Lois Lane leaves Metropolis driving 50 km/h. Three hours later, Superman leaves Metropolis to catch up to her, flying at 300 km/h.

When does Superman catch up with Lois?

Superman will catch up ____ hours after Lois left Metropolis.

Answer:

Grace jumps for 9 minutes.

Zoe jumps for 12 minutes.

Step-by-step explanation:

Let the time for which Grace jumps the rope = \(x\) minutes

Let the time for which Zoe jumps the rope = \(y\) minutes

As per question statement:

\(x+y=21 ..... (1)\)

Number of times Grace jumps in one minute = 66

Number of times Zoe jumps in one minute = 56

Number of times Grace jumps in \(x\) minutes = 66

Number of times Zoe jumps in \(y\) minutes = 56

As per question statement:

\(66x+56y=1266 ...... (2)\)

Multiplying equation (1) with 66 and subtracting equation (2) from it:

\(10y = 1386 - 1266\\\Rightarrow 10y=120\\\Rightarrow y =\bold{12\ min}\)

By equation (1):

\(x=21-12=\bold{9\ min}\)

Therefore, the answer is:

Grace jumps for 9 minutes.

Zoe jumps for 12 minutes.

The volume of a cube is increased by 27 times its actual volume if the surface area of the new cube is triple that of the original cube.

cube is a 3-dimensional surface having all sides equal.

hence, the volume of a cube=v =\((x)^3\)

where x represent the side of a cube

know if we triple the length of a cube I,e x=3x

        v\(=(3x)^3\\\\=3x*3x*3x\\\\=27x^3\)

hence, if a cube is increased to form a new cube such that the surface area of the new cube is triple that of the original cube.  its volume is increased by a factor of 27.

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Whether the two ratios are 2: 3 and 2: 3 or a proportion

4: 6 and 12: 18

\($\frac{4}{6}$\)   and

\($\frac{12}{18}=\frac{2}{3}$\)   and

2/3

=2: 3 and 2: 3

Yes the given two ratios form a proportion.

The complete question is:

Check whether the given two ratios form a proportion or not: 4: 6  12: 18

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The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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Answer:

The number is 4

Step-by-step explanation:

17 - 5 = 12

12 ÷ 3 = 4

Answer:

4

Step-by-step explanation:

17-5=12

4x3=12

Answer:

262144

Step-by-step explanation:

8*8*8*8*8*8

64*8*8*8*8*8

512*8*8*8*8

4096*8*8*8

32,786*8

262144

To prove that triangle ABC is congruent to Triangle ADC, the additional  information to use is; AB ≅ AD

Two or more triangles are said to be congruent if the sides and angles of one of the triangles are equal to the sides and angles of one of the other triangles.

Now, the congruency can be tested by five main postulates namely;

Now, in our given triangle, we are told that ∠CAB ≅ ∠CAD. Thus;

To prove that ΔABC ≅ ∠ADC by the SAS Congruency theorem, we can say that AB ≅ AD since the second side AC is already congruent by reflexive property of congruence.

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Answer:

You probably should have gave them 2/3 of what they did. I wouldn't call you a scammer, but it was not fair.

Answer:

-4(y-2)=12

-4y+8=12

-4y=4

y = -1

Step-by-step explanation:

Have a wonder rest of your day!!! I hope this helps you!!! :)

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Step-by-step explanation:

What graph are we talking about?

Mean is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

The score he has to get on the 100-point final exam to have an

average of 80 or better is 104 points or more.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Namid had an average of 74 on four history tests.

This means the total score on the four history papers.

Average score = Total score / Number of test

74 = Total score / 4

Total score = 74 x 4

Total score = 296

Now,

Average score = 80 and above

The mark to get on 100 points is to have an average score of 80 and above.

Let the marks be M.

(M + 296) / 5 = 80

M + 296 = 80 x 5

M + 296 = 400

M = 400 - 296

M = 104

Thus,

The score he has to get on the 100-point final exam to have an

average of 80 or better is 104 points or more.

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Part a: Future amount due on a compound interest loan is $12271.78.

Part b: The amount due on the loan would be $12033.64, if the compounding period is increased to monthly.

The formula for compounding is:

A = P(1 + r/100n)∧nt

P = $12,000

r = 0.07

Part a: compounded semiannually.

t = 4 years.

n = 2

A = 12000(1 + 0.07/100*2)∧2*4

A = 12000*1.00280

A = 12271.78

Thus, future amount due on a compound interest loan is $12271.78.

Part  b:

t = 4 years.

n = 12

A = 12000(1 + 0.07/100*12)∧12*4

A = 12000*1.0028038

A = 12033.64

Thus, if the compounding period is increased to monthly, the amount due on the loan would be $12033.64.

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Answer: $15,802

$15,865

Step-by-step explanation:

Answer: 19.42

Step-by-step explanation:

To find the distance, we need to use the distance formula.

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

With the given points, we can plug them in and solve.

\(d=\sqrt{(7-3)^2+(-11-8)^2}\)          [parenthesis]

\(d=\sqrt{(4)^2+(-19)^2}\)                       [exponent]

\(d=\sqrt{16+361}\)                               [add]

\(d=\sqrt{377}\)                                       [square root]

\(d=19.42\)

Now, we know the distance is 19.42.

The 95% confidence interval is: b) -1.38 to d) 3.44.

The value of the sample mean difference is 1.74, which falls:

b) within.

Here, we have to determine the 95% confidence interval for the difference of sample means and complete the statements, we need to use the sample mean difference provided and the confidence interval limits given as options.

We'll compare the sample mean difference to the interval to see if it falls within or outside the interval.

Given that the sample mean difference is 1.74, let's analyze the options:

Options for the confidence interval limits:

Lower limit options:

a) -1.26

b) -1.38

c) -3.48

d) -3.44

Upper limit options:

a) 1.26

b) 3.48

c) 1.38

d) 3.44

Since the sample mean difference is 1.74, we need to check if it falls within the interval formed by the lower and upper limits.

Looking at the options for the lower limit, the closest value to 1.74 is -1.38, and the closest value to the upper limit is 3.44.

So, the 95% confidence interval would be:

-1.38 to 3.44

Now, completing the statements:

The 95% confidence interval is: b) -1.38 to d) 3.44

The value of the sample mean difference is 1.74, which falls:

b) within

So, the completed statements are:

The 95% confidence interval is -1.38 to 3.44.

The value of the sample mean difference is 1.74, which falls within the 95% confidence interval.

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I'm assuming the given log equation is \(\log_{\text{x}}(49) = \text{x}\)

If so, then the exponential form is \(\text{x}^{\text{x}} = 49\)

This is because the general form \(\log_{\text{b}}(\text{x}) = \text{y}\) transforms into \(\text{y} = \text{b}^{\text{x}}\)

For both equations, the 'b' is the base.

Answer

      = 3. 3 75

Step-by-step explanation:

 27 / 3 = 3.375

Kellogg’s Froot Loops® cereal comes in 6 colors: orange, yellow, purple, red, blue, and green. The appropriate hypotheses for testing if the proportion of each color of Froot Loops is the same are:

(a.)H0: The colors of Kellogg’s Froot Loops are uniformly distributed. Ha: The colors of Kellogg’s Froot Loops are not uniformly distributed. These hypotheses propose that the distribution of colors in Froot Loops is either uniform (null hypothesis) or not uniform (alternative hypothesis). Option (b) is incorrect because it suggests that the null hypothesis states that the colors are not uniformly distributed, which is not the case. Option (c) proposes specific values for the proportions of each color. However, it assumes that the proportions are equal to 20, which may not be the appropriate assumption. Option (d) proposes that three specific colors have a proportion of 0.20, while the other three colors have unknown proportions. This hypothesis is too specific and does not account for all possible scenarios. Therefore, option (a) is the appropriate choice, as it allows for a general assessment of whether the colors of Froot Loops are uniformly distributed or not.

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I’m pretty sure it’d be y = -x - 2

lmk if it’s wrong.

kilograms ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

Answer:

10

Step-by-step explanation:

It's just symmetry. You see that the geometrical construction above has been rotated, so its properties will remain the same.

Answer:

\( \frac{596}{125} \)

should be it

Answer:

12 ,14 both are in the same line In same way but.one of the.line is ano

The function graph denotes the fact that the daily cost associated with making tennis balls is high if they don't make enough balls and then becomes high again if they make too many balls.

We have,

From the graph of the function.

The x-axis denotes the number of tennis balls manufactured.

The y-axis denotes the daily cost of manufacturing the tennis balls.

Now,

From the graph,

The coordinates can be as follows:

(1, 12) to (7, 4)

This shows that the cost decreased as the number of tennis balls manufactured increased.

And,

The coordinates from (7, 4) to (13, 12).

This shows that the cost increases as the number of tennis balls manufactured increases.

Thus,

The function graph denotes the fact that the daily cost associated with making tennis balls is high if they don't make enough balls and then becomes high again if they make too many balls.

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Required methods are (a) can be easily solved by factoring, (b) can be easily solved by completing the square, and (c) will require the quadratic formula to solve.

To determine which method is most suitable for solving a quadratic equation, we need to consider the coefficient values of the equation. If the coefficient of x² is 1, then the equation can be solved by factoring, as it is easier to factorize. If the coefficient of x² is not 1, then we need to complete the square to solve it. Completing the square is a suitable method for solving quadratic equations with a coefficient value other than 1. If the equation is not easily solvable by factoring or completing the square, we use the quadratic formula to solve it. Therefore, (a) can be easily solved by factoring, (b) can be easily solved by completing the square, and (c) will require the quadratic formula to solve.

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Answer:

i think it is 69.5 roses but i am not sure if it's correct

Step-by-step explanation:

Answer:

17×6=102 because he gave 2 boxes to his brother so he have 6 boxes

In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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