What is 7^1/2/(4^1/2-5^1/8)?

Answer:

21

Step-by-step explanation:

15-15=0

17-(-4)=21

sqrt(0^2+21^2)=21

Answer:

35.94 lb

Step-by-step explanation:

The net mass flow rate dm/dt = flow rate in - flow rate out

mass flow rate in = concentration in × volume flow rate in = 0.4 lb/gallon of salt × 5 gal/min = 2 lb/min

Let m(t) be the mass present at time, t.

So, the concentration at time, t = m(t)/volume of tank = m(t)/100

mass flow rate out = concentration out × volume flow rate out = m(t)/100 lb/gal× 5 gal/min = m(t)/20 lb/min

So, dm/dt = 2 lb/min - m(t)/20 lb/min

So, dm/dt = 2 - m(t)/20

dm/dt = [40 - m(t)]/20

separating the variables, we have

dm/[40 - m(t)] = dt/20

integrating, we have

∫dm/[40 - m(t)] = ∫dt/20

-1/-1 ×∫dm/[40 - m(t)] = ∫dt/20

1/-1 ×∫-dm/[40 - m(t)] = ∫dt/20

1/-1 ×㏑[40 - m(t)] = t/20 + C

-㏑[40 - m(t)] = t/20 + C

㏑[40 - m(t)] = -t/20 - C

taking exponents of both sides, we have

\(40 - m(t) = e^({\frac{-t}{20} - C}) \\40 - m(t) = e^{\frac{-t}{20}}e^{-C} \\40 - m(t) = Ae^{\frac{-t}{20}} (A = e^{-C})\\m(t) = 40 - Ae^{\frac{-t}{20}}\)

when t = 0 m(0) = 10 lb

So

\(m(t) = 40 - Ae^{\frac{-t}{20}}\\m(0) = 40 - Ae^{\frac{-0}{20}}\\10 = 40 - Ae^{0}\\10 = 40 - A\\A = 40 - 10 \\A = 30\)

So,

\(m(t) = 40 - 30e^{\frac{-t}{20}}\)

when t = 40 minutes, m(40) =

\(m(40) = 40 - 30e^{\frac{-40}{20}}\\m(40) = 40 - 30e^{-2}\\m(40) = 40 - 30 X 0.1353\\m(40) = 40 - 4.06\\m(40) = 35.94\)

So, at the end of 40 minutes, the amount of salt in the tank is 35.94 lb

Answer: 12

Step-by-step explanation:

Answer:

0.76 or 19/25

Step-by-step explanation:

Convert 4/10 so that it has a common denominator with 36/100.

4/10 x 10/10 = 40/100

Now that the denominator is the same, just add the top values.

40/100 + 36/100 = 76/100

We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.

Answer:

Step-by-step explanation:

\(\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\\)

\(\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\\)

\(\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}\)

Answer:

49

81

Step-by-step explanation:

Probability = number of possible outcome.

number of total outcome.

= orange counters = 81 - 32 = 49

49

81

Haleema would have approximately £3947.46 in her account after 2 years and 11 months, considering the monthly compounding interest of 5%.

To calculate the amount of money in Haleema's account after 2 years and 11 months, we need to consider the monthly compounding interest on the account.

The interest rate is given as 5% per year, which means the monthly interest rate is (5%/12) = 0.4167%.

Let's calculate the final amount using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = £3700, r = 0.004167, n = 12 (monthly compounding), and t = 2.917 (2 years and 11 months).

Plugging these values into the formula, we get:

A = £3700(1 + 0.004167/12)^(12*2.917)

A ≈ £3947.46

The amount of money in Haleema's account after 2 years and 11 months would be approximately £3947.46.

For more questions on compound interest

https://brainly.com/question/28020457

#SPJ8

Answer:

Step-by-step explanation:

The answer is B

The whole numbers are the + integer set. Since -sqrt(25) = - 5, this number is not included in the whole number set.

Answer:

0.66608

Step-by-step explanation:

Equipment = 3 fans

Mortality = 0.098

We are required to find probability that equipment gets to work for 5years

The question says forces of mortality is constant and also equal to 0.098

To calculate p(x>5)

We will do this by calculating exponentially

e^-0.098x5

= 0.612626394

Probability that at least 2 fans out of 3 are working

3(0.612626394)²+(1-0.612626394)+(0.612626394)³

= 1.1259333x0.3873736+0.2299255

= 0.6660823470

This is approximately

0.6608

this is the probability that the equipment will work for at least 5years

Answer:

(-1,4)

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

4 x 18 =72 + 9 =81

Answer:

Answer:

The Prime Factorization is:

2 x 5 x 11

Step-by-step explanation:

A 95% confidence that the true proportion of adults who regularly snore is between 0.682 and 0.818.

What is random sample ?

A random sample is a subset of a larger population that is chosen in such a way that every member of the population has an equal chance of being selected. In other words, a random sample is a sample that is chosen at random from the population, without any bias or preference for certain members of the population.

Random sampling is an important technique used in statistics and other fields that deal with large populations. By taking a random sample of the population, statisticians can make inferences about the entire population with a high degree of confidence, without having to survey or study every individual in the population. This is because a random sample is more likely to be representative of the population as a whole, and therefore the statistics derived from the sample are more likely to accurately reflect the characteristics of the population.

According to the question:
To calculate the 95% confidence interval for the proportion of adults who regularly snore, we can use the formula:

\(CI = p \± z\sqrt{p(1-p)/n}\)

where:

CI is the confidence interval

p is the sample proportion (in this case, 0.75 or 75%)

z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 95%, which corresponds to a z-value of 1.96)

n is the sample size (250 adults in this case)

Substituting the given values, we get:

p = 0.75

z = 1.96

n = 250

Plugging these values into the formula, we get:

\(CI = 0.75 \± 1.96\sqrt{0.75(1-0.75)/250}\)

Simplifying and solving for the upper and lower bounds of the confidence interval, we get:

CI = 0.75 ± 0.068

CI = (0.682, 0.818)

Therefore, we can say with 95% confidence that the true proportion of adults who regularly snore is between 0.682 and 0.818.

To know more about random sample visit:
https://brainly.com/question/30759604
#SPJ1

In tables, graphs and equations, we have x values and corresponding y values. On the graph, we can pick a point on the horizontal axis and draw a vertical line to touch the line on the graph. The y coordinate of the point where the vertical line touches the line on the graph is the corresponding y value. When we divide a y value by its corresponding x value, we would compare the result by dividing another y value by its corresponding x value. If the results are the same, then the value gotten is the constant of proportionality.

Answer:

câu này là 500 nhen

Answer:

x = 17/6

Step-by-step explanation:

First of all remove parenthesis by using distribution

6x + 9 - 12x + 24 = 16

Then collect all like terms

-6x + 33 = 16

After that move the constant to the right

- 6x = 16 - 33

Calculate 16 - 33

-6x = -17

Divide both sides

x = 17/6

Hope this helps!

Answer:

(-4, -4).

Step-by-step explanation:

In order to calculate the midpoint coordinates, we need to calculate the mean value of the x-coordinates and the mean value of the y-coordinates.

So we have:

M(x)=(-1+(-7))/(2)=(-8)/(2)=-4

M(y)=(-6+(-2))/(2)=(-8)/(2)=-4

Therefore the midpoint coordinates are (-4, -4).

There is approximately an 8.33% chance that two boys will pick the same style of watch from a set of 12 different styles.

To calculate the probability that two boys will pick the same style of watch from a set of 12 different styles, we need to know how many watches each boy will pick.

If each boy is picking one watch from the set of 12 styles independently, then we can calculate the probability as follows:

The first boy has 12 options to choose from.

The second boy also has 12 options, but in order to pick the same style as the first boy, he only has 1 option.

Therefore, the probability that both boys will pick the same style of watch is:

1/12

So, the decimal representation of this probability is approximately:

0.0833

Hence, there is approximately an 8.33% chance that two boys will pick the same style of watch from a set of 12 different styles.

For more such questions on chance , Visit:

https://brainly.com/question/30066918

#SPJ11

The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.

The volume of a solid is the three dimensional space the solid occupies.

The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;

Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³

Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³

70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³

The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0

The number of times Johnny needs to use the wheelbarrow is about 41 times

Learn more on calculating the volume of solids here: https://brainly.com/question/20704291

#SPJ1

Answer:

\(V=763.407\) yd^3

Step-by-step explanation:

Formula for volume of right circular cylinder.

\(V=\pi r^{2}*6\)

\(r=\frac{d}{2}\)

We are given the diameter (d) and the height (h).

First solve for r.

\(r=\frac{18}{2}\)

\(r=9\)

Now we have everything we need to find the volume. Plug in r into the volume formula.

\(V=\pi *9^{2} *3\)

\(V=763.407\) yd^3

Answer:

The sequence is increasing by 5 at each step. So, we can write:

a1 = 30

a2 = 30 + 5 = 35

a3 = 30 + 25 = 40

a4 = 30 + 35 = 45

a5 = 30 + 4*5 = 50

We notice that the nth term is given by:

an = 30 + (n-1)5

So, the explicit formula for the nth term is:

an = 25n + 5

b'

Let the given points be A(3,-5) and B(5,-1).

AB= sqrt of (5−3) ² +(−1+5)²

= sqrt of 4+16

= sqrt of 20

=2 sqrt of 5 units

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

For more such question on brand. visit :

https://brainly.com/question/29129317

#SPJ8

Answer:

26

Step-by-step explanation :

73 - 47 = 26  brainliest?

Answer:

29

Step-by-step explanation:

Answer:

The answer is 29

Answer:

2/5

Step-by-step explanation:

since the denominators are the same, the question is basically -4+6, which is 2.  But remember to include the denominator

Answer:

h ≅ 16.29 cm

\(\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}\)

Step-by-step explanation:

From the conical funnel;

Let the adjacent line at the base of the cone be radius (r) and the opposite ( vertical length) be the height (h)

Then;

\(tan \theta= \dfrac{r}{h}\)

\(tan \theta= \dfrac{8}{16}\)

\(tan \theta= \dfrac{1}{2}\)

∴

\(\dfrac{r}{h} = \dfrac{1}{2}\)

\(r = \dfrac{h}{2}\)

The volume (V) of the cone is expressed as:

\(V = \dfrac{1}{3}\pi r ^2 h\)

\(V = \dfrac{1}{3}\pi (\dfrac{h}{2})^2 h\)

\(V = \dfrac{\pi h^3}{3\times 4}\)

\(\dfrac{dv}{dt} = \dfrac{3 \pi h^2}{3 \times 4} \dfrac{dh}{dt}\)

\(\dfrac{dv}{dt} = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}\)

Given that:

\(\dfrac{dv}{dt} = 12 \pi\)

Then:

\(-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}\)

\(- \int 48 \ dt = \int h^2 \ dh\)

\(\dfrac{h^3}{3}= -48 t + c\)

\(At \ t = 0 \ ; h = 0\)

∴

\(\dfrac{0^3}{3} = -48(0) + c\)

c = 0

So;

\(\dfrac{h^3}{3}= -48 t + 0\)

\(\dfrac{h^3}{3}= -48 t\)

t = 30

\(\implies h = (-48(30))^{1/3}\)

h = 16.2865

h ≅ 16.29 cm

Thus;

from \(-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}\)

\(\dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} } =\dfrac{dh}{dt}\)

\(\dfrac{dh}{dt} = \dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} }\)

\(\dfrac{dh}{dt}=\dfrac{-12 \times 4} { {16.29^2} }\)

\(\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}\)

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

learn more about word problem from

https://brainly.com/question/21405634

#SPJ1

Answer:

\(V = 64\pi . [\frac{16}{3} - \sqrt{3} ]\)  unit^3 .. ( or equivalent )

Step-by-step explanation:

Solution:-

- The following surfaces are given as follows:

                                \(x^2 + y^2 = 4 \\\\x^2 + 4y^2 + z^2 = 64\)

- We will first have to investigate the region that lies inside both the cylinder and the ellipsoid or the region common to both surface.

Step 1: Coordinate transformation ( Cartesian ( x,y,z ) -> Polar ( r,θ,z )

- To convert the cartesian coordinates to polar/cylindrical coordinate system we will take the help of conversion equation given below:

                                \(x^2 + y^2 = r^2\)

- Make the substitution of the above equation in the given equation of the cylinder as follows:

                               \(r^2 = 4\\r = +/- 2\)

- Make the substitution of the transformation equation into the ellipsoid equation as follows:

                              \(4 ( x^2 + y^2 ) + z^2 = 64\\\\4.r^2 + z^2 = 64\\\\z^2 = 4 ( 16 - r^2 )\\\\z = +/- 2.\sqrt{16 - r^2}\)

Step 2: Sketch/Plot the region of volume

- We can either sketch or plot the surfaces in the cartesian coordinate system. I have utilized " Geogebra " 3D graphing utility.

- The purpose of graphing/sketching the surfaces is to "visualize" the bounds of the volume that lies inside both of the surfaces. This will help us in step 3 to set-up limits of integration. Moreover, the sketches also help us to see whether the enclosed volume is symmetrical about any axis.

- The plot is given as an attachment. From the plot we see that the volume of integration lies both above and below x-y plane ( z = 0 ). This result can be seen from the polar equation of surfaces ( +/- ) obtained.

- The Volume is defined by a shape of a vessel. I.e " Cylinder with two hemispherical caps on the circular bases "

- We see that enclosed volume is symmetrical about ( x-y ) plane. Each section of volume ( above and below x-y plane ) is bounded by the planes:

                         Upper half Volume:

                          \(z = 0 - lower\\\\z = 2\sqrt{16 - r^2} - upper\\\\\)

                        Lower Half Volume:

                         \(z = -2\sqrt{16-r^2} - lower\\\\z = 0 - upper\)

- We will simplify our integral manipulation by using the above symmetry and consider the upper half volume and multiply the result by 2.

Note: We can also find quadrant symmetry of the volume defined by the circular projection of the volume on ( x-y plane ); however, the attempt would lead to higher number of computations/tedious calculations. This invalidates the purpose of using symmetry to simplify mathematical manipulations.  

Step 3: Set-up triple integral in the cylindrical coordinate system

- The general formulation for setting up triple integrals in cylindrical coordinate system depends on the order of integration.

- We will choose the following order in the direction of "easing symmetry" i.e: (dz.dr.dθ)  

                             \(V = \int\limits^f_e\int\limits^d_c\int\limits^b_a {} \, dz.(r.dr).dQ\)

- Define the limits:

                 a: z = 0 - > ( x-y plane, symmetry plane )

                 b: z = 2√(16 - r^2) - > ( upper surface of ellipsoid )

            * Multiply the integral ( dz ) by " x2 "

                 c: r = 0  ( symmetry axis )

                 d: r = +2 ( circle of radius 2 units - higher )

              * Multiply the integral ( r.dr ) by " x2 "

                 e: θ = 0 ( initial point of angle sweep )

                 f: θ = 2π ( final point of angle sweep )

- The integral formulation becomes:

                       \(V = \int\limits^f_e 2*\int\limits^d_c2*\int\limits^b_a{} \, dz.(r.dr).dQ \\\\V = 4 \int\limits^f_e \int\limits^d_c\int\limits^b_a{} \, dz.(r.dr).dQ \\\\\)

Step 4: Integral evaluation

- The last step is to perform the integration of the formulation derived in previous step.

                        \(V = 4 \int\limits^f_e \int\limits^d_c{2.r.\sqrt{16 - r^2} } \, .dr.dQ\\\\V = 4 \int\limits^f_e {-\frac{2}{3} . (16 - r^2)^\frac{3}{2} } \,|\Limits^2_0 . dQ\\\\V = -\frac{8}{3} \int\limits^f_e { [ 24\sqrt{3} - 64] } .dQ\\\\V = -\frac{8}{3}. [ 24\sqrt{3} - 64] . 2\pi \\\\V = 64\pi . [\frac{16}{3} - \sqrt{3} ]\)Answer.

The volume of the solid inside the cylinder and the ellipsoid is \(\frac{8-4\sqrt{3}}{3}\pi\) cubic units.

The volume of a solid in cylindrical coordinates (\(V\)) can be determined by the following triple integral:

\(V = \iiint \, dz \,r\,dr \,d\theta\) (1)

The solid is constrained by the following equations in cylindrical coordinates:

Cylinder

\(r = 2\) (2)

Ellipsoid

\(4\cdot r^{2}+z^{2}= 64\) (3)

The integration limits can be identified by using the following intervals:

\(\theta \in [0, 2\pi]\), \(r \in [0, 2]\), \(z \in [-\sqrt{64-4\cdot r^{2}}, + \sqrt{64-4\cdot r^{2}}]\)

And the triple integral is the following form:

\(V = \int \limits_{0}^{2\pi}\int\limits_{0}^{+2} \int \limits _{-\sqrt{64-4\cdot r^{2}} }^{+\sqrt{64-4\cdot r^{2}}} \, dz\,r\,dr\,d\theta\) (4)

Now we proceed to integrate the expression thrice:

\(V = 2\int\limits_{0}^{2\pi}\int\limits_{0}^{+2} \sqrt{64-4\cdot r^{2}}\,r\,dr = \frac{4-2\sqrt{3}}{3} \int\limits_{0}^{2\pi} d\theta = \frac{8-4\sqrt{3}}{3}\pi\)

The volume of the solid inside the cylinder and the ellipsoid is \(\frac{8-4\sqrt{3}}{3}\pi\) cubic units.

We kindly invite to check this question on triple integrals: https://brainly.com/question/19484372

The Area of the parallelogram is 27.57 cm² .

If the length of the parallelogram with sides a and b , and the angle between the sides a and b is θ , then

Area of Parallelogram = a × b × Sin(θ)

In the question ,

it is given that

the length of the parallelogram is 4cm and 7 cm , and the angle between is 100° .

By substituting the values in the formula for Area of parallelogram

we get ,

Area = 4 × 7 × Sin(100°)

= 4 × 7 × 0.9848              ....because Sin(100°) = 0.9848  

= 27.57 cm²

Therefore , The Area of the parallelogram is 27.57 cm² .

The given question is incomplete , the complete question is

If the length of the sides of parallelogram is 4 cm and 7 cm and the angle between them is 100° , Work out the Area of the parallelogram ? Give your answer to 2 significant figures. ​

Learn more about Area here

https://brainly.com/question/17014062

#SPJ1

Answer:

Step-by-step explanation: