Find three consecutive integers such that when three times the third is increased by the first, the result is 8 less than five times the second.

The data being skewed and indicating higher wait times above 7 minutes due to a busy park is the most suitable description based on the given line plot.

The best description of the shape of the data is that it is skewed and might mean that the wait times were higher than 7 minutes because the park was busy.

Here's the explanation:

From the line plot, we can observe that there are 6 dots above 6, 5 dots above 7, 3 dots above 5, and 2 dots above 8.

The distribution is not symmetric, as the data points are not evenly spread around a central value.

The fact that there are more dots above 7 and 8 suggests that the wait times were higher than these values for a significant number of rides. This skewness in the data indicates that there were instances of longer wait times.

Additionally, the presence of dots above 5 and 6 suggests that there were some rides with shorter wait times as well.

However, the higher concentration of dots above 7 and 8 indicates that the park was likely busy, leading to longer wait times.

The option stating that the data is skewed and might mean that the wait times were higher than 7 minutes because the park was busy best aligns with the information provided by the line plot.

It acknowledges the skewness of the data towards higher wait times, suggesting that the park experienced increased demand and longer queues during the fair.

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(a) The amount of money accrued at the end of 5 years is given by S = 50e^(0.0575*5).

(b) It will take approximately t = ln(2) / 0.0575 years for the initial sum deposited to double.

(c) The solution to the differential equation y' - y^2 = 6y + 9 is y = -3 ± De^(-t), where D is an arbitrary constant.

(a) To find the amount of money accrued at the end of 5 years, we can solve the differential equation:

dS/dt = rS

Separating variables and integrating, we get:

∫ (1/S) dS = ∫ r dt

ln|S| = rt + C

Taking the exponential of both sides, we have:

S = e^(rt+C) = Ce^(rt)

Given that AED 50 is deposited initially, we can find the value of C. When t = 0, S = 50:

50 = Ce^(r * 0)

50 = C

Substituting C = 50 and r = 5.75% (converted to a decimal), we have:

S = 50e^(0.0575t)

At the end of 5 years (t = 5), the amount of money accrued is:

S = 50e^(0.0575 * 5)

(b) To find the number of years it takes for the initial sum deposited to double, we need to solve the equation:

2S = 50e^(0.0575t)

Dividing both sides by 50:

e^(0.0575t) = 2

Taking the natural logarithm of both sides:

0.0575t = ln(2)

Solving for t:

t = ln(2) / 0.0575

(c) The given differential equation is:

y' - y^2 = 6y + 9

Rearranging the equation:

y' = y^2 + 6y + 9

This is a separable differential equation. Separating variables and integrating, we have:

∫ (1/(y^2 + 6y + 9)) dy = ∫ dt

Applying partial fractions to the left side, we get:

∫ (1/(y + 3)^2) dy = ∫ dt

-ln|y + 3| = t + C

Taking the exponential of both sides and simplifying, we have:

|y + 3| = e^(-t-C) = De^(-t)

Since D is an arbitrary constant, we can write it as D = ±e^C. Thus, we have:

y + 3 = ±De^(-t)

Solving for y, we get:

y = -3 ± De^(-t)

where D is an arbitrary constant.

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The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting\(y = x^2\)and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression \(2\pi x(5x - x^2)dx\) from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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The grade point average received by hector is 3.75.

Your grade point average (GPA) is calculated by dividing the total number of credits you have earned in high school by the sum of all of your course grades. The majority of colleges and secondary schools use a 4.0 scale to report grades. A perfect score, or an A, is a 4.0.

The unit value for each course in which a student obtains one of the grades mentioned above is multiplied by the grade point total for that grade to determine the GPA. Then, divide the sum of these products by the sum of the units. The cumulative GPA is calculated by dividing the total grade points by the total number of units.

3 a and one is B received by Hector.

The A = 4.0, B = 3.0, C = 2.0, D = 1.0 is given by college

We have GPA= A+A+A+B/4

GPA=4+4+4+3/4

GPA= 15/4

GPA=3.75

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Complete question

Hector Ramirez received three A's and one B in his college courses. What is his grade point average? Assume each course is three credits. A = 4.0, B = 3.0, C = 2.0, D = 1.0

Answer:

D. $870; $31,320 from deposits and $3,680 from interest

Explanation:

In order to calculate the monthly payment, we use the formula below:

Given:

• The Financial Goal, A= $35,000

• Rate = 7.5% = 0.075

• Number of compounding period = 12 (Monthly)

• Time, t = 3 years

Substitute into the given formula:

The monthly payment is $870.

Option D is correct.

Answer:

False

True

Step-by-step explanation:

Hope this helps:)

Answer:

True on both.

Step-by-step explanation:

The slopes of lines do not change with dilations.

AD and A'D' are parallel.

CD and C'D' are both perpendicular to the x-axis.

True on both.

The length of the rectangular plot of land is 168 ft.

To find the length of the rectangular plot of land, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In the given diagram, we can see that the plot of land forms a right triangle, where the length of one leg is 874 ft and the length of the diagonal is 890 ft. Therefore, the length of the rectangular plot can be found as follows:

\(h^2 = a^2 +b^2\\b^2 = h^2 - a^2\\b = \sqrt{h^2-a^2} \\b= \sqrt{(890)^2- (874)^2}\\ b= \sqrt{792100- 763876}\\ b= \sqrt{28224}\\ b= 168\)

So, the length of the rectangular plot of land is 168 ft.

The lengths of the legs of a right triangle are related to the lengths of the sides of a rectangle in the following way:

If we draw a rectangle with sides of length "a" and "b", then the diagonal of the rectangle (which is the hypotenuse of the right triangle formed by the sides of the rectangle) will have a length equal to the square root of (\(a^2 + b^2\)).

Conversely, if we have a right triangle with legs of length "a" and "b", then we can form a rectangle by making the legs of the triangle the sides of the rectangle. The length of one side of the rectangle will be "a" and the length of the other side will be "b".

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Answer:

I would say B

Step-by-step explanation:

You would be making more money

Answer:

uh i don't really get the question you asked, but if it's asking for the improper fraction of 3 1/4, it's 13/4.

Step-by-step explanation:

The correct option is d. Neither Type I nor Type II error.  The concepts of Type I and Type II errors, and to use appropriate methods and sample sizes to minimize the risk of making such errors.

To understand why, let's first define Type I and Type II errors. Type I error is rejecting a true null hypothesis, while Type II error is failing to reject a false null hypothesis.

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Answer:

G(x) = 3x +2

Step-by-step explanation:

I do not know what the problem is asking for, but if it's asking for the function, here you go.

Answer:

shbdhsjdcjsvdbssegehehhehehejrjehe

Answer:

x ≤ 205.05

Step-by-step explanation:

x = dollar amt remaining for other books

30 + 14.95 + x ≤ 250

44.95 + x ≤ 250

x ≤ 205.05

x ≤ $205.05 is an inequality that correctly describes this situation.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Let's use x to represent the amount of money Ms. Edwards can spend on other books.

We know that Ms. Edwards can spend at most $250 in total and that she will already spend $30 + $14.95 = $44.95 on the reference books on birds and planets.

Therefore, the amount she has left to spend on other books is:

x = $250 - $44.95

x = $205.05

Ms. Edwards can spend up to $205.05 on other books.

To write this as an inequality, we can use the less than or equal symbol since Ms. Edwards cannot spend more than $205.05:

x ≤ $205.05

Therefore, the inequality that correctly describes this situation is:

x ≤ $205.05

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You didnt give a picture of the question showing the shorts

Answer:   $24.34

Step-by-step explanation:

28/X=115/100

Part/Whole= %/100

28=1.15*x

x=28/1.15

x=24.34

Answer: m= 1/2

Step-by-step explanation:

It rises +3 and shifts right 6, and if simplified gives you 1/2.

The ring R is said to consist of all functions f(x) that have an expression of the form f(x).

The given ring of trigonometric polynomials, R, consists of all the functions that have an expression of the form f(x). The expression f(x) is defined as below:f(x) = a0 + a1cos(x) + b1sin(x) + a2cos(2x) + b2sin(2x) + a3cos(3x) + b3sin(3x) + … + ansin(n*x) + bnsin(n*x)where n is a non-negative integer, and the coefficients a0, a1, b1, a2, b2, a3, b3, an, and bn are real numbers.In this way, every element of R is expressed as a trigonometric polynomial, and every trigonometric polynomial belongs to R. So, the ring R is said to consist of all functions f(x) that have an expression of the form f(x).Hence, this is the required proof.

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Answer:

44

Step-by-step explanation:

I'm assuming you're meant to multiply so I did 3(14)+2 and it gave me 44 :)

Answer:

so it should be 44

Step-by-step explanation:

So the sub for b is 14 so substitute the b to 14

Then 3(14) they are multiplying so multiply them should equal 42

Then add the 2 the answer should be 44

I hope that you understoood!

Answer:

that would be 3.5

Step-by-step explanation:

have a great day (:

Answer: 3 1/2

Step-by-step explanation: The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed. Therefore, a way to solve this problem is by multiplying (7/8 x 4/1) which will give us a final answer or result of 3.5 or 3 1/2.

The equation of the sphere is (x - 6)² + (y - 4)² + (z - 6)² = 6. To find the equation of a sphere, we need the center and the radius of the sphere.

Given the endpoints of one of its diameters, we can determine the center by finding the midpoint, and the radius by finding the distance between the center and one of the endpoints. Let's calculate the center first. The midpoint of the diameter with endpoints (5, 2, 5) and (7, 6, 7) can be found by taking the average of the corresponding coordinates:

Center:

x-coordinate: (5 + 7) / 2 = 6

y-coordinate: (2 + 6) / 2 = 4

z-coordinate: (5 + 7) / 2 = 6

So the center of the sphere is (6, 4, 6).

Next, let's calculate the radius. We can use the distance formula between the center and one of the endpoints:

Radius:

√[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

= √[(7 - 6)² + (6 - 4)² + (7 - 6)²]

= √[1 + 4 + 1]

= √6

The radius of the sphere is √6.

Finally, we can write the equation of the sphere in the standard form:

(x - h)² + (y - k)² + (z - l)² = r²

where (h, k, l) is the center and r is the radius.

Plugging in the values we found:

(x - 6)² + (y - 4)² + (z - 6)² = (√6)²

Simplifying, we have:

(x - 6)² + (y - 4)² + (z - 6)² = 6

Therefore, the equation of the sphere is (x - 6)² + (y - 4)² + (z - 6)² = 6.

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In response to the stated question, we may state that To accommodate scatter plot the provided data on the scatter graph, the grid must be at least 65 squares wide and 62 squares height.

"Scatter plots are graphs that show the association of two variables in a data collection. It is a two-dimensional plane or a Cartesian system that represents data points. The X-axis represents the independent variable or characteristic, while the Y-axis represents the dependent variable. These plots are sometimes referred to as scatter graphs or scatter diagrams."

To plot the supplied data on a scatter graph, we must ensure that the distance and height values are both within the grid.

The given distances are 37, 6, 71, and 28. As a result, the distance axis's minimum and maximum values are 6 and 71, respectively.

Height values are as follows: 61, 32, 94, 48. As a result, the lowest and maximum height axis values are 32 and 94, respectively. To ensure that all of the height values fit on the graph, we need a grid at least 94-32 = 62 squares tall.

To accommodate the provided data on the scatter graph, the grid must be at least 65 squares wide and 62 squares height.

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Answer:

1.79 or 43/24

Step-by-step explanation:

179 pregunta 43/24

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Here's the solution :

Product of xy and 3x³y + 7x²y² - 4xy³ :

product of x² + y³ and x⁴ - y¹ :

Answer: It will demonstrate closer because the numbers are whole, just got them right on the test. Hope this helped :3

Step-by-step explanation: Cause I guessed and got them right.

The value of the voltage of the electricity is 6 + j + 2j²

From the question, we have the following parameters that can be used in our computation:

C = 2 - j

I = 3 + 2j

The formula of voltage is given as

V = CI

Substitute the known values in the above equation, so, we have the following representation

V = (2 - j) * (3 + 2j)

Open the brackets

So, we have

V = 6 + 4j - 3j + 2j²

Evaluate the like terms

V = 6 + j + 2j²

Hence, the voltage is 6 + j + 2j²

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The perimeter of the rhombus LMNO is 48  units

In the rhombus LMNO,

The length of the side LM = The length of the side MN = The length of the side NO = The length of the side ON

Then,

The length of the side LM = 3x - 3

The length of the side MN = x + 7

Both are equal, then the equation will be

3x - 3 = x + 7

Group the like terms

3x - x = 7 + 3

2x = 10

x = 10 /2

x = 5

Substitute the value  in second equation

x + 7 = 5 + 7

= 12 units

The perimeter of the LMNO = 4 × 12

= 48 units

Hence, the perimeter of the rhombus LMNO is 48  units

The complete question is

What is the perimeter of rhombus LMNO ? A) 20 units B) 24 units C) 40 units D) 48 units

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Answer:

nobody knows, go to a shop

Step-by-step explanation:

Answer:

1/5 is 20% which means that it's greater than 19%

Step-by-step explanation:

Hope this helped :)

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

The mean absolute error (MAE) function is the best option for a data analyst who wants to quickly measure the difference between the predicted and actual outcomes of their data model. It provides a single number that represents the average difference between the two outcomes, and can be used to evaluate the performance of the model.

A data analyst can use the mean absolute error (MAE) function to quickly measure the difference between the predicted outcome and the actual outcome of their data model. The MAE is a common evaluation metric used in regression analysis to measure the average absolute difference between the predicted and actual values.
The MAE function calculates the absolute difference between each predicted value and its corresponding actual value, and then takes the mean of all the absolute differences. This provides the analyst with a single number that represents the average difference between the predicted and actual outcomes.
The bias() function is used to measure the difference between the predicted and actual values in terms of the overall direction of the difference. If the bias is positive, it means that the predicted values are higher than the actual values, and vice versa.
The correlation (cor()) function measures the strength and direction of the linear relationship between two variables. It can be used to determine if there is a relationship between the predicted and actual outcomes of the data model.
The standard deviation (sd()) function measures the spread of a dataset. It can be used to determine how much the predicted and actual outcomes deviate from the mean.
In conclusion, the mean absolute error (MAE) function is the best option for a data analyst who wants to quickly measure the difference between the predicted and actual outcomes of their data model. It provides a single number that represents the average difference between the two outcomes, and can be used to evaluate the performance of the model.

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9514 1404 393

Answer:

  $48,000 to start, with 6% raises

Step-by-step explanation:

The starting salaries are within a few percentage points of each other, so the majority of the difference in earnings will come because of the raises. The offer with the largest raise percentage is likely the best.

The earnings total can be figured as the sum of a geometric series with a first term of "starting salary" and a growth factor of (1+raise percentage). For starting salary 's' and raise percentage 'r', the total earnings in 6 years will be ...

  S = s((1+r)^6 -1)/r

Here are the total earnings, in thousands, for each of the offers:

  a) s = 49, r = .03, S = 316.95

  b) s = 51, r = .01, S = 313.75

  c) s = 48, r = .06, S = 334.82 . . . . best offer

  d) s = 50, r = .02, S = 315.41

The worker can earn the most from a starting salary of $48,000 and 6% increases each year.

C) a starting salary of $48,000 with a 6% increase each year

Answer:

\(26\) and \(28\).

Step-by-step explanation:

Let \(x\) denote the smaller one of the two even integers (\(x > 0\) since both integers are positive.) The larger one of the two consecutive even integer would be \((x + 2)\).

The square of the smaller integer would be \(x^{2}\).

Five times the larger integer would be \(5\, (x + 2)\).

Subtract five times the larger integer from the square of the smaller integer to get \((x^{2} - 5\, (x + 2))\).

The value of this expression should be equal to \(536\). In other words:

\(x^{2} - 5\, (x + 2) = 536\).

Rewrite and simplify this quadratic equation:

\(x^{2} + (-5)\, x + (- 546) = 0\).

Apply the quadratic formula to find possible values of \(x\):

\(\begin{aligned}x_{1} &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-5) + \sqrt{(-5)^{2} - 4 \times 1 \times (-546)}}{2}\\ &= \frac{5 + \sqrt{2209}}{2} \\ &=\frac{5 + 47}{2} \\ &= 26\end{aligned}\).

\(\begin{aligned}x_{2} &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{5 - \sqrt{2209}}{2} \\ &=\frac{5 - 47}{2} \\ &= -21\end{aligned}\).

Since \(x > 0\) (both numbers are supposed to be positive), \(x = 26\) would be the only valid solution.

Therefore, the two integers would be \(x = 26\) and \(x + 2 = 28\).