Combine like terms to create an equivalent expression. 1/7 - 3 (3/7n - 2/7)

Answer:

a) dV(s)  =  15,386 cm³

b) dS(s) = 4,396 cm²

c) dV(s)/V(s) = 1,07 %    and   dS(s)/ S(s)  =  0,71 %

Step-by-step explanation:

a) The volume of the sphere is

V(s) = (4/3)*π*x³        where x is the radius

Taking derivatives on both sides of the equation we get:

dV(s)/ dr  =  4*π*x²    or

dV(s)  =  4*π*x² *dr

the possible propagated error in cm³ in computing the volume of the sphere is:

dV(s)  = 4*3,14*(7)²*(0,025)

dV(s)  =  15,386 cm³

b) Surface area of the sphere is:

V(s) = (4/3)*π*x³  

dV(s) /dx  =  S(s) = 4*π*x³

And

dS(s) /dx  = 8*π*x

dS(s) = 8*π*x*dx

dS(s) = 8*3,14*7*(0,025)

dS(s) = 4,396 cm²

c) The approximates errors in a and b are:

V(s) =  (4/3)*π*x³     then

V(s) = (4/3)*3,14*(7)³

V(s) = 1436,03 cm³

And  the possible propagated error in volume is from a)  is

dV(s)  =  15,386 cm³

dV(s)/V(s)  = [15,386 cm³/1436,03 cm³]* 100

dV(s)/V(s) = 1,07 %

And for case b)

dS(s) = 4,396 cm²

And the surface area of the sphere is:

S(s) =  4*π*x³        ⇒   S(s) =  4*3,14*(7)²    ⇒ S(s) = 615,44 cm²

dS(s) = 4,396 cm²

dS(s)/ S(s)  =  [ 4,396 cm²/615,44 cm² ] * 100

dS(s)/ S(s)  =  0,71

Answer: 0%

Step-by-step explanation:

There's 40 students, and 40 students read physics. That means that every student reads physics. So, no student could read only chemistry.

Answer: Yes they form a proportion. The given equation is a true equation.

==========================================

Explanation:

The idea is that if we have

a/b = c/d

then that it is the same as

a*d = b*c

This is known as cross multiplication. We'll use this rule to get

15/12 = 4.5/3.6

15*3.6 = 12*4.5

54 = 54

We got the same value on both sides, meaning that the last equation is true. Consequently, it means the first equation is true as well (all three equations are true).

--------

You could also use your calculator to see that

15/12 = 1.25

4.5/3.6 = 1.25

showing that 15/12 = 4.5/3.6 is a true equation and the ratios form a proportion.

Answer:

15/12=4.5/3.6 = True

Step-by-step explanation:

Simplify the following:  Left-hand

15/12

Hint: | Reduce 15/12 to lowest terms. Start by finding the GCD of 15 and 12.

The gcd of 15 and 12 is 3, so 15/12 = (3×5)/(3×4) = 3/3×5/4 = 5/4:

Answer: 5/4

______________________________

Approximate the following:

4.5/3.6

Hint: | Express 4.5/3.6 in decimal form.

4.5/3.6 = 1.25:

Answer:  1.25 = 5/4

Answer:

0.05m^2

Step-by-step explanation:

5 divided by 100

Answer:

Explained below.

Step-by-step explanation:

(a)

The first and third quartiles of bowling scores are as follows:

Q₁ = 125 and Q₃ = 156

Then the inter quartile range will be:

IQR = Q₁ - Q₃

      = 156 - 125

      = 31

Any value lying outside the range (Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) are considered as unusual.

The range is:

(Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) = (125 - 1.5×31, 156 + 1.5×31)

                                               = (78.5, 202.5)

The bowling score of 200 lies in this range.

Thus, the bowling score of 200 is usual.

(b)

Compute the probability that the mean bowling score will be smaller than 150 as follows:

[tex]P(\bar X<150)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{150-155}{16/\sqrt{40}})[/tex]

                  [tex]=P(Z<-1.98)\\=1-P(Z<1.98)\\=1-0.97615\\=0.02385\\\approx 0.024[/tex]

Thus, the probability that in a sample of 40 bowling scores, the mean will be smaller than 150 is 0.024.

(c)

It is provided that, the lower the golf score the better.  

So, the best 5% of scores would be the bottom 5%.

That is, P (X > x) = 0.05.

⇒ P (Z > z) = 0.05

⇒ P (Z < z) = 0.95

⇒ z = 1.645

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\1.645=\frac{x-77}{3}\\\\x=77+(3\times 1.645)\\\\x=81.935\\\\x\approx 82[/tex]

Thus, the score is 82.

(d)

A z-scores outside the range (-2, +2) are considered as mild outlier and the z-scores outside the range (-3, +3) are considered as extreme outlier.

Compute the z-score for the golf score of 70 as follows:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

  [tex]=\farc{70-77}{3}\\\\=\frac{-7}{3}\\\\=-2.33[/tex]

As the z-score for the golf score of 70 is less than -2, it is considered as a mild outlier.

Answer:

B. FALSE

Step-by-step explanation:

Surface area of cone = πr(r + l)

Where,

r = r

l = 3r

S.A of cone = πr(r + 3r)

= πr² + 3πr²

S.A of cone = 4πr²

Surface area of cylinder = 2πrh + 2πr² = 2πr(h + r)

Where,

r = r

h = 2r

S.A of cylinder = 2πr(2r + r)

= 4πr² + 2πr²

S.A of cylinder = 6πr²

The surface are of the cone and that of the cylinder are not the same. The answer is false.

Answer:false

Step-by-step explanation:

False

Answer:

12/27

Step-by-step explanation:

Count all letters and all vowels then divide vowels by letters

The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.

The probability of any event suppose A, in an experiment is given as:

P(A) = n/S,

where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.

In the question, we are given an experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden".

We are asked to find the probability that the selected letter is a vowel.

Let the event of selecting a vowel from the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden" be A.

We can calculate the probability of event A by the formula:

P(A) = n/S,

where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.

The number of outcomes favorable to event A (n) = 12 (Number of vowels in the phrase)

The total number of outcomes in the experiment (S) = 27 (Number of letters in the phrase).

Now, we can find the probability of event A as:

P(A) = 12/27 = 4/9

∴ The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.

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(a) Let [tex]A(t)[/tex] denote the amount of sugar in the tank at time [tex]t[/tex]. The tank starts with only pure water, so [tex]\boxed{A(0)=0}[/tex].

(b) Sugar flows in at a rate of

(0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min

and flows out at a rate of

(A(t)/1080 kg/L) * (7 L/min) = 7A(t)/1080 kg/min

so that the net rate of change of [tex]A(t)[/tex] is governed by the ODE,

[tex]\dfrac{\mathrm dA(t)}[\mathrm dt}=\dfrac{49}{100}-\dfrac{7A(t)}{1080}[/tex]

or

[tex]A'(t)+\dfrac7{1080}A(t)=\dfrac{49}{100}[/tex]

Multiply both sides by the integrating factor [tex]e^{7t/1080}[/tex] to condense the left side into the derivative of a product:

[tex]e^{\frac{7t}{1080}}A'(t)+\dfrac7{1080}e^{\frac{7t}{1080}}A(t)=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]

[tex]\left(e^{\frac{7t}{1080}}A(t)\right)'=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]

Integrate both sides:

[tex]e^{\frac{7t}{1080}}A(t)=\displaystyle\frac{49}{100}\int e^{\frac{7t}{1080}}\,\mathrm dt[/tex]

[tex]e^{\frac{7t}{1080}}A(t)=\dfrac{378}5e^{\frac{7t}{1080}}+C[/tex]

Solve for [tex]A(t)[/tex]:

[tex]A(t)=\dfrac{378}5+Ce^{-\frac{7t}{1080}}[/tex]

Given that [tex]A(0)=0[/tex], we find

[tex]0=\dfrac{378}5+C\implies C=-\dfrac{378}5[/tex]

so that the amount of sugar at any time [tex]t[/tex] is

[tex]\boxed{A(t)=\dfrac{378}5\left(1-e^{-\frac{7t}{1080}}\right)}[/tex]

(c) As [tex]t\to\infty[/tex], the exponential term converges to 0 and we're left with

[tex]\displaystyle\lim_{t\to\infty}A(t)=\frac{378}5[/tex]

or 75.6 kg of sugar.

Answer:

A. No conclusion can be drawn regarding the means because the box plots only show medians and quartiles.

Step-by-step explanation:

A box display tells represents a five-number summary that consists of the minimum value, lower quartile, median, upper quartile and maximum value. It could also tell you which data point is an outlier, if there are any.

Mean value for a data set that can hardly be ascertained or derived from a box plot display itself.

Therefore, the statements regarding the means of both data sets that is most likely true is: "A. No conclusion can be drawn regarding the means because the box plots only show medians and quartiles."

Answer:

Step-by-step explanation:

perimeter of triangle=sum of lengths of sides=5x-7+3x-4+2x-6=10x-17

Answer:

10x - 17

Step-by-step explanation:

To find the perimeter of a triangle, add up all three sides

( 5x-7) + ( 3x-4) + ( 2x-6)

Combine like terms

10x - 17

Answer:

-36

Step-by-step explanation:

3*12=36

she is going down (negative) so, it is -36

not sure if this is what you are asking for, if not try this

0-12-12-12=-36

Hi there! :)

Answer:

[tex]\huge\boxed{2(14x - 41y)}[/tex]

(75x - 67y) - (47x + 15y)

Distribute the '-' sign with the terms inside of the parenthesis:

75x - 67y - (47x - (15y))

75x - 67y - 47x - 15y

Combine like terms:

28x - 82y

Distribute out the greatest common factor:

2(14x - 41y)

Answer:

x= -3     x = 1/2     x=-2

Step-by-step explanation:

f(x)=(x+3) (2x-1)(x+2)

Set equal to zero

0 =(x+3) (2x-1)(x+2)

Using the zero product property

x+3 =0   2x-1 =0    x+2 =0

x= -3    2x =1       x = -2

x= -3     x = 1/2     x=-2

Answer:

6

Step-by-step explanation:

18 : 9 · 3 = 2 · 3 = 6

Answer:

X= 15

Step-by-step explanation:

the above equation will be used to determine the value of x.

the above equation will be used to determine the value of x.

6x-12= 2x+20+18

6x-2x = 20+12+18

4x= 60.

X= 60/4

X= 15

x = 15

Answer:

2.7 in²

Step-by-step explanation:

Since ∆BAC and ∆EDF are similar, therefore, the ratio of their area = square of the ratio of their corresponding side lengths.

Thus, if area of ∆EDF = x, area of ∆BAC = 6 in², EF = 2 in, BC = 3 in, therefore:

[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]

[tex] \frac{6}{x} = (1.5)^2 [/tex]

[tex] \frac{6}{x} = 2.25 [/tex]

[tex] \frac{6}{x}*x = 2.25*x [/tex]

[tex] 6 = 2.25x [/tex]

[tex] \frac{6}{2.25} = \frac{2.25x}{2.25} [/tex]

[tex] 2.67 = x [/tex]

[tex] x = 2.7 in^2 [/tex] (nearest tenth)

Answer:

5.215 units (rounded up to three decimal places)

Step-by-step explanation:

To find the distance between points (3.1 , 0.3) and (2.7, -4.9)

We use the Pythagoras Theorem which states that for a right triangle of sides a,b and c then;

a² + b²  = c² ,  Where c is the hypotenuse.

In our case, the distance between the two points is the hypotenuse of triangle formed by change in y-axis and change in x-axis.

The distance (hypotenuse) squared = (-4.9 - 0.3)² + (2.7 - 3.1)² = 27.04 + 0.16 = 27.2

Hypotenuse (the distance between) = [tex]\sqrt{27.2}[/tex] = 5.215 units (rounded up to three decimal places)

Answer:

[tex]51\frac{4}{17}[/tex]

Step-by-step explanation:

If we add all of the fractions together, we 'd get 55/17 of an hour. The question is to find how many hours she spent exercising. Well, for that we'd just need to see how many seventeens fit inside 55. We could divide, but that'd lead us to a really long, weird number.

Since 17*3=51, we know that in total, three seventeens fit inside 55. Yet, there's still remainders.

55-51=4

So, our answer would be 51 (how many 17s go into 55) and 4/17 (the remainder.)

Hope this helps!! <3 :)

The equation is represented 3 units to the left of the complex plane and 2 units up.

A complex equation is an equation that involves complex numbers when solving it. A complex number is a number that has both a real part and an imaginary part.

Well to see how this is represented, we first need to multiply it out so we can see how it looks when it is simplified!

[tex]=(3-2i)(i^2)\\\\\\i^2=-1\\\\\\=(3-2i)(-1)\\\\\\=(-3+2i)[/tex]

We know that on a complex plane, our imaginary numbers are represented on the vertical axis.

So the original expression, (3-2i) would have been 3 units to the right on a complex graph and 2 units downward!

The equation I input above should be pretty straightforward, but one thing I didn't mention was that i^2 should = -1 when dealing with complex numbers!

Therefore, the equation 3-2i * i^2 is equal to -3 + 2i, this is graphed 3 units to the left and to units upward!

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Answer:

Step-by-step explanation:

60°=2×30°

one angle is double the angle of the same right angled triangle.

so hypotenuse is double the smallest side.

Hypotenuse=10

smallest side=10/2=5

third side =√(10²-5²)=5√(2²-1)=5√3

Answer:

-3

Step-by-step explanation:

[tex]8+3y = -1\\3y = -9\\y = -3[/tex]

Answer:

y = -3

Step-by-step explanation:

-1=3y+8

3y+8=-1

3y=-9

y=-3

Answer:

Total hours that Jenny ran = 3.63 hours.

Step-by-step explanation:

Jenny ran on Tuesday for = 2/5 hours or 0.4 hours.

Time consumed to run on Thursday = 11/6 hours or 1.83 hours.

Time consumed to run on Saturday = 21/ 15 hours or 1.4 hours.

Here, the total hours can be calculated by just adding all the running hours. So the running hours of Tuesday, Thursday, and Saturday will be added to find the total hours.

Total hours that Jenny ran = 0.4 + 1.83 + 1.4 = 3.63 hours.

Answer:

The two lines do not intersect, and are parallel to one another on a graph.

Step-by-step explanation:

A system of equations consists of two or more equations with two or more variables. The solution to these variables must satisfy all of the variables in the equations in the system at the same time. Usually, all the equations in the system are considered and solved simultaneously. A linear equation might have a unique solution, an infinite solution, or no solution at all.

A system with exactly one solution is called a consistent system, and it is said to be independent, and the graph of its lines intersects at the point that is the solution to the equations. A system with an infinite number of solution is said to be dependent and the lines are coincident on a graph.

If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, and the lines are parallel to one another on the graph.

For two lines of linear equations to have no solution, they must be parallel to each other i.e they must have the same slope.

The standard form of writing linear equation is expressed as y = mx + b

m is the slope of the line

b is the y-intercept

For two lines of linear equations to have no solution, they must be parallel to each other i.e they must have the same slope.

For instance, the system of equations y = 2x + 7 and y = 2x - 3 have no solutions because they have the same slope.

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Answer:

[tex]Mean = 53.25[/tex]

Step-by-step explanation:

Given

Low Temperature : 40−44 || 45−49 ||  50−54 || 55−59 || 60−64

Frequency: --------------- 3 -----------6----------- 1-----------3--- -----7

Required

Determine the mean

The first step is to determine the midpoints of the given temperatures

40 - 44:

[tex]Midpoint = \frac{40+44}{2}[/tex]

[tex]Midpoint = \frac{84}{2}[/tex]

[tex]Midpoint = 42[/tex]

45 - 49

[tex]Midpoint = \frac{45+49}{2}[/tex]

[tex]Midpoint = \frac{94}{2}[/tex]

[tex]Midpoint = 47[/tex]

50 - 54:

[tex]Midpoint = \frac{50+54}{2}[/tex]

[tex]Midpoint = \frac{104}{2}[/tex]

[tex]Midpoint = 52[/tex]

55- 59

[tex]Midpoint = \frac{55+59}{2}[/tex]

[tex]Midpoint = \frac{114}{2}[/tex]

[tex]Midpoint = 57[/tex]

60 - 64:

[tex]Midpoint = \frac{60+64}{2}[/tex]

[tex]Midpoint = \frac{124}{2}[/tex]

[tex]Midpoint = 62[/tex]

So, the new frequency table is as thus:

Low Temperature : 42 || 47 ||  52 || 57 || 62

Frequency: ----------- 3 --||- -6-||- 1-||- --3- ||--7

Next, is to calculate mean by

[tex]Mean = \frac{\sum fx}{\sum x}[/tex]

[tex]Mean = \frac{42 * 3 + 47 * 6 + 52 * 1 + 57 * 3 + 62 * 7}{3+6+1+3+7}[/tex]

[tex]Mean = \frac{1065}{20}[/tex]

[tex]Mean = 53.25[/tex]

The computed mean is greater than the actual mean

Answer: 3.2 feet.

Step-by-step explanation:

Given: The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation[tex]f(x) = -0.3x^2 + 2x[/tex], where [tex]f(x)[/tex] is the height of the path of the water above the ground, in feet, and [tex]x[/tex] is the horizontal distance of the path of the water from the end of the hose, in feet.

At x= 4 , we get

[tex]f(x) = -0.3(4)^2 + 2(4)=-0.3(16)+8 =-4.8+8=3.2[/tex]

Hence, when the water was 4 feet from the end of the hose,  its height above the ground is 3.2 feet.

Answer:

3.2 feet.

Step-by-step explanation:

[tex]\dfrac{x}{5}=-2\\\\x=-10[/tex]

Answer:

[tex]\huge \boxed{{x=-10}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{5} =-2[/tex]

We need the x variable to be isolated on one side of the equation, so we can find the value of x.

Multiply both sides of the equation by 5.

[tex]\displaystyle \frac{x}{5}(5) =-2(5)[/tex]

Simplify the equation.

[tex]x=-10[/tex]

The value of x that makes the equation true is -10.

Answer:

7200ft/per Hour divide it by mile ( 5280) makes 1.363 so maybe 1.4 Miles

Step-by-step explanation:

Work Shown:

1 mile = 5280 feet

1 hour = 3600 seconds (since 60*60 = 3600)

[tex]2 \text{ ft per sec} = \frac{2 \text{ ft}}{1 \text{ sec}}\\\\2 \text{ ft per sec} = \frac{2 \text{ ft}}{1 \text{ sec}}*\frac{1 \text{ mi}}{5280 \text{ ft}}*\frac{3600 \text{ sec}}{1 \text{ hr}}\\\\2 \text{ ft per sec} = \frac{2*1*3600}{1*5280*1} \text{ mph}\\\\2 \text{ ft per sec} = \frac{7200}{5280} \text{ mph}\\\\2 \text{ ft per sec} \approx 1.363636 \text{ mph}\\\\[/tex]

The result is approximate and the "36" portion repeats forever.

Answer:

Step-by-step explanation:

Hello, please consider the following.

m and n are the two numbers.

m + n = 24, right?

n = 2 m

We replace n in the first equation, it comes

m + 2m =24

3m = 24 = 3*8

So, m = 8 and n = 16

Thank you

The first number is 8 and second number is 16.

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Given that the sum of two numbers is twenty-four

The second number is equal to twice the first number

Let x and y are the two numbers.

According to the question,

m + n = 24,

n = 2m

Substitute the value of n in the first equation,

m + 2m =24

3m = 24

m = 24/3

m = 8

Substitute the value of m in the n = 2m

So, n = 2(8)

n = 16

Hence, the first number is 8 and second number is 16.

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Answer:

b

Step-by-step explanation:

Answer:

[tex]Slanted\ Roof = 20.77\ ft[/tex]

Step-by-step explanation:

The question has missing attachment (See attachment 1 for complete figure)

Given

Width, W = 20ft

Let the taller height be represented with H and the shorter height with h

H = 10ft

h = 8ft

Overhang = 8 inch

Required

Determine the length of the slanted roof

FIrst, we have to determine the distance between the tip of the roof and the shorter height;

Represent this with

This is calculated by

[tex]D = H - h[/tex]

Substitute 10 for H and 8 for h

[tex]D = 10 - 8[/tex]

[tex]D = 2ft[/tex]

Next, is to calculate the length of the slant height before the overhang;

See Attachment 2

Distance L can be calculated using Pythagoras theorem

[tex]L^2 = 2^2 + 20^2[/tex]

[tex]L^2 = 4 + 400[/tex]

[tex]L^2 = 404[/tex]

Take Square root of both sides

[tex]\sqrt{L^2} = \sqrt{404}[/tex]

[tex]L = \sqrt{404}[/tex]

[tex]L = 20.0997512422[/tex]

[tex]L = 20.10\ ft[/tex] -------Approximated

The full length of the slanted roof is the sum of L (calculated above) and the overhang

[tex]Slanted\ Roof = L + 8\ inch[/tex]

Substitute 20.10 ft for L

[tex]Slanted\ Roof = 20.10\ ft + 8\ inch[/tex]

Convert inch to feet to get the slanted roof in feet

[tex]Slanted\ Roof = 20.1\ ft + 8/12\ ft[/tex]

[tex]Slanted\ Roof = 20.10\ ft + 0.67\ ft[/tex]

[tex]Slanted\ Roof = 20.77\ ft[/tex]

Hence, the total length of the slanted roof in feet is approximately 20.77 feet