PLEASE HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answer:

25.9422 rounded to the nearest hundredth is 25.94.

Answer:

Step-by-step explanation:

The required sample size is determined by finding the z-score that corresponds to a 90% confidence interval and then using that z-score to calculate the sample size. In this case, the z-score is 2.24 and the sample size is 467.

In order to determine the required sample size to be 90% certain that we are within 4 IQ points of the true mean, we must first calculate the z-score that corresponds to a 90% confidence interval. This z-score is calculated by subtracting the lower bound of the interval from the mean, and then dividing this difference by the standard deviation. In this case, the z-score is 2.24. We then use this z-score to calculate the required sample size, which is calculated by taking the z-score, squaring it, and then multiplying it by the sample variance. In this case, the sample size is 467. This means that we need at least 467 samples in order to be 90% certain that we are within 4 IQ points of the true mean.

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Given:

Number of tomatoes Sheldon picks = \(4\dfrac{4}{10}\) kg

Rotten tomatoes = 1.5 kg

To find:

How many kilograms of tomatoes were not rotten?

Solution:

Number of tomatoes Sheldon picks = \(4\dfrac{4}{10}\) kg

                                                            = \(\dfrac{4(10)+4}{10}\) kg

                                                            = \(\dfrac{40+4}{10}\) kg

                                                            = \(\dfrac{44}{10}\) kg

                                                            = \(4.4\) kg

Rotten tomatoes = 1.5 kg

Remaining tomatoes which are not rotten is

Required tomatoes = Tomatoes Sheldon picks - Rotten tomatoes

                                = \(4.4-1.5\)

                                = \(2.9\) kg

Therefore, the tomatoes which were not rotten is 2.9 kg.

Answer:5 I think

Step-by-step explanation:

75-35=40 40 divided by 8 is 5

Answer:

The answer is 5=x (he is able to buy 5 videogames)

Step-by-step explanation:

First, you need to put this into an equation format with a variable (x) for the videogames. Here is what the equation should look like: 75 = 35 + 8x

75 being the total amount of money he has to spend, 35 being what he had to spend or knows he will spend on the controller, and the 8 is for each videogame. We put an 'x' behind the 8 to signal that we don't know how many games he can buy. So, then we need to solve the equation.

75=35+8x

-35 on both sides

So, 40=8x, then you divide by 8 to get x by itself

5=x

The 'x' in this equation is how many videogames he is able to buy. The way you could check your work is if you plugged 5 back into x. What I mean is this: 35+8(5) needs to equal 75, and it does, so you're good!

The function is cosine. The argument of the function is 4π/3. The function value is -0.5.

The cosine function is a periodic function that has a period of 2π. This means that the value of the cosine function repeats every 2π radians. The argument of the cosine function is the angle in radians.

When the argument of the cosine function is 4π/3, the value of the function is -0.5. This can be found using the unit circle. The unit circle is a circle with radius 1. The cosine of an angle is the x-coordinate of the point on the unit circle that is radians counterclockwise from the positive x-axis.

When the angle is 4π/3, the point on the unit circle is (-0.5, 0.866). This means that the cosine of 4π/3 is -0.5.

Therefore, the answer to the question is:

Function: cosine

Argument: 4π/3

Function value: -0.5

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The solution of the given system of equations is (-2, -4).

The given system of equations is:x² + 6x + 8 = 0x + 4 = 0To solve the system using graphing, follow the given steps below:Step 1: Graph both the equations on the same coordinate axes. For this, rewrite the given quadratic equation as y = x² + 6x + 8. Then, draw the graphs of y = x² + 6x + 8 and y = -4 on the same coordinate plane. The graphs of both equations intersect at x = -2. Therefore, the solution of the system is (-2, -4).

The graph of y = x² + 6x + 8 is given below: The graph of y = -4 is a straight horizontal line passing through the point (-4, 0).The graph of both the equations on the same coordinate axes is given below: Step 2: Identify the point of intersection of the graphs. The point of intersection of the graphs is the solution of the system. Therefore, the solution of the system is (-2, -4).

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The chosen values are:

a) h = 2 (no solution), any k

b) h ≠ 2 (unique solution), any k

c) h = 2 (many solutions), k = 16

To determine values of h and k that result in different solution scenarios for the given systems of equations, we can analyze the coefficient matrices and their determinants.

System 1:

x1 + h*x2 = 2

4x1 + 8x2 = k

a) For the system to have no solution, the coefficient matrix's determinant must be zero, while the augmented matrix's determinant is nonzero.

Taking the determinant of the coefficient matrix, we have:

| 1 h |

| 4 8 |

Determinant = (1 * 8) - (4 * h)

                     = 8 - 4h

For the system to have no solution, the determinant 8 - 4h must be zero. So we solve:

8 - 4h = 0

h = 2

Therefore, for no solution, h = 2. We can choose any value for k.

b) For the system to have a unique solution, the coefficient matrix's determinant must be nonzero.

So we need to ensure that 8 - 4h ≠ 0.

Choosing h ≠ 2 will satisfy this condition. We can choose any value for k.

c) For the system to have many solutions, the coefficient matrix's determinant must be zero, and the augmented matrix's determinant must also be zero.

For this case, we can choose h = 2 (as determined in part a), and k such that the augmented determinant is also zero.

For example, we can choose k = 16, which satisfies the equation 4 * 2 - 8 * 16 = 0.

Therefore, the chosen values are:

a) h = 2 (no solution), any k

b) h ≠ 2 (unique solution), any k

c) h = 2 (many solutions), k = 16

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This expression represents the division of 25 by 3.

a. 25/3 = 8.333...

b. 20 - 12/4 * 2 = 14

c. 32 % 7 = 4

d. 3 - 5 % 7 = -2

e. 18.0/4 = 4.5

f. 28 - 5/2.0 = 25.5

g. 17 + 5 % 2 - 3 = 15

h. 15.0 + 3.0 * 2.0 / 5.0 = 16.2

a. 25/3:

This expression represents the division of 25 by 3.

25/3 = 8.333...

b. 20 - 12/4 * 2:

Following the order of operations (parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right):

12/4 = 3

3 * 2 = 6

20 - 6 = 14

c. 32%7:

The % symbol represents the modulo operation (remainder after division).

32 % 7 = 4

d. 3 - 5%7:

Following the order of operations:

5 % 7 = 5 (since 5 divided by 7 leaves a remainder of 5)

3 - 5 = -2

e. 18.0/4:

This expression represents the division of 18.0 by 4.

18.0/4 = 4.5

f. 28 - 5/2.0:

Following the order of operations:

5/2.0 = 2.5 (division with floating-point numbers)

28 - 2.5 = 25.5

g. 17 + 5%2 - 3:

Following the order of operations:

5 % 2 = 1 (since 5 divided by 2 leaves a remainder of 1)

17 + 1 - 3 = 15

h. 15.0 + 3.0 * 2.0/5.0:

Following the order of operations:

3.0 * 2.0 = 6.0

6.0 / 5.0 = 1.2

15.0 + 1.2 = 16.2

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Answer:

20 grams is the same as option (a) 2000 mg.

Step-by-step explanation:

To convert grams to milligrams, you multiply the value in grams by 1000 because there are 1000 milligrams in one gram. Therefore, 20 grams is equal to 20 * 1000 = 2000 milligrams.

20 grams is equal to 20000 mg.

20 grams is equivalent to 20000 mg. To convert grams to milligrams, you need to multiply the number of grams by 1000 since there are 1000 milligrams in one gram. So, 20 grams multiplied by 1000 equals 20000 milligrams.

This question is regarding the conversion of grams (a metric unit of weight) to milligrams. 1 gram is equivalent to 1000 milligrams. Therefore, to convert 20 grams to milligrams, you would multiply 20 (the number of grams) by 1000 (the number of milligrams in 1 gram).

20 grams * 1000 = 20000 milligrams

So, 20 grams is the same as 20000 milligrams, which means the correct answer to your question is b. 20000 mg.

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The differentiation dy/dx of tan(x/y) = x + 6 is given by (tan(x/y) - 6 * (dy/dx)) / (1 - (x/y) * (sec^2(x/y) * (1/y))).

To evaluate the limit limx→1 \((x^1000 - 1)\)/ (x - 1), we can notice that the expression \(x^1000\) - 1 can be factored using the difference of squares formula: \(a^2 - b^2 = (a - b)(a + b).\)

So we have:

limx→1 \((x^1000 - 1) / (x - 1)\)

= limx→1 \([(x^500 - 1)(x^500 + 1)] / (x - 1)\)

Now, we can cancel out the common factor of (x - 1) in the numerator and denominator:

= limx→1 (x^500 + 1)

Substituting x = 1 into the expression, we get:

= 1^500 + 1

= 1 + 1

= 2

Therefore, the limit limx→1 (x^1000 - 1) / (x - 1) is equal to 2.

Regarding the differentiation dy/dx of tan(x/y) = x + 6, we need to use the quotient rule to differentiate implicitly.

First, let's rewrite the equation as y = x * tan(x/y) - 6y.

Differentiating implicitly, we have:

dy/dx = (d/dx)[x * tan(x/y)] - (d/dx)[6y]

Using the quotient rule on the first term:

(d/dx)[x * tan(x/y)] = tan(x/y) + x * (d/dx)[tan(x/y)]

To differentiate the tangent function, we use the chain rule:

(d/dx)[tan(x/y)] = sec^2(x/y) * (d/dx)[x/y]

= sec^2(x/y) * (1/y) * dy/dx

Substituting these derivatives back into the equation, we have:

dy/dx = tan(x/y) + x * (sec^2(x/y) * (1/y) * dy/dx) - (d/dx)[6y]

Now, let's solve for dy/dx by isolating the term:

dy/dx - (x/y) * (sec^2(x/y) * (1/y) * dy/dx) = tan(x/y) - (d/dx)[6y]

Factor out dy/dx:

dy/dx * (1 - (x/y) * (sec^2(x/y) * (1/y))) = tan(x/y) - (d/dx)[6y]

Combine the derivative of y with respect to x:

dy/dx * (1 - (x/y) * (sec^2(x/y) * (1/y))) = tan(x/y) - 6 * (dy/dx)

Multiply through by (y / (y - x * sec^2(x/y))):

dy/dx * (y / (y - x * sec^2(x/y))) * (1 - (x/y) * (sec^2(x/y) * (1/y))) = (tan(x/y) - 6 * (dy/dx)) * (y / (y - x * sec^2(x/y)))

Simplifying the equation:

dy/dx = (tan(x/y) - 6 * (dy/dx)) * (y / (y - x * sec^2(x/y))) / (y / (y - x * sec^2(x/y))) * (1 - (x/y) * (sec^2(x/y) * (1/y)))

dy/dx = (tan(x/y) - 6 * (dy/dx)) / (1 - (x/y) * (sec^2(x/y) * (1/y)))

Therefore, the differentiation dy/dx of tan(x/y) = x + 6 is given by (tan(x/y) - 6 * (dy/dx)) / (1 - (x/y) * (sec^2(x/y) * (1/y))).

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Performing a change of scale we will see that the actual distance is 4 miles.

We know that the scale is:

3/4 inch = 2 miles.

And the distance that Nicole found on the map is (1 + 1/2) inches.

We can rewrrite the scale as:

1 inch = (4/3)*2 miles

1 inch = (8/3) miles.

Then the actual distance will be:

distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.

The correct option is A.

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Answer:

$90

Step-by-step explanation:

Sorry to ask but can I have brainliest

There are 2002 different subsets of 5 students that can be selected from a classroom of 20. To calculate this, you can use the binomial coefficient formula.

The binomial coefficient is equal to nCr, where n is the total number of objects (in this case 20 students) and r is the number of objects you want to select (in this case 5 students).

Using the binomial coefficient, we can calculate that there are 20C5 = 2002 different subsets of 5 students that can be selected from a classroom of 20.

nCr = 20C5

20C5 = 20! / ((20-5)! 5!)

20! = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

5! = 5 x 4 x 3 x 2 x 1

20C5 = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / (5 x 4 x 3 x 2 x 1 x 15 x 14 x 13 x 12 x 11) = 2002

Therefore, there are 2002 different subsets of 5 students that can be selected from a classroom of 20.

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The residue of function \(\(f(z) = z^2 \sin\left(\frac{1}{z}\right)\)\) at singularity z = 0 is 1 and the function \(\(f(z) = \frac{\sinh z}{\cosh z}\)\) has no residue at the singularities \(\(z = (2n+1)\frac{\pi}{2}i\)\)  where \(\(\cosh z = 0\)\).

a) To compute the residue of the function \(\(f(z) = z^2 \sin\left(\frac{1}{z}\right)\)\) at the singularity z = 0, we can use the Laurent series expansion of the function around that point.

The Laurent series expansion of \(\(\sin\left(\frac{1}{z}\right)\)\) can be written as:

\(\[\sin\left(\frac{1}{z}\right) = \sum_{n=0}^{\infty} (-1)^n \frac{1}{(2n+1)!}\frac{1}{z^{2n+1}}\]\)

Multiplying this series by z², we have:

\(\(z^2 \sin\left(\frac{1}{z}\right) = \sum_{n=0}^{\infty} (-1)^n \frac{1}{(2n+1)!}\frac{1}{z^{2n-1}}\)\)

Now, we can see that the coefficient of  \(\(\frac{1}{z}\)\)  in this series is 0, and the coefficient of  \(\(\frac{1}{z^2}\)\) is 1.

Thus, the residue of (f(z)) at (z = 0) is 1.

b) To compute the residue of the function \(\(f(z) = \frac{\sinh z}{\cosh z}\)\) at the singularities, we need to identify the singular points of the function.

The function (cosh z) has a singularity when (cosh z = 0), which occurs at \(\(z = (2n+1)\frac{\pi}{2}i\)\)  for \(\(n \in \mathbb{Z}\)\).

At these singularities, the denominator becomes zero, and we need to examine the behavior of the function to compute the residues.

Considering the limit of (f(z)) as (z) approaches each singularity, we can evaluate:

\(\[\lim_{{z \to (2n+1)\frac{\pi}{2}i}} f(z) = \frac{\sinh((2n+1)\frac{\pi}{2}i)}{\cosh((2n+1)\frac{\pi}{2}i)}\]\)

Now, we know that \(\(\sinh(z) = \frac{1}{2}(e^z - e^{-z})\)\) and

Substituting these expressions into the limit, we have:

\(\[\lim_{{z \to (2n+1)\frac{\pi}{2}i}} f(z) = \frac{\frac{1}{2}(e^{(2n+1)\frac{\pi}{2}i} - e^{-(2n+1)\frac{\pi}{2}i})}{\frac{1}{2}(e^{(2n+1)\frac{\pi}{2}i} + e^{-(2n+1)\frac{\pi}{2}i})}\]\)

The numerator can be written as:

\(\[\frac{1}{2}(e^{(2n+1)\frac{\pi}{2}i} - e^{-(2n+1)\frac{\pi}{2}i}) = \frac{1}{2}(i^{2n+1} - (-i)^{2n+1}) = \frac{1}{2}(i - (-i)) = i\]\)

The denominator can be written as:

\(\[\frac{1}{2}(e^{(2n+1)\frac{\pi}{2}i} + e^{-(2n+1)\frac{\pi}{2}i}) = \frac{1}{2}(i^{2n+1} + (-i)^{2n+1}) = \frac{1}{2}(i + (-i)) = 0\]\)

Therefore, we have a removable singularity at \(\(z = (2n+1)\frac{\pi}{2}i\)\) because the numerator is nonzero and the denominator is zero.

At these singularities, the function can be extended analytically, and there is no residue.

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Answer:

Johann Peter Gustav Lejeune Dirichlet (German: [ləˈʒœn diʀiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician who made contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis

Answer:

\(\frac{d}{dx}\left(y\right)=\frac{2-6x+6y}{-6x+2y+1}\)

Step-by-step explanation:

\(3x^2-6xy+y^2=2x-y\\\mathrm{Treat\:}y\mathrm{\:as\:}y\left(x\right)\\\mathrm{Differentiate\:both\:sides\:of\:the\:equation\:with\:respect\:to\:}x\\\frac{d}{dx}\left(3x^2-6xy+y^2\right)=\frac{d}{dx}\left(2x-y\right)\\\frac{d}{dx}\left(3x^2-6xy+y^2\right)=6x-6\left(y+x\frac{d}{dx}\left(y\right)\right)+2y\frac{d}{dx}\left(y\right)\\\frac{d}{dx}\left(2x-y\right)=2-\frac{d}{dx}\left(y\right)\\6x-6\left(y+x\frac{d}{dx}\left(y\right)\right)+2y\frac{d}{dx}\left(y\right)=2-\frac{d}{dx}\left(y\right)\)

\(\mathrm{For\:convenience,\:write\:}\frac{d}{dx}\left(y\right)\mathrm{\:as\:}y^{'\:}\\6x-6\left(y+xy^{'\:}\right)+2yy^{'\:}=2-y^{'\:}\\\mathrm{Isolate}\:y^{'\:}:\quad y^{'\:}=\frac{2-6x+6y}{-6x+2y+1}\\y^{'\:}=\frac{2-6x+6y}{-6x+2y+1}\\\mathrm{Write}\:y^{'\:}\:\mathrm{as}\:\frac{d}{dx}\left(y\right)\\\frac{d}{dx}\left(y\right)=\frac{2-6x+6y}{-6x+2y+1}\)

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:  $12.

Step-by-step explanation:

4 overtime hours at the double-time rate =

4*2=8 regular hours.

Hence,

Mrs. Fisher worked her 40+8 regular hours  last week.

Mrs. Fisher worked her 48 regular hours  last week.

Her gross pay was $576.

So,

$576:48=

$12.

The fifth partial sum represents the sum of the first 5 terms in the sequence is equal to 2210.

The fifth partial sum represents the sum of the first 5 terms in the sequence.

What is the partial sum of sequence?

The partial sum of a sequence gives the sum of the first n terms in the sequence.

Thus, the fifth partial sum represents the sum of the first 5 terms in the sequence.

The given geometric sequence :

$400, $420, $441, $463, and $486.

The fifth partial sum of the above sequence will be :

$400+ $420+ $441+$463+$486=$2210

Therefore, the fifth partial sum represents the sum of the first 5 terms in the sequence equal to 2210.

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The rate of decomposition as per half life is 0.0000545 M.

what is half life?

Drug concentration decreases from 0.002M to 0.001M in 24 hours.

Again, Drug concentration decreases from 0.001M to 0.0005 M in subsequent 24 hours.

Therefore, t(1/2) = 24 hours

K= 0.693/t(1/2) = 0.693/24 = 0.028775 per hour.

K= 2.303/t Log (No/Nt)

Log(No/Nt) =Kt/2.303 =0.05015

No/Nt= Antilog (0.05015) = 1.1224

Nt= No/1.1224 = (0.0017818 M

Rate of decomposition as per half life is calculated as

(No-Nt)/t = 0.0000545 M

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The minimum Marissa should spend on eggs to use all of her chard leaves while keeping the recipe in the correct proportion is $3.40.

To use 10 chard leaves, the recipe calls for 6 eggs. Let's find out how many eggs we need to use 25 chard leaves in the same proportion:

10 chard leaves / 6 eggs = 25 chard leaves / x eggs

where x is the number of eggs needed.

Cross-multiplying, we get:

10 chard leaves * x eggs = 6 eggs * 25 chard leaves

Simplifying, we get:

x = (6 eggs * 25 chard leaves) / 10 chard leaves

x = 15 eggs

So, Marissa needs 15 eggs to use 25 chard leaves in the recipe.

Now, let's find out the cheapest way to buy 15 eggs. She can buy either a dozen eggs for $3.20 or a half-dozen eggs for $1.70. Since a dozen contains 12 eggs and a half-dozen contains 6 eggs, she can either buy:

1 dozen + 3 individual eggs = 15 eggs for $3.20 + $0.24 = $3.44

2 half-dozens = 12 eggs for $3.40

Therefore, the minimum Marissa should spend on eggs to use all of her chard leaves while keeping the recipe in the correct proportion is $3.40.

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The opening area for a 7 inch diameter channel is approximately 38.484 square inches.

The area of ​​a circular opening can be found using the circle area formula given by \(A = \pi r^2\). where A is the area and r is the radius of the circle. In this case, the duct diameter is 7 inches. The radius can be calculated by dividing the diameter by 2, so the radius is 7/2 = 3.5 inches.

Substituting the radius into the equation gives A = π(3,5)^2. Evaluating this formula gives A = \(\pi\)(12.25) ≈ 38.484 square inches. Rounding the result to the nearest thousandth, the area of ​​the channel opening is approximately 38.484 square inches.

Therefore, a 7 inch diameter duct has an orifice area of ​​approximately 38.484 square inches. 

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Answer:

Times 3

Step-by-step explanation:

Answer:

The average speed on the return trip is 2.44 miles/h.                  

Step-by-step explanation:

To find the average speed we need to use the following equation:

\( \overline{v} = \frac{d}{t} \)

Where:

d: is the distance

t: is the time

Since the question is to find the average speed on the return trip, we will take the data of the time and speed of only the return trip.

\(\overline{v} = \frac{d}{t} = \frac{5 + 1/2}{2 + 1/4} = 2.44 miles/h\)                

Therefore, the average speed on the return trip is 2.44 miles/h.

I hope it helps you!

The rains were especially damaging to Europe's food supply, rotting crops and spreading infections that affected cattle. The absence of a stable and adequate food supply resulted in starvation, which was the principal cause of said Great Famine of 1315-1322.

The bulk of Europe witnessed significant crop failure in 1314 and 1315. Before this, there had been a period of rapid population growth caused by agricultural development, which resulted in famine for a significant number of people. Around 5-12% of Northern Europe's population died from famine or accompanying illness.

Famine triggered class conflict and political unrest, destabilizing entire areas. Grain, wheat, grain, oats, bread, and salt were so expensive that many people also couldn't afford them even when they were available. To feed themselves, some abandoned their children and stole from and murdered others.

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The question is -

What was the primary cause of the great famine of 1315 - 1322? regional warfare disrupting agriculture an unprecedented series of locust swarms prolonged rainfall killing crops through flooding an extraordinary period of warmth.

Answer: It's option C, prolonged rainfall killing crops throughout flooding

Step-by-step explanation:

Answer:

The second and fourth answer are correct

Step-by-step explanation:

The width of the sidewalk if A rectangular piece of land measures 20 feet by 15 feet, James created a cement sidewalk, x feet wide, is 12.25 so, option A is correct.

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely cover the surface of a closed figure.

Given:

A rectangular piece of land measures 20 feet by 15 feet, James created a cement sidewalk, x feet wide,

the garden has an area of 150 square feet,

Calculate the width of the sidewalk as shown below,

Area of rectangular piece = area of garden + area of sidewalk

20 × 15 = 150 + x × x

300 = 150 + x²

x² = 300 - 150

x = √150

x = 12.25

Thus, the width of the sidewalk is 12.25 feet.

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Answer: hi want to be fwends

Step-by-step explanation:

There can 3 songs to be played for per quarter.

A unit conversion expresses the same property as a different unit of measurement.

Given that, It cost Sean 3.75 to play 45 songs on an old jukebox. The jukebox only accepts quarters.

Converting $3.75 into quarters,  ($1 = 4 quarters)

$3.75 = 3+0.75

= 3x4+0.75

= 12+3

= 15 quarters

So, he played 45 songs in 15 quarters

Therefore, in 1 quarters = 45/15

= 3

Hence, There can 3 songs to be played for per quarter.

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