Elijah's scout troop took a field trip to the local fire station. They learned that Benjamin Franklin established the first volunteer fire company in 1736! At the end of the trip, the scouts spun a spinner to determine what color fire helmet each got to take home. Here are the spinner results of the scouts who spun before Elijah: red, yellow, blue, yellow, green, yellow, red, blue, green, red, yellow, blue, yellow, green Based on the data, what is the probability of the spinner landing on red during Elijah's turn? Write your answer as a fraction or whole number.

To estimate the difference between proportions, sample around 3355 stalks from each section of the field.

In order to estimate the true difference between proportions of stalks damaged in the two sections of the sugarcane field, we need to determine the sample size required to achieve a desired level of precision and confidence.

To estimate the required sample size, we can use the formula for sample size determination for estimating the difference between two proportions. This formula is based on the assumption of a normal distribution and requires the proportions from each section.

Let's denote the proportion of stalks damaged in the middle section as p1 and the proportion of stalks damaged in the outer perimeter as p2. We want to estimate the difference between these proportions to within 0.02 (±0.02) with 90% confidence.

To calculate the required sample size, we need to make an assumption about the value of p1 and p2. If we don't have any prior knowledge or estimate, we can use a conservative estimate of p1 = p2 = 0.5, which maximizes the required sample size.

Using this conservative estimate, we can apply the formula for sample size determination:

n = (Z * sqrt(p1 * (1 - p1) +\(p2 * (1 - p2)))^2 / d^2\)

where:

Plugging in the values, we get:

n = (1.645 * sqrt(0.5 * (1 - 0.5) + 0.5 *\((1 - 0.5)))^2 / 0.02^2\)

n = (1.645 * sqrt\((0.25 + 0.25))^2\)/ 0.0004

n = (1.645 * sqrt\((0.5))^2\) / 0.0004

n =\((1.645 * 0.707)^2\) / 0.0004

n =\(1.158^2\) / 0.0004

n = 1.342 / 0.0004

n ≈ 3355

Therefore, the required sample size from each section of the field would be approximately 3355 stalks, in order to estimate the true difference between proportions of stalks damaged in the two sections to within 0.02 with 90% confidence.

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To estimate the true difference between proportions of stalks damaged in the two sections of the sugarcane field, approximately 665 stalks from each section should be sampled.

In order to estimate the true difference between proportions of stalks damaged in the middle and outer perimeter sections of the sugarcane field, a representative sample needs to be taken from each section. The goal is to estimate this difference within a certain level of precision and confidence.

To determine the sample size needed, we consider the desired precision and confidence level. The requirement is to estimate the true difference between proportions of stalks damaged within 0.02 (i.e., within 2%) with 90% confidence.

To calculate the sample size, we use the formula for estimating the sample size needed for comparing proportions in two independent groups. Since an equal number of stalks will be sampled from each section, the total sample size required will be twice the sample size needed for a single section.

The formula to estimate the sample size is given by:

n = [(Z * sqrt(p * (1 - p)) / d)^2] * 2

Where:

n is the required sample size per section

Z is the Z-value corresponding to the desired confidence level (for 90% confidence, Z = 1.645)

p is the estimated proportion of stalks damaged in the section (unknown, but assumed to be around 0.5 for a conservative estimate)

d is the desired precision (0.02)

Plugging in the values, we can calculate the sample size needed for each section.

n = [(1.645 * sqrt(0.5 * (1 - 0.5)) / 0.02)^2] * 2

n ≈ 664.86

Rounding up, we arrive at approximately 665 stalks that should be sampled from each section.

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The solution is : 72 miles is the scale of inches to miles.

Here, we have,

given that,

If 5 inches on a map covers 360 miles,

now, we have to find the scale of inches to miles.

we know that,

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor.

Maps use scale factors to represent the distance between two places accurately.

let, the scale of inches to miles = x

so, we have,

5 inchs = 360 miles

1 inch = x miles

i.e. x = 360/ 5 = 72 miles

Hence, The solution is : 72 miles is the scale of inches to miles.

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Answer:

negative

Step-by-step explanation:

Answer:

negative

Step-by-step explanation:

The annual net income and annual yield are $3400 and 2.335 respectively

a) To find the annual net income, we need to subtract the annual expenses from the annual rental income. The annual rental income can be calculated as follows:

$3,875 * 6 months = $23,250

The annual net income would be:

$23,250 - $19,850 = $3,400

b) The annual yield can be calculated as the annual net income divided by the total cost of the property, including the down payment:

$3,400 / ($185,900 - $40,000) = 0.023 or 2.33%

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Answer:

y=(x-8)(x+6)

Step-by-step explanation:

8 is a factor of 2, 6 adds up to 48

(also, my calculator can factor :P)

Hope this helps!

Answer:

y = (x - 8)(x + 6)

Step-by-step explanation:

In order to turn this into factored form, you need to find which two numbers add to -2 and multiply to -48. First, identify factors and see which ones have a difference of 2:

2 × 24

3 × 16

4 × 12

6 × 8

6 and 8 have a difference of 2 and multiply to 48. In order for them to add to -2 and multiply to -48 though, one must be negative. You can tell that 8 will be negative because -8 + 6 = -2 and -8 × 6 = -48.

At this point, you can write the factored form:

y = (x - 8)(x + 6)

(If you want to check your answer, you can just multiply the binomials using FOIL and see if they are the same as the given quadratic function)

Answer:

12/5

Step-by-step explanation:

4/5 x 3 = (4 x 3)/5 = 12/5 (2 and 2 fifths)

Answer:

Simplified:

Step-by-step explanation:

Given equation:

Multiply ONLY the numerator with the whole number to get the answer:

Simplify:

Answer: 10.6 tenths divided by .04 hundredths

Step-by-step explanation: i cant expain it srry

Answer:

265

Step-by-step explanation:

because you devide and i used a calculator but most people use paper 10.6÷0.04 equals 265

Answer:

answer 1: It forms a linear pair with one of the interior angles of the triangle

Step-by-step explanation:

The sum of an exterior angle and its adjacent interior angle is 180 degrees.

Also, linear pair of angles are supplementary.

The term that completes the blank and fits the description is an array

From the question, we understand that:

The term that fits the above highlights is array

Hence, the complete statement is:

array can hold multiple values within a single variable and is defined by having values between square brackets.

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Answer:

If r=0, there is absolutely no relationship between the two variables.

Step-by-step explanation:

option (a) is the correct answer. The required coating for the spherical ball bearing having a protective coating of 0.03 cm and a radius of approximately 6 cm is 12.564 cm3.

Given that: A spherical ball bearing is coated with 0.03 cm of a protective coating.The radius of this ball bearing is 6 cm.

the surface area of the sphere is:SA = 4πr2.

Therefore, the surface area of a spherical ball bearing with a radius of 6 cm is calculated as follows:SA = 4πr2= 4 × 3.14 × 6 × 6= 452.16 cm2

Now that the protective coating is applied to the sphere, the total surface area of the sphere will be as follows:

New Surface area = (4π(6 + 0.03)2) cm2= (4π(6.03)2) cm2= 457.08 cm2.

The difference between the two surface areas (without coating and with coating) will provide the area that needs to be coated.

A = New Surface area - Surface area without coating= 457.08 - 452.16= 4.92 cm2.

Therefore, the volume of the protective coating required is given as follows:Volume of coating = Area to be coated × Thickness of coating= 4.92 × 0.03= 0.1476 cm3 = 0.148 cm3 (approximately) .

Hence, the required coating for the spherical ball bearing having a protective coating of 0.03 cm and a radius of approximately 6 cm is 12.564 cm3 . Therefore, option (a) is the correct answer.

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Answer:

7.038

Step-by-step explanation:

35.06-2.098=32.962

40.00-32.962=7.038

Answer:

7.038

u can find the difference of 35.06 and 2.098 first.

afterwards, u can subtract the difference from 40.00 to get the answer of 7.038

hope it helps:)))

Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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Answer:

y=-3.5x+9

Step-by-step explanation:

the slope is determined by the y1-y2/x2-x1 which is equaled to -5-2/4-2 which is equaled to -7/2 which is -3 1/2 which is your m value in y=mx+b and you graph to get your b value (y-intercept) which is 9

Answer:

I know I'm a little late, but there are 10 different ways the plate can be filled.

Step-by-step explanation:

Formula:

Answer:

the first answer

Step-by-step explanation:

1/8 of the absolute value is 1/8 positive

anything from the absolute value is positive because absolute value is the value of how far away the number is from zero.

Answer:

-1/8

Step-by-step explanation:

Salma will have $4,762.80 in her account after 4 years with the given conditions.

The formula for compound interest is given as:

\(A=P(1 + r/n)^(^n^*^t)\) where A = final amount; P = principal (initial amount); R = interest rate (in decimal); N = number of times interest is compounded per unit time (usually per year); t = time (in years).

Given, P = $4000R = 4.7% (in decimal);

N = 4 (interest is compounded quarterly);

T = 4 (years).

Substituting the values in the formula,

\(A = $4000(1 + 0.047/4)^(^4^*^4)A = $4000(1.01175)^1^6A = $4,762.80\)

Therefore, Salma will have $4,762.80 in her account after 4 years with the given conditions.

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Answer:

it's 4 1/3

Step-by-step explanation:

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The distance from the origin is determined by the position of the object, which cannot be determined from the graph of velocity.

The graph shows the velocity of an object as a function of time. When the velocity is positive, the object is moving to the right, and when the velocity is negative, the object is moving to the left. The velocity is decreasing because the slope of the graph is negative, but it is not necessarily moving towards the origin.

The distance from the origin is determined by the position of the object, which cannot be determined from the graph of velocity.The object is moving towards the origin means the displacement from the origin is decreasing.

As time passes by, the object is moving towards the origin at a decreasing velocity. As the velocity is decreasing, the slope of the line decreases, and eventually the velocity becomes zero when the object reaches the origin.

The graph is showing the velocity of an object as a function of time. When the velocity is positive, the object is moving to the right, and when the velocity is negative, the object is moving to the left. The velocity is decreasing because the slope of the graph is negative, but it is not necessarily moving towards the origin.

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Answer:

the 30th term is 239

Step-by-step explanation:

The computation of the 30th term is as follows:

As we know that

a_n = a_1 + (n-1)d

where

a_1 is the first number is the sequence

n = the term

And, d = common difference

Now based on this, the 30th term is

= 152 + (30 - 1) × 3

= 152 + 29 × 3

= 152 + 87

= 239

Hence, the 30th term is 239

Answer:

Yesterday,Annie walked 9/10 mile to her friend's house.Together,they walked 1/3 mile to the library.Which is the best estimate for how far Annie walked yesterday? a)about 1/2 mile b)about 1 mile c)about 1 1/2 miles d)about 2 miles ===== 0.9 + 0.333 = 1.233 miles

Step-by-step explanation:

1) The value of function is,

⇒ (2x − 3)

2) The value of function is,

⇒ (5x + 7)

We have to given that;

Functions are,

f(x) = (x + 7) (2x − 3) and g(x) = (x + 7).

Hence, We get;

⇒ f (x) / g (x)

⇒ (x + 7) (2x − 3) / (x + 7)

⇒ (2x − 3)

And, Functions are,

f(x) = (5x+7) (-3x+11) and g(x) = (-3x + 11).

Hence, We get;

⇒ f (x) / g (x)

⇒ (5x+7) (-3x+11) / (-3x + 11).

⇒ (5x + 7)

Thus, 1) The value of function is,

⇒ (2x − 3)

2) The value of function is,

⇒ (5x + 7)

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the point (1, 7) is the only solution to the inequality y > |x| + 5.

To determine which of the given points is a solution of the inequality y > |x| + 5, we need to substitute the x and y coordinates of each point into the inequality and check if the inequality holds true.

a. (7, 1)

Substituting x = 7 and y = 1 into the inequality:

1 > |7| + 5

1 > 7 + 5

1 > 12

This inequality is not true, so (7, 1) is not a solution.

b. (0, 5)

Substituting x = 0 and y = 5 into the inequality:

5 > |0| + 5

5 > 0 + 5

5 > 5

This inequality is not true, so (0, 5) is not a solution.

c. (1, 7)

Substituting x = 1 and y = 7 into the inequality:

7 > |1| + 5

7 > 1 + 5

7 > 6

This inequality is true, so (1, 7) is a solution.

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Answer:

26.5

Step-by-step explanation:

Complimentary angles are 90 degrees

90-63.5=26.5

Answer:

698 fishes

Step-by-step explanation:

Generally, we can represent an exponential growth function as;

y = a•(1 + r)^t

originally, there were 3 fishes

The original value in this case means a = 3

After 6 weeks, there were 31

31 in this case is y

r is the increase percentage or rate

t is the time

So, we have it that;

31 = 3•(1 + r)^6

31/3 = (1 + r)^6

10.33 = (1 + r)^6

ln 10.33 = 6 ln (1 + r)

ln 10.33/6 = ln (1 + r)

e^0.3892 = (1 + r)

1 + r = 1.476

r = 1.476-1

r = 0.476 or 47.6%

So the growth percentage or rate is 47.6%

For 14 weeks, we simply have the value of t as 14;

So ;

y = 3•(1 + 0.476)^14

y = 3(1.476)^14

y = 698 fishes

The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

We have,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l

where:

a and b are the lengths of the two parallel sides (the bases) of the trapezoid

h is the height of the trapezoid (the perpendicular distance between the two bases)

l is the length of the prism (the distance between the two trapezoidal faces)

Now,

a = 9

b = 12

l = 15

Height h can be calculated using the Pythagorean theorem.

15² = (12 - 9)² + h²

h² = 225 + 9

h² = 234

h = √234

h = 15

Now,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l
V = ((9 + 12) / 2) x 15 x 15

V = 2362.5

And,

The surface area (A) of a trapezoidal prism can be calculated using the formula:

A = ph + 2B

where p is the perimeter of the trapezoidal base, h is the height of the prism, and B is the area of one of the bases.

So,

p = 12 + 8 + 12 + 8 = 44

h = 15

B = 12 x 8 = 96

Now,

Total surface area​.
= 44 x 15 + 2 x 96

= 660 + 192

= 852

Thus,

The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

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