How do you determine whether a system of linear equations has no solution, one solution, or infinitely many solutions? Explain each scenario.

The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

The equation of the ellipse is:

\($ \rm \frac{x^2}{81} +\frac{y^2}{20.25}\1=1\)

By identifying the center, symmetry properties, focus location, and the ratio between the lengths of the major and minor axes, we can determine the equation of the ellipse using the standard form equation\(\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1\), where (h, k) represents the center coordinates and a and b are the lengths of the major and minor axes, respectively.

Given the information provided, we can determine the equation of the ellipse.

1.Center at the origin:

Since the center of the ellipse is at the origin (0, 0), the equation of the ellipse will have the form

\(\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1\), where (h, k) represents the center.

2.Symmetric with respect to the x- and y-axes:

Since the ellipse is symmetric with respect to the x- and y-axes, the values of a and b in the equation will be the same. Let's denote this common value as c.

3.Focus at (9, 0):

The focus of the ellipse is given as (9, 0). Since the center is at the origin, the focus located 9 units to the right on the x-axis.

Therefore, a = 9.

4.Major axis is twice as long as minor axis:

The major axis is twice as long as the minor axis. Let's denote the length of the major axis as a(=9). Since the major axis is twice as long, the length of the minor axis is a/2=9/2=4.5

Now, we have all the information needed to determine the equation of the ellipse:

\(\frac{ (x - 0)^2}{a^2} +\frac{(y - 0)^2}{b^2} = 1\)

Simplifying further:

\(\frac{ x ^2}{9^2} +\frac{y^2}{4.5^2} = 1\)

Simplifying:

\(\frac{x ^2}{81} +\frac{y^2}{20.25} = 1\)

Therefore, the equation of the ellipse is:

\(\frac{x ^2}{81} +\frac{y^2}{20.25} = 1\)

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Answer:

The answer is A

Step-by-step explanation:

I am smart

The smallest number of instances at which the acceleration of the plane could equal zero on the open interval 0 < c < 6 is t= 25 to t= 30.

By the mean value theorem, somewhere between t = 0 and t = 15 , v'(t) = 0, because v(15)-v(0)/15-0 = 0. Also somewhere between t=25 and t=30, v'(t) = 0, because v(30) - v(25) / 30 - 25 = 0. This means a(t) = 0 for at least two values of t.

f(t) = 6+cos(t/10)+3sin(7t/40)

a(t) = f'(t) = 1/10 sin (t/10) + 21/40 cos (7t/40)

f'(23) = -.408 miles/min²

Average Velocity = 5.916 miles per minute

Average Speed is characterized as the adjustment of position or displacement of the object (∆x) partitioned when the time interval (∆t) in which the displacement happens. The average speed can be a positive or negative sign on the indication of the displacement of the object.

The total distance that the plane flies in 40 min is 229 miles.

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Answer:

Michelle < Staci < Kelly < Kyle

Kyle is the greatest distance from work, while Michelle is the closest to work.

Step-by-Step Explanation:

1 kilometer = 0.62137119 mile(s)

4.5 miles = 0.62137119 × 4.5 = 2.79617036 kilometers

4,200 meters = 4.2 kilometers

670,000 centimeters = 6.7 kilometers

So,

Michelle = 2.8 kilometers (rounded up)

Kelly = 5.6 kilometers

Staci = 4.2 kilometers

Kyle = 6.7 kilometers

So,

Michelle < Staci < Kelly < Kyle

Kyle is the greatest distance from work, while Michelle is the closest to work.

Hope this helps! ^^

The unsigned binary number 100101 is equal to 18 in base 10. The provided options (101, 21, 53, 37) do not match the conversion result.

The provided options (101, 21, 53, 37) do not match the conversion result of unsigned binary number to base.

To convert the unsigned binary number 100101 to base 10, we can use the following steps:
1. Identify the place values for each digit: (2^4) (2^3) (2^2) (2^1) (2^0)
2. Multiply the binary digits with their respective place values: (1×2^4) (0×2^3) (0×2^2) (1×2^1) (0×2^0)
3. Add the results: (16) + (0) + (0) + (2) + (0) = 18

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We can start by using the Maclaurin series for the arctangent function: arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ....

Then, we can substitute x/7 for x in this series to get the power series representation for f(x):

f(x) = arctan(x/7) = (x/7) - (x/7)^3/3 + (x/7)^5/5 - (x/7)^7/7 + ...

To find the first five non-zero terms, we can plug in x = 0 to each term and observe that all terms with odd powers of x will evaluate to 0. Therefore, the first five non-zero terms are:

f(x) = (x/7) - (x^3/3)/7^3 + (x^5/5)/7^5 - (x^7/7)/7^7 + (x^9/9)/7^9

Simplifying, we get:

f(x) = x/7 - x^3/147 + x^5/1715 - x^7/24010 + x^9/408410

The radius of convergence of the power series representation can be found using the ratio test:

lim |a(n+1)/a(n)| = lim [(x/7)^(2n+3)/(2n+3)(2n+2)]

= |x/7| lim [(x/7)^2/(2n+3)(2n+2)]

= 0, for any finite x

Since the limit is 0 for any finite value of x, the radius of convergence is infinite, which means that the power series representation converges for all values of x.

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➡We use the formula for the area of the circle and the area of the triangle to solve the problem.

➡√3/4 (side)2 = 17320.5 cm2

➡(side)2 = (17320.5 × 4)/√3 cm2

= (17320.5 × 4)/1.73205 cm2

side = √10000 × 4 cm²

= 100 × 2 cm

= 200 cm

∵Radius (r) = 1/2 × (length of side of triangle)

= 1/2 × 200 cm

= 100 cm

∴Area of shaded region = Area of ΔABC - Area of 3 sectors

= 17320.5 cm2 - 15700 cm2

= 1620.5 cm2

Step-by-step explanation:

To Find : Their present ages

Consider,

\(x + y = 46\\x = 46 -y\)

→ (x+4) : (y +4) = 7:2

→ x+4/y+4 = 7/2

→ 46-y+4/y+4 = 7/2

→ 50-y/y+4 = 7/2

→7y +28 = 100-2y

→ 7y +2y = 100 -28

→ 9y = 72

→ y = 8

Now put y = 8 in eq(1) .

→ x = 46 - y

→ x = 46 - 8

→ x = 38

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hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)

To find the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing with 50 people, follow these steps:

1. Since winning more than one prize is allowed, the probability of Bo winning the first prize is 1/50.

2. Likewise, the probability of Colleen winning the second prize is also 1/50.

3. Similarly, the probability of Jeff winning the third prize is 1/50.

4. Finally, the probability of Rohini winning the fourth prize is 1/50.

5. Since these events are independent, we can multiply the probabilities together to find the overall probability of this specific  :

  Probability = (1/50) * (1/50) * (1/50) * (1/50)

6. Calculate the result:

  Probability ≈ 0.00000016

7. Round the answer to two decimal places:

  Probability ≈ 0.00

So, the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing with 50 people is approximately 0.00.

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Answer:

8, 15, 16

Step-by-step explanation:

8, 15, 16 is not a Pythagorean triple because it doesn't satisfy the Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

When we plug this set of numbers into the theorem:

\(8^2 + 15^2 \stackrel{?}{=} 16^2\)

\(289 \neq 256\)

we get an inequality, not an equality which would make this set of numbers a Pythagorean triple.

Note that all of the other given triples satisfy the Pythagorean Theorem.

Answer:

14

Step-by-step explanation:

You divide 56/8 to get 7

Next you multiply that by 2 to get...

14

Hope this helps!

Answer: 14 stamps

Step-by-step explanation:

56/8=7 stamps per sheet

7 stamps= 1 sheet of paper

7 x 2= 14 stamps on 2 sheets

Answer:

y

Step-by-step explanation:

Answer:

The missing degree is 60, but the perimeter is 11 cm.

I hope this is correct, if it's incorrect, I'm sorry

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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To determine if the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution, we can check whether the vector b is in the span of the vectors {a1, a2, a3}.

In linear algebra, the augmented matrix represents a system of linear equations. The columns a1, a2, and a3 correspond to the coefficients of the variables in the system, while the column b represents the constants on the right-hand side of the equations. To check if the system has a solution, we need to determine if the vector b is a linear combination of the vectors a1, a2, and a3.

If the vector b lies in the span of the vectors {a1, a2, a3}, it means that b can be expressed as a linear combination of a1, a2, and a3. In other words, there exist scalars (coefficients) that can be multiplied with a1, a2, and a3 to obtain the vector b. This indicates that there is a solution to the linear system.

On the other hand, if b is not in the span of {a1, a2, a3}, it implies that there is no linear combination of a1, a2, and a3 that can yield the vector b. In this case, the linear system does not have a solution.

Therefore, determining whether the vector b is in the span of {a1, a2, a3} allows us to determine if the linear system corresponding to the augmented matrix [a1 a2 a3 b] has a solution or not.

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Answer:

6.  175/125=x/100

Cross products  equal 125x=17500

Solve for x and you get 140%

7.  20% of 720 is 144.  You need to find 120% so add the full 720 (100%) to the 144 and you get 864 (120%)

Step-by-step explanation:

Answer:

6. 140%    7. 864

Step-by-step explanation:

Step for #1:

1.) 175 ÷ 125 = 1.4

2.) 1.0=100   0.4=40

3.) 1.4 = 140%

Answer; 140%

Step for #2:

1.) 120% × 720 = ?

2.) 120 x 720 = 86,400

3.) 86,400 ÷ 100 = 864

Answer; 864

Answer:

10

Step-by-step explanation:

Answer:

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Step-by-step explanation:

The confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent. These two methods provide a range of plausible values (confidence interval) for the difference between two population proportions and involve the calculation of critical values to determine the margin of error.

On the other hand, the p-value method is not equivalent to the confidence interval and critical value methods. The p-value method involves calculating the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the sample data, assuming the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the difference between two population proportions.

To summarize:

- Confidence interval method: Provides a range of plausible values for the difference between two population proportions.

- Critical value method: Uses critical values to determine the margin of error in estimating the difference between two population proportions.

- P-value method: Determines the statistical significance of the observed difference between two population proportions based on the calculated p-value.

Hence, the confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

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Answer:

the board is 2.4 ft

Step-by-step explanation:

because 24/10 is 2.4

Answer:

dude where is the question

Answer:

It will cost: £28.28

Step-by-step explanation:

Area of sphere = 4 x π x r2

Area of Circle = 4 x π x 3^2 = 113.097 (radius is half of diameter)

113.097 / 0.25 = 28.28

Ricardo's time for the third race was 54.6 seconds.

We know that Ricardo ran the 400-meter race 3 times, and his fastest time was 54.3 seconds, his slowest time was 56.1 seconds, and his average time for all three races was 55.0 seconds.

To find his time for the third race, we can use the formula:

Total time = (Time for Race 1) + (Time for Race 2) + (Time for Race 3)

Since we know the times for two of the races, we can rewrite this formula as:

Time for Race 3 = Total time - Time for Race 1 - Time for Race 2

The total time for all three races can be found by multiplying the average time by 3:

Total time = 3 x 55.0 seconds = 165.0 seconds

Substituting in the values we know, we get:

Time for Race 3 = 165.0 seconds - 54.3 seconds - 56.1 seconds

Simplifying this expression, we get:

Time for Race 3 = 54.6 seconds

Therefore, Ricardo's time for the third race was 54.6 seconds.

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