standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 21.2 and the standard deviation was 5.7 The test scores of four students selected at random are 15,23,7 and 35 . Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.
The​ z-score for 15 is

Answer:

$39.055

Step-by-step explanation:

100% + 7% = 107%

\(\frac{y}{36.5} :\frac{107}{100}\)

y · 100 = 107 · 36.5

100y = 3905.5

100y ÷ 100 = 3905.5 ÷ 100

y = 39.055

The percentage of the data set within the range of 10 to 22 is 68.26%.

To find the percentage of the data set for a normally distributed variable with a mean of 16 and a standard deviation of 6, we can use the concept of z-scores and the standard normal distribution.

First, we need to convert the values to z-scores, which measure the number of standard deviations a particular value is from the mean. The formula for calculating the z-score is:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

In this case, we want to find the percentage of the data set within a certain range. Let's say we want to find the percentage of the data set between 10 and 22. We can calculate the z-scores for these values:

\(z1 = (10 - 16) / 6 = -1.0\)

\(z2 = (22 - 16) / 6 = 1.0\)

Next, we can use a standard normal distribution table or a calculator to find the area under the curve between these z-scores. The area between -1.0 and 1.0 represents the percentage of the data set within the range of 10 to 22.

Looking up the z-scores in the standard normal distribution table, we find that the area between -1.0 and 1.0 is approximately 0.6826. This means that approximately 68.26% of the data set falls within the range of 10 to 22.

Therefore, the percentage of the data set within the range of 10 to 22 is 68.26%.

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4. The magnitude of angle S is 40°. Answer A.

5. The value of x is 48°. Answer B.

6. The true conclusion is Trevor is correct because the point (4 , 0) satisfies both equations. Answer B.

7. The system of equations has infinitely many solutions. Answer D.

Two parallel lines cut by a transversal form several angles. Look at the top image on the left. Two types of alternate angles have the same magnitude of the angle

The tangent line of two parallel lines is equals

4. From the picture

5. Look at the top image on the right.

6. Solve the system of equations with the substitution method

7. The system of equations

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Answer:

y = 200 + 50x

Step-by-step explanation:

y = cost

x = number of months

The cost is equal to the cost to open the plan plus the monthly fee times the number of months

y = 200 + 50x

Answer:

y = 200 + 50x

Step-by-step explanation:

the cost = the base cost plus the monthly charge ($50 per the number of months you pay it)

hope this helps (/o.o)/<3

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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The probability of exactly one success in the binomial experiment would be 20. 4 %.

The probability that there is one success in a binomial probability which has a chance of success of 5 % can be found by the formula :

P ( X = 1) = (5 choose 1) x ( 0.05 ) x  (0.95 ) ⁴

= ( 0.05 ) x  ( 0. 95 ) ⁴

= 0.05 x 0.8145

= 0.040725

Multiplying both gives:

P(X = 1) = 5 x 0.040725

= 0.203625

In conclusion, the probability of one success is 0.203625 or 20. 4 %.

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Answer:

False

Step-by-step explanation:

Because it is convex, that is, it has bulges

Answer:

360

Step-by-step explanation:

So I did 5 x 6 x 6 x 2 =  360

Answer:

the last choice is the 6th term of expression

Step-by-step explanation:

all the work and steps is in the pic go check it out sorry if wrong and have a  wonderful day:)

Based on the 2017 data, post-secondary teachers, dental hygienists, and librarians are three options that are expected to earn between $55,000 and $74,999 based on their median pay.

The median pay is the midpoint of a set of salaries, where half of the workers earn less and half earn more. In this case, the link provided takes us to the 2017 median pay column for various occupations.

After reviewing the data, it appears that post-secondary teachers, dental hygienists, and librarians are expected to earn between $55,000 and $74,999 based on their median pay. The median pay for post-secondary teachers is $76,000, while the median pay for dental hygienists is $74,070. Lastly, the median pay for librarians is $59,050.

It's important to note that the median pay for carpenters, firefighters, and childcare workers are below $55,000. This means that half of the workers in these occupations earn less than $55,000 per year.

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Answer:

x f(x)

0 0

1 3

2 6

3 9

4 12

5 15

Step-by-step explanation:

since they gave the point (0,0) and slope 3

y=mx+b

0=3(0)+b

b=0

y=3x and then substitute

By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.

In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.

Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.

They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.

The homework may involve tasks such as:

Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.

They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.

Analyzing the truth value of conditional statements:

Students may be given conditional statements and asked to determine whether they are true or false.

They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.

Writing converse, inverse, and contrapositive statements:

Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.

This involves switching the positions of the hypothesis and conclusion or negating both parts.

Applying the laws of logic:

Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.

Constructing counterexamples:

Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.

They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.

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Answer: 288

Step-by-step explanation: 3 x 2 x 48

The momentum of an arrow with a mass of 2 kg traveling at a constant velocity of 10 m/s is 20 kg·m/s.

The momentum of an object can be calculated by multiplying its mass by its velocity. In this case, the mass of the arrow is 2 kg and the velocity is 10 m/s. By multiplying these values, we get the momentum of the arrow as 20 kg·m/s. Momentum is a vector quantity, meaning it has both magnitude and direction. In this case, since the arrow is traveling with a constant velocity, the momentum is in the same direction as the velocity.

Momentum is a fundamental concept in physics that describes the motion of an object. It is defined as the product of an object's mass and its velocity. In the first scenario, the mass of the arrow is given as 2 kg, and its velocity is stated as a constant 10 m/s. By multiplying the mass and velocity, we find that the momentum of the arrow is 20 kg·m/s. This value represents the quantity of motion possessed by the arrow and reflects the combined effect of its mass and speed.

Moving on to the second question, we are asked to determine the mass of a car traveling from Dubai to Abu Dhabi with a momentum of 180 kg·m/s and a velocity of 120 m/s. To calculate the mass, we rearrange the momentum equation and divide the momentum by the velocity. Doing so yields a mass of 1.5 kg for the car.

Finally, in the third question, Saleem's momentum is given as 35 kg·m/s, and his mass is 65 kg. To find his velocity, we rearrange the momentum equation once more and divide the momentum by the mass. The result is a velocity of 0.54 m/s for Saleem.

Momentum is a crucial concept in physics, as it helps us understand and quantify the motion of objects. By considering both mass and velocity, we can determine the momentum of an object and analyze its behavior. Remember, momentum is conserved in a closed system, meaning it remains constant unless acted upon by external forces. Understanding momentum allows us to explore the principles of motion and delve deeper into the laws of physics.

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The head circumference of a newborn boy who marks the start of the 75th percentile is approximately 35.38 cm.

To find the head circumference of a newborn boy who marks the start of the 75th percentile, we need to first find the z-score corresponding to the 75th percentile using the standard normal distribution.

The z-score formula is

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

To find the z-score that corresponds to the 75th percentile, we need to look up the z-score associated with a cumulative area of 0.75 under the standard normal distribution curve. This value can be found using a table or calculator and is approximately 0.674.

Now we can use the formula for the z-score to solve for the head circumference of a newborn boy at the 75th percentile

z = (x - μ) / σ

0.674 = (x - 34.5) / 1.3

0.674 × 1.3 = x - 34.5

0.8762 + 34.5 = x

x = 35.3762

x ≈ 35.38 cm

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Answer:

76

Step-by-step explanation:

decagon = 10 sides

3 heptagons = 3 × 7 = 21 sides

3 nonagons = 3 * 9 = 27 sides

3 hexagons = 3 * 6 = 18 sides

10 + 21 + 27 + 18 = 76 sides in total

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Answer:

Step-by-step explanation:

(2-2)/(10-8)= 0/2 = 0 is the slope

y - 2 = 0(x - 8)

y - 2 = 0

y = 2

Answer:

y = -3/4x + 9

Step-by-step explanation:

first, find the slope by taking the difference of the y-values / difference of the x-values

(-3-12) / (16-(-4)) which equals -15/20 or -3/4

now use that value to represent the 'm' in the formula in order to find 'b'

y = mx + b

-3 = -3/4(16) + b

-3 = -12 + b

9 = b

y = -3/4x + 9

Answer:

60

Step-by-step explanation:

60 plus 60 plus 60 is 180

has to add up to 180

Using an absolute value equation, the minimum acceptable mass for the sand of bag is of 48 ounces.

The absolute function is defined by:

It measures the distance of a point x to the origin.

For this problem, the difference between x and 50 is of 2 ounces, hence:

|x - 50| = 2.

Thus the minimum value is found as follows:

x - 50 = -2 -> x = 48.

The minimum acceptable mass for the sand of bag is of 48 ounces.

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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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nsweres el dodeel s  Step-by-step explanationen

The four distinct integers a, b, c, and d have the following properties:

1. When added in pairs, the sums obtained are 10, 18, 19, 20, 21, and 29.
2. The integers are distinct, meaning that no two integers are the same.

To find the four integers in increasing order, we can start by analyzing the given sums.

First, let's look at the smallest sum, which is 10. To obtain 10 by adding two distinct integers, we can have a + b = 10.

Next, let's consider the largest sum, which is 29. To obtain 29 by adding two distinct integers, we can have c + d = 29.

Now, let's consider the remaining sums: 18, 19, 20, and 21. Since these sums are all greater than 10 and less than 29, they cannot be obtained by adding the smallest and largest integers. This means that the remaining sums must be obtained by adding the middle two integers, b + c.

From this analysis, we can conclude the following:

1. a + b = 10
2. b + c = 18, 19, 20, or 21
3. c + d = 29

To find the four integers, we can start by finding the value of b. Since a + b = 10, we can subtract a from both sides to get b = 10 - a.

Next, we can substitute this expression for b into the equation b + c = 18, 19, 20, or 21. This will give us an equation involving c in terms of a.

Finally, we can substitute the expression for c into the equation c + d = 29 to find the value of d in terms of a.

By solving these equations, we can find the four distinct integers a, b, c, and d in increasing order.

Note: Since there are multiple possible values for b, c, and d depending on the specific sum obtained from b + c, there are multiple valid solutions to this problem.

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Answer:

10, 28, 46, 82

Step-by-step explanation:

this could be wrong im  not very good with domain and range

Answer:

V=20 in cubed

Step-by-step explanation:

The formula to find the volume of a pyramid is L×W×H÷3

Therefore V =20 in cubed

Hope that helped! If you have any further questions please message me! Good luck!

Chart object , Data visualization , Sunburst chart Circular hierarchy display. Waterfall chart: Incremental data representation. Sparklines Condensed trend summaries.

A chart object is a visual representation of data that helps in analyzing and presenting information. A sunburst chart is a specific type of chart that displays hierarchical data using concentric circles and arcs to represent categories and their relationships.

A waterfall chart, on the other hand, illustrates incremental changes in data over time or categories, showing positive and negative contributions to a cumulative total.

Sparklines are small, condensed charts embedded within a cell, providing a concise summary of data trends without the need for axes or labels. These visualization tools aid in data analysis, enabling users to effectively interpret and communicate information.

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Answer:

x = 13

Step-by-step explanation:

The triangles base angles are congruent, so the triangle is isosceles with the 2 legs being congruent, then

x = 13