Find the value of a in the parallelogram.

Answer:

Step-by-step explanation:

3(x + 4) - 5 = 2x + 4

solve for x

x = -3

In order to find the value of x, consider that the measure of the angle above angle of 142° is equal to the measure of the angle with expression 2(x+9).

Take into account that the sum of the angle of 142° and the angle above it is equal to 180°.

Then, you have:

142 + 2(x + 9) = 180

solve the previous equation for x, as follow:

142 + 2(x + 9) = 180 apply distribution property left side

142 + 2x + 18 = 180 simplify like terms left side

2x + 160 = 180 subtract 160 left side

2x = 180 - 160

2x = 20

x = 20/2

x = 10

Hence. the value of x is 10°

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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The correct answer is option D. No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal.Researchers investigated whether there is a difference between two headache medications, R and S.

Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication.To construct a confidence interval, we require that some conditions are satisfied. The assumptions that should be met for inference with a confidence interval for the difference in population means are as follows:The data is independent;The data in each group should be roughly normally distributed;Both groups have the same variance, and each group should have a large enough sample size so that the central limit theorem (CLT) holds. The CLT holds for the difference in the sample means since both samples are taken from a population that is normally distributed. We can also assume that the sample size is large enough to use the t-distribution since each sample has more than 30 observations. As a result, all of the conditions have been met. As a result, we may employ a t-distribution to make inferences about the population difference between the two headache medications.

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1. The equation for the cost of adult tickets is:

$8.97 x number of adult tickets

The equation for the cost of child tickets is:

$6.79 x number of child tickets

The equation for the cost of renting out the theater is:

$190

2. Yes, you can get at least 5 adult tickets and 4 kids tickets.

3. The most tickets you could have bought and met the given conditions is 9 adult tickets and 8 kids tickets.

4.  It would be a better deal to rent out the theater if you had more than 24 people.

You must be aware of the costs of adult and child tickets in order to determine if you can purchase at least 5 adult tickets and 4 child tickets. A cinema ticket for an adult costs $8.97 on average, while a ticket for a child costs $6.79 on average. 4 children's tickets would cost $27.16 and 5 adult tickets would cost $44.85 as a result. You would then have $202.49 remaining, which would be enough to pay for 7 additional child tickets. Thus, you can purchase at least 5 adult and 4 child tickets.

The most tickets you could have purchased while still fulfilling the requirements is nine adult and eight child tickets. The total price would be $135.05. The adult tickets would cost $80.73 and the child tickets would cost $54.32. You would now have $89.45, which is insufficient to purchase any additional tickets.

Renting out the theater might be a great option if you have more than 24 individuals. This is due to the fact that hiring out the theater costs $190 and allows for a maximum of 24 guests, both adults and children. Consequently, renting the theater would be less expensive than purchasing individual tickets if you had more than 24 individuals.

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Answer:

50-3W ≤ 60-5w

Number of week = 5 days

Step-by-step explanation:

Given:

Carlo card = $50

Diego card = $60

Note:

Coffee and Bagel = $3  

Tea and breakfast sandwich = $5

Computation:

Number of week = W

50-3W ≤ 60-5W

Number of week = 5 days

Answer:

\(\frac{3y+2}{6y^2}\\\)

Step-by-step explanation:

Given the expression

\(\frac{3y+2}{3y}/\frac{6y^2+4y}{3y+2} \\= \frac{3y+2}{3y} * \frac{3y+2}{6y^2+4y}\\= \frac{3y+2}{3y} * \frac{3y+2}{2y(3y+2)}\\= \frac{3y+2}{3y} * \frac{1}{2y}\\= \frac{3y+2}{6y^2}\\\)

Averagely, Ana practiced for a greater amount of time each day.

Mean for ana= (20 + 20 + 30 + 60 + 60 + 60 + 70 + 70 + 100 + 100 + 100 + 115 + 115 + 115)/14 = 69.6

Mean for tara= (20 + 20 + 30 + 30 + 45 + 45 + 45 + 70 + 70 + 70 + 75 + 90 + 90 + 120)/14 = 58.6

Median for ana= 70

Median for tara= (45 + 70)/2 = 57.5

Ana has the greater median and also has the greater mean.

Averagely, we can conclude that ana practiced for a greater amount of time each day.

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Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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Answer:

see below, answers underlined

Step-by-step explanation:

1. Change both fractions to decimals

1/5=0.20

1/7=0.14

The question is basically asking us to find a fraction between these 2 fractions.  We can pick any number between 0.20 and 0.14.

Let's pick 0.15.

Change 0.15 back to a fraction:

0.15=3/20

Hope this helps!

*There are multiple answers for this.  These include 4/25, 6/35, etc.*

Based on the given information, the terminal side of angle 0 lies in quadrant III.

To determine the quadrant in which the terminal side of angle 0 lies based on the given information, we can analyze the signs of the trigonometric functions:

(a) Since sine < 0 and cotangent < 0, we can determine the quadrant as follows:

Sine < 0 implies that the y-coordinate (vertical component) of the point on the unit circle corresponding to angle 0 is negative.

Cotangent < 0 implies that the x-coordinate (horizontal component) of the point on the unit circle corresponding to angle 0 is negative.

In quadrant III, both the x and y-coordinates are negative. Therefore, quadrant III is the correct answer in this case.

(b) The information provided in this option is incorrect. "esce" is not a recognized trigonometric function, and "cos > 0" does not provide enough information to determine the quadrant.

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With a 95% probability, 62 students should be sampled to be within 0.25 drinks of the population mean.

\(\alpha\) is the level obtained by subtracting 1 from the confidence interval and dividing by 2.

So,

\(\alpha\) = (1 - 0.95) ÷ 2 = 0.25

Now, find z in the Z-table, as z has a p-value of 1 - \(\alpha\).

As a result, z has a p-value of (1 - 0.025) = 0.975

so, z  = 1.96

Now, infer M as follows:

M = z × (σ ÷ √n) where n is the sample size and is σ the population standard deviation.

When M = 1, this is n.

According to the question, the standard deviation is roughly 1.

σ = 1

M = z × (σ ÷ √n)

0. 25 = 1.96 × (1 ÷ √n)

√n = 1.96 × (1 ÷ √n)

Square both sides,

(√n)² = ((1.96 × 1) ÷ 0.25)²

n = (7.84)²

n = 61.4656

n ≈ 62

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Answer:

Step-by-step explanation:

We have like bases in our m's, and the rule for the numerator, where those bases are multiplied, is that we can add the exponents on them to get a new power. We will also at the same time multiply 4 by 6:

\(\frac{24m^7}{3m^2}\)  As far as the numbers go, we will divide them to get 8; the rule for dividing like bases is that we subtract the lower exponent from the upper to get:

\(8m^5\), the third choice down

The expression [(4m³) x (6m⁴)] / 3m² will be equivalent to 8m⁵. The correct option is C.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression will be solved as below:-

[(4m³) x (6m⁴)] / 3m² = 24m⁷ / 3m²

Divide the numerator by the denominator to simplify the expression.

[(4m³) x (6m⁴)] / 3m² = 8m⁵

Therefore, the expression [(4m³) x (6m⁴)] / 3m² will be equivalent to 8m⁵. The correct option is C.

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Answer:

60 and

x=4

Step-by-step explanation:

False. In a static method of a class, you cannot use the "this" keyword to reference instance variables or instance methods of the same class.

A static method belongs to the class itself, not to any particular instance of the class, so it cannot access instance-specific information. Instead, you would need to use the class name followed by the variable name to access any static or instance variables within a static method of that same class. For example, if the class had an instance variable called "f" and a static method called "myStaticMethod", you could reference the instance variable from within the static method using "ClassName.f". It is important to note that if you attempt to reference an instance variable using "this.f" within a static method, you will receive a compilation error.

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As per the survey of 400 students, 60 of them bring their lunch everyday.

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute a percentage of a number of students, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Percent signifies for every 100. The sign "%" is used to denote it.

Examples

10% is the fraction 1/10.

20% is the same as the 15 fraction.

25% translates to a 1/4 fraction.

50% is the same as a half fraction.

75% corresponds to a 1/4 fraction.

90% is the same as the proportion (9)/10.

No dimension exists for percentages. Thus, it is referred to as a dimensionless number. If we say 50% of a number, we mean 50% of its total.

How to solve ?

15% of 400 = 15 * 400/100 = 60

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They make it all so complicated with all of the complex lines doing their own thing, though this is somewhat straight forward once you see it.

With the Domain, these are the x values that the line covers.

For this, it would be -5 ≤ x ≤ 4, because all of the x values are between these two values.

With the Range, these are the y values that the line covers.

For this, it would be -4 ≤ x ≤ 5, because all of the y values are between these two values.

With the X-Intercepts, these are the x values the line crosses for when the y value is 0.

For this, it would be -3 and -1.

With the max, it is the highest point within a graph, for where the y value is the greatest.

For this, it would be x = 4 at the coordinate (4, 5).

Answer:

You would have 20 games in total.

Step-by-step explanation:

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The artist will need a piece of string that is approximately 40 feet long. Therefore, the cost of the string will be approximately $42.

To calculate the length of the string needed to surround the semicircle canvas, we need to find the circumference of the semicircle. The formula for the circumference of a circle is C = 2πr, where r is the radius. However, since we only need the half-circle, we divide the circumference by 2.

C = (2π * 13) / 2 = 13π ≈ 40.84 feet

Rounding to the nearest foot, the artist needs a string that is approximately 41 feet long. Given the cost of $1.05 per foot, the total cost will be approximately $42.

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There are 18 different triples of natural numbers with a sum of 10, considering (1,8,1) and (8,1) as the same triple as (1,1,8).

To find the number of different triples of natural numbers with a sum of 10, we can consider different cases based on the value of the first number in the triple.

Case 1: The first number is 1.

In this case, we need to find the number of ways to represent 10 as a sum of the remaining two numbers. Since we have already considered (1,8,1) and (8,1) as the same triple as (1,1,8), we only need to find the ways to represent 10 using two numbers, excluding 1. The possible pairs are:

(2,8), (3,7), (4,6), (5,5)

Case 2: The first number is 2.

In this case, we need to find the number of ways to represent 8 as a sum of the remaining two numbers. The possible pairs are:

(1,7), (3,5), (4,4)

Case 3: The first number is 3.

In this case, we need to find the number of ways to represent 7 as a sum of the remaining two numbers. The possible pairs are:

(1,6), (2,5), (4,3)

Case 4: The first number is 4.

In this case, we need to find the number of ways to represent 6 as a sum of the remaining two numbers. The possible pairs are:

(1,5), (2,4), (3,3)

Case 5: The first number is 5.

In this case, we need to find the number of ways to represent 5 as a sum of the remaining two numbers. The possible pair is:

(1,4)

Case 6: The first number is 6.

In this case, we need to find the number of ways to represent 4 as a sum of the remaining two numbers. The possible pairs are:

(1,3), (2,2)

Case 7: The first number is 7.

In this case, we need to find the number of ways to represent 3 as a sum of the remaining two numbers. The possible pair is:

(1,2)

Case 8: The first number is 8.

In this case, we need to find the number of ways to represent 2 as a sum of the remaining two numbers. The only possible pair is:

(1,1)

Adding up the counts from each case, we get:

4 + 3 + 3 + 3 + 1 + 2 + 1 + 1 = 18

Therefore, there are 18 different triples of natural numbers with a sum of 10, considering (1,8,1) and (8,1) as the same triple as (1,1,8).

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The probability of getting a z-score greater than 0.15 is approximately 0.5693.

The probability of getting more than 2100 nails in a bag is approximately 0.5693.

The number of nails in a bag is a discrete random variable, so it's not appropriate to use a normal distribution to model it.

Also, the mean of 8.9 and standard deviation of 5.56 are for a single nail, not for a bag of 225 nails.

To answer the question, we need more information on the distribution of the number of nails in a bag.

Assuming that the distribution is approximately normal, the mean of the number of nails in a bag would be 225 * 8.9 = 2009 and the standard deviation would be the square root of 225 * (5.56)^2 = 59.11.

With these values, we can use a standard normal distribution to find the probability of getting more than 2100 nails in a bag:

z = (2100 - 2009) / 59.11 = 0.15

Note: This calculation assumes that the distribution is approximately normal, and that the mean and standard deviation of a single nail are accurate. These assumptions might not hold in practice, so the answer should be taken with caution.

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A) The population of Ghana will take 32 years to double from 25.2 million to 50.4 million.

B) At This Growth Rate, the Population will be 40 Million till 2061.

A) To calculate the time it will take for the population of Ghana to double, we can use the rule of 70. The rule of 70 states that to find the approximate number of years it takes for a quantity to double, we divide 70 by the exponential growth rate. So, for Ghana, we divide 70 by 2.19, which gives us approximately 31.96 years. Therefore, it will take about 32 years for the population of Ghana to double from 25.2 million to 50.4 million.

B) To calculate the time it will take for the population of Ghana to reach 40 million, we can use the same formula. We want to know when the population will double from its current size of 25.2 million to 40 million. So, we set up the equation:

25.2 million x 2 = 40 million

We can see that the population needs to double once to reach 50.4 million, and then increase by a smaller amount to reach 40 million. So, we need to find out how long it will take for the population to double once, and then add that time to the current year (2013) to find out when the population will be 40 million.

Using the rule of 70 again, we divide 70 by 2.19, which gives us 31.96 years. This is the amount of time it will take for the population to double from 25.2 million to 50.4 million. Therefore, the population will reach 40 million approximately 16 years after it has doubled from its current size, which is 2013 + 32 + 16 = 2061.

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Answer:

7) \(x \to x - 3\).

8) \(y \to y + 2\)

9) The entire quadratic equation did not get reflected.

Step-by-step explanation:

7) A horizontal translation to the right is of the form:

\(x \to x - a\)

Let \(y = -(x-3)^{2} + 2\), then the horizontal translation is represented by \(x \to x - 3\).

8) A vertical translation upwards is of the form:

\(y \to y + a\)

Let \(y = -(x-3)^{2} + 2\) , then the vertical translation is represented by:

\(y \to y + 2\)

9) The only component of the quadratic equation that was reflected was the part \((x-3) ^{2}\) along the x-axis. We can create the entire function by applying the following steps:

(i) \(f(x) = x^{2}\) (Original function)

(ii) \(f(x) = (x-3)^{2}\) (Horizontal translation)

(iii) \(f(x) = - (x-3)^{2}\) (Reflection)

(iv) \(f(x) = -(x-3)^{2} + 2\) (Vertical translation)

The entire quadratic equation did not get reflected.

\(Hello\) \(There!\)

Let's do step-by-step explanation!

\(10+(\frac{1}{2})\) \(4\) · \(48\)

Multiply and divide (left and right) \((\frac{1}{2} )\) · \(4\) · \(48: 96\)

\(=10+96\)

Add and subtract (left to right) \(10+96:106\)

Answer:

\(106.\)

Hopefully, this helps you!!

\(Emilychu\)

Answer:

(2,7)

Step-by-step explanation:

When you reflect something across the X-axis, the y coordinate changes sign.

Step-by-step explanation: Each angular point of a polygon, polyhedron, or any other figures such as squares, triangles, etc is a vertices. A vertices is simply an angular point in any figure.

Answer:

Vertices- Is the highest point also the top or apex  

The y intercept is where a line on a graph crosses the y axis when the x coordinate is 0.

Answer:

The point where the line is on the Y axis

Step-by-step explanation:

for example in the equation y=mx+b, b would be the y-intercept or in the equation y=4x+7, the y-intercept would be 7.

Answer:

theansweris a

Step-by-step explanation:

The line also passes through the coordinates (-1/2, 0) and (0, -1). Hence the correct equation of the graph is y <  -2x − 1

Inequality is are expressions not separated by an equal sign

The given graph given has a broken line and shaded below the graph. The correct inequality sign will be a less than sign

The line also passes through the coordinates (-1/2, 0) and (0, -1). Hence the correct equation of the graph is y <  -2x − 1

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