(2.4×10−4)+(5.9×10−3)

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Here,

Given: Total number of freshman =500

mean =75 and standard deviation =7

a) the percentage of scores that fell between 68 and 82

340 is the number of freshman whose  scores that fell between 68 and 82

thus,

percentage = 340 /500 * 100

=> percentage = 68%

b)the percentage of scores that fell between 61 and 75

237 is the number of freshman whose  scores that fell between 61 and 75

thus,

percentage = 237/500 * 100

=> percentage = 47.4%

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

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The family of functions P = C1e^t / (1 + C1e^t) is a solution to the differential equation dP/dt = P(1 - P) on an appropriate interval of definition.

In the first paragraph, we summarize that the family of functions P = C1e^t / (1 + C1e^t) is a solution to the differential equation dP/dt = P(1 - P). This equation represents the rate of change of the variable P with respect to time t, and the solution provides a relationship between P and t. In the second paragraph, we explain why this family of functions satisfies the given differential equation.

To verify the solution, we can substitute P = C1e^t / (1 + C1e^t) into the differential equation dP/dt = P(1 - P) and see if both sides are equal. Taking the derivative of P with respect to t, we have:

dP/dt = [d/dt (C1e^t / (1 + C1e^t))] = C1e^t(1 + C1e^t) - C1e^t(1 - C1e^t) / (1 + C1e^t)^2

      = C1e^t + C1e^(2t) - C1e^t + C1e^(2t) / (1 + C1e^t)^2

      = 2C1e^(2t) / (1 + C1e^t)^2.

On the other hand, evaluating P(1 - P), we get:

P(1 - P) = (C1e^t / (1 + C1e^t)) * (1 - C1e^t / (1 + C1e^t))

        = (C1e^t / (1 + C1e^t)) * (1 - C1e^t + C1e^t / (1 + C1e^t))

        = (C1e^t - C1e^(2t) + C1e^t) / (1 + C1e^t)

        = (2C1e^t - C1e^(2t)) / (1 + C1e^t)

        = 2C1e^t / (1 + C1e^t) - C1e^(2t) / (1 + C1e^t).

Comparing the two sides, we see that dP/dt = P(1 - P), which means the family of functions P = C1e^t / (1 + C1e^t) is indeed a solution to the given differential equation.

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Answer:

Step-by-step explanation:

55%  1,100 is 55% of 2,000

Answer:

l think B

Step-by-step explanation:

y+(8+2) its cant be A or C

Answer:

it is correct good job

Step-by-step explanation:

Answer:

0.3545

Step-by-step explanation:

Answer:

multiply

Step-by-step explanation:

2345567 in the subtract 578431111

Answer:

I think it will be 2,700000

We can rewrite the given time as:

First, remember that:

60s = 1 min

Then to write that amount in minutes, we just need to divide by 60, so we get:

(4.22x10^17)/60  mins=  7.03x10^15 mins

Now, remember that:

1 hour = 3600s

Then to get the time in hours, we need to divide by 3600:

(4.22x10^17)/3600 h = 1.17x10^14 hours.

Similarly, you can change to any time unit that you want, for example:

1 day = 24*3600 s

Then the time in days is:

(4.22x10^17)/(24*3600) days = 4.88x10^12 days.

And so on.

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\(16r^2s^2\) as the product of power is written as \((4rs)^2\)

The power of a product rule states that \((a^m)(a^n) = a^(m+n)\), where "a" is the base, "m" is the exponent of the first term, and "n" is the exponent of the second term. This rule allows us to simplify expressions where multiple variables are being raised to a power and multiplied together by adding the exponents.

For example, \((a^2)(a^3) = a^(2+3) = a^5\).

It is also important to remember that when we are using the power of a product rule, the bases must be the same. If we have different bases, we cannot use this rule.

For example, \((a^2)(b^3) = a^2 * b^3, not a^(2+3) = a^5\).

Rewritten as power of product:

\(16r^2 s^2= 4*4*r*r*s*s\\16r^2s^2= 4^2*r^2*s^2\\16r^2s^2=(4rs)^2\)

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When assessing whether a transformation has succeeded in meeting the assumptions of the Analysis of Variance (ANOVA), there are several steps you can follow:

Understand the assumptions: Familiarize yourself with the assumptions of ANOVA. The key assumptions include:

a. Normality: The residuals (the differences between observed and predicted values) should follow a normal distribution.

b. Homogeneity of variances: The variability of the residuals should be constant across all levels of the independent variable(s).

c. Independence: The observations should be independent of each other.

Visual inspection: Plot the residuals against the predicted values or the independent variable(s). Check for patterns or systematic deviations from randomness. Look for indications of non-normality, heteroscedasticity (unequal variances), or any other violations of assumptions.

Statistical tests: Perform appropriate statistical tests to assess the assumptions. Common tests include:

a. Normality tests: You can use tests like the Shapiro-Wilk test or the Anderson-Darling test to assess normality of residuals.

b. Homogeneity of variances tests: Levene's test or Bartlett's test can be used to assess homogeneity of variances.

c. Independence assumption: In experimental designs, independence is often assumed. However, in some cases, you may need to consider specialized tests or modeling techniques to address dependency.

Effect of transformation: If the assumptions are violated, consider applying transformations to the data. Common transformations include logarithmic, square root, or reciprocal transformations. Apply the transformation to the response variable and rerun the ANOVA. Repeat steps 2 and 3 to assess whether the transformed data meet the assumptions.

Assess the transformed data: Repeat the visual inspection and statistical tests on the transformed data to determine if the assumptions have been met. If the assumptions are still not satisfied, you may need to explore alternative statistical techniques or consider a more complex model.

Interpretation: Once you have satisfied the assumptions, you can interpret the results of the ANOVA. Be cautious and consider the limitations of your analysis, as transformations may affect the interpretation of the original data.

Remember that the appropriateness of a transformation depends on the specific context and data. It's always good practice to consult with a statistician or an expert in the field to ensure the validity of your analysis.

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The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each.

The amount of tickets is given as,

Ticket's amount = 3 x $13

Ticket's amount = $39

Then the amount spent on snacks is given as,

Snack's amount = 4 x $5

Snack's amount = $20

Then the total amount is given as,

Total amount = $39 + $20

Total amount = $59

The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.

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Answer:

7

Step-by-step explanation:

Molly bought 10 bags of the same dog food. She had a coupon for $5. She spent a total of $65. How much money was each bag of the dog food?

example:

ositive numbers

numbers greater than zero

Negative Numbers

numbers less than zero

Integers

whole numbers and their opposites

Absolute Value

The distance a number is from zero on a number line. ALWAYS POSITIVE

equation

A mathematical sentence that contains an equals sign.

more examples:

9- (-9)=

18

121 / -11

-11

2(n + 5) = −2

-6

9

−9x + 1 = −80

253 + 234=

487

−15 = −4m + 5

5

8n + 7 = 31

3

Hope this helps bsf

The value of x in the equation 8+4=2(x-1) is 7

To solve for x in the equation 8+4=2(x-1), we can follow these steps:

Simplify the left-hand side of the equation by adding 8 and 4 to get 12:

8 + 4 = 12

Simplify the right-hand side of the equation by distributing the 2 to the expression inside the parentheses:

2(x-1) = 2x - 2

Set the left-hand side and the right-hand side equal to each other:

12 = 2x - 2

Add 2 to both sides of the equation:

12 + 2 = 2x

14 = 2x

Divide both sides of the equation by 2:

14/2 = x

x = 7

Therefore, the value of x in the equation 8+4=2(x-1) is 7.

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Answer:

y=4x+3

Step-by-step explanation:

find the slope using y2-y1/x2-x1

11-3/2-0

simplify

8/2

simplify

4

find b by using the equation y=mx+b

since we know 4 is the slope, plug it in for m

plug an ordered pair into y=4x+b

3=4(0)+b

3=b

plug b in y=4x+b

y=4x+3

Answer:

\(\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}\)

The last option matches the correct solution

Step-by-step explanation:

Equation Solving

We have the following equation:

\(\displaystyle V=\frac{4}{3}\pi r^3\)

And it's required to solve it for r.

Solving this equation needs to perform some operations to have the r isolated from any other variables or constants.

It can be done by conveniently operating on both sides as follows:

Eliminate the denominator by multiplying by 3:

\(\displaystyle 3V=4\pi r^3\)

Move \(4\pi\) to the other side by dividing by \(4\pi\):

\(\displaystyle \frac{3V}{4\pi}= r^3\)

Swapping sides to have r at the left side:

\(\displaystyle r^3=\frac{3V}{4\pi}\)

Finally, take the cubic root and leave r alone:

\(\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}\)

The last option matches the correct solution

Step-by-step explanation:

2 _|_20, 10, 50

5 _|_ 10, 5, 25

1 _|_ 2, 1, 5

Further, it is not divisible.

So, LCM = 2×5×2×5

LCM = 100 is the answer.

Hope it helps :)

\(.\)

The area of the triangle is: 24 unit²

What is an area ?

Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is typically measured in square units, such as square meters or square feet. The area of a shape is calculated by multiplying its length by its width, or by using a specific formula for the shape.

We can find the area of the triangle by using the formula:

Area = 1/2 * base * height

where the base is the distance between points A and B, and the height is the distance from point C to the line containing AB.

The distance between points A and B is 4 units (since they have the same x-coordinate). To find the height, we can use the equation of the line containing AB, which is:

y = 4x - 3

Substituting x = 4 (the x-coordinate of point C) gives us:

y = 4(4) - 3 = 13

So the height is 13 - 1 = 12 units.  

Therefore, the area of the triangle is:

Area = 1/2 * base * height

= 1/2 * 4 * 12

= 24

So the answer is not one of the given choices. The correct answer is 24.

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The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

$65

Step-by-step explanation:

50 x 0.30

= 15

50 + 15

= 65

Therefore , the solution of the given problem of arithmetic mean comes out to be  2.5 to 12.5 there are three arithmetic means: 5, 7.5, and 10.

The typical values of a list, often known sequence as the organization's goals, are calculated by adding up all of the values on the list. Afterwards, these average figures are corrected using the percentage of list elements with the highest density. Growth patterns in mathematics are comparable. The true average of the numbers 5, 7, and 9 is 4, and by adding three, the number 21 becomes seven.

Here,

The following formula can be used to determine an arithmetic sequence's nth term:

=> an = a1 + d(n - 1)

The first term is known to be a1 = 2.5, and the fifth term is known to be a5 = 12.5. We can find d by using the above formula:

=> a5 = a1 + d(5 - 1) (5 - 1)

=> 12.5 = 2.5 + 4d

=> 10 = 4d

=> d = 2.5

Hence, 2.5 is the typical difference between two successive words.

The second, third, and fourth terms are the three arithmetic means. As a result, we have:

=> a1 = 2.5

=> a2 = a1 + d = 2.5 + 2.5 = 5

=> a3 = a2 + d = 5 + 2.5 = 7.5

=> a4 = a3 + d = 7.5 + 2.5 = 10

In this range of 2.5 to 12.5 there are three arithmetic means: 5, 7.5, and 10.

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The minimum is 29 cm and it represents the sensor's minimum height above the ground.

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.

In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

$500

Step-by-step explanation:

100-12=88

88/100=440/x

88x=100(440)

88x=44000

/88.  /88

x=500

hopes this helps

To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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Alice is 55 km from her starting point after walking a distance of 55 km along the perimeter of the park.

To find the distance Alice is from her starting point after walking along the perimeter of the park, we can use the concept of congruent sides in a regular hexagon.

The perimeter of a regular hexagon is equal to the sum of its six congruent sides. Given that each side of the hexagon is 22 km long, the total perimeter of the hexagon is 6 * 22 km = 132 km.

Since Alice walks a distance of 55 km along the perimeter of the park, we can determine the number of complete laps she makes around the hexagon by dividing the distance she walked by the perimeter of the hexagon: 55 km / 132 km = 0.4167 laps.

As Alice starts and ends at a corner of the hexagon, each complete lap brings her back to the same corner. Therefore, the fractional part of the number of laps represents the portion of the hexagon's perimeter she has traveled beyond the starting corner.

To find the remaining distance from Alice's current position to the starting point, we calculate the fractional part of the number of laps and multiply it by the perimeter of the hexagon: 0.4167 * 132 km = 55 km.

A regular hexagon is a polygon with six congruent sides. In this problem, the regular hexagon represents the shape of the park, and each side of the hexagon has a length of 22 km. The perimeter of the hexagon is found by multiplying the length of one side by the number of sides, which is 6. Therefore, the perimeter of the hexagon is 6 * 22 km = 132 km.

When Alice walks along the perimeter of the park for a distance of 55 km, we need to determine how many complete laps she makes around the hexagon. By dividing the distance she walked by the perimeter of the hexagon, we find that she completes approximately 0.4167 laps.

Since Alice starts and ends at a corner of the hexagon, each complete lap brings her back to the same corner. Therefore, the fractional part of the number of laps represents the portion of the hexagon's perimeter she has traveled beyond the starting corner.

In this case, multiplying 0.4167 by 132 km gives us a result of approximately 55 km. Therefore, Alice is 55 km from her starting point after walking a distance of 55 km along the perimeter of the park.

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Answer:

2835 its basically multiple

Answer:

10

Step-by-step explanation:

Answer:

10 shoes

Step-by-step explanation:

Step 1: State what is known

Giles has 10 socks for every 5 pairs of shoes

He has 20 socks

Step 2: Set up the ratio

Let 'x' represent how much shoes Giles has

10 socks : 5 shoes

20 socks : x shoes

Step 3: Convert ratio into fraction

\(\frac{Socks}{Shoes}\)

10 socks : 5 shoes = \(\frac{10}{5}\)

20 socks : x shoes = \(\frac{20}{x}\)

Step 4: Set ratio equal to each other and solve

\(\frac{10}{5}=\frac{20}{x}\\ 10x = 100\\\frac{10x}{10}=\frac{100}{10}\\x = 10\)

Therefore Giles has 10 shoes when he has 20 socks

Matrix A + Matrix B

Can be represented as

a11 = -7

a12 = 2

a21 = 5

a22 = - 8

b11 = 0

b12 = 0

b21 = 0

b22 = 0

Matrix A + Matrix B

a11 + b11

-7 + 0 = -7

a12 + b12

2 + 0 = 2

a21 + b21

5 + 0 = 5

a22 + b22

-8 + 0 = -8

The answer is option C

Answer:

4.8

Step-by-step explanation:

5x-2=2*11

5x=24

x=24/5

x=4.8