what are the coordinates of the point on the directed line segment from (-4,7) to (7,-4) that partitons the segment into a ration of 6 to 5?

Option D is incorrect because it gives a value that is not consistent with the scatter plot and the line of fit. The correct answer is: The y-intercept is 40.98. The machine starts with 40.98 ounces of diet soda.

In the context of a graph, the y-intercept is the point where a straight line or curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero. Mathematically, it is the value of y when x = 0 in the equation of the line or curve. The y-intercept is also known as the initial value or starting point of the graph. It is often denoted as (0, b), where b is the y-coordinate of the intercept point.

The y-intercept of the line of fit represents the starting point of the relationship between the two variables, in this case, the amount of diet soda in the machine and the time after the machine is filled. Therefore, the y-intercept value of 40.98 means that the machine starts with 40.98 ounces of diet soda when it is filled.

Option A is incorrect because the y-intercept is a starting value, and it does not represent a rate of change.

Option B is also incorrect because it suggests that the machine loses 4.8 fluid ounces of diet soda every hour, which is not what the y-intercept represents.

Option D is incorrect because it gives a value that is not consistent with the scatter plot and the line of fit.

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Answer:

12 lunches.

Step-by-step explanation:

Theresa:

$8.50 * 11 = $93.50 so she can buy 11 lunches with her gift card.

Colin:

$6 * 12 = $72 so he can buy 12 lunches with his gift card.

So Colin can buy one more lunch than Theresa. Therefore, if Theresa buys 12 lunches, she will go over her gift card.

Answer:

56

Step-by-step explanation:

56 would be the arc. reasoning is because line CG form an arch of 56 and Angle A and C also form a angle of 34

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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The opposite side of the right triangle (x) is approximately 6.888 inches long.

To solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:

sin(35) = opposite/12

To solve for the opposite, we can multiply both sides by 12:

opposite = 12 * sin(35)

sin(35) as approximately 0.574:

opposite = 12 * 0.574

opposite ≈ 6.888

Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.

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The missing lengths of the geometric systems are listed below:

Case A: x = √5, y = √6

Case B: x = 3, y = √34

Case C: x = 10, y = √104

Case D: x = 6, y = √13

Case E: x = √2, y = 2, z = √8

Case F: x = 2√51

In this problem we find six geometric systems formed by addition of triangles, whose missing lengths are determined by means of Pythagorean theorem:

r = √(x² + y²)

Where:

Now we proceed to determine the missing lengths for each case:

Case A

x =√(2² + 1²)

x = √5

y = √(x² + 1²)

y = √6

Case B

x = 8 - 5

x = 3

y = √(3² + 5²)

y = √34

Case C

x = √(6² + 8²)

x = 10

y = √(10² + 2²)

y = √104

Case D

x = 15 - 9

x = 6

y = √(7² - 6²)

y = √13

Case E

x = √(1² + 1²)

x = √2

y = √(2 + 2)

y = 2

z = √(2² + 2²)

z = √8

Case F

x = 2 · √(10² - 7²)

x = 2√51

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Weighing the available information and assigning a probability.

A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It solely represents the subject's thoughts and prior experience and does not include any formal computations. A "gut instinct" used when making a deal is an illustration of subjective probability.

So, as per the definition of subjective probability

Dividing the number of favourable events by the number of possible events and Studying the fraction of times in the past a particular event has happened, both can be determined through calculations mathematically accurate but for Weighing the available information and assigning a probability we might use a "gut instinct". Thus

Weighing the available information and assigning a probability.

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Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

Answer:

I and II only

Step-by-step explanation:

plug in the x and y

Answer:

40 feet (after 1.5 seconds).

Step-by-step explanation:

The height h of the ball after t seconds is modeled by the function:

\(h(t)=-16t^2+48t+4\)

And we want to determine the ball's maximum height.

Since the given function is a quadratic, the maximum height occurs at the vertex point.

For quadratics, the vertex point is given by the formulas:

\(\displaystyle \Big(-\frac{b}{2a},f\Big(-\frac{b}{2a}\Big)\Big)\)

In this case, a = -16, b = 48, and c = 4.

Therefore, the t-coordinate at which the vertex occurs is:

\(\displaystyle t=-\frac{48}{2(-16)}=\frac{48}{32}=\frac{3}{2}\)

So, the maximum height occurs after 1.5 seconds.

Then the maximum height will be:

\(\begin{aligned}\displaystyle h\Big(\frac{3}{2}\Big)&=-16\Big(\frac{3}{2}\Big)^2+48\Big(\frac{3}{2}\Big)+4\\\\ &=-16\Big(\frac{9}{4}\Big)+24(3)+4\\\\&=-4(9)+72+4\\\\&=40\text{ feet}\end{aligned}\)

So, the maximum of the ball is 40 feet (after 1.5 seconds).

Answer:

The answer is 118.

Step-by-step explanation:

You would plug in 6 for x. You would then do 18 times 6 to get 108. Then you would add 10 to 108 to get 118.

Answer:

Given

f(x)= 18x+10

f(6)=18(6)+10

f(6)=108+10

f(6)=118

Step-by-step explanation:

to solve this problem you will need to insert 6 every place there is an X in the equation, and then follow the order of operations.

\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 4700\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &11 \end{cases} \\\\\\ 4700=Pe^{0.04\cdot 11} \implies 4700=Pe^{0.44}\implies \cfrac{4700}{e^{0.44}}=P\implies 3027\approx P\)

Answer:

45?

Step-by-step explanation:

Answer:

4 number x value is 10 in

5 number x value is 12mi

use formula of h2=p2+b2

The verdict which is true about the radius of all three arcs when constructing an angle bisector is; - No; the second two arcs must have the same radius but it can be different from the first.

The correct answer option is option C.

Recall that an angle at point, O is formed by the intersection of two lines; say lines A and B.

Hence, in a bid to draw the Angie bisector of the angle; AOB, three arcs are needed.

The first arc is an arc drawn by placing the pivot of the compass at the point, O and drawing an arc which intersects lines A and B. The radius of this first arc in discuss can be any value.

Subsequently, the other two arcs are propagated using the points of intersection of the first arc with both lines such that the two arcs intersect.

It is however noteworthy to know that these two arcs must have the same radius.

Ultimately, the second two arcs must have the same radius but it can be different from the first.

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Answer:

neither

Step-by-step explanation:

got it right 2020

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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In a one-period binomial model of an option value, the probabilities of an up-move and a down-move are "calculated from the model inputs."

The number of survivors, x, in n independent tests is described by a binomial model. The number of tests must be predetermined, the results—success or failure—must be statistically independent for each test, and the survival probability—p—must be constant throughout the tests. When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of observing a specified number of "successes."

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The measure of <1 is 147 degree.

Given:

m∠2 = 12x - 15

m∠7 = 3x + 21

Since angles 2 and 7 are alternate Exterior angles, they are congruent.

So, 12x - 15 = 3x + 21

12x - 3x = 21 + 15

9x = 36

x = 4

So, <2 = 12x - 15= 48 - 15 = 33

Now, <1 + <2 = 180 (Linear Pair)

<1 + 33 = 180

<1 = 147 degree

Thus, the measure of <1 is 147 degree.

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Answer:

B. no, the survey represented both groups in the population of students

Step-by-step explanation:

It says, "surveyed all students"

we can say that the congruence `x² ≅ 1 (mod p)` has a solution if and only if `p = 2` or `p ≅ 1 (mod 4)`. Hence, the solution is p = 2 or p ≅ 1 (mod 4).

The given congruence `x² ≅ 1 (mod p)` has a solution if and only if `p = 2` or `p ≅ 1 (mod 4)`.

A solution is a value or set of values that can be substituted into an equation to make it true.

For example, the solution to the equation `x² - 3x + 2 = 0` is `x = 1` or `x = 2`.

Solution for the given congruence: The given congruence is `x² ≅ 1 (mod p)`.

We need to find the value of `p` for which the congruence has a solution.

Now, if the congruence `x² ≅ 1 (mod p)` has a solution, then we can say that `x ≅ ±1 (mod p)` because `1² ≅ 1 (mod p)` and `(-1)² ≅ 1 (mod p)`.

This implies that `p` must divide the difference of `x - 1` and `x + 1` i.e., `(x - 1)(x + 1) ≅ 0 (mod p)`.

This gives us two cases:

Case 1: `p` divides `(x - 1)(x + 1)` i.e., either `p` divides `(x - 1)` or `p` divides `(x + 1)`. In either case, we get `x ≅ ±1 (mod p)`.

Case 2: `p` does not divide `(x - 1)` or `(x + 1)` i.e., `p` and `x - 1` are coprime and `p` and `x + 1` are coprime as well.

Therefore, we can say that `p` divides `(x - 1)(x + 1)` only if `p` divides `(x - 1)` or `(x + 1)` but not both.

Now, `(x - 1)(x + 1) ≅ 0 (mod p)` implies that either `(x - 1) ≅ 0 (mod p)` or `(x + 1) ≅ 0 (mod p)`.

Therefore, we get two cases as follows:

Case A: `(x - 1) ≅ 0 (mod p)` implies that `x ≅ 1 (mod p)` and `x ≅ -1 (mod p)`.

Case B: `(x + 1) ≅ 0 (mod p)` implies that `x ≅ -1 (mod p)` and `x ≅ 1 (mod p)`.

Thus, we can conclude that if the congruence `x² ≅ 1 (mod p)` has a solution, then either `x ≅ 1 (mod p)` and `x ≅ -1 (mod p)`, or `x ≅ -1 (mod p)` and `x ≅ 1 (mod p)`.

Therefore, we can say that `p` must be such that it divides `(x - 1)(x + 1)` but not both `(x - 1)` and `(x + 1)` simultaneously. Hence, we get the following two cases:

Case 1: If `p = 2`, then `(x - 1)(x + 1)` is always divisible by `p`.

Therefore, `x ≅ ±1 (mod p)` for all `x`.

Case 2: If `p ≅ 1 (mod 4)`, then `(x - 1)` and `(x + 1)` are not both divisible by `p`.

Hence, `p` must divide `(x - 1)(x + 1)` for all `x`.

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Answer:

a) If y varies inversely with c, we can write the equation:

y = k/c

where k is the constant of variation. To find the value of k, we can use the given information that y = 3 when c = 8. Substituting these values into the equation, we get:

3 = k/8

Solving for k, we get:

k = 24

Therefore, the equation that models the variation is:

y = 24/c

b) To find y when x = 72, we need to first determine the value of c. Since we know that y varies inversely with c and we have an equation that models the variation, we can solve for c by substituting the given values of x and y:

y = 24/c

3 = 24/c (since y=3 when x=8)

Solving for c, we get:

c = 8

Now that we know the value of c, we can use the equation that models the variation to find y when x = 72:

y = 24/c

y = 24/8

y = 3

Therefore, when x = 72, y = 3.

Step-by-step explanation:

To approach this type of problem, you have to make a couple of reasonable assumptions - first, that each worker works at the same pace, and second, that the effort to build each wall is the same.

Next, figure out how much effort is required to build one wall. The effort is measured in “working days”. So, how many days does one worker need to build one wall, or how many workers would be required to build one wall in one day? We can calculate this by dividing the 25 worker days used to build five walls by the number of walls (5). So we need five worker days per wall.

(5 workers) x (5 days) = 25 worker-days;

25 worker days/5 walls = 5 worker days per wall.

With 100 workers, it will take five days to build 100 walls. Each worker will build one wall in 5 days. So it will also take 5 days for all 100 workers to build all 100 walls.

100 x 5 = 500 worker days;

500 worker-days / 100 workers = 5 days (answer)

The transformations to the parent function in this problem are given as follows:

The first transformation is that the function was multiplied by -1/2, meaning that:

The translations are given as follows:

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Every polynomial function of odd degree with real coefficients will have at least one real root or zero.

This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.

The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.

For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.

It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.

The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.

In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.

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The percentage of ball that hit into the outfield would be represented by the equation = 15/8 = X/100. That is A.

The total number of balls that that where present at the battling practice by Alexis = 15.

The number of balls that hit into the outfield = 8

The number of balls that hit outside the outfield = 15-8= 7

The percentage (x) of the balls that are outside the outfield;

X = 8/15 × 100/1

x ×15 = 8 × 100

15/8 = X/100.

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