Consider the function shown on the graph. Complete the statements to make them true.

Answer:

angle K is 30 degrees

Step-by-step explanation:

A triangle adds up to 180 degrees. since LM and KM are congruent angle L and M are both 75 degrees each you subtract from 180 and you get 30 degrees

A 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

We know that, the confidence interval is:

\(\bar{x}\pm z\frac{\sigma}{n}\)

where,

\(\bar{x}\) is the sample mean.

z is the critical value.

n is the sample size.

σ (OR s) is the standard deviation for the population.

In this question, we need to calculate the 95% confidence interval for an experiment that found the sample mean temperature for a certain city in August was 101.82, with a population standard deviation of 1.2

The critical value is z = 1.96

We have been given x¯ = 25.6, σ = 0.6 and n = 150

\(\Rightarrow \bar{x}+ z\frac{\sigma}{\sqrt{n} } \\\\= 25.6+ 1.96\frac{0.6}{\sqrt{150} } \\\\=25.67\)

And

\(\Rightarrow \bar{x}- z\frac{\sigma}{\sqrt{n} } \\\\= 25.6- 1.96\frac{0.6}{\sqrt{150} } \\\\=25.504\)

Required interval is (25.504, 25.67)

Thus, the mean weight level( 25.6 grams) is accurate.

Therefore, a 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

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The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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Answer:

8,8,8,7

Step-by-step explanation:

5,6,7,8,8,10,12

8 is the median since its the number in the middle

8 is the mode since it is the repeated number

7 is the range since 12-5 is 7

all the numbers added and divided by the number of numbers is the mean

(5+6+7+8+8+10+12)/7=8

Answer:

It is B

Step-by-step explanation:

B:3=b

bx3=B

Answer: 1, 3, 5, 7, 9, . . . . , 37. Therefore, 361 is the sum of first 19 odd numbers.

Step-by-step explanation:

Answer:

247.21

Step-by-step explanation:

equation for height :  c= a2 + b2

4.82 + 9.32

≈10.46566

equation for surface area: A=5 /4tan(54°)a2+5a /2h2+(atan(54°) /2)2

5 /4·tan(54°)·72+5·7 /2·7.972+(7·tan(54°) /2)2

≈247.21018

round to nearest hundredth: 247.21

The quadratic roots are imaginary of the equation 5x² - 4x + 5 = 0.

What is the discriminant of a polynomial?

The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.

It is represented as ‘D’

D = b² - 4ac

Where,

a is the coefficient of x²

b is the coefficient of x

c is a constant term

Nature of the roots of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

We have given,

Quadratic equation:  5x² - 4x + 5 = 0.

As we know that,

D = Discriminant  Or

D = b² - 4ac.

D = (-4)² - 4(5)(5).

D = 16 - 100.

D = -84.

D < 0, Roots are imaginary.

The quadratic roots are imaginary.

Hence, The quadratic roots are imaginary of the equation 5x² - 4x + 5 = 0.

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|x - 3| = 3 - 8

|x -3| = -5

x - 3 = -5

x = -2

x-3 = 5

x = 8

x = 8, -2

But if you try and check that these solutions work, you will find that they do not. Since the absolute value equation has a negative value, there is no real solution.

Answer: No Solution

Step-by-step explanation:

|x-3| + 8 = 3

subtract 8 from both sides

|x-3| = -5

There is no real solution since absolute value equation cannot be negative

Answer:

0.950 L

Step-by-step explanation:

ml/1000 = L

Answer:

Step-by-step explanation:

p = k / sqrt(q)

The first job is to find k.

p = 12

q = 36

Solution for k

12 = k / sqrt(36)

sqrt(36) = +/- 6

Multiply both sides by +/-6

12 * +/- 6 = k

k = +/- 72

Solution for q = 16

p = +/-72/ sqrt(16)

p  = +/- 72 / sqrt(16)

p = +/- 72 / +/-4

p = 18

Answer:

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. ... and another pair of corresponding sides are equal in two right triangles.

No, the use of the binomial distribution may not be appropriate for calculating the probability that exactly six 18-20 year olds consumed alcoholic beverages in a random sample of ten.

The binomial distribution assumes that the trials are independent, there are only two possible outcomes (success or failure), and the probability of success remains constant throughout the trials. In the case of consuming alcoholic beverages, the assumption of independence may not hold, as one person's decision to consume alcohol may influence another person's decision. Additionally, the probability of consuming alcohol may not remain constant throughout the sample, as some people may have stronger tendencies or preferences for drinking than others.

A more appropriate distribution for this scenario may be the hypergeometric distribution, which takes into account the finite population size (i.e. the total number of 18-20 year olds from which the sample is drawn) and the varying probabilities of success (i.e. the varying number of individuals in the population who consume alcohol).

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Sebastian, this is the solution to the first problem you uploaded:

Let's recall that the interior angles of a triangle add up to 180 degrees.

Then if E =

Using Chebyshev's theorem, we can determine the percentage of the data within specific ranges based on the mean and standard deviation.

Chebyshev's theorem provides a lower bound for the proportion of data within a certain number of standard deviations from the mean, regardless of the shape of the distribution.

To calculate the percentage of data within a given range, we need to determine the number of standard deviations from the mean that correspond to the range. We can then apply Chebyshev's theorem to find the lower bound for the proportion of data within that range.

For example, if we want to find the percentage of data within one standard deviation from the mean, we can use Chebyshev's theorem to determine the lower bound. According to Chebyshev's theorem, at least 75% of the data falls within two standard deviations from the mean, and at least 89% falls within three standard deviations.

To calculate the percentage within a specific range, we subtract the lower bound for the larger range from the lower bound for the smaller range. For example, to find the percentage within one standard deviation, we subtract the lower bound for two standard deviations (75%) from the lower bound for three standard deviations (89%). In this case, the percentage within one standard deviation would be 14%.

By using Chebyshev's theorem, we can determine the lower bounds for the percentages of data within various ranges based on the mean and standard deviation. Keep in mind that these lower bounds represent the minimum proportion of data within the given range, and the actual percentage could be higher.

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Answer: A = 40°, Angle B = 60° and Angle C = 80°. The angles sum to 180°, so at least one triangle may be drawn.

Step-by-step explanation: Did this help

Answer:

Patterns

Step-by-step explanation:

Deductive reasoning is used to prove conjectures to be true

Answer:

patterns

Step-by-step explanation:

Deductive reasoning is a simple form of arriving at a conclusion by joining two or more pieces of information. Deductive reasoning is used to prove conjectures to be true.

The expression that represents the shaded length of the number line would be = 3/20 × 9/20. That is option C.

A number line is defined as the graduates line that is used to represent the position of both positive and negative real numbers.

The shaded length of the number line contains 20 bars with a total of 9 shaded bars.

There are a total number of 3 per each bar of the number line, therefore, the shaded length of the number line would be = 3/20 × 9/20.

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The parametric equations for the tangent line to the curve x=t^4-1, y=t^5+1, z=t^3 is

x = 15 + 27000t

y = 33 + 759375t

z = 8 + 675t

To find the parametric equations for the tangent line to the curve x=t^4-1, y=t^5+1, z=t^3 at the point (15, 33, 8), we need to first find the derivative of each component with respect to t, evaluated at t=15. This will give us the direction vector of the tangent line, which we can use to write the parametric equations.

Taking the derivatives, we have:

dx/dt = 4t^3

dy/dt = 5t^4

dz/dt = 3t^2

Evaluating at t=15, we get:

dx/dt = 4(15)^3 = 27000

dy/dt = 5(15)^4 = 759375

dz/dt = 3(15)^2 = 675

So the direction vector of the tangent line at the point (15, 33, 8) is <27000, 759375, 675>. To write the parametric equations, we can use the point-slope form:

x = x0 + at

y = y0 + bt

z = z0 + ct

where (x0, y0, z0) is the given point and (a, b, c) is the direction vector we just found. Plugging in the values, we get:

x = 15 + 27000t

y = 33 + 759375t

z = 8 + 675t

These are the parametric equations for the tangent line to the curve x=t^4-1, y=t^5+1, z=t^3 at the point (15, 33, 8).

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Answer:

B. Write each student's name on a slip of paper and put the slips in a

bag. Randomly draw a slip of paper. The student whose name is

on the paper wins.

C. Roll a number cube. If it lands on 1 or 3, Alina wins. If it lands on 2

or 4, Robert wins. If it lands on 5 or 6, Makayla wins.

Step-by-step explanation:

The ways a fair decision can be made about who goes to the dinner from the list of available options is as follows:

Probability is simply how likely something is to happen. This is used whenever one is not sure about the outcome of an event.

Therefore the correct answers are option B and option C.

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Answer c

Step-by-step explanation:

To determine the type of triangle BCD, we can analyze the given information about the angles in the triangle and the fact that ABD is a straight line.

We are given that angle ABC is 124 degrees, and angle BDC is 62 degrees.

Since ABD is a straight line, the sum of angles ABC and BCD should be 180 degrees.

Therefore, we can find the measure of angle BCD by subtracting the measures of angles ABC and BDC from 180 degrees:

\(BCD = 180 - (ABC + BDC)\\\\BCD = 180 - (124 + 62)\\\\BCD = 180 - 186\\\\BCD = -6\)

We find that the measure of angle BCD is -6 degrees. However, angles in a triangle cannot have negative measures. This indicates that there is an error in the given information or calculations.

As it stands, the given information does not allow us to determine the type of triangle BCD. It is essential to ensure the accuracy of the angle measurements and verify the consistency of the given information to draw valid conclusions about the type of triangle.

Please double-check the measurements and provide any additional information or corrections to proceed with determining the type of triangle BCD accurately.

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Answer:

$0.60

Step-by-step explanation:

Given that:

The ratio of number of cookies to the cost of cookies as:

Number of cookies : Cost of cookies = 15 : 9

It means, we get 15\(x\) number of cookies when we pay $9\(x\).

To find:

An equivalent ratio to represent the cost of 1 cookie.

Solution:

Here, we have to find nothing but the unit price or the price of 1 cookie.

This can simply be done by dividing the total cost of cookies with the total number of cookies.

Total cost of 15\(x\) cookies is given as $9\(x\)

Using unitary method:

Let us divide both the sides with 15\(x\), we get:

Total cost of \(\frac{15x}{15x}\) cookies is given as \(\frac{\$9x}{15x}\)

Total cost of 1 cookie is given as $0.60

The percentage of men is more than 72 inches tall will be 0.15866.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x – μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

Suppose the mean height for men is 70 inches, with a standard deviation of 2 inches.

Then the percentage of men are more than 72 inches tall will be

z = (72 – 70) / 2

z = 1

The percentage of men is more than 72 inches tall will be

P(x > 72) = P(z > 1)

P(x > 72) = 1 – P(x < 72)

P(x > 72) = 1 – 0.84134

P(x > 72) = 0.15866

Thun, the percentage of men are more than 72 inches tall will be 0.15866.

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The sample in this example is D) the small group of college students who are observed. The correct option is D.

The researcher has identified college students as her group of interest, but it is not feasible or practical to observe or study all college students. Therefore, she needs to select a subset of college students, which is known as a sample. In this case, she has chosen to observe a small group of local college students, which is the sample. It is important to note that the sample needs to be representative of the larger population of interest, in this case, all college students, in order for the results to be applicable to the larger group.

While the sample in this example is only a small group of local college students, the researcher would need to ensure that they are representative of all college students in order for the results to be generalizable.

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Answer:

cylider?

Step-by-step explanation:

Answer:

The normal force is the force that a surface makes on an object that lies on that surface.

As the book rest flat in the table, the force acting on the book will be the gravitational force. This force pulls down the book against the table, then the normal force will be opposite to this, then the direction of this force is upwards. Being more exact, the normal force always acts on the normal direction to a given surface, to find the normal of a surface, you need to find the plane of the surface, then any perpendicular line to that surface will be "normal" to the surface (and the normal direction points away from the surface) then if the book is resting on top of the table, the direction of the normal will be upwards..

Then the force that acts on the book is normal to the surface of the table,

Here's a more detailed explanation: To determine if a graph is a function, you can use the vertical line test. The vertical line test states that if you can draw a vertical line that intersects the graph in more than one place, then the graph is not a function.

Determining whether a graph represents a function is an important concept in mathematics, especially in algebra and calculus. A function is a set of ordered pairs where each input is associated with exactly one output.

So, if you take a ruler or a straight edge and place it vertically on the graph, and it intersects the graph in two or more points, then the graph is not a function. This is because if two points in the graph have the same x-value, they must have different y-values, since functions can only have one output for each input.

On the other hand, if you place a vertical line anywhere on the graph and it intersects the graph in only one point, then the graph is a function.

It's also important to remember that a function must also pass the horizontal line test, which means that no horizontal line can intersect the graph in more than one place.

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