex]10^{5}[/tex]) ( 3 x [tex]10^{n}[/tex]) = 1.5[tex]10^{12}[/tex]

(5x3) ([tex]10^{5+n}[/tex]) = 1.5 x[tex]10^{12}[/tex]

15 x ([tex]10^{5+n}[/tex]) = 1.5 x [tex]10^{12}[/tex]

1.5 x [tex]10^{1}[/tex] ([tex]10^{5+n}[/tex]) = 1.5 X [tex]10^{12}[/tex]

1.5 X [tex]10^{1}[/tex] X  [tex]10^{5+N}[/tex] = 1.5 X [tex]10^{12}[/tex]

1.5 X [tex]10^{1+5+N}[/tex] = 1.5 X [tex]10^{12}[/tex]

1.5  X [tex]10^{6 + 6}[/tex] = 1.5 X [tex]10^{12}[/tex]

1.5 X [tex]10^{12}[/tex] = 1.5 X [tex]10^{12}[/tex]