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Among the three students the weight of Darren at birth was the lowest with 8.25 pounds.

What is weight?

Weight gauges how much gravity is pulling on a body.

The weight formula is provided by -

w = mg

Since weight is a force, it has the same SI unit as a force, which is Newton (N).

The students from lightest to heaviest weight at birth are -

Darren (8.25 pounds) < Joel (8.34 pounds) < Rebecca (8.388 pounds)

This is because 8.25 is less than 8.34, and 8.34 is less than 8.388. In other words, Darren weighed the least at birth, followed by Joel, and then Rebecca weighed the most.

It's important to note that the differences in weight between the students are relatively small, and all three weights are within a narrow range.

However, when comparing weights, even small differences can be significant.

Therefore, the lowest weight was of Darren (8.25 pounds).

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The length of the arc CD is 14.13 centimeters.

Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:

L  = (a/360°)*2*pi*R

Where pi = 3.14

Here the angle is a = 45°

And R = 18cm, so we can replace that in the formula above to find the length.

L = (45°/360°)*2*3.14*18cm = 14.13cm

That is the length of the arc CD.

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Answer:43/50

Step-by-step explanation:

you must divide both the numerator and denominator by 2

86/100 can be simplified to 43/50 by dividing both the numerator and denominator by 2, which is the greatest common factor. 86/100 can also be written as 0.86 or 86%.

Using a trigonometric relation we can see that x = 83.7

We can see that x is the hypotenuse of the given angle, and we know the measure of the adjacent catehtus to the given angle, then we can use the trigonometric relation:

cos(48°) = 56/hypotenuse

cos(48°) = 56/x

Solving that for x, we will get:

x = 56/cos(48°) = 83.7

That is the value.

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Part a: x intercepts are (4.414, 0) and (1.586,0) and y intercept = (0, 7).

Part b: From the graph, vertex = (3, -2).

In mathematics, a quadratic equation is a second-degree polynomial with the conventional form ax² + bx + c = 0, where a, b, and c are mathematical coefficients and a 0. Second degree refers to an equation where at least one term has been raised to a power of two. The value of the variable x in a quadratic equation is unknown, so we must discover the answer.

Given quadratic function for the macroeconomic variable

Q(x) = x² − 6x + 7.

Part a: x and y intercept:

x-intercept occurs when the function becomes zero.

Put Q(x) = 0

0 = x² − 6x + 7.

Find the factors:

x² − 6x + 7 = 0

a = 1 , b = -6 , c = 7 using the quadratic formula.

x = [-b ± √(b² - 4ac)]/ 2a

x = [6 ± √(36 - 4*1*7)]/ 2*1

x = 3 ± √2

Now,

x = 3 + √2

x = 4.414

and x = 3 - √2 = 1.586

Thus, x intercepts are (4.414, 0) and (1.586,0)

Y-intercept, when x = 0

Q(x) = 0² − 6(0) + 7.

Q(x) = 7

y intercept = (0, 7)

Part b: using the graphing tool, draw the graph of the given quadratic function.

Mark the points  (4.414, 0),  (1.586,0), and  (0, 7).

From the graph, vertex = (3, -2).

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The hyperbola equation centered at the origin with the vertices is x²/(t² + 22) - y²/(t² - 27) = 1

Because the hyperbola is centered at the origin, its standard form equation is:

(x²/a²) - (y²/b²) = 1

Where a denotes the distance between the center and the vertices and b denotes the distance between the center and the co-vertices.

Because the distance between the center and each vertex is √(t² + 72),

We get:

√(t² + 72) = a√(c² - a²) is the distance between the center and each focus, where c is the distance between the center and each focus.

We know that the distance between the center and each focus is √(27),

Thus we can calculate:

√(27 - a²) = √(27 - (t² + 72))

When we simplify, we get:

27 - a² = 27 - t² - 49

a² = t² + 22

When a² is substituted, we get:

(x²/(t² + 22)) - (y²/b²) = 1

Now we must locate b.

Because the distance between the center and each co-vertex is b, we get:

√(a² - 72) = b

√(t² + 22 - 49) = b

√(t² - 27) = b

When b² is substituted, we get:

(x²/(t² + 22)) - (y²/(t² - 27)) = 1

As a result, the hyperbola equation is: x²/(t² + 22) - y²/(t² - 27) = 1

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The median is the middle value in a data set when the values are arranged in order, so it would help the real estate agent to set a price that is not too high or too low compared to other similar houses. The student is misrepresenting their performance by reporting the mean as the average, which does not accurately reflect their performance due to the outlier.

In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and dividing the sum by the number of values. The mean is often used to summarize a set of data with a single value that represents the "center" of the data.

Here,

1. For the first situation, the mode would be the most appropriate measure of central tendency because it would tell the supermarket manager which type of lettuce is purchased most often. The mode is the value that appears most frequently in a data set, so it would indicate which type of lettuce is the most popular among customers.

For the second situation, the mean would be the most appropriate measure of central tendency because it would give the average score of all the tests taken during the grading period. The mean is calculated by adding up all the scores and dividing by the number of scores, so it would give a good representation of the student's overall performance.

For the third situation, the median would be the most appropriate measure of central tendency because it would provide a value that is in the middle of the data set, with half of the comparable houses above and half below the selling price.

2. The student is reporting the mean as the average. The mean is calculated by adding up all the grades and dividing by the number of grades, so in this case, the mean would be (97 + 97 + 75 + 70 + 55)/5 = 78.8%. However, this is not an accurate representation of the student's course performance because the mean is sensitive to outliers, which in this case is the low grade of 55%.

If we calculate the median instead, which is the middle value when the grades are arranged in order, we get 77%, which is closer to the actual performance of the student. The median is not affected by outliers, so it provides a better representation of the center of the data set. The student is misrepresenting their performance by reporting the mean as the average, which does not accurately reflect their performance due to the outlier.

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The median is 77%, which is closer to the actual performance of the student.

what is mean?

In statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in a data set and dividing by the total number of values. The mean is also known as the arithmetic mean or the average. It is commonly used to summarize data and is one of the most widely used measures of central tendency. However, the mean can be sensitive to outliers, which are extreme values that can skew the average and make it less representative of the data set.

The student is reporting the mean as the average. The mean is calculated by adding up all the grades and dividing by the number of grades. In this case, the mean would be:

(97 + 97 + 75 + 70 + 55) / 5 = 78.8%

However, this is not an accurate representation of the student's course performance because the mean is sensitive to outliers, which in this case is the low grade of 55%. If we calculate the median instead, which is the middle value when the grades are arranged in order, we get:

75%, 70%, 55%, 97%, 97%

The median is 77%, which is closer to the actual performance of the student. The median is not affected by outliers, so it provides a better representation of the center of the data set.

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Answer:

7.07cm

Step-by-step explanation:

The statements that are true include the following:

A. the function is increasing over the interval -8 ≤ x ≤ -2.

B. the function is constant over the interval -2 ≤ x ≤ 2.

A. the function is decreasing over the interval 3 ≤ x ≤ 7.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over the interval -2 ≤ x ≤ 2, increasing over the interval -8 ≤ x ≤ -2, and decreasing over the interval 3 ≤ x ≤ 7.

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The longest cart that can pass through the second doorway is 85 inches or less in length.

e) To demonstrate that AABC~ACFD, we want to show that they have the very shape and that their comparing sides are corresponding.

To start with, we can see that point An is normal to the two triangles. Moreover, point BAC is harmonious to point FDC in light of the fact that they are both right points.

Additionally, point ABC is consistent to point ACF on the grounds that they are substitute inside points framed by the cross-over AC converging equal lines Stomach muscle and FD.

Then, we want to show that the relating sides are corresponding. We can begin by contrasting Stomach muscle and FD. We are given that Stomach muscle = 13 inches, and we can see that FD is the flat distance between the two entryways.

How about we call this distance x. Then, at that point, we can set up an extent:

Stomach muscle/FD = 13/x

To find the length of AC, we can utilize the Pythagorean Hypothesis. We know that BC = Cd = 60 inches, so:

[tex]AC^2 = AB^2 + BC^2[/tex]

[tex]AC^2 = 169 + 3600[/tex]

[tex]AC^2 = 3779[/tex]

[tex]AC = \sqrt{(3779)[/tex]

Presently, we can set up another extent:

AC/CF = Stomach muscle/FD

Subbing the qualities we viewed as before, we get:

[tex]\sqrt{(3779)}/CF = 13/x[/tex]

Increasing the two sides by x, we get:

[tex]x * \sqrt{(3779)}/CF = 13[/tex]

Addressing for CF, we get:

[tex]CF = x * \sqrt{(3779)}/13[/tex]

Thus, we have shown that AABC~ACFD on the grounds that they have similar shape and their comparing sides are relative.

f) The longest truck that can go through the subsequent entryway is a truck whose length is equivalent to or not exactly the level distance between the two entryways. This is on the grounds that the entryways are lined up with one another, so the main limitation on the length of the truck is the level distance between the two entryways.

We are given that the main entryway is 72 inches west of the beginning of the subsequent entryway, and we know that BA = 13 inches. In this way, the flat distance between the two entryways is:

FD = 72 + BA = 85 inches

Subsequently, the longest truck that can go through the subsequent entryway is a truck that is 85 inches or less long.

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we would expect about 36 students to score between Sally's score and the mean on the IQ test.

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

We can use the normal distribution formula to calculate the number of students who would be expected to score between Sally's score and the mean:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

First, we need to calculate the z-score for Sally's score:

z = (114 - 100) / 12 = 1.17

To find the number of students who would be expected to score in this range, we multiply this proportion by the total number of students:

0.1210 x 300 ≈ 36.3

So, we would expect about 36 students to score between Sally's score and the mean on the IQ test.

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Interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.

Compound interest is the term for interest that is earned on interest.

This may be shown using simple math: if you start with $100 and it earns 5% interest every year, you will have $105 at the end of the first year.

At the end of the second year, you will have $110.25.

So, we know that:
Principal amount = $25000

Interest rate = 4.7%

Time = 2 years

Compounded annually

Then, using the compounding calculator:

(Refer to the graph attached below)

The amount after 2 years will be $27,405.23.

Interest in this is:
$27,405.23 - $25,000

$2,405.23

Therefore, interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.

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Correct question:

Find the interest earned on a $25,000 deposit for 2 years at 4.7% interest, compounded annually.

Answer:

The probability of choosing a bay horse can be calculated by dividing the number of bay horses by the total number of horses:

Probability of choosing a bay horse = number of bay horses / total number of horses

In this case, we know that there are 5 bay horses and a total of 18 horses:

Probability of choosing a bay horse = 5 / 18

Therefore, the probability of choosing a bay horse is 5/18.

Step-by-step explanation:

Answer:

18/5

Step-by-step explanation:

because a/b equals 18/5

Answer:

Step-by-step explanation:

if he uses 2/6 for his pasta, he should use 2/6 on his pizza (assumption) therefore, he should have used 4/6 of his tomato sauce jar

Answer:

To solve 5(98) =___(100-2) using the distributive property, we can distribute the 5 to both the 100 and the -2:

5(98) = 5(100 - 2)

Now, we can use the distributive property to simplify the right side:

5(98) = 5(100) - 5(2)

Multiplying, we get:

490 = 500 - 10

Simplifying further, we get:

490 = 490

Therefore, the equation is true, and we have verified the distributive property.

Answer:

C. DBA, DB, DC, AC, AB

Step-by-step explanation:

Answer:

We are given that the monthly profit, P, from a product is given by the quadratic function:

P = -x^2 + 105x - 1050

To find the lowest price of the product that gives a monthly profit of $1550, we need to solve the equation:

Rearranging this equation, we get:

To solve for x, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -1, b = 105, and c = -2600.

Substituting these values, we get:

x = (-105 ± sqrt(105^2 - 4(-1)(-2600))) / 2(-1)

x = (-105 ± sqrt(11025 - 10400)) / (-2)

x = (-105 ± sqrt(625)) / (-2)

We can simplify this expression to:

x = (-105 ± 25) / (-2)

Therefore, the two possible values of x are:

x = (-105 + 25) / (-2) = 40

x = (-105 - 25) / (-2) = 50

Since we are looking for the lowest price that gives a monthly profit of $1550, the answer is $40. Therefore, the lowest price of the product that gives a monthly profit of $1550 is $40.

Answer:

Step-by-step explanation:

hello, it seems this is problematic im sorry but I'm not sure if you could put a better picture.

Answer:

Algebraic expression:

y - 3 - (5y - 6)

Simplified: -4y + 3

Step-by-step explanation:

"Subtract 5y−6 from y−3" means the 5y-6 is being taken away from the y-3.

y-3 up front and then minus 5y-6. Use parenthesis to keep things organized.

(y-3) - (5y-6)

This is the algebraic expression.

well, tbh, we don't really need the first set of parenthesis.

y-3 - (5y-6)

This is good enough.

Then, to simplify use distributive property. That minus that we wrote in the middle, it has to go to both the 5y and also to the -6.

y-3 - 5y - -6

= y - 3 - 5y + 6

combine like terms

= -4y + 3

The number of students who belong to neither club is 6 students.

The number of students who are not in either club is 6.

Let's say that there are x students in the classroom.

We know that 1/2 of the students belong to the Chess Club, so 1/2 * x = 6 students belong to the Chess Club.

We also know that 1/3 of the students belong to the Drama Club, so 1/3 * x = 4 students belong to the Drama Club.

Since 1/4 of the students belong to both clubs, then 1/4 * x = 3 students belong to both clubs.

Therefore, the number of students who belong to only one club is 6 - 3 = 3 students.

The number of students who belong to neither club is 6 + 3 - 3 = 6 students.

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Answer:

700 minutes

Step-by-step explanation:

First you need to see how much London even practices in one week. So we will divide the total minutes (t) 525 from the total weeks (w) 3:

t / 3 = m

where m equals the amount of minutes London practices in 1 week.

1) rewrite:

t / 3 = m

2) plug in variables:

525 / 3 = m

3) divide:

525 / 3 = 175

Therefore every week, London practices for 175 minutes.

Secondly, we are going to add 1 more week (175) to the total minutes London spent practicing for the 3 weeks (525).

t = m + m

Where t = total minutes altogether (4 weeks) and m equals the minutes of the 3 weeks and the minutes of 1 week.

1) rewrite:

t = m + m

2) plug in:

t = 525 + 175

2) add:

t = 700

Therefore, London would practice 700 minutes in 4 weeks if she practices the same amount every week.

Answer:

The given line has a slope of 1/4. The slope of any line perpendicular to this line will have a slope equal to the negative reciprocal of 1/4, which is -4.

We are also given that the line passes through the point (0, 2). Using point-slope form, we can write the equation of the line as:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (0, 2). Substituting the values, we get:

y - 2 = -4(x - 0)

Simplifying, we get:

y - 2 = -4x

Adding 2 to both sides, we get the final equation of the line:

y = -4x + 2

Therefore, the equation of the straight line passing through the point (0, 2) which is perpendicular to the line y = 1/4x + 5 is y = -4x + 2.

The cost of painting the entire surface area of the pyramid, including its square base, is approximately $85.44.

What is the cost of painting?

The Great Pyramid of Giza has a square base, so the surface area of the base is simply the area of a square with side length 1.6 meters:

Area of base = (1.6 m)² = 2.56 m²

To find the surface area of the rest of the pyramid, we need to find the area of each of the four triangular faces. Each face is a right triangle with one leg equal to the slant height of the pyramid (which we can find using the Pythagorean theorem) and the other leg equal to half the length of one side of the base.

The slant height can be found using the Pythagorean theorem:

slant height = √((height)² + (1/2 × base)²)

slant height = √((2.4)² + (0.8)²) ≈ 2.53 meters

Then, the area of one triangular face is:

Area of triangular face = (1/2)baseheight

Area of triangular face = (1/2)(1.6 m)(2.53 m) ≈ 2.03 m²

Since there are four triangular faces, the total surface area of the pyramid is:

Total surface area = 4 × (Area of triangular face) + (Area of base)

Total surface area = 4 × (2.03 m²) + 2.56 m²

Total surface area ≈ 10.68 m²

Therefore, the cost of painting the entire surface area of the pyramid at a rate of $8 per square meter is approximately:

Cost = Total surface area × Cost per m²

Cost = 10.68 m² × $8/m²

Cost ≈ $85.44

So, the cost of painting the entire surface area of the pyramid, including its square base, is approximately $85.44.

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The solution of the inequalities is x = 11 and y = 9.

The value of x nickels is 0.05x dollars, and the value of y pennies is 0.01y dollars.

The total value of Sebastian's coins will be:

0.05x + 0.01y dollars

Writing the given conditions as a system of inequalities:

Sebastian has at least 20 coins: x + y ≥ 20

The total value of Sebastian's coins is at most $0.65: 0.05x + 0.01y ≤ 0.65

Solving the inequalities, we substitute y ≥ 20 - x into the second inequality:

0.05x + 0.01(20 - x) ≤ 0.65

0.05x + 0.2 - 0.01x ≤ 0.65

0.04x + 0.2 ≤ 0.65

0.04x ≤ 0.45

x ≤ 11.25

The largest possible whole number value for x is 11.

Solving for the value of y from the first inequality:

x + y ≥ 20

11 + y ≥ 20

y ≥ 9

The closest possible whole number value for y is 11

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