Quadratic equations from algebraic fractions:
Solve
2/x + 5/(x+2) = 1
Leave your answer in surd form.

Therefore ,we reject the null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0

The square root of the variance is used to calculate the standard deviation, a statistic that gauges a dataset's dispersion from its mean. The standard deviation, which is proportional to the square root of variance, is calculated by comparing the variance of each data point to its mean.

Here,

The null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0

Alternate hypothesis , [tex]H_{A}[/tex]= [tex]u_{d}[/tex] ≥ 0

thus,

[tex]d^{'}[/tex]=(14 + 11 + 7 + 11 -2 + 5 + 0 +5)/9

[tex]d^{'}[/tex]=4.44

[tex]S_{d}[/tex]=6.747

t=[tex]\frac{d^{'}-D}{\frac{S_{d}}{\sqrt{n} } }[/tex]

Putting values in above equation

[tex]d_{f}[/tex]=9-1=8

α=0.10 => t(0.1,8)

t=[tex]\frac{d^{'}-D}{\frac{S_{d}}{\sqrt{n} } }[/tex] = 1.397

Therefore ,we reject the null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0

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Therefore the mean number of sample of 40 households results in 102 television sets is 2.55 & the probability of that the sample mean is 2.55 or higher is 0.412

The likelihood of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these situations, we state that there is a likelihood that the event will occur or not.

Here,

Given:

mean number of tv sets (n)= 2.24

standard deviation ([tex]{S_d} }[/tex]) = 1.38

sample of 40 households results in 102 television sets so ,

mean number (n') = 102/40 =2.55

its mean number =2.55

the probability that the sample mean is 2.55 or higher

=> Z = [tex]\frac{n^{'}-n }{S_d} }[/tex]

=> Z =(2.55-2.24)/1.38

=>Z = 0.2246

the normal distribution of probability =

P=[tex]\frac{1 *e^{\frac{-1}{2}Z^{2} } }{\alpha \sqrt{2\pi } }[/tex]

P=0.588

therefore P(x<2.55)=0.588

=>P(2.55< x)= 1-0.588=0.412

Therefore the probability of that the sample mean is 2.55 or higher is 0.412

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The temperature at 6 pm is given as follows:

-40.2 ºF.

To obtain the temperature at 6 pm, we keep looking at the temperature for each interval given in the problem.

At 9 am, the temperature is given as follows:

-10.2ºF.

Between 9am and noon, the temperature rose 1.9°F, hence the temperature at noon is given as follows:

-10.2 + 1.9 = -8.3ºF.

Between noon and 3pm, the temperature dropped 16.4°F, hence the temperature at 3 pm is given as follows:

-8.3 - 16.4 = -24.7ºF.

Between 3pm and 6pm, the temperature dropped 15.5°F, hence the temperature at 6 pm is given as follows:

-24.7 - 15.5 = -40.2 ºF.

(subtracting the decline from the previous temperature, as we did for previous intervals).

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Answer:   (4b, -3a)

Reason:

When reflecting over the line y = x, we swap the positions of the x and y coordinates.

The reflection rule is [tex](\text{x},\text{y}) \to (\text{y},\text{x})[/tex]

As an example: [tex](2,3) \to (3,2)[/tex]

The solution to the inequality 4x + 10 < 6 is x < -1.

Given the inequality;

4x + 10 < 6

Solve for x.

Move all terms not containing x to the right side of the inequality by subtracting 10 from both sides of the inequality.

4x + 10 < 6

4x + 10 - 10 < 6 - 10

4x < 6 - 10

Subtract 10 from 6

4x < -4

Divide each term by 4 and simplify

4x < -4

4x/4 < -4/4

Simplify the left-hand side

x < -4/4

Simplify the right-hand side

x < -1

The result in inequality form is x < -1.

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The percentage change of the first quantity with reference to the second quantity: 480 units, 560 units is: -14.29%.

First step is to find the difference between the two numbers

Difference = New Number - Original Number

Difference =  480 -560

Decrease  = -80

Now let find the percentage change

Percentage change = Decrease  / Original Number × 100

Percentage change = -80 /560 × 100

Percentage change = -14.29%

Therefore we can conclude that the percentage change is -14.29%.

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The time that it will take for the shadow to travel 1150 miles is; 30 minutes

Let y represent the distance in miles    

Let x represent the time in minutes

The shadow travels 2300 miles in 1 hour or 60 minutes and in the first 20 minutes the shadow traveled 766 ²/₃ miles or 2300/3 miles

Thus, the coordinates are;

(60, 2300) and (20,  2300/3)

The slope is;

m = (2300 - 2300/3)/(60 - 20)

m = 115/3 mi/min

Thus, the linear equation in point slope form is;

y - 2300 = (115/3)(x - 60)

This gives;

y = (115/3)x

When y = 1150 miles, we have;

1150 = (115/3)x

x = 30 minutes

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The solution of the inequality 9x + 6  ≥  132 and -7x + 19 < -128 is x ≥ 14 and x > 21.

Compound inequalities are a type of inequality that has two or more parts.

In other words, a compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality as follows:

9x + 6 ≥ 132 and -7x + 19 < -128

Let's solve them independently.

9x + 6 ≥ 132

subtract 6 from both sides of the inequality

9x + 6 ≥ 132

9x + 6 - 6 ≥ 132 - 6

9x ≥ 126

divide both sides by 9

x ≥ 126 / 9

x ≥ 14

-7x + 19 < -128

subtract 19 from both sides of the inequality

-7x + 19 - 19 < - 128 - 19

-7x < - 147

divide both sides by - 7

x > - 147 / -7

x > 21

Therefore, the solution is  x > 21 and x ≥ 14

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The flux = 0

According to the divergence theorem, the volume integral of the divergence of a vector point function "F" taken over the volume "V" encompassed by the surface "S" is equal to the surface integral of the normal component of F taken over the closed surface "S." As a result, the divergence theorem is symbolically represented as:∬ v ∫ ▽ F → .

The sphere is presumably closed, so we can use the divergence theorem.

▽ F  =d(xy)/dx + d(yz)/dy + d(zx)/dz

▽ F =x + y + z

Now convert to spherical coordinates:

x=ρsinφcosθ,

y=ρsinφsinθ,

z=ρcosφ

The flux is then given by the volume integral for the radius 6

[tex]\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} = 36 }[/tex]   f.ds = [tex]\int\limits\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} < =36 }[/tex] (x+y+z) dv

Thus the flux = 0

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Option D (No, as there are two heights associated with the wrist circumference of 16 cm.

An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph.

The wrist circumferences and heights of six kids in Alyssa's class are represented by a collection of points in the graph that is shown.

The height is represented by the y axis, and the wrist circumference by the x axis.

Any relation is referred to as a function if there is only one value of y for any given value of x. The graph is referred to as a function if it passes the vertical line test, which requires that a vertical line be drawn and only touch the graph once.

There are two y values (162 and 165) on the above graph for the x value of x=16.

The graph is not a function as a result.

Among the possibilities The correct response is option D, "No," since the wrist circumference of 16 cm pairs with two heights.

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Answer: C: 4.9

The original answer is 4.8989, so I rounded 8 to the nearest hundredth and got the answer of 4.9. Having a Mathematics calculator also helps with math like this.

Answer:

= 3/32

Step-by-step explanation:

What is 11/32 - 2/8?

11/32 - 8/32 = 3/32

Answer: 1134 m^2

Step-by-step explanation:

First, you would plug in "9" to replace the variable. It would be 7(9) and 4(9). Parenthesis means multiplication.

Then, you would multiply. 7 x 9 = 63, 4 x 9 = 36

The area of a triangle is bh/2. So, 63x36=2268, 2268/2=1134.

I believe the answer is 1134 m^2.

504 ways are there to line up all of the tas such that each tas with recitation partner(s) is standing next to them

Given :

cs 2050 has 9 recitation sections. 6 of the recitation sections are led by a pair of tas, and 3 recitation sections are led by a trio of tas. there are also 5 tas who do not teach recitation.

Number of ways = 9P6 * 9C3 * 1 / 5!

= 9! / ( 9 - 6 ) ! * 9! / ( 9 - 3 ) ! * 1 / 5!

= 9! / 3! * 9! / 6! * 1/5!

= 9 * 8 * 7 * 6 / 3 * 2 * 9 * 8 * 7

= 9 * 8 * 7

= 504 ways

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Answer:

3 years

Step-by-step explanation:

Let x = number of years, and let y = height at x years.

Lawson:

Initial height: 14

Annual growth: 3

equation: y = 3x + 14

Ezra:

Initial height: 8

Annual growth: 5

equation: y = 5x + 8

We want to know the number of years, x, when the heights are equal.

y = y

3x + 14 = 5x + 8

-2x = -6

x = 3

The value of the test statistic is  0.711, for the    test at the 5% level of significance that the population variances differ in a random sample  of 20 patients.

Since the information given to us is from a random sample of 20 patients who visited a clinic at medical center 1, a researcher found that the variance of the waiting time (in minutes) was 128.0. in a random sample of 15 patients in the clinic of medical center 2, the researcher found the variance to be 178.8, and tested at the 5% level of significance that the population variances differ. The test statistic for this problem is calculated using the F-test. The formula for the F-test is:

F-test = (variance of sample 1) / (variance of sample 2).  Therefore, the test statistic for this problem is F-test = 128.0 / 178.8 = 0.711.  

To determine the p-value, we need to look up the F-distribution with (df1 = 20-1 = 19, df2 = 15-1 = 14) at a significance level of 5

%. The p-value is 0.347.  Therefore, at a 5% level of significance, the test statistic is 0.711 and the p-value is 0.347. We cannot reject the null hypothesis that the population variances are equal.

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Answer:

Below

Step-by-step explanation:

There are three ATOMS in each MOLECULE H2 O    

                                   (two hydrogen one Oxygen)

Each mole of MOLECULES = 6.022 x 10^23

     6.022 X 10^23     X 3  = 1.81 x 10^24 atoms

The probability that her first flight was delayed exists 0.975.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

Let event that First flight on time be denoted as OT and event that a flight exists delayed be D;

P(OT) = 0.15 and P(D) = 1 - P(OT) = 1 - 0.15 = 0.85

Let event that Luggage will make connecting flight be L and that it won't make it be L',

Given that there is a 0.95 chance that luggage will arrive on time, this is a conditional probability and can be expressed as follows:

P(L/OT) = 0.95 and also P(L/D) = 0.65

From this P(L'/OT) = 1 - P(L/OT) = 1 - 0.95 = 0.05

and P(L'/D) = 1 - P(L/D) = 1 - 0.65 = 0.35

The question is asking for the probability that the first flight was delayed (D) provided that her Luggage was not there (L').

Let the equation of conditional probability be;

P(D/L') = P( D and L')/ P(L')

P(D and L') = P(D) × P(L'/D) = 0.85 × 0.35 = 0.2975

P(L') = P(OT) × P(L'/OT) + P(D) × P(L'/D)

     = 0.15(0.05) + 0.85(0.35)

     = 0.305

P(L/OT) = 0.297/0.305

             = 0.975

Therefore, the probability that her first flight was delayed is 0.975.

The complete question is:

Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight is on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65.

Question: Suppose you pick up Leah in Denver and her luggage is not there.

What is the probability that her first flight was delayed?

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Answer:

There is no solution

Step-by-step explanation:

x - 4y = 15

3x -12y = 12

Times the first equation by -3

-3x +12y = -45

3x - 12y = 12

0 = -33

So, there is no solution.

The exponential growth of three sections is given below.

Exponential growth means whose growth more rapid in proportion.

An exponential function is of the form , where b is a positive number not equal to 1.

The value of b determines whether tha function is an exponential growth or an exponential decay.

An exponential function is an exponential growth if b > 1 and an exponential decay if b <1.

Given the function= y 4(5/6)^x

B= 5/6 < 1

Therefore, the function  is an exponential decay.

Given the function

Therefore, the function  is an exponential growth.

Therefore, the function  is an exponential growth is y= 129(1.63)^x is an exponential growth.

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Any expression that contains the square root of a number is a radical expression it was in my DoNow but I got this wrong so my teacher told me it was this .

Answer:

10 kg is indeed the answer as given by Dr. Mani. Let us see how that comes. 30 kg minus 26 kg = 1/5 of water. So, weight of water = 5 times 4 = 20 kg.

Step-by-step explanation:

Answer:

if it filled 25 kg it the one qurter will be 9

Step-by-step explanation:

because to know the weight when it is filled =(25-5)=20kg .

now,

the first quarter =20÷4+4=9kg

The perimeter of the isosceles  triangle with side lengths 3·x, (4·x - 7), and (1/2·x + 9) is 51[tex]\frac{1}{14}[/tex]

An isosceles triangle is a triangle that has a pair of congruent sides and according to the triangle inequality theorem, a pair of congruent angles.

The lengths of the sides of the isosceles triangle are;

3·x, 4·x - 7, and 1/2·x + 9

Let the sides, 3·x and 4·x - 7 represent the congruent sides of the triangle, we get;

3·x = 4·x - 7

4·x - 3·x = x = 7

x = 7

The length of the sides of the triangle, found by plugging in x = 7 in the specified expressions for the lengths of the sides of the triangle are therefore;

Length of the first side; 3·x = 3 × 7 = 21

The length of the second specified side; 4·x - 7 = 4 × 7 - 7 = 21

Length of the third specified side; (1/2×x) + 9 = (1/(2 × 7)) + 9 = 1/14 + 9

The perimeter of the triangle is the sum of the lengths of the sides of the triangle, therefore;

The perimeter of the triangle is; 21 + 21 + 1/14 + 9 = 51 [tex]\frac{1}{14}[/tex]

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The power or pow() function achieves the same result as the operator "^" in mathematics.

The power of an integer is calculated using the pow() function. The power raised to the base number is returned by the pow() function, which takes two parameters (the base value and the power value). This is denoted by "^".  This function in computer programming helps to determine the value of an integer raised to a certain power.  This is written as,

pow = power = ^ (Power operator)

In mathematics, it also helps to calculate the number raised to power.  For instance, 3^2 = 3²=9. The blank can be filled with the pow() function.

The complete question is -

The ________ function does the same thing as using the mathematical ^ operator.

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The independent variables, the ones that are intentionally manipulated, are temperature and surface time.

The dependent variable, the one that you measure the response in, is the reaction time.

The physical concept of temperature indicates in the numerical form how hot or cold something is. Temperature is measured with a thermometer.

Thermometers are calibrated in numerous temperature scales that historically have depended on various reference factors and thermometric materials for definition. The most common scales are the Celsius scale with the unit image °C (previously referred to as centigrade), the Fahrenheit scale (°F), and the Kelvin scale (okay), the latter being used predominantly for clinical functions. The kelvin is one of the seven base units within the worldwide machine of gadgets (SI).

Absolute zero, i.e. 0 kelvin or −273.15 °C, is the bottom factor within the thermodynamic temperature scale. Experimentally, it can be approached simplest very intently, however, no longer genuinely reached, as diagnosed in the 0.33 law of thermodynamics. it'd be not possible to extract power as the warmth from a body at that temperature.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

so the longest leg of the larger triangle will be "z" and the shorter leg of it will be "y", so let's find those fellows using proportions

[tex]\cfrac{x}{16}=\cfrac{9}{x}\implies x^2=144\implies x=\sqrt{144}\implies \boxed{x=12} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{x}=\cfrac{25}{16}\implies \cfrac{y}{12}=\cfrac{25}{16}\implies y=\cfrac{(12)(25)}{16}\implies \boxed{y=\cfrac{75}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{z}=\cfrac{9}{x}\implies \cfrac{~~ \frac{75 }{4 } ~~}{z}=\cfrac{9}{12}\implies \cfrac{75}{4z}=\cfrac{3}{4}\implies 300=12z \\\\\\ \cfrac{300}{12}=z\implies \boxed{25=z}[/tex]

Closure is one of the Gestalt principles of grouping which states that elements are perceived as being grouped together if they are near each other and form a closure.

Proximity is another Gestalt principle of grouping which states that elements that are close together are perceived as being related. In the illustration below, the three squares appear to be grouped together because of their proximity to each other.

Continuity is another Gestalt principle of grouping which states that elements are perceived as being grouped together if they are arranged in a continuous line or curve. In the illustration below, the three triangles appear to be grouped together because they are arranged in a continuous line.

Illusory contours is another Gestalt principle of grouping which states that elements are perceived as being grouped together if they create an illusion of a contour or shape.

Similarity is another Gestalt principle of grouping which states that elements are perceived as being related if they have similar characteristics or features. In the illustration below, the two triangles appear to be grouped together because they are the same color and size.

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The median number of telephone line in thousands is 0

The number of telephone lines in each country = 250000

From the given dot plot

The data set will be

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250, 250, 250, 250, 250, 500, 750, 750, 1000, 1000, 1250, 1750

The median of the data set is the middle term of the ordered data set. The order of the data set maybe ascending or descending order

There are 28 terms in the data set the middle terms will be 14th and 15th

Both 4th and 15 terms are 0

Therefore, the median is 0

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If a caterer made a sandwich 6feet 6inches long for a party and 3 feet 8 inches added to the sandwich The total length of the sandwich is 122 inches

The height of the sandwich = 6 feet 6 inches

Convert to the inches

We know 1 feet = 12 inches

6 feet 6 inches = 6 × 12 + 6

= 72 + 6

= 78 inches

The height added to sandwich = 3 feet 8 inches

Convert to inches

3 feet 8 inches = 3 × 12 + 8

= 36 + 8

= 44 inches

The new height of the sandwich = 78 + 44

= 122

Therefore, the final height of the sandwich is 122 inches

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