Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate​ planes, using triple integrals.

Answer:

[tex]\sf a) \ 2.5\\b) \ 7.5[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{250}{100}[/tex]

[tex]\sf Express \ as \ a \ decimal.[/tex]

[tex]=2.5[/tex]

[tex]\sf Multiply \ 3\% \ with \ 250.[/tex]

[tex]\displaystyle 250 \times \frac{3}{100}[/tex]

[tex]\displaystyle \frac{750}{100}=7.5[/tex]

Answer:

[tex]P(\overline X < 2.3) = 0.9999[/tex]

Step-by-step explanation:

Given that:

mean = 2

standard deviation = 0.5

sample size = 50

The probability that the sample mean is less than 2.3 hours is :

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{2.3 - 2.0}{\dfrac{0.5}{\sqrt{50}}})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{0.3}{0.07071})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq 4.24268)[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq 4.24)[/tex]

From z tables;

[tex]P(\overline X < 2.3) = 0.9999[/tex]

Answer:

The third answer (C).

Step-by-step explanation:

This graph starts at 10. So it needs the +10 at the end.

Also the slope is -1/2 because the graph goes down one, right two. Rise/run.

Answer:

y= -1/2x+10

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.

For the the given graph, the y-intercept is 10. The slope can be determined by finding the rate of change between any two points on the graph, such as (2,9) and (8,6).

Answer:

Step-by-step explanation:

Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.

Volume of a cone V = πr²h/3

If the diameter and the height are equal, then r = h

V = πh²h/3

V = πh³/3

If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min

Using chain rule to get the expression for dV/dt;

dV/dt = dV/dh * dh/dt

From the formula above, dV/dh = 3πh²/3

dV/dh =  πh²

dV/dt = πh²dh/dt

20 = πh²dh/dt

To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.

20 = π(11)²dh/dt

20 = 121πdh/dt

dh/dt = 20/121π

dh/dt = 20/380.133

dh/dt = 0.0526ft/min

This means that the height of the pile is increasing at  0.0526ft/min

Answer:

acute isosceles triangle

vertex angle, y =  44.0 degrees. (smallest angle)

Step-by-step explanation:

If the sides are in the ratio 4:4:3,

two of the sides have equal lengths, so it is an isosceles triangle.

Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.

To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.

The base angle x is given by the ratio

cos(x) = 1.5/4 = 3/8

Consequently the base angle is  arccos(3/8) = 68.0 degrees.

The vertex angle equals twice the complement of 68.0

vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)

you can imagine this as a venn diagram. the "or" event would consist of everything in both sides and the middle of the venn diagram because you can choose form either event x or event y.

the "and" event would consist of everything in the middle of the venn diagram because you choice must be a part of both event x and event y.

the complement of an event is just everything that is not included in the event. for example, in a coin flip, the complement of heads is tails. in a dice roll, the complement of {1,2} is {3,4,5,6}

so if you come across these just think "either or" or "both and." and remember that the complement is everything excluding what is listed.

i apologize if this does not help, im not that great at explaining things

Answer:

d - 12.50 = 17

add 12.50 to both sides to get d alone.

d = 12.50 + 17

Answer:

It's B d= 17 + 12.50

Step-by-step explanation:

Got it right on edg

Answer:

[tex] -3n - 7 [/tex]

Step-by-step explanation:

Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.

Using the slope-intercept formula, y = mx + b, let's find the equation.

Where,

m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]

[tex] m = \frac{-13 + 10}{1} [/tex]

[tex] m = \frac{-3}{1} [/tex]

[tex] m = -3 [/tex]

Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept

[tex] y = mx + b [/tex]

[tex] -10 = -3(1) + b [/tex]

[tex] -10 = -3 + b [/tex]

Add 3 to both sides:

[tex] -10 + 3 = -3 + b + 3 [/tex]

[tex] -7 = b [/tex]

[tex] b = -7 [/tex]

The equation of the given linear function can be written as:

[tex] y = -3x - 7 [/tex]

Or

[tex] f(x) = -3x - 7 [/tex]

Therefore, if the input is n, the output would be:

[tex] f(n) = -3n - 7 [/tex]

Hi there!! (✿◕‿◕)

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A.) 7.2 x 10^-5 = 0.000000072

B.) 6.3 x 10^-9 = 0.0000000063

C.) 4.54 x 10^-5 = 0.0000454

D.) 7.041 x 10^-10 = 0.0000000007041

Hope this helped!!  ٩(◕‿◕｡)۶

The numbers can be written as;

A.) 7.2 x 10^{-5} = 0.000000072

B.) 6.3 x 10^{-9} = 0.0000000063

C.) 4.54 x 10^{-5} = 0.0000454

D.) 7.041 x 10^{-10} = 0.0000000007041

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given the parameters

We need to Write these as normal numbers

A.) 7.2 x 10^{-5} = 0.000000072

B.) 6.3 x 10^{-9} = 0.0000000063

C.) 4.54 x 10^{-5} = 0.0000454

D.) 7.041 x 10^{-10} = 0.0000000007041

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Answer:  A.   A=(1000-2w)*w      B. 250 feet

C.  125 000 square feet

Step-by-step explanation:

The area of rectangular is A=l*w    (1)

From another hand the length of the fence is 2*w+l=1000        (2)

L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.

Express l from (2):

l=1000-2w

Substitude l in (1) by 1000-2w

A=(1000-2w)*w        (3)   ( Part A. is done !)

Part B.

To find the width w  (Wmax) that corresponds to max of area A   we have to dind the roots of equation (1000-2w)w=0  ( we get it from (3))

w1=0  1000-2*w2=0

w2=500

Wmax= (w1+w2)/2=(0+500)/2=250 feet

The width that maximize area A is Wmax=250 feet

Part C.   Using (3) and the value of Wmax=250 we can write the following:

A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets

Answer:

The mean for all such groups randomly selected is 0.09*800=72.

Step-by-step explanation:

The value of the standard deviation is 7.

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

The standard deviation is calculated by using the formula,

[tex]\sigma = \sqrt{Npq}[/tex]

N = 600

p = 9%= 0.09

q = 1 - p= 1 - 0.09= 0.91

Put the values in the formulas.

[tex]\sigma = \sqrt{Npq}[/tex]

[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]

[tex]\sigma[/tex] = 7

Therefore, the value of the standard deviation is 7.

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Answer:

Option (B)

Step-by-step explanation:

If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.

Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]

a + c = 172°

Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.

Therefore, a = c

⇒ a = c = 86°

Therefore, a = 86°

Option (B) will be the answer.

Answer:

(3) x ≥ -3

(4) 2.5 gallons

(4) -12x + 36

Step-by-step explanation:

Hey there!

1)

Well its a solid dot meaning it will be equal to.

So we can cross out 1 and 2.

And it's going to the right meaning x is greater than or equal to -3.

(3) x ≥ -3

2)

Well if each milk container has 1 quart then there is 10 quarts.

And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.

(4) 2.5 gallons

4)

16 - 4(3x - 5)

16 - 12x + 20

-12x + 36

(4) -12x + 36

Hope this helps :)

Answer:

Option (D)

Step-by-step explanation:

In the picture attached,

An obtuse angle triangle ABC has been given.

By applying Sine rule in the triangle,

[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]

Since, m∠A + m∠B + m∠C = 180°

45° + 110° + m∠C = 180°

m∠C = 180°- 155° = 25°

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]

[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]

b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]

b = 15.56

b ≈ 15.56

[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]

a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]

a = 11.712

a = 11.71

Therefore, Option (D) will be the answer.

Answer:

The hypothesis test is a two-tail test

Step-by-step explanation:

The test hypothesis:

Null hypothesis                  H₀       p = 0,39         or   p  =  p₀

Where p₀ is a nominal proportion (established proportion) and

Alternate hypothesis         Hₐ       p  ≠  0,39        or  p ≠  p₀

Is a two-tail test, (≠) means different, we have to understand that different implies bigger and smaller than something.

For a test to be one tail-test, it is necessary an evaluation only in one sense in relation to the pattern ( in this case the proportion )

When the wavelength of a diffraction grating is decreased,  the distance between lines decreases.

The diffraction grating is used to carry out interference experiments. It consists of a  number of small lines that are constructed to be close to each other and produce an interference pattern.

The outcome of decreasing the wavelength of incident light on a diffraction grating is that the distance between lines decreases.

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Answer:

Step-by-step explanation:

Given that:

If C(x) =  the cost of producing x units of a commodity

Then;

then the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

We are to consider a given function:

[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]

And the objectives are to determine the following:

a) the total cost at a production level of 1000 units.

So;

If C(1000) = the cost of producing 1000 units of a commodity

[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]

[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]

[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]

[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]

[tex]C(1000) = $310491.1064[/tex]

[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]

(b) Find the average cost at a production level of 1000 units.

Recall that :

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

SO;

[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]

Using the law of indices

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]

c(1000) =$ 310.49 per unit

(c) Find the marginal cost at a production level of 1000 units.

The marginal cost  is C'(x)

Differentiating  C(x) = 54,000 + 130x + 4x^{3/2} to get  C'(x) ; we Have:

[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]

[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]

[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 319.7366596[/tex]

[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]

(d)  Find the production level that will minimize the average cost.

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

the production level that will minimize the average cost is c'(x)

differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]

Also

[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]

[tex]x^2 = 27000\sqrt{x}[/tex]

[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]

x= 0;  or  [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900

Since  production cost can never be zero; then the production cost = 900 units

(e) What is the minimum average cost?

the minimum average cost of c(900) is

[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]

c(900) = 60 + 130 + 4(30)

c(900) = 60 +130 + 120

c(900) = $310 per unit

Answer:

a) Central area = 0.95, df = 10 t = (-2.228, 2.228)

(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)

(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)

(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)

(e) Upper-tail area = 0.01, df = 30 t= 2.457

(f) Lower-tail area = 0.025, df = 5 t= -2.571

Step-by-step explanation:

In this question, we are to determine the t critical value that will capture the t-curve area in the cases below;

We can use the t-table for this by using the appropriate confidence interval with the corresponding degree of freedom.

The following are the answers obtained from the table;

a) Central area = 0.95, df = 10 t = (-2.228, 2.228)

(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)

(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)

(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)

(e) Upper-tail area = 0.01, df = 30 t= 2.457

(f) Lower-tail area = 0.025, df = 5 t= -2.571

Answer:  203,280

Step-by-step explanation:

Given: A catering service offers 11 appetizers, 12 main courses, and 8 desserts.

Number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet.

Total number of ways to do this: [tex]^{11}C_9\times ^{12}C_2\times^{8}C_3[/tex]

[tex]=\dfrac{11!}{9!2!}\times\dfrac{12!}{2!10!}\times\dfrac{8!}{3!5!}\\\\=\dfrac{11\times10}{2}\times\dfrac{12\times11}{2}\times\dfrac{8\times7\times6}{3\times2}\\\\= 203280[/tex]

hence , this can be done in 203,280 ways.

Answer:

D. 2

Step-by-step explanation:

The y-intercept is when the graph crosses the y-axis when x = 0. In that case, simply plug in x as 0:

y = -1/2(0) + 2

y = 2

Therefore, the graph crosses the y-axis at 2.

Answer:

D

Step-by-step explanation:

our equation is y= [tex]\frac{-1}{2}[/tex] x +2

so the answer is 2

if we want to verify our answer we can follow these steps

the y-intercept is given by calculating the image of 0

so it's right

Answer:

x = -8 and x= 7

Step-by-step explanation:

recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.

Hence the asymptototes will occur in x-locations where the denominator , i.e

(x+8)(x-7) = 0

solving this, we get

(x+8) = 0 ----> x = -8

or

(x-7) = 0 ------> x = 7

hence the asymptotes occur x = -8 and x= 7

Answer:

x = -8 and x = 7.

Step-by-step explanation:

The vertical asymptotes are lines that the function will never touch.

Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.

[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.

x + 8 = 0

x = -8

x - 7 = 0

x = 7

The vertical asymptotes are at x = -8 and x = 7.

Hope this helps!

Answer:

70

Step-by-step explanation:

You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.

Answer:

[tex]x = -5[/tex]

Step-by-step explanation:

We can simplify this equation down until x is isolated.

[tex]2x - 3 + 3x = -28[/tex]

We can combine the like terms of x.

[tex]5x - 3 = -28[/tex]

Add 3 to both sides.

[tex]5x = -25[/tex]

Now we can divide both sides by 5.

[tex]x = -5[/tex].

So x = -5.

Hope this helped!

Answer:

x=-5

Step-by-step explanation:

first combine like terms

5x-3=-28

add on both sides

5x=-25

divide

x==-5

Answer:

 [tex]x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]

Step-by-step explanation:

According to the given situation, The computation of all x in a set of a real number is shown below:

First we have to determine the [tex]\bar x[/tex] so that [tex]A \bar x = 0[/tex]

[tex]\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right][/tex]

Now the augmented matrix is

[tex]\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right][/tex]

After this, we decrease this to reduce the formation of the row echelon

[tex]R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right][/tex]

[tex]R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]

[tex]R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]

[tex]R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right][/tex]

[tex]R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]

[tex]R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]

[tex]= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0[/tex]

[tex]x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]

By applying the above matrix, we can easily reach an answer

Answer: 0.5

Step-by-step explanation:

If the probability of the time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. Therefore, the probability that a flight is between 125 and 140 minutes is 0.5

Answer:

x=0.2136

Step-by-step explanation:

Answer:

x=0.214 rounded to the thousandths

Step-by-step explanation:

2.35=11x

divide each side by 11 to isolate the x

x=0.214 rounded to the thousandths

Answer:

1

Step-by-step explanation:

[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]

Answer:

3/11

Step-by-step explanation:

There are eleven equal parts.

So the denominator is 11.

He copies 8 parts on Sunday.

11-8=3.

He copied 3 parts on Saturday.

Hope this helps ;) ❤❤❤

Answer:

3x

Step-by-step explanation:

39*x / 13

39/13 * x

3*x

3x

Answer:

3x

Step-by-step explanation:

We are given the expression:

39*x /13

We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.

(39*x /13) / (13/13)

(39x/13) / 1

3x / 1

When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.

3x

The expression 39*x/13 can be simplified to 3x

Answer:

4.87

Step-by-step explanation:

According to the given situation, for calculation of standard deviation for the number of people first we need to calculate the variance which is shown below:-

Variance is

[tex]np(1 - p)\\\\ = 500\times (0.05)\times (1 - 0.05)[/tex]

After solving the above equation we will get

= 23.75

Now the standard deviation is

[tex]= \sqrt{\sigma} \\\\ = \sqrt{23.75}[/tex]

= 4.873397172

or

= 4.87

Therefore for computing the standard variation we simply applied the above formula.