Two hikers walk on a trail in the direction of increasing mile marker numbers. Mandy starts at mile marker 1 and hikes at a rate of 2.5 miles per hour. At the same time, Rita starts at mile marker 2 and hikes at a rate of 3 miles per hour. The equation 2.5h+1=3h+2 represents the number of hours h it will take Mandy to catch up with Rita.

The values of a, b, and c are -2, 7, and 3, respectively. Hence, the function is: f(x) = -2\(x^{2}\) + 7x + 3

What is Function ?

Function can be defined in which it relates an input to output.

Given that f(x) = a\(x^{2}\)+  bx + c, we have:

f(1) = a(1) + b(1) + c = a + b + c = 8 .....(1)

f'(x) = 2ax + b, so f'(1) = 2a(1) + b = 2a + b = 3 .....(2)

f''(x) = 2a, so f''(1) = 2a = -4 .....(3)

From equation (3), we get:

2a = -4

a = -2

Substituting this value of a into equation (2), we get:

2(-2) + b = 3

b = 7

Now, we can substitute the values of a and b into equation (1) to get:

-2 + 7 + c = 8

c = 3

so we get c as 3 and f(x) = -2\(x^{2}\) + 7x + 3 as a final resultant.

Therefore, the values of a, b, and c are -2, 7, and 3, respectively. Hence, the function is: f(x) = -2\(x^{2}\) + 7x + 3

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Normal CurveThe normal curve is a bell-shaped curve that is symmetrical, and the curve's mean, median, and mode all are equal and located at the center. It is also called the Gaussian curve after the mathematician Carl Friedrich Gauss. Normal distribution is a common statistical analysis technique used to model various phenomena in probability theory, physics, finance, and social science. It can be characterized by its mean and standard deviation.MeanMean is the arithmetic average of the numbers in a dataset. To find the mean, sum all the numbers in the dataset and then divide by the total number of values in the dataset. For the given problem, the mean is 500.Standard DeviationThe standard deviation is a measure of the spread of data from its mean. It measures how far the data values are from their mean. For the given problem, the standard deviation is 100.(b)Convert SAT-Math score of a student with 590 to z-score.z-score = (score - mean) / standard deviationz-score = (590 - 500) / 100 = 0.9(C)What percentage of students would have a SAT-Math score greater than 590?The formula for calculating the percentage of students with a SAT-Math score greater than 590 is:P(Z > 0.9) = 1 - P(Z ≤ 0.9)From the normal distribution table, the area to the left of 0.9 is 0.8159, and the area to the right of 0.9 is 1 - 0.8159 = 0.1841. Therefore, the percentage of students with a SAT-Math score greater than 590 is 18.41%.(d)What percent of students would be expected to have a SAT-Math score between 450 and 550?We can calculate the z-scores for each of the scores using the formula,z-score = (score - mean) / standard deviationz-score for 450 = (450 - 500) / 100 = -0.5z-score for 550 = (550 - 500) / 100 = 0.5From the normal distribution table, the area to the left of -0.5 is 0.3085, and the area to the left of 0.5 is 0.6915. The area between these two values is 0.6915 - 0.3085 = 0.3830, which is 38.3%.(e)What is the probability of having a SAT-Math score less than 540?The formula for calculating the probability of having a SAT-Math score less than 540 is:P(Z < (540 - 500) / 100)From the normal distribution table, the area to the left of 0.4 is 0.6554. Therefore, the probability of having a SAT-Math score less than 540 is 0.6554 or 65.54%.

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1. Characteristics of normal curve: The normal curve is a type of probability distribution.

Some of the characteristics of the normal curve are:

It is a bell-shaped curve, symmetrical and unimodal with a single peak in the center of the curve.It is characterized by a mean, median, and mode that are all equal.It is asymptotic, meaning that the tails of the curve extend to infinity without ever touching the x-axis.

2. Conversion of SAT score to z-score:

Formula to find z-score is: z = (x - μ) / σ

where z = z-score, x = raw score, μ = mean and σ = standard deviation

So, for a student with a math SAT-Math score of 590, the z-score would be:

z = (590 - 500) / 100z = 0.9

Therefore, the z-score for a student with a math SAT-Math score of 590 is 0.9.3.

Percentage of students with SAT-Math score greater than 590:

To find the percentage of students who would have a SAT-Math score greater than 590, we need to find the area under the normal curve to the right of the z-score corresponding to 590.

Using a standard normal table, we find that the area to the right of a z-score of 0.9 is 0.1841 or 18.41%.

Therefore, approximately 18.41% of students would have a SAT-Math score greater than 590.

4. Percentage of students with SAT-Math score between 450 and 550:

To find the percentage of students who would be expected to have a SAT-Math score between 450 and 550, we need to find the area under the normal curve between the z-scores corresponding to 450 and 550.

Using a standard normal table, we find that the area to the left of a z-score of -0.5 is 0.3085, and the area to the left of a z-score of 0.5 is 0.6915.

Therefore, the area between -0.5 and 0.5 is:

0.6915 - 0.3085 = 0.3830 or 38.30%

Therefore, approximately 38.30% of students would be expected to have a SAT-Math score between 450 and 550.5.

Probability of having a SAT-Math score less than 540:

To find the probability of having a SAT-Math score less than 540, we need to find the area under the normal curve to the left of the z-score corresponding to 540.

Using a standard normal table, we find that the area to the left of a z-score of 0.4 is 0.6554.Therefore, the probability of having a SAT-Math score less than 540 is approximately 65.54%.

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There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.

Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.

Here, we will use the combination rule to find out the possible triangles,Thus, the total number of possible triangles = 15C3                                                                      = (15.14.13) / (1.2.3) = 455

Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.

For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.

And 12/3 = 4 dots would be between any two connecting dots.

Taking 1st connecting dot, the second connecting dot would be

1 + 4 + 1 = 6th

Similarly, the third connecting dot would be 6 + 4 + 1 = 11th

So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);

After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:

So, there are 455 - 5 = 450 triangles that are not equilateral triangles.

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Answer:

17s-109t

Explanation:

Given the expression

First, we open the brackets.

Next, we collect terms with s together (do same for t).

We then simplify to get:

Translation of the Ax=0 solution set yields the Ax-b solution set since Ax-b is consistent. The Ax = b solution set is therefore a single vector if and only if the Ax = 0 solution set is a single vector, which occurs if and only if Ax 0 has only the trivial solution.

Finding the solution to an equation is like finding the solution to a puzzle. A mathematical equation proves the equality of two algebraic expressions. Determine the values of the variables that make the equation a true statement in order to solve an equation. An equation's solution is any value that causes the equation to be true.

given

Let's suppose that there is a solution to the equation ax = b.

Now, we want to demonstrate that the trivial solution exists for the equation ax = b when ax = 0.

Ax = 0 is homogeneous.

In the event that this equation was true for b, we define

To be a set of vectors with the form ax = b

w = m + gh

The subscript "h"

A solution to ax = 0 is gh.

Ax=b is in the form of w= m+gh based on the information we know had.

with

m = ax=solution b's

Soulution of gh = ax=0

Only a simple solution, ax = 0, exists.

gh = 0

where gh = 0

The relationship between ax=b and w=m

Ax = b thus has no alternative solutions.

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The pay for software engineers will go up relative to the pay for office clerks. Then the pay for software engineers will go up relative to the pay for office clerks.

What is decision-making?

The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.

If the demand increases more rapidly for software engineers than for office clerks.

you expect to happen to the average pay for the two occupations will be

As the demand for software engineers increases then the number of clerks is also increased. Thus, the pay for software engineers will go up relative to the pay for office clerks.

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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The dimensions of the poster with an area of 392 square inches is equal to 14 inches and 28 inches.

Area of rectangular poster to print = 392 square inches

Let us assume that dimensions of the posters are,

Width of the poster is x inches and the length of the poster is y inches.

Area of the rectangular poster is,

xy = 392

Add 2 inches to the top and bottom margins for a total of 4 inches

And 1 inch to the left and right margins for a total of 2 inches.

Total area of the poster including the margins using the following equation,

Total area = (x + 2) × (y + 4)

Minimize the total area of the poster while still satisfying the area constraint.

Use the first equation to solve for one variable

And substitute it into the second equation,

y = 392/x

Total area = (x + 2) × (392/x + 4)

⇒ Total area = 4x + 392 +784/x + 8

⇒Total area = 4x + 400 +784/x

Minimize the total area, take the derivative of this expression with respect to x and set it equal to 0,

d/dx (4x + 400 +784/x ) = 0

⇒  4 + 0 - 784/x² = 0

⇒ x² = 784 /4

⇒ x = 14

Substituting this value of x back into the equation for y, we get,

y = 392/14

  = 28

Therefore, the dimensions of the poster should be 14 inches by 28 inches.

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The correct answer is option 1. The version of the sample variance where you divide by n is biased.

This is because dividing by n will produce a biased downward population variance estimate. We must divide by n-1 rather than n to correct this bias. Mathematically, this can be expressed as:

Population Variance = s2 = ∑ (x - μ)2 / n Sample Variance = s2 = ∑ (x - x(bar))2 / (n-1)

In other words, we must subtract 1 from the sample size in the denominator when calculating the sample variance. This is due to the fact that the sample variance and the sample mean are both unbiased estimators of the population variance, respectively.

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Complete Question:

which of the following statements is true?

group of answer choices

Answer:

Total number of people surveyed = 118

Number of people who own dogs = 78

Number of people who own cat = 44

Number of people who own both cats and dogs = 26

Number of people who only own dogs = 78 - 26 = 52

Number of people who own only cats = 44 - 26 = 18

Only dog owners + Only cat owners + Both + Neither = Total people surveyed

52 + 18 + 26 + Neither = 118

Neither = 22(answer)

A null hypothesis refers to a statistical hypothesis that assumes that there is no difference between two groups or variables. The null hypothesis may either be rejected or not rejected based on the statistical results obtained from a hypothesis test. A hypothesis test is a statistical test that is conducted to either accept or reject the null hypothesis based on the statistical results obtained.

When is the null hypothesis rejected?The null hypothesis is rejected when the p-value is less than or equal to a preconceived level of significance, α (usually set at 0.05 or 0.01).The null hypothesis is rejected when the calculated test statistic (such as t-test, z-test, or F-test) is greater than or equal to the critical value corresponding to the level of significance α.

When is the null hypothesis not rejected?The null hypothesis is not rejected when the p-value is greater than the preconceived level of significance, α. This means that there is not enough evidence to reject the null hypothesis.The null hypothesis is not rejected when the calculated test statistic is less than the critical value corresponding to the level of significance α. This means that there is not enough evidence to reject the null hypothesis.

In conclusion, the null hypothesis is rejected when the p-value is less than the preconceived level of significance α or when the calculated test statistic is greater than or equal to the critical value corresponding to the level of significance α. On the other hand, the null hypothesis is not rejected when the p-value is greater than the preconceived level of significance α or when the calculated test statistic is less than the critical value corresponding to the level of significance α.

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Equation of the line passing through  (1, -9) and (1, 12) is y = -9

The equation to the line in  slope intercept form

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

calculation of slope, m for (1, -9) and (1, 12)

(y - y₁) /  (x - x₁)   = m

m = (-9 - 12) /  (1 - 1)

m = 1 / 0

m = undefined slope (this is the slope of vertical line)

equation of the line  (1, -9)

(y - -9) = 0

y + 9 = 0

y = -9

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Answer:

130°

Step-by-step explanation:

Arc QPN is formed by angle QNT. Angle QNT is formed by an intersecting tangent and chord meaning arc QPN is two times the measure of angle QNT.

65° · 2 = 130°

Answer:

Step-by-step explanation:

simplify the following

3ab+2ab-ab =                            (3 + 2 = 5)

5ab - ab =                                  (5 - 1 = 4)

4ab

just ask a normal question my guy

Answer:

25.5 mi

Step-by-step explanation:

12 22.5  X

Let X be the shortest distance we are trying to find.

a units 2 b units 2 c units 2

12 units 2 + (22.5)=c units 2

144+506.25=c units 2

650.25=c units 2

\(\sqrt{x} 650.25\)=c units 2

25.5

It appears to be a constant connection that the square matrix has n eigenvalues, where n is the dimensions (not dimensions as in Rank, but as in # of Column values) of the square matrix.

similar to: a 3x3 matrix square, which has 3 Eigenvalues and only permits eigenvalue decomposition in the event that the matrix is diagonasible.

I think it has to do with how mirror-reflective and inverse the dimensional features of the Matrix can be, and how its linear structure is strong enough to support a dimensional cube.

When it comes to interaction, eigenvalue decomposition can be used to systematically eliminate it.

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Answer:

12.4 cm

Step-by-step explanation:

arc AB is calculated using

arc = circumference × fraction of circle

      = 2πr × \(\frac{90}{360}\)

      = 2π × 7.9 × \(\frac{1}{4}\)

       = \(\frac{7.9\pi }{2}\) ≈ 12.4 cm ( to the nearest tenth )

Using the given exponential function,

The rate of the disease spreading is approx. 140 peoples per day affected.

let P be the number of people's that are contacting a new disease.

given exponential function about the new disease modeled by population is

P(t) = 3725/(1 +1.72 e⁻⁰·⁵²ᵗ) ---(1)

where t is time measured in days

we want to calculate the rate of diseases spreading on day 4 i.e t = 4

putting the value t = 4 in above formula, we get

P(t=4) = 3725/(1 + 1.72 e⁻⁽⁰·⁵²⁾⁴)

=> P( t= 4) = 3725 / (1 + 1.72× e⁻⁰·²⁸)

=> P(t=4) = 3725/(1 + 1.72× 0.124)

=> P(t = 4) = 3725/(1+ 0.2148)

=> P(t=4) = 3725/1.2148

=> P(t = 4) = 3066.14

Hence, after 4 days of diseases spread , total 3066 people's are affected from it .

rate of diseases spreading per day is equal to (3725-3066)/4 = 659/4 = 139.75

so, rate of spreding diseases is 139.75 ~ 140 peoples per day .

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A function which could be used to determine the total amount of revenue the company earns from selling moving boxes include the following: B. r(x) = -49x² + 567x.

From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (equation):

R(x) = x × P(x)

Where:

Since it is a revenue function, we would simply substitute the value of the unit price and evaluate as follows:

Revenue, R(x) = x × P(x)

P(0) = 567

By substituting the given parameters into the formula, we have;

Revenue, R(x) = x × (567 - 49x)

Revenue, R(x) = -49x² + 567x

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Answer:

y= 0 1 2 3 4

Step-by-step explanation:

just minus 2 by all of the numbers from x

Answer:

She can buy 1 bullitin board.

Step-by-step explanation:

1347 divided by 75 is 17.96

I HOPE THIS HELPS. EVEN THIS IS NOT THE ANSWER, I HOPE IT HELPS YOU FIND THE ANSWER.

Answer:

I'm gonna say false

GDP or Gross Domestic Profit is the money that is being spent/made inside the country. So it stands to reason that if people are spending more, the GDP would go up.

Hope this helps!

Answer:

the answer is 90 i believe

Step-by-step explanation:

Answer:

area = 69 cm²

Step-by-step explanation:

pink figure is a parallelogram ( opposite sides are parallel)

white figure is a rectangle

the shaded area = area of parallelogram - area of rectangle

                            = 10 × 9 - (3 × 7)

                           = 90 - 21

                           = 69 cm²

Answer:

B

Step-by-step explanation:

sum of the interior angles of a triangle is 180

180-(75+70+?)=35

Answer:

80g

Step-by-step explanation:

Answer:

80g

Step-by-step explanation:

80g

To make 4 banana oat muffins instead of the original recipe's 6, you would need 1/2 cup of oats.

The recipe states that to make 6 banana oat muffins, you need 3/4 cup of oats. Since you want to make 4 muffins instead, you can calculate the proportion of oats needed by setting up a ratio. By cross-multiplying, we find that (4/6) * (3/4) = (2/3) * (3/4) = 6/12 = 1/2. Therefore, you would need 1/2 cup of oats to make 4 banana oat muffins.

This calculation accounts for the adjustment in the recipe's quantities based on the desired serving size. Since you are making two-thirds of the original batch size, you proportionally reduce the amount of oats required by two-thirds, resulting in the need for 1/2 cup of oats.

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