Which equation has a constant of proportionality equal to 3 33? Choose 1 answer: Choose 1 answer:

The total number of  positive even integers that satisfied the inequality 4x - 15 ≤ 125 is equal to 17.

The inequality is equal to,

4x - 15 ≤ 125

Adding 15 to both sides, we get,

⇒ 4x ≤ 140

Dividing both sides by 4, we get,

⇒x ≤ 35

Since we are looking for positive even integers,

Find the number of even integers less than or equal to 35.

The even integers less than or equal to 35 are,

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34

There are 17 even integers less than or equal to 35 that satisfy the inequality 4x - 15 ≤ 125.

Therefore, there are 17 positive even integers which satisfy the given inequality .

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the slope of the graph is 3 and the y-intercept is -27. This means that the graph crosses the y-axis at the point (0,-27).

Answer:

y = -3x - 27

Step-by-step explanation:

9x - 3y = 81

-3y = 9x + 81

-3y/3 = 9x/3 + 81/3

-y = 3x + 27

y = -3x - 27

Since the circle is divided into 12 equal sections by radii, the measure of any one of the 12 equal central angles would be:

360 degrees (total angle measure of a circle) ÷ 12 (number of sections) = 30 degrees

Therefore, any one of the 12 equal central angles would have a measure of 30 degrees.

The binary number 1011011 is equal to the denary number 91.

1011011two is converted to  denary by writing the numbers and assigning powers of 2 from zero to the number of digits available. For the problem, we have zero to six. then multiply out and add

= 1 x 64 + 0 x 32 + 1 x 16 + 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1

this results to

= 64 + 0 + 16 + 8 + 0 + 2 + 1

then the addition is equal to

= 91.

hence, the binary number 1011011 is equal to the denary number 91.

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The probability that he has exactly 7 hits in his next 7 at bats is  0.0106%.

To find the probability that a baseball player with a batting average of 0.31 gets exactly 7 hits in his next 7 at-bats, we can use the binomial distribution formula:

P(X=k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{n-k}[/tex]

where:

P(X=k) is the probability of getting k hits in 7 at-bats

n is the number of trials (in this case, 7 at-bats)

k is the number of successes (in this case, 7 hits)

p is the probability of success on a single trial (in this case, the batting average of 0.31)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

Using this formula, we can calculate the probability as follows:

P(X=7) = (7 choose 7) * [tex]0.31^{7}[/tex] * [tex](1-0.31)^{7-7}[/tex]

P(X=7) = 1 * [tex]0.31^{7}[/tex]* [tex]0.69^{0}[/tex]

P(X=7) = 0.000106288

Therefore, the probability that the baseball player with a batting average of 0.31 gets exactly 7 hits in his next 7 at-bats is approximately 0.000106 or 0.0106%.

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Answer:   = 8[tex]\pi[/tex]

Step-by-step explanation:

The length of AB is 12, which is the diameter, so

r=6

You need to find the angle of BOD. It is on the bottom half.  Also, AOC is the same angle

180-20 =160  now divide by 2

<BOD=80

In order to find area you multiply the fractional portion by the area

A(BOD) = [tex]\frac{80}{360} \pi r^{2}[/tex]

            =[tex]\frac{8}{36} \pi 6^{2}[/tex]                I reduced by 10 and the 36's cancel out

            = 8[tex]\pi[/tex]

To determine which account would be a better investment for Phoebe, we need to calculate the future value of each account after one year and compare them.

Account A earns simple interest, which means that the interest is calculated only on the initial investment. After one year, the investment in Account A would be worth:

$10,000 + ($10,000 x 0.09) = $10,900

Account B earns interest that is compounded annually, which means that the interest is calculated on the initial investment plus any previously earned interest. After one year, the investment in Account B would be worth:

$10,000 x (1 + 0.09)^1 = $10,900

As we can see, both accounts would have the same value of $10,900 after one year. Therefore, the choice between the two accounts depends on Phoebe's investment goals and preferences.

If Phoebe wants a simple and straightforward investment that provides a guaranteed return, Account A would be the better choice.

If Phoebe is willing to take on some risk and wants the potential for higher returns, Account B would be the better choice as the compounding of interest can lead to a higher return over a longer period of time.

Answer:

The difference is meaningful because the means are separated by about 3 MADs.

Answer:

Step-by-step explanation:

Using the frequency table provided, the mean number of games to complete a randomly selected championship from among those considered in the table is 4.333 games. The standard deviation of Y is 0.655 games.

The first team to four victories in a competition wins the title. The table provides the game lengths for the championship matches.

Let X be the total number of games required to win a championship, and let Y represent the total number of games required to win a championship chosen at random from those taken into account in the table.

Using the frequency table provided, the mean number of games to complete a randomly selected championship from among those considered in the table is 4.333 games. The standard deviation of Y is 0.655 games.

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The account balance is b) $3,796.

To calculate the account balance after two years, we need to use the formula for the future value of an annuity due:

FV = Pmt x [[tex](1+r/n)^{nt}[/tex] - 1] x (1 + r/n)

where:

Pmt is the monthly payment ($150 in this case)

r is the annual interest rate (5.5%)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years (2 in this case)

Plugging in the numbers, we get:

FV = $150 x [[tex](1+0.055/12)^{(12*2)}[/tex] - 1] x (1 + 0.055/12)

FV = $150 x [1.1247 - 1] x 1.004583

FV = $150 x 0.1247 x 1.004583

FV = $18.69 x 1.004583 x 24

FV = $449.56

So the account balance after two years, rounded to the nearest dollar, is $450. Therefore, the closest answer is option B: $3,796.

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The perimeter of the tiles is 53 inches.

The perimeter of the two dimensional figure is the sum of the whole sides of the figure,

Therefore, let's find the base of the other triangle and the height of the other as follows:

using trigonometric ratios,

cos 35  = adjacent / hypotenuse

cos 35 = x / 12

cross multiply

x = 12 cos 35

x = 9.82982453147 inches

sin 35 = opposite / hypotenuse

sin 35° = y / 12

cross multiply

y = 12 sin 35

y = 6.88291723621

Therefore, lets use Pythagoras's theorem to find the height of the other triangle.

9 + 6.88 = 15.88

Therefore,

15.88² - 8² = h²

252.267059932 - 64 = h²

h = √188.267059932

h = 13.7210422345

Therefore,

perimeter of the figure = 8 + 9 + 13.72 + 12 + 9.83

perimeter of the figure = 52.55

perimeter of the tiles = 53 inches

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For two vectors u and v, the magnitude and direction of the sum of vectors, u +v, are equal to the 1.75 and 35.14°.

The formula to determine the magnitude of a vector (in two dimensional space) v = (x, y) is [tex]|v| =\sqrt {(x² + y²)}[/tex]. We have two vectors say v and u.

Magnitude of vector u = 5

direction of vector u = 265°

Magnitude of vector v = 8

direction of vector v = 105°

[tex]\vec u = ( 5cos(265°), 5sin(265°)) [/tex]

[tex]= (−0.436 , −4.981) [/tex]

[tex]\vec v = ( 8cos(105°), 8sin(105°)) [/tex]

[tex]= (−1.294 ,4.829 ) [/tex]

We have to determine the magnitude and direction of the sum, [tex] \vec u + \vec v[/tex]. Vector addition means putting two or more vectors together. Two vectors, a and b, can be added together using vector addition, and the resultant vector can be written as : a + b.

[tex] \vec u + \vec v = (-0.436 + (-1.294), -4.981 +4.829) [/tex]

[tex]= (- 1.730, -0.251) [/tex]

Now, the magnitude of the sum of two vectors is [tex]| \vec u + \vec v | = \sqrt{ {(u + v)_x}^{2} + {(u+v)_y}^{2} } [/tex]

[tex]= \sqrt{ 1.730² + 0.251²} [/tex]

[tex]= 1.74811355466 [/tex] ~ 1.75

Now, direction of vector which is sum of vectors : Let x be angle between componets of vector ( u + v) then direction is [tex]tan ( \theta) = \frac{-0.251}{-1.730} [/tex]

[tex]\theta = tan^{-1}(0.1451)[/tex]

= 35.14°

Hence, required value is 35.14°.

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The probabilities are given as follows:

The Poisson distribution was used, as we have only the mean of the distribution, and the Poisson distribution was then approximated to the normal.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For the Poisson distribution, the standard deviation is the square root of the mean, hence the mean and the standard deviation for the normal distribution are given as follows:

[tex]\mu = 150, \sigma = \sqrt{150} = 12.15[/tex]

The probability of less than 100 customers per day, using continuity correction, is one subtracted by the p-value of Z when X = 99.5, hence:

Z = (99.5 - 150)/12.15

Z = -4.16

Z = -4.16 has a p-value of 0.

The probability of more than 185 customers is one subtracted by the p-value of Z when X = 184.5, hence:

Z = (184.5 - 150)/12.15

Z = 2.84

Z = 2.84 has a p-value of 0.9977.

Hence:

1 - 0.9977 = 0.0023 = 0.23%.

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Answer:

0.25

Step-by-step explanation:

In the provided problem, the sampling mean  for a random sample of 35 employees from a population of hourly workers in South Carolina with an average hourly wage of $17.52 and a standard deviation of $6.00 per hour is being sought after.

Even if the underlying population is not normally distributed, the central limit theorem predicts that with a high sample size, the sampling distribution of the means will be about normally distributed.

In this case, since the sample size is large enough (n=35), we can assume that the sampling distribution of the means will be approximately normally distributed with a mean of $17.52 and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.

In summary, a small survey of 35 employees from the Carolina group of hourly workers yielded a mean of $17.5 as determined by the  testing distribution of means.

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Answer: Is a plane figure with at least 3 straight sides and angles, and typically five or more sides.

Step-by-step explanation:

AUB and AnB for the set A and B is  { } ( empty set)

To find A U B, we need to combine all the elements of A and B and remove duplicates:

A U B = {2, 3, 4, 5, 7, 8}

To find A n B, we need to find the elements that are common to both A and B:

A n B = {} (since there are no elements common to both sets A and B)

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95% confidence that the sample mean for the bio/total carbon ratio of blended fuels will fall within the interval is 0.9390 ± 0.002696, which is (0.9364, 0.9416).

We can use the formula for the margin of error for a 95% confidence interval for the population mean, given by:

the margin of error = 1.96 × standard deviation / √(sample size)

where the standard deviation of the sampling distribution of the sample mean is given by:

standard deviation = population standard deviation / sqrt(sample size)

Substituting the given values, we have:

standard deviation = 0.0080 / √(34) = 0.001375

margin of error = 1.96 × 0.001375 = 0.002696

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The question is -

Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 34 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.

If the true mean is .9390 with a standard deviation of .0080, within what interval will 95 percent of the sample mean to fall? (Round your answers to 4 decimal places.)

Step-by-step explanation:

We can use the formula for continuously compounded interest to find the balance in Amadou's account after 20 years:

A = Pe^(rt)

where A is the balance, P is the initial investment, e is Euler's number (approximately 2.718), r is the interest rate, and t is the time in years. Plugging in the values given, we get:

A = 760e^(0.81*20)

A ≈ $91,012.43

Now we can use the formula for annually compounded interest to find the balance in Mia's account after 20 years:

A = P(1 + r)^t

Plugging in the values given, we get:

A = 760(1 + 0.83)^20

A ≈ $33,883.24

Finally, we can subtract Mia's balance from Amadou's balance to find the difference:

$91,012.43 - $33,883.24 ≈ $57,129.19

So Amadou would have about $57,129 more in his account than Mia after 20 years.

Answer:  

a

Step-by-step explanation:

reflection acrossv y=-3

Statement b) 'The spread of the data is the same for both towns' and c) 'The interquartile range is less for Town A than Town B' are true.

a) The median is greater for town A:

To find the median, we need to arrange the data in order:

Town A: 0, 0, 0, 1, 2, 2, 3, 4, 5, 10

Town B: 2, 2, 4, 4, 5, 6, 8, 9, 12

The median for town A is 2 and the median for town B is 5. Therefore, statement (a) is false.

b) The spread of the data is the same for both towns:

To compare the spread of the data, we can look at the range, which is the difference between the largest and smallest values.

Town A: Range = 10 - 0 = 10

Town B: Range = 12 - 2 = 10

Both towns have the same range, so statement (b) is true.

c) The interquartile range is less for Town A than Town B:

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). To find the quartiles, we need to arrange the data in order:

Town A: 0, 0, 0, 1, 2, 2, 3, 4, 5, 10

Q1 = 0.5, Q3 = 4

Town B: 2, 2, 4, 4, 5, 6, 8, 9, 12

Q1 = 2.5, Q3 = 9

The IQR for town A is 3.5 (4 - 0.5) and the IQR for town B is 6.5 (9 - 2.5). Therefore, statement (c) is true.

d) The modes are the best representation of the data for both towns:

The mode is the value that occurs most frequently in the data.

Town A: The mode is 0, which occurs three times.

Town B: There are two modes, 2 and 4, which each occur twice.

While the modes are a useful summary of the data, they may not be the best representation in this case since there are only ten data points for each town. Therefore, statement (d) is false.

e) The mean number of inches of snow per day was twice as much as in Town B as in Town A:

To compare the means, we need to calculate them for each town:

Town A: Mean = (2+0+5+4+2+10+1+3+0+0)/10 = 2.7

Town B: Mean = (4+4+9+8+12+2+2+2+6+5)/10 = 5.2

The mean for town B is approximately 1.9 times greater than the mean for town A, but not twice as much. Therefore, statement (e) is false.

Correct Question :

Two friends both claim that their towns received more snow during January. They picked ten random days in the month and listed the number of inches of snow that fell on those days in each of their towns.

Town A: 2, 0, 5, 4, 2, 10, 1, 3, 0, 0

Town B: 4, 4, 9, 8, 12, 2, 2, 2, 6, 5

Choose all true statements :-

a) The median is greater for town A

b) The spread of the data is the same for both towns

c) The interquartile range is less for Town A than Town B

d) The modes are the best representation of the data for both town

e) The mean number of inches of snow per day was twice as much as in Town B as in Town A

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Answer:

63 more women than men.

Step-by-step explanation:

Let's start by finding out how many women and men on average buy tickets per day:

For women: (356 tickets) / (3 days) = 118.67 tickets per day

For men: (329 tickets) / (3 days) = 109.67 tickets per day

So on average, 9 more women than men buy tickets per day.

To find out how many more women than men will buy tickets during the first 7 days, we need to multiply the difference per day by the number of days:

9 (more women per day) x 7 (days) = 63

Answer: 336in^3

Step-by-step explanation: In order to find the volume of a trapezoidal prism, you'll need to go by the formula of 1/2 (base 1 + base 2) x height x length.

In this case, you'll need to do 1/2 ( 10 + 4) x 6 x 8 and you should receive the answer of 336.

Lines AC and RS are skew lines

Skew lines are lines that exist in different planes and are does not intersect each other directly.

The following are properties of skew lines;

1. They continue in two directions

2. They are in different planes

3. They are never parallel

4. They never intersect

5. They are never perpendicular

As we can see from the diagram, line AC and RS are not on thesame place and they are not parallel lines. They do not intersect each other.

This means that line AC and RS has shown skew lines property and they are therefore skew lines.

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The percentage daily value for protein for a serving of miso soup is around 16%.

The percentage daily value will be calculated by the formula -

Percentage daily value = mass of protein in miso soup/ amount of daily requirement of protein × 100

Assuming the daily value of protein to be 50 gram based on the question. Keep the values in formula -

Percentage daily value = [tex] \frac{8}{50} \times 100[/tex]

Cancelling zero and performing multiplication and division

Percentage daily value is 16%.

Hence, the daily value of protein in miso soup is 16%.

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The wellbeing of a community can be significantly harmed by poor service delivery. It may result in dangers to one's health and safety, a decline in quality of life, negative economic effects, and social unrest.

The quality of service that is rendered to the members of a community contributes to the level of development and self actualization of the members of the community.

As such, the community may suffer economically as a result of poor service delivery. Poor transportation infrastructure, for instance, can drive up the cost of goods and services, and bad water supply can have an impact on the local economy's agricultural and industry.

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3 + 6 + 1 + 4 or 2 + 3 + 4 + 5

Step-by-step explanation:

3 + 6 + 1 + 4 or 2 + 3 + 4 + 5

The bracket should be placed 40 inches away from the vertex (0,0) looking at the equation y=1/160x^2 models a solar cooker.

The equation with a vertex is : y = ax²

We know that the focus of a parabola is normally at the point (h, k + p), where (h, k) is the vertex of the  parabola  and 'p' is the distance between the vertex and the focus.  

Since the vertex at the origin is  (0,0), the parabolic equation then becomes;

y = (1/4p)x²

1/4p = 1/160

4p = 160

p = 160 ÷ 4

p = 40

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