a, b ∈q , then (a+ b)∈ …………… । *​

Answer:

x= -5.1

Step-by-step explanation:

The solution  to f(x) = g(x) is where to two graphs intersect

The graphs meet at

about x=2  and x = -5

The best answer listed is  x = -5.1

Answer:

x = −5.1

Step-by-step explanation:

I took the practice test

Answer:

The critical value used is T = 3.747.

The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{127+174+157+120+161}{5} = 147.8[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(127-147.8)^2+(174-147.8)^2+(157-147.8)^2+(120-147.8)^2+(161-147.8)^2}{4}} = 23.188[/tex]

Confidence interval:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 5 - 1 = 4

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 3.747, which is the critical value used.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.747\frac{23.188}{\sqrt{5}} = 38.856[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 147.8 - 38.856 = 108.944  

The upper end of the interval is the sample mean added to M. So it is 147.8 + 38.856 = 186.656.

The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).

9514 1404 393

Answer:

  3.49

Step-by-step explanation:

The growth factor is one more than the growth rate:

  growth factor = 1 + growth rate

  = 1 + 249% = 1 +2.49

  growth factor = 3.49

Answer:

The man would be 40 years old.

Step-by-step explanation:

Blood pressure as function of age:

Is given by the following equation:

[tex]P = 0.006A^2 - 0.02A + 120[/tex]

Find the age of a man whose normal blood pressure measures 129 mmHg.

This is A for which P = 129. So

[tex]129 = 0.006A^2 - 0.02A + 120[/tex]

[tex]0.006A^2 - 0.02A - 9 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

Quadratic equation with [tex]a = 0.006, b = -0.02, C = -9[/tex]. So

[tex]\Delta = (-0.02)^2 - 4(0.006)(-9) = 0.2164[/tex]

[tex]A_{1} = \frac{-(-0.02) + \sqrt{0.2164}}{2*(0.006)} = 40.4[/tex]

[tex]A_{2} = \frac{-(-0.02) - \sqrt{0.2164}}{2*(0.006)} = -37.1[/tex]

Age has to be a positive number, so rounding to the nearest year:

The man would be 40 years old.

Answer:

The minimum number of parallel faces that a prism should have is three pairs

Answer:

The minimum number of parallel faces that a prism should have is three faces

Answer:

y - 8 = -2(x + 1)^2

Step-by-step explanation:

The vertex of this parabola is (-1, 8).  It opens downward, so the x^2 term has a negative coefficient.  The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).

Through the vertex form of the equation of a parabola we get:

y - (8) = a(x - (-1)) + 7, or

y - 8 = a(x + 1)^2.  Find coefficient a by substituting the coordinates (-3, 0) in this equation:

0 - 8 = a(-3 + 1)^2, or

-8 = a(-2)^2, or a = -2

The desired equation is

y - 8 = -2(x + 1)^2

Answer: d=7 inches

r=7/2

r=3.5

A=πr²

A=3.14(3.5inch)²

A=3.14×12.25inch²

A=38.465inch²

A≈38.47inch²

Answer:

Answer is -1

Step-by-step explanation:

i1 = i 

i2 = -1 

i3 = -i

i4 = 1

i0 × i1 × i2 × i3 × i4 = 1 × i  × (- 1) × (- i) × 1 = i2 = - 1

Answer:the answer is -1

Step-by-step explanation:

Answer:

The answer is "8.74 and 36.46 years"

Step-by-step explanation:

Mean (life-time)=22.6 years

standard deviation= 3.1 years

We must find out how many standard deviations are 95% of the data.  

[tex]1 - \frac{1}{k^2} = 0.95\\\\1 - 0.95 = \frac{1}{k^2}\\\\\frac{1}{k^2} = 0.05\\\\\frac{1}{0.05} =k^2\\\\k^2 = 20\\\\ k = 4.47[/tex]

Calculating the lower limit and upper limit:

[tex]Lower\ limit = 22.6 - 4.47(3.1) = 22.6 - 13.86 = 8.74\\\\Upper\ limit = 22.6 + 4.47(3.1) = 22.6 + 13.86 = 36.46[/tex]

Limit is 8.74 years to 36.46 years

Answer:

If you're asking what cosine 3 is it's 0.9999986292247

Step-by-step explanation:

I don't really understand the question

Answer:

Small (11.5) is 37 cents per ounce.

Large (27.8) is 36 cents per ounce.

27.8 ounces is the better buy.

Answer:

2.5 x 2.5 = 6.25cm^2 (area of one side)

6.25 * 6 = 37.25cm^2 (area of all sides)

Step-by-step explanation:

Answer:  option C is correct

Step-by-step explanation:[tex]s=( \alpha +\beta +c)/2\\2s=\alpha +\beta +c\\2s-\beta -c=\alpha \\\alpha =2s-\beta -c[/tex]

Answer:

The answer:

I think the choose (1) 1

Answer:

[tex]m\angle H = 30^o[/tex]

Step-by-step explanation:

Given

See attachment

Required

Find [tex]m\angle H[/tex]

To calculate [tex]m\angle H[/tex], we make use of:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

So, we have:

[tex]\cos(H) = \frac{GH}{HI}[/tex]

This gives:

[tex]\cos(H) = \frac{10\sqrt3}{20}[/tex]

[tex]\cos(H) = \frac{\sqrt3}{2}[/tex]

Take arccos of both sides

[tex]m\angle H = cos^{-1}(\frac{\sqrt3}{2})[/tex]

[tex]m\angle H = 30^o[/tex]

Answer:

V = 192 m^3

Step-by-step explanation:

The volume of a cuboid is given by

V = l*w*h

V = 4m * 6m *8m

V = 192 m^3

=================================================

Work Shown:

ED/DF = AB/AC

x/24 = 12/16

16x = 24*12

16x = 288

x = 288/16

x = 18

------------

Explanation:

Because the triangles are similar, we can form the proportion shown above. There are many variations of the proportion that can happen, but they all lead to the same result x = 18.

So for instance, another proportion you could solve is ED/AB = DF/AC.

The key is to keep up the same pattern when forming the ratios.

What I mean by that is when I formed ED/DF I divided the vertical side over the horizontal side for triangle EDF. So to form the second fraction, we must do the same division (vertical over horizontal) for triangle ABC.

Answer:

9sin (3)and f,(0)=4,AND f(0)=2

Answer:

7% = .07 = [tex]\frac{7}{100}[/tex]

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

y = - 2x + 5

y = -2x + 20

Set the two equations equal

- 2x + 5  = -2x + 20

Add 2x to each side

- 2x+2x + 5  = -2x+2x + 20

5 = 20

This is never true so there are no solutions

Answer:

no solution

Step-by-step explanation:

Hi there!

We are given this system of equations:

y=-2x+5

y=-2x+20

and we want to find the solution (the point in which the lines intersect)

There are 3 ways to solve a system, but let's use substitution in this case

Both equations are set to y, so they should be equal to each other via a property known as transitivity (if a=b and b=c, then a=c)

-2x+5=-2x+20 (the same as y=y)

Now let's solve for x

add 2x to both sides

5=20

In this case, we got an untrue statement. If this happens, then the lines won't intersect.

If they won't intersect, there's no solution

Hope this helps!

Your answer is:

A) 0; it represents no correlation between x and y

keep dreaming

Step-by-step explanation:

The relation between kg and lbs is :

1 kg = 2.2046 lbs

We need to find the values of 1kg/2.2046lbs and 2.2046lbs/1kg.

So,

[tex]\dfrac{1\ kg}{2.2046\ lbs}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

and

[tex]\dfrac{2.2046\ lbs}{1\ kg}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

Hence, this is the required solution.

Answer:

Both are same as 1.

Step-by-step explanation:

1 kg = 2.2046 lbs

So,

[tex]\frac{1 kg}{2.2046 lbs }=\frac{1 kg }{1 kg} = 1[/tex]

And

[tex]\frac{2.2046 lbs}{1 kg }=\frac{1 kg }{1 kg} = 1[/tex]

Answer:

It multiplies

Step-by-step explanation:

if the number of hours changes to example to 2 then you multiply 60 by 2 resulting in 120miles in 2 hours

Close the path by connecting D to A. Then by Green's theorem, the integral over the closed path ABCDA - which I'll just abbreviate C - is

[tex]\displaystyle \oint_C (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy \\\\ = \iint_{\mathrm{int}(C)}\frac{\partial(4x+y)}{\partial x} - \frac{\partial(\sin(x)+9y)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy[/tex]

(where int(C ) denotes the region interior to the path C )

The remaining double integral is -5 times the area of the trapezoid, which is

[tex]\displaystyle -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy = -\frac52\times(12+4)\times4=-160[/tex]

To get the line integral you want, just subtract the integral taken over the path DA. On this line segment, we have x = 0 and dx = 0, so this integral reduces to

[tex]\displaystyle\int_{DA}y\,\mathrm dy = \int_{12}^0y\,\mathrm dy = -\int_0^{12}y\,\mathrm dy = -72[/tex]

Then

[tex]\displaystyle \int_{ABCD} (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy = -160 - (-72) = \boxed{-88}[/tex]

Answer:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (15,2.2) and (5,1.6):

[tex]m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}[/tex]

Therefore, the slope of the line is [tex]\frac{\displaystyle 3}{\displaystyle 50}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]

Plug in a given point and solve for b:

[tex]1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b[/tex]

Therefore, the y-intercept is [tex]\frac{\displaystyle 13}{\displaystyle 10}[/tex]. Plug this back into [tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]

I hope this helps!

Answer:

angle k is acute.

Step-by-step explanation:

it is less than 90 degrees

Answer:

a., b.

Step-by-step explanation:

Angle K looks like an acute angle with measure between 0 and 90 degrees.

Answer: a., b.

Answer:

2538

2.5%

Step-by-step explanation:

The population equayio since year 2000 can be modeled mathematically as :

P = 2538(1.025)^t

This is an exponential growth function which is represented by the general formula :

y = a(b)^t

Where, a is the initial population ;

b = growth factor ; b = (1 + r) where r = growth rate

Comparing the equations, the population in year 2000 represents the initial population, a = 2538

The percentage Rate of increase in population is :

(1 + r) = 1.025

r = 1.025 - 1

r = 0.025 ; 0.025 * 100% = 2.5%

Answer:

closing price of the fast food stock was $997.50

closing price of the toy company stock was $598.50

the price per fast food share was $28.50

Step-by-step explanation:

x = price per share fast food

y = price per share toy company

35x + 63y = 1596

x = y + 19

=>

35(y+19) + 63y = 1596

35y + 665 + 63y = 1596

98y + 665 = 1596

98y = 931

y = $9.50

=>

x = 9.5 + 19 = $28.50

the value of the whole fast food stock was

35x = 35×28.5 = $997.50

the cake if the whole toy company stock was

63y = 63×9.5 = $598.50

Answer:

Hence the confidence interval (2.2, 3.52).

Step-by-step explanation:

Hence,

The point estimate = [tex]\bar x_{1} - \bar x_{2}[/tex]

= 7.9 - 5.04

= 2.86

Given CI level is 0.98, hence α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.326

Margin of Error

ME = tc x sp

ME = 2.326 \ 0.2817

ME = 0.6552

CI = ([tex]\bar x_{1} - \bar x_{2}[/tex] - tc x sp , [tex]\bar x_{1} - \bar x_{2}[/tex] + tc x sp)

CI = (7.9 - 5.04 - 2.326 x 0.2817 , 7.9 - 5.04 - 2.326 x 0.2817

CI = (2.2 , 3.52)