Simon is factoring the polynomial. x2−4x−12 (x−6)(x+______) What value should Simon write on the line? −6 −2 2 6

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:

The answer to your question is: 99 m²

Step-by-step explanation:

Data

height = 11 m

area of the square base = 9 m²

Formula

Volume of a right rectangular prism = area of the base x height

                                                           = 11 x 9     substitution

                                                           = 99 m²

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

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:

At most 5 -->  x ≤ 5

Larger than 5 -->  x > 5

Below 5 -->  x < 5

Not less than 5 -->  x ≥ 5

Step-by-step explanation:

I learned how to figure this out like this: "The smaller number eats the bigger one", since the symbols "<" and ">" looks like an open mouth.

The symbols "≥" and "≤" mean that it is larger or equal to the number shown.

In the first case, it means that the number that represents "x" could be any up to the number 5 (including it). And in the last case, it means that the number that represents "x", could be any starting from 5(including it).

Answer:

a. When two variables change in the same direction, one remaining larger than the other by the same factor - direct relationship

b. To insert between neighboring points or estimate by taking an average of known values - interpolate

c. A relationship between two variables in which the product remains constant. When one variable increases the other decreases in proportion so that the product is unchanged - inverse relationship

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.

Let [tex]\mu[/tex] be the population mean.

Null hypothesis : [tex]\mu=12[/tex]

Alternative hypothesis : [tex]\mu<12[/tex]

Since Alternative hypothesis is left tailed so , the test is a left tailed test.

Given : n=33 > 30 , so we use z-test.

Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

i.e. [tex]z=\dfrac{11.2-12}{\dfrac{1.6}{\sqrt{33}}}\approx-2.87[/tex]

Using z-value table,

P-value for left tailed test =[tex]P(z<-2.87)=0.0020524[/tex]

Since , the p-value (0.0020524) is less than the 0.05 level of significance, it means we reject the null hypothesis.

Therefore, we have enough evidence to support the claim that the mean completion time has decreased under new management.

Answer:

The answer to your question is: 3) between 12 and 13

Step-by-step explanation:

Just get the square root of 151, and compare your result with the options.

√ 151 = 12.28

Then, the only possibility is (3) 12 and 13.

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 is below

Step-by-step explanation:

1. y = 3x                is a linear function because it doesn't have any power

2. y =- 2+5x          is a linear function because it doesn't have any power

3. 2x + y= 10          is a linear function because it doesn't have any power

4. f(x) = 4x^2         it isn't a linear function because x is elevated to a power

5. -3/x + y = 15      is a linear function because it doesn't have any power

6. x + y + 8            is a linear function because it doesn't have any power

The first, second, third and sixth functions are linear functions, as they comply with the standard linear function format, y = mx + c. The fourth and fifth functions are not linear because they do not follow this standard format.

A linear function is a function whose graph is a straight line. The general form of a linear function is y = mx + c, where m is the slope of the line, and c is the y-intercept.

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60 ≥ 35 + 5t

-35 -35

25 ≥ 5t

5 5

t≤5

his mistake was that he used ≤ for at least instead of using ≥. so at end, when I solved, I saw that Sven should spend 5 minutes or less on each scale.

Answer:

A

Step-by-step explanation:

A: The possibility of promoting child labor is a concern about globalization

Answer:

The answer to your question is:

length = 12

width = 6

Step-by-step explanation:

Perimeter of a parallelogram = 2 length + 2 width

We know that width = length - 6

So

          60 = 2 length + 2(length -6)

          60 = 2 length + 2 length - 12

           60 - 12 = 4 length

           48 = 4 length

         length = 48/4 = 12 meters

         width = length - 12

                    = 12 - 6

                     = 6

Answer:

12

6

Step-by-step explanation:

Answer:

The equation that models this problem is w(4 + w) = 12

Step-by-step explanation:

we know that

The area of a rectangle is

[tex]A=LW[/tex]

we have

[tex]A=12\ in^2[/tex]

so

[tex]12=LW[/tex] -----> equation A

[tex]L=W+4[/tex] ----> equation B

substitute equation B in equation A and solve for W

[tex]12=(W+4)W[/tex]

therefore

The equation that models this problem is w(4 + w) = 12

Answer:

The answer is w(4+w)=12

Step-by-step explanation:

Answer:

The answer is 9.10, ($9.10).

Step-by-step explanation:

Oh just to let you know that other answer (joke) was such a loser joke.

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:

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:

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.

Answer:

16.197 seconds

Step-by-step explanation:

the time and the final place fot both cars is the same.

for the Boxster we have

X = Vboxster . T

being

X the distancance from the initial place of the Boxter to the meeting point

Vboxster the speed of the Boxster (26m/s)

T the time

and for the Scion

X = Xo + Vscion . T

Being

Xo the initial point of the Scion (115m)

X the distancance from the initial place of the Boxster to the meeting point

Vscion the speed of the Scion (18.9 m/s)

T the time

                 Xo + Vscion . T  = Vboxster . T

                                    Xo   = Vboxster . T - Vscion . T

                                   Xo   = (Vboxster  - Vscion) . T

Xo/(Vboxster  - Vscion)   =  T

    115m/ (26-18.9) m.s-1 = T

                          16.197 s = T

Answer:

a)t = 16.2s  : time it takes for the Boxster to catch the Scion

b)The displacement of the Boxster (db) is 115 m more than the displacement of the Scion(ds)

db =ds+115

Step-by-step explanation:

Conceptual analysis

We apply the formula for constant speed movement:

v= d/t Formula (1)

v = speed in m/s

d: distance in m

t: time in s

Problem development

The time of Scion (ts) is equal time of Boxster (tb)

t (s) =tb=t

The displacement of the Boxster is 115 m more than the displacement of the Scion

db =ds+115

we apply formula (1 )car kinematics  :

Scion kinematics

18.9=ds/t

t =ds /18.9 Equation (1)

Boxster kinematics

26=db/t

26=(ds+115)/t

t=(ds+115)/26 Equation (2)

Equation (1) = Equation (2)

ds /18.9 =(ds+115)/26

18.9(ds+115)= 26 ds

18.9ds+18.9*115=26 ds

2173.5= 26 ds-18.9ds

2173.5=7.1ds

ds =2173.5÷7.1

ds=306.12m

We replace ds=306.12m in the equation (1)

t =306.12÷18.9

t = 16.2s

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:

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: Jill got the larger smoothie and its volume is 1609.14 cubic cm.

Step-by-step explanation:

Since we have given that

Jill purchased the cylindrical container.

Height of container = 8 cm

Radius = 8 cm

So, volume of cylindrical container would be

[tex]\pi r^2h\\\\=\dfrac{22}{7}\times 8\times 8\times 8\\\\=1609.14\ cm^3[/tex]

Marcy purchased the rectangular container.

Height of container = 8 cm

Width = 8 cm

Length = 8 cm

so, volume of rectangular container would be

[tex]l\times b\times h\\\\=8\times 8\times 8\\\\=512\ cm^3[/tex]

Hence, Jill got the larger smoothie and its volume is 1609.14 cubic cm.

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:

[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:

a) 4.9 % of all parts is defective or 0.049 of the total parts.

b)  0.5102 is the probability that the defective part was supplied by S1

Step-by-step explanation:

N is the total number of parts from supplier S1, S2 and S3.

N1 = 0.5*N is the total number of part supplied by S1

N2 = 0.2*N is the total number of part supplied by S2  

N3 = 0.3*N is the total number of part supplied by S3

a) if Nd1 is the number of defective parts from supplier S1, Nd2 is the number of defective parts from supplier S2 and Nd3 is the number of defective parts from supplier S3, the the total defective parts Nd is:

Nd = Nd1 + Nd2 + Nd3, where

Nd1 = 0.05*N1 = 0.05*0.5*N = 0.025*N,

Nd2 = 0.03*N2 = 0.03*0.2*N = 0.006*N,

Nd3 = 0.06*N3 = 0.06*0.3*N = 0.018*N,

Then Nd = Nd1 + Nd2 + Nd3 =  0.049*N, so Nd/N = 0.049

b) [tex]P(S1 \vert d) = \frac{P(S1,d)}{P(d)} = \frac{P(d \vert S1)}{P(d)} = \frac{0.05*0.5}{0.049} \approx 0.5102[/tex]

for the last expression I used the Bayes tehorem.

[tex]P(S1 \vert d)[/tex] is the probability that occur S1 given that d (defective) is true. This a conditional probability.

see at https://en.wikipedia.org/wiki/Bayes%27_theorem

The overall defect portion from all suppliers is 4.9%. If a part is defective, the probability that it was supplied by S1 is approximately 51.02%.

To determine what portion of all the parts is defective, we calculate a weighted average of the defect rates based on the supplier portion contributions. The calculation is as follows:

The overall defect rate is the sum of these contributions, which is [tex]2.5 + 0.6 + 1.8 = 4.9%.[/tex]

For part (b), the probability that the defective part was supplied by S1 can be found using Bayes' theorem:

If a part is defective, the probability of it being from S1 is the probability that S1 provided a defective part over the probability that any part is defective. This probability is ([tex]0.50 * 0.05) / 0.049 = 0.025 / 0.049 \approx 0.5102 or 51.02%.[/tex]

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Answer:

They're are all correct.

Step-by-step explanation:

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

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