4. Show that Polygon A is congruent to Polygon B.

The integral evaluated is (7/5)rsin(5r) + (49/25)cos(5r) + C.

Given Integral to evaluate using integration by parts method is :∫7rcos(5r)dr

Let us consider the given function as a product of two functions for applying the formula for integration by parts.

The formula for integration by parts is:

∫udv = uv - ∫vdu

Where u and v are the functions of x, and the choice of u and v decide how easy the integration will be.

Let us consider u = 7r and

dv = cos(5r)dr

Then we get,du/dx = 7 and

v = (1/5)sin(5r)

Now applying the formula of integration by parts, we get:

∫7rcos(5r)dr = (7r)(1/5)sin(5r) - ∫(1/5)sin(5r)7

dr= (7/5)rsin(5r) + (49/25)cos(5r) + C,

where C is the constant of integration.

Thus, the integral is evaluated using integration by parts is (7/5)rsin(5r) + (49/25)cos(5r) + C.

Answer: the integral evaluated is (7/5)rsin(5r) + (49/25)cos(5r) + C.

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Answer: Looks like u already answered the question

Step-by-step explanation:

The expression 4[(3/4)y - 2 + (1/2)y] is equivalent to the expression 5y - 8 and 3y - 8 + 2y.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 4[(3/4)y - 2 + (1/2)y]

Simplify the expression, then we have

⇒ 4[(3/4)y - 2 + (1/2)y]

⇒ 3y - 8 + 2y

⇒ 5y - 8

The expression 4[(3/4)y - 2 + (1/2)y] is equivalent to the expression 5y - 8 and 3y - 8 + 2y.

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Answer:

3.88

Step-by-step explanation:

Given that

42x = 163

It set 2x = 3

and x = 32

We need to tell the mistake and mentioned the correct answer

if we solve the above equation i.e.

42x = 163

x = 3.88

Hence, in this way it should be calculated

The same would be considered and relevant

Hence, the correct answer is 3.88

The even integers are 10,12 and 14.

Concept:  An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Let x,x+2,x+4 be the least, middle and greatest integer respectively.

According to the question,

15< x+x+2+x+4< 21

(3x+6)/2> 15      and    (3x+6)/2< 21

30< 3x+6                      3x+6> 42

24<3x                            3x<36

8<x                                x>12

x=10

x+2=12

x+4=14

Hence, The even integers are 10,12 and 14.

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Answer:

\(\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right\)

Step-by-step explanation:

The coordinates are:

\(\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right\)

The parallelogram is attached below.

To verify if these coordinates form a parallelogram, we show that:

Using Distance Formula

\(AB = \sqrt{(6-8)^2+(9-3)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} $ units\)

\(CD = \sqrt{(2-4)^2+(7-1)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} $ units\)

\(AC = \sqrt{(8-4)^2+(3-1)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} $ units\)

\(BD = \sqrt{(6-2)^2+(9-7)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} $ units\)

Since AB=CD; and AC=BD, the coordinates A, B, C, and D form the vertex of a parallelogram.

The water is running out at 1800 gal/min at the end of 11 minutes. The correct answer is 1800gal/min.

Given the function Q(t) = 50(20 - x)^2 represents the number of gallons of water in a swimming pool t minutes after the pool has started to drain. Here, we need to find how fast the water is running out at the end of 11 minutes. Let's differentiate the given function with respect to time (t). Q(t) = 50(20 - x)^2

Differentiating both sides with respect to time (t), we get, dQ/dt = 50 × 2(20 - x) (-dx/dt)

On substituting t = 11, we have Q(t) = Q(11) = 50(20 - x)^2

And, dx/dt = - 2

We need to calculate dQ/dt at t = 11

Therefore, dQ/dt = 50 × 2(20 - x) (-dx/dt) = 50 × 2(20 - x) × 2= 200(20 - x)

At t = 11, Q(t) = 50(20 - x)^2⇒ Q(11) = 50(20 - x)^2= 50(20 - 11)^2= 50(9)^2= 4050 gal/min

Substituting x = 11 in dQ/dt, we get, dQ/dt = 200(20 - 11)= 200 × 9= 1800

Therefore, the water is running out at 1800 gal/min at the end of 11 minutes.

Hence, the correct option is 1800 gal/min.

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Answer:

20

Step-by-step explanation:

1 hour is 60 minutes 1/3x60=20

Answer:

1200 seconds

Step-by-step explanation:

1/3 of an hour is 20 minutes. There are 60 seconds in a minute. 60 times 20 = 1200.

Answer:

\(69.8637\)

(4d.p)

The statement "When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events" is true.

When two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event. In such cases, the joint probability of both events can be found by multiplying their individual probabilities. Mathematically, this can be expressed as P(A ∩ B) = P(A) * P(B). This rule holds true for independent events and is a fundamental concept in probability theory.

Now, let's examine the other statements:

1. The probability of the union of two events can exceed one:

This statement is false. The probability of an event is always between 0 and 1, inclusive. When you consider the union of two events, the probability of their combined occurrence cannot exceed 1. It is possible for the sum of the individual probabilities of the two events to exceed 1, but the probability of their union will never be greater than 1.

2. When events A and B are mutually exclusive, then P(A ∩ B) = P(A) + P(B):

This statement is false. Mutually exclusive events are events that cannot occur at the same time. If events A and B are mutually exclusive, their intersection (A ∩ B) will be an empty set, and therefore, the probability of their intersection is 0 (P(A ∩ B) = 0). The correct statement for mutually exclusive events is P(A ∪ B) = P(A) + P(B), where P(A ∪ B) represents the probability of the union of events A and B.

3. The union of events A and B consists of all outcomes in the sample space that are contained in both event A and B:

This statement is false. The union of events A and B, denoted as A ∪ B, consists of all outcomes that belong to either event A or event B or both. In other words, it includes all outcomes that are in A, in B, or in both A and B. The intersection of events A and B (A ∩ B) represents the outcomes that are contained in both A and B.

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In simplest radicle form, the length of the third side = 9 units.

Given,

Side A = 7 units.

Side B = 4√2 units.

To find Side C, we use the Pythagorean formula,

a² = b² + c²

7² = \(4\sqrt{2}^{2}\) + c²  

c² = 49 + 32

c² = 81

√c² = √81

c = -9,9.

c ≠ -9 as negative values are not considered for dimensions.

Hence, the length of the third side is 9 units.

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Your question is incomplete. The complete question is:

With reference to the figure below,  find the length of the third side. If necessary, write in the simplest radical form.

Answer:?

The following list shows how many brothers and sisters some students have:

2, 4, 3, 3, 4, 2, 4, 3, 3, 2, 3, 4

State the mode.

Step-by-step explanation:

Answer:

N=138

Step-by-step explanation:

(4x+6) + N = 180

In order to complete this problem we need to solve for x. 4x+6=7x-21

Subtract on both sides

Subtract again

Divide

x=9

Plug it in now so 4 times 9 plus 6. 36, plus 6 = 42.

plug it in to the equation 42+N=180

                                         -42       -42

                                                    138 = N

Answer:

Download graphing calc it helps a lot <4

Answer:

In 11/20, 11/100, and 11/15, the numerator is 11.

In 6/11, the denominator is 11.

The population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

All these elements are taken into account when formulating the population growth formula.

r = [(b + i) - (d + e)]/1000

Put the values in the formula.

r =  [(2,000 + 100) - (500 + 200)]/1000

r = 2100 - 700/ 1000

r = 1.4

Thus, the population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

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The probability that a randomly chosen value from this normal population will be greater than 57 is approximately 0.0297, or 2.97%.

To find the probability that a randomly chosen value will be greater than 57 from a normal population with a mean (μ) of 40 and a standard deviation (σ) of 9, you will need to follow these steps:

1. Calculate the z-score:

The z-score represents the number of standard deviations a value is away from the mean.

To calculate the z-score, use the formula:

z = (X - μ) / σ, where X is the value in question (57 in this case).

2. In this case, z = (57 - 40) / 9 = 17 / 9 ≈ 1.89.

3. Look up the z-score in a standard normal distribution table (or use a calculator or software) to find the probability of obtaining a z-score less than 1.89.

The table value for a z-score of 1.89 is approximately 0.9703.

4. Since we want the probability that the value is greater than 57, we need to find the probability of obtaining a z-score greater than 1.89.

To do this, subtract the table value from 1:

1 - 0.9703 = 0.0297.

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Answer:

9 ft

Step-by-step explanation:

3*3 = 9

Answer:

380

Step-by-step explanation:

The general formula for the total surface area of a regular pyramid is T. S. A. =12pl+B where p represents the perimeter of the base, l the slant height and B the area of the base.

yo ur answer is 380

HOPE IT HELPS YOU PLEASE MARK ME THE BRAINLIEST

Answer:

honestly i dont know :(

Step-by-step explanation:

Answer:

a: -5

k: 1/4

d: 3

c: 2

\(g(x) =2-\frac{5}{4(x-3)}\)

Step-by-step explanation:

Explanation is in Picture. Reflections across x-axis make a negative.

For b), look up 'Transformations of the 1/x function' and watch the video by Ragini Narasimhan. He explains it well

The answer is 5.1 completes the inequality.

Hence, The answer is 5.1 completes the inequality.

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Answer:

x = -15 and x = -2

Step-by-step explanation:

x+2 = \(\sqrt{-13x-26}\)

first step is to square both sides to eliminate the square root symbol

(x+2)² = -13x - 26

now use the 'foil' method on (x+2)² to get:

x² + 4x + 4 = -13x - 26

add 13x to each side to get:

x² + 17x + 4 = -26

add 26 to each side to get:

x² + 17x + 30 = 0

(x+15)(x+2) = 0

x+15 =0;  x = -15

x+2 =0;   x = -2

Answer:

4

Step-by-step explanation:

This question basically asks you to substitute the value of x to find the value of function g(x).

Given x = -2,

g(-2) = -4(-2) - 4 = 8 - 4 = 4

Answer:

4

Step-by-step explanation:

g(x) = -4x - 4

Let x = -2

g(-2) = -4(-2) - 4

          = 8 -4

           =4

Answer:

1/2=20/40 19/20=38/40

Step-by-step explanation:

so the first option

Answer: 32.6%

Step-by-step explanation:

percentage is whatever number you have x100 which would move the decimal point right 2 points and in this case would move the decimal from .326 to 32.6

The number of days that Aubrey can drive to stay in her budget is 5 days.

> means greater than

< means less than

≥ means greater than or equal to  

≤ less than or equal to  

Total amount that can be spent ≤ (cost to rent a car per day x number of days) + (cost per mile x total miles driven)

$130 ≤ ($22.15 x dd) + ($0.07 x 275)

130 ≤ ($22.15dd) + ($0.07 x 275)

130  ≤  $22.15dd + 19.25

130 - 19.25  ≤ $22.15dd

110.75  ≤ 22.15d

d  ≤ 110.75 / 22.15

d  ≤ 5

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Answer:

C) All squares are rhombuses. Rhombeses have 4 sides that are the same length. Therefore, all squares have 4 sides that are the same length.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

5-2=3

Just do it the other way to find the answer!

I hope this helps!

Answer: x = 3

Step-by-step explanation:

we subtract 2 from both sides, in order to get the variable by itself.

x + 2 (- 2) = 5 (- 2)

x = 3

To determine the necessary sample size to obtain an interval width of 50 ppm for a confidence level of 95%, we need to use the formula for sample size calculation for estimating a population mean.

The formula for sample size calculation is:

n = (Z * σ / E)^2

In this case, the desired margin of error is 50 ppm, which means the interval width is 2 * E = 50 ppm. Therefore, E = 25 ppm.

The Z-score corresponding to a 95% confidence level is approximately 1.96.

Given that the investigators made a rough guess of 175 for the value of σ (standard deviation) before collecting data.

We can substitute these values into the sample size formula:

n = (1.96 * 175 / 25)^2

Simplifying the calculation:

n = (7 * 175)^2

n = 1225^2

n ≈ 1,500,625

Therefore, a sample size of approximately 1,500,625 would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%.

To obtain an interval width of 50 ppm with a confidence level of 95%, a sample size of approximately 1,500,625 is required. This is calculated using the formula for sample size estimation, considering a desired margin of error of 25 ppm and a standard deviation estimate of 175. The Z-score corresponding to a 95% confidence level is used to determine the sample size.

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Answer:

15/48

Step-by-step explanation:

The numerator is the number above the line so in this scenario, the numerator is 5 and 3. 5x3=15

The denominator is the bottom number so 6 and 8. When you multiply those you get 48.

15/48.

Answer:

48=16 If that is what you mean

Step-by-step explanation:

1. Multiply

5 over 6  × 3 over 8   = ( 5 × 3 ) over ( 6 × 8 )

5 × 3

6 × 8

 = 15 over 48

Multiply the numerators and denominators.

Reduce fraction to lowest terms

15 over 48

 = ( 15 ÷ 3 ) over ( 48 ÷ 3 )

= 5 over 16

3 is the greatest common divisor of 15 and 48. Reduce by dividing both numerator and denominator by 3.

\(\frac{5}{16} = 0.313\) ← extra

Answer:

6.4

Step-by-step explanation:

To do this you just have to multiply 40 by 2 to get 80 and than divide by 12.5 and you get 6.4