Help me with this please

Answer:

0.5x(x + 2) = 24

x² + 2x - 48 = 0

x² + (x + 2)² = 100

Step-by-step explanation:

A = bh/2

A = x(x + 2)/2 = 24

0.5x(x + 2) = 24

0.5x² + x = 24

x² + 2x = 48

x² + 2x - 48 = 0

x² + (x + 2)² = 10²

x² + (x + 2)² = 100

Answer:

HP = 2

HJ = 2.5

HJ = 2.5

GK = √29

Step-by-step explanation:

I assume that HK and GJ are perpendicular, so triangles GPH, GPK, JPH, and JPK are right triangles.

Use the Pythagorean theorem.

a² + b² = c²

(GP)² + (HP)² = (GH)²

5² + (HP)² = (√29)²

25 + (HP)² = 29

(HP)² = 4

HP = 2

(HP)² + (PJ)² = (HJ)²

2² + (1.5)² = (HJ)²

4 + 2.25 = (HJ)²

(HJ)² = 6.25

HJ = 2.5

If GHJK is a kite, then KJ = HJ and GK = GH.

HJ = 2.5

GK = √29

Answer:

√89 / 8

Step-by-step explanation:

r = hypotenuse = √(5² + 8²) = √89

csc θ = 1/sin θ

sin θ = opp/hyp = height / √89 = 8/ √89

csc θ = hyp / opp = 1 / (8/ √89) = √89 / 8

Answer: No it is not up to code

Step-by-step explanation:

So we can use trig ratios to solve this:

tan theta = 3.5/40

.: theta = arctan(3.5/40)

theta is about 5

Since 5 > 4.8, these dimensions do not comply with regulation.

Step-by-step explanation:

( - ∞, + ∞ )      x  can have any value....there are no x values where x is undefined .

Possible number(s) of positive real zeros are 1 or 0 and Possible number(s) of negative real zeros: 2 or any even number

To determine the possible number of positive and negative real zeros of the polynomial q(x) = -7x^3 + 9x^2 - 8x + 2, we can use Descartes' rule of signs.

(a) Possible number(s) of positive real zeros:

For the polynomial q(x), we count the number of sign changes in the coefficients when we write them in descending order:

-7x^3 + 9x^2 - 8x + 2

There is only one sign change, from -8x to +2. Thus, there is exactly 1 positive real zero or none at all.

Possible number(s) of negative real zeros:

To determine the possible number of negative real zeros, we substitute -x into the polynomial:

-7(-x)^3 + 9(-x)^2 - 8(-x) + 2

Simplifying the expression:

7x^3 + 9x^2 + 8x + 2

Again, we count the number of sign changes in the coefficients:

7x^3 + 9x^2 + 8x + 2

There are two sign changes, from 7x^3 to 9x^2 and from 9x^2 to 8x. Thus, there are either 2 negative real zeros or any even number of negative real zeros.

In summary:

(a) Possible number(s) of positive real zeros: 1 or 0

(b) Possible number(s) of negative real zeros: 2 or any even number

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The conditional probability is solved and the tiles are chosen

Given data ,

A bucket contains 60 polygon tiles. Of the tiles, 12 are triangles, 15 are squares, 8 are pentagons, 10 are hexagons, 6 are heptagons, and the rest are octagons.

So , Total number of polygon tiles = 60

Number of triangles = 12

Number of squares = 15

Number of pentagons = 8

Number of hexagons = 10

Number of heptagons = 6

Number of octagons = 9

Now , probability of event 1: At least four sides, given that it's not a hexagon

P ( A ) = ( 15 + 8 + 6 + 9 ) / 60

P ( A ) = 0.6333

P ( A ) = 63.33 %

And , Probability: P(not a square | less than 7 sides) P ( B )

P ( B ) = ( 12 + 8 + 10 + 6 ) / 60

P ( B ) = 0.6

P ( B ) = 60 %

Hence , the probabilities are solved

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Answer:

D. For every 1-inch increase in height, walking speed increases by 4.7 m/min.

The most fun game at the moment seems to be playing a videogame.

If a student is selected randomly from the 59 students who participated in the survey, the probability of choosing a student playing a videogame is 35.6%.

Probability refers to the chance or likelihood of an expected event, outcome, or success occurring given the possibility of many events, outcomes, or successes.

Probability values are stated as decimals, fractions, or percentages when they lie between 0 and 1.

The number of students going to a party = 6

The number of students playing a videogame = 21

The number of students taking a nap = 11

The number of students drawing a picture = 8

The number of students reading a good book = 7

The number of students playing sports = 6

The total number of student participants in the survey = 59

The probability of choosing a student playing a videogame = 35.6% (21 ÷ 59 × 100)

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in triangle ABC, AB is approximately 26.83 inches and BC is approximately 35.78 inches.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles.

In triangle ABC, let's denote the length of AB as b and the length of BC as a.

Using the Pythagorean theorem on triangles ABN and BCN, we can find that:

AN² + BN² = AB²

BN² + CN² = BC²

Plugging in the given values, we get:

24² + 18² = b²

18² + (40 - b)² = a²

Simplifying, we get:

b² = 720

a² = 4b² - 1600

a² = 4(720) - 1600

a² = 1280

Taking the square root of both sides, we get:

b = √{720} = 26.83

a = √{1280} = 35.78$

Therefore, in triangle ABC, AB is approximately 26.83 inches and BC is approximately 35.78 inches.

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Answer:

192pi units^3

Also correct: 603.19

Step-by-step explanation:

The number of possible outcomes is 36.

Given that a 6-sided die has been rolled twice we need to find the sample space has how many possible outcomes,

Therefore, in one roll there will be 6 outcomes, and when it is rolled twice it will be = 6 × 6 = 36

The sample space =

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

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

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

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

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

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

There are 36 possibilities for (a,b).

This total number of possibilities can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b.

So, the total number of joint outcomes (a,b) is 6 times 6 which is 36. The set of all possible outcomes for (a,b) is called the sample space of this probability experiment.

Hence the number of possible outcomes is 36.

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Answer:

x=8/5

Step-by-step explanation:



The approximate probability that the 40 players have a mean salary of at most 4 million dollars is approximately 0.9985 or 99.85%.

Given that the sample size is 40, we can use the Central Limit Theorem to approximate the normal distribution of sample means. The mean of the sample means will be the same as the population mean, which is 3.3 million dollars. The standard deviation of the sample means (also known as the standard error) can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, it will be 1.5 million dollars divided by the square root of 40.

Let's calculate the standard error:

Standard Error = 1.5 million dollars / sqrt(40) ≈ 0.237 million dollars.

Now, we want to find the probability that the 40 players have a mean salary of at most 4 million dollars. We can convert this to a standard normal distribution by calculating the z-score:

Z = (X - μ) / SE

where X is the value we want to find the probability for (4 million dollars), μ is the population mean (3.3 million dollars), and SE is the standard error (0.237 million dollars).

Z = (4 - 3.3) / 0.237 ≈ 2.95

To find the probability corresponding to this z-score, we can refer to a standard normal distribution table or use statistical software. Assuming a standard normal distribution, the approximate probability can be found to be about 0.9985.

Therefore, the approximate probability that the 40 players have a mean salary of at most 4 million dollars is approximately 0.9985 or 99.85%.

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Answer:

Sure. Here are the steps on how to solve for the dimensions of the rectangular field that will produce the greatest area:

Let x and y be the width and length of the rectangular field, respectively.

The perimeter of the rectangular field is 2x + 4y = 19300 feet.

The area of the rectangular field is xy.

We want to maximize the area, so we need to minimize the perimeter.

We can minimize the perimeter by setting x = y.

Plugging in x = y into the equation 2x + 4y = 19300, we get 4x = 19300.

Solving for x, we get x = 4825 feet.

Since x = y, we know that y = 4825 feet.

Therefore, the dimensions of the rectangular field that will produce the greatest area are 4825 feet by 4825 feet.

To round off your answers to two decimal places, you can use the following formula:

rounded_value = (value * 100) // 100

In this case, the rounded values for x and y are 4825.00 and 4825.00, respectively.

Step-by-step explanation:

The problem is about maximizing the area of a rectangular field given a fixed amount of fencing. Length and width of the rectangle are assumed as x and y, respectively. The total fencing equation is x + 5y = 19300 and the area equation is A=xy. Substituting to get equation in terms of one variable, it turns into a calculus problem to find the dimensions that maximize area.

This particular problem solution requires use of calculus to maximize the total area of a rectangular field, given a fixed fencing limit. We need to maximize the rectangle area with the total fence length being 19300 ft. Here are the steps to create a mathematical model for this problem:

This is a calculus problem where we find the maximum point using the derivative of the area equation. However, the exact dimensions would need further calculations. It's important to note that this task requires comprehensive knowledge of calculus and algebra.

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To improve the fairness of a passenger survey on a railway line, it would be ideal to over-sample data from groups that are less likely to be represented in the regular ridership during peak hours of 7:00 am to 5:00 pm. One such group could be passengers who use the railway line during off-peak hours, such as early mornings or late evenings.

Over-sampling these groups will provide a more comprehensive picture of the ridership patterns and preferences of all passengers, rather than just those who use the railway line during peak hours. This approach will lead to a more accurate assessment of the passenger experience and needs and, therefore, allow for better decision-making when it comes to improving services and amenities.

Other groups that could be over-sampled include passengers with disabilities, seniors, and students who may have different transportation needs and experiences compared to the general ridership. By considering the unique experiences and needs of all passengers, railway companies can work towards creating a more inclusive and accessible transportation system.

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The 10th term of the geometric sequence with a first term of 12 and a fourth term of 24 is 6,144.

To find the 10th term of a geometric sequence, we need to know the common ratio (r) of the sequence. We can find this by dividing the fourth term by the first term:
r = 24/12 = 2
Now that we know the common ratio, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where a1 is the first term and n is the term we want to find. Plugging in the values we know:
a10 = 12 * 2^(10-1)
a10 = 12 * 2^9
a10 = 12 * 512
a10 = 6,144
Therefore, the 10th term of the geometric sequence with a first term of 12 and a fourth term of 24 is 6,144.
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the function f(x) = x^4 - 8x^2 has a relative minimum at x = 2 and x = -2.

To determine the values of x at which the function f(x) = x^4 - 8x^2 has a relative minimum, we need to find the critical points of the function and then analyze their nature using the second derivative test.

Step 1: Find the derivative of f(x):

f'(x) = 4x^3 - 16x

Step 2: Set the derivative equal to zero to find the critical points:

4x^3 - 16x = 0

Step 3: Factor out common terms and solve for x:

4x(x^2 - 4) = 0

Solving for x, we get:

x = 0 (critical point)

x^2 - 4 = 0

x^2 = 4

x = ±2 (critical points)

Step 4: Analyze the nature of the critical points using the second derivative test:

To apply the second derivative test, we need to find the second derivative of f(x):

f''(x) = 12x^2 - 16

Evaluate f''(x) at each critical point:

f''(0) = 12(0)^2 - 16 = -16

f''(2) = 12(2)^2 - 16 = 44

f''(-2) = 12(-2)^2 - 16 = 44

The second derivative test states that if f''(x) > 0, then the function has a relative minimum at that point. If f''(x) < 0, then the function has a relative maximum.

From the calculations above, we find that f''(2) = 44 > 0 and f''(-2) = 44 > 0. Thus, both x = 2 and x = -2 correspond to relative minimum points.

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Answer: ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle.

Step-by-step explanation:

ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle.

Step-by-step explanation:

I assume this is   5^(2n+3)   though it is not actually posted this way

5^(2n + 3 ) = 5^2n * 5^3

                   = (5^n)^2 * 5^3      we know 5^n = 8

                       (8)^2 + 5^3  = 64 + 125 = 189

The total number of subjects (n) in the study is 30. This is because the researcher gathered 15 men and 15 women, which gives a total of 30 participants in the study. Each participant was given a memorization task to perform in two different environments, one with music and one without music.

Therefore, each participant performed the task twice, resulting in a total of 60 data points (30 participants x 2 environments).

It is important to note that the researcher is interested in the effect of two independent variables, gender and environment, on the dependent variable of memorization. By including both men and women in the study, the researcher can examine if there are any gender differences in memorization abilities.

By having two different environments, the researcher can examine if there are any environmental factors that may affect memorization. Multiple independent variables and measures of the dependent variable can provide a more complete understanding of the phenomenon being studied.

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Answer:

See explanation below.

the numbers are 27 and 36

or

the numbers are 4 and 13

Step-by-step explanation:

Let the numbers be x and y.

"the difference between two positive numbers is 9"

y - x = 9

One of your statements is:

"one number is three times less than four times the other"

Are you sure the first word times belongs there?

If so, then the second equation below is correct.

y = 4x/3

y = x + 9

y = 4x/3

4x/3 = x + 9

4x = 3x + 27

x = 27

y = x + 9

y = 27 + 9

y = 36

Answer: the numbers are 27 and 36

If the second statement is really:

"one number is three less than four times the other number"

without the first word "times"

then the second equation is

y = 4x - 3

The equations are:

y - x = 9

y = 4x - 3

4x - 3 - x = 9

3x = 12

x = 4

y - 4 = 9

y = 13

Answer: the numbers are 4 and 13

Answer:

So if x = 5, then lines u and v are parallel.

Step-by-step explanation:

If the two angles are equal to each other, then lines u and v are parallel.

So set those 2 angles equal to each other, solve for x.

2 + 25x = 127

25x = 127-2

25x = 125

x = 5

So if x = 5, then lines u and v are parallel.

Answer:

x = 1 and x= 2

Step-by-step explanation:

First of all, divide all by 5.

x² - 3x + 2 =0

Using factorisation method, we need two numbers that add up to -3, but the same two numbers multiply with one another to produce answer of 2.

Format is (x    ) (x     ) = 0

-1 and -2, when added, produce result of -3. (-1 + -2 = -1 -2 = -3)

When multiplied, they give result of +2 (-1 X -2 = +2)

(x – 1) (x – 2) = 0.  We have x – 1 = 0, x = 1. We also have x – 2 = 0, x = 2.

These are the solutions of the equation.

Answer:

53

Step-by-step explanation:

Answer:

Step-by-step explanation:

he had 39 sweets

then he receive 39*2[twice as much as 39] + 39 [the sweet he had before he got more sweet]

39*2=78+39=117-25[the number of sweet he had taken out of the 117 sweets he had before]

117-25=92

Billy has 92 sweets left

To determine the sample size needed for a desired margin of error, we need additional information such as the population size and the desired level of confidence. Without this information, it is not possible to calculate the exact sample size.

The sample size calculation involves considering factors such as the variability of the population, the desired level of confidence, and the margin of error. These factors help in determining the appropriate sample size to achieve the desired precision in estimating population parameters.

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how many customers must be sampled if he wants the confidence interval to have a margin of error of 0.06  ----------- g

Based on the information provided, we cannot conclusively determine how drivers react to sudden large increases in the price of gasoline. However, we can use the recorded speeds of cars passing the service station before and after the price increase to determine if there is a statistically significant difference in speeds.

A hypothesis test can be conducted to determine if there is a significant difference in means between the two groups. If the p-value is less than the significance level, we can conclude that the speeds differ and suggest that the price increase had an impact on driver behavior. However, if the p-value is greater than the significance level, we cannot conclude that there is a significant difference in speeds and suggest that other factors may have influenced driver behavior.

To determine how drivers react to sudden large increases in the price of gasoline, we can follow these steps:

1. Collect data: The statistician recorded the speeds (mph) of cars passing a large service station before and after the price of gasoline increased by 15 cents.

2. Analyze the data: Compare the recorded speeds before and after the price increase to see if there's a noticeable difference.

3. Conduct a hypothesis test: Perform a statistical test to determine if the observed differences in speeds are significant or due to chance. For example, you can use a paired t-test or another appropriate test based on the data collected.

4. Draw conclusions: If the test shows a significant difference in speeds, we can conclude that drivers' behavior changed in response to the price increase. Otherwise, we cannot confidently say that the speeds differ due to the price increase.

By following these steps, you can determine if drivers' speeds differ as a result of sudden large increases in the price of gasoline.

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