A geologist gathered data about the total shoreline and maximum depth of several area lakes and organized the data into this table. Total Shoreline (miles) 22 17 10 23 12 35 7 Maximum Depth (feet) 101 85 59 113 64 158 33 She then used a graphing tool to display the data in a scatter plot, with x representing the total miles of shoreline and y representing the maximum depth. She also used the graphing tool to find the equation of the line of best fit: y = 4.26x + 10.908. Based on the line of best fit, what is the approximate maximum depth of a lake that has 31 miles of shoreline? A. 121 feet B. 132 feet C. 138 feet D. 143 feet

When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

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The standard deviation for the number of people with the genetic mutation in such groups of 100 is 1.4

From the information given,

About 2% of the population has a particular genetic mutation, and 100 people are randomly selected.

The standard deviation for the number of people with the genetic mutation in such groups of 100 is obtained below;

The required standard deviation is,

p = 0.02 and n = 100;

1 - p = 1 - 0.02

       = 0.98

σ = \(\sqrt{n*(1-p)*p}\)

σ = \(\sqrt{100*0.02*0.98}\)

σ = 1.4

The standard deviation for the number of people with the genetic mutation in such groups of 100 is 1.4

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The width of the swimming pool is 1.624yards.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

Here, we have,

a swimming pool can hold 9.745 cubic yards of water.

i.e. V = 9.745

it has a length of 3 yards and a height of 2 yards.

i.e. l= 3

    h=2

so, width = w = V/(l*h)

i.e. w = 1.624

Hence, the width of the swimming pool is 1.624yards.

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Answer:

4

Step-by-step explanation:

because The square root of 16 is 4, which is a rational number.

Answer:

4

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

the y-intercept at x = -1 is -5

Answer:

The sum of all the geometrical figures in this questions equals 74 total sides - Quadrilaterals have four sides (rectangles, rhombi), Dodecagons have twelve sides, Hexagons have six sides.

5 Quadrilaterals - 4 * 5 = 20

4 Dodecagons - 12 * 4 = 48

1 Hexagon - 6 * 1 = 6

20 + 48 + 6 = 74 total sides.

The polynomial 9x^2 + 4 is equivalent to (3x+2i)(3x-2i). The answer is A.

Polynomials are algebraic expressions that consist of variables and coefficients where arithmetic operations can be performed.

A polynomial is expanded if no variable appears within parentheses and all like terms have been combined.

To expand a polynomial, multiply its factors (often by using the distributive property) or perform the indicated operations.  Then combine all like terms.

Expanding each of the options provided using FOIL method:

a) (3x+2i)(3x-2i)

= 9x^2 - 2ix + 2ix - 4i^2

= 9x^2 - 4i^2            *(i^2 = -1) note that i is an imaginary number and i squared is equal to -1

= 9x^2 - 4(-1)

= 9x^2 + 4

b) (3x+2)(3x-2)

= 9x^2 + 6x - 6x - 4

= 9x^2 - 4

c) (3x + 2i)^2

= 9x^2 + 6ix + 6ix + 4i^2          *(i^2 = -1)

= 9x^2 + 12ix - 4

d) (3x + 2)^2

= 9x^2 + 6x + 6x + 4

= 9x^2 + 12x + 4

Hence, the polynomial 9x^2 + 4 is equivalent to (3x+2i)(3x-2i). The answer is A.

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Answer:

The answer would not be 0, it would be -12, and here is why.

4x^4+ 16x+31x^2=62x-90.

In thia case i ignpored the variable, i think its a variable..

You woulkd add 62+16, you get 78.

78-90= -12

The probability that an endure all battery selected at random will last more than 610 hours is 0.3%

What is the Z score?

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

Z score is used to determine by how many standard deviations the raw score is above or below the mean, The z score is given by:

\(z = \frac{x - \mu}{\sigma}\)

where,

x = raw score

μ = mean

σ = standard deviation

Given that μ = 500, σ = 40, for x > 610:

z = (610 - 500) / 40

= 2.75

From the normal distribution table, P(z > 2.75) = 1 - P(z < 2.75) = 1 - 0.9970 = 0.0030 = 0.3%

Hence, the probability that an endure all battery selected at random will last more than 610 hours is 0.3%

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There are 84 ways a student can arrange the schedule consisting of 8;00 am classes ,9;00 am classes and 10;00am classes.

The fundamental counting principle states that if there are p ways to do one thing, and q ways to do another thing, then there are p×q ways to do both things For example  Suppose we have 3 shirts (call them A , B , and C ), and 4 pairs of pants (call them w , x , y , and z ). Then we have 3×4=12.

If an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m × n.Then we can use formula to find.

Now we get

8;00 am classes =7 ways

9;00 am classes=4 ways

10;00 am classes=3 ways

So that the event could occur in following sequence

7.4.3 = 84  ways

Hence 84 ways can student arrange the schedule.

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Question

Choose the correct form of the missing verb in each sentence.

The field trip for the preschoolers

✔ starts

 at 10:00 a.m.

Several of the students in the class

✔ arrive

 early.

Answer:

x = 12

DEG = 130 degrees

Step-by-step explanation:

Since EF bisects the angle that means that the two "mini" angles are equal degrees. So 6x-7 (DEF) = 2x+41 (GEF)

6x-7=2x+41

-2x      -2x

4x-7=41

+7      +7

4x=48

/4      /4

x=12

so now pick an equation and replace x with 12, since you know that x=12

GEF = 2x+41

GEF = 2(12)+41

GEF = 24+41

GEF = 65 degrees

Remember how the DEF and GEF and equal degrees? That means that they are both 65 degrees, so by adding the angles together you get DEG

65 + 65 = 130

 :D   2 btw

Step-by-step explanation:

File name: “TestClass.java” import java.util.Scanner; public class TestClass {

A recursive function is one that generates a series of terms by iterating over or using its foregoing terms as input. This function is typically understood in terms of an arithmetic-geometric series with terms that share similar differences.

File name: “TestClass.java”

import java.util.Scanner;

public class TestClass {

     //Define main() method

     public static void main(String[] args) {

           // Construct a Scanner object

           Scanner scr = new Scanner(System.in);

           //Ask the user to enter a decimal number

           System.out.print("Enter a decimal number: ");

           //Get the decimal number from the user

           int decinum = scr.nextInt();

           // Display the binary number

           System.out.println("The binary equivalent of the decimal value"

                 + decinum + " is " + dec2Bin(decinum));

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Answer:

69w^2 + 17w

Step-by-step explanation:

1. PEMDAS - simplify using steps

2. Put together all like terms.

3. Add or subtract together.

5w(14w) + 3w^2 + 8w - 4w^2 + 9w

69w^2 + 17w

Hope this helps:)

Answer:

9w² - 18w

or

9w(w - 9)

Step-by-step explanation:

Let's start by applying the distributive property to all of the expressions:

5w(2w - 7) + w(3w + 8) - 4w² + 9w

10w² - 35w + 3w² + 8w - 4w² + 9w

Now, combine the like terms:

9w² - 18w

You could stop there, but if you wanted to, you could factor out a 9 and a w:

9w(w - 9)

Hope that helps :) If you have any questions, please comment on this thread! I'm more than willing to help!

If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

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Answer: $24 after 4 years

Step-by-step explanation:

1.5% = 0.015

Take 400 times 0.015 = $6 per year

6 times 4 = $24 after 4 years

The rate of change of the exponential function in this problem represents a decay, and the rate of decrease is of 3.7%.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which:

The function in this problem is given as follows:

y = 20(0.963)^x.

As 0.963 < 1, this is an exponential decay function, and the decay rate is given as follows:

1 - r = 0.963

r = 1 - 0.963

r = 0.037

r = 3.7%.

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Answer:

The equation in standard form is:

x^2-40x-6000 = 0

Step-by-step explanation:

Let the length of the field be x yards.

Now the width of the field is 40 yards less than the length of the field.

Thus, the width of the field would be (x-40) yards

Now, to calculate the area of the field, we simply multiply the length of the field by the width of the field.

Hence;

Since the shape is rectangular, the area is the product of the length and that of the width

x(x-40) =6,000

x^2 -40x = 6,000

x^2-40x-6000 = 0

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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Option (a) \(-\frac{23}{3}\)  is the smallest among the four option because it has negative value. We can easily find it by seeing negative value but we do by taking LCM of denominator .

The smallest multiple that two or more numbers share is known as the least common multiple. Least Common Multiple short form is LCM.

We can find LCM of these number by taking least common multiple.

LCM of 3, 3, 17, 13 is 663 .

(a) \(-\frac{22}{3} *663 = -22*221\)

\(= -4862\)

(b) \(\frac{4}{3} * 663 = 4 * 221\)

\(= 884\)

(c) \(\frac{6}{17} *663 = 6 * 17\)

\(= 102\)

(d) \(\frac{2}{13}*663 = 2*51\)

\(=102\)

So, the Smallest no \(-\frac{22}{3}\).

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9514 1404 393

Answer:

  50°

Step-by-step explanation:

Angle DEG is also angle DEC. It subtends arc DC as does inscribed angle DFC. Inscribed angles that subtend the same arc have the same measure.

  ∠DFC = ∠DEG = 50°

Answer: 50

Step-by-step explanation: Khan Academy

To create a clean and minimalist look for a line graph, it is generally recommended to remove the gridlines, tick marks, and possibly the axis titles. These elements can clutter the graph and distract from the main focus, which is the data itself.

The primary objective of a line graph is to visually represent the data in a clear and concise manner. To achieve a clean look, it is often beneficial to remove unnecessary elements that do not contribute directly to the understanding of the data.

Gridlines, while they can assist in reading values, can create visual noise and make the graph appear cluttered. Removing gridlines allows the data points to stand out more prominently. Similarly, tick marks along the axes can be reduced or eliminated to minimize distractions and focus attention on the plotted data.

Axis titles, though important for providing context, may sometimes be redundant or self-explanatory based on the nature of the graph or if the data is accompanied by clear labels. If the graph is already labeled adequately, removing the axis titles can help create a cleaner and less cluttered appearance.

It's important to consider the specific context and intended audience of the graph. Adjustments should be made in a way that maintains clarity and readability while achieving a clean and visually appealing design.

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The statement is true: if the function f(x) is bounded by m and M on the interval [a, b], where m is the absolute minimum and M is the absolute maximum, then the integral of f'(x) over the same interval is equal to M(b-a) - m(b-a). This relationship holds true for any continuously differentiable function.

Let F(x) be an antiderivative of f'(x). By the Fundamental Theorem of Calculus, we have:

∫[a,b] f'(x) dx = F(b) - F(a)

Since f(x) is bounded by m and M, we know that m ≤ f(x) ≤ M for all x in [a, b]. This implies that F'(x) = f(x) is also bounded by m and M. Thus, F(x) takes on its absolute maximum M and its absolute minimum m on [a, b].

Therefore, we have:

m ≤ F'(x) ≤ M

Integrating both sides of the inequality over the interval [a, b], we get:

∫[a,b] m dx ≤ ∫[a,b] F'(x) dx ≤ ∫[a,b] M dx

m(b-a) ≤ F(b) - F(a) ≤ M(b-a)

But we know that F(b) - F(a) is equal to the integral of f'(x) over [a, b]. Therefore, we can rewrite the inequality as:

m(b-a) ≤ ∫[a,b] f'(x) dx ≤ M(b-a)

Hence, we can conclude that:

∫[a,b] f'(x) dx = M(b-a) - m(b-a) = (M - m)(b-a)

Therefore, the integral of f'(x) over the interval [a, b] is equal to M(b-a) - m(b-a).

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This is the answer to your problem

The length of the garden is 99 m.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the area of the rectangle is 8811 \(m^{2}\) and the width is 89 m. Substituting these values into the formula, we get:

8811 \(m^{2}\) = Length x 89 m

To solve for the length, we can divide both sides of the equation by 89 m:

Length = 8811 \(m^{2}\) / 89 m

Simplifying, we get:

Length = 99 m

Therefore, the length of the garden is 99 m.

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Answer:

(0,6), (6,0)

Step-by-step explanation:

Answer:

Whatttttttttttttttttt

Answer:

11

Step-by-step explanation:

7 + 4 = 11

Answer:

11

Step-by-step explanation:

If a = 7, then a + 4 = 7 + 4 = 11

Hope that this helps!