The equation e=1200+11t represents your elevation e in feet for each minute t you hike from a trailhead. If you graphed this equation, what would the slope represent?

(g *f)(x) = (2x+8)^4

replace x with -3

(2(-3)+4)^4 =

(-6+4)^4 =

= (-2)^4

= 16

a. [tex]\( P(X = 66) \approx 0.014 \)[/tex]

b. [tex]\( P(X = 77) \approx 0 \)[/tex]

c. [tex]\( P(X \geq 66) \approx 0.015 \)[/tex]

d. Option C: Yes, 66 is significantly high; probability [tex]\( < 0.05 \).[/tex]

To solve this problem, we'll use the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k} \][/tex]

Where:

[tex]- \( n \) is the number of trials (77 adults in this case)\\- \( k \) is the number of successes (the number of adults believing in reincarnation)\\- \( p \) is the probability of success (the proportion of adults believing in reincarnation, which is 0.40 in this case)\\- \( \binom{n}{k} \) is the binomial coefficient, which represents the number of ways to choose \( k \) successes out of \( n \) trials.[/tex]

Now let's calculate the probabilities:

a. Probability that exactly 66 of the selected adults believe in reincarnation:

[tex]\[ P(X = 66) = \binom{77}{66} \cdot (0.40)^{66} \cdot (1 - 0.40)^{77 - 66} \][/tex]

b. Probability that all of the selected adults believe in reincarnation:

[tex]\[ P(X = 77) = \binom{77}{77} \cdot (0.40)^{77} \cdot (1 - 0.40)^{77 - 77} \][/tex]

c. Probability that at least 66 of the selected adults believe in reincarnation:

This is the sum of probabilities from 66 to 77.

[tex]\[ P(X \geq 66) = \sum_{k=66}^{77} \binom{77}{k} \cdot (0.40)^{k} \cdot (1 - 0.40)^{77 - k} \][/tex]

Let's calculate these probabilities.

a. Probability that exactly 66 of the selected adults believe in reincarnation:

[tex]\[ P(X = 66) = \binom{77}{66} \cdot (0.40)^{66} \cdot (0.60)^{11} \]\[ = \frac{77!}{66!(77-66)!} \cdot (0.40)^{66} \cdot (0.60)^{11} \]\[ \approx 0.014 \][/tex]

b. Probability that all of the selected adults believe in reincarnation:

[tex]\[ P(X = 77) = \binom{77}{77} \cdot (0.40)^{77} \cdot (0.60)^{0} \]\[ = (0.40)^{77} \]\[ \approx 0 \][/tex]

c. Probability that at least 66 of the selected adults believe in reincarnation:

[tex]\[ P(X \geq 66) = \sum_{k=66}^{77} \binom{77}{k} \cdot (0.40)^{k} \cdot (0.60)^{77 - k} \]\[ \approx 0.015 \][/tex]

So, for the options:

d. If 77 adults are randomly​ selected, is 66 a significantly high number who believe in​ reincarnation?

C. Yes, because the probability that 66 or more of the selected adults believe in reincarnation is less than 0.05.

Answer with explanation:

It is given that two chords  AB and CD intersect at point E.

 Also, A E= 10, E B=4 , CE=8

So, By Intersecting chord Theorem

⇒A E × E B = CE × E D

⇒10 × 4= 8 × ED

⇒ 40 =8× DE

Dividing both sides by , 8 we get

DE= 5 unit

Option: B, DE=5 unit

Final answer:

The equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4) is y = −(2/3)x − 2. We found this by first converting the given line into slope-intercept form to find the slope, and then using the point-slope form with the given point.

Explanation:

To find the equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4), we first need to determine the slope of the given line. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope. We can rewrite the given equation in slope-intercept form by isolating y:

2x + 3y = 3

3y = −2x + 3

y = −(2/3)x + 1

This shows that the slope (m) of the given line is −(2/3). Since parallel lines have the same slope, the slope of the new line will also be −(2/3). Now we use the point-slope form of a line which is y − y1 = m(x − x1), where (x1,y1) is a point on the line. Plugging in the given point (3, −4) and the slope −(2/3), we get:

y − (−4) = −(2/3)(x − 3)

Distributing the slope on the right side and moving −4 to the other side gives us the final equation:

y = −(2/3)x + 2 + −4

y = −(2/3)x − 2

This is the equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4).

A quadratic polynomial can have 0, 1, or 2 real roots, including repeated roots. The roots are determined by the discriminant. Numbers 4, 5, or 6 are not possible numbers of real roots for a quadratic polynomial.

In Mathematics, specifically in Algebra, a quadratic polynomial with real coefficients can have either 0, 1, or 2 real roots, including any repeated roots. The number of roots is determined by the discriminant (the value under the square root in the quadratic formula). If the discriminant is greater than 0, the quadratic has 2 real roots. If it equals 0, there is 1 real root (a repeated root), and if it is less than 0, there are no real roots (there are 2 complex roots instead). Consequently, the possible number of real roots for a quadratic polynomial is not 4, 5, or 6.

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A quadratic polynomial with real coefficients can have 0, 1, or 2 real roots. Only '0 real roots' is a valid choice. This is determined based on the discriminant of the quadratic equation.

A quadratic polynomial with real coefficients is of the form [tex]\( ax^2 + bx + c = 0 \)[/tex], where ( a, b, ) and ( c ) are real numbers.

The number of real roots of a quadratic polynomial can be determined by its discriminant, [tex]\( \Delta = b^2 - 4ac \)[/tex]:

1. If [tex]\( \Delta[/tex] > 0, the polynomial has two distinct real roots.

2. If [tex]\( \Delta[/tex] = 0, the polynomial has one real root (a repeated root).

3. If [tex]\( \Delta[/tex] < 0, the polynomial has no real roots (it has two complex conjugate roots).

Based on this, the possible number of real roots, including repeated roots, for a quadratic polynomial with real coefficients are:

- ( 0 ) (when the discriminant is negative, there are no real roots)

- ( 1 ) (when the discriminant is zero, there is one repeated real root)

- ( 2 ) (when the discriminant is positive, there are two distinct real roots)

Given the options:

- 0

- 4

- 5

- 6

The only valid number of real roots for a quadratic polynomial with real coefficients from the provided options is: 0

The number of possible outcomes for the two remaining games is 9.

The number of possible outcomes for the two remaining games can be found by multiplying the number of outcomes for each game. Since each game can have three possible outcomes (win, lose, or tie), there are a total of 3 outcomes for each game. Therefore, the number of possible outcomes for the two games is 3 x 3 = 9.

Final answer:

The graph of g(x)=⌊x⌋-3 is the same as the graph of f(x)=⌊x⌋ but shifted downward by 3 units because of the subtraction of 3, resulting in each step being 3 units lower.

Explanation:

The student has asked how the graph of g(x)=⌊x⌋-3 differs from the graph of f(x)=⌊x⌋. The function ⌊x⌋ represents the greatest integer function or floor function, which maps a real number to the largest integer less than or equal to it. The graph of f(x) is a step function that jumps up by 1 at each integer value of x. The graph of g(x) will be exactly the same as f(x) but will be shifted downward by 3 units due to the -3 in the function. This means that each step on the graph of g(x) will occur at an integer value of y that is 3 less than the corresponding step on the graph of f(x). For example, where f(x) has a step at y=0, g(x) will have a step at y=-3.

Answer:

[tex]x= +-\frac{7}{4}[/tex]

Step-by-step explanation:

[tex]16x^2= 49[/tex]

Solve the equation for x

To solve the equation , we need to isolate x

To get x alone , we need to remove the numbers attached with x

To remove 16 we divide both sides by 16

[tex]x^2 = \frac{49}{16}[/tex]

Now to remove square from x we take square root on both sides

[tex]\sqrt{x^2} = \sqrt{\frac{49}{16}}[/tex]

square root (49) = 7

square root (16)= 4

So , [tex]x= +-\frac{7}{4}[/tex]

When we take square root we include +-

Answer:

3 x 10^8

Step-by-step explanation:

I got it right on Kahn Academy :D

The length of the diagonal is:

                          20.3147

We know that if we draw a diagonal in a rectangle such that the length and width of a rectangle are a and b then the length of the diagonal act as a hypotenuse of a  right angled triangle with two sides of triangle as a and b.

Hence, we will use the Pythagorean Theorem to find the length of the hypotenuse (c) as follows:

[tex]c^2=a^2+b^2[/tex]

[tex]c^2=(15)^2+(13.7)^2\\\\c^2=225+187.69\\\\c^2=412.69\\\\c=\pm \sqrt{412.69}\\\\c=\pm 20.3147[/tex]

Since, length can't be negative.

Hence, we have:

[tex]c=20.3147[/tex]

Final answer:

Using the Pythagorean theorem, the length of the diagonal for a rectangular garden measuring 15 m by 13.7 m is approximately 20.31 meters.

Explanation:

The student is asking about finding the length of the diagonal of a rectangle. The rectangle has dimensions of 15 m (length) and 13.7 m (width). To find the diagonal, we can use the Pythagorean theorem, which is applicable in a right-angled triangle and states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The diagonal of the rectangle can be considered as the hypotenuse (c) of a right-angled triangle with the other two sides being the lengths and the width of the rectangle.

Using the dimensions of the garden:

Length (a) = 15 m

Width (b) = 13.7 m

Diagonal (c) = ?

Applying the Pythagorean theorem:

c^2 = a^2 + b^2

c^2 = 15^2 + 13.7^2

c^2 = 225 + 187.69

c^2 = 412.69

c = [tex]\sqrt{412.69}[/tex]

c ≈ 20.31 m

So, the length of the diagonal from one corner of the garden to the other is approximately 20.31 meters.

Slope = 4/3, y intercept = -5/3

 see attached picture:

we have

[tex]y=\frac{1}{2}x+3[/tex]

we know that

the slope m of the line is equal to

[tex]m=\frac{1}{2}[/tex]

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For [tex]y=0[/tex] find the value of x

[tex]0=\frac{1}{2}x+3[/tex]

[tex]x=-6[/tex]

The x-intercept is the point [tex](-6,0)[/tex]

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For [tex]x=0[/tex] find the value of y

[tex]y=\frac{1}{2}*0+3[/tex]

[tex]y=3[/tex]

The y-intercept is the point [tex](0,3)[/tex]

therefore

the answer is the option

B. Plot the Y-intercept (0,3) and use the slope of 1/2 to find a second point

Final answer:

To graph the line y = 1/2x + 3, plot the y-intercept (0,3) and use the slope of 1/2 to find another point on the line.

Explanation:

The correct procedure to graph the line represented by the equation y = ½x + 3 is to start by plotting the y-intercept and then using the slope to find a second point. The y-intercept is the point where the line crosses the y-axis. In this equation, the y-intercept is (0, 3) because when x is 0, y is 3. The slope of the line is ½, which means that for every 1 unit increase in x, y increases by ½ a unit. Therefore, starting at the y-intercept (0, 3), you can go up ½ unit and right 1 unit to find another point on the line.

The correct answer to the multiple-choice question is:

B. Plot the Y-intercept (0,3) and use the slope of 1/2 to find a second point

Answer:

6 movies

Step-by-step explanation:

You pay each month for satellite TV = $30

and for every movie you purchase = $2.50

Let the number of the movies you purchase be x

The equation will be

30 + 2.50x = 45

2.50x = 45 - 30

2.50x = 15

x = [tex]\frac{15}{2.5}[/tex]

x = 6

You purchased 6 movies during the month.

f(x) = 3x+2

f(5) = 3(5) +2 = 15 +2 =17

 Answer is D. 17