Here is a rule for making a list of numbers: Each number is 1 less than twice the previous number.
Pick a number to start with, then follow the rule to build a list of 5 numbers.

Answer:

86.6 feet (3 s.f.)

Step-by-step explanation:

Please see attached picture.

tan60°= height of tower/ 50

Height of tower

= 50tan60°

= 50√3

= 86.6 ft (3 s.f.)

tanѲ= opp/ adj

Answer:

C & D

Hope this helps and have a great day!

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Answer:

8.33

Step-by-step explanation:

1hr=60 minutes

?hr = 500 minutes

To find how many hours, divide 500 by 60

500/60 = 8.33

500 minutes = 8.33 hours

Answer:x= 2

Step-by-step explanation:

X+16/3= 3x

3(x+16/3)=3(3x) [in order to cancel out the divided by 3]

X+16=9x

16=8x

2=x

The equation that does NOT pass through quadrants III or IV is found to be y = -2x² + 3. So, option B is the correct answer choice.

The equations that pass through quadrants III or IV are those whose x and y values are negative or whose x value is negative and y value is positive.

A. y = x - 2 passes through quadrants III and IV because it can take on negative x and y values in those quadrants.

B. y = -2x² + 3 does not pass through quadrant III because all values of x in quadrant III are negative and when you square a negative number, the result is positive. Thus, the y-value would be positive, which is not possible for this equation.

C. y = x passes through all quadrants because it can take on positive and negative x and y values in all quadrants.

D. y = x² passes through quadrants I and II because it takes on positive x and y values in those quadrants. It does not pass through quadrants III or IV because all x values in those quadrants are negative and when you square a negative number, the result is positive, so the y-value would also be positive.

Therefore, the equation that does NOT pass through quadrants III or IV is B. y = -2x² + 3.

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The research hypothesis posits that the more caffeine consumed by a subject, the longer a subject will stay awake (H1: rxy > 0). In this case, we are given the correlation coefficient r(10) = 0.653 and p < 0.05.

To interpret these results, we need to understand the correlation coefficient (r) and the p-value. The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, it represents the relationship between caffeine consumption and staying awake.

The correlation coefficient ranges from -1 to 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable also tends to increase. A negative value indicates a negative relationship, where as one variable increases, the other tends to decrease. The closer the value is to 1 or -1, the stronger the relationship.

In this case, the correlation coefficient is 0.653, which is positive. This suggests a moderate positive relationship between caffeine consumption and staying awake.

The p-value, on the other hand, measures the probability of obtaining the observed correlation coefficient (or a more extreme one) if the null hypothesis were true. The null hypothesis (H0) states that there is no relationship between caffeine consumption and staying awake.

In this case, we are given that p < 0.05. This means that the probability of obtaining a correlation coefficient as extreme as 0.653, or more extreme, under the assumption that there is no relationship, is less than 0.05. This is considered statistically significant.

Based on these results, we can conclude that there is a statistically significant positive relationship between caffeine consumption and staying awake. However, it's important to note that correlation does not imply causation. Other factors could be influencing the relationship, and further research would be needed to establish a causal relationship.

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Answer:

I think there should be 950 at the first .. then the answer will be subtract 150

Answer:

Question 3 of 10 The answer should be 7

Step-by-step explanation:

The reason is  because if it is out of 100 7/100 is still 7%

Answer:

-The slopes of EF and GH are both.

-Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.

Step-by-step explanation:

I don't know the step by step process.

Answer:

Step-by-step explanation:

No sol because 37=-3 is false

Answer:

no answer

Step-by-step explanation:

in first equation x-y= 37 make y in the other side then it will be x=37+y

substitute x in the second equation which is x- y= -3

then it will be

37+y-y= -3

there will be no answer

x2−4x+3=0

For this equation: a=1, b=-4, c=3

1x2+−4x+3=0

Step 1: Use quadratic formula with a=1, b=-4, c=3.

x=

−b±√b2−4ac

2a

x=

−(−4)±√(−4)2−4(1)(3)

2(1)

x=

4±√4

2

x=3 or x=1

Answer:

x = 1, x = 3

Step-by-step explanation:

x² - 4x + 3 = 0

consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term (- 4)

the factors are - 1 and - 3 , since

- 1 × - 3 = + 3 and - 1 - 3 = - 4 , then

(x - 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 3 = 0 ⇒ x = 3

The values of x and y are 23.3 and 106 as per given diagram.

What is Alternate Interior Angles?

Hence, (3x + 4)° = 74°

3x = 74° - 4°°

x = 70° / 3

x = 23.3

What is Interior Angles on the Same Side of the Transversal?

Hence, (3x+4)° + y° = 180°

74° + y° = 180°

y = 106°

Hence, the values of x and y are 23.3 and 106 as per given diagram.

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Answer:

2*4*3

Step-by-step explanation:

The number of blocks is the same as the volume. So start with the formula for the volume of a rectangular prism, that being length*width*height. Then use the picture to count out that the length is 4 blocks, width is 2 blocks and height is 3 blocks. Then we can plug these values into our equation and get the answer: 2*4*3

Answer:

two

Step-by-step explanation:

Answer:

two lol

Step-by-step explanation:

The probability of a boy chosen at random being less than 62 inches tall is 0.9082. Hence, the solution is 0.9082.

The given data are: Mean = 58 inches Standard deviation = 3 inches

Let X be the height of a boy taken at random. Then, X ~ N(58, 3)

Thus, the z-score of 62 inches is calculated using the formula as follow s:z = (X - μ) / σ

Where X = 62 inchesμ = 58 inchesσ = 3 inches

Now, the z-score of X = 62 inches is calculated as follow

s:z = (62 - 58) / 3z = 1.3333 (rounded off to four decimal places)

The probability of a boy being less than 62 inches is the probability corresponding to the z-score of 1.3333.

The probability is calculated using the z-table. From the z-table, we find that P(Z < 1.3333) = 0.9082

Note: The normal distribution is a continuous probability distribution that describes the spread of a random variable in a symmetrical pattern. The normal distribution is also referred to as the Gaussian distribution or the bell curve.

In general, the normal distribution is characterized by two parameters, i.e., mean and standard deviation.

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The domain is 0 ≤ x ≤ 52. The maximum number of laws that she can mow with 13 gallons is of 52, and the minimum number is of 0.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at y = 13, hence the intercept b is given as follows:

b = 13.

When x increases by 20, y decays by 5, hence the slope m is given as follows:

m = -5/20

m = -0.25.

Hence the function is:

y = -0.25x + 13.

From the intercept, the minimum amount can be mowed is given as follows:

0.

The maximum amount is given as follows:

-0.25x + 13 = 0

0.25x = 13

x = 13/0.25

x = 52.

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Answer:

A:33

B:22

C:74

Step-by-step explanation:

A:

2x2x2=8

5x5=25

8+25=33

B:

7x7=49

3x3x3=27

49-27=22

C:

8x8=64

square root of 100 is 10

64+10=74

i hope this helps :)

(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x

The probability mass function p(x) can be derived from the cdf by taking differences:

p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06  x = 10.1  x = 20.17 x = 30.36  x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)

The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.

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Null Hypothesis, \(H_{0}\): The heart transplant operation had no impact on the patient's survival rates. Alternative Hypothesis, \(H_{A}\): It was asserted that recipients of heart transplants had a higher chance of surviving than recipients of organs from other donors.

The large distribution from binomial, Poisson, etc. is approximated by the normal distribution. Furthermore, the variables are discrete and few, and we are working with counted data rather than real observations. Chi-square distribution should be used in the current scenario. We can determine if the two groups are the same or different by using the chi-square test. As a result, a confidence interval cannot be created.

In other words, the Null Hypothesis is true if the average for the two groups (control and treatment) is equal. In the alternative theory, The averages for the two groups (control and treatment) are different.

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Answer:

1/24 (fraction form)

hope this helps

The solution to the quadratic equation x^2 = -6x - 17, expressed in exact simplest form, is x = 3 - √26.

To solve the quadratic equation x^2 = -6x - 17 using the quadratic formula, we can follow these steps:

1. Identify the coefficients:

  The given quadratic equation is in the form ax^2 + bx + c = 0.

  In this case, a = 1, b = -6, and c = -17.

2. Apply the quadratic formula:

  The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

  x = (-b ± √(b^2 - 4ac)) / (2a)

  Plugging in the values from our equation:

  x = (-(-6) ± √((-6)^2 - 4(1)(-17))) / (2(1))

  x = (6 ± √(36 + 68)) / 2

  x = (6 ± √104) / 2

  x = (6 ± 2√26) / 2

3. Simplify the solutions:

  We can simplify the solutions by canceling out the common factor of 2:

  x = (3 ± √26)

Therefore, the solutions to the quadratic equation x^2 = -6x - 17, expressed in exact simplest form, are x = 3 + √26 and x = 3 - √26.

The two solutions indicate that the quadratic equation has two distinct real roots.

To verify these solutions, we can substitute them back into the original equation x^2 = -6x - 17:

For x = 3 + √26:

(3 + √26)^2 = -6(3 + √26) - 17

9 + 6√26 + 26 = -18 - 6√26 - 17

35 + 6√26 = -35 - 6√26

35 = -70 (Not true)

For x = 3 - √26:

(3 - √26)^2 = -6(3 - √26) - 17

9 - 6√26 + 26 = -18 + 6√26 - 17

35 - 6√26 = -35 + 6√26

35 = 35 (True)

The equation is satisfied only when x = 3 - √26. Therefore, the solution x = 3 + √26 is extraneous and can be disregarded.

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Answer:

1. x = 8

2. x = 12

3. x = 11

4. x = 6

Step-by-step explanation:

1.

102 + 102 = 204

360 - 204 = 156

156 / 2 = 78

78 = 10x - 2

78 + 2 = 10x

80 = 10x

80 / 10 = x

x = 8

2.

81 = 7x - 3

81 + 3 = 7x

84 = 7x

84 / 7 = x

x = 12

3.

77 = 6x + 11

77 - 11 = 6x

66 = 6x

66 / 6 = x

x = 11

4.

115 + 115 = 230

360 - 230 = 130

130 / 2 = 65

65 = 8x + 17

65 - 17 = 8x

48 = 8x

48 / 8 = x

x = 6

Answer:

0.43 cubic yards

Explanation:

We know that 1 cubic yard is equivalent to 46656 cubic inches. So, we can convert 19845 cubic inches into cubic yards as:

Therefore, the answer is 0.43 cubic yards

Answer:

63.75

Step-by-step explanation:

The equation for finding the area of a triangle is 1/2b x h

b = base

h = height

b = 15

h = 8.5

15(1/2) x 8.5

7.5 x 8.5 = 63.75

Answer:

A = 63.75 ft^2, or 63 3/4 ft^2

Step-by-step explanation:

The formula for the area of a triangle of base b and height h is

A = (1/2)(b)(h).

With h = 8.5 ft and b = 15 ft, the area of the triangle in question is

A = (1/2)(8.5)(15)ft^2, or

A = 63.75 ft^2, or 63 3/4 ft^2

"a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years.

The 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].According to the central limit theorem , a sampling distribution of the means is usually distributed in a normal distribution, given a big enough sample size, which means that it has a bell-shaped curve. It has a standard deviation that can be estimated by dividing the population standard deviation by the square root of the sample size. Using the formula below,

we can calculate the 95% confidence interval for the population average.= 13.8 ± (1.96 × 7.3 / √45)

= 13.8 ± (1.96 × 1.088)

= 13.8 ± 2.13The limits are calculated by adding and subtracting the calculated value from the sample mean.13.8 + 2.13

= 15.9313.8 - 2.13

= 11.67Therefore, the 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].

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A given shape that is bounded by three sides and has got three internal angles is referred to as a triangle. Thus the value of PB is 8.0 units.

A given shape that is bounded by three sides and has got three internal angles is referred to as a triangle. Types of triangles include right angle triangle, isosceles triangle, equilateral triangle, acute angle triangle, etc. The sum of the internal angles of any triangle is \(180^{o}\).

In the given question, point P is such that <APB = <APC = <BPC = \(120^{o}\). Also, line PB bisects <ABC into two equal measures. Thus;

<ABP = \(30^{o}\)

Thus,

<ABP + <APB + <BAP = \(180^{o}\)

30 + 120 + <BAP = \(180^{o}\)

<BAP = \(180^{o}\) - 150

<BAP = \(30^{o}\)

Apply the Sine rule to determine the value of PB, such that;

\(\frac{AP}{Sin B}\) = \(\frac{BP}{Sin30}\)

\(\frac{8}{Sin30}\) = \(\frac{BP}{Sin 30}\)

BP = \(\frac{8*Sin30}{Sin 30}\)

     = \(\frac{4}{0.5}\)

BP = 8.0

Therefore, the value of BP = 8 units.

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A parabola is the set of all points in a plane that are equidistant from both a point called the focus and a line called the: directrix

A parabola is a plane curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

A parabola is approximately U-shaped.

It is the graph of a quadratic function.

A fix point is called as the focus and a fixed straight line is the directrix of the parabola.

The fixed point does not lie on the fixed line. (i.e., the focus does not lie on the directrix of the parabola).

Therefore, A parabola is the set of all points in a plane that are equidistant from both a point called the focus and a line called the: directrix

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Therefore, the pH of the resulting solution is approximately 3.04.

To determine the pH of the resulting solution, we need to consider the dissociation of HCl in water. HCl is a strong acid and completely dissociates into H+ ions and Cl- ions in water.

First, let's calculate the amount of H+ ions added to the solution. Since the initial concentration of HCl is 0.010 M and 10 mL of it is added, the amount of HCl added is:

(0.010 M) * (0.010 L) = 0.0001 moles

Since HCl dissociates completely, this means we have also added 0.0001 moles of H+ ions to the solution.

Next, let's calculate the total volume of the resulting solution. Since 10 mL of HCl is added to 100 mL of water, the total volume is:

10 mL + 100 mL = 110 mL = 0.110 L

Now, we can calculate the concentration of H+ ions in the resulting solution:

[H+] = (moles of H+) / (total volume)

= 0.0001 moles / 0.110 L

= 0.000909 M

Finally, we can calculate the pH of the solution using the equation:

pH = -log[H+]

pH = -log(0.000909)

= 3.04

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