which of the following integrals represents the area of the part of the plane in the first octant? group of answer choices

RA ≅ RB . Option A is correct.

In a triangle if any of the two angles are equal, then the sides opposite to the equal angles are also equal.

Given,

          ∠RAB ≅∠RBA

Also, side opposite to  ∠RAB is side RB

and, side opposite to  ∠RBA is side RA

Hence, side RA and side RB are equal.

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the diameter to allow an elongation of 0. 38 mm therefore required diameter is 7.65 mm

Given the data in the question;

F = 11100 N

l₀ = 310 mm = 0.31 m

E = 207 GPa = 207 × 10⁹ N/m²

Δl = 0.38 mm = 0.0005 m

So, lets assume the deformation is elastic;

d₀ = √(  [4l₀F] / [πEΔl] )

we substitute

d₀ = √(  [4 × 0.38 × 11100] / [π × (207 × 10⁹) × 0.0005]] )

d₀ = √( 10123.2 / 172787595.947 )

d₀ = √( 5.85875 × 10⁻⁵ )

d₀ = 0.007654 m

d₀ = ( 0.007654 × 1000 )mm

d₀ = 7.65 mm

Therefore, required diameter is 7.65 mm

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Answer:3.2

Step-by-step explanation:

Answer:

a₁ = -27

a₂ = -32

a₃ = -37

a₄ = -42

a₅ = -47

a₅₂ = -282

Step-by-step explanation:

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

Given explicit formula:

[tex]a_n=-5n-22[/tex]

To find the first 5 terms, substitute n = 1 through 5 into the given formula:

[tex]\begin{aligned}\implies a_1&=-5(1)-22\\&=-5-22\\&=-27\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_2&=-5(2)-22\\&=-10-22\\&=-32\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_3&=-5(3)-22\\&=-15-22\\&=-37\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_4&=-5(4)-22\\&=-20-22\\&=-42\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_5&=-5(5)-22\\&=-25-22\\&=-47\end{aligned}[/tex]

To find the 52nd term, substitute n = 52 into the given formula:

[tex]\begin{aligned}\implies a_{52}&=-5(52)-22\\&=-260-22\\&=-282\end{aligned}[/tex]

A) The number of pounds that the beverage cans are recycled in an hour is 119772 pounds

B) The number of tons that the beverage cans are recycled in an average day is 2397 ton

C) The number of Kilograms that the beverage cans are recycled in a day is 57528000 kg

The pound is the main unit of sterling, and the term "pound" is frequently used to refer to British currency in general, which is often qualified in foreign contexts as the British pound or the pound sterling.

In 2002 about 34 beverages can weigh one pound.

In one minute 113204 beverage cans are recycled.

In one hour, 60 minutes number of beverage cans recycled=113204×60

=6792240

34 beverage cans weight 1 pound

1 beverage cans weight=1/34 pounds

A) 6792240 beverage can weigh=1

=(1/34)(6792240) pound

=119771.765 pound

≈119772 pound

B) So, In 24 hours, no. of pounds recycled

=119772×24 pound

=119772×24×0.0005 ton

=2397.26 ton

≅2397 ton in one day.

C) So, In 24 hours, no. of tons recycled

=2397×24 ton

=2397×24×1000 kg

=57528000 kg

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Answer:

x = 22/5; m∠TKW=m∠XHK = 15.2°

Step-by-step explanation:

Angles TKW and XHK are corresponding angles (as they lie on the same side of the traversal and on the bottom left side of their respective lines) and are thus congruent and equal.

By setting the two equations equal to each other, we can find the value.

After this, we can plug in x for any one of the equations and find the measure of both angles:

[tex]8x-20=3x+2\\8x=3x+22\\5x=22\\x=\frac{22}{5} \\\\TKW=8(\frac{22}{5})-20\\ TKW=\frac{176}{5}-20\\ TKW=\frac{76}{5}=15.2\\ TKW=XHK[/tex]

If f (a) = b, then the point that is on the graph of f(x) is; (a, b)

The domain of a function is defined as the set of all possible input values that makes the function possible. Meanwhile, the range of a function is the set of all possible output values that makes the function possible.

Now, we are given that f(a) = b.

Usually when denoting the value of the input of a function, we can say for example that f(x) = y which means that at the input value of x, the output of the function is y and as such, (x, y) is a coordinate of the function or graph.

Thus, in our question, we can say that (a, b) is a coordinate of the graph f(a) = b

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The rate the candle burn down is 7 / 4 inches per hour.

The [tex]17\frac{1}{2}[/tex] inches candle burns down in 10 hours.  The rate the candle burn down in inches per hour can be calculated as follows:

In math, a rate is a ratio that compares two different quantities which have different units.

Hence,

rate  = length of the candle / time

length of the candle = 35  /2 inches

time  = 10 hours

rate = 35  / 2 ÷ 10

rate = 35 / 2 × 1  /10

rate = 35 / 20

rate = 7 / 4 inches per hour

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Work Shown:

P(D) = P(D and A) + P(D and B)

P(D) = P(D given A)*P(A) + P(D given B)*P(B)

P(D) = 0.6*0.5 + 0.7*0.5

P(D) = 0.30 + 0.35

P(D) = 0.65

The notation "P(D given A)" means that we follow the upper branch "A", and then go to sub-branch D to determine the 0.6; similar logic is applied for P(D given B).

The probability of getting D is 0.65.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have two events A and B.

So, P(D) = P (AD) + P (BD)

P(D) = P (0.5 x 0.6) + P (0.5 x 0.7)

P(D) = 0.30 + 0.35

P(D) = 0.65

Thus, the probability of getting D is 0.65.

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The blanks are filled as below

Collinear points are those that are situated along a single straight line.

Collinear points are those that are on a line either close to or far from another point, it can be more than two points.

While coplanar points imply lying on the same plane

In the diagram,

E, F, and G are collinear points

D, B, E, F, and G are coplanar points

A, B, and C are another collinear points

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The length of the segment connecting (-4, 3) and (-5,2) is 1.4.

The length of a line segment can be measured by measuring the distance between its two endpoints.

Therefore, the length of the segment connecting (-4, 3) and (-5,2) can be found as follows:

length of the segment = √(2 - 3)² + (-5 + 4)²

length of the segment = √(-1)² + (-1)²

length of the segment = √1 + 1

length of the segment = √2

length of the segment = 1.41421356237

length of the segment = 1.4

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The surface area of the rectangular prism is 18 sq cm greater than the surface area of the cube.

Here, we are given a rectangular prism and a cube as shown in the figure below.

The three sides of the prism are- 2, 3 and 6

Thus, the total surface area of the cube will be-

2 [(2*3) + (3*6) + (6*2)]

= 2[6 + 18 + 12]

= 2*36

= 72 cm square

Now, the side of the cube is 3 cm

Thus, the total surface area of the cube will be-

6( 3*3 )

= 6*9

= 54 cm square

Thus, the difference between the surface area of prism and cube is = 72 - 54

= 18 cm square.

Thus, the surface area of the rectangular prism is 18 sq cm greater than the surface area of the cube.

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Your question was incomplete. Check for the missing figure below.

Answer:

√130

Step-by-step explanation:

                              |

          ?                  |         7

                              |

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

            9

a² + b² = c²

7² + 9² = c²

49 + 81 = c²

130 = c²

√130 = √c²

√130 = c

I hope this helps!

Answer: 2

Step-by-step explanation:

Answer:

your answer is 5.

Step-by-step explanation:

The Height of trees are equal after 4 years and the height is 54 inches.

A linear equation is a equation which draws straight line on the plot

when plotted.

Given,

Height of tree A at the time of planting = 38 inches

Height of tree B at the time of planting = 22 inches

Each year  tree A grow = 4 inches

Each year  tree B grow = 8 inches

Let's make an equation for the height of the trees,

H = 38 +4t

H = 22+8t

Now the time when height of both the trees will equal

38 + 4t = 22 + 8t

4t = 16

t = 4

Hence , After 4 years the height of both the trees will equal and the height of both the trees after 4 years will be 54 inches.

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The correlation coefficient r between an employee's age, x, and annual income, y, given as 0. 923, will vary by 85.2% of its value.

The Pearson correlation coefficient, sometimes referred to as Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply the correlation coefficient, is a statistical indicator of the linear relationship between two sets of data. A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together. With a correlation value of 1, there is a fixed proportional rise in one variable for every positive increase in the other. For instance, shoe sizing increases almost perfectly with foot length.

Here,

The correlation coefficient= 0.923

The percent of variation,

=correlation coefficient²*100

=0.923²*100

=85.192%

=85.2%

When the correlation coefficient r between an employee's age, x, and yearly income, y, is provided as 0. 923, the percent of variance will be 85.2%.

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The measure of the numbered angles are:

m ∠1 = 42°

m ∠2 = 48°

m ∠3 = 132°

m ∠4 = 90°

From the question, we are to determine the measure of each numbered angle.

From the given information,

Line l is parallel to line m and line PQ is perpendicular to line RQ.

Since line PQ is perpendicular to line RQ,

Then, we can write that

48° + m ∠1 = 90°

m ∠1 = 90° - 48°

m ∠1 = 42°

Also,

Since line PQ is perpendicular to line RQ,

m ∠4 = 90°

Since line l is parallel to line m,

m ∠2 = 48° (Alternate interior angles)

m ∠3 + m ∠2 = 180° (Linear pair theorem)

m ∠3 + 48° = 180°

m ∠3 = 180° - 48°

m ∠3 = 132°

Hence, the measure of angle 3 is 132°

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the amount invested at 4% interest rate = P = $1228.57

The amount invested at 5% interest rate = 2P = $2457.14

What is principle interest ?

Every mortgage payment is made up of principal and interest, which are its two main components. The principal, which you borrow for your mortgage, and the interest, which you pay each month to use the loan, are the same thing. You may select the finest mortgage choice for you by being aware of both principle and interest.

We will use the simple interest formula: A=P(1+rt)

where: A=total amount accrued, P=principal, r=rate of investment, t=time (years, here). r and t are given, and we know that the total amount accrued from both accounts minus the invested amounts (principals) will be $175.

A1=P(1+0.04*1) simplified: A1=P(1.04)

A2=2P(1+0.05*1) simplified: A2=2P(1.05)

because the amount invested in the account with interest rate of 5% is twice as much as the amount invested at 4% interest rate.

A1+A2-P-2P=175 because the total income is $175.

Substituting in equations 1 and 2 we get:

P(1.04)+2P(1.05)-P-2P=175

1.04P+2.1P-3P=175

3.14P-3P=172

0.14P=172

P=1228.57

So, the amount invested at 4% interest rate = P = $1228.57

The amount invested at 5% interest rate = 2P = $2457.14

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Standard form of ellipse has equation [tex]\frac{y^2}{a^2} +\frac{x^2}{b^2} =1[/tex] where, a and b are the halves of the length of major and minor axis respectively.

Given that,

Length of major axis(2a)=6.

So

a=6/2

 =3

Length of minor axis(2b)=4.

So

b=4/2

 =2

Putting in equation of standard ellipse. We get

[tex]\frac{y^2}{3^2} +\frac{x^2}{2^2} =1[/tex]

After simplifying

4y² + 9x² = 36

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Based on the features of a proportional graph: A. Yes, it is a proportional relationship because the line intersects with the point of origin (0, 0).

The graph of a proportional relationship is a straight line that must surely pass through the point of origin, (0, 0)

A proportional relationship between two variables x and y can be written in slope-intercept form as y = mx, where the slope or constant of proportionality is represented by the value of m.

The graph above shows a straight line that intersects the point of origin at (0, 0).

Since the line intersects (0, 0), we can conclude that: A. the graph shows a proportional relationship because the line intersects with the point of origin (0, 0).

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The set of ordered pairs which represents a function as required in the task content is; { (-2, 0), (-5, -5), (-1, 3), (2, 0) }.

It follows from the task content that the set of ordered pairs which represents a function is to be identified among the answer choices.

It is noteworthy to know that a function is a special kind of relation in which case each input value is assigned only one output value.

Put simply, no one input value has more than one output value assigned to it.

On this note, the answer choice which correctly represents a function among the answer choices is; { (-2, 0), (-5, -5), (-1, 3), (2, 0) }.

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Answer: Z=80

Step-by-step explanation:

The marked-up price of the desk in the furniture store is $158.92.

The markup is the difference added to the cost of a product or service.

The markup represents the seller's profit on the cost.

The markup differs from the margin, which is the ratio of the seller's profit to the sales price.

The wholesale price of a desk = $137

Markup rate = 16%

Marked-up price = $158.92 ($137 x 1.16)

Thus, the desk is sold at the marked-up price of $158.92.

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Answer:

8.m = ∞

9.[tex]m=\frac{20c-39}{54}[/tex]

Step-by-step explanation:

8.The equation is a vertical line, so the slope is ∞

so the answer for 8. is m = ∞

9.Switch sides:

2.7m + 1.95 = c

Multiply both sides by 100:

2.7m · 100 + 1.95 · 100 = c · 100

Refine:

270m + 195 = c · 100

Move 195 to the right side so it would be: 270m = c · 100 - 195

And now Divide both sides by 270

[tex]\frac{270m}{270}[/tex] = [tex]\frac{c*100}{270}[/tex] - [tex]\frac{195}{270}[/tex]

And now all that's left is to Simplify it

so the answer for answer 9. is [tex]m=\frac{20c-39}{54}[/tex]

Answer:

460000 milligrams converted to pounds would be 1.01 pounds.

Step-by-step explanation:

They both Bihn and Inscoe can do same work in 3(1/13) hours.

How to solve work time problems?

Efficiency = (work)/(time)

Bihn can write one test =  Eight hours

Bihn's one hour work = 1/8

Inscoe can write one test = Five hours

Inscoe's one hour work = 1/5

Bihn and Inscoe 's one hour work =  1/8 + 1/5

= (5 + 8)/40

= 13/40

Both Bihn and Inscoe can do same work in 40/13

= 3(1/13) [13 * 3 + 1]

Hence, they both Bihn and Inscoe can do same work in 3(1/13) hours.

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