"Heavy Water" is a name given to a compound used in some nuclear reactors. Heavy water costs about $1,500 per gallon. If a nuclear plant spent $10,500 on heavy water, how many gallons of water were bought?

TIP

pencil =$0.12

Eraser= $0.52

Pen=$0.44

STEP 1

Three students each bought 3 pencils and an eraser.

STEP 2

Two students each bought a pen and 2 pencils

STEP 3

Total cost

THE CORRECT OPTION IS OPTION B

Answer:

(5,354 + x)

or

536.4*x

Step-by-step explanation:

We know that x = 10.

Now we want to write an expression (in terms of x) for the number 5,364.

This could be really trivial, remember that x = 10.

Then:  (x - 10) = 0

And if we add zero to a number, the result is the same number, then if we add this to 5,364 the number does not change.

5,364 = 5,364 + (x - 10) = 5,364 + x - 10

5,364 = 5,354 + x

So (5,354 + x) is a expression for the number 5,364 in terms of x.

Of course, this is a really simple example, we could do a more complex case if we know that:

x/10 = 1

And the product between any real number and 1 is the same number.

Then:

(5,364)*(x/10) = 5,364

(5,364/10)*x = 5,364

536.4*x = 5,364

So we just found another expression for the number 5,364 in terms of x.

1

Explanation:

7/7 - 2/5

Using compatible numbers:

7/7 = 1 as it is closer and equal to 1

so we have: 1 - 2/5

2/5 is approximately 0 as it is closer to 0 than 1

= 1 - 0 = 1

7/7 - 2/5 using compatible number = 1

Answer:

2.2

Step-by-step explanation:

The best answer would be 213.

Assuming that the sign denotes summation, we are adding from k=4 to k=9.

To get, we change k=4 to k=9.

We simplify obtaining,

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Summarizing mainly entails entering the values k=4, 5, 6, 7, 8, and 9 into the formula section 5K+3 and adding them all together.

So, the result is:

(5(4)+3)+(5(5) + 3) + (5(6) + 3) + (5(7) +3) + (5(8) + 3) + (5(9) + 3) 23+28+33 +38+43 + 48

= 213

Know more about simplification

https://brainly.com/question/28780542

#SPJ4

The expression for the probability of getting at least one six in n throws of fair dice is 1 - (5/6)ⁿ.

The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

In this problem, we use the complement rule to find the probability of getting at least one six in n throws of a fair dice by subtracting the probability of not getting any sixes in n throws from 1.

Here we have

A fair dice is thrown n times.

The probability of getting at least one six in n throws of a fair dice is equal to 1 minus the probability of not getting any sixes in n throws.

The probability of not getting a six on any one throw  = 5/6

[ Since there are 5 possible outcomes that are not six and 6 possible outcomes in total ]

Therefore,

The probability of not getting any sixes in n throws is (5/6)ⁿ.

So, the probability of getting at least one six in n throws is:

P(at least one six) = 1 - P(no sixes) = 1 - (5/6)ⁿ

Therefore,

The expression for the probability of getting at least one six in n throws of fair dice is 1 - (5/6)ⁿ.

Learn more about Probability at

https://brainly.com/question/9473940

#SPJ1

The root of the function \(\(f(x) = 5\cos(x) - \sqrt{x^2 + 1} + 2^{x-1}\)\) lies within the interval \(\([-1, 0]\)\).

To find the interval where the root of the given function lies, we need to analyze the behavior of the function within certain intervals. Let's consider the interval  \(\([-1, 0]\)\).. For \(\(x = -1\)\), we have \(\(f(-1) = 5\cos(-1) - \sqrt{(-1)^2 + 1} + 2^{-2}\)\). Since \(\(\cos(-1)\)\) is positive and the other terms are also positive, the value of \(\(f(-1)\)\) is positive.

Now, for \(\(x = 0\)\), we have \(\(f(0) = 5\cos(0) - \sqrt{0^2 + 1} + 2^{-1}\)\). Since \(\(\cos(0)\)\) is positive and the other terms are positive, the value of \(\(f(0)\)\) is positive.

As the function is continuous, and it changes sign from positive to negative within the interval  \(\([-1, 0]\)\) (as \(\(f(-1)\)\) and \(\(f(0)\)\) have different signs), by the Intermediate Value Theorem, there exists at least one root of the function within this interval. Therefore, we can conclude that the root of \(\(f(x)\)\) lies within the interval  \(\([-1, 0]\)\).

To learn more about function refer:

https://brainly.com/question/25638609

#SPJ11

Answer:  Hence sum of interior angles of a convex 16-sided polygon would be 180∘×(16−2)=180∘×14=2520∘

Step-by-step explanation:

Answer:

------------------------

To find the sum of the interior angles of a 16-sided polygon, you can use the formula:

In our case, n = 16.

Substitute the value of n into the formula:

The matching choice is D.

The correct scientific notation for the number 0.00050210 is 5.0210 x 10^(-4).

Here's a step-by-step explanation:

1. To convert a decimal number to scientific notation, we need to move the decimal point until we have a number between 1 and 10. In this case, we need to move the decimal point 4 places to the right to get 5.0210.

2. Next, we determine the power of 10 by counting the number of places we moved the decimal point. In this case, since we moved it 4 places to the right, the power of 10 is -4.

3. Finally, we write the number in the form of "a x 10^n", where "a" is the number between 1 and 10 (5.0210 in this case), and "n" is the power of 10 (-4 in this case).

So, the correct scientific notation for 0.00050210 is 5.0210 x 10^(-4).

to know more about scientific notation here:

brainly.com/question/19625319

#SPJ11

Question- The correct scientific notation for the number 0.00050210 is: a. 5.0210 x 10° b. 5.021 x 10 c. 5.021 x 10 d. 5.0210 x 10 e. None of the choices listed are correct.

The scientific notation for 0.00050210 is 5.0210 x 10^-4. It was calculated by moving the decimal point 4 places to the right, resulting in 5.0210, and then multiplying by 10 to the power of -4.

The given number is 0.00050210. We're trying to express it in scientific notation which is a shorthand way to write numbers that are either very large or very small by representing them as the product of a number (between 1 and 10) and a power of ten.

First, let's consider the number 0.00050210. We shift the decimal point 4 places to the right until we have a number that is between 1 and 10. So, we get 5.0210. Then, we multiply by 10 to the power of minus the number of places we moved the decimal (in this case, -4) to write the scientific notation.

So, the scientific notation of 0.00050210 is 5.0210 x 10^-4.

https://brainly.com/question/2005529

#SPJ11

The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.

1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".

2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".

Therefore, the value of the expression "true && !false" is "true".

to know more about expression here:

brainly.com/question/15994491

#SPJ11

Answer:56

Step-by-step explanation:bc thats the answer

Answer:

£16.25

Step-by-step explanation:

Jon. £9 to nearest pound so £9.50

Ellie. £6.50 to the nearest 50p so £6.75. £

9.5+6.75 = £16.25

From what we know about rounding, we will see that the possible total amount of money is given by the inequality:

£14.75 ≤ M ≤ £16.23

When we round a given number to a given place, what we need to do is look at the number at the right of that place.

So we know that Jon, to the nearest pound has £9.

We know that to the nearest £0.50, so we look at the half of 0.5, which is 0.25, for example:

1.23 would be rounded to 1.

1.25 would be rounded to 1.50

1.27 would be rounded to 1.50

Ellie has £6.50, then she has:

So, adding the minimums and maximums together we get:

minimum = £8.50 + £6.25 = £14.75

maximum  = £9.49 +  £6.54 =  £16.23

So the possible total amount of money, defined by M, is in the interval:

£14.75 ≤ M ≤ £16.23

If you want to learn more about rounding, you can read:

https://brainly.com/question/19288016

Answer:

The Answer would be C: (0,-2) and (4,0)

Step-by-step explanation:

Pls gib brainlist

The line y = (-1/3)x + 5 is perpendicular to the line y = 3x + 2.

To determine which lines are perpendicular to the line y = 3x + 2, we need to find the negative reciprocal of the slope of the given line.

The equation y = 3x + 2 is in slope-intercept form, where the coefficient of x represents the slope of the line.

In this case, the slope is 3.

To find the negative reciprocal of 3, we first take the reciprocal, which is 1/3.

Then, we change the sign to get the negative reciprocal, which is -1/3.

So, any line with a slope of -1/3 will be perpendicular to the line y = 3x + 2.

Let's consider a few examples:

y = (-1/3)x + 5:

This line has a slope of -1/3, so it is perpendicular to y = 3x + 2.

y = 2x - 1:

This line has a slope of 2, which is not the negative reciprocal of 3. Therefore, it is not perpendicular to y = 3x + 2.

y = (-1/6)x + 4:

This line has a slope of -1/6, which is not the negative reciprocal of 3. Hence, it is not perpendicular to y = 3x + 2.

For similar question on perpendicular.

https://brainly.com/question/1202004  

#SPJ11

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Market researchers want to know what factors influence customers to spend more time in a shop. They have estimated the probability density function of the time spent in the shop to be f(x) = { sin(πx/40)/20, 0 ≤ x ≤ 40}. Using the symmetry of f(x), the expected value of time spent in the shop can be calculated to be 20 minutes.

The market researchers are interested in understanding what makes customers stay longer in the shop. To do this, they have estimated the probability density function of the time spent in the shop to be f(x) = { sin(πx/40)/20, 0 ≤ x ≤ 40}.

The expected value of time spent in the shop can be calculated by finding the mean of the probability density function. As the function is symmetric around x = 20, we can use the symmetry to simplify the computation. This gives us:

E(T) = ∫₀⁴₀ x f(x) dx = 2 ∫₀²₀ x f(x) dx

= 2 ∫₀²₀ x sin(πx/40)/20 dx

= (1/π) ∫₀⁴₀ 40t sin(t) dt (where t = πx/40)

= (1/π) [40 sin(t) - 40t cos(t)] from t = 0 to t = π

= (1/π) [40 sin(π) - 40(π) cos(π) - 40 sin(0) + 40(0) cos(0)]

= 20

Therefore, the expected value of time spent in the shop is 20 minutes.

The researchers plan on interviewing customers who spend more than one standard deviation longer or shorter than the expected value of time spent in the shop. The standard deviation can be calculated using the formula:

σ = √[∫₀⁴₀ (x - 20)² f(x) dx]

= √[2 ∫₀²₀ (x - 20)² f(x) dx]

= √[2 ∫₀²₀ (x² - 40x + 400) sin(πx/40)/800 dx]

= √[(1/π²) ∫₀⁴₀ (t² - 80t + 1600) sin(t) dt] (where t = πx/40)

= √[(1/π²) (π/2)]

= √(2/π)

≈ 0.7979

Therefore, the researchers will ask a customer for an interview if they spend more than 20 + 0.7979 × 1 = 20.7979 minutes or less than 20 - 0.7979 × 1 = 19.2021 minutes in the shop.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ11

The number of bracelets is 4.

The number of bracelets is 8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Number of bracelets = x

Number of necklaces = y

Amount of gold in each bracelet = 8 grams

Amount of gold in each necklace = 16 grams

Now,

x + y = 12 _____(1)

x = 12 - y ____(2)

8x + 16y = 160 ______(3)

Substituting (2) in (3) we get,

8(12 - y) + 16y = 160

96 - 8y + 16y = 160

96 + 8y = 160

8y = 160 - 96

8y = 64

y = 8

Now,

x = 12 - y

x = 12 - 8

x = 4

Thus,

The number of bracelets and necklaces that were made is 4 and 8.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Sam travels on the highway for approximately 1.4 hours.

We know that Sam's total travel time is 1.5 hours plus the time he spends on the highway, which we'll call "x" hours. So his total travel time can be represented as:

Total travel time = 1.5 + x

We also know that the total distance he travels is 140 miles. We can use the formula:

distance = rate x time

to set up two equations, one for his travel on city roads and one for his travel on the highway. Let's start with the city roads:

distance = rate x time

distance = 35 mph x 1.5 hours

distance = 52.5 miles

So Sam travels 52.5 miles on city roads, which means he still has to travel:

140 miles - 52.5 miles = 87.5 miles

on the highway. Now we can set up an equation for his travel on the highway:

distance = rate x time

87.5 miles = 65 mph x x hours

Solving for x, we get:

x = 87.5 miles / (65 mph)

x ≈ 1.35 hours

Learn more about distance here

brainly.com/question/4931057

#SPJ4

I have solved the question in general, as the given question is incomplete:

The complete question is:

Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads , on which can he travel an average of 35 mph for a total of 1.5 hours . Sam also takes the highway , on which he travels an average of 65 mph for a total of x hours . approximately how long does Sam travels on the highway , to the nearest tenth of an hour ?

Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

#SPJ1

Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Option (E) is the correct answer.

The authors of both passages mention chimpanzees in order to : provide an example of an animal considered to be highly intelligent.

Both passages discuss dogs' intelligence, whether they are intelligent or not, and frequently make a comparison between a dog's intelligence and a chimpanzee's (an animal whom both the authors consider to be highly intelligent).

Intelligence is widespread in the animal kingdom. Chimpanzees, for instance, are incredibly intelligent. They can demonstrate compassion, use tools, and have great memories and are social beings that exhibit traits like empathy, altruism, self-awareness, cooperation in problem solving, and learning by doing. They also appear to be able to learn from examples and experiences. In some memory tests, chimpanzees even outperform humans. Therefore, the best response to the question in this scenario is Option E.

Find more on animal's intelligence related problems at : brainly.com/question/18887406

#SPJ4

Answer:

feknienveve

Step-by-step explanation:

enineivneuinvruneuvnur

Answer:

It would take him 11 hours.

Step-by-step explanation:

What you want to do is found out how many miles he drove in 1 hour. In order to do that, divide 189 by 7. By doing that, you get the answer of 27. Now that you have how much he drove in 1 hour. To find out how much it would take him to drive 297 miles, you also divide 297 by 27 to get 11. Which means that it would take him 11 hours to drive 297 miles. I hope this was helpful.

Answer:

300

Step-by-step explanation:

Answer: 55

Step-by-step explanation:

Let the number of cars washed last year be denoted as x.

This year, he washed 14 fewer cars than during last year's car wash. This will be denoted as x-14.

We can then represent them in an equation as:

x + (x - 14) = 96

2x - 14 = 96

2x = 96 + 14

2x = 110

x = 110/2

x = 55

Therefore, he washed 55 cars this year

Answer:

40%

Step-by-step explanation:

(850-510)/850 = 340/850 = 2/5 = 40%

Answer: 40% I looked it up

Step-by-step explanation:

The formula for calculating the required sample size to estimate the population mean with a 90% confidence level is given by:

n = ((z_(α/2)×σ) / E)²Here, z_(α/2) is the z-value for the given level of confidence (90% in this case), σ is the population standard deviation (6.8 in this case), and E is the maximum error we can tolerate (0.02 in this case).

Substituting the given values in the formula, we get:

n = ((z_(α/2)×σ) / E)²n = ((1.645×6.8) / 0.02)²n = 1910.96

Rounding up to the nearest whole number, we get the required sample size to be 1911.

Therefore, a sample size of 1911 is required to estimate the population mean with a 90% confidence level and an error of less than 0.02.

To know more about sample size visit:

https://brainly.com/question/30100088

#SPJ11

The probability of obtaining the number of successes indicated in problems 51–58 is 0.42.

Probability is absolutely how in all likelihood something is to happen. every time we're unsure about the final results of an occasion, we can talk about the chances of sure results—how in all likelihood they may be. The analysis of occasions ruled by using probability is called facts.

The opportunity of an event may be calculated with the aid of the opportunity formula by means of truly dividing the favorable wide variety of results by way of the overall variety of feasible effects.

Probability is the department of mathematics regarding numerical descriptions of ways possibly an occasion is to occur, or how likely it's miles that a proposition is actual. The chance of an event is more than a few between zero and 1, in which, roughly talking, 0 shows the impossibility of the event and 1 suggests fact.

Cells x doute the no of surrell and

"p' denotes the probability of turrets

D= 5

H=pkin = 50-xo-5 = 250

σ = SD(X) = √√rbg

= √√5=x05x=5 = 14.№33

The probability of obtaining $45-26

= P(-5-250 < x-M 22605-250)

14.233

= P(-03864 < 2 2 0-7332)

8.4200

0.42

Learn  more about probability  here https://brainly.com/question/14192140

#SPJ4

Answer:

The bottom right.

Step-by-step explanation:

Hope its correct.

Answer:

D

Step-by-step explanation:

Answer:

x=16/3

Step-by-step explanation:

4=3/4x+0

4=3x/4

4=3x/2square

4times4=16

3x/3=16/3

x=16/3

From the probability, the quantity of various passwords that are conceivable assuming each character might be any lowercase letter or digit is 2,821,109,907,456 passwords

The most effective method to ascertain the probability

The accompanying information can be concluded:

Number of lower case letters = 26

Number of digits = 10

Total Characters = 26 + 10 = 36

Length of secret word = 8

The quantity of various passwords are conceivable assuming each character might be any lowercase letter or digit will be:

= (26+10)⁸ various passwords

= 2,821,109,907,456 passwords

The quantity of various passwords that are conceivable assuming each character might be any lowercase letter or digit, and something like one person should be a digit will be:

= 36⁸ - 26⁸

= 2,612,282,842,880 passwords

Finally, the probability that a substantial secret phrase will be produced will be:

= (36⁸ - 26⁸)/36⁸

= 0.93

to know more about probability click here:

https://brainly.com/question/25870256

#SPJ4