The rectangle has a length of 4x+3 and a width of 3x. Show your work.

A. Find the perimeter.


B. Find the area.


C. Find the perimeter and area if x = 8.

Answer:

28

Step-by-step explanation:

[tex]k(x) = 5x -6\\\therefore k(4) = 5\times 4 -6\\\therefore k(4) = 20 -6\\\therefore k(4) = 14\\\\\because (k+k)(4) = k(4) + k(4)\\\therefore (k+k)(4)= 14+14\\\huge\red{\boxed{\therefore (k+k)(4) = 28}}[/tex]

Answer:

A line in form of y = ax + b has the gradient a.

      2y = -6x + 1

<=> y = -3x + 1/2

=> The gradient of this line: g = -3

Hope this helps!

:)

The slope represents the gradient of the line. Then the gradient of the line will be - 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

2y = - 6x + 1

Convert the equation into a slope-intercept form. Then we have

2y = - 6x + 1

y = - 3x + 1/3

The slope represents the gradient of the line. Then the gradient of the line will be - 3.

More about the linear equation link is given below.

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Answer:

Horizontal shift to the RIGHT of one unit

Step-by-step explanation:

When looking at a square root equation, the transformation form is:

[tex]f(x) = a\sqrt{b(x-h)} +k[/tex]

'h' represents a horizontal shift of the graph. Therefore, in this instance:

[tex]f(x) = \sqrt{x-1}[/tex]

This means that there is a horizontal shift to the RIGHT of one unit.

Answer:

A 98% confidence interval for the mean age is:

= ( 13.78, 19.10) months

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 16.44 months

Standard deviation r = 9.47 months

Number of samples n = 69

Confidence interval = 98%

z(at 98% confidence) = 2.33

Substituting the values we have;

16.44+/-2.33(9.47/√69)

16.44+/-2.33(1.140054028722)

16.44+/-2.656325886922

16.44+/-2.66

= ( 13.78, 19.10) months

Therefore, A 98% confidence interval for the mean age is:

= ( 13.78, 19.10) months

Answer:

Step-by-step explanation:

I assume that there is only one right answer in each multiple-choice question

If so:

P=(1/3)*(1/5)

P=1/15

P=0.06666666666

P≈0.067

P≈6.7%

Answer:

(a)[tex]x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3[/tex]

(b) 12

(c)[tex]2\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]G$iven A=\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right][/tex]

We are to compute the quadratic form [tex]x^TAx[/tex] for A.

Part A

[tex]x=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right][/tex]

[tex]x^TAx = \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right][/tex]

[tex]= \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3x_1+2x_2+0x_3\\2x_1+2x_2+1x_3\\0x_1+1x_2+0x_3\end{array}\right][/tex]

[tex]= x_1(3x_1+2x_2+0x_3)+x_2(2x_1+2x_2+1x_3)+x_3(0x_1+1x_2+0x_3)\\= x_1(3x_1+2x_2)+x_2(2x_1+2x_2+x_3)+x_3(x_2)[/tex]

[tex]= 3x_1^2+2x_1x_2+2x_1x_2+2x_2^2+x_2x_3+x_2x_3\\\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3[/tex]

Part B

[tex]x=\left[\begin{array}{ccc}-2\\-1\\5\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(-2)^2+4(-2)(-1)+2(-1)^2+2(-1)(5)\\=3*4+4*2+2-10\\=12+8+2-10\\=12[/tex]

Part C

[tex]x=\left[\begin{array}{ccc}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(\frac{1}{2})^2+4(\frac{1}{2})(\frac{1}{2})+2(\frac{1}{2})^2+2(\frac{1}{2})(\frac{1}{2})\\\\=\frac{3}{4}+1+ \frac{1}{2}+\frac{1}{2}\\\\=2\frac{3}{4}[/tex]

Answer:

1a) 90 = 2y + 2(2x)        1b) 45 - 2x = y          

Step-by-step explanation:

1a) 90 = 2y + 2(2x)        

1b) 90 = 2y + 2(2x)           Use the equation from above and multiply

90 = 2y + 4x

-4x          - 4x               Subtract 4x from both sides

90 - 4x = 2y                 Divide both sides by 2

45 - 2x = y

Answer:

375000

Step-by-step explanation:

We have that in this case the following proportion would be fulfilled:

Price * Distance / area

Now, we have that for a distance of 45 km and an area of 900 m ^ 2 the price is 250,000, now for a distance of 40 km but with an area of 1,200 m ^ 2, how would the price be, we replace:

250000 * 45/900 = P * 40/1200

12500 * 1200/40 = P

P = 375000

Which means that for these conditions the price is 375000.

Answer:

B. n=36, p=0.98, x=12

Step-by-step explanation:

98% of bottles have the correct amount.

The probability is equal to 0.98

That is p = 0.98

A bottle of water is supposed to have 12 ounces.

That is the expected value is 12

X = 12

36 bottles has all bottles properly filled

The possible sample space is 36

N = 36

In this case, the complement would be selecting a number less than or equal to 7; the probability of this occurring is [tex]\boxed{\frac{7}{10}}.[/tex]

Answer:

it is 3/10

Step-by-step explanation:

Answer:

[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]

And we got for the solution:

[tex] x_1= 2.885 , x_2 = -0.485[/tex]

And the value sof y are using the function y =2x-3:

[tex] y_1=2.77, y_2=-3.97[/tex]

Step-by-step explanation:

For this case we have this function given:

[tex] y = 2x-3[/tex]  (1)

And the circle with center the origin and radius 4 is given by;

[tex] x^2 +y^2 = 16[/tex]  (2)

We can solve fro y from the last equation and we got:

[tex] y = \pm \sqrt{16-x^2}[/tex]   (3)

Now we can set equal equations (3) and (1) and we got:

[tex] 2x-3 = \sqrt{16-x^2}[/tex]

[tex] (2x-3)^2=16-x^2[/tex]

[tex] 4x^2 -12x +9 = 16-x^2[/tex]

[tex] 5x^2 -12x -7=0[/tex]

And using the quadratic equation we got:

[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]

And we got for the solution:

[tex] x_1= 2.885 , x_2 = -0.485[/tex]

And the value sof y are using the function y =2x-3:

[tex] y_1=2.77, y_2=-3.97[/tex]

Answer:

45 books

Step-by-step explanation:

12=51.60

how about 193.50

193.50 x 12=2322 / 51.60=45 books    

Solution,

Books Price

12 51.60

X(suppose) 193.50

In case of Direct proportion,

12/X=51.60/193.50

or,51.60x=2322( cross multiplication)

or,X=2322/51.60

X=45

Hope it helps

Good luck on your assignment

Answer:

C.

Step-by-step explanation:

Hello!

Given the variable:

X: childhood asthma prevalence

With mean μ= 2.22%

and standard deviation σ= 1.39%

You have to calculate the probability of the sample average of childhood asthma prevalence in a sample of n= 30 cities is greater than 2.5%

We don't know the distribution of the variable, but remember that thanks to the central limit theorem, since the n ≥ 30, we can approximate the sampling distribution to normal:

X[bar]≈N(μ;σ²/n)

And use the standard normal distribution to calculate the asked probability:

P(X[bar]>2.5)= 1 - P(X≤2.5)

Calculate the Z value for the given X[bar] value:

[tex]Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } } = \frac{2.5-2.22}{\frac{1.39}{\sqrt{30} } }= 1.10[/tex]

Using the Z-tables you have to look for the value of

P(Z≤1.10)= 0.86433

1 - 0.86433= 0.13567

Then P(X[bar]>2.5)= 1 - P(X≤2.5)= 1 - P(Z≤1.10)= 1 - 0.86433= 0.13567

13.567% of the 30 cities will have a mean childhood asthma prevalence greater than 2.5%

I hope this helps!

Answer:

Input:

x/x + 1 - 1/x - 1 + 2×x/x^2 - 1

Result:

1/x

Answer:

hope this.helps you

Answer:

n = 66 (to the nearest whole number)

66 randomly selected players must be surveyed

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-M.E

M.E = zr/√n

Making n the subject of formula;

n = (zr/M.E)^2 ........1

Given that;

Mean = x

Standard deviation r = 2.7 inches

Number of samples = n

Confidence interval = 95%

z(at 95% confidence) = 1.96

Margin of error M.E = 0.65 inches

Substituting the given values into equation 1;

n = (zr/M.E)^2

n = (1.96×2.7/0.65)^2

n = 66.28464852071

n = 66 (to the nearest whole number)

66 randomly selected players must be surveyed

Answer:

28

Step-by-step explanation:

10=x 4=y

P=2(x+y)

P=2(10+4)

P=2(14)

P=28

Answer:

a. December 16

Step-by-step explanation:

18 June + 180 days = 15 December

Since 2 options given,

a. December 16 is the answer

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

i did it on edge

Answer:

Step-by-step explanation:

Consider the function of the rate of flow of money in dollar per year is

[tex]f(t)= 400e^{0.03t}[/tex]

The objective is to find the present value of this income over 10 years period an assume an annual interest rate of 8% compounded continuously.

Given that,

[tex]f(t)= 400e^{0.03t}[/tex]

r = 0.08, t = 10

if f(t) is the rate of  continuously money flow at an interest rate r to T year,

the present value is,

[tex]P= \int\limits^T_0 {f}(t)e^{-rt} \, dt[/tex]

Now input the values to get

[tex]p=\int\limits^{10}_0 400e^{0.03t}*e^{-0.08t} dt[/tex]

[tex]=400\int\limits^{10}_0 e^{0.03t}*^{-0.08t} dt[/tex]

[tex]= 400\int\limits^{10}_0 e^{-0.05t} dt[/tex]

[tex]=400(-\frac{e^{-0.05t}}{0.05} )|_0^1^0[/tex]

[tex]=-\frac{400}{0.05} (e^{-0.05*10}-e^{-0.05*0})\\\\=-\frac{400}{0.05} (e^{-0.5}-e^{*0})\\\\=3147.75[/tex]

[tex]225-49x^2[/tex]

[tex]-49x^2+225[/tex]

[tex]=(7x+15)(-7x+15)[/tex]

Answer:

(15+7x)(15-7x)

Step-by-step explanation:

225-49 x² = 15² - (7x)² = (15+7x)(15-7x)

Step-by-step explanation:

We have [tex]\mathrm{dx} / \mathrm{dt}=0.1 \mathrm{ft} / \mathrm{sec},[/tex] and we want

dy/dt.

[tex]x[/tex] and [tex]y[/tex] are related by the Pythagorean Theorem [tex]x^{2}+y^{2}=(13 f t)^{2}[/tex]

Differentiate both sides of this equation with respect to [tex]t[/tex] to get [tex]2 x \frac{d x}{d t}+2 y \frac{d y}{d t}=0[/tex]

[tex]\frac{d y}{d t}=-\frac{x}{y} \frac{d x}{d t}[/tex]

When [tex]x=12 \mathrm{ft},[/tex]  

we have,  

[tex]y=\sqrt{(13 \mathrm{ft})^{2}-(12 \mathrm{ft})^{2}}=5 \mathrm{ft}[/tex]

therefore

[tex]\frac{d y}{d t}=-\frac{12f t}{5 f t} \cdot \frac{1 f}{\sec }=-\frac{12}{5} \frac{f t}{\sec }[/tex]

Answer:

.

Step-by-step explanation:

Answer:

  76.9 million people per year

Step-by-step explanation:

The increase was 3,000 million people in 39 years, so the number per year was ...

  3000/39 ≈ 76.9 . . . . million people per year

Answer:

The answer is 1/6.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

OPTION A

Answer: 6 1/6

Step-by-step explanation:

6 can go into 37 6 times

6x6=36

with 1 left over

The fraction 37/6 can be changed to the mixed number​ as 6 1/6 if the fraction is 37/6.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The fraction is:

= 37/6

We can write the above number as:

= (36 + 1)/6

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 36/6 + 1/6

= 6 + 1/6

Or

= 6 1/6 (mixed fraction)

Thus, the fraction 37/6 can be changed to the mixed number​ as 6 1/6 if the fraction is 37/6.

Learn more about the fraction here:

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Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

[tex]t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2[/tex]

you replace t1 from the first equation in the second equation:

[tex](1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}[/tex]

Then, for t2 = 0 and t2=1/2 you obtain for t1:

[tex]t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2[/tex]

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths  intersect are:

[tex]r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)[/tex]

B) You have the following two trajectories of two independent particles:

[tex]r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)[/tex]

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

[tex]t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t[/tex]

From the first equation you have:

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

This values does not have a physical meaning, then, the particle do not collide

answer: DNE

Step-by-step explanation:

45°+90°+60°+X°=360° (being complete angle)

or,195°+X°=360°

or,X°=360°-195°

or,X°=165°

Therefore,valueof X is 165°.

Answer:

165

Step-by-step explanation:

The sum of angles at a point is always 360 degrees and you know all the angles apart from x. so 360-90-45-60=165.

Better notation would be 360 = x+45+60+90 and then you have to find out what x is by rearangin the equation.

Answer:

The 99% confidence interval for the population mean is between 10.12 minutes and 13.58 minutes.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575*\frac{3}{\sqrt{20}} = 1.73[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 11.85 - 1.73 = 10.12 minutes

The upper end of the interval is the sample mean added to M. So it is 11.85 + 1.73 = 13.58 minutes

The 99% confidence interval for the population mean is between 10.12 minutes and 13.58 minutes.

Answer:

12white

12 coloured

12-12=0