Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x+2y+3z=6.

Answer:

A ≈ 346.36

Step-by-step explanation:

To find the answer, you must use the formula, A=πr²

Since only the diameter was provided, you need to divide it by 2 to find the radius. 21 divided by 2 equals 10.5, so that will be your radius.

Another formula that can be used while using only the diameter would be A= 1/4 π d²

Answer:

It is a sequence topic.

The general term of the sequence is 25+3(n-1) where n is the number of the term (here it is the row no.)

So the 20th term is the term with n=20. Substitute n=20 into the above general term, we will get 25+3(20-1) .

Please go on by yourself to work out the answer.

Answer:

336

Step-by-step explanation:

A total of 512 possible words can be made.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a 8 letters word "FGHIJKLM"

Assume that there are [y] possible combinations. Then, the total number of [x] digit words that can be made are -

y = 8ˣ

y = 8ˣ

y = 8 x 8 x 8

y = 512

Therefore, a total of 512 possible words can be made.

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Answer:

(x - 6)^2 + (y + 4)^2 = 4

Step-by-step explanation:

formula for a circle

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

(h,k) is the center

r is the radius

(6,-4) is center

2 is radius

Substitute in numbers and watch the negatives.

Answer:

Option 3 (C)

Step-by-step explanation:

It is the only one that changes the same amount every time ( times 2 )

Answer:

it should be 314.16, so I would choose 314

Answer:

compounded daily as this added up would be the best

Step-by-step explanation:

Answer:

136 mm²

Step-by-step explanation:

[tex]A=a^{2} +2a\sqrt{\frac{a^{2} }{4} } +h^{2}[/tex]

[tex]A=6^{2} +2(6)\sqrt{\frac{6^{2} }{4} } +8^{2}[/tex]

[tex]A=36 +12\sqrt{\frac{36 }{4} } +64[/tex]

[tex]A=36 +12\sqrt{9 } +64[/tex]

[tex]A=36 +12(3)+64[/tex]

[tex]A=36 +36+64[/tex]

A = 136

Answer:

consist of either a single capital letter or a capital letter and a small letter.

Step-by-step explanation:

A chemical reaction can be defined as a reaction in which two or more atoms of a chemical element react to form a chemical compound.

In Chemistry, a chemical element can be defined as any pure substance that is typically made up of only atoms and cannot be broken down into simpler substances through chemical processes. Thus, the atomic number (the number of protons in the nuclei of an atom) of a particular chemical element distinguishes from other chemical elements.

Generally, all chemical elements are denoted or represented by a symbol, which may either be single capital letter or a capital letter and a small letter.

This ultimately implies that, the symbols for elements with accepted names consist of either a single capital letter or a capital letter and a small letter. For example, the symbol for sodium is Na, copper is Cu, carbon is C, oxygen is O, iron is Fe, nitrogen is N, magnesium is Mg, potassium is K, argon is Ag, hydrogen is H, helium is He, phosphorus is P, etc.

Answer:

(40,2700)

Step-by-step explanation:

Given

[tex]D(p)=3500-20p[/tex]

[tex]S(p)=2500+5p[/tex]

Required

The equilibrium point

To do this, we have:

[tex]D(p) = S(p)[/tex]

So, we have:

[tex]2500+5p = 3500-20p[/tex]

Collect like terms

[tex]20p+5p = 3500-2500[/tex]

[tex]25p = 1000[/tex]

Divide both sides by 25

[tex]p = 40[/tex]

Substitute [tex]p = 40[/tex] in [tex]D(p)=3500-20p[/tex]

[tex]D(40) = 3500 - 20 * 40[/tex]

[tex]D(40) = 2700[/tex]

Hence, the coordinates of the equilibrium is: (40,2700)

[tex]\longrightarrow{\green{ D. \:3 {a}^{4} \sqrt{2a} }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \sqrt{18 {a}^{9} } \\ \\ ➝ \: \sqrt{2 \times 3 \times 3 \times {a}^{9} } \\ \\ ➝ \: \sqrt{2 \times ({3})^{2} \times {( {a}^{4}) }^{2} a } \\ \\ [∵( { {a}^{4} )}^{2} a = {a}^{4 \times 2 + 1} = {a}^{9}] \\ \\ ➝ \: 3 \times {a}^{4} \sqrt{2a} \\ \\ ➝ \: 3 {a}^{4} \sqrt{2a} [/tex]

[tex]\pink{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]

Answer:

The answer is [tex]3a^{4}\sqrt{2a}[/tex]

Step-by-step explanation:

To simplify the radical, start by factoring 9 out of 18 for step 1. Next, for step 2, rewrite 9 as [tex]3^{2}[/tex]. Then, factor out [tex]a^{8}[/tex] for step 3. For step 4, rewrite [tex]a^{8}[/tex] as [tex](a^{4})^{2}[/tex]. Then, for step 5, move the 2 in the radical. Rewrite [tex]3^{2}(a^{4})^{2}[/tex]as [tex](3a^{4})^{2}[/tex] for step 6. Then, add parentheses to the radical for step 7. Finally, for step 8 pull the terms out from under the radical, and the answer is [tex]3a^{4}\sqrt{2a}[/tex].  

Step 1: [tex]\sqrt{9(2)a^{9} }[/tex]

Step 2: [tex]\sqrt{3^{2}*2a^{9}[/tex]

Step 3:  [tex]\sqrt{3^{2}*2(a^{8}a) }[/tex]

Step 4: [tex]\sqrt{3^{2}*2((a^{4})^{2}) }[/tex]

Step 5: [tex]\sqrt{3^{2}(a^{4})^{2}*2a }[/tex]

Step 6: [tex]\sqrt{(3a^{4} )^{2}*2a }[/tex]

Step 7:  [tex]\sqrt{(3a^{4})^{2}*(2a) }[/tex]

Step 8: [tex]3a^{4}\sqrt{2a}[/tex]

Answer:

Sylvia=16

brother=8

Step-by-step explanation:

8+7=15

16-1=15

Answer:

x = 93

Step-by-step explanation:

*for angle labels, see picture below

Using angle addition postulate, we can say that angle EAC is the sum of angle CAB and angle BAE:

m<EAC = m<CAB + m<BAE

m<EAC = x + 39

Since line l and m are parallel, you can say that angle ACD is an alternate interior angle to angle EAC. This means they are equal.

Now, we can write an equation to solve for x:

m<EAC = m<ACD

x + 39 = 132

x = 93

Answer:

x=93°

Step-by-step explanation:

If l ıı m

l=180° ; 132°+?(y) =180° (Co-interior angle)

Find the value of y

132°+y=180°(Transpose)

y=180°-132°

y=48°

...

Find x

39°+x+48°=180°(Transpose)

x=180°-48°-39°

x=93°

Answer:

The predicted final exam grade is 83

Step-by-step explanation:

Given

[tex]\bar x = 75[/tex] -- midterm mean

[tex]\sigma_x = 10[/tex] --- midterm standard deviation

[tex]\mu =75[/tex] --- final mean

[tex]\sigma = 10[/tex] --- final standard deviation

[tex]r = 0.8[/tex]

Required

The predicted final grade of student who score 85 in midterm

The prediction is represented as:

[tex]y = \alpha + \beta x[/tex]

Where:

[tex]\beta = r * \frac{\sigma}{\sigma_x}[/tex]

[tex]\beta = 0.8 * \frac{10}{10}[/tex]

[tex]\beta = 0.8 * 1[/tex]

[tex]\beta = 0.8[/tex]

and

[tex]\alpha = \mu - r * \bar x[/tex]

[tex]\alpha = 75- 0.8 * 75[/tex]

[tex]\alpha = 75- 60[/tex]

[tex]\alpha = 15[/tex]

So:

[tex]y = \alpha + \beta x[/tex]

[tex]y = 15 + 0.8x[/tex]

For a student who gets 85, the prediction is:

[tex]y = 15 + 0.8*85[/tex]

[tex]y = 15 + 68[/tex]

[tex]y = 83[/tex]

Answer:

5 is the answer. hhhjjh y fl jj g gshwhwjqjajajw

Answer:

c

Step-by-step explanation:

it's 5

Answer:

0.0918 = 9.18% probability that the battery life is at least 8.1 hours.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 7.5 hours

This means that [tex]\mu = 7.5[/tex]

Standard deviation 27 minutes.

An hour has 60 minutes, which means that [tex]\sigma = \frac{27}{60} = 0.45[/tex]

What is the probability that the battery life is at least 8.1 hours?

This is 1 subtracted by the p-value of Z when X = 8.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8.1 - 7.5}{0.45}[/tex]

[tex]Z = 1.33[/tex]

[tex]Z = 1.33[/tex] has a p-value of 0.9082.

1 - 0.9082 = 0.0918

0.0918 = 9.18% probability that the battery life is at least 8.1 hours.

Answer:

We can write sin x in terms of tan x/2 using the formula:

⇒ sin x = (2 tan (x/2)) / (1 + tan2(x/2))

Therefore, using the above formula, we can find the values of tan x/2 by putting the value of sin x.

⇒ -4/5 = (2 tan (x/2)) / (1 + tan2(x/2))

Now, if we replace tan (x/2) by y, we get a quadratic equation:

⇒ 0.8y2 + 2y + 0.8 = 0

⇒ 2y2 + 5y + 2 = 0

By using the quadratic formula, we get y = -0.5, -2

Hence, the value of tan (x/2) = -0.5, -2

Now, we have two solutions of tan (x/2).

Now, let's check for the ideal solution using the formula tan x = (2 tan (x/2)) / (1 - tan2(x/2)).

For tan (x/2) = -0.5:

⇒ tan x = 2(-0.5) / 1 - (-0.5)2 = -4/3

It is also given that x lies in the third quadrant. We know that tan is positive in the third quadrant, and here we get tan x = -4/3 which is negative.

Hence, we can say that tan (x/2) = -0.5 is not a correct solution. Hence it is rejected.

Now let's check for tan (x/2) = -2.

⇒ tan x = 2(-2) / 1 - (-2)2 = 4/3

Here, we get tan x = 4/3 which is positive.

Hence, we can say that tan (x/2) = -2 is a correct solution.

Answer:

3/4

Step-by-step explanation:

as 1 hour is 60 minutes, to express in fraction form, we have to divide.

so

45/60 can be simplified to 3/ 4 when 15 is taken out as common of both. so the answer is 3/4

Answer:

3/4

Step-by-step explanation:

1 hour= 60 minutes

45/60

simplify the fraction by dividing the numerator and denominator by 5

45÷5=9 and 60÷5=12

new fraction =9/12

simplify 9/12 by dividing the numerator and denominator by 3

9÷3=3 and 12÷3=4

Ans.=3/4

45 minutes is 3/4 of an hour

Answer:

16.2 cm

Step-by-step explanation:

use the pythagoran theorem

a² + b² = c²

15² + 6² = c²

225 + 36 = c²

261 = c²

Take the square root of both sides

16.1554944214 = c

Rounded

16.2 cm

Answer:

40x - 300,000

7,500

Step-by-step explanation:

profit  = revenue - cost

p(x) = 75x - (35x + 300,000)

p(x) = 40x - 300,000

Break even is when profit is zero

40x - 300,000 = 0

40x = 300,000

x = 7,500

The functions that represents the​ total-profit function would be p(x) = 40x - 300,000. so the correct option is A.

Function is a type of relation, or rule, that maps one input to specific single output.

Given that for a certain company ​C(x) =35x+300,000 represents; the total cost​ function, and ​R(x)=75x represents the total revenue function.

WE can calculate the profit by the following formula;

Profit  = revenue - cost

p(x) = 75x - (35x + 300,000)

p(x) = 40x - 300,000

Now Break even is when profit is zero,

40x - 300,000 = 0

40x = 300,000

x = 7,500

Hence, the break-even point is 7500.

Therefore,  the functions that represents the​ total-profit function would be p(x) = 40x - 300,000. so the correct option is A.

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Answer:

Arc QR = 111.5°

Step-by-step explanation:

Given:

Arc QR = (3x + 38)°

Arc PS = (5x - 10)°

m<QMP = 68°

Required:

Measure of arc QR

Solution:

Recall: Angles of intersecting chords theorem states that the angle formed equals half of the sum of the intercepted arcs

This by implication means:

m<1 = ½(arc QR + arc PS)

We are given arc QR, and arc PS.

m<1 = 180° - m<QMP (angles on a straight line)

m<1 = 180° - 68°

m<1 = 112°

Plug in the values into the equation and solve for x

112° = ½(3x + 38 + 5x - 10)

Multiply both sides by 2

2*112 = 3x + 38 + 5x - 10

224 = 3x + 38 + 5x - 10

Add like terms

224 = 8x + 28

224 - 28 = 8x + 28 - 28

196 = 8x

196/8 = 8x/8

24.5 = x

x = 24.5

✅Let's find arc QR

Arc QR = (3x + 38)°

Plug in the value of x

Arc QR = 3(24.5) + 38 = 73.5 + 38

Arc QR = 111.5°

[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The value of [tex]x°[/tex].

[tex]\sf \bf {\boxed {\mathbb {SOLUTION :}}}[/tex]

[tex]\longrightarrow{\blue{ x°\:=\:35° }}[/tex] 

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

We know that,

[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]

➪ [tex]x°[/tex] + 125° + 20° = 180°

➪ [tex]x°[/tex] + 145° = 180°

➪ [tex]x°[/tex] = 180° - 145°

➪ [tex]x°[/tex] = 35°

Therefore, the value of [tex]x°[/tex] is 35°.

Now, the three angles of the triangle are 35°, 125° and 20°.

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY:}}}[/tex]

✒ 35° + 125° + 20° = 180°

✒ 180° = 180°

✒ L. H. S. = R. H. S.

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]

Answer:

-5.55-4.2c

Step-by-step explanation:

-5.55-8.55c+4.35c

-8.55c and 4.35c are like terms so you have to combine them.

-8.55c+4.35c=-4.2c

-5.55 is NOT a like term so it is on its own.

final answer -> -5.55-4.2c

*** don't forget -5.55 is negitive  ***

hope this helped negative:)

Answer:

x = 16

Step-by-step explanation:

4x - 2 = 3x + 14

4x - 2 + 2 = 3x + 14 + 2

4x = 3x + 16

4x - 3x = 3x - 3x + 16

x = 16

Answer:

[tex] \frac{3}{5} [/tex]

Step-by-step explanation:

using SOHCAHTOA

[tex]sin = \frac{opposite}{hypoteneus} [/tex]

Therefore

[tex]sin = \frac{3}{5} [/tex]

The value of sin B is 3/5.

Trigonometry is one of the branches of mathematics which deals with the relationship between the sides of a triangle (right triangle) with its angles. There are 6 trigonometric functions for which the relation between sides and angles are defined.

We have,

P = 3

B = 4

H = 5

Using Trigonometry

sin B = P /H

sin B = 3/5

Thus, the value of sin B is 3/5.

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Answer:

84 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the length of the base and h is the height

A = 1/2 ( 5+9) * 12

A = 1/2 (14) * 12

A =84

Answer:

[tex] = \binom{4}{8} . \binom{6}{ - 3} \\ = (4 \times 6) + (8 \times - 3) \\ 24 + ( - 24) \\ = 0 \\ since \: inner \: product \: is \: zero : \\ the \: vectors \: are \: perpendicular[/tex]

Answer:

0

The vectors are perpendicular

Step-by-step explanation:

(4,8) (6,-3)

The inner product is also known as the dot product

4*6 + 8*-3 = 24-24 = 0

The  vectors are perpendicular since the dot product is zero

Answer:

Step-by-step explanation:

2x+11+6x-7=180 (being linear pair)

8x+4=180

8x=180-4

8x=176

x=176/8

x=22

MHA=2x+11

=2*22+11

=44+11

55

MHT=6x-7

=6*22-7

=132-7

=125

=

Answer:

2X+11+6X-7 =180

8X+4 =180

8X. =180-4

8X. =176

X. =22

MHA=2X+11

=44+11

=55

MHT=6X-7

=132-7

=125