Given that a quadratic function has a vertex at (-3,-9) and goes through the point (0,9)

Answer:Without additional information about the circle C or the position of point C, it is not possible to determine the radius of the circle.

Step-by-step explanation:

Part(1)

The measure of the angle will be 45°.

Part(2),

The formula for the shadow is,

6² + x² = 16²

A basic mathematical theorem relating to the lengths of a right-angled triangle's sides is known as the Pythagorean theorem. According to this rule, the square of the length of the hypotenuse (the side that faces the right angle) in any right-angled triangle equals the sum of the squares of the lengths of the other two sides.

Part(1),

To find the angle x, we can use the inverse tangent function. Let's call the length of Joel's shadow "s". Then we have:

tan(x) = opposite/adjacent = 16/s

Taking the inverse tangent of both sides, we get:

x = tan⁻¹(16/s)

We know that Joel's height is 6 ft, so the hypotenuse of the right triangle formed by Joel and his shadow is:

= √(6² + s²)

Now we can use the Pythagorean Theorem to solve for s. Rearranging the formula for h, we have:

s = √(h² - 6²)

Substituting the value of h with the expression above, we get:

s = √((√(6² + s²))² - 6²)

Simplifying this expression, we get a quadratic equation in terms of s:

s² - 256 = 0

Solving for s, we get:

s = ±16

Since s represents the length of the shadow, it must be positive. Therefore, s = 16 ft.

Substituting s into the equation for x, we get:

x = tan⁻¹(16/16) = tan⁻¹(1) = 45°

So the measure of the angle x is 45 degrees.

Part(2),

The formula for a shadow can be written as,

6² + x² = 16²

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$259,587 of Cheyenne's household belongings would be covered.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The amount of personal property coverage provided by the insurance is 80% of the insured value of the home:

Personal property coverage = 0.8 x insured value of home

Personal property coverage = 0.8 x $324,484

Personal property coverage = $259,587.20

Therefore, $259,587 of Cheyenne's household belongings would be covered.

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The requried given sum 100 + 100 = 200 is true.

When we add two numbers, we unite them to get a new total value. In this case, we are adding 100 and 100, which gives us a total of 200. Therefore, the statement "100 + 100 = 200" is true based on the rules of addition in mathematics.

If the context of the question is different, for instance, if the "+" symbol represents concatenation (joining of two strings), then the answer might be different. But based on the premise that the "+" symbol represents an addition, the statement "100 + 100 = 200" is true.

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If a hypothesis test is conducted to see if there is evidence that the average wait time is 5 minutes, the p-value is 0.040.

To calculate the p-value for the hypothesis test, we need to perform the following steps:

Step 1: State the null and alternative hypotheses.

In this case, the null hypothesis (H0) is that the average wait time for customers during the lunch hour is 5 minutes. The alternative hypothesis (Ha) is that the average wait time is not 5 minutes.

Step 2: Determine the test statistic.

We can use a t-test since we do not know the population standard deviation. We calculate the t-value using the formula:

t = (x' - μ) / (s / √n)

where x' is the sample mean, μ is the population mean (5 minutes), s is the sample standard deviation, and n is the sample size (15).

Step 3: Calculate the p-value.

We can use a t-distribution table or software to find the p-value associated with our calculated t-value. Alternatively, we can use the t-test function in Excel or other statistical software to calculate the p-value directly.

Assuming a two-tailed test and a significance level of 0.05, if the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than 0.05, we fail to reject the null hypothesis.

Suppose the sample mean is 6.2 minutes, the sample standard deviation is 1.3 minutes, and the sample size is 15. Then the t-value is:

t = (6.2 - 5) / (1.3 / √15) = 2.22

Using a t-distribution table or software with 14 degrees of freedom (15 - 1), we find the p-value to be approximately 0.040, which is less than 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that the average wait time for customers during the lunch hour is not 5 minutes.

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The solution set for the given inequality is:

8/3 > x > 14/9  or in interval form, (14/9, 8/3)

Here we have the compound inequality:

1/3> (x - 1)/5 >1/9

To solve it, we need to isolate the variable x, so let's do that:

First we can multiply all the inequality by 5, then we will get:

1/3> (x - 1)/5 >1/9

5/3 > x - 1 > 5/9

Now add 1.

5/3 + 1 > x > 5/9 + 1

Now simplify it to get:

8/3 > x > 14/9

Thus, the solution set is (14/9, 8/3)

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The appropriate test to use for examining the correlation between age in years and score on a driving test (0-100) is the Pearson correlation coefficient test, assuming the data meets the assumptions of normality and linearity.

Based on the information provided, the appropriate test to use would be the Pearson correlation coefficient test, which is used to measure the strength and direction of the linear relationship between two continuous variables.

However, before conducting the Pearson correlation test, it is important to ensure that the data meets the assumptions of normality and linearity. The Shapiro-Wilk test you ran assesses normality, but you need to also check for linearity.

If the data meets the assumptions of normality and linearity, you can then use the Pearson correlation test to determine the strength and direction of the relationship between age and driving test score.

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The figure have area of the hexagon equal to 432 cm², area of the circle equal to 254.6 cm², and the area of the shaded region equal to 177.4 cm² to the nearest tenth.

Area of the hexagon = 1/2 × 6 × 16cm × 9cm

Area of the hexagon = 432 cm²

Area of the circle = 22/7 × 9cm × 9cm

Area of the circle = 254.6 cm²

Area of the shaded region = 432 cm² - 254.6 cm²

Area of the shaded region = 177.4 cm²

Therefore, the figure have area of the hexagon equal to 432 cm², area of the circle equal to 254.6 cm², and the area of the shaded region equal to 177.4 cm² to the nearest tenth.

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Answer:

[tex]|x-8|=6[/tex]

Step-by-step explanation:

Let's begin by finding the midpoint of 2 and 14. To do this, we'll add the numbers and then divide by 2.

2+14=16

16/2=8

The number that is the same distance between 2 and 14 is 8.

Now, let's find how far away each number is from 8.

8-2=6

14-8=6

2 and 14 are 6 away from 8.

Let's set up the absolute value equation using these two values.

Since 8 is the midpoint, this will be what the absolute value expression is equal to.

Since each number is 6 away from 8, this is the number (6) we will be taking away from 2 and 14.

Remember that absolute value is just distance.

In other words, 2 is 6 away from 8, and 14 is also 6 away from 8.

Or, the distance between a number x and 8 is 6.

Using this knowledge, we have:

[tex]|x-8|=6[/tex]

Answer:

|x-8|=6

Step-by-step explanation:

i checked rsm its correct :3

The x-coordinate of the point of intersection of the two lines is 2.

To get the x-coordinate of the spot where the two lines intersect:

1. We can solve the system of equations given by the two lines simultaneously, which means we need to eliminate one of the variables (x or y) to obtain an equation in one variable that we can solve.

2. One way to eliminate a variable is to add or subtract the two equations in a way that cancels out one of the variables. In this scenario, we can combine the two equations:

(7x + 4y) + (9x - 4y) = 18 + 14

16x = 32

Dividing both sides by 16, we get:

x = 2

So the x-coordinate of the point of intersection of the two lines is 2.

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Answer: 10    C

Step-by-step explanation:

Variability is the range of numbers.

here it goes from 2-12

so

12-2=10

Answer: 3, 12

Step-by-step explanation:

you divided by 2 to get top row so divide 6 by 2.  3 is in the first box

for bottom row you multiplied middle row by 3 so 12 is in the bottom row

The number of elements in power set A where A = { x: x² + 3 < 2, x ∈R }  is equal to  n[P(A)] = 1.

The set A represented as ,

A = { x: x² + 3 < 2, x ∈R }

First, we need to determine the set of values that satisfy the inequality

x² + 3 < 2.

Subtracting 3 from both sides of the inequality gives us,

⇒ x² < -1

However, this inequality has no real solutions, since the square of any real number is always non-negative.

This implies,

The set A is empty,  A = {}.

The power set of the empty set contains only the empty set itself,

so P(A) = {{}}.

This implies, the number of elements in P(A) denoted as n[P(A)] is 1.

Therefore, the number of elements in power set A is equal to  n[P(A)] = 1.

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Answer:

Step-by-step explanation:

graph 1 :   y = - |x +1| +1

graph 2:  y = |x+1|

Answer:

I believe it is D. A line passes through the point (0, 0) and continues through the point (12, 3).

Step-by-step explanation:

Please give brainliest thx

The area of triangle CDE is 17.5 square units.

To find the area of triangle CDE, we can use the general formula:

Area = 1/2 * base * height where the base and height are two sides of the triangle. We can also use the distance formula to find the lengths of these sides.

First, let's find the length of side CD: CD = sqrt[(7-4)² + (8-4)²] = sqrt[3² + 4²] CD = √25 = 5

Next, let's find the length of side DE: DE = sqrt[(2-7)² + (9-8)²] = sqrt[5² + 1²] = DE = √26

Now, we need to find the height of the triangle. One way to do this is to use the formula for the area of a triangle:

Area = 1/2 * base * height

Rearranging this formula, we get: height = 2 * Area / base

We know the base is CD, which we found to be 5. We can find the area of triangle CDE using the shoelace formula, which gives:

Area = 1/2 * |(48 + 79 + 24) - (47 + 82 + 94)| = 17.5

Therefore, the height of triangle CDE is: height = 2 * Area / base = 2 * 17.5 / 5 = 7

Now we can use the formula for the area of a triangle to find the area of triangle CDE: Area = 1/2 * base * height = 1/2 * 5 * 7 = 17.5

Therefore, the area of triangle CDE is 17.5 square units.

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All the work is correct since the volume of the cube is 132.651 cubic inches as it is given.

From the given figure we can see that,

Length of the base (L) = 5.1 inches.

Width of the base (W) = 5.1 inches.

The Area of the Base of the Cube = (B) = L*W = 5.1*5.1 = 26.01 square inches.

The height of the cube (h) = 5.1 inches.

The Volume of the Cube is given by,

V = B*h

V = 26.01(5.1)

V = 132.651 cubic inches.

Hence the work is correct, the volume of the cube is 132.651 cubic inches.

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The question is incomplete. The complete question will be -

"determine if the work is correct or incorrect:

"

log 72 to the base 2n is equal to log 18 to the base n if n is equal to [tex]2^{1/10}[/tex].

We can use the change-of-base formula to convert both logarithms to a common base, such as base 10:

log 72 / log 2n = log 18 / log n

We can simplify log 72 as follows:

[tex]log 72 = log (2^3 * 3^2) = 3 log 2 + 2 log 3[/tex]

Similarly, we can simplify log 18 as:

[tex]log 18 = log (2 * 3^2) = log 2 + 2 log 3[/tex]

Substituting these expressions into the original equation, we get:

(3 log 2 + 2 log 3) / log 2n = (log 2 + 2 log 3) / log n

Multiplying both sides by log n * log 2n, we get:

(3 log 2 + 2 log 3) log n = (log 2 + 2 log 3) log 2n

Expanding the logarithms using the power rule, we get:

[tex]3 log (n^3) + 2 log (n^2) = log (2n) + 2 log (n^3)[/tex]

Simplifying and rearranging terms, we get:

[tex]3 log (n^3) - 2 log (n^3) = log (2n) - 2 log (n^2)[/tex]

[tex]log (n^9) = log (2n / n^2)[/tex]

[tex]log (n^9) = log (2/n)[/tex]

Taking the exponential of both sides, we get:

[tex]n^9 = 2/n[/tex]

Multiplying both sides by n, we get:

n^10 = 2

Taking the 10th root of both sides, we get:

[tex]n = 2^{1/10}[/tex]

Therefore, log 72 to the base 2n is equal to log 18 to the base n if n is equal to [tex]2^{1/10}[/tex]

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The volume of the cone is  37. 68 cubic units

The surface area is  75. 36 square units.

The formula for calculating the volume of a cone is expressed as;

Volume = πr²h/3

From the information given, we have that;

radius = 3 units

h = 4 units

Substitute the values, we get;

Volume = 3.14 × 3² × 4/3

Divide the values

Volume = 37. 68 cubic units

The formula for surface area is expressed as;

Surface area = πrl + πr²

Substitute the values

Surface area = 3.14 × 3 × 5 + 3.14 × 3²

Surface area = 47. 1 + 28. 26 = 75. 36 square units.

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Answer:

75°/360° = 5/24

Area of sector = (5/24)(π)(10^2)

= 125π/6 square inches

= 65.4 square inches

Length of arc = (5/24)(2π)(10)

= 25π/6 inches

= 13.1 inches

Answer:

it is 5.4 kilometers from White Beach across the lake to the Lodge.

Step-by-step explanation:

Based on the information provided, we can calculate the distance from White Beach across the lake to the lodge by adding the distances from Canoeville to White Beach and from Canoeville to the lodge.

Distance from Canoeville to White Beach: 2.4 km

Distance from Canoeville to the Lodge: 3.0 km

Total distance from White Beach across the lake to the Lodge:

2.4 km + 3.0 km = 5.4 km

So, it is 5.4 kilometers from White Beach across the lake to the Lodge.

The probability that each player will have $1 after 2019 rings of the bell is: (c) 1/3.

To solve this problem, we need to think about the possible outcomes of the game. Each time the bell rings, each player has a 1/2 probability of giving $1 to one of the other two players. This means that after one ring of the bell, there are 2^3 = 8 possible outcomes, as each player can either give or not give money to each of the other players.

After two rings of the bell, there are 2^8 = 256 possible outcomes. After three rings, there are 2^12 = 4,096 possible outcomes. And so on.

To find the probability that after 2019 rings of the bell, each player will have $1, we need to find the total number of possible outcomes and the number of outcomes in which each player has $1.

The total number of possible outcomes after 2019 rings of the bell is 2^(3*2019) = 2^6057.

To count the number of outcomes in which each player has $1, we can use a combinatorial argument. We need to distribute 2019 dollars among the three players in such a way that each player ends up with exactly $1. This is equivalent to choosing two numbers between 0 and 2019, inclusive, and giving the first player the smaller amount, the second player the difference between the larger and smaller amounts, and the third player the remaining amount.

The number of ways to choose two numbers between 0 and 2019 is (2019+2) choose 2 = 2036 choose 2 = 2,066,530.

Therefore, the probability that each player will have $1 after 2019 rings of the bell is:

2,066,530 / 2^6057 = 1/3

So the answer is (c) 1/3.

In the game where Raashan, Sylvia, and Ted each start with $1 and a bell rings every 15 seconds, the probability that after the bell has rung 2019 times, each player will have $1 is (a) 1/7.

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From Bayes' Theorem, an event, the probability that the blue cab involved in accident as well as witness also identified it as blue cab is equals to the 0.41 or 41%.

Bayes' Theorem states that the conditional probability of an event, is based on the occurrence of another event, is equal to the like of the second event the first event multiplied by the probability of the first event. According to scenario, it is found that a cab was involved in a hit and run accident at night. Number of cab companies operates in city = 2 (blue and green)

Probability that green cab involved in accident, P(G) = 85% = 0.85

Probability that blue cab involved in accident, P(B) = 15% = 0.15

Now, the cab which is identified by witness was a blue cab. Here, probability that witness is correct to identification a blue cab = P(W/B) = 0.80

Probability that witness is wrong to identify the blue cab = P(W/G) = 0.20

Using the Baye's theorem, Probability that accident was caused by blue cab provided witness identifies is written as [tex]P(B/W) = \frac{ P(B ∩W) }{P(W)} = \frac{ P(B) P( W/B)}{W}[/tex]

Total Probability, [tex]P(W) = \frac{P(B)}{P(W/B)}+ \frac{P(G)}{P(W/G)}[/tex]

= 0.15 x 0.8 + 0.85 x 0.2 = 1.2 + 1.7 =0.29

[tex]P(B/W) = \frac{ P(0.15×0.8}{0.29}[/tex]

= 0.12/0.29 = 0.413 = 41%

Hence, required probability value is 41%.

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Answer:

Step-by-step explanation:

To find the solution for p(x) = m(x), we need to set the two expressions equal to each other and solve for x:

2ln(x) - 1 = ln(x+6)

First, we can simplify the left side by using the logarithmic identity that states ln(a^b) = b ln(a):

ln(x^2) - 1 = ln(x+6)

Next, we can eliminate the natural logarithm by exponentiating both sides with the base e:

e^[ln(x^2) - 1] = e^[ln(x+6)]

e^[ln(x^2)] * e^[-1] = x + 6

x^2 * 1/e = x + 6

Multiplying both sides by e gives:

x^2 = e(x + 6)

Expanding the right side gives:

x^2 = ex + 6e

Rearranging gives:

x^2 - ex - 6e = 0

This is a quadratic equation in x. We can solve for x using the quadratic formula:

x = [e ± sqrt(e^2 + 4*6e)]/2

Simplifying gives:

x = [e ± sqrt(e^2 + 24e)]/2

Therefore, the solution for p(x) = m(x) is x = [e ± sqrt(e^2 + 24e)]/2.

Answer:

x ≈ 3.40295

Step-by-step explanation:

We want to find the value(s) of x that satisfy the equation p(x) = m(x), where p(x) = 2ln(x) - 1 and m(x) = ln(x + 6).

So, we have:

2ln(x) - 1 = ln(x + 6)

First, let's simplify the equation by using the properties of logarithms:

ln(x^2) - ln(e) = ln(x + 6)

ln(x^2/e) = ln(x + 6)

Now we can eliminate the natural logarithm by taking the exponential of both sides:

x^2/e = x + 6

x^2 - ex - 6e = 0

We can solve this quadratic equation using the quadratic formula:

x = [-(-e) ± sqrt((-e)^2 - 4(1)(-6e))] / (2(1))

Simplifying:

x = [e ± sqrt(e^2 + 24e)] / 2

Therefore, the solutions for p(x) = m(x) are:

x = [e + sqrt(e^2 + 24e)] / 2  or  x = [e - sqrt(e^2 + 24e)] / 2

Note that since the argument of the natural logarithm must be positive, we must discard the negative solution, which is not valid. So the only solution is:

x = [e + sqrt(e^2 + 24e)] / 2

We can approximate this value using a calculator or computer software. For example, if we use e = 2.71828, we get:

x ≈ 3.40295

Therefore, the solution for p(x) = m(x) is x ≈ 3.40295.

The correct answer is b. On average, LinkedIn users would send between 5.48 and 8.72 total messages per year with the new algorithm.

The 95% confidence interval provided by Yue Bing suggests that the true difference in the average number of messages sent per year between the two groups of users (those using the new algorithm and those using the old algorithm) is likely to be between 5.48 and 8.72. This means that we can be 95% confident that the true difference in the average number of messages sent per year falls within this range. It does not necessarily mean that all LinkedIn users will send more or fewer messages with the new algorithm, but rather that the average number of messages sent by users using the new algorithm is likely to be within this range.
Your answer: d. On average, all LinkedIn users would send more messages with the new algorithm than with the old algorithm.

Explanation: Yue Bing computed a 95% confidence interval for the difference between the two parameters, which is (5.48, 8.72) messages per year. Since the entire interval is positive, this indicates that the new recommendation algorithm likely leads to an increase in the average number of messages sent by LinkedIn users compared to the old algorithm.

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(50/100)×60= 30

(5/100)× 60= 3

(1/100)×60= 0.6

55% percentage of matches has sparx FC won.

We have,

Number of games won = 11

Drawed games= 3

Lost games= 6

So, the percentage of won

= 11 / 20 x 100

= 11 x 5

= 55%

Thus, 55% of games won.

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Two gallons, or eight quarts, of green paint were purchased by Blanca. She still has 2 and 1/2 quarts of paint after using 5 and a half quarts.

The 2 gallons of green paint that Blanca bought can be divided into 8 quarts.

She applied 5 and 1/2 liters of paint to her front patch and swing.

We can deduct the amount utilized from the initial amount to get the amount of paint she still has.

8 quarts minus 5 and a half quarts equals 2 and a half quarts.

It's crucial to remember that having extra paint on hand for touch-ups or unforeseen scenarios is always a smart idea when working with paint.

Blanca may want to consider purchasing an additional quart of paint to ensure she has enough for her project.

Hence,  Blanca still has 2 and 1/2 quarts of paint after using 5 and a half quarts.

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Answer: 40% drive and 60% take the bus.

Step-by-step explanation:

    We will divide the number of students who drive to school by the total number of students, and then multiply by 100 to turn it into a percentage.

         [tex]\displaystyle \frac{250}{250+375} *100= 40\%[/tex]

    Next, we will divide the number of students who ride the bus to school by the number of students who ride the bus, and then multiply by 100 to turn it into a percentage.

         [tex]\displaystyle \frac{375}{250+375} *100= 60\%[/tex]

The minimum amount that the person should be ready to accept today is Rs. 28258.86, as this is the present value of the future cash flows discounted at a rate of 14%.

To determine the minimum amount that a person should be ready to accept today from a debtor who has to pay Rs. 5000 today and a series of future payments, we need to calculate the present value of these future cash flows. The present value of a future cash flow is the value of that cash flow in today's terms, given a certain interest rate.

Using the formula for present value, we can calculate the present value of the future cash flows as follows:

PV = (5000/(1+0.14)⁰) + (6000/(1+0.14)) + (8000/(1+0.14)²) + (9000/(1+0.14)³) + (10000/(1+0.14)⁴)

Simplifying this equation, we get:

PV = 5000 + 5263.16 + 5805.37 + 6049.53 + 6139.80

Therefore, the present value of the future cash flows is Rs. 28258.86.

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