Lucas and Erick are factoring the polynomial 12x3 – 6x2 + 8x – 4. Lucas groups the polynomial (12x3 + 8x) + (–6x2 – 4) to factor. Erick groups the polynomial (12x3 – 6x2) + (8x – 4) to factor. Who correctly grouped the terms to factor? Explain.

Answer:

[tex] \frac{1}{9 - 4i} [/tex]

I'm not sure

Answer:

y = x - 2

Step-by-step explanation:

y = x + b

3 = 5 + b

y = x - 2

We can use the slope intercept form of a line.

y = mx+b where m is the slope and b is the y intercept

y = 1x +b

Substitute the point into the equation

3 = 1*5+b

3 = 5+b

Subtract 5 from each side

3-5 = 5+b-5

-2 =b

y = x-2

Answer:

y=2/3x+1

Step-by-step explanation:

The slope is 2/3 and the y-intercept is 1.

Answer:

The average rate of change is 12x=12.0x.

Description:

Function: x= 1x = 3  convert to short form: x 1x 3

Interval:  x= 1  ,       x 3

Steps:

Input:  Find the average rate of change of f(x)=3x2 on the interval [x,3x].

We have that a=x, b=3x, f(x)=3x2

Thus, f(b)−f(a)b−a=3((3x))2−(3(x)2)3x−(x)=12x.

Answer: the average rate of change is 12x=12.0x.

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Hope this helps.

Answer:

3

Step-by-step explanation:

A P E X

Answer:

51 1/3 hours

Step-by-step explanation:

Multiply the amount of sleep per day (7 1/3) by the number of days in a week (7), to get the total amount of sleep (51 1/3 hours)

Answer:

5q + 9

Step-by-step explanation:

Combine like terms to simplify the expression.

Have a blessed day!

Answer:

7q+9

Step-by-step explanation:

6q+4+q+5

6q+q+4+5

=7q+9

Answer:

Step-by-step explanation:

hey

(f*g)(x) = f(g(x)) = f(2) = 2

second answer is correct

thanks

Answer: -1

Step-by-step explanation:

You want to find an angle that is coterminal to 495. So, subtract 360 degrees until youre in the range of 0-360. I got 495 - 360 = 135°

Tangent is equal to [tex]\frac{sin(theta)}{cos(theta)}[/tex], we already solved theta which was 135°

This next part is hard to explain to someone who doesnt know their trig circle, idk if you do. The angle 135 is apart of the pi/4 gang. So we know this is going to be some variant of √2/2. Sine of quadrant 1 and 2 is gonna be positive:

[tex]sin135=\frac{\sqrt{2} }{2}[/tex]

Now lets do cosine of 135°, which again is apart of the pi/4 gang because its divisible by 45°. Its in quadrant 2 so the cosine will be negative.

[tex]cos135=-\frac{\sqrt{2} }{2}[/tex]

The final step is to divide them. They are both fractions so you should multiply by the reciprocal.

[tex]\frac{\sqrt{2} }{2} *-\frac{2}{\sqrt{2} } =-\frac{2\sqrt{2} }{2\sqrt{2} } =-1[/tex]

Answer:

The area of the rectangle increasing at the rate of 140 cm²/s

Step-by-step explanation:

Rectangle area:

A rectangle has two dimensions, length l and width w.

It's area is:

A = l*w.

When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

We apply implicit differentiation to solve this question:

[tex]A = l*w[/tex]

So

[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]

Length is 20, so [tex]l = 20[/tex].

Width is 10, so [tex]w = 10[/tex]

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s.

This means that [tex]\frac{dl}{dt} = 8, \frac{dw}{dt} = 3[/tex]

So

[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]

[tex]\frac{dA}{dt} = 20*3 + 10*8 = 140[/tex]

Area in cm².

So

The area of the rectangle increasing at the rate of 140 cm²/s

Answer:

a rigt angle is a total of 90 degrees so subtratct 51 from 90 and you get 39 degrees.

Answer:

C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.

Step-by-step explanation:

She performed an hypothesis test with the sample of size n=15 that she takes. The t-statistic has a value of 6.661.

The degrees of freedom for this sample size are:

[tex]df=n-1=15-1=14[/tex]

The P-value for a statistic t=6.661 and 14 degrees of freedom is:

[tex]\text{P-value}=P(t>6.661)=0.00001[/tex]

With these P-value we know that the effect is significant and the null hypothesis is rejected. There is enough evidence to support the claim that the mean height of Mountain Ash trees is greater than the coastal Douglas Firs.

Answer:

2000

Step-by-step explanation:

2500 / 100 = 25 (1%)

25 X 20 =500 (20%)

2500 - 500 =2000

Answer:

There is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks

Step-by-step explanation:

The slope (0.2) is the rate of change in Y-hat for each unit change in x.

In this specific case, since Y-hat is the revenue, in millions, and x is the number of clicks, in thousands, the best interpretation is that there is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks

Answer:

y + 7 = -2/3 (x - 1)

Step-by-step explanation:

Point-slope form is y - y1 = m (x - x1)

-7 is y1, -2/3 is m, and 1 is x1

When you plug the values in, you get y + 7 = -2/3 (x - 1)

Answer:

0.45

Step-by-step explanation:

9/20 is the same as 0.45

Answer:

0.45

Step-by-step explanation:

9/20= 9*5/20*5= 45/100= 0.45

Answer:

f(x)= 4x or y=4x

Step-by-step explanation:

X represents minutes and the 4 is how many dishes she can wash.

Answer:

-4 please brainliest me

Step-by-step explanation:

9.68x+21.6-6.23x=2.3x+17

lets move it to the left

9.68x+21.6-6.23x-(2.3x+17)=0

Then, We add all the numbers together, and all the variables

3.45x-(2.3x+17)+21.6=0

We get rid of parentheses

3.45x-2.3x-17+21.6=0

We add all the numbers together, and all the variables

1.15x+4.6=0

We move all terms containing x to the left, all other terms to the right

1.15x=-4.6

x=-4.6/1.15

x=-4

x= -8 makes the equation true.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

9.68x + 21.6 -6.23x = 2.3x + 17​

Now, solving for x

9.68 x - 6.23x - 2.3x = 17 - 21.6

1.15x= -4.6

x= -4.6 / 1.15

x= -8

Hence, x= -8 makes the equation true.

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Answer:

Mathematics could make scientists to have a preliminary understanding of the dimensions, perimeters, areas and volumes of different craters on Mars.

Step-by-step explanation:

Martian Craters are series of craters formed on the surface of Mars. The study of a planets crater gives an understanding of the properties of matter that lies under the crater.

Mathematics can be applied to determine the dimensions, perimeter, area and volume of the features of a crater using appropriate conversions and theorems.

The Pi in the sky theorem can be applied to determine the area and perimeter, even volume of different craters on the Mars surface. Also, eingenfunction expansion theorem gives a preliminary knowledge of the craters.

By measurements and conversions processes, the features of Martian crater could be studied from images.

Answer:

The IV will run [tex]66.67 \ ml /hr[/tex]

Step-by-step explanation:

From the question we are told that

   The mass of Magnesium sulfate is  [tex]m_g = 30 \ g[/tex]

   The volume of the Magnesium sulfate  [tex]V_R = 500ml[/tex]

   The rate at which the dose of the solution (Magnesium sulfate + Lactated Ringers. ) is infused is  [tex]R = 4g/hr[/tex]

The concentration of Magnesium sulfate in Lactated Ringers  is mathematically evaluated as

         [tex]C_m = \frac{m_g}{V_R}[/tex]

substituting values

          [tex]C_m = \frac{30}{500}[/tex]

          [tex]C_m = 0.06\ g/ ml[/tex]

This implies that

     0.06 g of Magnesium sulfate is in every 1 ml of  Lactated Ringers

So  4 g  of  Magnesium sulfate is in x ml of  Lactated Ringers

So

        [tex]x = \frac{4}{0.06}[/tex]

       [tex]x = 66.67 \ ml[/tex]

So the amount of the solution in ml that is been infused in 1 hour is  

      [tex]66.67 \ ml /hr[/tex]

Answer:

D = 0 , Dx = 4 , Dy = -6 , Dz = 2

Step-by-step explanation:

As per cramer's rule,

D = |   7    6    4  |  = 0

      |   3    3    3  |

      |   4    4    4  |

Dx =  |  10    6    4  | = 4

        |   1    3    3    |

        |   2    4    4   |

Dy = |   7    10    4  | = -6

       |   3    1     3   |

       |   4    2    4   |

Dz =  |  7    6    10 | = 2

        |   3    3    1   |

        |   4    4    2  |

Answer:

a) [tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]

b)  See Below for proper explanation

Step-by-step explanation:

a) The objective here  is to Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.

The function is [tex]e^x + 3 \ cos \ x[/tex]

The expansion is of  [tex]e^x[/tex] is [tex]e^x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ...[/tex]

The expansion of cos x is [tex]cos \ x = 1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...[/tex]

Therefore; [tex]e^x + 3 \ cos \ x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ... 3[1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...][/tex]

[tex]e^x + 3 \ cos \ x = 4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} + \dfrac{x^3}{3!}+ ...[/tex]

Thus, the first three terms of the above series are:

[tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]

b)

The series for [tex]e^x + 3 \ cos \ x[/tex] is [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!} + 3 \sum \limits^{\infty}_{x=0} ( -1 )^x \dfrac{x^{2x}}{(2n)!}[/tex]

let consider the series; [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!}[/tex]

[tex]|\frac{a_x+1}{a_x}| = | \frac{x^{n+1}}{(n+1)!} * \frac{n!}{x^x}| = |\frac{x}{(n+1)}| \to 0 \ as \ n \to \infty[/tex]

Thus it converges for all value of x

Let also consider the series [tex]\sum \limits^{\infty}_{x=0}(-1)^x\dfrac{x^{2n}}{(2n)!}[/tex]

It also converges for all values of x

Answer:

[tex] P(A) = 0.21[/tex]

We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:

[tex] P(A') = 1-P(A)[/tex]

Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:

[tex] P(A')=1-0.21= 0.79[/tex]

Step-by-step explanation:

For this problem we know that the probability that a freshman at a certain college takes an introductory statistics class is 0.21, let's define of interest as A and we can set the probability like this:

[tex] P(A) = 0.21[/tex]

We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:

[tex] P(A') = 1-P(A)[/tex]

Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:

[tex] P(A')=1-0.21= 0.79[/tex]

Answer:

1.46666 miles / minutes

88 miles per hour

Step-by-step explanation:

The speed is distance over time

44 miles / 30 minutes

1.46666 miles / minutes

or if we want in miles per hour

44 miles / .5 hours

88 miles per hour

Answer:

1.467 mile/minute

Step-by-step explanation:

you should divide the distance on the time i.e. 44/30

Answer:

The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 18, \pi = \frac{5}{18} = 0.2778[/tex]

99.5% confidence level

So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 - 2.81\sqrt{\frac{0.2778*0.7222}{18}} = -0.01 = 0[/tex]

We cannot have a negative proportion, so we use 0.

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 + 2.81\sqrt{\frac{0.2778*0.7222}{18}} = 0.5745[/tex]

The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).

Answer:

$900

Step-by-step explanation:

If she holds $500 and she is charged 15%; it means

The interest she pays per month is ;

$500 × 15/100 = $75

Then annually meaning for 12 months, she pays;

$75 × 12 = $900

Her annual interest on her current card is $900.

Therefore,

She will be taxed 15% if she holds $500, which means

The monthly interest she pays is;

$500 × 15/100 = $75

She then pays annually, which is for a full year;

$75 × 12 = $900

Hence, Her annual interest on her current card is $900.

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Answer:

0.6042 or 29/48

Step-by-step explanation:

-5/16 = -0.3125

7/24 = 0.2917

0.2917 - -0.3125 = 0.6042

0.6042 ≅ 29/48

Answer:

29/48

Step-by-step explanation:

-5/16 + x= 7/24

x= 7/24-(-5/16)

x=7/24+5/16

x= 2*7/2*24+ 3*5/3*16

x=29/48

Answer:

2.5

Step-by-step explanation:

[tex]9(u-2)+1.5u=8.25 \\\\9u-18+1.5u=8.25\\\\10.5u-18=8.25\\\\10.5u=26.25\\\\u=2.5[/tex]

Hope this helps!

[tex]answer = \frac{25}{56} \\ solution \\ \frac{3}{7} + \frac{1}{56} \\ = \frac{3 \times 8 + 1}{56} \\ = \frac{24 + 1}{56} \\ = \frac{25}{56} \\ hope \: it \: helps \: \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

25/56

Step-by-step explanation:

3/7 + 1/56

We have to find the L.C.M of 7 and 56

The L.C.M of 7 and 56 is 56

Now, we have to change the denominators to 56

we dont need to change the denominator of 1/56 to 56 as it is already 56

[tex]\frac{3}{7}[/tex] * [tex]\frac{8}{8}[/tex] = [tex]\frac{24}{56}[/tex]

Now we can add the fractions

[tex]\frac{24}{56} + \frac{1}{56}[/tex] [tex]= \frac{25}{56}[/tex]

Hope it helped :>