50 POINTS

What is the value represented by the letter E on the box plot of the data?

45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90

Answer:

36

Step-by-step explanation:

2(10)+4^2

20+4^2

20+16

36

Answer: The result of the math formula =2*10+4^2 is 28.

To calculate this formula, you first need to perform the exponentiation operation of 4^2, which is 16. Then, you multiply 2 by 10, which gives you 20. Finally, you add 20 to 16, which gives you the final answer of 28.

This is the answer plz tell me if its wrong

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos45° = \(\frac{1}{\sqrt{2} }\) , then

cos45° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{3}{c}\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

c = 3\(\sqrt{2}\)

Answer:

The reason one must apply a force to a box in order for the box to move is to overcome the friction generated by the box against the plane the box is sitting.

The box at rest has zero friction against the surface on which it sits.  Once a force is applied, a box's movement is resisted by the friction created from contact with the surface.

In order for the box to move, one must generate more force than is being generated by the friction of the surface onto the box, allowing the box to move.

Cheers.

Answer:I think it's 7, but im not sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 root 32 - 15 root 2

20 root 2 - 15 root 2

5 root 2

please have a look of photo for exact answet

Answer:

I do know

Step-by-step explanation:

The area of the water's surface is approximately 981.25 square units.

Since the water depth is 10, the water fills up half of the hemispheric bowl. Therefore, we need to find the surface area of a circle with radius 25 (the base of the hemisphere) and divide it by 2.

The surface area of a circle with radius r is given by A = πr^2. So, the surface area of the circle with radius 25 is:

A = π(25)^2 = 625π

Dividing by 2, we get

625π/2

So the surface area of the water's surface is 625π/2 square units.

Approximating the value of π as 3.14, we get:

625π/2 ≈ 625(3.14)/2 ≈ 981.25

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Answer:

3 meters/second

Step-by-step explanation:

acceleration = rate of change of speed (velocity)/change in time

                     = 16 - 4/4

                     = 12/4 = 3 m/s

Answer:

D

Step-by-step explanation:

The opposite of negative is positive therefore,

the opposite of -2 is positive 2.

2 is locaded at D.

Answer:

when you cross multuply it would become w(y-z)=x.So the final answer is =>wy-wz=x

The items with the shortest lifespan will last less than approximately 4.3 years.

In a normally distributed lifespan, the mean represents the average lifespan of the items, and the standard deviation indicates how spread out the data points are from the mean. In this case, the manufacturer's items have a mean lifespan of 6.5 years and a standard deviation of 1.7 years.

To find the duration at which the 4% of items with the shortest lifespan will last, we need to calculate the z-score corresponding to the desired percentile. The z-score measures the number of standard deviations a data point is from the mean.

Using a standard normal distribution table or a statistical calculator, we can find the z-score that corresponds to the 4th percentile. In this case, since we want to find the items with the shortest lifespan, we are interested in the area to the left of the z-score. The z-score corresponding to the 4th percentile is approximately -1.75.

Next, we can use the formula for z-score to find the corresponding lifespan duration:

z = (x - μ) / σ

Rearranging the formula, we can solve for x (the lifespan duration):

x = z * σ + μ

Plugging in the values, we have:

\(x = -1.75 * 1.7 + 6.5 = 4.3 years\)

Therefore, the items with the shortest lifespan, comprising approximately 4% of the total, will last less than approximately 4.3 years.

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Answer:

7/4

Step-by-step explanation:

Slope is Rise over Run  or the difference in the Y points over the difference in the X points.  (x,y)

Rise is a total of 14 points, Run is a total of 8 points.

So slope is 14/8 which can be simplified to 7/4

Answer:

Part A: A = 8

B = 20

C = 28

D = 35  

E = 37

F = 72

G = 43

H = 57

I = 200

Part B: 18.5%

Part C:

D = People who do not like Orange Juice

B = People who do not like Apple Juice

I use the values of B and D because these are the values that represent dislike for that juice, and also because adding them together creates a value for not liking either juice.

D = 35

B = 20

So there is a greater dislike for Orange Juice.

Step-by-step explanation:

To prove that triangle FGE and triangle IJH we need information like the two sides of each triangle and the included angle to be congruent.

To prove two triangles are similar by the SAS is that you need to show that two sides of one triangle are proportional to two corresponding sides of another triangles, with the included corresponding angles being congruent.

For the SAS postulate you need two sides and the included angle in both triangles.

Side-Angle-Side (SAS) postulate:-

If two sides and the included angles of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. SAS postulate relate two triangles and says that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

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Answer:

it increased by 33.3%

In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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The doubling time formula is used to calculate the time required for a quantity to double in size at a constant growth rate. The formula is: doubling time = ln(2) / r

Where ln(2) is the natural logarithm of 2, and r is the annual growth rate expressed as a decimal. The doubling time represents the number of time units it takes for the quantity to double, such as years, months, or days, depending on the time unit used for the growth rate. This formula is commonly used in many fields, such as finance, biology, and demography, to estimate the future growth of a quantity based on its current growth rate.

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The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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The random number 0.23, when interpreted in the given frequency distribution of demand, would correspond to a demand of 1.

In order to interpret the random number 0.23, we need to refer to the frequency distribution of demand. A frequency distribution provides information about the different values of a variable and their corresponding frequencies or probabilities. However, since the frequency distribution of demand is not provided, we cannot determine the exact values and frequencies for each demand level.

Nevertheless, assuming that the demand levels in the frequency distribution are discrete and start from 0, it is likely that the random number 0.23 falls within the range of the cumulative probabilities for a demand level of 1. The cumulative probability represents the probability of observing a value less than or equal to a particular demand level.

To interpret the random number, we can compare it to the cumulative probabilities associated with each demand level. If the random number falls within the cumulative probability range of a specific demand level, then that demand level would be the interpretation. Since the random number 0.23 falls within the range for a demand of 1, we can conclude that the demand corresponding to the random number 0.23 is 1.

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The formula for the margin of error in a confidence interval is:
Margin of error = (Z-score) x (standard deviation of the population) / √(sample size)
The formula for the confidence interval is:
Confidence interval = sample mean ± margin of error
The formula for the Z-score is:
Z-score = (x - μ) / (σ / √n)
Where:
x = the sample mean
μ = the population mean
σ = the population standard deviation
n = the sample size

We can combine the formulas to solve the problem:
109.08 = x - (Z-score) x (5.68 / √n)
111.36 = x + (Z-score) x (5.68 / √n)
Subtract the first equation from the second equation:
2.28 = 2 x (Z-score) x (5.68 / √n)
Simplify:
Z-score = 2.28 / (2 x 5.68 / √n) = 0.8√n
Find the Z-score corresponding to a 95% confidence level (two-tailed):
Z-score = 1.96
Substitute in the equation:
0.8√n = 1.96
Solve for n:
n = (1.96 / 0.8)² = 6.07
Round up to the nearest whole number:
n = 7
Therefore, the correct answer is: For a sample size of 7, 95% of the sample means fall within the interval between 109.08 and 111.36.

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The single natural logarithm expression is ln(2). Therefore, correct answer is (a)

The expression in the form \(e^a=b\) can also be written as In b = a  which is called as logarithmic expression.

Properties of Logarithms:

1. In (mn) = In m + In n

2. In \(a^m =\) m In a

3. In \(e^a\) = a.

The natural logarithm expression is:

4 + ln 2 - ln 4

Apply the product and quotient rule of natural logarithm:

4 + ln 2 - ln 4  = In (4 × 2/4)

Evaluate the quotient:

4 + ln 2 - ln 4  = In (2)

Hence, the single natural logarithm expression is ln(2).

The correct option is (a)

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Answer:

B: ln 4.

Step-by-step explanation:

Answer:

four billion two hundred fifty-eight million one hundred forty-five thousand three hundred ninety-seven

Step-by-step explanation:

Answer:

Word form-

four billion, two hundred fifty-eight million, one hundred forty-five thousand, three hundred ninety-seven.

Step-by-step explanation:

True. For simpler amount analysis and management, data can be grouped into classes that represent related categories.

Data can be grouped into groups in order to identify patterns, trends, and similarities that can then be utilised to influence decisions. As classes may be used to organise and make data easier to interpret, this can be very helpful when working with huge datasets. Classes can also be used to find outliers and abnormalities in data, which can improve results and offer more precise insights. With classes, data can be processed and analysed more quickly and correctly, enabling more effective decision-making.For simpler analysis and management, data can be grouped into classes that represent related categories. With the process of categorising, data can be divided into smaller, easier-to-manage chunks for easier analysis.

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Recursion is a function that calls itself and creates separate copies with their own parameters and variables. Base cases are essential to prevent infinite recursion.

The term you are referring to is "recursion". Recursion is a powerful programming technique that involves a function calling itself in order to solve a problem. Each time the function is called, a new copy of the function is created, with its own set of parameters and variables. Recursion can be used to solve a wide range of problems, from simple mathematical calculations to complex algorithms.

One important aspect of recursion is the need for base cases. These are the conditions that stop the recursion from continuing indefinitely.

Without base cases, the function would continue to call itself forever, resulting in an infinite loop. Base cases are usually simple conditions that can be easily checked, such as the value of a variable reaching a certain threshold.

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The answer is -1

(AKA the second option)

For the angle \( \theta \) in standard position with the point (-4, 5) on its terminal side

\( \sin \theta = \frac{5}{\sqrt{41}} \),

\( \cos \theta = \frac{-4}{\sqrt{41}} \),

\( \tan \theta = -\frac{5}{4} \),

\( \csc \theta = \frac{\sqrt{41}}{5} \),

\( \sec \theta = -\frac{\sqrt{41}}{4} \),

\( \cot \theta = -\frac{4}{5} \).

To find the values of the trigonometric functions for the angle \( \theta \) in standard position with the point (-4, 5) on its terminal side, we can use the given coordinates to determine the values of the trigonometric ratios.

First, let's calculate the values of sine, cosine, and tangent:

1. Sine (\( \sin \)): Sine is defined as the ratio of the opposite side to the hypotenuse in a right triangle. In this case, the opposite side is the y-coordinate (5) and the hypotenuse can be calculated using the Pythagorean theorem:

  \( \text{Hypotenuse} = \sqrt{(-4)^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41} \)

  Therefore, \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{\sqrt{41}} \).

2. Cosine (\( \cos \)): Cosine is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, the adjacent side is the x-coordinate (-4) and the hypotenuse is the same as calculated above:

  \( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{-4}{\sqrt{41}} \).

3. Tangent (\( \tan \)): Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle:

  \( \tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{-4} = -\frac{5}{4} \).

Now, let's calculate the values of the reciprocal trigonometric functions:

4. Cosecant (\( \csc \)): Cosecant is the reciprocal of sine:

  \( \csc \theta = \frac{1}{\sin \theta} = \frac{\sqrt{41}}{5} \).

5. Secant (\( \sec \)): Secant is the reciprocal of cosine:

  \( \sec \theta = \frac{1}{\cos \theta} = \frac{\sqrt{41}}{-4} = -\frac{\sqrt{41}}{4} \).

6. Cotangent (\( \cot \)): Cotangent is the reciprocal of tangent:

  \( \cot \theta = \frac{1}{\tan \theta} = -\frac{4}{5} \).

Therefore, for the angle \( \theta \) in standard position with the point (-4, 5) on its terminal side, we have:

\( \sin \theta = \frac{5}{\sqrt{41}} \),

\( \cos \theta = \frac{-4}{\sqrt{41}} \),

\( \tan \theta = -\frac{5}{4} \),

\( \csc \theta = \frac{\sqrt{41}}{5} \),

\( \sec \theta = -\frac{\sqrt{41}}{4} \),

\( \cot \theta = -\frac{4}{5} \).

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Answer:

c

Step-by-step explanation:

Answer:

D is false

Step-by-step explanation:

\(2c - d \\ 2( - 3) - 6 \\ ( - 6) - 6 \\ = - 12\)