A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.

What is the total distance the car travels in this 30 second interval? Your must show your work but you may use your calculator to evaluate. Give 3 decimal places in your answer and include units.


Im not really sure how to go about this? Would I use the trapezoidal rule i dont know please help.

Answer:

[tex] v(t) = 8t +5[/tex]

And that represent the instantaneous velocity at a given time t.

And then we just need to replace t =2 in order to find the instantaneous velocity and we got:

[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]

Step-by-step explanation:

For this case we have the position function s(t) given by:

[tex] s(t) = 4t^2 + 5t+5[/tex]

And we can calculate the instanteneous velocity with the first derivate respect to the time, like this:

[tex] v(t) = s'(t)= \frac{ds}{dt}[/tex]

And if we take the derivate we got:

[tex] v(t) = 8t +5[/tex]

And that represent the instantaneous velocity at a given time t.

And then we just need to replace t =2 in order to find the instantaneous velocity and we got:

[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]

Answer: it will take both of them 2.4 hours to complete the job.

Step-by-step explanation:

Person A can complete a job in 6 hours. This means that the rate at which Person A can complete the job per hour is 1/6

Person B can complete the same job in 4 hours. This means that the rate at which Person A can complete the job per hour is 1/4

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/6 + 1/4 = 5/12

Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

5/12 = 1/t

t = 12/5

t = 2.4 hours

Answer:

3 hours for miss patrick 5 hours for mr shah

Step-by-step explanation:

Answer: they have to work for 11.25 hours.

Step-by-step explanation:

Let x represent the number of months for which they have to work to make the same amount.

Each month, Miss Patrick spends $60 on transportation to work, and earns $24.50 per hour. This means that if she works for x hours in a month, the total amount that she would have is

24.5x - 60

Each month, Mr. Shah spends $150 on lab equipment and earns $32.50 per month. This means that if he works for x hours in a month, the total amount that he would have is

32.5x - 150

For them to have the same amount, the number of months would be

32.5x - 150 = 24.5x - 60

32.5x - 24.5x = - 60 + 150

8x = 90

x = 90/8

x = 11.25 hours

Answer: the area of the shaded region is 21.5 cm²

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Diameter of circle = 10 cm

Radius = diameter/2 = 10/2 = 5 cm

Area of circle = 3.14 × 5² = 78.5 cm²

The length of each side of the square is 10 cm. The area of the square would be

10² = 100 cm²

Therefore, the area of the shaded region would be

100 - 78.5 = 21.5 cm²

Answer:

5 5/6

Tell me if u got it right

Answer:

The last one, the one which is not passing through the origin

Step-by-step explanation:

y = mx + c (generally)

For direct proportion, c has to be 0.

The last graph is the one which is not passing through the origin.

Using the slope of a line, a positive slope tells us that the line is increasing.

From the left to the right of graph, it shows that a person is climbing. A negative slope tells us that there is a fall.

We have;

y = mx + c

For direct proportion, c has to be zero.

Therefore, we can conclude that the last graph is the one that's not passing through the origin.

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poyo and churizzo uiouigyuftydfyitfogpghlhbl

Answer:B

Step-by-step explanation:

if you substitute any convenient value of x into f(x)= 2x-1 you see that it holds true when looking for the corresponding value of y.

For example,if you substitute x=5 into function B you get:

f(5)= 2(5) -1 = 10- 1 =9

Now,if you go on x =5 on the graph and check the corresponding value of y you that this value it is indeed 9.

Answer:

Step-by-step explanation:

Look at the picture.

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{\Delta y}{\Delta x}=\dfrac{rise}{run}[/tex]

We have:

[tex]rise=4\\run=2\\b=-1[/tex]

The slope:

[tex]m=\dfrac{4}{2}=2[/tex]

Substitute to the equation of a line:

[tex]y=2x+(-1)=2x-1[/tex]

The possible range for the side length of the square is that it is greater than 37 inches, but less than 49 inches.

The perimeter of a square is given by the formula P=4s, where s is the length of one side of the square. Since we know the perimeter must be greater than 148 and less than 196 inches, we can create inequality equations to solve for the side lengths, s.

Given the lowest limit, 148 < 4s. Divide both sides by 4, we get 37 < s.

Given the highest limit, 4s < 196. Again, divide both sides by 4, we get s < 49.

So, we conclude that the length of a side, s, must be less than 49 inches but greater than 37 inches to meet the required conditions of the question.

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Answer:

no

Step-by-step explanation:

no

Answer: They need 18 teachers more.

Step-by-step explanation:

Hi, to solve this problem, first, we have to divide the expected number of children (14,700) by 70.

We obtain that they are expecting 210 groups of 70 children each. Since the school district needs 3 teachers for every 70 children, we have to multiply the number of groups (210) by the number of teachers per group (3).

We obtained the total number of teachers needed for 14,700 children.

Since at this time the district has 612 teachers, to find the teachers missing we have to subtract the actual number of teachers (612) to the number of teachers needed (630).

They need 18 teachers more.

Answer:

A.

Step-by-step explanation:

Since the line goes down 4 and right 5, your slope would be -4/5 and since your y-intercept is at (0,-5) you would plug that in for b.

I hope this helped! Please mark Brainliest if you can :)

Answer:

  1. Exponential

Step-by-step explanation:

The problem statement is insufficient to describe the behavior.

_____

The capacitor's voltage is described by a differential equation such that its rate of change is proportional to the difference of the battery voltage and the capacitor voltage. The solution to the differential equation is a function that is exponential with time.

Answer:

(a) The probability of no customers are waiting in a line is 0.01832.

(b) The probability of 4 customers are waiting in a line is 0.19537.

(c) The probability of 4 or fewer customers are waiting in a line is 0.62885.

(d) The probability of 4 or more customers are waiting in a line during the visit is 0.56652.

Step-by-step explanation:

The number of customers waiting in a line between 4 PM and 7 PM (X) follows a Poisson distribution with parameter λ = 4.

The probability mass function of a Poisson distribution is:

[tex]P(X=x)=\frac{e^{-4}(4)^{x}}{x!} ;\ x=0, 1, 2,...[/tex]

(a)

Compute the probability that no customers are waiting in a line during the visit as follows:

[tex]P(X=0)=\frac{e^{-4}(4)^{0}}{0!}=\frac{0.01832\times1}{1}=0.01832[/tex]

Thus, the probability of no customers are waiting in a line is 0.01832.

(b)

Compute the probability that 4 customers are waiting in a line during the visit as follows:

[tex]P(X=4)=\frac{e^{-4}(4)^{4}}{4!}=\frac{0.01832\times256}{24}=0.19537[/tex]

Thus, the probability of 4 customers are waiting in a line is 0.19537.

(c)

Compute the probability that 4 or fewer customers are waiting in a line during the visit as follows:

P (X ≤ 4) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)

             [tex]=\frac{e^{-4}(4)^{0}}{0!}+\frac{e^{-4}(4)^{1}}{1!}+\frac{e^{-4}(4)^{2}}{2!}+\frac{e^{-4}(4)^{3}}{3!}+\frac{e^{-4}(4)^{3}}{3!}+\frac{e^{-4}(4)^{4}}{4!}\\=0.01832+0.07326+0.14653+0.19537+0.19537\\=0.62885[/tex]

Thus, the probability of 4 or fewer customers are waiting in a line is 0.62885.

(d)

Compute the probability of 4 or more customers are waiting in a line during the visit as follows:

P (X ≥ 4) = 1 - P (X < 4)

              = 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)

              [tex]=1-\frac{e^{-4}(4)^{0}}{0!}+\frac{e^{-4}(4)^{1}}{1!}+\frac{e^{-4}(4)^{2}}{2!}+\frac{e^{-4}(4)^{3}}{3!}+\frac{e^{-4}(4)^{3}}{3!}\\=1-0.01832-0.07326-0.14653-0.19537\\=0.56652[/tex]

Thus, the probability of 4 or more customers are waiting in a line during the visit is 0.56652.

Answer:

(a) 0.42

(b) 0.28

(c) 0.88

Step-by-step explanation:

Let probability that the bank stock will appreciate over a year, P(A) = 0.70

Probability that the electric utility will increase over the same period, P(B) = 0.60

Also, it is given that the two events are independent.

(a) Probability that both stocks appreciate during the period = Bank stock will appreciate * Electric utility will appreciate = P(A) * P(B)

     = 0.70 * 0.60 = 0.42 .

(b) Probability that the bank stock appreciates but the utility does not is given by;

     P(A) * (1 - P(B)) = 0.70 * (1 - 0.60) = 0.70 * 0.40 = 0.28 .

(c) Probability that at least one of the stocks appreciates = P(A [tex]\bigcup[/tex] B)

    P(A [tex]\bigcup[/tex] B) = P(A) + P(B) - P(A [tex]\bigcap[/tex] B)

                   = 0.70 + 0.60 - (0.70 * 0.60)   { because both events are

                                                                           independent }

                   = 1.3 - 0.42 = 0.88 .

Answer:

  x = 1/3 . . . . math facts or logarithms are involved; take your pick

Step-by-step explanation:

When you are solving for a variable that is in an exponent, logarithms are often useful. Taking the log of both sides of this equation, you have ...

  log(8^x) = log(2)

Using the rules of logarithms, that is ...

  x·log(8) = log(2)

  x = log(2)/log(8) . . . . . divide by the coefficient of x

You can find the value of this on your calculator, and it will tell you the value is  0.333333333333 or as many digits as your calculator displays. That is a clue that the exact answer is probably 1/3.

__

You should recognize that 8 = 2·2·2 = 2^3, so log(8) = 3log(2) and the above solution becomes ...

  x = log(2)/(3log(2)) = 1/3

__

Recognizing that 8 = 2^3, you can make that substitution into the original equation to get ...

  (2^3)^x = 2

  2^(3x) = 2^1

  3x = 1 . . . . . . . matching exponents; equivalent to taking logs base 2

  x = 1/3 . . . . . .  divide by 3

__

All of the above using 2 as a base of exponents is just dancing around the fact that you already know the math fact ...

  8^x = 2 = 8^(1/3)

  x = 1/3 . . . . . equating exponents; equivalent to taking logs base 8

Answer:

y = 97°

Step-by-step explanation:

z = 180 - 55 - 42 = 83

Total angle in a triangle is 180°

y = 180 - z = 180 - 83 = 97°

Supplementary angles

The equation 0.75x + 2.5y = 60 represents the relationship between the number of pounds of fertilizer (x), and the number of ounces of weed killer (y) that Bill bought with his $60.

The question is asking for an equation that could describe how the 60 dollars was spent on fertilizer and weed killer. To represent this relationship, we can set up a linear equation, with x representing the pounds of fertilizer and y representing the ounces of weed killer. Given that each pound of fertilizer costs 75 cents and each ounce of weed killer costs $2.50, the total amount spent on these two items can be represented as 0.75x + 2.5y = 60. This equation depicts how Bill's 60 dollars were allocated to the two items.

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Answer:

First is to define the language in which to make the statement, I chose the language C, because it is the most common. To initialize the variable, the first thing is to define the type, in this case it is an integer type.

In language C, that is determined by int, then the name of the variable, in this case it would be age. We close with; To finish the order. Then we give the courage that asks us to initiate.

In the end, it would look like this:

int age;

age = 15;

int weight;

weight = 90;

Final answer:

To declare and initialize two integer variables called age and weight, one can use the code 'int age = 15, weight = 90;'.

Explanation:

To declare and initialize two integer variables in most programming languages, you can use a single line of code. For the variables age and weight, the statement might look like this:

int age = 15, weight = 90;

This line of code creates two variables of type integer named age and weight. The variable age is initialized with the value 15, and weight is initialized with the value 90.

The use of the comma in the statement allows for both variables to be declared and initialized in one concise statement.

Answer:

Option iii) and iv) are the correct option

Step-by-step explanation:

Correct option is  - III and IV only

I) investors indifference curves are parallel they canno be intersect (False)

II) Indifference curve always be in a positive slope hence the statement is (False)

III) In a set of indifference curves, the higher the risk , the higher the return and as such the highest offers the greatest utility. (True)

IV) Indifference curve of investors with a same risk return trade off might intersect . (True)

Answer:

All real numbers

Step-by-step explanation:

The given exponential function is

[tex]y = {3}^{x} - 2[/tex]

This function is obtained by shifting, the parent function down by 2 units.

The parent function is

[tex]y = {3}^{x} [/tex]

The domain is the values of x for which the function is defined.

The exponential function is defined everywhere and the same applies to the transformed function.

Therefore the domain is all real numbers.

In a parallelogram with one given angle of 80°, the opposite angle equals 80°, and the two adjacent angles are 100° each, resulting from the properties of parallelograms.

The subject of this question is Mathematics, specifically geometry involving angles in a parallelogram. Given that one angle (Angle B) is 80° in a parallelogram, we can determine the measures of the remaining angles using the properties of parallelograms. Adjacent angles in a parallelogram are supplementary, meaning they add up to 180°. Therefore, if Angle B is 80°, then Angle C (adjacent to B) is 180° - 80° = 100°. Since a parallelogram has two pairs of parallel sides, opposite angles are equal. Therefore, Angle D equals Angle B (80°), and Angle A equals Angle C (100°).

Answer:

Austin should score between 85 and 100 in the final exam to have an average between 85 and 95, since reaching 96 is mathematically impossible.

Step-by-step explanation:

The problem has to be solved in two parts, the first to obtain an average of 85 and the second to obtain an average of 96.

In the first part with an average of 85 would be as follows.

Let x be the final exam grade.

Weighted average = (85 + 2 * X) / 3

85 = 85/3 + (2/3) * X

Rearranging

X = (3/2) * (85- (85/3))

Resolving

X = 85, therefore you must take 85 in the final test to get an average of 85.

The second part with an average of 96:

96 = 85/3 + (2/3) * X

Rearranging

X = (3/2) * (96- (85/3))

Resolving

X = 101.5, therefore you must take 101.5 in the final test to get an average of 96, therefore it is impossible to have an average of 96, because the highest score is up to 100.

Taking 100 your average would be:

Weighted average = (85 + 2 * 100) / 3 = 95

Then Austin should score between 85 and 100 in the final exam to have an average between 85 and 95, since reaching 96 is mathematically impossible.

Austin should score between [tex]85[/tex] and [tex]100[/tex] in the final exam to have an average between [tex]85[/tex]  and [tex]95[/tex].

Let us consider that  [tex]X[/tex] be the final exam grade.

So that, Weighted average [tex]= \frac{85 + 2 * X}{3}[/tex]

               [tex]85 =\frac{85}{3} + \frac{2}{3} X\\\\\frac{2}{3} X=85-\frac{85}{3} \\\\X=85[/tex]

Thus, you must take 85 in the final test to get an average of 85.

The second part with an average of 96:

[tex]96 = \frac{85}{3} + \frac{2}{3} X\\\\\frac{2}{3}X=96-\frac{85}{3}\\ \\ X=101.5[/tex]

Thus,  it is impossible to have an average of 96, because the highest score is up to 100.

Taking 100 your average would be:

Weighted average [tex]=\frac{85 + 2 * 100}{3} =95[/tex]

Hence,  Austin should score between 85 and 100 in the final exam to have an average between 85 and 95.

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Answer:

The probability that a corn crop has either an ear worm infestation, a corn borer infestation

P(EUB) = 0.27

Step-by-step explanation:

Explanation:-

Addition theorem on probability:-

If S is a sample space, and E , F are any events in S then

P(EUF) = P(E) +P(F) -P(E n F)

Let 'E' be the event that a corn crop has an infestation of ear worms

let 'B' be the event that a corn crop has an infestation of corn bores

P(EUB) = P(E) +P(B) -P(E n B)

given P(E) = 0.24 and P(B) = 0.16 and P(E n B) =0.13

P(EUB) = P(E) +P(B) -P(E n B)

P(EUB) = 0.24 + 0.16 - 0.13

           = 0.27

The probability that a corn crop has either an ear worm infestation, a corn borer infestation

P(EUB)=0.27

The probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.

You are asked to find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both. This situation relates to the basic rules of probability, specifically the rule for the probability of the union of two events.

The formula to find the probability of event E (ear worm infestation), event B (corn borer infestation) or both happening is: P(E or B) = P(E) + P(B) - P(E and B).

Plugging in the given values, we get: P(E or B) = 0.24 + 0.16 - 0.13 = 0.27.

Therefore, the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.

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Answer: 291.6 days

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering Henry's loan,

P = 2500

R = 9.3%

I = 186

186 = (2500 × 9.3 × T)/100

186 = 232.5 T

T = 186/231.6

T = 0.8 years

Assume that there are 365 days in a year, it would be

0.8 × 3645 = 291.6 days

Answer:

Total price of the album including tax is $10.08

Step-by-step explanation:

Sales price without discount and tax = $12

% discount = 20%

Sales price with discount = 12 - (20/100 × 12) = 12 - 2.4 = $9.6

% sales tax = 5%

Tax = 5/100 × 9.6 = $0.48

Total price of the album including tax = $9.6 + $0.48 = $10.08

Answer:

Final price = 9.6*(105/100) = 9.6*1.05 = 10.08 $

Step-by-step explanation:

The original price of the album is 12 to find out the price after the discount is applied we need to compute 100% - 20% = 80% of the original price. So we can use the following expression:

Price after discount = original price * (80/100)

Price after discount = 12 * (80/100)

Price after discount = 12 * 0.8 = 9.6 $

Now we have to include the sale tax of 5%, since it's a tax we need to add it to the original value so 100% + 5% = 105% of the sale's price:

Final price = Price after discount * (105/100)

Final price = 9.6*(105/100) = 9.6*1.05 = 10.08 $

Answer:

The correct answer are 28 and 32.

Step-by-step explanation:

Given p: A number is greater than 25, that is, the possible numbers are 26, 27, 28, 29, 30, 31, 32, 33, 34, .... and so on. And

q: A number is less than 35, that is the possible numbers are 34, 33, 32, 31, 30, 29, 28, 27, 26, .... and so on.

Now, p ∧ q is true when both p and q are true, this means that we have to find numbers that follow the criterion of both p and q.

So, p ∧ q = {26, 27, 28, 29, 30, 31, 32, 33, 34}. Therefore, the correct answers are 28 and 32.

The ratio of milk cartons left over to milk cartons taken from the 100 initially provided in the cafeteria is 2:3.

The number of milk cartons put out for breakfast in the cafeteria was 100 and after breakfast, there were 40 milk cartons left. This means that the number of milk cartons taken at breakfast is 100 - 40, which is 60. Thus, the ratio of milk cartons left over to milk cartons taken is 40:60.

We can simplify this ratio by finding the greatest common divisor (GCD) of both numbers. In this case, the GCD of 40 and 60 is 20, so by dividing both numbers by 20, we get a simplified ratio of 2:3. Therefore, the ratio of milk cartons left over to milk cartons taken is 2:3.

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Answer:

Step-by-step explanation:

7) The formula for determining the area of a parallelogram is expressed as

Area = base × height.

Length of base = Area/height

Therefore,

Length of base = 7/2 = 3.5 feet

8) The formula for determining the area of a trapezoid is expressed as

Area = 1/2(a + b)h

Where

a and b are the length of the bases

h is the height. Therefore

21 = 1/2(2 + 4)h

21 = 3h

h = 21/3 = 7 inches

9) Area = base × height.

Height = Area/Length of base

Height = 28/14 = 2 inches

10) a and b are 10 inches each.

Area = 1/2(a + b)h

Therefore,

35 = 1/2(10 + 10)h

35 = 10h

h = 35/10

h = 3 inches

Answer:

Option 1 is the only untrue statement of the 4 statements.

The only wrong statement about the confidence interval above is the one about the total of 95% of all teenage girls having BMI between 19.5 and 26.3.

Step-by-step explanation:

The question provides that for the BMI of girls with age between 13 and 19, the 95% confidence interval has a lower limit of 19.5 and an upper limit of 26.3.

We will take the statement one after the other.

Statement 1: A total of 95% of all teenage girls have BMI between 19.5 and 26.3.

This is a wrong statement. It doesn't not follow the definition for confidence interval for a set of sample.

Rather confidence interval, expresses that the true value (mean) exists in the (lower limit, upper limit) range with a confidence level of 95%.

Statement 2: The margin of error is 34.

The margin of error is usually used to calculate the lower and upper limit of the confidence interval.

Basically, the interval is usually between

(Sample mean ± margin of error)

If the sample mean = xbar

And the margin of error = α

xbar - α = lower limit of the confidence interval = 19.5

xbar + α = upper limit of the confidence interval = 26.3

xbar - α = 19.5

xbar + α = 26.3

summing these together

xbar = (19.5+26.3)/2 = 22.9

and the margin of error = (22.9 - 19.5) or (26.3 - 22.9) = 3.4.

So, this statement is correct!

Statement 3: The value z in the margin of error is 1.96.

The margin of error is given as the product of the z-multiplier (from the z-tables) and the sample standard deviation.

The z-multiplier for a 95% confidence interval, as obtained from literature and the z-tables is truly 1.96.

This statement is very true.

Statement 4: A total of 95% of all SRS of size n contain the true mean BMI.

Just like I described the meaning of confidence interval in the explanation under the first statement, this is as close to the meaning of confidence interval as can be. This statement is also very true.

Hence, only statement 1 is not correct of the 4 statements.