linear equations in one variable

Answer: 3

Step-by-step explanation:

3rd, lands on a vowel.

Answer: The spinner lands on a vowel.

Step-by-step explanation:

Probability to land on purple section: 1/10

Probability to land on letter D: 1/10

Probability to land on vowel: 3/10 (A, E, I)

Probability to land on red section: 2/10

3/10 > 2/10 > 1/10

A student attempts a 10-question multiple-choice test where each question presents four options, and the student makes random guesses for each answer. So the probability of (a) P(5)= 0.058 and (b) P(More than 3)= 0.093.

Part 1: Calculation of probability of getting 5 questions correct

(a) P(5)The formula used to find the probability of getting a certain number of questions correct is:

P(k) = (nCk)pk(q(n−k))

Where, n = total number of questions

(10)k = number of questions that are answered correctly

p = probability of getting any question right = 1/4

q = probability of getting any question wrong = 3/4

P(5) = P(k = 5) = (10C5)(1/4)5(3/4)5= 252 × 0.0009765625 × 0.2373046875≈ 0.058

Part 2: Calculation of probability of getting more than 3 questions correct

(b) P(More than 3) = P(k > 3) = P(k = 4) + P(k = 5) + P(k = 6) + P(k = 7) + P(k = 8) + P(k = 9) + P(k = 10)

P(k = 4) = [tex]10\choose4[/tex](1/4)4(3/4)6 = 210 × 0.00390625 × 0.31640625 ≈ 0.02

P(k = 5) = [tex]10\choose5[/tex](1/4)5(3/4)5 = 252 × 0.0009765625 × 0.2373046875 ≈ 0.058

P(k = 6) = [tex]10\choose6[/tex](1/4)6(3/4)4 = 210 × 0.0002441406 × 0.31640625 ≈ 0.012

P(k = 7) = [tex]10\choose7[/tex](1/4)7(3/4)3 = 120 × 0.00006103516 × 0.421875 ≈ 0.002

P(k = 8) = [tex]10\choose8[/tex](1/4)8(3/4)2 = 45 × 0.00001525878 × 0.5625 ≈ 0.001

P(k = 9) = [tex]10\choose9[/tex](1/4)9(3/4)1 = 10 × 0.000003814697 × 0.75 ≈ 0.000

P(k = 10) = [tex]10\choose10[/tex](1/4)10(3/4)0 = 1 × 0.0000009536743 × 1 ≈ 0

P(More than 3) = 0.020 + 0.058 + 0.012 + 0.002 + 0.001 + 0.000 + 0≈ 0.093

Therefore, the probabilities of the given situations are: P(5) ≈ 0.058, P(More than 3) ≈ 0.093.

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In monopolistic competition, the end result of entry and exit is that firms end up with a price that lies on the downward-sloping portion of the average cost curve.

Monopolistic competition is a market condition in which many small firms compete with each other by selling slightly varied, but essentially comparable goods or services at somewhat different prices. These companies enjoy some market power, but they are not monopolies because their products or services are close substitutes for each other.

The equilibrium price in a monopolistically competitive market is a long-run, but not a short-run, outcome of entry and exit. Because the market is monopolistic, entry and exit do not have an immediate impact on the price; it simply alters the number of producers operating in the market. Over time, the entry and exit of producers in the industry will increase or decrease the number of substitutes available, driving demand curves and resulting in the price of the commodity settling on the down-sloping portion of the average cost curve in the long run.

Therefore, it can be concluded that the end result of entry and exit in monopolistic competition is that companies end up with a price that lies on the downward-sloping portion of the average cost curve.

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In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.

The median, a statistician's measure of central tendency, divides a dataset into two equally sized half. When the data is organized from smallest to largest, it is the midway value (or largest to smallest). The median is the average of the two middle values when there are an even number of values. Since it is unaffected by extreme values, the median is frequently employed as a measure of central tendency when a dataset contains outliers or is skewed.

given

None of the claims are untrue.

The mean will be greater than the median if a density curve is tilted to the right.

The mean and median are equal in a density curve that is symmetric.

In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.

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The lower limit of a 90% confidence interval for the average difference in the number of days the temperature was above 90 degrees between 1948 and 2018 is -22.8 days and the upper limit is 28.6 days.

The margin of error for the 90% confidence interval is 25.4 days.

The 90% confidence interval does provide evidence that the number of 90-degree days increased globally comparing 1948 to 2018.

The 99% confidence interval also provides evidence that the number of 90-degree days increased globally comparing 1948 to 2018.

If the mean difference and standard deviation stay relatively constant, decreasing the degrees of freedom would make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.

Lowering the confidence level would also make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.

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The radius of the cylinder is r = 13 cm

The radius of a cylinder is the radius of the circular base of the cylinder.

Since the volume of a cylinder is 15, 919.8 cm³. If the height is 30 cm, we require it radius.

Using the formula for volume of a cylinder V = πr²h where

Making r subject of the formula, we have that

r = √V/πh

Since

Substituting the values of the variables into the equation for the radius, we have that

r = √V/πh

r = √(15,919.8 cm³/[3.142 × 30 cm])

r = √(15,919.8 cm³/94.26 cm)

r = √168.8924 cm²

r = 12.995 cm

r ≅ 13 cm

So, the radius r = 13 cm

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Answer: -17x+3

Step-by-step explanation:

y=2x+3 and y=15-x

15x-2x+3

-17x+3

you can try this

Yes, there is a chance that the bottled water you are drinking is just tap water packaged in a bottle. According to a study by the Natural Resources Defense Council, 25% of bottled water is just tap water that has been packaged in a bottle. [Scientific American, July 2003]

Bottled water is drinking water that has been packaged in bottles or containers for sale. Bottled water can come from a variety of sources, such as municipal supplies, springs, wells, and other sources. In some cases, bottled water is treated or purified to remove impurities and contaminants. However, not all bottled water is purified or treated, and some may be just tap water that has been packaged in a bottle.

Purified water is water that has been treated to remove impurities and contaminants. Purified water can come from any source, including municipal supplies, wells, and other sources. Purification methods may include filtration, reverse osmosis, distillation, or other methods. Purified water is commonly used in medical and industrial applications, as well as in homes for drinking and cooking.

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If an Estate dealer sells houses and makes a commission of GHc3750 for the first house sold and receives GHc500 increase in commission for each additional house sold, for reaching a total commission of GHc6500, she must have sold 6.5 houses.

The number of houses the estate dealer sold to reach a total commission of GHc6500 can be determined using the mathematical operations of subtraction, division, and addition.

The total commission received = GHc6,500

The commission for the first house = GHc3,750

The commission for the remaining houses sold = GHc2,750 (GHc6,500 - GHc3,750)

The commission for additional sale of each house = GHc500

The number of additional houses sold = 5.5 (GHc2,750/GHc500)

The total number of houses sold = 6.5 (5.5 + 1 or the first house)

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If sin(2x) = cos(x), where 0° ≤ x < 180°, then,  The possible angle values of x are 90°, 30° and 150°.

The sine and the cosine are trigonometric functions of the angles. The sine and cosine of an acute angle are defined in the context of a right triangle: for a given angle, its sine is the ratio of the length of the side opposite the angle to the length of the longest side of the angle. triangle (the hypotenuse ), and the cosine is the adjacent side The ratio of the length to the hypotenuse.

According to the Question:

Given that,

sin(2x) = cos(x) where 0° ≤ x < 180°

We know that:

sin(2x) = 2 sin(x) cos(x)

⇒ 2 sin(x) cos(x) = cos(x)

Subtract cos(x) on both sides

2 sin(x) cos(x) - cos(x) = 0

cos(x) (2sinx-1)=0

It means, cos(x) = 0 and (2sin x -1 ) = 0

cos x = cos0           and        sinx(x) = 1/2

x = 90°                     and        x = 30°, 150°

Hence, the possible values of x are 90°, 30° and 150°.

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Answer: x = 8.7

Step-by-step explanation:

You are given the reference angle: 60°, the hypotenuse and the leg of which to find.

X is opposite in reference to 60° and you are given the hypotenuse.

Sine works with the hypotenuse and the opposite: sin∅ = opp/hyp

sin(60°) = x/10

To figure out x, you must transpose, to make x the subject. X is being divided by 10, so to undo that you must multiply, and what you do to one side, you must do to the next to balance the equation.

10 x sin(60) = x/10 x 10

= X = sin(60) x 10

sin(60) = 0.866

X = 0.866 x 10

X = 8.66

You can round off to one decimal place or leave the answer as is.

X = 8.7 (1 d.p)

Answer:

Step-by-step explanation:

Choose three values for

x and substitute in to find the corresponding y values.(0,−3),(1,0),(2,3)

You can choose any of these three pairs or the equation y=3x-3

We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;

[tex] \purple{ \mathfrak{x \times 6 = 12 \times 5}}[/tex]

[tex] \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}[/tex]

[tex] \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}[/tex]

[tex] \large \purple{ \mathfrak{x = 2 \times 5}}[/tex]

[tex] \large \boxed{ \red{ \mathfrak{x =10}}}[/tex]

False. A mean difference of zero does not necessarily indicate that the peppers are well distributed between the two groups.

Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used to describe a wide variety of physical, logical, and abstract objects. Numbers are used to represent quantities, lengths, temperatures, money, and many other measurements. They are also used to represent abstract ideas, such as the number of days in a year or the number of colors in a rainbow.

Although the mean may be equal between the two groups, the distribution of the peppers could be skewed and not evenly distributed. For example, one group could have all large peppers and the other all small peppers and the mean would be equal. This would not be considered well distributed. To ensure the peppers are evenly distributed, one should check the standard deviation or range of the data to see if the peppers are spread across both groups.

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Answer:  A mean difference of zero indicates the peppers

are not well distributed between the two groups.

Why: Part B Answers

What do large differences of the means of each group indicate? Select the correct answer.

The peppers with different weights aren’t properly distributed between the two groups.

So they arent distributed well

Answer:

(x-7)(x+6)

factor and see what works

The following is the recursive formula for the arithmetic sequence in this issue:

c(1) = -16.

c(n) = c(n - 1) - 17.

An arithmetic sequence is a series of numbers where each term is obtained by adding a fixed constant, known as the common difference, to the previous term. For example, in the sequence 2, 5, 8, 11, 14, 17, each term is obtained by adding 3 to the previous term.

The formula for finding the nth term of an arithmetic sequence is: a(n) = a(1) + (n-1)d, where a(1) is the first term, d is the common difference, and n is the term number. For example, to find the 10th term of the sequence 2, 5, 8, 11, 14, 17, we would use the formula a(10) = 2 + (10-1)3 = 29. Arithmetic sequences have many practical applications, such as in finance, where they can be used to calculate the interest earned on an investment over time.

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As a result, one cup of tea costs £0.65 and one cup of coffee costs £3.15.

Cost computation helps in deciding on pricing, manufacturing output, and sales. It also helps in figuring out the costs of the products and services the company sells.

Let's assume that a cup of tea costs t and a cup of coffee costs c.

We can infer the following based on the initial piece of knowledge:

3t + 1c = 5.10 --------------(1)

We learn the following from of the second piece of information:

1t + 4c = 8.30 --------------(2)

We can find the solutions to t and c because we have two equations with two variables.

Equation (1) is multiplied by 4 and equation (2) is taken away to yield the following result:

9t = 5.90

Therefore:

t = 0.65

Using t = 0.65 as the replacement in equation (1), we get:

3(0.65) + 1c = 5.10

1c = 5.10 - 1.95

1c = 3.15

Therefore:

c = 3.15

As a result, one cup of tea costs £0.65 and one cup of coffee costs £3.15.

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Answer:

1034 x 10⁷

Step-by-step explanation:

the seven just means to multiply by 10 seven times

Let me know if this helps.

Given a normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points.Using the empirical rule for normal distributions, the probability that in a randomly selected game the player scored less than 26 points is required .Empirical Rule: For a normal distribution with a mean µ and a standard deviation σ, the probability of an observation being within k standard deviations of the mean is approximately:•

68% of the observations fall within one standard deviation of the mean.• 95% of the observations fall within two standard deviations of the mean.• 99.7% of the observations fall within three standard deviations of the mean.Here, the mean is 20 points and the standard deviation is 3 points. We need to find the probability of getting less than 26 points.z-score = (x - µ) / σ = (26 - 20) / 3 = 2σ = 2According to the empirical rule, 95% of observations fall within 2 standard deviations of the mean.So, the probability that the player scored less than 26 points is 95%.Therefore, the final answer is 95% rounded to one decimal place. Answer: 95%.

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Answer: 38 I think if it's not right I'm sorry I'm bad at math that's like the only thing I suck at

Step-by-step explanation:

If the expression 1/2x was placed in the form ax^b where a and b are real numbers, then a + b equal to option (4) -1/2

The given expression is 1/(2x), which can be rewritten as:

1/(2x) = 1/2 × (1/x)

Here, we can see that the expression can be written in the form of ax^b, where a = 1/2 and b = -1.

To see why a = 1/2, notice that 1/2 is the coefficient of (1/x). And to see why b = -1, note that x^(-1) is the exponent on the variable x

So, we have:

1/(2x) = (1/2) × x^(-1)

And, a + b = (1/2) + (-1)

Add the numbers

= -1/2.

Therefore, the correct option is (4) -1/2.

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The probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 from a small hospital is 9/19, given 6 out of 19 are General Practitioners, 5 out of 19 are under 40, and 2 are both.

To find the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40, we need to add the probabilities of these two events and subtract the probability of selecting a doctor who is both a General Practitioner and under the age of 40, since we don't want to count that case twice:

P(General Practitioner or under 40) = P(General Practitioner) + P(Under 40) - P(General Practitioner and under 40)

we know 6 out of 19 doctors are General Practitioners, 5 out of 19 doctors are under the age of 40, 2 doctors are both General Practitioners and under the age of 40.

Therefore:

P(General Practitioner) = 6/19

P(Under 40) = 5/19

P(General Practitioner and under 40) = 2/19

Substituting these values into the formula:

P(General Practitioner or under 40) = 6/19 + 5/19 - 2/19

= 9/19

Therefore, the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 is 9/19.

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Answer: The two angles are 117 degrees and 63 degrees.

Step-by-step explanation:

Supplementary angles are two angles whose sum is 180 degrees. Let the two angles be 13x and 7x, where x is a constant of proportionality.

We know that the sum of the angles is 180 degrees, so:

13x + 7x = 180

Combining like terms, we get:

20x = 180

Dividing both sides by 20, we get:

x = 9

So the measures of the angles are:

13x = 13(9) = 117 degrees

7x = 7(9) = 63 degrees

Therefore, the two angles are 117 degrees and 63 degrees.

Answer:

y=-17

Step-by-step explanation:

1-2(9)=1-18=-17

Answer: y = -17

Step-by-step explanation:

Using PEMDAS, you need to do the multiplication first. 2 times x is 18, because the value of x is 9. You will then get 1 - 18. This is -17, so y = -17. I hope that this helped! :)

Answer:

30cm

Step-by-step explanation:

Perimeter of an equilateral triangle = 3L

Mathematically we have;

P = 3L

Where P = perimeter of the triangle

L = Length

Therefore;

90 = 3L

Divide both side by 3

L = 30cm

Therefore, the length of each side of the triangle is 30cm.

Answer:

The profit made is given by the difference between the total revenue and the total production cost:

P = R - C

Substituting the given expressions for R and C, we get:

P = 33.70N - (750 + 16.95N)

Simplifying:

P = 16.75N - 750

Therefore, the equation relating P to N is P = 16.75N - 750

The most distance Talia can go each day while staying within her budget is 320 miles.

In this case, our goal is to write an inequality before moving on to solve it.

We begin with the daily rental fee and the cost per mile.

This is stated as $30 per day and $0.20 per mile in the question.

She is required to spend a total of $94.

This means that the total cost of the rental automobile and the cost per mile must be $94 or less.

Let m be the maximum number of miles she can travel.

Hence, we may write the inequality as follows: 30 + 0.2 m 94.

This inequality is what we can now solve;

0.2m ≤ 94 - 30

0.2m ≤ 64

m ≤ 64/0.2

320 miles = m

The most distance Talia can go each day while staying within her budget is 320 miles.

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