3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box?

  The probability of winning a 4/19 lottery game where 4 numbers are picked from a range of 19 = 0.00135

The probability of winning a 4/19 lottery game is 0.00135.

This is because the probability of winning is the number of possible combinations divided by the total number of possible combinations.

In this case, there are 4^4 (256) possible combinations, and 19^4 (38416) total combinations.

So, 0.00135 = 256/38416.

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability. The probability of an impossible event is 0; that of an event that is certain to occur is 1.

The probabilities of two complementary events A and B – either A occurs, or B occurs – add up to 1. A simple example is the tossing of a fair (unbiased) coin. If a coin is fair, the two possible outcomes ("heads" and "tails") are equally likely; since these two outcomes are complementary and the probability of "heads" equals the probability of "tails", the probability of each of the two outcomes equals 1/2 (which could also be written as 0.5 or 50%).

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9) If point ( x , y) rotates 90◦ clockwise about the origin. Then,

(x , y)------> (y,-x)

B (-2,0)-------> B’(0,2)

C (-4, 3) -------->C’ (3,4)

Z (-3, 4) --------->Z’ (4,3)

X (-1, 4) --------->X’ (4,1)

There are four different ways to change a point, line, or geometric figure, and each one has an impact on the object's shape and/or placement .The Pre-Image refers to the object's initial shape, and the Image, after the transformation, refers to the object's ultimate shape and location.

Hence, transformation of an equation into another equation whose roots are opposite of the roots of a provided equation in which we replace xx3.

10) Reflection across y=x. K(-5,-2) , A(-4,1) , I(0,-1) , J(-2,-4)

Reflection across y=x

(x , y)------> (y, x)

K (-5,-2) -------> K’(-2,-5)

A (-4, 1) -------> A’(1,-4)

I (0,-1) -------> I’(-1,0)

J (-2,-4) -------> J’(-4,-2)

Transformations can be divided into four categories: translation, rotation, reflection, and enlargement.

Hence, transformation of an equation into another equation whose roots are reciprocals of the roots of a given equation in which we replace xx1.

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Answer:

R=12/0.5 - 24 ohms

Step-by-step explanation:

If a divides b and a divides c, then a divides (bm + cn).

To prove that if a divides b and a divides c, then a divides (bm + cn), we can use the properties of divisibility.

Given:

a|b, which means b is divisible by a.

a|c, which means c is divisible by a.

We want to show that a|(bm + cn), which means (bm + cn) is divisible by a.

By definition, if a divides b, then there exists an integer k₁ such that b = ka. Similarly, if a divides c, there exists an integer k₂ such that c = ka.

Now, let's substitute these expressions into (bm + cn):

(bm + cn) = (ka)m + (ka)n

= kam + kan

= a(km + kn)

We can see that (bm + cn) can be written as a times the integer (km + kn). Since (km + kn) is an integer, this implies that (bm + cn) is divisible by a.

Therefore, if a divides b and a divides c, then a divides (bm + cn).

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Answer:

8 x (5 - 2) = ( 8 x 5) - ( 8 x 2)

Step-by-step explanation:

8 x (5 - 2) = ( _ x 5) - ( _ x 2)

Distribute

8 x (5 - 2) = ( 8 x 5) - ( 8 x 2)

Answer: Since 343 is a perfect CUBE, the length of each edge of the BLOCK can be found. Each edge is 7 centimeters long.

Step-by-step explanation: 7×7×7=343

Answer:

96

Step-by-step explanation:

12 x 8 = 96

Answer:

m>-3

Step-by-step explanation:

6-9 = -3

m>-3

Answer: 24

Step-by-step explanation:

If I am correct I'm pretty sure its about 24 sorry is I am wrong

Answer:

about 24

Step-by-step explanation:

the length is like 6 ½

and the the width is almost 4

It took Michelle approximately 16 years to pay off her loan.

We have,

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal amount (initial loan)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We can rearrange this formula to solve for t:

t = ln(A/P) / (n * ln(1 + r/n))

Plugging in the given values.

t = ln((12500 + 9425)/12500) / (1 * ln(1 + 0.0754/1))

t = ln(1.753) / (ln(1.0754))

t = 16.02

Thus,

It took Michelle approximately 16 years to pay off her loan.

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By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25

The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1

Let us solve this problem by applying the Kuhn-Tucker theorem.

Let us first write down the Lagrangian function:

L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)

Then, we find the first order conditions for a maximum:

Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0

Ly = x - 8λ₁y - 2λ₁x = 0

Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0

Lλ₂ = 2x - y + 1 = 0

The complementary slackness conditions are:

λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0

λ₂(2x - y + 1) = 0

Now, we solve for the above equations one by one:

From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1

Substitute this in equation (1), we get:

8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0

Simplifying, we get:

10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)

From equation (2), we can write x = 8λ₁y + 2λ₁x

Substitute this in equation (1), we get:

8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0

Simplifying, we get:

-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)

Solving equations (4) and (5) for λ₁ and λ₂, we get:

λ₁ = 1/20 and λ₂ = 9/100

Then, substituting these values in the first order conditions, we get:

x = 2/5 and y = 9/5

Therefore, the maximum value of xy is:

2/5 x 9/5 = 18/25

Hence, the required answer is 18/25.

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Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

9514 1404 393

Answer:

  (x, y, z) = (x, x+2, 3x+1)

Step-by-step explanation:

We can add twice the second equation to the first to get ...

  [eq4] -3x +0y +z = 1

Adding the first and second equations gives ...

  [eq5] -x +y +0z = 2

Solving [eq4] for z gives ...

  z = 3x +1

Solving [eq5] for y gives ...

  y = x +2

Then the solution triple is (x, y, z) = (x, x+2, 3x+1).

The example of a  hypothesis is: a person is innocent until proven guilty. The statement is true

Here the given situation is

A person is innocent until proven guilty.

The hypothesis test is defined as the test in statistics whereby an analyst tests an assumption regarding a population parameter. In hypothesis test using the data from the different types of t sample and the determine the other parameters of the population

The null hypothesis is defined as the a statement of what the statistician expects NOT to find.

Here the given situation is a person is innocent until proven guilty. Therefore, it is a null hypothesis.

In hypothesis test we assume that null hypothesis until it is proven

Therefore, the given statement true

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The mean of the data set is approximately 3.778. And the median is 5, and the mode is also 5.

The mean, median, and mode of the given data set -3, 4, 5, 5, -2, 7, 1, 8, are as follows:

Mean: The mean is the average value of a set of numbers. To find the mean, we sum up all the numbers in the dataset and divide the sum by the total number of values. In this case, the mean is \(\frac{( -3 + 4 + 5 + 5 + -2 + 7 + 1 + 8 + 9 ) }{9} = \frac{34 }{ 9}\) ≈ 3.778.

Median: The median is the middle value when the data set is arranged in ascending or descending order. In this case, the data set arranged in ascending order is -3, -2, 1, 4, 5, 5, 7, 8, 9. Since the data set has an odd number of values, the median is the middle value, which is 5.

Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is 5 because it appears twice, more frequently than any other number in the data set.

To summarize, the mean of the data set is approximately 3.778, the median is 5, and the mode is also 5.

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The equivalent exponential decay function is given as m(t) = 10000\((0.729)^{t}\)

What is an exponential function?

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Mathematical functions with exponents include exponential functions. f(x) = bx, where b > 0 and b 1, is a fundamental exponential function.

Here, we have

Given: The value of a car that depreciates over time can be modeled by the function M(t) = 10000\((0.9)^{3t}\)

An exponential function is in the form

y = abˣ

where y and x are variables, a is the initial value of y, and b is the multiplier.

Let m(t) represent the value of the car after t years, hence the exponential decay is given by:

m(t) = \(10000(0.9)^{3t}\)

m(t) = 10000\((0.9)^{3(t)}\)

m(t) = 10000\((0.729)^{t}\)

Hence, The equivalent exponential decay function is given as m(t) = 10000\((0.729)^{t}\)

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In conclusion, 95.4% of students have GMAT scores between 400 and 800.

Calculate z score need to find the proportion of scores that fall within the range of 400 to 800.

\(z=\frac{x- mean}{standard deviation}\)

This formula tells us how many standard deviations away from the mean a given score is.

Given:

Mean= 600

Standard deviation = 100.

For the 400 scores:-

\(z=\frac{400-600}{100} \\z= -2\)

For the 800 scores:-

\(z=\frac{800-600}{100} \\z=2\)

Now we will use the standard normal distribution table to find the percentage of values between -2 and 2.

According to the standard normal distribution table, the percentage of values between -2 and 2 is approximately 95.45%.

Therefore, approximately 95.45% of students have GMAT scores between 400 and 800.

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Answer: The answer is -1

Step-by-step explanation:

-4(y - 2) = 12

-4y + 8 = 12

      - 8   - 8

_____________

  -4y  =  4

  ________

  -4        -4

      y = -1

7.54 and 0.46 are the solutions to the given quadratic equations

Given the quadratic equation below:

x^2-18x+8=0

We need to determine the solutions to the given quadratic expression. Using the general formula below:

x = -b±√b²-4ac/2a

From the equation

a = 1

b = -18

c = 8

Substitute

x = 18±√18²-4(1)(8)/2(1)
x= 18±√324-32/2

x =18± 17.08/2

x = 35.08/2 and 0.92/2

x = 17.54 and 0.46

Hence the two solutions to the given quadratic equation are 17.54 and 0.46

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Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer:

\(\textsf{B)} \quad \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)=280x^6y^{13}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}\\\end{minipage}}\)

Given expression:

\((2x^2y^3+y)^7\)

Therefore:

Therefore:

\(\displaystyle (2x^2y^3+y)^7=\sum^{7}_{k=0}\binom{7}{k} (2x^2y^3)^{7-k}(y)^{k}\)

To find the 4th term in the binomial expansion, substitute k = 4 into the equation:

\(\implies \displaystyle \sum^{7}_{k=0}\binom{7}{4} \left(2x^2y^3\right)^{7-4}\left(y\right)^{4}\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{(7-4)!4!} \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(35 \cdot 8x^6y^9y^4\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(280x^6y^{13}\right)\right)\)

Therefore, the expression that correctly shows how to use the binomial theorem to determine the 4th term in the expansion is:

\(\displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)=280x^6y^{13}\)

Answer:

P(t)=25000(1.12)^t

Step-by-step explanation:

only answering so i can go back to not watching ads :/ but hope u dont get it wrong even tho i gave right answer

Answer:

P(t) = 25000 x 1.12^t

Step-by-step explanation:

25000 times 1.12 because it is increasing by a factor of 1.12.

Yes, the electron pair repulsion determines the molecular shape, we can use  VSEPR to find out how.

What is VSEPR theory?

The amount of valence electron pairs present in the outermost shell is used by the valence shell electron repulsion theory (VSEPR) to predict the structure of molecules.

The number of valence shell electron bond pairs between atoms in a molecule is used in the valence shell electron repulsion theory (VSEPR), a model for predicting 3D molecular form.

VSEPR theory predicts that BeF2 should be a linear molecule, with a 180o angle between the two Be-F bonds.

The VSEPR theory, therefore, predicts a trigonal planar geometry for the BF3 molecule, with an F-B-F bond angle of 120o.

we can predict that a tetrahedral molecule in which the H-C-H bond angle is 109o28'.

Hence we can predict the molecular shape, using VSEPR theory.

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Step-by-step explanation:

just multiply.

you apply a fraction to a quantity by multiplying the fraction with the quantity.

a.

2/3 of 3/4 = 2/3 × 3/4 = 6/12 = 1/2

b.

2/5 of 3/4 = 2/5 × 3/4 = 6/20 = 3/10

c.

2/5 of 4/5 = 2/5 × 4/5 = 8/25

d.

4/5 of 3/4 = 4/5 × 3/4 = 12/20 = 3/5

this is what I got for it

Answer:

Step-by-step explanation:

Because we have 3 unknowns, we need to come up with 3 equations. If the total number of animals is 440 and that number is made up of a combination of goats (g), ducks (d), and chickens (c) the first equation is

g + d + c = 440

The next equation is found in the fact that the number of ducks is one-quarter the number of chickens:

\(d=\frac{1}{4}c\) and solving for c gives us that

c = 4d

The last equation says that of the total number of animals, 440, half the goats and half the ducks got away, leaving only 320 animals behind. The last equation, the tricky one, is:

\(440-\frac{1}{2}g-\frac{1}{2}d=320\) and simplifying that:

\(-\frac{1}{2}g-\frac{1}{2}d=-120\) and because nobody hates fractions more than I do, I'm going to get rid of them by multiplying everything by 2 to get:

-g - d = -240

We've got these equations now, but what I'm going to do is to sub in what c equals (c = 4d) for c in the first equation:

 g + d + 4d = 440 and

 g + 5d = 440 and pair that with the one right above:

-g -  1d = -240 and use elimination to solve. The g's cancel each other out, leaving us with 4d = 200 and d = 50. So there were 50 ducks originally. Now we will sub that in to solve for c:

c = 4d so

c = 4(50) and

c = 200. Now we will sub both those values into the very first equation we put together to solve for g:

g + 200 + 50 = 440 and

g + 250 = 440 so

g = 190.

Add them all together just to be sure we have the 440 that we were told we had in the beginning (and we do, so we're all done!)

Step-by-step explanation:

The block of wood is 3cm on each side so it is a cube.

The volume of a cube is given by s^3. So the volume of this block is 3cm x 3cm x3 cm = 27 cm^3.

density = mass/volume =27 g / 27 cm^3 = 1 g/cm^3.

the answer is 1 g/cm^3. I hope this helps!

Answer:

8.50

Step-by-step explanation:

it’s 8.50 this is because if you need to round it to the nearest tenth, you just think is 9 closer to 10? Yes and so you make 48 into 8.50