a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). find the dimensions of a norman window of maximum area if the total perimeter is 14 feet.

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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Triangle ABC is congruent to ADC.

Two triangles are congruent if all of their corresponding parts are congruent. This means that congruent triangles will have three pairs of congruent sides and three pairs of congruent angles.

Given information,

AB = AD

BC = CD

and

AB = AD

CB = CD

also

AC = AC (common sides)

Hence triangles ABC and ADC are congruent to each other.

Congruence in two or more triangles depends on the measurements of their sodes and angles. The three sides of a triangle determine its size and the three angles of a triangle determine its shape. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.  

Given question is incomplete.

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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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For the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given that, P equals atmospheric pressure (atm), V equals liters of volume (L), n equals the number of moles, R is the gas constant (0.0821 Latm/(molK)), and T equals Kelvins of temperature (K).

Take into account the following circumstances: a 3,500 mL tank containing 27 moles of argon gas was pressurized to 12 atm.

The ideal gas equation is,

PV=nRT

There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

Thus, for the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.

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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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The cheetah traveled 15.334 miles approximately.

SOLUTION:

Given, Suppose the cheetah sprinted at maximum speed for 8 minutes

Then, slowed to 40mph the next 8 minutes  

We have to find how far would the cheetah have traveled

Now, we know that, maximum speed of cheetah is 68 – 75 mph, as we want maximum we are taking 75 which greater than 68.

So, cheetah sprinted at 75 mph for 8 minutes and then sprinted at 40 mph for next 8 minutes.

First let us convert 8 minutes into hours,

Total distance traveled = distance traveled with 75 mph speed + distance traveled with 40 mph speed

Hence, the cheetah traveled 15.334 miles approximately

Answer:

Step-by-step explanation:

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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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 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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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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Answer:

Step-by-step explanation

33

The equation of the line in slope-intercept form is: y = 1/4x + 5.

To write the equation of a line in slope-intercept form, first, find the slope of the line using two points on the graph.

Slope (m) = change in y / change in x = 1/4

m = 1/4.

The y-intercept is the point where the line intercepts the y-axis, which is at 5. Therefore, the y-intercept is b = 5.

To write the equation of the line in slope-intercept form, substitute m = 1/4 and b = 5 into y = mx + b:

y = 1/4x + 5.

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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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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 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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You're correct answer would be $14.

[tex]35/20 = 1.75[/tex]

[tex]8x1.75=14[/tex]

Answer:

14

Given:

[tex]20 books= 35[/tex]

Step-by-step explanation:

[tex]35/20=1.75[/tex]

[tex]8*1.75= 14[/tex]

The value of this golden ratio = 1/2 (1 + √5) = 1.618

Ratio:

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.

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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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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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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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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

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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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]

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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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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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 total area of all four walls is 150sq.m

What do you mean by surface area?

A solid object's surface area is a measurement of the total area that the surface of the object takes up. In mathematics, the area of a plane region or plane area refers to the area of a shape or planar lamina, whereas the area of a surface or the boundary of a three-dimensional object is referred to as the surface area.

Solution Explained:

Given in question,

Base floor area = 25sq.ft

Height = 6ft

So, the total area of all four walls is,

= Area of base X Height

= 25 X 6

= 150 sq.m

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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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Answer:

The answer to the second question is B

Step-by-step explanation:

Cosine is a trigonometric function that is the ratio between the side next to an acute angle in a right triangle and the hypotenuse.