i need help in expanded form and simplify the problem

Answer: -1/2

Step-by-step explanation:

The slope of a line tells you how steep the line is, and what direction it is going in. We can calculate the slope by seeing how much the line moves horizontally and vertically.

We can calculate the slope using [tex]\frac{rise}{run}[/tex], which is how much a point rises (goes up or down) and runs (goes left or right) to go to the next point.

Let's take two points on the graph: (-2, 0) and (0, -4). The rise will be the difference of the y-values, and the run will be the difference of the x-values.

[tex]\frac{-2-0}{0-(-4)}=\frac{-2}{4}=\frac{-1}{2}[/tex]

Hence, the slope of this line is [tex]\frac{-1}{2}[/tex]

The net Change in latitude and longitude of the helicopter are; 28.47° and 7.35° respectively.

The net change in latitude of the helicopter can be evaluated as follows;

x = |-6.20° - 22.27°| = |-28.47°|

x = 28.47°

The net change in longitude of the helicopter can be evaluated similarly as follows;

y = |106.80° - 114.15°| = |-7.35°|

x= 7.35°

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Considering the piece-wise function described, the catering cost for a dinner with 40 guests is of $600.

A piece-wise function is a function that has different definitions, depending on the input.

In this problem, considering between 0 and 40 guests, the definition is the open circle at (0, 100) and goes up to a closed circle at (40, 600), hence the catering cost for a dinner with 40 guests is of $600.

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Answer:

600

Step-by-step explanation:

edge

No this does not indicate that the population proportion of women athletes who graduate from the university is now less than 67%.

Given long term graduation rate of 67%, sample size of 36  and the women athletes graduated is 23.

We have to find whether  the given information shows  that the population proportion is less than 67%.

First we have to create hypothesis for this :

[tex]H_{0}[/tex]:P=0.67

[tex]H_{1}[/tex]:P<0.67

Under null hypothesis the test statistic is

z=p bar-p/[tex]\sqrt{p(1-p)/n}[/tex]

where p bar=23/36

=0.638

z=(0.638-0.67)/[tex]\sqrt{0.67(1-0.67)/36[/tex]

=-0.032/[tex]\sqrt{0.67*0.33/36}[/tex]

=-0.032/[tex]\sqrt{0.0064}[/tex]

=-0.032/0.078

=-0.41

Now we have to find the left tailed critical at 0.01 significance level using z table.

z=-2.33

Since the z value does not fall in the critical region,therefore we fail to reject the null hypothesis. So we can conclude that there is not sufficient evidence to say that the population proportion of women athletes who graduate from the university is now less than 67%.

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Question is incomplete as it should specify the signficance level of 0.01 to be used.

The linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

Cubic equations are polynomials of third grade, whose standard and factor forms are shown below:

Standard form

y = a · x³ + b · x² + c · x + d

Factor form

y = (x - r₁) · (x - r₂) · (x - r₃)

Where r₁, r₂, r₃ are the zeros of the cubic equation.

There are several approaches to find the roots of the polynomial, in this question we decided to use the graphical approach, which offers sufficiency and quickness for analysis. The roots of the polynomials are the points that pass through the x-axis.

In accordance with the image attached below, the polynomial has three real roots: r₁ = - 20, r₂ = - 5, r₃ = 15. Then, the linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

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Length of BD is 11 units.

The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.

Let length of AE be x

By intersecting chords theorem,

AE(ED) = BC(DE)

x(x + 12) = (x +2)(x +5)

x² + 12x= x² + 7x + 10

5x = 10

x = 2

BD = BE + DE

= x + x +7

= 2x + 7

= 2(2) + 7

= 11 units

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Answer:

52 degrees

Step-by-step explanation:

Really easy, i learned it this summer

1. 180-128=52

2. 3=52 cus  alternate interior angles

(p p) would produce Tautology.

Tautology:

It is needless repetition of an idea, statement, or word Rhetorical repetition, tautology ('always and for ever'), banal metaphor, and short paragraphs are part of the jargon.— Philip Howard. b : an instance of such repetition The phrase "a beginner who has just started" is a tautology.

A tautology is an expression or phrase that says the same thing twice, just in a different way. For this reason, tautology is usually undesirable, as it can make you sound wordier than you need to be and make you appear foolish.

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⊰___________________ ___________________________________ __⊱

Answer:

Yes, it is a polynomial

Step-by-step explanation:

This polynomial is a trinomial, since it has 3 terms (the prefix tri means three) and its degree is 3 (the degree of a polynomial is the largest exponent in that particular polynomial).

Done !! Hope this made sense to you !!

⊰________________________________________________________⊱

[tex]\small{\pmb{\tt{CALLIGRAPHY}}[/tex]

The ways that can be used to solve a quadratic equation include:

Factorization

Using the quadratic formula.

Completing the squares.

It should be noted that a quadratic equation simply means an algebraic equation of the second degree in x.

Here, the factorization, using the quadratic formula, and completing the squares method can be used.

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Answer:

-3

Step-by-step explanation:

Step-by-step explanation:

"t t hours" ????

you mean 11 hours ?

13 gallons now.

2 gallons are used (and therefore disappear from the tank) per hour.

so, in 5 hours 5×2 = 10 gallons will be used.

that leaves 13 - 10 = 3 gallons in the tank.

in 11 hours 11×2 = 22 gallons would have been used.

but there are only 13 gallons in the tank.

so, if he does not fill up, he will have 0 gallons left after 11 hours. in fact, already after 13/2 = 6.5 hours.

the point :

when you use 2 gallons per hour, that means in t hours you are using t × 2 or 2t gallons.

Answer: 156 degrees

Step-by-step explanation:

The y-value of the terminal point of the vector is 3.

In this question we must apply a matricial form of rotation, which is a kind of rigid transformation. This transformation is defined by the following formula:

[tex]\vec A' = \vec T\cdot \vec A[/tex], where [tex]\vec A' , \vec A \in \mathbb{R}_{1 \times 2}[/tex], [tex]\vec T \in \mathbb{R}_{2 \times 2}[/tex]

If we knw that [tex]\vec A = \left[\begin{array}{c}- 4\\3\end{array}\right][/tex] and [tex]\vec T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], then the transformed vector column is:

[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \cdot \left[\begin{array}{cc}-4\\3\end{array}\right][/tex]

[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}4\\3\end{array}\right][/tex]

The y-value of the terminal point of the vector is 3.

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Answer: B, D, E

Step-by-step explanation:

The dividend is [tex]2x^2+9x+7[/tex] while the divisor is x + 1

Option A is correct

The coefficient outside the division block is -1.

This means that the divisor = x + 1

Also, the coefficients of the dividend are:

2, 9, 7

The highest exponent is 2 since there are three terms in the polynomial. Three terms show that the expression is a quadratic expression

Therefore, the dividend is [tex]2x^2+9x+7[/tex]

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The interquartile range of the data set is 8

To do this we have to arrange in ascending order

= 8,9,9,9,10,11,13,15,17,18,22

Q2 = The median of the data is 11.

We have to find the median of the half before 11 and the median of the half after 11.

We would have

8,9,9,9,10

Q1 = 9

And 13,15,17,18,22

Q3 = 17

The interquartile range is

Q3 - Q1

= 17 - 9

= 8

The interquartile range of the data set is 8

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Correct question

Study the following data set.

{8,15,9,18,9,17,22,10,11,9,13}

What is the interquartile range of the data set?

The rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).

Herein we have the graph of a rational function of the form f(x) = p(x)/q(x) . The domain of these kind of functions is all real numbers except those values of x such that q(x) = 0. Graphically speaking, there is a vertical asymptote when a discontinuity exists and an horizontal asymptote for x → ± ∞.

In accordance with the picture, there are one horizontal asymptote and one vertical asymptote. As the horizontal asymptote of the function is distinct of 0, then the grade of p(x) is the same grade of q(x). Therefore, we have a rational function of the form:

f(x) = (2 · x + k)/(x + 3)     (1)

If we know that x = 0 and y = 2.4, then the value of k is:

2.4 = (2 · 0 + k)/(0 + 3)

2.4 = k/3

k = 7.2

Therefore, the rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).

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The equation becomes of the pressure is   P = 90 + 10 sin(π/36(t +4 ))

By observation the sine function should be of form P=  90 + 10 sin(ω(t − c)) as it oscillates about 90 and with a factor of 10. Let time be represented by the variable t in hours from 12.00 AM.

At 2:00 P.M. that is t= 14 hours the pressure is 100 mmHg

Substituting it in the equation we get,

100 = 90 + 10 sin(ω(t − c))

10 = 10  sin(ω(14 − c))

1 = sin(ω(14 − c))

ω(14 − c) = π/2                           -1)

At 2:00 A.M. that is t= 2 hours the pressure is 80 mmHg

80 = 90 + 10 sin(ω(t − c))

-10 = 10 sin(ω(2 − c))

3π/2 = ω(2 − c)                           -2)

dividing 2) with 1) we get

3 = (14 − c) /(2 − c)  

6 - 3c = 14 - c

2c = -8

c = - 4

Substituting the value of c in 1) we get,

ω(14 − (-4)) = π/2

ω18 =  π/2

ω = π/36

Thus the equation becomes  P = 90 + 10 sin(π/36(t +4 ))

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Answer:

intimately there are three types of angles a cute angle and angle between zero and 90° right angle and angle 90 degree angle of two angle and angle between 90 and 180 degree

The solutions are: θ = 90º, 270º, 30º, and 150º

Given,

sin2θ = cosθ

sin2 θ = 2sinθ cosθ

2sinθ cosθ = cosθ

2sinθ cosθ - cosθ = 0

factor

cosθ(2sinθ-1) = 0

cosθ = 0 or 2sinθ - 1 = 0

cosθ = 0 when θ=90º or θ=270º (look on the unit circle)

2sinθ - 1 = 0

2sinθ = 1

sinθ = 1/2

look at the unit circle and see that sinθ=1/2 when θ=30º

sin is positive in Quadrant2 as well as Quadrant 1

180º-30º=150º

θ=150º

answers: θ=90º, 270º, 30º, and 150º

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Answer:

The remaining 15 athletes did not participate in any type of flexibility program

Answer:

too small

Step-by-step explanation:

Using the normal distribution, the diameter that represents the 49th percentile is of 1.52 units.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Using a calculator, the mean and the standard deviation for the diameters are given as follows:

[tex]\mu = 1.524, \sigma = 0.1226[/tex]

The 49th percentile is X when Z = -0.025, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.025 = \frac{X - 1.524}{0.1226}[/tex]

X - 1.524 = -0.025 x 0.1226

X = 1.52.

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Step-by-step explanation:

x, y = 2 numbers

x = 2y

y - x/2 = 20

this is impossible to solve. there is no solution.

because the first equation tells us

y = x/2

and so the second equation is

x/2 - x/2 = 20

0 = 20

so, again, no solution.

Answer:

1/3 = slope

Step-by-step explanation:

Start with

y = mx + b    

                  b = -5 given ,  now sub in the given point to calculate m =slope

-4 = m(3) - 5      add 5 to both sides

1 = m(3)               divide through by 3

1/3 = m = slope

The perimeter of the new rectangular piece of glass is 80m.

Here, a rectangular piece of glass has a perimeter of 20 meters.

As we know the perimeter P of a rectangle is given by the formula,

P = 2l+2w...(1)

Therefore,

20 = 2l + 2w

20 = 2(l + w)

20/2 = l + w

10 = l + w ....(2)

Now, both the length and width of the rectangle are multiplied by 4,

That is,

The new length of the rectangle is, l = 4l

The new width of the rectangle is, w = 4w

Therefore by substituting this in the equation(1) we get,

P = 2(4l) + 2(4w)

P = 8l + 8w

P = 8(l+w)....(3)

Substitute equation (2) in (3),

That is,

P = 8*10

P = 80m

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The mean of the sample is x-bar is determined to be 59.2 and population standard deviation, σ, is known to be 3.8. The 90% confidence interval about μ if the sample size, n, is 45 be  58.27< μ<60.13

A simple random sample of size n is drawn from a population whose population standard deviation, σ, is known to be 3.8. The sample mean, x-bar, is determined to be 59.2.

Hence,

n=45

σ=3.8

x-bar=59.2

The z value for the 90% confidence interval is z=1.645.

Then, μ=(x-bar)±(z×σ/[tex]\sqrt{n}[/tex])

μ=59.2±(1.645×3.8/[tex]\sqrt{45}[/tex])

μ=59.2±0.9318

59.2-0.9318<μ<59.2+0.9318

58.27< μ<60.13

Therefore, The 90% confidence interval about μ if the sample size, n, is 45 be  58.27< μ<60.13

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