Solve the following System of Three Equations:
x−3y+z=−15
2x+y−z=−2
x+y+2z=1

Answer:

  4.32%; no

Step-by-step explanation:

The value of 0.24 differs from the mean by 0.84 -0.24 = 0.60. 2 standard deviations from the mean would be a difference of 2×0.35 = 0.70.

A statistical calculator says the probability of a depth less than 0.24 mm for the given distribution is about 4.32%.

The value differs from the mean by less than 2 standard deviations, so is not considered unusual.

Answer:

45

Step-by-step explanation:

We can first expand the expression:

n(n+p) - n

= n^2 + np + n

Then, we can plug in values of n and p into the expression:

n^2 + np + n = (5)^2 + (5)(3) + 5 = 25 + 15 + 5 = 45

Answer:

35

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify

Answer:

A coefficient is a number that is in front of a variable. A number that is multiplied by a variable in a variable expression; in an expression such as 3ab, the numerical coefficient of ab is 3. The word constant means unchanging. Since a number’s value never changes, a number with no variable factors is a constant. A constant is a numerical term in an expression. a term that has no variables

Example: 5a+4  The coefficient is 5 and the constant is 4 because it does not have a variable in front of it.

Hope this helps

Answer:

The value is  [tex]y'(t) = \frac{k}{\sqrt{y(t)} }[/tex]

Step-by-step explanation:

From the question we told that are

      The rate of growth of mice is inversely proportional to the square of the population

   This above statement can be mathematically represented as

        [tex]\frac{d y }{dt} \ \ \ \alpha \ \ \frac{1}{\sqrt{y(t)} }[/tex]

Here  [tex]y(t)[/tex] is the population

=>     [tex]\frac{d y }{dt} = \frac{k}{\sqrt{y(t)} }[/tex]

=>     [tex]y'(t) = \frac{k}{\sqrt{y(t)} }[/tex]

Answer:

The area of the surface is 2.72 units

Step-by-step explanation:

The area of a curve y = (x) a ≤x ≤ b rotated about the y axis is given by:

[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]

y = 4 - x²

dy / dx = -2x

(dy/dx)² = (-2x)² = 4x²

Hence:

[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\\\s=\int\limits^0_3 {2\pi x\sqrt{1+4x^2} } \, dx\\\\Let\ u = 1+4x^2\ \\\frac{du}{dx}=8x\\\frac{du}{8x}=dx\\\\Substituting\ value\ of\ u \ and\ dx:\\ \\s=\int\limits^0_3 {2\pi x\sqrt{u} } \, \frac{du}{8x} \\\\s=\frac{\pi }{4} \int\limits^0_3 {\sqrt{u} } \, du\\\\s=\frac{\pi }{4}|\frac{2}{3}u^{3/2}|_0^3\\\\s=\frac{\pi }{4}*\frac{2}{3}(5.196)\\\\s=2.72\ units[/tex]

The area of the surface is 2.72 units

The area of the resulting surface is [tex]37.3437\pi[/tex].

A curve is an object that is similar to a line, but that does not have to be a straight line. A curve may be regarded as a trace left by a moving point.

Given:

[tex]y=4-x^{2}[/tex] , [tex]0 \leq x\leq 3[/tex]

Surface area[tex]=2\pi \int_{a}^{b}x\sqrt{1+\left ( \frac{dx}{dy} \right )^{2}dy}[/tex]

[tex]x=\sqrt{4-y} \ , \ \frac{dx}{dy}=-\frac{1}{2\sqrt{4-y}}[/tex]

when [tex]x=0 \ , \ y=4[/tex]

         [tex]x=3 \ , \ y=-5[/tex]

Area of surface[tex]=2\pi \int_{-5}^{4}\sqrt{4-y}\sqrt{1+\frac{1}{4\left ( y-4 \right )}dy}[/tex]

[tex]=2\pi \int_{-5}^{4}\sqrt{4-y+\frac{4-y}{4\left ( y-4 \right )}dy} \\ =2\pi \int_{-5}^{4}\sqrt{4-y+\frac{1}{4}dy} \\ =\frac{2\pi }{2}\int_{-5}^{4}\sqrt{17-y} \ dy \\ =\pi \int_{-5}^{4}\sqrt{17-y} \ dy[/tex]

Solving with calculator:

[tex]\Rightarrow \pi\left [ \frac{1}{6}\left ( 37\sqrt{37}-1 \right ) \right ][/tex]

[tex]=37.3437\pi[/tex]

Learn more about the topic Curve: https://brainly.com/question/8771120

[tex]PV=nRT\implies P=V^{-1}nRT[/tex].

Hope this helps.

Answer:

(64)^-4= 1/64^4= 1/16777216

Step-by-step explanation:

Area of a rectangle is base times height.

A = bh

A = (12 in) (2.5 in)

A = 30 in²

Answer:

Step-by-step explanation:

d = 200 miles

B rate = x

A Rate = x + 20

Each has traveled two hours

The total distance each travels after two hours is 200 miles (they pass each other).

d = r * t

2*x + 2*(x + 20) = 200      Remove the brackets

2x + 2x + 40 = 200           Combine like terms

4x + 40 = 200                   Subtract 40 from each side

4x = 200 - 40                  

4x = 160                           Divide by 4

x = 160/4

x = 40

There B's rate is 40 miles / hour

A's rate is 40 + 20 = 60 miles / hour

Answer:

7.1

Step-by-step explanation:

Using the distance formula

d = sqrt (  (x2-x1)^2 + ( y2-y1)^2)

    sqrt (  (-5-2)^2 + ( -3- -2)^2)

    sqrt(   ( -7)^2  + ( -3 +2)^2)

   sqrt(   ( 49  + 1)

   sqrt( 50)

  7.071067812

To the nearest tenth

7.1

Answer:

7.1 units

Step-by-step explanation:

We can use the distance formula to find the distance between these two points.

The distance formula is:

[tex]\sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex].

x1 is 2, x2 is -5, y1 is -2, and y2 is -3, so we can plug these values into the equation.

[tex]\sqrt {\left( {2 - (-5) } \right)^2 + \left( {-2 - (-3) } \right)^2 }\\\\\sqrt {7^2 + 1^2}\\\\\sqrt{49+1}\\\\\sqrt{50}\approx7.1[/tex]

Hope this helped!

Answer:

Rylee spent $25 for fuel at the gas station. This money is leaving her bank account, so represent the amount with a negative sign: -$25.

Step-by-step explanation:

None. the expression explains it.

Answer:

60cm²

Step-by-step explanation:

Length = 6cm

Breadth = 10cm

Area of rectangle = l×b

=( 10 ×6)cm

= 60cm²

Hope it helps.

Answer:

[tex]\Huge \boxed{\mathrm{60 \ cm^2 }}[/tex]

Step-by-step explanation:

Area of a rectangle is length × width.

The length of the rectangle is 10 cm.

The width of the rectangle is 6 cm.

[tex]\Rightarrow 10 \cdot 6 \\\\\\ \Rightarrow 60[/tex]

The area of the rectangle is 60 cm².

Answer:

Apply the 15% discount first, and the final purchase price is $332.50.

Step-by-step explanation:

The 15% discount of the two coupons should be applied first so that the final price is cheaper.

The final purchase price at the department store is $332.5.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Cost = $450

Two coupons.

Offer = 15% discount

off = $50

Now,

15% discount first and then $50 off.

(450 - 15/100 x 450) - 50

= (450 - 67.5) - 50

= $332.5

Now,

$50 off first and then the 15% discount.

(450 - 50) = 400

400 - 15/100 x 400

= 400 - 60

= $340

We see that,

When the 15% discount is applied first the final price is cheaper.

Thus,

15% discount should be applied first.

The final purchase price is $332.5.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

Explanation:

Remember: we have to isolate the variable x, so that means we have to get x by itself.

Step 1:

Let’s look at our equation:

[tex]6x+57=2x+315[/tex]

Let’s subtract 2x from both sides of the equation, since our goal is to isolate the variable. You could also subtract 6x from both sides, but you would end up with a negative number, and I find it easier to deal with positive numbers.

[tex]6x(-2x)+57=2x(-2x)+315\\4x+57=315[/tex]

Step 2:

Now, let’s subtract 57 from both sides of our equation.

[tex]4x+57(-57)=315(-57)\\4x=258[/tex]

Step 3:

Since we have to isolate x, let’s divide both sides of the equation by 4.

[tex]4x/4=x\\258/4=64.5[/tex]

Our final answer: x = 64.5

None of your options is the correct answer. Notify your teacher, tutor, etc. since there none of the options are correct.

Answer:

Step-by-step explanation:

Given the function f(x,y) = ye^x

To evaluate f(2,1), we will substitute x = 2 and y = 1 into the given function to have;

f(2,1) = 1×e^2

f(2,1) = e^2

f(2,1) = 7.3891(to 4dp)

For f(2.5, 1.65), x = 2.5 and y =1.65

f(2.5, 1.65) = 1.65e^2.5

f(2.5, 1.65) = 1.65×12.1825

f(2.5, 1.65) = 15.2281 (to 4dp).

∆z = f(2.5, 1.65) - f(2, 1)

∆z = 15.2281-7.3891

∆z = 7.8390

dz = fxdx + fydy

fx is the differential of the function with respect to x keeping y constant.

Since f(x,y) = ye^x

fx = ye^x + 0e^x

fx = ye^x

dx = x2-x1 = 2.5-2

dx = 0.5

fy = e^x

dy = (y2-y1) = 1.65-1

dy = 0.65

Using the point (2, 1) for x and y and substituting the values gotten into dz function:

dz =ye^x(0.5) + e^x(0.65)

If x = 2 and y = 1

dz = 1e^2(0.5) + e^2(0.65)

dz = 7.3891(0.5)+7.3891(0.65)

dz = 7.3891(0.5+0.65)

dz = 7.3891(1.15)

dz = 8.4975

Answer:

The linear speed of the bike is 19.242 miles per hour.

Step-by-step explanation:

If sliding between the bottom of the wheel and ground can be neglected, the motion of the wheel can be well described by rolling, which is a superposition of coplanar pure rotation and translation, The speed of the bike occurs at the center of the wheel, where resulting instantaneous motion is pure translation parallel to ground orientation. The magnitude of the speed of bike ([tex]v_{B}[/tex]), measured in inches per second, is:

[tex]v_{B} = R\cdot \omega[/tex]

Where:

[tex]R[/tex] - Radius, measured in inches.

[tex]\omega[/tex] - Angular speed, measured in radians per second.

Now, the angular speed must be converted from revolutions per minute into radians per second:

[tex]\omega = \left(154\,\frac{rev}{min} \right)\cdot \left(2\pi\,\frac{rad}{rev} \right)\cdot \left(\frac{1}{60}\,\frac{min}{s} \right)[/tex]

[tex]\omega \approx 16.127\,\frac{rad}{s}[/tex]

The speed of the bike is: ([tex]R = 21\,in[/tex] and [tex]\omega \approx 16.127\,\frac{rad}{s}[/tex])

[tex]v_{B} = (21\,in)\cdot \left(16.127\,\frac{rad}{s} \right)[/tex]

[tex]v_{B} = 338.667\,\frac{in}{s}[/tex]

Lastly, the outcome is converted into miles per hour:

[tex]v_{B} = (338.667\,\frac{in}{s} )\cdot \left(3600\,\frac{s}{h} \right)\cdot \left(\frac{1}{63360}\,\frac{mi}{in} \right)[/tex]

[tex]v_{B} = 19.242\,\frac{mi}{h}[/tex]

The linear speed of the bike is 19.242 miles per hour.

Answer: The equation in math form is [tex]\frac{1}{5}c[/tex] - 9.

Step-by-step explanation:

So the givens are:

9 less than one-fifth of c

Let's put this equation in math form:

[tex]\frac{1}{5}c[/tex] - 9

Hence your answer!

Answer:

Differences=

[tex] {120cm}^{3} [/tex]

Step-by-step explanation:

Volume of first box=15cm×4cm×8cm

[tex]480 {cm}^{3} [/tex]

Volume of second box=10cm×9cm×4cm

[tex] {360cm}^{3} [/tex]

Answer:

You should multiply the exponents "-3" and "-6"

Then your answer is:

Hope this helps..

Best of luck!

Answer:

Step-by-step explanation:

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(4^{-3}\right)^{-6}=4^{-3\left(-6\right)}\\\\-3\left(-6\right)=18\\\\=4^{18}[/tex]

Answer:

1/8x + 1/2 y

Step-by-step explanation:

Charlotte gets 1/4x from dayna

Charlotte now has

1/4x+y

She lends 1/2 of this

1/2  ( 1/4x +y)

1/8x + 1/2 y

its hard to explain and show work but so you know the answer is no and its because they converted yards to miles and did the formula for ft to miles instead of yd to miles they did 5280 ft per mile and not 1760 yd per miles

Answer:

13.63 miles per hour

Step-by-step explanation:

100 yards / 15 sec  converted to miles per hour

100 yards  x  60 sec  x   60 min   x  1 mile       =  13.63 miles/hr

   15 sec           1 min            1 hr         1760 yards

the mistake on Mrs Dukes is the conversion from miles to yards.

1 mile = 1760 yards NOT 5280 yards

Answer:

We have a total investment of $20,000 in two different amounts A and B.

Then:

A + B = $20,000.

And we know that the interest of the amount A is 7%, and the interest of the amount B is 10%. (i will assume that both interests are yearly interest)

And after one year, Hank earns $1,640 thanks to those interests, then we have that:

(7%/100%)*A + (10%/100%)*B = $1,640

And we can write this as:

0.07*A + 0.1*B = $1,640

Then we have a system of equations:

A + B = $20,000

0.07*A + 0.1*B = $1,640

To solve this, the first step is isolating one of the variables in one of the equations.

Let's isolate A in the first equation:

A + B = $20,000

A = $20,000 - B.

Now we can replace this in the other equation:

0.07*A + 0.1*B = $1,640

0.07*($20,000 - B) + 0.1*B = $1,640

$1,400 - 0.07*B + 0.1*B = $1,640

0.03*B = $1,640 - $1,400 = $240

B = $240/0.03 = $12,000

Then we have:

A = $20,000 - $12,000 = $8,000

Hank invests $12,000 in the 10% account and $8,000 in the 7% one.

Answer:

  x = 3

Step-by-step explanation:

Maybe you want the equation of the line.

__

A vertical line has undefined slope. Its equation is of the form ...

  x = constant

In order for the line to go through a point with an x-coordinate of 3, the constant must be 3.

  x = 3 . . . . equation of the line

Answer:3/8

Step-by-step explanation:

The simplest form of  

15 /40  is  3 /8 .

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 15 and 40 is 5

Divide both the numerator and denominator by the GCD

15 ÷ 5

40 ÷ 5

Reduced fraction:  

3 /8

Therefore, 15/40 simplified to lowest terms is 3/8.

Answer:

Sn is the trivial subgroup

Step-by-step explanation:

To prove that α must be the identity permutation and also Sn is the trivial subgroup we have to make assumptions :

when we assume   α  is not an identity permutation

α(i) = -j   but since n ≥ 3 we will make  another assumption of a number k

hence we will choose : β = ( i k )

from these assumptions we can deduce that

        αβ (i) = α(k) ≠ -j   since α(i) = -j

also   βα (i) = β(-j) = -j

from the equations above we can conclude that

 αβ ≠  βα   which is in contradiction to the expression : αβ=βα . this simply shows that  α must be the identity permutation, and the number of permutations of Sn is true for every number of permutation of Sn provided it is other than  the identity

hence the center Sn is the trivial subgroup

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-74,-76) and (-35,4)

The distance between the points is

We have the final answer as

Hope this helps you

Answer:

64 dollars

Step-by-step explanation:

8 children and 8 adults

2 dollars for a child and 6 dollars for an adult

cost for children

8 children * 2 dollars each = 16

cost for adults

8 adults * 6 dollars each = 48

Add the two costs together

16+48 =64

Answer:

8×2=16

8×6=48

48+16=64