Suppose the six people consist of three mar- ried couples and each couple wants to sit together with the older partner on the left. how many ways can the six be seated together in the row?

Answer:

1. 36 liters

2. 3 kg

Step-by-step explanation:

because 12 liters is 4kg if you multiply both by 3 you’ll get that 12 kg is equal to 36 liters

also, if you divide both by 4, you’ll see that 1kg is equal to 3 liters. Then with this knowledge, yiucc be an see that if you multiply both by 3; 3 kg will be 9 liters! :)

Answer:

1.) 36 litres

2.) 3 kg

Step-by-step explanation:

In this case there is a ratio of 1:3 of mass to volume.  If we know the mass, the volume is 3 times that.  If we know the volume, the mass is that divided by 3.

√64 is rational.

Hope this helps :)

❄ Hi there,

let us consider this –

Is [tex]\sqrt{64}[/tex] a rational or irrational number?

Well, to answer that we need to work out [tex]\sqrt{64}[/tex].

And we know that

[tex]\sqrt{64} =8[/tex]

and 8 is a rational number.

That's it!

❄

**Disclaimer** Hi there! I assumed the unit [ mph ] represents miles per hour and [ m/s ] represents meters per second. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer: [tex]\Large\boxed{23~m/s}[/tex]

Step-by-step explanation:

Given information

Speed = 52 mph

Given conversion factors

1 mile ≈ 1609 meters

1 hour = 3600 seconds

Convert the unit from mph to m/s using conversion factors

The basic idea is that you utilize the factors and cancel out unnecessary units

[tex]\dfrac{52~miles}{1~hour} \times\dfrac{1~hour}{3600~seconds} \times\dfrac{1609~meters}{1~miles}[/tex]

Simplify by multiplication

[tex]=\dfrac{52~miles}{3600~Seconds} \times\dfrac{1609~meters}{1~miles}[/tex]

[tex]=\dfrac{52\times 1609~meters}{3600~Seconds}[/tex]

Simplify the fraction

[tex]=\dfrac{83668~meters}{3600~Seconds}[/tex]

[tex]\Large\boxed{\approx23~m/s}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The mistake that the researcher made is that; neither critical nor obtained Chi squares can have negative values

A chi-square statistic is one way to show a relationship between two categorical variables. In statistics, there are two types of variables: numerical (countable) variables and non-numerical (categorical) variables.

The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.

Now, Chi square (χ²) is the sum of a set of squared values, and as such it can never be negative. The minimum chi - squared value would be obtained if each Z = 0 so that χ² would also be 0. There is no upper limit to the χ² value. Similarly, the critical chi square cannot also be negative.

Thus, we can conclude that the mistake that the researcher made is that neither critical nor obtained Chi squares can have negative values

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Using a calculator, the line of best fit for the function is given by:

y = 51.7x - 5.7.

To find the equation, we need to insert the points (x,y) in the calculator. For this problem, a linear regression is used because the data only increases.

From the given table, the points are:

(1, 68), (2,97), (3, 134), (4, 176), (5, 241), (6,335).

Inserting these points on the calculator, the line of best fit for the function is given by:

y = 51.7x - 5.7.

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Answer:

4.25 × 10^-4

Step-by-step explanation:

0.00045-2.5x10^-5

= (4.5 × 10^-4) - (0.25 × 10¹ × 10^-5)

= (4.5 × 10^-4) - (0.25 × 10^{1-5} )

= (4.5 × 10^-4) - (0.25 × 10^-4)

= (4.5 - 0.25) × 10^-4

= 4.25 × 10^-4

Answer:

2

Step-by-step explanation:

just because all three numbers are even

Hope this helps

The greatest common factor of 30, 22, and 8 will be 2.

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.

In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.

For example in 6 and 12 6 is the highest common factor.

The factor of 30 ⇒ 2,3,5

The factor of 22 ⇒ 2,11

The factor of 8 ⇒ 2,4

The only common factor among 30,22 and 8 is 2 so it will be the greatest common factor.

Hence "The greatest common factor of 30, 22, and 8 will be 2".

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The solution for the given differential equation is lnlxl = [tex]\frac{-x}{y} +C[/tex]

Given,

[tex](y^{2} +y^{x} )dx - x^{2} dy =0[/tex]

Here,

x = vy, dx = vdy + ydv

y = ux, dy = udx + xdu

Then,

[tex]((ux)^{2} +(ux)x)dx-x^{2} (udx+xdu)=0\\=u^{2} x^{2} dx+ux^{2} dx-x^{2} udx-x^{3} du=0\\=u^{2} x^{2} dx=x^{3} du\\=\frac{x^{2} }{x^{3} } dx=\frac{1}{u^{2} } du[/tex]

Now,

[tex]\int\limits^a_b {\frac{1}{x} } \, dx =\int\limits^a_b {u^{-2} } \, du[/tex]

l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{u^{-1} }{(-1)} +C[/tex]

l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{-1}{u} +C[/tex]

y = ux

u = [tex]\frac{y}{x}[/tex]

That is l[tex]n[/tex]l[tex]x[/tex]l [tex]=\frac{-x}{y} +C[/tex]

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Adam says that the number 4 has four factors. The above statement is incorrect as 4 only three factors 1,2, and 4.

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Answer:

j = 7.8.

Step-by-step explanation:

The slope of the line = difference in y-values / corresponding difference in x-values.

Slope = (7-3) / (j-5) = 10/7

so 10(j - 5) = 7*4

10j - 50 = 28

10j = 78

j = 7.8.

Answer:

x^2/ 16 + y^2/4 = 1

Step-by-step explanation:

The major axis is 4 and that goes with the x variable.  It is the major axis because 4 is a larger value than 2.

4 x 4 = 16

2 x 2 = 4

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

In this problem we know the coordinates of a vertex, a co-vertex and the center of an ellipse. Based on this information, we find an ellipse whose major axis is parallel to the x-axis. whose formula in standard form is:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

The major semiaxis has a length of 4 units and the minor semiaxis has a length of 2 units. If we know that (h, k) = (0, 0), a = 4 and b = 2, then the equation of the ellipse is:

x² / 16 + y² / 4 = 1

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

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Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.

The surface area of a sphere is simply the total area that covers its outer surface.

The surface area of a sphere is expressed as;

A = 4πr²

Where r is radius and π is pi. ( π = 3.14 )

Given the data in the question;

We substitutes the given values into the equation above.

A = 4πr²

320cm² = 4 × 3.14 × r²

320cm² = 12.56 × r²

r² = 320cm² / 12.56

r² = 25.477707cm²

r = √25.477707cm²

r = 5.05cm

Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.

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Answer:

The radius is 5.05 centimeters.

Hope this helps!

Step-by-step explanation:

Answer:

The slope of line p is 3 and the slope of line q is -3.

The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.

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Answer:

Positive

Step-by-step explanation:

5a < 2a

Divide 2 on both sides

5/2a < a

The list of the possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin goes as follows,

AH, BH, CH, DH, AT, BT, CT, DT

The possible outcomes for spinning a spinner (assuming that the spinner has four sectors, A, B, C, D) are: A, B, C, D  (4 outcomes)

Now, the possible outcomes for flipping a fair coin are: Tales (T) and Heads (H) (2 outcomes)

For each possible outcome of the spinner, there can be two possible outcomes associated, because of the flipping of the fair coin. Hence, the total possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin are 4 × 2, i.e. 8 outcomes.

These possible outcomes are AH, BH, CH, DH, AT, BT, CT, DT.

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Using translation concepts, the expression for h(x) is given as follows:

[tex]h(x) = \sqrt{x + 4} - 1[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent function is:

[tex]f(x) = \sqrt{x}[/tex]

For the translations, we have that:

Then the expression for h(x) is given as follows:

[tex]h(x) = \sqrt{x + 4} - 1[/tex]

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Th find the kicker with the greatest goal success rate, Coach Salinas should:

Statistics refers to the method of collecting data for the purpose of analysis, making of inferences and drawing of conclusions about the data collected.

Statistics usually involve numerical data in large quantities.

Statistical data can be used to make predictions about future events. They are also used to make decisions. For example, the statistical data of soccer players such as games/goal ratio, number of complete dribbles per match, number of successful take-ons, number of tackle or interceptions per game can be used in deciding which soccer player a football team should buy.

In the given scenario, Coach Salinas wants to compare the kicking statistics for kickers on their team in order to find the kicker with the greatest goal success rate.

To do this, Coach Salinas should:

In conclusion, statistical data is important in making decisions.

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Answer:

A and D are the answers.

Step-by-step explanation:

2a is 2 x a

Substitute a =5

2 x 5 =10

Now we have:

10^2-c

Substitute c = 10

(2 - 10 = - 8)

So,it's now 10^ - 8 (10 to the power of - 8)

Ans: 10^ - 8 (or 1 x 10^ -8)

Hope this helps!

The area of the surface is 144.708

The equation of the given surface is,

z=g(x,y)=xy

Solving the partial derivatives,

∂g∂x=y,∂g∂y=x

Substituting to the formula

S=∬√1+( ∂g∂x)2+(∂g∂y)2dA

Thus,

S=∬√1+(y)2+(x)2dAS=∬√1+x2+y2dA

The region in the XY-plane is defined by the intervals  0≤θ≤2π,0≤r≤4

Converting the integral into polar coordinates,

S=∫2π0∫40√1+r2rdrdθ

Integrating with respect to r

S=∫2π0[13(1+r2)32]40dθ

S=∫2π0(17√173−13)dθ

Integrating with respect to θ

S=(17√173−13)[θ]2π0

S≈144.708

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The claim is wrong, or your question is incorrectly entered.

[tex]x=1 \implies f(3) = f(3) + f(1) \implies f(1) = 0[/tex]

[tex]x=3 \implies f(9) = f(3) + f(3) = 2f(3)[/tex]

[tex]x=9 \implies f(27) = f(3) + f(9) = 3 f(3)[/tex]

[tex]x=27 \implies f(81) = f(3) + f(27) = 4f(3)[/tex]

Then

[tex]f(1) - f(3) - f(9) - f(27) = 0 - f(3) - 2f(3) - 3f(3) = -6f(3) \neq 4f(3) = f(81)[/tex]

at least if [tex]f(3)\neq0[/tex].

The area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex]

Given that the grid has squares with side lengths of 1.5 cm.

We are required to find the area of the composite figure.

The area of the composite figure is approximate to the area of the rectangle plus the are of the semicircle at the top of the rectngle plus the semicircle at the right side of the rectangle.

Finding the area of the rectangle.

A=(3*1.5)(4*1.5)=27 [tex]cm^{2}[/tex]

Finding the area of the semicircle at the top of the rectangle.

A=1/2 π[tex](2*1.5)^{2}[/tex]=4.5 π [tex]cm^{2}[/tex]

Finding the area of the semicircle at the right of the rectangle.

A=1/2 π[tex](1.5*1.5)^{2}[/tex]

=2.53π [tex]cm^{2}[/tex]

Total area =27+4.5π+2.53π

=27+7.03π

Use π=3.14

=27+7.03*3.14

=49.1 [tex]cm^{2}[/tex]

Hence the area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex].

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the number of gallons that must be applied is 94 gallons.

Density is simply defined as the ratio of the mass to the volume occupied by an object or substance.

It is denoted with rho, 'ρ'

The formula for density is given as;

Density = mass/ volume

From the information given, we have that

To determine the volume, we need to make it the subject from the formula

Volume = density × mass

Volume = [tex]\frac{9. 4}{100}[/tex]

Volume = 0. 094

The number of gallons is given as;

= Volume × 1000

= 0. 094 × 1000

= 94 gallons

Thus, the number of gallons that must be applied is 94 gallons.

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Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

The answer to why Lynn wants to wait would be:

Therefore, Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

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The complete question is shown below:

Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. Lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might Lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?

a. Using a credit would cause the store to lose money because even if she pays back her bill in full, she will still need to pay the credit card company additional dollars for the convenience of borrowing money.

b. Using cash would cause the store to lose a large amount of money because credit card companies offer incentives to stores based on the number of people who use their cards.

c. She might forget to pay the credit card bill, which would make her purchase more expensive due to interest payments and late charges.

d. She would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

Recall the power series expansions of [tex]\sin(x)[/tex] and [tex]e^x[/tex].

[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1}[/tex]

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{1}{n!} x^n[/tex]

By substituting [tex]3x[/tex] for [tex]x[/tex] in the latter series, we have

[tex]\displaystyle e^{3x} = \sum_{n=0}^\infty \frac{1}{n!} (3x)^n = \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

Then the series expansion of [tex]f(x)[/tex] is

[tex]\displaystyle f(x) = x^3 \sin(x) + e^{3x+2} \\\\ ~~~~~~~~ = x^3 \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2(n+2)} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.

In the question the given function is,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

We know that series representation of sin x and eˣ are:

   ⇒ [tex]e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]

             = [tex]\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Substituting the series representation in the function we get,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

⇒ [tex]f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Hence [tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]  is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².

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Answer:

Step-by-step explanation:

7/3=7:

what will seven over three equals seven divide be

7/3 is a division (7:3)

so

your answer is :

3

(7/3=7:3)

Answer:

NONE of these statements are true

[tex] \frac{d}{dx} (f(x).g(x)) = f'(x).g(x) + g'(x).f(x)[/tex]

[tex] \frac{d}{dx} ( \sqrt{x {}^{2} + x} ) {}^{2} = \frac{2x + 1}{2 (\sqrt{x {}^{2} + x}) {}^{2} } = \frac{2(2x + 1)(x {}^{2} + x) }{2|x²+x|} = \frac{(2x + 1)(x { }^{2} +x)}{|x²+x|} [/tex]

[tex] \frac{d}{dx} ( \sqrt{f(x)} ) = \frac{f'(x)}{2 \sqrt{f(x)} } [/tex]

Answer:

supposed to make the subject y then slope is -2

Step-by-step explanation:

the inner WU arc angle is 23x - 5.

the outer WU arc angle is 37x + 5.

together they must be 360°, as this is the full circle.

so, we have

360 = 23x - 5 + 37x + 5 = 60x

x = 6

therefore, the angle at V is

V = 5x + 17 = 5×6 + 17 = 30 + 17 = 47°

inner WU arc angle = 23x - 5 = 133°

outer WU arc angle = 37x + 5 = 227°

this also fits with

V = (outer arc angle - inner arc angle)/2 =

= (227 - 133)/2 = 94/2 = 47°

Answer:

40° to the left and 3/2 units down

Step-by-step explanation:

See attached image.