4x-2(3x+7)=____x-_____

Answer:

$8 per person

Step-by-step explanation:

32 divided by 4 is 8

32 : 4 = 8 : 1

The  work required to pump the water out of the spout is 70.9 * 10⁶ joules which is 71 M Joules approx.

Let the spherical tank be divided into a series of horizontal disks.

Let x be the height of each disk, g = gravity and p = density

Volume of each disk = πr2dx

Where r is the radius of each disk and dx is the thickness

By Pythagoras r² = 6² - x²= 36 -x²

Therefore Volume = π*(36-x²)*dx cubic metres

The distance each disk has to be lifted to escape the top of the spout = 2 + 6-x meters = (8-x)

Work needed to lift each disk to outlet = distance * mass where

mass = volume * density * gravity

        = pi(36-x²)*p*g = 9800pi(36-x²)dx

dW =  (8-x)* 9800pi(36-x²)dx

Since we have already accounted for the height of the spout, the work required is obtained by integrating the above expression from the bottom of the tank to the top. In other words, - 6 to + 6.

W = ⌠(8-x)*9800pi(36-x2)dx = 9800pi⌠[288 - 36x - 8x² +x³]dx

The odd terms evaluate to zero and we can rewrite the above as 2* I from 0 to 6.

W = 9800pi*2 [288x - 8x³/3] at x = 6 = 1152*19600π Joules = 22579200π joules = 70963200j

Total work required = 70.9 * 10⁶ joules

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Step-by-step explanation:

You can find your answer by taking integral from 0 to 7 and then dividing it by 7.

The equation the completes the proof in step 6 is m<w + m<x = m<x + m<z

In step 4 of the proof, we have the following equation

m<w + m<x = m<y + m<z

In step 5, we have

m<x = m<y

When m<x = m<y is substituted to the equation in step 4, we have:

m<w + m<x = m<x + m<z

Hence, the equation the completes the proof in step 6 is m<w + m<x = m<x + m<z

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Answer:

A) 175π / 9 squared inches,

Step-by-step explanation:

Radius = 10 inches

AB = BD = 10 = radius

Triangle ABD is isosceles

Angle DAB = Angle BDA = 35 degrees,

Base angles theroem

35 + 35 + x = 180, angles in triangle

x = 180 - 70

x = 110 degrees

Angle DBC is supplementary with ABD

110 + x = 180

x = 70

70 degrees is angle for the sector

70 is 70/360, 7/36 of the circle

The area will also be 7/36 of the circle area

Area of circle = πr^2

Area =  100π

Area of sector = (100π * 7) / 36

Area of sector = 700π / 36

Simplified area = 175π / 9 squared inches

The average speed formula is given by:

\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)

Let's calculate the total distance first. The car travels 120 miles from point A to point B, and then returns the same distance. Therefore, the total distance is \(\displaystyle\sf 2 \times 120 = 240\) miles.

Now, let's calculate the total time. The time taken to travel from A to B can be calculated using the formula \(\displaystyle\sf \text{Time} = \frac{\text{Distance}}{\text{Speed}}\).

For the journey from A to B:

\(\displaystyle\sf \text{Time}_1 = \frac{120}{30} = 4\) hours

For the return journey from B to A:

\(\displaystyle\sf \text{Time}_2 = \frac{120}{40} = 3\) hours

The total time for the round trip is the sum of the individual times:

\(\displaystyle\sf \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 + 3 = 7\) hours

Now, we can calculate the average speed:

\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{240}{7} \approx 34.29\) miles per hour.

Therefore, the average speed for the round trip is closest to 34.29 miles per hour.

Answer:

The correct answer is point F!

Step-by-step explanation:

Hope it helped :D

Answer:

point f

Step-by-step explanation:

-5 in x and 5 and y

ANSWER: POINT F

Answer:

The correct answer is 9

Step-by-step explanation:

I can assure you this is absolutely correct.

Answer:

1/2 cup of chocolate chips

Step-by-step explanation:

Given ratio:

Let x be the unknown amount of chocolate chips:

\(\implies \sf \dfrac{1}{3}:2=x:3\)

\(\implies \sf \dfrac{\frac{1}{3}}{2}=\dfrac{x}{3}\)

Cross multiply:

\(\implies \sf 3 \cdot \dfrac{1}{3}=2 \cdot x\)

\(\implies \sf 1=2x\)

\(\implies \sf x=\dfrac{1}{2}\)

Therefore, 1/2 a cup of chocolate chips will be needed for 3 cups of flour.

Let that be x

Answer:

the questions of Albania we don't know language of albera please don't disturbance and give me 10 marks

Answer:

Side RT

Step-by-step explanation:

The hypotenuse is the longest side on a right angle triangle, making it the side RT.

Answer:

x=70°

Step-by-step explanation:

x+110=180 linear pair

x=180-110=70

Answer:

\(\textsf{Area}=\dfrac{5\pi -3}{12} \approx 1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}\)

Step-by-step explanation:

To find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector.

An isosceles triangle is made up of two congruent right triangles.

To find the height of the right triangles (and thus the height of the isosceles triangle), use the cosine trigonometric ratio.

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

Given values:

Substitute these values into the cosine ratio to calculate the height of the right triangles (and thus the height of the isosceles triangle):

\(\cos \left(\dfrac{5\pi}{12}\right)=\dfrac{x}{1}\)

\(x=\cos \left(\dfrac{5\pi}{12}\right)\)

\(x=\dfrac{\sqrt{6}-\sqrt{2}}{4}\)

The base of one of the right triangles can be found by using the sine trigonometric ratio.

\(\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

Given values:

Substitute these values into the sine ratio to determine the base of the right triangle:

\(\sin \left(\dfrac{5\pi}{12}\right)=\dfrac{y}{1}\)

\(y=\sin \left(\dfrac{5\pi}{12}\right)\)

\(y=\dfrac{\sqrt{6}+\sqrt{2}}{4}\)

The base of the isosceles triangle is twice the base of the right triangle, so the base of the isosceles triangle = 2y.

Therefore the area of the isosceles triangle is:

\(\begin{aligned}\textsf{Area of isosceles triangle}&=\dfrac{1}{2} \cdot \sf base \cdot height\\\\&=\dfrac{1}{2}\cdot 2y \cdot x\\\\&=\dfrac{1}{2} \cdot 2\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\dfrac{4}{16}\\\\&=\dfrac{1}{4}\sf \;square\;units\end{aligned}\)

To find the area of the sector of the circle, use the area of a sector formula (where the angle is measured in radians).

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}\)

Given values:

Substitute the values into the formula:

\(\begin{aligned}\textsf{Area of the sector}&=\dfrac{1}{2} \cdot (1)^2 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot 1 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{5\pi}{12}\;\; \sf square\;units\end{aligned}\)

Finally, to find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Area of the shaded region}&=\sf Area_{sector}-Area_{isosceles\;triangle}\\\\&=\dfrac{5\pi}{12}-\dfrac{1}{4}\\\\&=\dfrac{5\pi}{12}-\dfrac{3}{12}\\\\&=\dfrac{5\pi -3}{12}\\\\&=1.05899693...\\\\&=1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}\)

Therefore, the area of the shaded region is (5π - 3)/12 or approximately 1.06 square units (3 significant figures).

From the function we will have:

a. f(-1):

b. f(0):

c. f(2):

d. We will find the values as follows:

e. The domain of the function is all the real numbers:

Answer:

4.5

Step-by-step explanation:

Answer:

-5/4

Step-by-step explanation:

Let \((x_1,y_1)=(-4,4)\) and \((x_2,y_2)=(0,-1)\). The slope of the line would be:

\(\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}\)

Answer: -5/4

Step-by-step explanation:

To find the slope between two points, you can use the formula:

Slope = (y2 - y1)/(x2 - x1)

Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:

slope = (4 - (-1))/(-4 - 0)

slope = (4 + 1)/(-4)

slope = 5/-4

Therefore, the slope between the two points is -5/4.

A. Is the answer of this question

Answer:

Step-by-step explanation:

Current office area:

Temporary office dimensions:

Temporary office area:

The difference is:

Correct choice is A

Answer:

64 feet

Step-by-step explanation: 8 x 8 = 64, we know to duplicate 8 since it is a Square Garden.

Hope this Helps!

Answer:

I belive it would be 1/5. ;;;

Using binomial distribution, P(X≥10)=0.8349

Binomial distribution is a discrete probability distribution which gives only two possible results on experiment which is success and failure.

\(P(X=x) = nC_{x} p^{x} (1-p)^{n-x}\),  where \(nC_{x} = \frac{n!}{x!(n-x)!}\)

In this problem, given that n=14, p=0.8

The desired probability is,

P(X≥10) = P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)

\(P(X=x) = nC_{x} p^{x} (1-p)^{n-x}\)

P(X=10)= \(14C_{10}(0.8)^{10} (1-0.8)^{14-10}\) = 0.1720

P(X=11) = \(14C_{11}(0.8)^{11} (1-0.8)^{14-11}\)=0.2501

P(X=12) = \(14C_{12}(0.8)^{12} (1-0.8)^{14-12}\) = 0.2501

P(X=13) = \(14C_{13}(0.8)^{13} (1-0.8)^{14-13}\) = 0.1539

P(X=14) = \(14C_{14}(0.8)^{14} (1-0.8)^{14-14}\) =0.0088

Then,  P(X≥10)= 0.1720+0.2501+0.2501+0.1539+0.0088

Hence,  P(X≥10) = 0.8349

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Given the negative numbers:

You need to remember that negative numbers are those numbers less than zero. Therefore:

a. Given the phrase "-33 rushing yards in a football game", you know that the rushing yards are represented by a negative number and it is less than zero. Therefore, it indicates a loss.

b. Given the phrase "Stock market performance for the day: -125.68 points". You can also identify that it is less than zero, therefore, it lost -125.68 points.

Hence, the answers are:

a. Loss.

b. Loss.

Answer: D and F

Step-by-step explanation:

3 to the power of 4 means 3x3x3x3.

3x3 is 9

9x3 is 27

And 27x3 is 81

9 to the power of 2 means 9x9

9x9 equals 81

We will like to find the derivative of the function

then

In this process we use the chain rule

to find the derivative of

therefore

Answer:

400 ft sq

Step-by-step explanation:

Area = Length x Width x Height

10 x 10 x 4

100 x 4

400

Have a great day!!

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Answer:

\(\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}\)

=

\(\frac{ \sqrt{2} }{a + b} \)

Step-by-step explanation:

\(\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}\)

\((a - b)( \frac{ {2}^{ \frac{1}{2} } }{(a + b)(a - b)} )\)

\( \frac{(a - b)( {2}^{ \frac{1}{2} }) }{(a - b)(a + b)} = \frac{ \sqrt{2} }{a + b} \)

The 7.335 is the value of acceleration needed to achieve the condition that ensure its newest model can stop in 8 sec when traveling at 80 mph.

The car will move a maximum time 8 seconds when the brake is activated.

Initial velocity; u = 80 mph = (1.467 x 80) = 117.36 ft/s

Final velocity as it stops, v = 0 m/s

To find the car's deceleration, use the following kinematic equation.

v = u + 2at

0 = 117.36 + 2(a)(8)

a = -117.6/16 ft/s²

|a| = 7.335 ft/s²

Therefore, 7.335 is the value of acceleration needed to achieve the condition that ensure its newest model of car can stop in 8 sec when traveling at 80 mph.

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Answer:

Its B.

Step-by-step explanation:

Because \(11^{2}\) + \(12^{2}\) does not equal \(15^{2}\)

121 + 144 \(\neq\) 225

265 \(\neq\) 225

Answer:

B. 3188.5 cubic inches.

Step-by-step explanation:

The volume of a cone is calculated using the following formula:

Volume = (1/3) * π * r² * h

Where:

In this problem, we are given that r = 17 inches and S.h = 20 inches.

First we need to find height h.

py using Pythagorous theorem,we get

c²=a²+b²

here c= slight height and a is radius

20²=17²+b²

20²-17²=b²

111=b²

b=√(111)

Plugging these values into the formula, we get:

Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches

Therefore, the volume of the cone is 3188.5 cubic inches.

Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.

Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.

Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.

In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.

Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.

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