evalute the following integral.
Help me...step by step​

Answer:

55

Step-by-step explanation:

To find the average you add up all numbers given then divide by the amount of numbers there were. The mean, or average, of the original 5 people was 13 since their ages added was 65, which you divide by 5 for 13. The new mean once the 6th person entered the room was 20. So, you do 6 [number of people] times 20 [average] to get 120. Taking 65 [added amount of original ages of the 5 people] away from 120 [the new added up ages of all 6 people], you get 55. This means 55 would be the 6th person's age.

Sorry if the explanation is confusing!

Call the total ages of the 6 people, x

To calculate the mean age of 6 people, we take the total age (x) and divide by the amount of people (6)

So, x : 6 = 20

-> The total ages of the 6 people are 20 x 6 = 120

We can calculate the 6th person's age by taking 120 and minus the total age of the other 5

-> 120 - (13+12+13+15+12) = 55

So, the 6th person's age is 55.

Using the given information, the percent error is 52%

From the question, we are to calculate the percentage error

From the given information,

Prediction = 23 people

Actual = 48 people

Using the formula,

[tex]Percent \ error = \frac{|Prediction - Actual|}{|Actual|}\times 100\%[/tex]

[tex]Percent \ error = \frac{|23 - 48|}{|48|}\times 100\%[/tex]

[tex]Percent \ error = \frac{|-25|}{|48|}\times 100\%[/tex]

[tex]Percent \ error = \frac{25}{48}\times 100\%[/tex]

Percent error = 52.083%

Percent error ≈ 52%

Hence, the percent error is 52%

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Answer:

3

Step-by-step explanation:

Start with the amount that he wants to pay with gigabytes and subtract the amount of his bill without gigabytes.

58.50-46.50=12

 Then divide that amount by the price of each gigabyte to determine how many gigabytes he can use while staying in budget.

12/4=3

Answer: 3

Inequalities help us to compare two unequal expressions. The gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that Elijah pays a flat cost of $46.50 per month and $4 per gigabyte. He wants to keep his bill at $58.50 per month. Therefore, we can write the inequality for this condition as,

$46.50 + $4(x) ≤ $58.50

46.50 + 4x ≤ 58.50

4x ≤ 58.50 - 46.50

4x ≤ 12

x ≤ 12/4

x ≤ 3

Hence, the gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.

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The statement that's true about the triangle is that WXY + YXZ = 180°.

It should be noted that in the question, the options are related to a linear pair.

According to the linear pair, when a line cuts another line at a point, then the sum of the adjacent angles formed at the point will be 180°.

Therefore, WXY + YXZ = 180°.

The correct option is C.

The complete question is:

Which statement regarding the diagram is true?

m∠WXY = m∠YXZ

m∠WXY < m∠YZX

m∠WXY + m∠YXZ = 180°

m∠WXY + m∠XYZ = 180°

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From the straight line AB and CD with point M as midpoint of both lines, AM = BM = 3.2 cm and CM = DM = 2 cm

An equation is an expression that shows the relationship between two or more variables and numbers.

m as the midpoint of both ab and cd, hence:

AM = BM = AB/2 = 6.4/2 = 3.2 cm

CM = DM = CD/2 = 4/2 = 2 cm

From the straight line AB and CD with point M as midpoint of both lines, AM = BM = 3.2 cm and CM = DM = 2 cm

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Answer:

147

Step-by-step explanation:

Angles in a triangle add up to 180:

x + 23 + 10 = 180

x = 147

The equivalent expression to2-1/y/3+1/y is [tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]

Equivalent expressions are expressions does not look the same but when a value is being replaced with their variable, they end up giving the same result.

From the information given:

We have are to determine the equivalent expression to:

[tex]\mathbf{=\dfrac{(2-\dfrac{1}{y})}{(3+ \dfrac{1}{y})}}[/tex]

So if we multiply both the numerator and the denominator with 1/y, we have:

[tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]

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Answer:

The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.

Step-by-step explanation:

Example: What is the HCF of {12,42,14}

Answer: The HCF is 2 as the biggest number they can all be divided by is 2. {12,42,14} = {2^2*3,2*3*7,2*7} The factors in each number is 2.

Answer:

well the value of x is 2 and the value of y is 1##

Step-by-step explanation:

I hope it will help you

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

What is [tex]\bf{\bigg(\dfrac{2}{5}\bigg)^2[/tex]?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

When we have a fraction that is raised to a specific power, we raise both the numerator and the denominator to that power.

[tex]\bf{\dfrac{2^2}{5^2}}=\dfrac{4}{25}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Answer:}[/tex]

                    [tex]\bf{=\dfrac{4}{25}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

Hence the expression [tex]$(y+7)(y+4)=y^{2}+11 y+28$[/tex]

Step-by-step explanation:

- The given expression is (y+7)(y+4).

- We have to multiply the given expression.

- Multiply the (y+7) by 4 , multiply the (y+7) by y then add like terms.

[tex]\begin{array}{r}y+7 \\\underline {\times \quad y+28} \\4 y+28 \\\underline {y^{2}+7 y }\\y^{2}+11 y+28\end{array}[/tex]

An airplane flying at a constant speed of 600 miles per hour, will travel 1350 miles in 135 minutes.

The average speed of any object is the ratio of the total distance the object travels, and the total time taken by the object to cover that distance.

Thus, Average speed = Total Distance/Time taken.

In the question, we are asked the distance traveled by airplane in 135 minutes at the constant speed of 600 miles per hour.

First, we need to convert the time from minutes to hours as our speed is given in miles per hour.

To convert minutes to hours, we divide it by 60.

Thus, the time = 135/60 hours = 2.25 hours.

Now, we substitute the speed = 600 miles per hour, and time = 2.25 hours in the formula:

Average speed = Total Distance/Time taken

or, 600 = Distance/2.25,

or, Distance = 600*2.25 miles,

or, Distance = 1350 miles.

Thus, an airplane flying at a constant speed of 600 miles per hour, will travel 1350 miles in 135 minutes.

The question is incomplete. The complete question is:

"An airplane flies with a constant speed of 600 miles per hour. How far can it travel in 135 minutes".

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Answer:

We know,

Distance,d = speed × time

d = 600 × 2.25

d = 1350km

Hence, the airplane can travel 1350km in 135 minutes with a speed of 600 miles.

Answer: the total area with the extension S≈82,3 foot²,  S>S'.

Step-by-step explanation:

D₁=8 foot    D₂=10 foot    a wide extension = 4 foot.

1) Let the total area with the extension S is the area of the circular table S₁

plus a wide extension S₂.

Considere S₁:

[tex]R_1=\frac{D_1}{2} \\R_1=\frac{8}{2} \\R_1=4 foot.\\S_1=\pi* R_1^2\\S_1=\pi *4^2\\S_1=16*\pi \\S_1\approx50,3\ foot^2.\\[/tex]

[tex]S_2=8*4\\S_2=32 \ foot^2.[/tex]

[tex]S\approx50,3+32\\S\approx82,3 \ foot^2.[/tex]

2)\ Considere S':

[tex]R_2=\frac{D_2}{2} \\R_2=\frac{10}{2} \\R_2=5 \ foot.\\S'=\pi *R^2\\S'=\pi *5^2\\S'=25*\pi \\S'\approx78,5\ foot^2.[/tex]

S>S'.

Good luck an' have a nice day!

Answer:

  a) 2.5

  b) 6.25

Step-by-step explanation:

For similar figures, the ratio of any corresponding linear dimensions is the same. The ratio of areas is the square of that.

The ratio of linear dimensions, larger to smaller, is ...

  (30 yd)/(12 yd) = 2.5

Perimeter is a linear dimension, the sum of side lengths. The ratio of perimeters is 2.5.

The ratio of areas, larger to smaller, is the square of the scale factor for side lengths:

  (2.5)² = 6.25

The ratio of the areas of the larger to smaller figure is 6.25.

The expected number of pairs of adjacent cards which are both black is  650 / 51

For each pair of cards, the probability that they are both black is 26/52 * 25/ 51 = 25 / 102,

So since there are 52 pairs in the circle, the expected number of pairs which are both black is

25 / 102 * 52 = 650 / 51

Probability is genuinely how probable something is to happen. Every time we're unsure about the final results of an occasion, we can speak approximately the chances of sure results—how probably they're.

The evaluation of occasions governed by chance is referred to as statistics.

A sequence of movements where the outcomes are constantly unsure. The tossing of a coin, deciding on a card from a deck of playing cards, throwing a cube. It's far a single final results of an experiment. Getting a Heads even as tossing a coin is an event.

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The value of x will be equal to 33.94 units.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Given that:-

Given that the radius of the circle is 12 units which are PO = 12 and OR = 12, QR = x , ∠O = 60 So ∠Q = 30.

First, we will calculate the Length OQ by angle property in triangle OQR.

[tex]Sin 30=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin 30 = \dfrac{12}{OQ-12}[/tex]

[tex]\dfrac{1}{2}=\dfrac{12}{OQ-12}[/tex]

OQ - 12 = 24

OQ = 36

Now applying the Pythagorean theorem in the triangle OQR.

H² = P² + B²

36² = 12² + x²

x² = 1296 - 144

x = √1152

x = 33.94

Therefore the value of  x will be equal to 33.94 units.

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Answer:

area = 78

Step-by-step explanation:

Area of triangle = 1/2  x  base  x  perpendicular height

                            ⇒ 1/2  x  13  x  12

                            ⇒ 78 units²

Answer:

39

Step-by-step explanation:

37 = 96 %

x  = 100%

[tex]x =\frac{37(100)}{96} =38.54= 39[/tex]

[tex]\huge\boxed{39\ \text{students}}[/tex]

Note: The numbers in this problem are a little weird and don't work out perfectly. I'll demonstrate at the end of this answer how something seems a little off in the problem, but we'll get as close as possible.

We know from the problem that 37 students are equal to 96% of the class.

Let's write this as an equation:

[tex]37=0.96x[/tex]

Divide both sides of the equation by [tex]0.96[/tex] to isolate [tex]x[/tex].

[tex]38.54\approx x[/tex]

We'll round this to [tex]39[/tex] as the final answer.

It's important to note that you can't have partial students, only whole numbers.

If we do the math here, 37 out of 39 students is about 95%.
Also, 37 out of 38 is about 97%.

I'm not sure how the original writer of the question got 96%, but I suppose 39 is the best answer with what's been given.

Answer:

(x - 4)^2 + (y + 1)^2=9

Step-by-step explanation:

The equation of a circle can be written using a kinda of fill-in-the-blank method if you know the coordinates of the center and the radius.

If the center is (h,k) and the radius is r, then fill in those given numbers into:

(x-h)^2 + (y-k)^2 =r^2

The center of your circle is (4, -1).

Fill in 4 for the h, -1 for the k and 3 for the r.

(x-4)^2+(y- -1)^2= 3^2

Simplify.

(x-4)^2+(y+1)^2=9

Answer:

===========

Let the number of apples in each bag is x, then the number of bags is 20/x.

Since the number of apples in each bag is greater than one and number of bags is greater than one, we have the following conditions:

The factors of 20 between 1 and 20 are:

The possibilities are:

Answer:

5/6

Step-by-step explanation:

The numbers on a six-sided die are as shown:

1, 2, 3, 4, 5, 6

The even numbers are:

2, 4, 6

The numbers greater than 3 are:

3, 4, 5, 6

Both lists together are:

2, 3, 4, 5, 6

Because 5 out of 6 numbers satisfy these conditions, the probability of satisfying these conditions is 5/6.

Answer:

cos=24/25

tan=7/24

Step-by-step explanation:

sin=opposite/hypotenuse

therefore 7 is the opposite and 25 is the hypotenuse.

using pythagorean theorem we can find the adjacent. i.e hypotenuse squared= sum of adjacent squared and opposite squared.

h^2= a^2+ O^2

25 squared - 7 squared= 576

which is equal to 24 squared.

therefore adjacent=24

cos=adjacent/hypotenuse

cos=24/25

tan=opposite/adjacent

tan=7/24.

Answer:

[tex]\cos(\theta)= \dfrac{24}{25}[/tex]

[tex]\tan(\theta)=\dfrac{7}{24}[/tex]

Step-by-step explanation:

Definitions of primary trig functions

For a given acute angle in a right triangle :

...where the hypotenuse is the side across from the right angle, the opposite side is the side not touching the angle theta, and the adjacent side is the side touching the angle theta (but that isn't the hypotenuse).

We are already given the ratio for the Sine function, so we need to find the Cosine and Tangent function ratios.  It will be helpful to visualize what this triangle looks like.

The given equation states [tex]\sin(\theta)=\frac{7}{25}[/tex], so there is some right triangle, with a specific angle theta, that has a ratio of sides (opposite to hypotenuse) of 7 to 25.  For ease, we'll consider the triangle that has actual side lengths of 7 and 25 for those sides.  (See attached diagram)

Given that information, we can identify that the unknown side length is the adjacent side length.  Since the triangle is a right triangle, this value can be found through the Pythagorean Theorem.

The Pythagorean Theorem states that for any right triangle, [tex]a^2+b^2=c^2[/tex] where "c" is the length of the hypotenuse of the triangle, and "a" and "b" are the lengths of the other two sides of the triangle (often called "legs").  It does not matter which leg is chosen to be side "a" or side "b" due to the commutative property of addition, but "c" must be the hypotenuse.

[tex]a^2+b^2=c^2[/tex]

Substituting known values, and simplifying...

[tex]a^2+(7)^2=(25)^2[/tex]

[tex]a^2+49=625[/tex]

Subtracting 49 from both sides to begin to isolate "a", and simplifying...

[tex](a^2+49)-49=(625)-49[/tex]

[tex]a^2=576[/tex]

Applying the square root property to isolate "a", and simplifying/calculating...

[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]

[tex]a=\pm 24[/tex]

[tex]a=24[/tex]  or  [tex]a=-24[/tex]

Under the assumption that the triangle is an acute triangle, the adjacent side length is a positive value, so we reject the negative solution, deducing that the adjacent side length must be 24.

Side note:  If there is more information in the context of the question that suggests that theta may be larger than 90°, then other factors will need to be taken into account.

Returning to the trig ratio definitions, we can identify the requested cosine and tangent ratios

[tex]\cos(\theta)=\dfrac{\bold{adjacent} \text{ side length}} {\bold{hypotenuse} \text{ length}} = \dfrac{24}{25}[/tex]

[tex]\tan(\theta)=\dfrac{\bold{opposite} \text{ side length}} {\bold{adjacent} \text{ side length}}=\dfrac{7}{24}[/tex]

The correct answer is option A which is ZA = 3 cm

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The triangle is shown below.

From the triangle, A is the concurrency point of angle bisectors of all vertices.

Consider ΔAYD,

Using the Pythagorean theorem,

AD² = AY² + YD²

5² = AY² + 4²

25 = AY² + 16

AY² = 25 - 16

AY² = 9

AY = √9 = 3 cm

Consider triangles ADY and ADZ.

∠AYD ≅∠AZD=90

∠ADY≅∠ADZ ( Angle bisector)

AD ≡ AD (common side)

The two triangles are congruent by the AAS postulate.

Therefore, by CPCTE, AY=ZA=3 cm

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Answer: 3cm

Step-by-step explanation: Trust Me! Answer is correct on Edge quiz!

Good Luck! :)

ZA= 3cm

Answer:

It's either 16 or -16

Step-by-step explanation:

Subtract 41 and 57 and you get one of those two.

My bet is 16 due to you not being able to have a negative amount of bills in your wallet in real life.

Answer:

ok so we can just add 20 + 45 then divide by 2

20+45=65/2=32.5

32.5

Hope This Helps!!!

Answer: 5

Step-by-step explanation:

By the inscribed angle theorem.

[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]

The conditional probability illustrates that's there's a 2/8 that the event A occurs.

It should be noted that probability simply means the likelihood of the occurence of an event.

In this case, it can be delivered that P(AID) and P(DIA) aren't equal.

Hence, P(D|A) has event A as its given event, resulting in 2/8 for a probability.

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Answer:

[tex](-\infty, -1)\ \cup\ (0, 2)[/tex]

Step-by-step explanation:

So if you expand out the two binomials (k-2)(k+1), you'll get: [tex]k^2+k-2k-2[/tex]. which simplifies to: [tex]k^2-k-2[/tex]. Multiplying this by the k gives you: [tex]k^3-k^2-2k[/tex]. As you can see the degree is odd, this means that this polynomial will have two opposite end behaviors. And as you can see the leading coefficient is positive, meaning that this function will go towards positive infinity as k goes towards positive infinity. Also we if look at the original equation given, it's in factored form, with the zeroes as k=0, k=2, and k=-1. So given this we can draw a simple graph to see when the value of the equation is negative. If you look at the graph I drew you'll see that it's negative from (-infinity, -1) and then negative from (0, 2)

Answer: This really depends on how long you have to reach this goal.

Let’s say you want to make this amount in one month.

There is about 4 weeks in a month so you’ll need to divide 2112.24 by 4.

That would be 528.06 per week.

To find an amount per day you’ll need to divide 528.06 by 7.

That would be about 75.5 per day.

Please let me know if this doesn’t help.