Approximate the value of the given integral by use of the trapezoidal rule, using the given value of n. 3 6 se dx, n=2 7x 2 ... 3 6 dx 7x 2 (Round to four decimal places as needed.)

correct me if I am wrong

Answer:

70feet

Step-by-step explanation:

during the

1st sec it travels 28 ft

2nd sec =28-7=21ft

3rd sec= 21-7=14ft

4th sec= 14-7= 7ft

last sec=7-7=0ft, at this point the car stops.

so altogether it travels 28+21+14+7+0= 70 feet

Answer:

175 Kg

Step-by-step explanation:

Convert 385 pounds into kg given the fact that 1 kg = 2.2 pounds.

385 : 2.2 =

175 Kg

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

a) The function is │f'(x)│≤ 7. b) The │f(b) - f(a)│ ≤ 7 │b - a│ for all values of a and b.

a) To find the maximum value of │f'(x)│, we need to consider the maximum value of the derivative of f(x). The derivative of f(x) = 7 sin(x) is f'(x) = 7 cos(x).

The maximum value of │f'(x)│ occurs when cos(x) is equal to 1, which happens when x = 0 degrees (or 0 radians). Therefore, the maximum value of │f'(x)│ is │7 cos(0)│ = 7.

So, │f'(x)│≤ 7.

b) According to the mean value theorem, if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one value c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

In this case, let's consider f(x) = 7 sin(x) on the interval [a, b]. By the mean value theorem, we have:

│f(b) - f(a)│ ≤ │f'(c)│ │b - a│

Since │f'(c)│ is equal to │7 cos(c)│, and │cos(c)│ is always less than or equal to 1, we can say that │f'(c)│ ≤ 7.

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(a) Two-hypothesis are used for each experiment,

(b) They go by the names of Null and Alternate Hypothesis.

(c) We actually test the Alternate hypothesis.

Part(a) : In most experimental designs, there are two hypotheses: the null hypothesis (H₀) and the alternative hypothesis (Hₐ).

Part(b) : The Hypotheses are generally classified as "Null-Hypotheses" or "Alternative-Hypotheses".

The "Null-Hypothesis" (H₀) is defined as a statement that assumes there is no significant difference or relationship between variables or that an intervention has no effect.

The "Alternative-Hypothesis" (Hₐ) is defined as a statement that assumes there is a significant difference or relationship between variables or that an intervention has an effect.

Part (c) : The hypothesis being-tested in an experiment is generally the "Alternative-Hypothesis" (Hₐ) because the "Null-Hypothesis" (H₀) is assumed to be true until evidence is found to reject it.

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The given question is incomplete, the complete question is

(a) How many hypothesis are used for each experiment?

(b) What name do they go by?

(c) Which one we actually test?

Answer:

2 answers: 200 adults or 150 adults and 100 children

Theres many answers to this problem

Answer:

78°F

Step-by-step explanation:

75.5°F on Saturday...

75.5 + 6 = 81.5 on Sunday

81.5 - 3.5 = 78°F on Monday

The expression that represents the temperature change is

N = L + 6°F + 3.5°F

The temperature on Monday is 85°F.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Temperature:

Saturday = L= 75.5°F ______(1)

Sunday = M = Rose by 6°F

M = L + 6 _____(2)

Monday = N = Dropped by 3.5°F

N = L + 6 - 3.5 _____(3)

The expression that represents the temperature change:

From (1), (2), and (3) we get

N = L + 6°F + 3.5°F

The temperature on Monday:

N = 75.5 + 6 + 3.5

N = 85°F

Thus,

The expression that represents the temperature change is

N = L + 6°F + 3.5°F

The temperature on Monday is 85°F.

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Answer:

\(r\leq 10.8\)

OR

\(r\leq 10\)

Step-by-step explanation:

Given that:

Amount of water in the aquarium = 9 gallons

Weight of water in the aquarium = 85 pounds

Total weight that aquarium can hold = 112 pounds

Weight of each rock = 2.5 pounds

To find:

The inequality to find the number of rocks, \(r\) that can put in her tank.

Solution:

First of all, let us find more weight that the aquarium can hold after putting the water in the aquarium.

Additional weight that can be put in the aquarium = Total weight - Weight of water = 112 - 85 = 27 pounds

This 27 pounds can be of rocks.

Let the number of rocks that can be put in the aquarium = \(r\)

Total weight of \(r\) number of rocks = Weight of one rock multiplied by \(r\)=2.5\(r\)

Now, this weight of rocks must be lesser than or equal to 27 pounds.

Therefore, the in equality is:

\(2.5r\leq =27\\\Rightarrow r \leq 10.8\\OR\\\Rightarrow r \leq 10\)

Using the gradient of the curve given, the value of a is 6

The stationary point of a curve is a point where the slope of the curve is equal to zero. So, to find the value of a, we need to set the derivative of the curve equal to zero and solve for x.

dy/dx = 2(x + 3)^(1/2) - x

Setting this equal to zero, we have:

2(x + 3)^(1/2) - x = 0

Expanding the square root and rearranging, we get:

x = 2(x + 3)^(1/2)

Squaring both sides of the equation, we have:

x^2 = 4(x + 3)

Expanding the right side and rearranging, we have:

x^2 - 4x - 12 = 0

Using the quadratic formula, we can find the values of x that satisfy this equation:

x = [-(-4) ± √((-4)^2 - 4(1)(-12))] / 2(1)

x = [4 ± √(16 + 48)] / 2

x = [4 ± √64] / 2

x = [4 ± 8] / 2

So, the two possible values of x are:

x = 6, x = -2

Since we are looking for a positive value of x, the only solution that works is x = 6.

Therefore, the value of a is equal to 6.

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The ratio that represents the tangent of ∠G in the given  right angled triangle GHI is found to be 13/85.

All right-angled triangles with as one of whose angles are similar if we fix an acute angle. As a result, the ratio between equivalent pairs of sides is the same in all such triangles are defined by trigonometric ratios.

The hypotenuse is the side that faces the right angle. We designate the leftover side as the adjacent and the side across as the opposite.

Given data:

ΔGHI is the right angled triangle at ∠I = 90°.

GI = 84, IH = 13, and HG = 85.

Then,

tanθ = opposite / adjacent.

tangent G = HI / GH

tangent G = 13/ 85

Thus, the ratio that represents the tangent of ∠G in the given  right angled triangle GHI is found to be 13/85.

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Answer: C; 3 4/2

Step-by-step explanation:  A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.

An exponential always crosses at (0,1) This function crosses at (0.6) meaning it has shifted up 5 units or +5. These means only answer options A and D are possible solutions. Also, since the graph starts high and ends low and leveling out, this means the base is less than 1. Only 3/4 is less than 1. Answer A is the solution.

hope this helps, thank you! :)

Step-by-step explanation:

-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4

Answer:

8 inches cubed

Step-by-step explanation:

s = 2

V = 2^3 = 8

Step-by-step explanation:

We can immediately eliminate answers B and C because we have >, meaning that the circle on the number line has to be open.

-2x+7>17

subtract 7 on both sides

-2x>10

divide by -2. remember that dividing by a negative flips the greater than or less than sign.

x<-5

the answer is D

The best description for this histogram is that it is symmetrical. The correct option is A.

A histogram is a graphical representation of data that uses bars of varying heights. Each bar in a histogram categorizes numbers into ranges. Taller bars indicate that there is more data in that range. A histogram depicts the shape and distribution of continuous sample data.

A histogram is a diagram made up of rectangles, with the area proportional to the frequency of a variable and the width equal to the class interval. A histogram is a type of graph that is commonly used to depict frequency distributions.

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Answer: A

Step-by-step explanation: just finished taking the test

The actual dimensions of Abigail's house are 18 ft by 20 ft.

Abigail's house is represented by a scale drawing with dimensions of 9 cm by 10 cm. We are told that 6 cm on the scale drawing equals 12 ft. To find the actual dimensions of Abigail's house, we need to determine the scale factor.

First, we calculate the scale factor by dividing the actual length (12 ft) by the corresponding length on the scale drawing (6 cm). The scale factor is 12 ft / 6 cm = 2 ft/cm.

Next, we can use the scale factor to find the actual dimensions of Abigail's house. We multiply each dimension on the scale drawing by the scale factor.

The actual length of Abigail's house is 9 cm * 2 ft/cm = 18 ft.
The actual width of Abigail's house is 10 cm * 2 ft/cm = 20 ft.

Therefore, the actual dimensions of Abigail's house are 18 ft by 20 ft.

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Answer:

1/2 a cup or 0.5 cups per serving

Step-by-step explanation:

If you were to divide 7 by 14 you would get 0.5. The reason as to why you would divide 7 by 14 is because if she eats twice a day that would be 7 more times then if she were to be fed once a day. So if you  were to feed her twice a day that would be 14 times a week.

Don't think this helped at all but I tried my hardest, sorry if you get your problem wrong. Hope you have a good day :D

The function f(x) = 150,000(0.85)^x can be used to determine the number of tickets the Houston Ballet Company will sell over time. In this function, the 150,000 represents the initial number of tickets sold before any time has passed (when x = 0).

It serves as the starting point or baseline for the exponential decay of ticket sales over time. As x increases, the function evaluates the number of tickets sold at a particular time, where each subsequent value of x represents a subsequent unit of time (such as days, weeks, months, etc.). The term (0.85)^x represents the decay factor, as it is less than 1 (0.85). Thus, the function models a situation where ticket sales decrease exponentially over time from the initial value of 150,000.

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The sums of series using Polya's four-step problem-solving strategy in (a), (b) and (c) are 79800, 150975, and 1560 respectively.

a sequence is, more or less speaking, a description of the operation of adding infinitely many quantities, one after the opposite, to a given starting quantity. The examine of series is a chief part of calculus and its generalization, mathematical evaluation. series are utilized in maximum areas of mathematics, even for reading finite structures (which includes in combinatorics) thru producing features.

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All the events in the sample space that are not part of the specified event are called Complement of Event.

Complement of event:

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.

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The answer is (f) None of the above.

We can use the inclusion-exclusion principle to find the cardinality of the set A ∪ (B ∩ C). The formula is:

n(A ∪ (B ∩ C)) = n(A) + n(B) + n(C) - n(B ∪ C) - n(A ∩ B ∩ C)

We are given the values of n(A), n(B), n(C), n(A ∩ B), n(B ∩ C), and n(C ∩ A) from the Venn diagram. We can use these values to find n(B ∪ C) and n(A ∩ B ∩ C) as follows:

n(B ∪ C) = n(B) + n(C) - n(B ∩ C)

n(A ∩ B ∩ C) = n(A) + n(B) + n(C) - n(A ∪ B) - n(B ∪ C) - n(C ∪ A) + n(A ∩ B ∩ C)

Substituting the values from the Venn diagram, we get:

n(B ∪ C) = 50 + 28 - 16 = 62

n(A ∩ B ∩ C) = 18 + 16 + 28 - 50 - 62 - 20 + 10 = 0

Therefore,

n(A ∪ (B ∩ C)) = n(A) + n(B) + n(C) - n(B ∪ C) - n(A ∩ B ∩ C) = 32 + 50 + 20 - 62 - 0 = 40

So the answer is (f) None of the above.

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The probability that a point within the white circle lies on the red circle is P = 0.44

The probability will be given by the quotient between the area of the red square and the area of the circle.

On the diagram we can only see two squares, so Im assuming that it should say "square" instead of circle.

The area of the large square is:

A = 3*3 = 9

The area of the red square is:

A' = 2*2 = 4

Then the probability is:

P = 4/9 = 0.44

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Answer:

14.3 yd

Step-by-step explanation:

apply the pythagorean Theorem formula:

= sqrt(14^2 +3^2)

= sqrt(205)

roughly 14.3 yd

The sum of interior Angles of Hexagon is always 720°

Any hexagon's internal angles add up to 720° in all cases. By dividing 720° by 6, we may get the size of each interior angle of a regular hexagon. As a result, we have:

720°÷6 = 120°

In a regular hexagon, each inside angle is 120°.

An example of a regular hexagon with equal-length sides and angles is shown in the diagram below. By multiplying the six 120° angles together, we can demonstrate that the result is 720°.

Therefore, the interior angles of a hexagon are always added up to 720°.

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The actual step response plots would require specific values for time and magnitude scaling, which cannot be accurately depicted in a textual format.

To sketch the pole-zero plots for each system, we first need to identify the poles and zeros of each transfer function.

For G1(s) = (s + 2)^2:

- Pole: s = -2 (double pole)

For G2(s) = (s + 0.5)^0.5:

- Pole: s = -0.5 (single pole)

For G3(s) = (s + 0.5)(s + 2):

- Poles: s = -0.5, s = -2 (single poles)

Now, let's plot the pole-zero plots and the step responses for each system:

Pole-zero plot for G1(s):

- Pole at s = -2 (double pole)

- Zero at s = None (no zero)

Step response of G1(s):

- Time constant: T = 1/2 = 0.5 (from the dominant pole)

- The step response of G1(s) will exhibit an overshoot and multiple oscillations before settling to the steady-state value.

Pole-zero plot for G2(s):

- Pole at s = -0.5 (single pole)

- Zero at s = None (no zero)

Step response of G2(s):

- Time constant: T = 1/0.5 = 2 (from the dominant pole)

- The step response of G2(s) will show a slower rise time and smoother approach to the steady-state value compared to G1(s).

Pole-zero plot for G3(s):

- Poles at s = -0.5, s = -2 (single poles)

- Zero at s = None (no zero)

Step response of G3(s):

- The step response of G3(s) will resemble that of G1(s) since it shares the dominant pole at s = -2. However, the additional pole at s = -0.5 in G3(s) might introduce some damping and affect the transient response.

By observing the step responses of G1(s) and G2(s), we can verify their time constants:

- For G1(s), the time constant T = 0.5, as determined from the dominant pole at s = -2.

- For G2(s), the time constant T = 2, as determined from the dominant pole at s = -0.5.

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A loan fee is an amount a consumer pays for a loan. This includes taking out a car loan, credit card, or mortgage. Common loan fees include interest rates, origination fees, service fees, late fees, etc. Gross Loan Fees are typically associated with your credit card and consist of any outstanding balance plus any other fees incurred if you carry overdue amounts to your credit card.

If you know three numbers related to your credit card account: credit card (or loan) balance, APR, and billing cycle length, you can calculate your loan fees.

Current Balanced Owned =$785

APR = 24.42%

Let’s suppose the billing cycle is 30 days, then

Finance charge = $15.76

The new balance you owe = $800.76.

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i think its 50 u need to multiply √5 *√5 that is 5

Answer:

\(\boxed{\color{blue}\textsf{The weight of the Aluminium oxide is \textbf{900 grams . }}}\)

Step-by-step explanation:

Here we are given 9 moles of \(\sf Al_2O_3\) and we need to find its weight in grams . So we know the formula to find the number of moles as ,

\(\qquad\boxed{ \sf N_{(moles)}= \dfrac{Weight(in \ grams )}{Molecular \ weight }}\)

Now the molecular mass of \(\sf Al_2O_3\) is , equal to 26*2 + 16*3 = 52 + 48 = 100 g

Using the formula to find the Number of moles :-

\(\sf\implies \sf N_{(moles)}= \dfrac{Weight(in \ grams )}{Molecular \ weight } \\\\\sf\implies 9 =\dfrac{ W}{ 100g }\\\\\sf\implies W = 9 \times 100 g \\\\\sf\implies\boxed{\pink{\frak {Weight_{(Al_2O_3)}= 900 grams }}}\)

Answer:

no way is these points omg i love it