Sam and Amanda are brother and sister. Sam has twice as many brothers as sisters, and Amanda has five times as many brothers as sisters. How many boys and girls are there in this family?

Answer:

d:) 1024

Step-by-step explanation:

Evaluate (4 x^3)^2 where x = 2:

(4 x^3)^2 = (4×2^3)^2

Multiply each exponent in 4×2^3 by 2:

4^2 (2^3)^2

Multiply exponents. (2^3)^2 = 2^(3×2):

2^(3×2)×4^2

4^2 = 16:

2^(3×2)×16

3×2 = 6:

2^6×16

2^6 = (2^3)^2 = (2×2^2)^2:

(2×2^2)^2 16

2^2 = 4:

(2×4)^2 16

2×4 = 8:

8^2×16

8^2 = 64:

64×16

| | 6 | 4

× | | 1 | 6

| 3 | 8 | 4

| 6 | 4 | 0

1 | 0 | 2 | 4:

Answer:  1024

Answer:

L=13.715

Step-by-step explanation:

Given that

x=t + cos t

y= t - sin t

0 ≤ t ≤ 3π

[tex]\dfrac{dx}{dt}=1-sin\ t[/tex]

[tex]\dfrac{dy}{dt}=1-cos\ t[/tex]

We know that length of parametric curve given as

[tex]L=\int_{a}^{b}\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2}dt[/tex]

[tex]\left(\dfrac{dx}{dt}\right)^2=1+sin^2 t-2t\ sint[/tex]

[tex]\left(\dfrac{dy}{dt}\right)^2=1+cos^2 t-2t\ cost[/tex]

Now by putting the values

[tex]L=\int_{0}^{3\pi}\sqrt{3-2sin\ t-2cos\ t}\ dt[/tex]

Now by using calculator

L=13.715

To find the curve length for ( x = t + cos t ) and ( y = t - sin t ) over [tex]\( 0 \le t \le 3\pi \):[/tex]

1. Calculate derivatives:

[tex]\[ \frac{dx}{dt} = 1 - \sin t, \quad \frac{dy}{dt} = 1 - \cos t \][/tex]

2. Set up integral:

 [tex]\[ L = \int_0^{3\pi} \sqrt{(1 - \sin t)^2 + (1 - \cos t)^2} \, dt \][/tex]

3. Simplify integrand:

  [tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]

4. Calculate numerically:

 [tex]\[ L \approx 21.2694 \][/tex]

The curve length is approximately ( 21.2694 ).

To find the length of the curve given by the parametric equations ( x = t + cos t ) and ( y = t - sin t ) for[tex]\( 0 \le t \le 3\pi \)[/tex] , we use the formula for the arc length of a curve defined by parametric equations:

[tex]\[ L = \int_a^b \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt \][/tex]

1. **Find the derivatives of ( x ) and ( y ) with respect to ( t ):**

  For [tex]\( x = t + \cos t \):[/tex]

 [tex]\[ \frac{dx}{dt} = 1 - \sin t \][/tex]

  For[tex]\( y = t - \sin t \):[/tex]

 [tex]\[ \frac{dy}{dt} = 1 - \cos t \][/tex]

2. **Set up the integral for the arc length:**

[tex]\[ L = \int_0^{3\pi} \sqrt{\left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2} \, dt \][/tex]

3. **Simplify the integrand:**

[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 \][/tex]

  Expand both terms:

[tex]\[ \left(1 - \sin t\right)^2 = 1 - 2\sin t + \sin^2 t \][/tex]

  [tex]\[ \left(1 - \cos t\right)^2 = 1 - 2\cos t + \cos^2 t \][/tex]

  Add the expressions together:

[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 = (1 - 2\sin t + \sin^2 t) + (1 - 2\cos t + \cos^2 t) \][/tex]

[tex]\[ = 1 - 2\sin t + \sin^2 t + 1 - 2\cos t + \cos^2 t \][/tex]

  [tex]\[ = 2 - 2\sin t - 2\cos t + \sin^2 t + \cos^2 t \][/tex]

  Recall that[tex]\( \sin^2 t + \cos^2 t = 1 \):[/tex]

[tex]\[ = 2 - 2\sin t - 2\cos t + 1 \][/tex]

[tex]\[ = 3 - 2(\sin t + \cos t) \][/tex]

  So the integrand becomes:

[tex]\[ \sqrt{3 - 2(\sin t + \cos t)} \][/tex]

4. **Set up the integral for the arc length:**

[tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]

5. **Calculate the integral:**

  This integral is complex and generally requires numerical methods or a calculator to evaluate.

  Using a calculator:

[tex]\[ L \approx \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \approx 21.2694 \][/tex]

Thus, the length of the curve, correct to four decimal places, is approximately ( 21.2694 ).

Answer:

  If production is to be maximized, Jerry should build fences and Tom should make dishes.

Step-by-step explanation:

Tom can build more fences per day than Jerry, and Jerry can make more dishes per day than Tom. Each has his special skill, and production will be maximized when that special skill is utilized.

Answer:

  f(x) = -1/3x² -2x

Step-by-step explanation:

For vertex (h, k) and scale factor "a", the vertex form of a quadratic is ...

  y = a(x -h)² +k

For the given vertex, the vertex form function with scale factor "a" is ...

  f(x) = a(x +3)² +3

If that goes through the point (-6, 0), then we have ...

  f(-6) = a(-6 +3)² +3 = 0

  9a = -3 . . . . . . . subtract 3

  a = -1/3 . . . . . . . divide by 9

In standard form, the equation is ...

  f(x) = (-1/3)x² -2x

Answer: x= - 3, y = 7

Step-by-step explanation:

Answer:

1,2,3,4,6,9,12,18,36 Is correct one

Answer:

1, 2, 3, 4, 6, 9, 12, 18, 36

Step-by-step explanation:

Answer:

They're are all correct.

Step-by-step explanation:

I went each of them carefully. They are all correct.

Answer:

x=-y/g

Step-by-step explanation:

m-y=m+gx

m-m-y=gx

-y=gx

x=-y/g

Answer:

Step-by-step explanation:

1) The greatest common factor of 72 and 112 is 8, so the least common multiple is ... 72×112/8 = 1008.

The least common multiple of 72 and 112 is 1008.

__

2) The house number will be a multiple of 1008 between 3000/1008 = 2.98 and 4000/1008 = 3.96. The only integer in that range is 3, so Peter's house number is ...

  3 × 1008 = 3024

Peter's house number is 3024.

Answer: 2 hours

Step-by-step explanation:

Given : Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively.

Let t be the time taken by both of them working together.

Then, according to the question, we have

[tex]\dfrac{1}{t}=\dfrac{1}{3}+\dfrac{1}{6}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{2+1}{6}\ \ [\because\ L.C.M. (3,6)=6]\\\\\Rightarrow\dfrac{1}{t}=\dfrac{3}{6}=\dfrac{1}{2}\\\\\Rightarrow t=2[/tex]

Hence, it will take 2 hours by the two machines .

Answer:

Choice 3 is your answer

Step-by-step explanation:

The format of the function when you move it side to side or up and down is

f(x) = (x - h) + k,

where h is the side to side movement and k is up or down.  The k is easy, since it will be positive if we move the function up and negative if we move the function down from its original position.

The h is a little more difficult, but just remember the standard form of the side to side movement is always (x - h).  If our function has moved 3 units to the left, we fit that movement into our standard form as (x - (-3)), which of course is the same as (x + 3).  Our function has moved up 5 units, so the final translation is

g(x) = f(x + 3) + 5, choice 3 from the top.

Final answer:

Jimmy earned $190 for working on 500 parts. This includes $37.50 for the first 150 parts, $52.50 for the next 150 parts, and $100 for the 200 parts beyond the initial 300.

Explanation:

Jimmy's earnings can be calculated by dividing the parts he worked on into three segments that correspond to different pay rates.

The first 150 parts at $0.25 each.

The next 150 parts (from part 151 to 300) at $0.35 each.

Any parts above 300 at $0.50 each.

So the calculation would be as follows:

First segment: 150 parts × $0.25 = $37.50

Second segment: 150 parts × $0.35 = $52.50

Third segment: 200 parts (500 - 300) × $0.50 = $100.00

Adding these amounts together will give us the total earnings:

$37.50 + $52.50 + $100.00 = $190.00

Therefore, Jimmy earned a total of $190 yesterday.

Answer:

A. simpson's paradox

Step-by-step explanation:

The Simpson's paradox was named after Edward Simpson, the person who described this paradox for the first time in 1951. In this paradox, you find two contrary patterns. For example, a positive and a negative correlation, depending on how data is analyzed. The differences in the analyses are how data are grouped. This paradox is observed often in social researches. Most of the times, results are affected by the sample on each group or additional information related to the data.

Answer:

  4. Functions: 1, 2, 4, 5, 7, 8, 11, 12

  5. y = -1/2x+5/2, x ≤ -1; 2x +1, x > -1.

      y = 2, x < 0; x, 0 ≤ x ≤ 3; 3 x > 3.

Step-by-step explanation:

4. A list of ordered pairs is a function of no x-values are re-used. In (3) and (6), the value x=2 is used more than once.

A graph represents a function if it passes the "vertical line test." A vertical line cannot intersect the graph in 2 or more points. (9) and (10) both fail that test.

If the relation is not listed here as being "not a function," then it is one of the answers to question 4.

__

5. The first step in writing the equation of a piecewise function is to identify the pieces. These are generally bounded by points of discontinuity--jumps in the function value, or changes in the slope of lines.

The second step is to identify the section of the function that boundary points belong to. Solid dots are part of the function definition; open circles are not.

Left Graph

The left piece ends at x=-1. There is a solid dot attached to the left piece, so its definition will be for the domain x ≤ -1. That line has slope -1/2, since is drops 1 unit for each 2 to the right. If extended, it would intersect the y-axis at y = 2 1/2 = 5/2. So, the piece on the left is y = -1/2x + 5/2 for x ≤ -1.

The right piece starts at x=-1, but does not include that point. It has a rise of 2 for each 1 to the right, so its slope is 2. It crosses the y-axis at y=1, so the piece on the right is y = 2x + 1 for x > -1.

You can use the method of your textbook author to combine theses pieces into one equation. The method shown above is one way to do it.

__

Right Graph

This graph has a discontinuity at x=0 and a change in slope at x=3. It can be described by 3 pieces. The point at x=0 does not belong to the left piece, but goes with the middle piece.

The left piece of the function is the constant 2, so has the equation y = 2 for x < 0.

The middle piece has a slope of 1 and a y-intercept of 0, so has the equation y = x for 0 ≤ x ≤ 3.

The point at x=3 belongs to both the middle piece and the right piece, so can be part of both function definitions, if you like. Generally, it is better form to include any given x-value in only one of the pieces of the function. So the equation for the right piece can be y = 3 for x > 3.

Answer:

The answer to your question is: 800.4 km

Step-by-step explanation:

Data:

111 km to east

444 km to north

555 km to east

How far is from her starting position?

See the picture please

To do this problem, we must to find the hypotenuse of a right triangle where one cathetus is 444 km and the other one is the sum of 111 and 555km.

them the pythagorean theorem says c² = a² + b²

                                                              c² = 444² + (111+555)²

                                                               c² = 444² + 666²

                                                                c² = 197136  + 443556

                                                               c² = 640692

                                                                c = 800.4 km

Answer: 7.211

Step-by-step explanation:

TRUST ME, IF IT"S WRONG YOU CAN GIVE ME 1 STAR, IF YOU GET IT RIGHT PLEASE SUBSCRIBE TO ICONIC COOKING, THANK YOU, LUV YOU

Answer:

1.333 is more close to 1.5 than 1.25 .

Step-by-step explanation:

We are given:

You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture.

First divide 6 by 4: we get,

6/4 = 1.5 inches

This is the ratio to achieve.

Now divide 20 by 16

20/16 = 10/8

10/8 = 5/4

5/4 = 1.25 inches

Now divide 24 by 18

24/18 = 12/9

12/9 = 4/3

4/3 = 1.333 inches

1.333 is more close to 1.5 than 1.25 .

Answer:

There are 795 combinations.

Step-by-step explanation:

The number of ways or combinations in which we can select k element from a group of n elements is given by:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

So, if Miriam want to choose 3 movies with at least two comedies, she have two options: Choose 2 comedies and 1 foreign film or choose 3 comedies.

Then, the number of combinations for every case are:

1. Choose 2 Comedies from the 10 and choose 1 foreign film from 15. This is calculated as:

[tex]10C2*15C1=\frac{10!}{2!(10-8)!}*\frac{15}{1!(15-14)!}[/tex]

[tex]10C2*15C1=675[/tex]

2. Choose 3 Comedies from the 10. This is calculated as:

[tex]10C3=\frac{10!}{3!(10-3)!}=120[/tex]

Therefore, there are 795 combinations and it is calculated as:

675 + 120 = 795

Answer:

The probability is 0.9993

Step-by-step explanation:

This situation follows a Binomial distribution in which we have:

So, the probability that x of the n elements are success is given by:

[tex]P(x)=nCx*p^{x}*(1-p)^{n-x}[/tex]

That means that the probability that x adults from the 66 use their smartphone in meeting or classes is:

[tex]P(x)=66Cx*0.52^{x}*(1-0.52)^{66-x}[/tex]

Where 66Cx is calculated as:

[tex]66Cx=\frac{66!}{x!(66-x)!}[/tex]

Then, the probability that at least 22 of them use their smartphone in meeting or classes is:

P = P(22) + P(23) + P(24) +... + P(64) + P(65) + P(66)

Therefore, replacing x for each number from 22 to 66 on the equation of P(x), and making a sum with all the probabilities, we get that:

P = 0.9993

Answer:

You have to replace x for each density

Step-by-step explanation:

Density = Mass / Volumen

1,000 g = 1 kg

1,000,000 cm^3 = 1 m^3

g/cm^3 = 1000 kg/m^3

Using density as x

[tex]volumen \: = \frac{50000}{x} \\ volumen \: sphere \: = 4\pi {r}^{3} \\ 4\pi {r}^{3} = \frac{50000}{x} \\ r = \sqrt[3]{ \frac{50000}{4\pi {x}^{} } } [/tex]

Density can be defined as the mass per unit volume of a given substance.

The formula is given as:

Density = Mass / volume

The radius of the Aluminum sphere is 16.43cm and the radius of the Lead sphere is 10.17 cm

1 kg = 1000g

50kg = ?

Cross Multiply

50kg × 1000g/ 1 kg

= 50,000g

The mass of lead and Aluminum is 50,000g

The density of Aluminum is 2.69 g/cm³.

Mass of Lead is 50,000g

Volume = Mass/ Density

Volume of Aluminum = 50,000g/ 2.69 g/cm³

Volume of Aluminium = 18587.360595 cm³

The Volume of the Aluminum Sphere = 18587.360595 cm³

The formula to find the radius is given as

(3V/4π)[tex]^{1/3}[/tex]

= (3 × 18587.360595/ 4π)[tex]^{1/3}[/tex]

The radius of the lead sphere = 16.43 cm

The density of lead is 11.34 g/cm³.

Mass of Lead is 50,000g

Volume = Mass/ Density

Volume of Lead = 50,000g/ 11.34 g/cm³

Volume of Lead = 4409.1710758 cm³

The Volume of a Lead Sphere = 4409.1710758 cm³

The formula to find the radius is given as

(3V/4π)[tex]^{1/3}[/tex]

= (3 × 4409.1710758/ 4π)[tex]^{1/3}[/tex]

The radius of the lead sphere = 10.17 cm

Therefore, the radius of the Aluminum sphere is 16.43cm and the radius of the Lead sphere is 10.17 cm.

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Answer:

[tex]1.486*10^8[/tex]

[tex]9.118*10^3[/tex]

Step-by-step explanation:

By definition, the form of Scientific notation is:

[tex]a*10^n[/tex]

Where the base is 10, "a" is any number from 1 to 10 but not including 10,  and "n" is an integer.

Therefore to write a number in Scientific notation, the decimal point must be after the first digit and the power "n" must indicate how many places the decimal point is moved.

We know that:

[tex]148.6\ million=148,600,000\ millions[/tex]

Then, we need to move the decimal point 8 places to the left:

[tex]=1.486*10^8[/tex]

To write $9,118 in scientific notation, we need to move the decimal point 3 places to the left:

[tex]=9.118*10^3[/tex]

Answer:7

Step-by-step explanation:

Answer: $61 because you have to do 10 x3 to get 30 then + $1 because $1 is equal to 5 pounds

The inequality to represent the losing bids can be written as:

b < 17000.

The winning bid for Superman's cape from the 1978 movie was $17,000.

To represent the amounts of all the losing bids, we need to write an inequality that indicates bids that are less than $17,000.

Let "b" represent the amount of a bid.

The inequality to represent the losing bids can be written as:

b < 17000

This inequality states that any bid "b" that is less than $17,000 would be a losing bid. The symbol "<" signifies "less than."

So, any bid amount smaller than $17,000 falls into the category of losing bids.

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The inequality representing all losing bids for Superman's cape is b < 17,000, where b is the amount of any losing bid. Bidders must consider auction strategies and valuations to avoid overbidding and the winner's curse.

The question involves creating an inequality to represent the losing bids in an auction where Superman's cape was sold for $17,000. The variable b is introduced to represent the amount of any losing bid. The inequality that represents all the losing bids would be b < 17,000. since any bid that is less than $17,000 would not win the auction.

The Expression  [tex]\((\frac{p^4q}{p^8})^2\)[/tex] simplifies to [tex]\(\frac{1}{p^8}\)[/tex].

The correct option is D.

To simplify the expression (p⁴q/p⁸)², we can simplify the numerator and denominator separately, and then simplify the exponent:

Numerator: p⁴q

Denominator: p⁸

To simplify the numerator, we divide the exponents of p:

[tex]\(p^4q = \frac{p^4}{p^8}\)[/tex]

Now, we can simplify the expression [tex]\((\frac{p^4}{p^8})^2\)[/tex]:

[tex]\((\frac{p^4}{p^8})^2 = \frac{p^4}{p^8} \cdot \frac{p^4}{p^8} = \frac{p^4 \cdot p^4}{p^8 \cdot p^8}\)[/tex]

Simplifying the numerator and denominator further:

[tex]\(\frac{p^4 \cdot p^4}{p^8 \cdot p^8} = \frac{p^{4+4}}{p^{8+8}} = \frac{p^8}{p^{16}}\)[/tex]

Finally, we can simplify the expression to:

[tex]\(\frac{p^8}{p^{16}} = p^{8-16} = p^{-8} = \frac{1}{p^8}\)[/tex]

Therefore, [tex]\((\frac{p^4q}{p^8})^2\)[/tex] simplifies to [tex]\(\frac{1}{p^8}\)[/tex].

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Answer:

1.28 or 128

Step-by-step explanation:

you would take 32 and divide it by.25

Answer:

  x = ±6

Step-by-step explanation:

The left side is the difference of squares, so factors accordingly:

  (2x -12)(2x +12) = 0

The zero factor property tells you the product will be zero when one or more factors is zero.

  2x -12 = 0

  x -6 = 0 . . . . divide by 2

  x = 6 . . . . . . one solution to the equation

__

  2x +12 = 0

  x + 6 = 0 . . . . divide by 2

  x = -6 . . . . . . . the other solution to the equation

Answer:

Multicollinearity

Step-by-step explanation:

There were 100 total students surveyed.

There are 41 freshman students that have an ATM card.

The probability is the number of freshman that have an ATM card over the total number of students.

The probability becomes 41/100

Now divide the fraction to get the decimal answer:

41/100 = 0.410

For this case we have that by definition, the equation of a line in the point-slope form is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

[tex](x_ {0}, y_ {0})[/tex]: It is a point through which the line passes

m: It's the slope

We have according to the graph, that the line goes through:

[tex](x_ {1}, y_ {1}): (- 2, -1)\\(x_ {2}, y_ {2}) :( 2,1)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {1 - (- 1)} {2 - (- 2)} = \frac {1 +1} {2 + 2} = \frac {2} {4} = \frac {1} {2}[/tex]

Thus, the line is of the form:

[tex](y-y_ {0}) = \frac {1} {2} (x-x_ {0})[/tex]

We substitute a point:

[tex](y-1) = \frac {1} {2} (x-2)[/tex]

Answer:

[tex](y-1) = \frac {1} {2} (x-2)[/tex]

Answer:

No.

Step-by-step explanation:

The equation does not match the form of any conic section.

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

Answer:

Step-by-step explanation:

Let's get this in a form we can better recognize.  we'll rearrange it until we have y by itself.

x^2 + xy = 1

xy = 1 - x^2

y = 1/x - x

There, much better.  Now,  just looking at the graph you can tell there's no symmetry along the x or y axis.  If you do not know how to check for symmetry along x=y or origin symmetry let me know.  But checking for those does show that there is no symmetry along y = x but there is origin symmetry.  

To determine that you just make all x and ys negative, and then see if you can get back to the original.  Again, let me know if you don't get determining symmetry through algebra and I'd be happy to explain each of the variations; x ais, y axis, y=x and origin.