Find the work done by the force field f(x, y, z) = y + z, x + z, x + y on a particle that moves along the line segment from (1, 0, 0) to (5, 3, 2).

Hello there! You can do something like:
2/3 of a cake was sitting in the kitchen. You decide to eat 1/4 of it. How much of the whole cake did you eat?
Hope this helps you!

You made
2/3 batch of cookies but then you decided to give away
1/4 to some friends... How much did you give away?

The answer is D since 1/4 of the pineapple juice will give you the pinejuice

Answer: D

Step-by-step explanation: y costs less than p, only  1/4

as much. This translates to y =  1/4p or y =p/4.

2 yards. 2 inches is 2 yards because 1 yard is 36 inches

A snail moved distance of 2 yards.

What is metric conversion?

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

Given that, over a two-hour time period, a snail moved 72 inches.

We know that, 1 yard = 36 inches

Now, distance in yards = 72/36

= 2 yards

Therefore, a snail moved 2 yards.

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The answer would be C) Triangle ABC. This would because it matches with triangle XYZ's each respective angle. Hope this helped!

Answer:

(C) ΔABC

Step-by-step explanation:

Congruence: Two figures or shapes can be congruent if they have same dimensions and shape.

From the given information, ΔXYZ is congruent to ΔABC as when according to the respective angles of ΔXYZ, the respective angles of the ΔABC matches and this makes them congruent to eachother.

Rest other options fails to satisfy the congruence criteria, thus option C is correct.

Hence, ΔXYZ is congruent to ΔABC.

51.25% is the answer for the problem

Answer:

48.75%

Step-by-step explanation:

If total number of people that voted = 240

Number of votes Garth got = 117

% vote he got = Number of Garth vote/Total number if vote ×100℅

% vote gotten by Garth = 117/240×100%

% vote gotten by Garth = 48.75%

Answer:

Option A.

Step-by-step explanation:

The original price of a television in a store = $250.00

The store is marking down the price of a television 25 percent from the original price.

25% = [tex]\frac{25}{100}[/tex] = 0.25

The expression can be used to find the marked down price

250 - ( 25% of 250)

= 250 - (0.25)(250)

Option A. is the answer.

red is most likely in the second situation because it is closer to a whole than the first.  i think

If the question asks, "in which situation is a car chosen at random most likely to be red?", then the answer is on the transporter lorry

Car Park: 4 red, 10 cars total, 40% are red.

Transporter Lorry: 3 red, 5 cars total, 60% are red

Given that in a national highway Traffic Safety Administration (NHTSA) report, data provided to the NHTSA by Goodyear stated that the mean tread life of a properly inflated automobile tires is 45,000 miles. Suppose that the current distribution of tread life of properly inflated automobile tires is normally distributed with mean of 45,000 miles and a standard deviation of 2360 miles.

Part A:

Find the probability that randomly selected automobile tire has a tread life between 42,000 and 46,000 miles.
The probability that a normally distributed data set with a mean, μ, and standard deviation, σ, is between two numbers, a and b is given by:
[tex]P(a \ \textless \ X \ \textless \ b) = P(X \ \textless \ b) - P(X \ \textless \ a) \\ \\ P\left(z\ \textless \ \frac{b-\mu}{\sigma} \right)-P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]
Given that the the mean tread life of a properly inflated automobile tires is 45,000 miles a standard deviation of 2360 miles.
The probability that randomly selected automobile tire has a tread life between 42,000 and 46,000 miles is given by:
[tex]P(42,000 \ \textless \ X \ \textless \ 46,000) = P(X \ \textless \ 46,000) - P(X \ \textless \ 42,000) \\ \\ P\left(z\ \textless \ \frac{46,000-45,000}{2,360} \right)-P\left(z\ \textless \ \frac{42,000-45,000}{2,360} \right) \\ \\ =P(0.4237)-P(-1.271)=0.66412-0.10183=\bold{0.5623}[/tex]


b. Find the probability that randomly selected automobile tire has a tread life of more than 50,000 miles.
The probability that a normally distributed data set with a mean, μ, and standard deviation, σ, is greater than a numbers, a, is given by:
[tex]P(X \ \textgreater \ a) = 1-P(X \ \textless \ a) \\ \\ =1-P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]
Given that the the mean tread life of a properly inflated automobile tires is 45,000 miles a standard deviation of 2360 miles.
The probability that randomly selected automobile tire has a tread life of more than 50,000 miles is given by:
[tex]P(X \ \textgreater \ 50,000) = 1 - P(X \ \textless \ 50,000) \\ \\ =1-P\left(z\ \textless \ \frac{50,000-45,000}{2,360} \right)=1-P(z\ \textless \ 2.1186) \\ \\ =1-0.98294=\bold{0.0171}[/tex]


Part C:

Find the probability that randomly selected automobile tire has a tread life of less than 38,000 miles.
The probability that a normally distributed data set with a mean, μ, and standard deviation, σ, is less than a numbers, a, is given by:
[tex]P(X \ \textless \ a) =P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]
Given that the the mean tread life of a properly inflated automobile tires is 45,000 miles a standard deviation of 2360 miles.
The probability that randomly selected automobile tire has a tread life of less than 38,000 miles is given by:
[tex]P(X \ \textless \ 38,000) = P\left(z\ \textless \ \frac{38,000-45,000}{2,360} \right) \\ \\ =P(z\ \textless \ -2.966)=\bold{0.0015}[/tex]


d. Suppose that 6% of all automobile tires with the longest tread life have tread life of at least x miles. Find the value of x.
The probability that a normally distributed data set with a mean, μ, and standard deviation, σ, is greater than a numbers, x, is given by:
[tex]P(X \ \textgreater \ x) = 1-P(X \ \textless \ a) \\ \\ =1-P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]
Given that the the mean tread life of a properly inflated automobile tires is 45,000 miles and a standard deviation of 2360 miles and that the probability that all automobile tires with the longest tread life have tread life of at least x miles is 6%.

Thus:
[tex]P(X \ \textgreater \ x) =0.06 \\ \\ \Rightarrow1 - P(X \ \textless \ x)=0.06 \\ \\ \Rightarrow P\left(z\ \textless \ \frac{x-45,000}{2,360} \right)=1-0.06=0.94 \\ \\ \Rightarrow P\left(z\ \textless \ \frac{x-45,000}{2,360} \right)=P(z\ \textless \ 1.555) \\ \\ \Rightarrow \frac{x-45,000}{2,360}=1.555 \\ \\ \Rightarrow x-45,000=2,360(1.555)=3,669.8 \\ \\ \Rightarrow x=3,669.8+45,000=48,669.8[/tex]
Therefore, the value of x is 48,669.8


e. Suppose that 2% of all automobile tires with the shortest tread life have tread life of at most x miles. Find the value of x.
The probability that a normally distributed data set with a mean, μ, and standard deviation, σ, is less than a numbers, x, is given by:
[tex]P(X \ \textless \ x) =P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]
Given that the the mean tread life of a properly inflated automobile tires is 45,000 miles and a standard deviation of 2360 miles and that the probability that all automobile tires with the longest tread life have tread life of at most x miles is 2%.

Thus:
[tex]P(X \ \textless \ x)=0.02 \\ \\ \Rightarrow P\left(z\ \textless \ \frac{x-45,000}{2,360} \right)=1-0.02=0.98 \\ \\ \Rightarrow P\left(z\ \textless \ \frac{x-45,000}{2,360} \right)=P(z\ \textless \ 2.054) \\ \\ \Rightarrow \frac{x-45,000}{-2,360}=2.054 \\ \\ \Rightarrow x-45,000=-2,360(2.054)=-4,847.44 \\ \\ \Rightarrow x=-4,847.44+45,000=40,152.56[/tex]
Therefore, the value of x is 40,152.56

16.5 ___________________

A fraction is a way to describe a part of a whole. The number of teaspoons of cough syrup that the client will take each day is 4 1/2 teaspoons.

What is a Fraction?

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

What is Mixed Fractions?

A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,

2 1/2

= (2×2 + 1)/2

= 5/2

= 2.5

Given that a client is instructed to take 1 1/2 teaspoons of cough syrup 3 times a day. Therefore, the number of teaspoons of cough syrup that the client will take each day is,

Number of teaspoons = 3 × 1 1/2 teaspoons

                                     = 3 × (2×1 + 1)/2

                                      = 3 × 3/2

                                      = 9/2  

                                      = 4 1/2

                                      = 4.5

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Let these there numbers be assigned to variables x, y and z. Since you want to find the sum, add all numbers. However, the sum has boundaries between 10 and 20. Therefore, you will have to use inequality symbols. The two addition equations that could be formulated are:

x+y+z > 10
x+y+z < 20

Final answer:

Shailen could have written two possible addition equations like 4 + 3 + 8 = 15 or 5 + 7 + 6 = 18. Both of these sum up to an even number between 10 and 20. Order of numbers doesn't matter in addition due to its commutative property.

Explanation:

The problem is asking for two possible addition problems that Shailen could be solving if his sum ends up being an even number between 10 and 20. This involves an understanding of the properties of addition and how different number combinations can result in an even sum.

Here are two possible addition equations that meet the conditions:

4 + 3 + 8 = 15

5 + 7 + 6 = 18

In both cases, the sums fall between 10 and 20 and are even. It's worth noting commutativity of addition, which says the order in which numbers are added doesn't change the sum. Hence, you can rearrange the numbers in the addition (e.g., 3 + 4 + 8 or 8 + 4 + 3) and the sum will still remain the same.

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The tomato is not picked because they do not need it nomore and that it only ways 4 ounces.

$250. You would divide $1000 by 4 to get each 1/4 equaling $250, that would allow the dryer to be $750 which is 3x250, and 750+250 is 1000. So the washer is $750 and the dryer is $250

The washer is worth $750 the dryer is 150

Given that work hours in new zombie are 200 in year 1 and productivity is $8 per hour worked.

The new zombie's real gdp in year 1 is given by 200 x $8 = $1,600

If work hours increase to 210 in year 2 and productivity rises to $10 per hour.

The new zombie's real gdp in year 2 is given by 210 x $10 = $2,100

The new zombie's rate of economic growth is given by

[tex]\frac{\$2,100-\$1,600}{\$1,600} \times 100\%= \frac{\$500}{\$1,600} \times100\%=31.25\%[/tex]

Final answer:

New Zombie's real GDP in year 1 is $1600 and in year 2 is $2100, resulting in a rate of economic growth of 31.25%.

Explanation:

To calculate the real GDP of New Zombie we must multiply the work hours by the productivity (value produced per hour).

For year 1, the real GDP is calculated as follows:

200 hours * $8 per hour = $1600.

For year 2, we calculate the real GDP as:

210 hours * $10 per hour = $2100.

Now, to find the rate of economic growth from year 1 to year 2, we use the formula:

((GDP in year 2 - GDP in year 1) / GDP in year 1) * 100

= (($2100 - $1600) / $1600) * 100

= 31.25%.

Thus, New Zombie's rate of economic growth is 31.25%.

Parameterize the line segment (call it [tex]C[/tex]) by

[tex]\mathbf r(t)=\langle0,0,1\rangle(1-t)+\langle2,1,0\rangle t=\langle2t,t,1-t\rangle[/tex]

where [tex]0\le t\le1[/tex]. Then the work done by [tex]\mathbf f(x,y,z)[/tex] along the line segment is

[tex]\displaystyle\int_C\mathbf f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\mathbf f(x(t),y(t),z(t))\cdot\langle2,1,-1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1\langle2t-t^2,t-(1-t)^2,(1-t)-(2t)^2\rangle\cdot\langle2,1,-1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(t^2+8t-2)\,\mathrm dt=\frac73[/tex]

Hello!

First, let's write the problem.
[tex]9\le \:17-4x[/tex]
We are going to switch sides in order to have the x on the left side.
[tex]17-4x\ge \:9[/tex]
Subtract 17 from both sides.
[tex]17-4x-17\ge \:9-17[/tex]
[tex]-4x\ge \:-8[/tex]
We have two options, divide both sides by -4, or multiply both sides by -1 in order to reverse the inequality. Let's try the second option.
[tex]\left(-4x\right)\left(-1\right)\le\left(-8\right)\left(-1\right)[/tex]
[tex]4x\le \:8[/tex]
Divide both sides by 4.
[tex]\frac{4x}{4}\le \frac{8}{4}[/tex]

Our final answer would be,
[tex]x\le \:2[/tex]

You can feel free to let me know if you have any questions regarding this!
Thanks!

- TetraFish

The decimal... lol  thats what mt grandmom told me

The decimal point without the decimal point there is no decimal at all. 
i hoped that works ill give you an example if you are still confused 

if you are trying to turn this number 89 into a decimal you would have to do 8.9 if you don't than  89 is just a number not a decimal if you forget the decimal you will more than likely get the question incorrect.

Convert 16 tenths into .16 so 
5 - .16 = 4.84

The answer is 0.8347. Mean u = 1/m = 3.6 per hour Time x = 0.5 hour Exponential Probability = P(X <= x) Going by the Cumulative distribution function P(X <= x) = 1 - e^(-mx) P(X < .5) = 1 – exp^(-3.6 x 0.5) = 1 – 0.1653 = 0.8347

Is it D?
I'm in middle school, so I'm not totally sure...

The recursive formula for the given AP series 2,5,8,11,14 is a₁ = 2 and [tex]a_{n} =a_{n-1} + 3[/tex] so option (D) will be correct.

What is Arithmetic progression?

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2

Given an ap series,

2,5,8,11,14

The first term (a₁) = 2

The nth term of AP can be given as

[tex]a_{n} =a_{n-1} + d[/tex] where d is a common difference.

d = 5 - 2 = 3

So,

[tex]a_{n} =a_{n-1} + 3[/tex]

Hence "The recursive formula for the given AP series 2,5,8,11,14 is a₁ = 2 and [tex]a_{n} =a_{n-1} + 3[/tex] ".

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It cost $1.77 more to park in A

To find your answer, simply subtract the smaller total from the larger.
5.52 - 3.75 = 1.77
It cost $1.77 more to park in parking lot A than it does to park in B.

A2 + B2 = (A + Bi)(A – Bi) so the answer is (x + 4i)(x - 4i)

Answer:

The product of factors irreducible over the reals are [tex]x^2+16=(x+4i)(x-4i)[/tex]

Step-by-step explanation:

Given : Quadratic form  [tex]x^2+16[/tex]

To find : Write the quadratic as a product of factors irreducible over the reals?

Solution :

To find the product first we have to find the roots of the quadratic.

[tex]x^2+16=0[/tex]            

[tex]x^2=-16[/tex]  

Root both side,

[tex]\sqrt{x^2}=\sqrt{-16}[/tex]    

[tex]x=\pm 4i[/tex]  

So,The factors of the quadratic equation is [tex](x+4i)(x-4i)[/tex] in the form of complex number.

Therefore, The product of factors irreducible over the reals are [tex]x^2+16=(x+4i)(x-4i)[/tex]

The point slope form of the line has the following form:

y – y1 = m (x – x1)

 

The slope m can be calculated using the formula:

m = (y2 – y1) / (x2 – x1)

m = (3 - 0) / (0 – 4) = - ¾

 

So the whole equation is:

y – 0 = - ¾ (x – 4)

y = - ¾ (x – 4) or

y = - 0.75 (x – 4)

24 is the result. 1/3 of 36 is 12 so you are subtracting 12 from 36.

 1/3=0.33 so then you do 36.00-0.33=35.67 

Hope i helped

1/6 and 1/2. 

Multiply them together you get 1/12.

[tex] \frac{1}{3} (\frac{1}{4}) = \frac{1}{12} [/tex]

least 3/5, 0.65, 0.75, 7/8 greatest

The area of a parallelogram, like a rectangle, is base times height. The base is 2 units. the height is 5 units, from y=3 to y=8
2 * 5 = 10
The area therefore, is A) 10 units.

10 units squared should be your answer

Answer:

→Number of people in the fitness club= 36 People

→Number of people who lifted weights [tex]=\frac{3}{8}\times 36=\frac{108}{8}[/tex]

→Number of people who did cross training [tex]=\frac{1}{3}\times 36=12[/tex]

=12 People

→Number of people who were running

 [tex]=1-\frac{3}{8}-\frac{1}{3}\\\\=\frac{24-9-8}{24}\\\\=\frac{7}{24}[/tex]

To determine the fraction of people running in the fitness studio, subtract the fractions of people lifting weights and doing cross training from the total, which comes to 7/24.

The fraction representing the number of people running can be found by adding the fractions of people lifting weights and doing cross training and subtracting that from the total, which gives the fraction of people running. Here's how:

Given: 3/8 lifting weights, 1/3 doing cross training, and the total is 1 (representing the whole).To find the fraction running: 1 - (3/8 + 1/3) = 1 - (9/24 + 8/24) = 1 - 17/24 = 7/24.

25%

3.24*.25= .81
3.24+.81=4.05

Answer:

percent increase = 25%

Step-by-step explanation:

The price of a gallon of milk has increased from $3.24 to $4.05

LEt x be the percentage increase

intitial cost + initial cost times percentage = new cost

[tex]3.24 + 3.24 (\frac{x}{100})= 4.05[/tex]

Subtract 3.24 from both sides

[tex]3.24 (\frac{x}{100})= 0.81[/tex]

divide by 3.24 on both sides

[tex](\frac{x}{100})= 0.25[/tex]

Multiply both sides by 100

x= 25 %

the answer is A 5(5^3/2/5)^2

5(5^3/2/5)^2

= 5 (125/2/5)^2


= 5 ( 125/2  x 1/5 ) ^2

= 5 ( 12.5) ^2 

= 5 x 156.25

= 781.25 >>>>>>>>>>>>>>>>>>>>>>>> Not equal to 125

= 

So your equation will be:

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

First, divide everything by 2

x+6+x+2 = x+4+2x-2

Then, combine like terms

2x+8 = 3x+2

Move the variables (the x's) to one side and the numbers to the other by subtracting 2x from one side and then 2 from the other

6 = 1x or 6 = x

Now that you know that x = 6, you go back to Earl's length and width equations

Length = x+2
Width = x+6

And plug in the value of x you got (6)

Length = 6+2 = 8
Width = 6+6 = 12

There are you answers! Hope this helped! (remember to add units, in this case the units are feet)