Find the point, M, that is midway between P=(5,−8,−6) and Q=(-7,-2,-8).

Check the picture below.

so, we really graph the EQUATION of the expression, in this case we'd graph then h y = x² + 2x + 1. and y = −x² + 4x + 1.

then we notice that on the equation of the left-hand-side, it has "y>", meaning that "y is greater than", but never equals to that parabola, so, the line is dashed, meaning the border of the parabola is not part of the shaded area, or TRUE region.

for the one on the right-hand-side, we have "y⩾" or "y is greater than or equals", so the line is a solid line, pointing out the border of that parabola is included in the shaded part or TRUE region.

to check what section is true or not true, well, we can always pick a point on either side and check, so for example hmmmm let's check for the left-hand-side, hmmm the point above the parabola say hmmmm (2 , 3), so x = 3 whilst y = 3

[tex]3 > (2)^2+2(2)+1\implies 3 > 4+4+1\implies 3 > 9\leftarrow \textit{is this true?}[/tex]

is 3 really greater than 9? well hell nope, so that's "false", so that region is the false region, thus is not shaded, that way we know the other region is the "true" region, and so that's the one we shade.

The equation for the slope intercept form of a perpendicular line will be;

⇒ y - y₁ = - 1/m₂ (x - x₁)

Where, m₂ is slope of perpendicular line.

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The slope-intercept form of a perpendicular line.

Now,

We know that;

The product of slopes of perpendicular lines are - 1.

That is, Let m₁ be the perpendicular line and m₂ is there corresponding line.

Then, m₁ m₂ = - 1

⇒ m₁ = - 1/m₂

Thus, The equation for the slope intercept form of a perpendicular line will be;

⇒ y - y₁ = - 1/m₂ (x - x₁)

Where, m₂ is slope of perpendicular line.

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The graph of given function and its explanation is explain below.  

Parabola a bend shaped by the convergence of a cone with a plane lined up with a straight line in its surface : a bend framed by a moving so that its separation from a proper point is equivalent to its separation from a decent line. : something that is bowl-formed. allegorical.

Graph of the function f(x)=x^2 which is a parabola is  

One of the ways of charting this is to involve plug in a couple of x-esteems and find out about the shape. Since the x qualities continue to get squared, there is a remarkable increment on one or the other side of the y-pivot. You can see this by connecting a couple of values:

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The orthocenter is the point at where the triangle's elevations intersect.

The orthocenter will be located on the triangle JKL.

In Euclidean geometry, any three non-collinear points define a unique triangle as well as a unique plane.

A triangle is a three-sided closed shape. The Heron's formula and Pythagoras theorem are two significant formulas relating to triangles.

The orthocenter is the point at where the altitudes intersect. Because each altitude is orthogonal to the base, the prefix ortho- is appropriate for describing their point of junction.

The orthocenter of a right triangle is the vertex of the right angle and so lies on the triangle.

Therefore,

The orthocenter is the point at where the triangle's elevations intersect.

The orthocenter will be located on the triangle JKL

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The density of unknown liquid is 7.447 kg/m³

According to the question,

Density of a solid aluminum cylinder : d = 2700 kg/m³

Weight of cylinder in the air = 0.66N

Weight of cylinder when immersed in an unknown liquid = 0.26N

The volume of the cylinder : v = m /d

where , m is mass of cylinder and d is density

Mass of cylinder : m = g/W

Where , g is acceleration due to gravity = 9.8m/s²

And w is weight of cylinder in air = 0.66N

Substituting the values of g and w

Therefore , m = 9.8 / 0.66

=> m = 14.8 kg

So, Volume of cylinder = 14.8 / 2700

=> V = 5.481 ×  10⁻³m³

To calculate the density of liquid ,

Density of liquid  = Upthrust / (volume of object × acceleration due to gravity)

Upthrust of the liquid = 0.66 - 0.26

=> 4 × 10⁻¹N

Volume of cylinder = 5.481 ×  10⁻³m³

Acceleration due to gravity  = 9.8m/s²

Therefore , The density of unknown liquid = 4 × 10⁻¹N / (5.481 ×  10⁻³m³ × 9.8m/s²)

=> 4 × 10⁻¹N / 53.71×  10⁻³

=> 0.4 / 0.05371

Hence , the density of liquid is 7.447 kg/m³

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By solving a system of two simultaneous linear equation, it can be calculated that

There are 6 1p coin, 8 2p coin, 5 5p coin and 1 10p coins in the pot

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here a system of two simultaneous linear equation needs to be solved

Number of coins in a pot = 20

The coin are 1p, 2p,5p and 10p

Probability of 1p coin is [tex]\frac{3}{10}[/tex]

So number of 1 p coins = [tex]\frac{3}{10} \times 20 = 6[/tex]

Probability of 2p coin is [tex]\frac{2}{5}[/tex]

So number of 2 p coins = [tex]\frac{2}{5} \times 20 = 8[/tex]

Let the number of 5p coin be x and number of 10p coins be y

6 + 8 + x + y = 20

x + y  =20 - 14

x + y = 6 ..... (1)

Value of 6 1p coin = 6 [tex]\times[/tex] 1 = 6p

Value of 8 2p coin = 8 [tex]\times[/tex] 2 = 16p

Value of x 5p coin = x [tex]\times[/tex] 5 = 5x p

Value of y 10p coin = y [tex]\times[/tex] 10 = 10y p

Total value = 6 + 16 + 5x + 10y

                   = 5x  + 10y + 22

By the problem,

5x + 10y + 22 = 57

5(x + 2y) = 57 - 22

x + 2y = [tex]\frac{35}{5}[/tex]

x + 2y = 7 ....... (2)

Subtracting (1) from (2)

y = 1

Putting the value of y in  (1)

x + 1 = 6

x = 6 - 1

x = 5

There are 6 1p coin, 8 2p coin, 5 5p coin and 1 10p coins in the pot.

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As always when trying to find the equation of a line, start with slope, as we will be working in slope-intercept form. The key word here is "perpendicular." Perpendicular lines always have Opposite Reciprocal slopes. An opposite reciprocal is the negative of the reciprocal of the ratio, or in simpler terms, a flipped fraction with a flipped sign.

[tex]-3=-\frac31\\m=(-1)-\frac13\\m=\frac13[/tex]

So, our equation so far is:

[tex]y=\frac13x+b[/tex]

How do we solve for b? This lies in the given coordinates. To find the y-intercept given slope, you also need to be given any other coordinate pair that lies on the line. Here, we are given (4, -6). This means that for this pair of this line, x = 4 and y = -6. This means we can solve for the missing value. Let's put it in algebraic form.

[tex]y=\frac13x+b\\-6=\frac134+b\\-6=1\frac13+b\\-6-1\frac13=1\frac13-1\frac13+b\\b=-7.333[/tex]

So, our function is:

[tex]y = \frac13x-7.333[/tex]

a) The z-value is = 1.15

b) The p-value is 0.124. the null hypothesis is true.

What is a z-value?

When a value is given a Z-value, it shows how far off from the standard deviation it is. The number of standard deviations a given data point is above or below the mean is represented by the Z-value, also known as the standard value.

The level of variability within a particular data collection is effectively reflected in the standard deviation. Standard values for raw scores above the mean are positive, while standard values for raw scores far below mean are negative.

Solution Explained:

GIven in the question,
x = 620 and n = 1200

First we find the sample proportion,

P = x/n

  = 620/1200

  = 0.517

H0:p=.50 is the null hypothesis to be tested.

H1:p>.50 is the alternate hypothesis that needs to be examined as well.

We must use the Minitab software to test for the Z and P values and draw conclusions based on the results.

As a consequence, the

1. Z is solved to have a value of 1.15.

2. A P value of 0.124 is used. We would decide against rejecting the null hypothesis because the P value is so high.

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The triangles ABC and XYZ are congruence by the AAS congruence rule.

Given, two triangles ABC and XYZ

now, ∠A = ∠X

∠B = ∠Y

BC = YZ

so, on using the AAS Congruence rule

ΔABC ≅ ΔXYZ

therefore, the triangles ABC and XYZ are congruence by the AAS congruence rule.

Hence, the triangles ABC and XYZ are congruence by the AAS congruence rule.

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To solve the equation we can use the given options, except calculate the lcd of terms

An equation is an equality between two algebraic expressions.

To solve an equation we must try to isolate the variable on one side of the equation. Some alternatives may be:

Therefore, the wrong option is to obtain the lcd of two like terms.

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The value of the mathematical expression given as bd/a + c if a = -2, b = 3, c = -12 and d = -4 is -6

From the question, we have the following expression that can be used in our computation:

bd/a + c

Also from the question, we have the following values that can be used in our computation:

a = -2, b = 3, c = -12 and d = -4

The next step is substitution

Substitute a = -2, b = 3, c = -12 and d = -4 in the expression bd/a + c

So, we have the following representation

bd/a + c = 3 * -4/-2 - 12

Next, we evaluate the quotient of -4 and -2

This gives

bd/a + c = 3 * 2 - 12

Next, we evaluate the product of 3 and 2

This gives

bd/a + c = 6 - 12

Lastly, we evaluate the difference of 6 and 12

This gives

bd/a + c = -6

Hence, the solution is -6

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Complete question

bd/a + c

If a = -2, b = 3, c = -12 and d = -4

Proved that X² is not an unbiased estimator for μ²

Given,

The length of the square plot = μ

The area of the square plot = μ²

You have to make the independent measurements X₁, X₂,.....Xₙ

Variance = σ²

a) We have to show that X² is not an unbiased estimator for μ²

Here,

E(X²) = V(X) + [E(X)]²

= σ²/n + μ² ≠  μ²

Then,

X² is not an unbiased estimator for μ²

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When a transversal crosses a pair of parallel lines same side interior angle pair are supplimentary.

What is angle?

Angle is the space between two intersecting lines or surface at or close to the point where they meet.

Sol-We are given that two parallel lines are intersected by  a transversal.

We have to find pair of supplementary angles.

Supplementary angle: Two angles whose sum is equal to 180 degrees are called supplementary angles.

Corresponding angles.

It is not necessary that sum of corresponding angles is always equal to 180 degrees.Therefore, pair of angles are not always supplementary.

Thus  it is true.

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The correct option the value of x is 12, as the sum of the interior angles of the polygon is derived as 900° by using the formula (n - 2)×180°.

In calculating the interior angles of a polygon, we apply the formula (n - 2)×180° where is the number of sides.

The polygon has 7 sides, so n = 7

(n - 2) × 180° = (7 - 2) × 180°

(n - 2) × 180° = 5× 180°

(n - 2) × 180° = 900°

hence, we add all the given interior angles and equate them to 900°

12x-9+10x+5+136+10x+10x+9+133+9x+14 = 900°

51x + 288° = 900°

51x = 900° - 288° {subtract 288° from both sides}

51x = 612

x = 612/51 {divide through by 51}

x = 12

Therefore, the value for x in the interior angles of the polygon with 7sides is 12.

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By the Rational root theorem or the Rational root test, rational roots are defined as the roots of equations of any polynomial consisting of one variable of any power.

Where all the coefficients are integers.

For the solution/root of a polynomial to be rational. Then the root would be rational if and only if the coefficient of the variable with the highest degree is divisible by 'q', and the coefficient independent of the variable or having the variable with degree 0 is divisible by 'p'.

Where p/q makes up the rational roots of the polynomial.

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The p-value to the strength of the case in favor of the null hypothesis is

0.20 → A good chance H0 is correct.

0.05 → A slight chance H0 is true.

0.01 → Very poor chance H0 is true.

0.001→ Extremely poor chance H0 is true.

The p-value lets you know how likely the information you have noticed is to have happened under the invalid speculation if the p-value is underneath your edge of importance (commonly p < 0.05), then, at that point, you can dismiss the null hypothesis, yet this doesn't guarantee to imply that your elective speculation is valid.

P-value is frequently used to advance believability for studies or reports by government offices. For instance, the United States Census Bureau specifies any examination with a p-value more noteworthy than 0.10 should be joined by an explanation that the thing that matters isn't measurably quite the same as zero The Census Bureau likewise has guidelines set up specifying what p-values are acceptable for different distributions

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Answer:

The two percent could be 100% and 400%.

Step-by-step explanation:

This would result in the length being multiplied by 4.

Volunteers drive through a test course with several of the new and old style signs the rate of the one-tailed test shows up the best.

a) This is a one-tailed test, on the grounds that the researchers are attempting to prove that the higher reflectivity will make the signs more visible to drivers. The visibility will be equal to or less than the null hypothesis, while the visibility will be greater in the alternative hypothesis.

b) A type I error is rejecting the null hypothesis when it ought not to be rejected.

c) The failure to reject the null hypothesis when it should be rejected is a type II error.

d) The power of the test is the probability of dismissing the invalid speculation when it is indeed false.

e) When the significance level is decreased, the test's power decreases. The hypothesis test's acceptance region grows as the level of significance is decreased, increasing the probability that the null hypothesis will not be rejected. A Type II error is more likely to occur because the null hypothesis is less likely to be rejected.

f) The test's power will decrease when the sample size is reduced. The acceptance region will grow larger and the probability of rejecting the null hypothesis will decrease with a smaller sample size.

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The required operating time, total expense and receipt are 33hours, $759 and $759 respectively.

How to get hours in operation?

It is time taken by worker or operator to operate particular work.

We have given,

Spend money = $594

Average hourly operating cost = $5.

Average hourly receipt = $23

Let time taking in operation be h,

594 + 5h = 23h

18h = 594

h = 33 hours.

and

Total expense = 23h =$23(33) =$ 759

receipt =594 + 5h = 594 + 5(33) = 594 + 165 =$ 759  

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To eliminate negative exponents the base is inverted by taking its reciprocal, and the exponent then becomes positive.

Given:

Eliminating negative exponents:

Example:

1)  [tex]x^{-5}[/tex]

on reciprocal:

= 1/x^5

eliminated negative

2) [tex]x^{-7}y^{-4}[/tex]

= x^-7*1/y^4

= 1/x^7y^4

Therefore To eliminate negative exponents the base is inverted by taking its reciprocal, and the exponent then becomes positive.

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Using the balance sheet figures at the beginning of the year and the income statement figures at the end of the year.

Hence,  Using the balance sheet figures at the beginning of the year and the income statement figures at the end of the year.

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Yes, 3 cm 4 cm 5 cm can be a scalene triangle. It is obvious that the lengths of each of the triangle's sides varies from one another.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all interior angles, however, is always equal to 180 degrees. The roots and trunks of the brachial plexus and the third segment of the subclavian artery exit the neck through the scalene triangle, also referred to as the interscalene triangle, which is situated laterally at the base of the neck. A triangle with three uneven sides is referred to as a scalene triangle.

Given,

Sides 3cm, 4 cm and 5 cm

The sides of a triangle are 3 cm, 4 cm, 4 cm, and 5 cm in length. It is obvious that the lengths of each of the triangle's sides varies from one another. As a result, the triangle in question is a scalene triangle.

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The maximum rate of change of f at the given point is 0.3678

Rate of change

Rate of change defined as the percentage change in value over a defined period of time, and it represents the momentum of a variable.

Given,

Here we the function  f(x, y) = [tex]xe^{-y}[/tex], (1, 0)

Now, we need to find the the maximum rate of change of f at the given point.

We know that, the average rate of change of f(x) on the interval [a, b] is written as,

=> f(x) = (fb) - f(a)/ b - a

Here the value of a = 1 and b = 0.

So, apply the values on the function to solve it,

f(1,1) = 1e⁻¹

f(1,1) = 1 x 0.3678

f(1,1) = 0.3678

Similarly, the value of f(0,0) is,

=> f(0,0) = 0e⁰

=> f(0,0) = 0 x 1

=> f(0,0) = 0

So, the rate of change is,

=> R = 0 - 0.3687/0-1

=> R = 0.3678.

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The value of mean is 59.8 and the variance of the sampling distribution is 1440.46

Given,

In the question:

The distance X is measured in miles and the sampling distribution of X is given by;

X :-      0        10    50     100

P(X) : - 1 /12    1/6   1/3    5/12

Calculate the mean and variance of this sampling distribution.

Now, According to the question:

The variance of a random variable provides an idea of the dispersion of the random variable with respect to its hope. It is then defined as shown in the image.

Then you first calculate E [x] and E [[tex]x^{2}[/tex]], and then be able to calculate the variance.

E[x] = 0 × 1/12 + 10 × 1/6 + 50 × 1/3 + 100 × 5/12

E[x] = 1.6 + 16.6 + 41.6

Mean/ E[X] = 59.8

So E[X]²= 59.8² = 3576.04

On the other hand

E[[tex]x^{2}[/tex]] = [tex]0^2[/tex] × 1/12 + [tex]10^2[/tex] × 1/6 + [tex]50^2[/tex] × 1/3 + [tex]100^2[/tex] × 5/12

E[[tex]x^{2}[/tex]] = 0 + 16.6 + 833.3 + 4166.6

E[[tex]x^{2}[/tex]]  = 5016.5

Then the variance will be:

Var[x]=  E[[tex]x^{2}[/tex]]  - E[X]²

Var[x] =  5016.5 - 3576.04

Var[x] = 1440.46

Hence, The value of mean is 59.8 and the variance of the sampling distribution is 1440.46

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Answer:

Alexa will run 50 yards.

They will run 150 yards together.

Step-by-step explanation:

Since Crystal is twice the age of Alexa, we can divide 100 yards by 2, and Alexa will only be running 50 yards.

Since Crystal ran 100 yards, and Alexa ran 50 yards:

100 + 50 = 150 yards ran together.

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The value of m + n is 12 where , m is 4 and n is 8

Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots. It was discovered by Francois Vieta. The simplest application of Vieta’s formula is quadratics and are used specifically in algebra.

Rearranging the log

[tex]\frac{8}{\log n \log m}(\log x)^2 - \left(\frac{7}{\log n}+\frac{6}{\log m}\right)\log x - 2013 = 0[/tex]

Using the Vieta's Theorem,

The sum of the possible values of log x is [tex]\frac{\frac{7}{\log n}+\frac{6}{\log m}}{\frac{8}{\log n \log m}} = \frac{7\log m + 6 \log n}{8} = \log \sqrt[8]{m^7n^6}[/tex]

But the sum of the possible values of log x is the logarithm of the product of the possible values of x. Thus the product of the possible values of x is equal to [tex]\sqrt[8]{m^7n^6}[/tex]

It remains to minimize the integer value of [tex]\sqrt[8]{m^7n^6}[/tex].

   Since m, n>1 , we can check that m = 2² and n = 2³.

Hence , m = 4 and n = 8

m + n = 4 + 8

=> 12

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The sample size of the given question is 83  and the t-test value is -0.6578.

Hypotheses:

H0 : Ha:  ц < 7.

Sample mean = 6.5

SD = 1.1

n = 83

ц =7

Null hypothesis:   ц >= 7

Alternative hypothesis:    ц < 7

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by

t = (mean - ц )/ ц \sqrt{n}

t-test is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value.    

t =  -0.5 / 0.76

  = -0.6578

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The only true statement about the quadratic equation is option b:

"The 'a-value' of the function is negative."

We know that the range of a particular quadratic equation is (-∞, 8]

So, our quadratic equation has a maximum, this means that the parabola opens downwards, and has a maximum in the vertex at y = 8.

Because the parabola opens down, we know that the leading coefficient (also called the "a-value") is negative, so the things we know are:

Then the only true statement is B:

"The 'a-value' of the function is negative."

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Jean-Auguste-Dominque Ingres believed history was the best subject for art, a preference that can be seen in his work Jupiter and Thetis

Jean Auguste Dominique Ingres was an early 19th-century painter with a long French name and a very famous teacher. Ingres was taught the art of painting by the great French master Jacques-Louis David. David epitomized the Neoclassical movement in art, which reinvigorated Greek and Roman forms, often in the styles of the Italian Renaissance, an earlier culture to venerate classical civilization.

Jupiter and Thetis is an 1811 painting by  Jean-Auguste-Dominique Ingres, in the Musée Granet, Aix-en-Provence, France. Painted when the artist was yet 31, the work severely and pointedly contrasts the grandeur and might of a cloud-born Olympian male deity against that of a diminutive and half-bare nymph. Ingres' subject matter is borrowed from an episode in Homer's Iliad when the sea nymph Thetis begs Jupiter to intervene and guide the fate of her son Achilles; who was at the time embroiled in the Trojan War, this show how he believed history was the best subject for art.

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