the number of ants per acre in the forest is normally distributed with mean 45,000 and standard deviation 12,073. let x

The missing side in the similar figure below is 42.

We are given a diagrammatic expression of two triangles and we are asked to find the missing side in a similar triangle. To be able to solve this question, we need to understand what are triangles and the possible types of triangles.

A triangle is a plane figure that has three sides and three angles. The major types of triangles include:

The example of the triangle given is a right-angle triangle and can be solved by using the Pythagoras theorem.

The Pythagoras theorem states that the hypotenuse squared is equal to the sum of the opposite squared and the adjacent squared.

hyp² = opp² + adj²

48² = x² + 24²

2304 = x² + 576

x² = 2304 - 576

x² = 1728

x = √1728

x = 41.57

x ≅ 42

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The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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Answer:

Hundredths place

Step-by-step explanation:

6 in 6.54 is ones place

5 in 6.54 is tenths place

4 in 6.54 is hundredths

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In terms of measures of spread, Group B has a wider IQR than Group A

The comparative dot plots show the points scored in a game by two groups, Group A and Group B. Both groups have a similar spread, with most of the dots clustered around the middle of the distribution. However, there are some differences in the tails of the distribution that affect the measures of spread.

For Group A, the lowest score is 41, and the highest score is 50. The interquartile range (IQR), which is the range containing 50% of the scores, is approximately from 45 to 48. The range, which is the difference between the highest and lowest scores, is 9.

For Group B, the lowest score is 41, and the highest score is 50. The interquartile range (IQR) is approximately from 43 to 49. The range is also 9.

This indicates that Group B has a more variable distribution of scores within the middle 50% of the distribution, indicating a more variable distribution of scores within the middle.

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The sum of the angles of the triangle below are angle A = 34.91°, angle B = 86.41°, and angle C = 58.68°.

According to the triangle sum theorem, a triangle's internal angles can be added up to 180 degrees. The triangle sum theorem, often referred to as the angle sum theorem of the triangle, states that the total of the measures of a triangle's internal angles in a Euclidean space adds up to 180 degrees, whether the triangle is acute, obtuse, or right.

Let a = 8, b = 14 and c = 12 for the given triangle.

Then,

cos (A) = (b² + c² − a²) / 2bc

cos (A) = (14² + 12² - 8²)/ (2)(14)(12)

cos (A) = (196 + 144 - 64)/ 336

cos (A) = 0.82

A = cos⁻¹ (0.82)

A = 34.91°

Similarly, for angle B.

Cos (B) = (c² + a² − b²)/2ca

Cos (B) = (12² + 8² - 14²)/ (2)(12)(8)

A = cos⁻¹ (0.0625)

B = 86.41°

The sum of all the angles of a triangle is 180:

A + B + C = 180°

34.91° + 86.41° + C = 180°

C = 58.68°

Hence, the sum of the angles of the triangle below are angle A = 34.91°, angle B = 86.41°, and angle C = 58.68°.

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he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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Step-by-step explanation:

sin A = opposite/ Hypotenuse

Sin A = 5/7

Hello !

sin(A) = opposite/hypotenuse = 5/7

arcsin(5/7)  ≈ 45,58°

sin(A) = 5/7

the angle A ≈ 45,58°

Answer:

option C : 2

Step-by-step explanation:

because there can be one triangle from BA till 20cm . and other till D

hope it helps you

Option C) 2

Triangle 1 = From BA to 20cm

Triangle 2 = From BA to D

Answer:

when x equals -3 y equals -23

when x equals 0, y equals -8

when x equals 3, y equals 7

when x equals 6, y equals 22

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The last one looks like its not true

Answer:

Step-by-step explanation:

4) looks wrong , or untrue.  

The missing sides of the triangle DEF are DE = 25 and DF = 50.

Those triangles look the same but are different in size.

And in similar triangles,

the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.

Given:

In the diagram below, triangle ABC is similar to triangle DEF.

So, the ratio of the corresponding side is constant.

The ratio = BC/EF = 14/35 = 0.4

To find the other sides of the triangle DEF, divide the evaluated ratio by the length of the corresponding side.

So, DE = AB / 0.4 = 10/0.4 = 25

And DF = 20/0.4 = 20/0.4 = 50

Therefore, DE = 25 and DF = 50.

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Answer:

switch them up

Step-by-step explanation:

As the given equation is (36)ˣ⁺²  = 6 , then the solution for the given equation is x ≈ -1.54.

The given equation in the question is (36)ˣ⁺²  = 6

according to the given equation , the goal is to solve the equation for x.

For solving this equation ,

we'll have to use logarithmic operations which is as follows:  

log36(6) = x+2.

We will be further using a calculator to determine the logarithmic value: log36(6) ≈ 0.4607.

Now, By subtracting 2 from both sides, we will get the value of x as:

x ≈ -1.54.

When we round off this value to the nearest 100th, we will get  -1.54.

Thus , the solution for the given equation is x ≈ -1.54.

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Answer:

Triangle

Step-by-step explanation:

It has three side unlike the others can't have three sides

The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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The points that are non-coplanar to Plane J are E and F

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

The plane

By definition, a non-coplanar point is a point that is not on a plane

using the above as a guide, we have the following:

The points that are non-coplanar to Plane J are E and F

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The tables that show a valid probability density function, are tables 1 to 3

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

Table of values

For a table to show a valid probability density function, the following must be true

Sum of P(X = x) = 1

Using the above as a guide, we have the following:

Table 1: Sum = 0.37  + 0.06 + 0.01 + 0.56 = 1

Table 2: Sum = 3/8 + 3/8 + 1/4 = 1

Table 3: Sum = 1/8 + 1/8 + 1/8 + 3/8 + 1/4 = 1

Table 4: Sum = 0.03 + 0.01 + 0.61 + 0.31 + 0.21 = 1.17

Table 5: Sum = 1/10 + 3/10 + 4/5 + 1/5 = 1.4

Hence, the tables are tables 1 to 3

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Answer:

I might be wrong but i think C sorry if im wrong tho

Step-by-step explanation:

<3

Answer:

A. 31 Km

Step-by-step explanation:

\(circumference = 2\pi \:r\)

radius equals the diameter divided by 2

\(r = \frac{d}{2} \)

In this case the diameter is 10, so the radius is 5.

finally,

\(2\pi(5) = 31.415\)

rounded to the nearest whole number gives us

31 Km.

The 98% confidence interval for the true mean statistics anxiety score μ is approximately (39.023, 39.777).

To calculate the 98% confidence interval for the true mean statistics anxiety score μ, we can use the formula:

\(\[\text{CI} = \bar{X} \pm Z \cdot \left(\frac{\sigma}{\sqrt{n}}\right)\]\)

where \(\bar{X}\) is the sample mean (39.4), Z is the Z-score corresponding to the desired confidence level (in this case, 98% corresponds to a Z-score of 2.33), σ is the population standard deviation (0.9), and n is the sample size (33).

Plugging in the values, we get:

CI = 39.4 ± 2.33 * (0.9/√33).

Calculating this expression, we find:

CI = 39.4 ± 2.33 * (0.162),

CI ≈ 39.4 ± 0.377.

Therefore, the 98% confidence interval for the true mean statistics anxiety score μ is approximately (39.023, 39.777).

This means that we are 98% confident that the true average statistics anxiety score for all undergraduate students in the U.S. falls within this interval.

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Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

what's the full question

Answer:

I think it is 30 inches

Step-by-step explanation:

Answer: C

Step-by-step explanation: on edge 2023

Answer:

(0, -1)

Step-by-step explanation:

((4 + (-4))/2, (2 + (-4))/2) =

(0/2, -2/2) =

(0, -1)

Answer:

the minimum possible time for Emma to reach the island is approximately 2.9583 hours, when she starts swimming at a point 5/6 km east of the cottage.

Step-by-step explanation:

We can use the concept of minimum distance to find the minimum possible time for Emma to reach the island. Let's assume that Emma walks to some point P along the shoreline and then swims to the island. We want to find the point P that minimizes the total distance that Emma has to cover.

Let the distance from the cottage to point P be x km. Then the distance from point P to the island is (3 - x) km. Using the Pythagorean theorem, we can find the distance from the cottage to the island as follows:

distance^2 = x^2 + (3 - x)^2 + 2^2

distance^2 = 10x - 6x^2 + 13

To minimize the distance, we can take the derivative of the distance equation with respect to x and set it equal to zero:

d(distance^2)/dx = 10 - 12x = 0

x = 5/6 km

Substituting x = 5/6 km into the distance equation, we get:

distance^2 = 25/3 km^2

distance = 5/sqrt(3) km

Therefore, the minimum possible time for Emma to reach the island is the time it takes her to walk to point P (distance x) plus the time it takes her to swim to the island (distance 3 - x), divided by her swimming speed:

time = x/4 + (3 - x)/3

time = (3x + 12 - 4x)/12

time = (12 - x)/4

time = (12 - 5/6)/4

time = 2.9583 hours (rounded to 4 decimal places)

Therefore, the minimum possible time for Emma to reach the island is approximately 2.9583 hours, when she starts swimming at a point 5/6 km east of the cottage.

Let's call the point where Emma starts swimming P. We can draw a diagram to visualize the situation:

Cottage ---------- Q ---------------- Island

x km 3 km 2 km

The distance from the cottage to Q is x km, and the distance from Q to the island is 2 km. The total distance Emma will have to travel can be expressed as:

d = √(x^2 + 2^2)

The time it will take Emma to walk the distance from the cottage to point P is:

t1 = x / 4

The time it will take Emma to swim from point P to the island is:

t2 = √((d - x)^2 + 2^2) / 3

The total time it will take Emma to reach the island can be expressed as:

T = t1 + t2

To find the minimum possible value of T, we can take the derivative of T with respect to x and set it equal to zero:

dT/dx = (1/4) - (d-x)/3√((d-x)^2+4) = 0

Solving for x, we get:

x = (3/5)d

Substituting this value of x back into the expression for T, we get:

T = (3/20)d + (2/5)√(5)

Rounding to the nearest hundredth, we get:

T ≈ 0.96 hours

Therefore, the minimum possible time it will take Emma to reach the island is approximately 0.96 hours.

Answer: B) 0.28

Step-by-step explanation:

Given that:

Lean/Healthy Overweight/ ObeseSelf Esteem Low 18 32 High 32 18

                Overweight/Obese      Lean/Healthy               Total

Low          32                                   18                                 50

High         18                                    32                                50

Total         50                                   50                               100

the phi correlation coefficient is defined by Ф = √x²/n

where n = 100 ( total number of response )

x² = [(32×32 - 18×18)² × 100] / [50 × 50 × 50 × 50]

Ф = √ [(700)² x 100) / (50)⁴ × 100

Ф = 700 / 50²

Ф = 0.28

Therefore option B) is the correct answer

Answer:

-27

Step-by-step explanation:

5(-3)^3(5)^-1

5(-27)(1/5)

-135(1/5)

-135/5

-27

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Answer:

Hello,

60L

Step-by-step explanation:

Quantity of water /Quantity of milk =2/1

Quantity of mixture= Quantity of water +Quantity of milk =60L

Quantity of milk =40 L

Quantity of water =20 L

Let say x the quantity of water to be added

New ratio =1/2=40/(20+x)

20+x=80 (cross products)

x=60 (L)