On a coordinate plane, a curved line with minimum values of (negative 1.5, negative 2) and (1.5, 2), and a maximum value of (0, 4), crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 4).
Which is an x-intercept of the graphed function?

(0, 4)
(–1, 0)
(4, 0)
(0, –1)

The distance between the point (-6, -3) and the line defined by r = (2, 3) + s(7, -1), s ∈ ℝ, is equal to √18.(option a)

To find the distance, we can use the formula for the distance between a point and a line in two-dimensional space. The formula states that the distance (d) between a point (x₀, y₀) and a line Ax + By + C = 0 is given by the formula:

\(d = |Ax_0 + By_0 + C| / \sqrt{A^2 + B^2}\)

In this case, the line is defined parametrically as r = (2, 3) + s(7, -1), s ∈ ℝ. We can rewrite this as the Cartesian equation:

7s - x + 2 = 0

-s + y - 3 = 0

Comparing this to the general equation Ax + By + C = 0, we have A = -1, B = 1, and C = -2.

Substituting the values into the distance formula, we get:

d = |-1(-6) + 1(-3) - 2| / √((-1)² + 1²)

= |6 - 3 - 2| / √(1 + 1)

= |1| / √2

= √1/2

= √(2/2)

= √1

= 1

Therefore, the distance between the point (-6, -3) and the line is √18. Thus, the correct answer is option a) √18.

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The correct option is C,  We can use the formula for the nth term in a binomial expansion, which is (n-1)C(r-1) * a^n-r * b^.

Where  n is the total number of terms, r is the term we are looking for, a and b are the coefficients of the variables x and y respectively, and C is the combination function.

In this case, the expression is given as -39xy12, which means that a = -39, b = 1, and the total number of terms is 13 (since the exponent of y is 12). Therefore, we can plug in these values into the formula and solve for the 12th term by setting r = 12:

(12-1)C(12-1) * (-39)^(13-12) * (1)^12 = 12C11 * (-39) * 1 = -468 * 39 = -18252

Therefore, the 12th term in the expanded form of the expression is -18252.

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Answer:

15 minutes

Step-by-step explanation:

2 hours equals 120 minutes.

so if you divide 120 by 1/8 you get 15

which would be the amount of time she spent playing the trumpet.

Hope this helps!! :)

To determine the experimental probability of each outcome based on the table, we can calculate the ratio of the number of times each outcome occurred to the total number of trials (in this case, 50). The experimental probability represents the likelihood of an event based on actual observed data.

According to the table, the cup landed open side up 3 times, closed side up 7 times, and on its side 40 times out of 50 trials. To find the experimental probability for each outcome, we divide the number of occurrences by the total number of trials.

Experimental probability of landing open side up: 3/50 = 0.06 or 6%

Experimental probability of landing closed side up: 7/50 = 0.14 or 14%

Experimental probability of landing on its side: 40/50 = 0.8 or 80%

Therefore, based on the observed data, the experimental probability of the cup landing open side up is 6%, landing closed side up is 14%, and landing on its side is 80%.

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Answer:

It is 49

Step-by-step explanation:

Divide 98 by 2 to get semicircle radius.

Answer:

49 meters

Step-by-step explanation:

The radius is half of the diameter

98 divided by 2 is 49 which is the radius of the semicircle

The expressions for a_n, b_n, and c_n are:
a_n = 1 - F(12n; 2n, 0.2), b_n = 5/6, c_n = 25/(36n)
To derive the expression for a_n, b_n, and c_n, we consider the random variable S_n, which represents the aggregate amount of claims from n insurance policies. Each claim amount is represented by the non-negative random variable X_i, assumed to follow a gamma distribution with parameters (2, 0.2). The premium for each policy is denoted as G = 12, and the total premium for n policies is 12n. We aim to find the probability that the aggregate claim amount exceeds the total premium, P(S_n ≥ 12n).

Let's start by noting that the sum of independent gamma random variables follows a gamma distribution. Specifically, if X_i ~ Γ(2, 0.2), then the sum of n independent X_i's, S_n = ∑ i=1^n X_i, follows a gamma distribution with parameters (2n, 0.2). This is due to the property of the gamma distribution under summation.
Now, we want to calculate the probability P(S_n ≥ 12n), which represents the event that the aggregate claim amount exceeds the total premium. To derive this expression, we can utilize the cumulative distribution function (CDF) of the gamma distribution.
The CDF of a gamma distribution with parameters (k, λ) is given by F(x; k, λ) = Γ(k, λx) / Γ(k), where Γ(a, x) denotes the upper incomplete gamma function and Γ(a) is the gamma function.
Therefore, a_n can be expressed as a_n = 1 - F(12n; 2n, 0.2), where F(12n; 2n, 0.2) represents the CDF evaluated at 12n for the gamma distribution with parameters (2n, 0.2).
To find b_n and c_n, we need to utilize the expected value and variance of the gamma distribution. The mean and variance of a gamma distribution with parameters (k, λ) are E[X] = k / λ and Var[X] = k / \(λ^2\)\(λ^2\), respectively.
For our case, E[S_n] = E[∑ i=1^n X_i] = ∑ i=1^n E[X_i] = ∑ i=1^n 2 / 0.2 = 10n. Since G = 12, we have b_n = E[S_n] / (12n) = (10n) / (12n) = 5 / 6.
Similarly, Var[S_n] = Var[∑ i=1^n X_i] = ∑ i=1^n Var[X_i] = ∑ i=1^n 2 / (0.2)^2 = 50n. Therefore, c_n = Var[S_n] / (12n)^2 = (50n) / (12n)^2 = 25 / (36n).
In summary, the expressions for a_n, b_n, and c_n are given by:
a_n = 1 - F(12n; 2n, 0.2)
b_n = 5 / 6
c_n = 25 / (36n)

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810 minutes

13 hours 30 minutes

Step-by-step explanation:

Let the unknown value be x

\(5\:miles = 45 \: minutes\\90\:miles = x\:minutes\)

Sole the proportion for x ; Cross Multiply

\(5\times \:x =90 \times 45\\\\5x\: = 4050\)

Divide both sides of the equation by 5

\(\frac{5x}{5} = \frac{4050}{5} \\\\x = 810 \:minutes =\\13 \:hours \:30\:minutes\)

The  volume of the following rectangular prism in terms of x is 4x+ 0.5)(0.5x)(x - 2)

The formula for calculating the volume of a prism is expressed as

V = lwh

l is the length

w is the width

h is the height

Given the following

l =4x + 0.5

w = 1/2x

h = x - 2

Find the volume

V(x) = (4x+ 0.5)(0.5x)(x - 2)

Hence the  volume of the following rectangular prism in terms of x is 4x+ 0.5)(0.5x)(x - 2)

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Answer:

80 cm as a fraction of 4 m is \(\frac{1}{5}\)

Step-by-step explanation:

To write the fraction of two different quantities you must put them in the same units

Example: To write 5 grams as a fraction of 1 kilogram

Let us use the same way to solve the question

∵ 1 meter = 100 centimeters

∴ 4 meters = 4 × 100 = 400 centimeters

→ Now put 80 centimeters as a numerator and 400 centimeters as

  a denominator

∵ The fraction is \(\frac{80}{400}\)

→ Divide up and down by 80 to simplify it

∴ The fraction = \(\frac{\frac{80}{80}}{\frac{400}{80}}\)

∵ 80 ÷ 80 = 1

∵ 400 ÷ 80 = 5

∴ The fraction in its simplest form = \(\frac{1}{5}\)

∴ 80 cm as a fraction of 4 m is \(\frac{1}{5}\)

Answer:

52

Step-by-step explanation:

6+7=13

6:7=13

x:28

28/7=4

so you have to multiply by 4

4x6=24

24 boys and 28 girls

24+28=52

Answer:

52

Step-by-step explanation:

Lets put the ratio like this: 6x (boys) : 7x (girls)

because we know that the amount of girls is 28 we can set them equal as so:

7x = 28

÷ divide both sides by 7

x = 4

now add 6x + 7x to get the total people = 13x and because x equals 4, we can multiply 13 by 4. Which is 52

HOPE THIS HELPS :)

Answer:

no is the correct answer

Answer:

False

Step-by-step explanation:

The cube of 9 is 729 and 729 is smaller ( not greater ) than 1,000.

HOPE THIS HELPED

So i think its $4.35.

Step-by-step explanation:

I did addition to find out this answer my calculations seem to be correct.

$3.85 + 50 cents = 4 dollars and 35 cents

Answer:

$110.30 is the answer because you add $22.06 because that is 25% of 88.24

Step-by-step explanation:

Answer:

The answer is $110.3.

Step-by-step explanation:

To increase by 25%, you multiply by 1.25, which means it is 0.25 plus 1.

You then multiply this to 88.24.

#teamtrees #WAP (Water And Plant)

Answer:

i think A

Step-by-step explanation:

The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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Answer:

-0.86667

Step-by-step explanation:

m = -13 / 15 = -0.86667

Answer: 3.75

Step-by-step explanation: 15 divided by 4 equals 3.75

Explanation

The unit rate os obtained as shown as follows:

Answer is A. The unit rate is equal to $17.

Answer: 42

Step-by-step explanation:

Here given numbers : 28 and 63

so Mean = √x * y

let x = 28 and y = 63

So mean proportion between them is:

M = √63 * 28

M = √1764

M = 42

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Answer:

Simplifying

4x + 9 = 12x + -3

Reorder the terms:

9 + 4x = 12x + -3

Reorder the terms:

9 + 4x = -3 + 12x

Solving

9 + 4x = -3 + 12x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12x' to each side of the equation.

9 + 4x + -12x = -3 + 12x + -12x

Combine like terms: 4x + -12x = -8x

9 + -8x = -3 + 12x + -12x

Combine like terms: 12x + -12x = 0

9 + -8x = -3 + 0

9 + -8x = -3

Add '-9' to each side of the equation.

9 + -9 + -8x = -3 + -9

Combine like terms: 9 + -9 = 0

0 + -8x = -3 + -9

-8x = -3 + -9

Combine like terms: -3 + -9 = -12

-8x = -12

Divide each side by '-8'.

x = 1.5

Simplifying

x = 1.5

Step-by-step explanation:

Answer:

48x^2-120x+27

Step-by-step explanation:

P.S. - x^2 means x squared.

Answer:

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b, and geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.

Answer:

She lost $54

Step-by-step explanation: Just trust me

If it was right mark as Brainleist

Answer:

The answer is $54.00.

Step-by-step explanation:

To find the how much money, we just need to multiply 600 by 0.09.           600 x 0.09 = 54.

  600

x 0.09

------------

 5400      

Now you just move the decimal 2 places to the left, and you get 54.00! The answer is $54.00. Hope this helped! :]      

From the figure of the triangle, the length of LK is calculated to be 10

The knowledge used here is that of similar triangles.

In similar triangles the sizes of the triangles are not equal however the ratio of the sizes are equal

The formula for the similar triangle used here is:

JR / JL = SR / LK

from the given figure

JL = 2JR,  SR = 5

plugging the values into the equation gives

JR / 2JR = 5 / LK

1 / 2 = 5 / LK

LK = 10

The length of KL = 10 units

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Answer:

10 1/8

Step-by-step explanation:

-2 1/4 * -4 1/2

~Turn into improper fractions

-9/4 * -9/2

~Multiply both numerators and denominators

81/8

~Turn into a mixed number

10 1/8

Best of Luck!

Answer:

10 1/8

Step-by-step explanation:

0.625

Explanation:
We know that 0.125 is equal to 1/8, so you can then multiply 0.125 by 5.

Dividing 5/8, It's Equal To 0.625

Step-by-step explanation:

5/8 = O.625

Answer: 96 books.

Step-by-step explanation:

48x2