Please help ASAP! thank you!!

To find the displacement and total distance traveled by the object from t=0 to t=6, we need to integrate the velocity function over the given time interval.

The displacement can be found by integrating the velocity function v(t) with respect to t over the interval [0, 6]. The integral of v(t) represents the net change in position of the object during this time interval.

The total distance traveled can be determined by considering the absolute value of the velocity function over the interval [0, 6]. This accounts for both the forward and backward movements of the object.

Now, let's calculate the displacement and total distance traveled using the given velocity function v(t) = t^2 - (1/t) - 12 over the interval [0, 6].

To find the displacement, we integrate the velocity function as follows:

Displacement = ∫[0,6] (t^2 - (1/t) - 12) dt.

To find the total distance traveled, we integrate the absolute value of the velocity function as follows:

Total distance = ∫[0,6] |t^2 - (1/t) - 12| dt.

By evaluating these integrals, we can determine the displacement and total distance traveled by the object from t=0 to t=6.

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Answer:

8 triangles

Step-by-step explanation:

I took this question to mean that we have the lengths, 2, 6, and 7 and have multiple copies of them. Using these lengths, what are all of the triangles that can be made?

2x2x2

6x6x6

7x7x7

2x6x7

6x6x7

6x7x7

2x6x6

2x7x7

2x2x6 and 2x2x7 don’t make a triangle.

So, 8 triangles can be made.

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Answer:

For the first part of 4 questions wrong: he would get 42 points

For the second part 48 points

Step-by-step explanation:

For the first part of 4 questions wrong: he would get 42 points because 50 divided by 2 is 25 and 25 minus 4 is 21 and 21 times 2 is 42.

For the last part I'm guessing x = 1 so again 50 divided by 2 is 25 and 25 minus 1 is 24 and 24 times 2 is 48

I think it is right.

Answer: first one 42

The second one is 50-2x

explanation: score with 4 questions wrong

Available points 50. Points lost=points per question x4=2x4=8 final score 50-8=42

Score with x questions wrong: available points 50 points lost=points per questionx4=2*x=2x final score =available points-points lost =50-2x

Answer:

D. (1, 5)

Step-by-step explanation:

the solution to the system of equations is the point of lines intersect => (1, 5)

divide cost by quantity. The lowest rate is the best buy:

26/8 = 3.25 each

30/5 = 6.00 each

15/4 = 3.75 each

39/12 = 3.25 each

45/10 = 4.50 each

The 8 for 26 and the 12 for 39 are both the same price each and are the better buys.

If a costumer is sending 200 texts than in that case the plan b is cheaper that plan a.

According to the information given in the question,

There are two plans given by the telephone company.

The first plan is,

Plan a - Where people will pay 10 cents for each text sent or received.

The second plan is,

Plan b - Where people will pay 12 dollars per month, and pay additional 2 cents for each text sent or received.

Now let us assume,

10 cents = 0.1 dollars

2 cents = 0.02 dollar

So according to the question the value of plan a seems less than the value of plan b,

Plan a < Plan b

could be written as,

0.1x < 0.02x + 12

Where let x be the number of texts sent by the costumer.

x = 200

Let keep the value of x in both the plans,

Plan a = 0.1x

= 0.1 x 200

= 20

Plan b = 0.02x + 12

= 0.02 x 200 + 12

= 4 + 12

= 16

If a costumer is sending 200 texts then in that case

Plan a is giving the output = 20

Plan b is giving the output = 16

In that case the plan b is cheaper than a.

Therefore, if a costumer is sending 200 texts than in that case the plan b is cheaper that plan a.

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Answer:

4

Step-by-step explanation:

2 + 2 = 4

The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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Answer:

100% -> 6.50

100 - 25 = 75

75% -> 6.50/100 x 75

            = 4.875

            ≈ 4.88    

Answer:

$4.875 or if rounded $4.88

Step-by-step explanation:

Hope this helped

also u just have to subtract 6.50 by 25%

The solution to the system of inequalities y ≤ 2x + 2 and y < -2x - 3 can be represented by a graph. The inequality y ≤ 2x + 2 represents a line with a slope of 2 and y-intercept of 2. The inequality y < -2x - 3 represents a line with a slope of -2 and y-intercept of -3. ( The graph attached)

The inequality y ≤ 2x + 2 represents a line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 2. To graph this inequality, we can first plot the line by using the y-intercept, which is the point (0,2) on the graph. Then, we can use the slope to find additional points that fall on the line, such as (1,4) or (-1,0). Once we have plotted several points, we can connect them to form the line.

The inequality y < -2x - 3 represents a similar line, but with a different slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. To graph this inequality, we can use the same process as before by first plotting the y-intercept (0,-3), and then using the slope to find additional points that fall on the line.

The solution to the system of inequalities is the area that lies on one side of the first line and the opposite side of the second line, which is the area between the two lines. This area can be represented by shading the region below the first line and above the second line on the graph. It is important to note that the solution region is not including the lines themselves, because the inequalities are strict inequalities.

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Answer:

2

Step-by-step explanation:

To find the slope of a line, we can use the formula \(\frac{y_{1}-y_{2}}{x_{1}-x_{2}}\). We can choose the first two sets, (0,2) and (3,8). 8-2=6 and 3-0=3, so \(\frac{6}{3} = 2\). The slope of the line is 2

Answer:

2/8 + 1/4 + 3/6 = 1

Step-by-step explanation:

2/8 = 0.25

1/4 = 0.25

3/6 = 0.5

0.25 + 0.25 + 0.5 = 1

Answer:

600⁰00000000000000000

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The circumference of the circle is 25.12 inches. The Option C.

The Circumference, also perimeter of circle means the ratio of circumference to diameter of any circle.

The length of the segment represents radius of the circle which half length of diameter. So, the diameter is:

= 2 * 4 inches

= 8 inches.

The circumference is found using C = πd.

C = π*d

C = 3.14 * 8 inches

C = 25.12 inches.

Full question:

What is the circumference of the circle? Use 3.14 for π.

circle with a segment drawn from the center of the circle to a point on the circle labeled 4 inches

A. 157.75 inches

B. 50.24 inches

C. 25.12 inches

D. 12.56 inches.

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Answer:

e = $8.15n

Although this doesn't require an explanation, I am always open to solve any confusion.

Side Note: I used variable E assuming that the period before 'E' was supposed to be a comma which means it was a given variable.

Answer:

E= 8.15n

Step-by-step explanation:

Answer:

Your correct answer is -b/2a

Step-by-step explanation:

What you need to do is  find the coordinates of the vertex from the equation itself, using this formula: x = -b/2a

At the fidelity credit union, the mean number of customers who arrive hourly at the drive-through window is 4.9. It is required to determine the probability of fewer than 1 customer arriving in any hour.

Answer: 0.00796.

The solution to this problem is discussed below:

The given information implies that the mean value of the Poisson distribution, λ = 4.9.

In a Poisson distribution, the probability of x occurrences during a particular interval is given by:

P(x; λ) = e–λ λx / x!

Where e is approximately equal to 2.71828.

Let x = 0 since we need the probability of less than 1 customer in an hour.

P(x < 1) = P(x = 0) + P(x = 1) + P(x = 2) + …P(x < 1) = e-4.9 4.90 / 0!P(x < 1) = e-4.9 1P(x < 1) = 0.00796

The probability of fewer than 1 customer arriving in any hour is 0.00796 (rounded to four decimal places)

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Answer:

A. SSS

Step-by-step explanation:

The probability that a randomly selected household with a savings account has no checking account is approximately 0.149, or 14.9%.

To compute the probability that a randomly selected household with a savings account has no checking account, we can use Bayes' theorem. Let S denote the event that a household has a savings account, and C denote the event that a household has no checking account.

We want to find P(C | S), the probability that a household with a savings account has no checking account.

Using Bayes' theorem, we have:

P(C | S) = P(S | C) * P(C) / P(S)

We know that 40% of households with no checking accounts have savings accounts, so P(S | C) = 0.4. We also know that 21.5% of households have no checking accounts, 66.9% have regular checking accounts, and 11.6% have NOW accounts, so P(C) = 0.215.

Finally, we can use the law of total probability to find P(S), the overall probability of a household having a savings account:

P(S) = P(S | C) * P(C) + P(S | regular checking) * P(regular checking) + P(S | NOW) * P(NOW)

= 0.4 * 0.215 + 0.716 * 0.669 + 0.793 * 0.116

≈ 0.576

Substituting these values into the equation for Bayes' theorem, we get:

P(C | S) = 0.4 * 0.215 / 0.576

≈ 0.149

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Complete question is:

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.

Compute the probability that a randomly selected household with a savings account has no checking account.

The probability that a randomly selected student prefers the arts or does not prefer literature is 8/11.

There are different ways to approach this problem, but one possible method is to use the concept of complement events.

First, we can calculate the probability of a randomly selected student preferring the arts. This is simply the proportion of students in the sample who prefer the arts, which is 9 out of 3+9+10 = 22. So, the probability is:

P(arts) = 9/22

Next, we can calculate the probability of a randomly selected student preferring literature. This is the proportion of students in the sample who prefer literature, which is 7+8 = 15 out of 22. So, the probability is:

P(literature) = 15/22

To find the probability of a student preferring the arts or not preferring literature, we can use the complement event that consists of students who do not prefer literature. This is the complement of the event "preferring literature", and its probability is:

P(not literature) = 1 - P(literature) = 1 - 15/22 = 7/22

Finally, we can use the addition rule for disjoint events (i.e., events that cannot occur at the same time) to calculate the probability of the event "preferring the arts or not preferring literature".

Since these events are not mutually exclusive (i.e., some students may prefer both the arts and literature), we need to subtract their intersection (i.e., students who prefer both) to avoid double-counting. Therefore, the probability is:

P(arts or not literature) = P(arts) + P(not literature) - P(arts and literature)

= 9/22 + 7/22 - 0

= 16/22

= 8/11

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The value of (x + 4)² will be x² + 8x + 16

The value of (7x + 5y)² will be 49x² + 70xy + 25y²

The value of (4x + 5y)² will be 16x² + 40xy + 25y²

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

The value of (x + 4)² will be:

(x + 4)²

= (x + 4)(x + 4)

= x² + 4x + 4x + 16

= x² + 8x + 16

(7x + 5y)² will be:

= (7x + 5y)(7x + 5y)

= 49x² + 35xy + 35xy + 25y²

= 49x² + 70xy + 25y²

(4x + 5y)² will be:

= (4x + 5y)(4x + 5y)

= 16x² + 20xy + 20xy + 25y²

= 16x² + 40xy + 25y²

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7h-15h+40=-72

40+72=15h-7h

112=8h

h=14

it equals -8.

4k + 13 = 3k + 5

4k + 13 - 13 = 3k + 5 - 13

4k = 3k - 8

4 k  −  3 k  = 3k - 8 - 3k

k = -8

Answer:

Step-by-step explanation: Acute

Answer:

Step-by-step explanation:

acute

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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