GEOMETRY PROOFS!!!!!

The ordered pair of the force of the parabola will be (2, -1).

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

A parabola has a directrix of y = - 3 and a vertex at (2,1).

Since the directrix is upward, utilize the condition of a parabola that opens up or down.

(x − h)² = 4p(y − k)

The separation from the concentration to the vertex and from the vertex to the directrix is |p|. Deduct the worth of the directrix from the y direction of the vertex to track down p.

p = − 1 + 1 / 2

p = − 1/2

Then the equation is given as,

(x − 2)² = 4(1/2)(y + 1)

(x − 2)² = 2(y + 1)

The ordered pair of the force of the parabola will be (2, -1).

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the slope of the given point is m=−3/4

For a farmer interested in data-driven decision-making regarding effect of 3 fertilizers on the crop yield the hypothesis testing used to determine any potential difference in the yield between the three fertilizers is ANOVA test (Option C).

Hypothesis testing refers to the statistical inference method utilized to determine if the available data sufficiently supports a particular hypothesis. Hypothesis testing enables decision makes to establish probabilistic statements about population parameters. ANOVA test stands for Analysis of Variance and refers to a statistical test utilized to evaluate the difference between the means of more than two groups. A one-way ANOVA uses one independent variable and a two-way ANOVA uses two independent variables. As the farmers want to evaluate the difference between three fertilizers' effect on crop yield, the appropriate test is ANOVA test.

Note: The question is missing options which are a) Two sample t-tests. b) Paired t-test. c) ANOVA test. d) One sample t-test.

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Since in the question we reject the alternative hypothesis hence type II error occurs.

What is Type I error?

When the null hypothesis is true but rejected in hypothesis testing, type 1 errors often confused with false positives occur. A general assertion or default attitude that there is no connection between two measurable phenomena is known as the null hypothesis.

What is Type II error?

Type II errors take place when you fail to reject the null hypothesis even though it is untrue.

The average number of insect parts per 100 gm in this problem is 75. This number cannot be demonstrated by the test to be larger than 75. This indicates that the test is producing a "false negative" since it is not detecting these insect parts.

Hence, this is a Type II error.

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The slope-intercept form of the equation can be written as y = -x - 19

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis). Equation of line is the equation that is satisfied by each point that lies on that line.

The equation given is y + 9 = -(x + 10)

Rewriting this equation in y = mx + c format;

y + 9 = -(x + 10)

y + 9 = -x - 10

y = -x - 10 - 9

y = -x - 19

The equation is y = -x - 19

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The zeroes of the polynomial are -2,1,3,-1

The locations where a polynomial becomes 0 overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (-1). The largest power of the variable x is referred to as a polynomial's degree.

In general, the value of P(k) at x = k is denoted by P(k), and it can be found by substituting x by k in P if P(x) is a polynomial in x and k is any real number. The real number k is referred to as the zero of a polynomial P(x) if P(k) = 0.

Given:- The polynomial is f(x)=(x+2)(x-1)(x-3)(x+1)

The polynomial is divided into its factors

we equate each of the factors with the term 0

x+2=0

x=-2

x-1=0

x=1

x-3=0

x=3

x+1=0

x=-1

Hence the zeroes of the polynomial f(x)=-2,-2,1,3

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Answer:

6

Step-by-step explanation:

Each coordinate is six times the corresponding coordinate in the preimage.

The probability that a randomly selected tire will have a life of at least 38,100 miles is 0.9115.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

Let, the life expectancy of a particular brand of tire is normally distributed with a mean of 30,000 and a standard deviation of 6,000 miles.

So, μ = 30000, σ = 6000, x = 38100.

Therefore,

z  = (x - μ) / σ

   = (38100 - 30000) / 6000

   = 8100 / 6000

   = 81 / 60

z  = 1.35

Now,

P(X = 38100) = P(z = 1.35) = 0.9115

Hence, the probability that a randomly selected tire will have a life of at least 38,100 miles is 0.9115.

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The perimeter of the smaller square would be = 12feet. That is option B.

Perimeter can be defined as the summation of all the sides and edges of an object.

Scale factor is also defined as the ratio of difference between an original object and a newly formed object.

A square has four sides and it's perimeter = 24 ft

This means that the sides of the square= 24/4 = 6ft.

If the original (smaller square) dialted by a factor of 1/2 to have 6 ft as its sides, it means that it's original side of the small square is 3ft.

This is because to form the bigger square, 1/2 × 6 = 3ft.

Therefore, the perimeter of small square = 3+3+3+3 = 12ft.

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Answer: The number of no votes is 1876 votes.

What is the ratio?

"The ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another".

For the given situation,

Let x be the number of votes.

The ratio of yes votes : no votes = 3x:2x

Total = 5x

Total votes = 4690 votes

⇒

Divide by 5 on both sides,

⇒

Thus the number of no votes =

⇒

⇒

Hence we can conclude that the number of no votes is 1876 votes.

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Step-by-step explanation:

Answer:

IMPORTANT- Triangle Sums up to 180.

Step-by-step explanation: According to the symbol, both sides are congruent. Which means they have the same degrees (Also known as an isosceles triangle). Since the left side of the angle measures 58.5 degrees, the right side angle is also 58.5. Sum up both sides --->

= 58.5+58.5 = 117

*every triangle sum to 180*

= Whole triangle degrees Subtract ( - ) to 117 = 180-117 = 63

So subtracting the whole triangle measure (180*) to 117 ( 117 is the degrees of both sides together)  is 63. So "x" is equal to 63 degrees.

Answer: "x" equals 63 degrees.

For Double checking:

Turn "x" into 63 and add all the sides measures and check if it sum's up to 180 (which is the measure of the whole triangle.)

Numerical Setup for double-checking :

58.5+ 58.5 +X(63) =180

58.5 +58.5 +63 = 180

Answer:

1/2

Step-by-step explanation:

(-6-(-4)/(3-7)

(-6+4)/-4

-2/-4

1/2

Answer: f^−1(x)=2x−10

Explanation: switch the x and y to get:

x = y/2 + 5

Then isolate y by multiplying 2 on both sides and moving 10:

2x = y + 10

- 10 -10

2x -10 = y

The domain of the given function f(x) is {x| –4 < x ≤ 4}. Option A is correct.

First, let us understand the domain of a function:

The domain of a function is the set of all possible inputs for the function.

We are given the following;

All points of the step function f(x) are graphed.

We need to determine the domain of f(x).

The unfilled / open dot shows that we don't include that number.

The filled / closed dot shows that we can include that number.

So, we can see that it is open at -4 and closed at 4.

So, it is written as -4 < x and 4 ≥ x.

So, the domain is -4 < x and 4 ≥ x.

Thus, the domain of the given function f(x) is {x| –4 < x ≤ 4}. Option A is correct.

Please find the given graph below:

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Answer:

3.82%

Step-by-step explanation:

The number of pairs that must be randomly selected from the set {1,3,5,7,9,11,13,15} to guarantee that at least one pair of these numbers add up to 16 is 5.

In the given set {1,3,5,7,9,11,13,15}, there are four pairs that sum up to 16, which are (1,15), (3,13), (5,11), and (7,9). Let k numbers be picked from the set. Consider k = 5, then using the pigeonhole principle, for one of the pairs described above, both of the endpoints must have been picked. Hence, if 5 numbers are picked from the set, then there exists a pair with a sum of 16.

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Answer:

(-1, -4)

Step-by-step explanation:

Make the y value the opposite value.

Answer:

-10.24

You can double check this answer by plugging it in for u, so -10.24 dived by 2 then plus 3, which indeed equals -2.12

so, u does equals -10.24

a) The percentage of students who passed the exam, given that they completed the exam review is of 73%.

b) The percentage of students who passed the exam, given that they did not complete the exam review, is of 27%.

c) There is a positive association between passing the exam and completing the exam review.

A percentage is obtained by the division of the desired amounts by the total amounts, multiplied by 100%.

For item a, these amounts are given as follows:

Hence the percentage is of:

p = 55/75 = 0.73 = 73%.

For item b, these amounts are given as follows:

Hence the percentage is of:

p = 20/75 = 0.27 = 27%.

There is a positive association between passing the exam and completing the exam review, as the percentage of students who passed completing the review, found in item a, is greater than the percentage of students who passed without completing the review, found in item b.

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The length of x is 4.1.

Given:

Base = 9 + 4.5 = 13.5

From figure:

= [tex]\sqrt{9^{2}+5^{2} }[/tex]

= [tex]\sqrt{81+25}[/tex]

= [tex]\sqrt{96}[/tex]

= 9.797

4.5 opposite is equal to 4.5.

5 opposite equal to 5 and remaining to x - 5.

According to pythagorean theorem:

= [tex]\sqrt{4.5^{2}+(x-5)^{2} }[/tex]

[tex]13.5^{2} +x^{2} =(\sqrt{96}+\sqrt{4.5^{2} +(x-5)^{2} })^{2}[/tex]

[tex]\sqrt{13.5^{2} +x^{2} }[/tex] - [tex]\sqrt{96} = \sqrt{20.25+x^{2} +25 -10x}[/tex]

squaring on both sides

182.25 + [tex]x^{2}[/tex] - 96 = [tex]x^{2}[/tex] - 10x + 45.25

10x = 45.25 + 96 - 182.25

10x = 41

x = 4.1.

Therefore the value of x is 4.1.

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Answer:

tan 25° = b / 8 m

Step-by-step explanation:

You need to know what the ratios are.

sin X = opp/hyp

cos X = adj/opp

tan X = opp/adj

For angle B, the opposite leg is b, ad the adjacent leg is 8 m.

The hypotenuse is AB.

sin B = sin 25° = opp/hyp = b/AB

tan B = tan 25° = opp/adj = b / 8 m

Answer:

4 metters por el significado

The nth term of this quadratic sequence 4,9,16,25,36 is [tex]n^{2} + 2n + 1[/tex]

Given that:

the given sequence is 4,9,16,25,36

nth term of quadratic sequence is [tex]an^{2}+bn+c[/tex]

Now lets find out the value of each variable a,b,c

a = second difference divide by 2

lets find out second difference

4,9,16,25,36

the first difference between the terms are

5,7,9,11

The second difference between the terms

2,2,2

the value of a = second difference / 2

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

a = 1

Now we find the value of b

3a + b = first term of first difference

3a + b = 5

3(1) + b = 5

3 + b = 5

b = 5 - 3

b = 2

Now find the value of c

a + b + c = first term

a + b + c = 4

1 + 2 + c = 4

3 + c = 4

c = 1

Now we replace all the values to find the nth term

 [tex]an^{2}+bn+c\\ \\n^{2}+2n+1[/tex]

Hence the answer is the nth term of this quadratic sequence 4,9,16,25,36 is [tex]n^{2} + 2n + 1[/tex].

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Circumference = pi x d

Circumference = 3.14 x 24 =  75.36

I hope this helps!

well, we know that R, S and T are on the same straight line, hmmmm wait a second!! that means that the slope for RS must be the same as the slope for ST, heck, what's the slope for ST anyway?

[tex]S(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad T(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ -6 }{ -2 } \implies 3[/tex]

ahha!! that means that the slope for RS is really 3, hmmmm

[tex]R(\stackrel{x_1}{4}~,~\stackrel{y_1}{t})\qquad S(\stackrel{x_2}{3}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{t}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{4}}} ~~ = ~~\stackrel{\textit{\LARGE m}}{3} \\\\\\ \cfrac{8-t}{-1}=3\implies 8-t=-3\implies 11-t=0\implies 11=t[/tex]

Answer:

x = 13  x = 1

Step-by-step explanation:

(13-7) = 6

6^2 = 36

1-7 = -6

(-6)^2 = 36

It is possible that the ball may reach a height of 5 meters in accordance with the quadratic formula.

The height of the ball as a function of time is represented by a quadratic equation, in which we must determine if the ball may reach a height of 5 meters. First, substitute the height in the quadratic equation:

- 5 · t² + 9 · t + 2 = 5

5 · t² - 9 · t + 3 = 0

Second, use the quadratic formula to determine the roots of the resulting quadratic equation:

t = - (- 9) / (2 · 5) ± [1 / (2 · 5)] · √[(- 9)² - 4 · 5 · 3]

t = 9 / 10 ± (1 / 10) · √(81 - 60)

t = 9 / 10 ± √21 / 10

t = (9 ± √21) / 10

Since all roots of the quadratic equations are real, then the ball can reach a height of 5 meters above the ground.

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