A man saves 4% of his monthly
income of $19,540, the percentage
Savings is increased in the ratio
3:2 Calculate the savings from
the monthly
income.​

Answer:

k(x) = 6x

Step-by-step explanation:

A function shows the relationship between two or more variables. It shows the relationship between an independent and a dependent variable.

Given that the amount of water being poured into the tube is given by f(x) = 12x, where x is in minutes and the amount of water draining out of the tub is given by the function g( x )=6x. The amount of water remaining in the tube after x minutes is gotten by finding the difference between the amount of water entering the tube and the amount leaving the tube after x minutes. If k is the function representing the amount of water in the tube after x minutes, it is given by:

k(x) = f(x) - g(x)

k(x) = 12x - 6x

k(x) = 6x

Answer:

IV. A+{1, 2, 3, 6, 12}

Step-by-step explanation:

The set of natural numbers form a poset number under relation of > or =. The discrete variables are used to form a poset. The symbols for divisibility in poset form are when an integer is divided by the variable without integer. The correct answer is therefore 4th option.

Answer:

m∠Q = 61°

m∠S = 61°

m∠R = 58°

Step-by-step explanation:

Since we have an isosceles triangle, we know that ∠Q and ∠S are congruent.

Step 1: Definition of isosceles triangle

2x + 41 = 3x + 31

41 = x + 31

x = 10

Step 2: Find m∠Q

m∠Q = 2(10) + 41

m∠Q = 20 + 41

m∠Q = 61°

Step 3: Find m∠S

Since m∠Q = m∠S,

m∠S = 61°

Step 4: Find m∠R (Definition of a triangle)

Sum of angles in a triangle adds up to 180°

m∠R = 180 - (61 + 61)

m∠R = 180 - 122

m∠R = 58°

Answer :

1

Step-by-step-explanation :

[tex] {x}^{2} + 4x + 5 - {(x + 2)}^{2} \\ {x}^{2} + 4x + 5 - ( {x}^{2} + 4x + 4) \\ [/tex]

[tex]{x}^{2} + 4x + 5 - {x}^{2} - 4x - 4 = {x}^{2} - {x}^{2} + 4x - 4x + 5 - 4 = 5 - 4 = 1[/tex]

Answer:

(x+1)  •  (x-5)

Step-by-step explanation:

The first term is,  x2  its coefficient is  1 .

The middle term is,  -4x  its coefficient is  -4 .

The last term, "the constant", is  -5  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -5 = -5  

Step-2 : Find two factors of  -5  whose sum equals the coefficient of the middle term, which is   -4 .

     -5    +    1    =    -4    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  1  

                    x2 - 5x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-5)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-5)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-5)

Answer:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.

Answer:

Events are independent if the outcome of one effect does not effect the outcome

Step-by-step explanation:

Answer:

The correct answer, again, is A; Z = -0.6

Answer:

im pretty sure its A; Z = -0.6 sorry if im wrong

Step-by-step explanation:

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P [tex](x_0,y_0,z_0)[/tex] is

[tex]z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\[/tex]

Now the partial derivatives of f are

[tex]f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}[/tex]

[tex]\\\\=\frac{1}{9-8}[/tex]

= 1

Now

[tex]f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}[/tex]

= -8

So, the tangent equation is

[tex]z - 0 = 1\times (x - 9) -8\times (y - 1)[/tex]

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

The equation of the tangent plane is [tex]x-8y-z=1[/tex]

An equation of the tangent plane to the given surface at the point [tex]P(x_0,y_0,z_0)[/tex] is,

[tex]z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)[/tex]

The function is,

[tex]z = ln(x-8y)[/tex]

And the point is (9,1,0)

Now, calculating [tex]f_x,f_y[/tex]

[tex]f_x(x,y)=\frac{1}{x-8y}\\ f_y(x,y)=\frac{x-8}{x-8y}[/tex]

Now, substituting the given points into the above functions we get,

[tex]f_x(9,1)=\frac{1}{9-8(1)}=1\\ f_y(x,y)=\frac{-8}{9-8(1)}=-8[/tex]

So, the equation of the tangent plane is,

[tex]z-0=1(x-9)-8(y-1)\\z=x-8y-1\\x-8y-z=1[/tex]

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Answer:

b

Step-by-step explanation:

y = x + 1

The correct answer is (B). The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the "m" in front of the "x" variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn't give us y = 2 is (B).

Option B is correct.

Given:

Line A passes through the point [tex](-1,2)[/tex].

To find:

Which of the given equations cannot be the equation of line A.

Solution:

If Line A passes through the point [tex](-1,2)[/tex], it means the equation of Line A must be satisfied by the point

In option A, consider the given equation is:

[tex]y=1-x[/tex]

Substituting [tex]x=-1,y=2[/tex], we get

[tex]2=1-(-1)[/tex]

[tex]2=1+1[/tex]

[tex]2=2[/tex]

This statement is true. So, [tex]y=1-x[/tex] can be the equation of line A.

Similarly, check for the other options.

In option B,

[tex]y=x+1[/tex]

Substituting [tex]x=-1,y=2[/tex], we get

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

[tex]2=0[/tex]

This statement is false. So, [tex]y=x+1[/tex] cannot be the equation of line A.

In option C,

[tex]x=-1[/tex]

It is a vertical line and it passes through the point [tex](-1,2)[/tex] because the x-coordinate is [tex]-1[/tex]. So, [tex]x=-1[/tex] can be the equation of line A.

In option D,

[tex]y=x+3[/tex]

Substituting [tex]x=-1,y=2[/tex], we get

[tex]2=-1+3[/tex]

[tex]2=2[/tex]

This statement is true. So, [tex]y=x+3[/tex] can be the equation of line A.

Therefore, the correct option is B.

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Answer:

The two odd numbers are 15 and 17

Step-by-step explanation:

Given

Let the odd numbers be represented with x and y

Let x be the greater number

[tex]x + 5y = 92[/tex]

Required

Find x and y

Since x and y are consecutive odd numbers and x is greater, then

[tex]x = y + 2[/tex]

Substitute y + 2 for x in [tex]x + 5y = 92[/tex]

[tex]y + 2 + 5y = 92[/tex]

Collect Like Terms

[tex]y + 5y = 92 - 2[/tex]

[tex]6y = 90[/tex]

Divide both sides by 6

[tex]\frac{6y}{6} = \frac{90}{6}[/tex]

[tex]y = \frac{90}{6}[/tex]

[tex]y = 15[/tex]

Substitute 15 for y in [tex]x = y + 2[/tex]

[tex]x = 15 + 2[/tex]

[tex]x = 17[/tex]

Hence; the two odd numbers are 15 and 17

Answer:

Maths

Step-by-step explanation:

Answer:

The two odd numbers are 15 and 17

Step-by-step explanation:

Given

Let the odd numbers be represented with x and y

Let x be the greater number

Required

Find x and y

Since x and y are consecutive odd numbers and x is greater, then

Substitute y + 2 for x in  

Collect Like Terms

Divide both sides by 6

Substitute 15 for y in  

Hence; the two odd numbers are 15 and 17

Answer:

5

Step-by-step explanation:

Steps of calculation:

Answer is 5

Answer: B) The linear speed is 4750 inches per second, so this car would qualify.

Step-by-step explanation: To determine linear speed using revolutions per second, i.e., angular speed (ω):

v = ω.r

where r is radius.

As ω is in revolutions per second, transform into rad/s:

ω = 36 revolutions/s

1 revolution = 2π rad

ω = 36.2π rad/s

ω = 72π rad/s

Radius is 21 inches, which can be written as

r = 21 inches/rad

Linear speed is

v = [tex]\frac{72.\pi rad}{s} .\frac{21 in}{rad}[/tex]

v ≈ 4750 inches per seconds

Converting to miles per hour:

v = [tex]4750.\frac{5}{88}[/tex]

v = 270mph

At linear speed of 4750 inches per second, a car with wheel of radius 21-inch can qualify.

Answer:

Above is correct

Step-by-step explanation:

The more accurate value is 6.57881347896059, which you can round however you need. I picked two decimal places.

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

Explanation:

Let's pick a starting value of the car. It doesn't matter what the starting value, but it might help make the problem easier. Let's say A = 1000. Half of that is 1000/2 = 500.

So we want to find out how long it takes for the car's value to go from $1000 to $500 if it depreciates 10% per year.

The value of r is r = 0.10 as its the decimal form of 10%

t is the unknown number of years we want to solve for

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

y = A(1 - r)^t

500 = 1000(1 - 0.1)^t

500 = 1000(0.9)^t

1000(0.9)^t = 500

0.9^t = 500/1000

0.9^t = 0.5

log( 0.9^t ) = log( 0.5 )

t*log( 0.9 ) = log( 0.5 )

t = log( 0.5 )/log( 0.9 )

t = 6.57881347896059

Note the use of logs to help us isolate the exponent.

Answer:

(3,-1)

Step-by-step explanation:

Graph boths functions (picture below)

Answer:

The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Step-by-step explanation:

Given that:

F(x,y) = 8 sin (xy) at (0,9)

The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]

[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]

[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]

We can conclude that the  maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Answer:

(A)

Step-by-step explanation:

That rule isn't used in the elimination methods for systems of equations, but, rather, it is used in substitution methods. The other rules are used in elimination.

Please tell me if I got it wrong.  I really hope it is correct.

A. Add the left side of equation 2 to the left side of equation 1.

B. Multiply equation 2 by 3. Then subtract the result from equation 1.

C. Add equation 2 to equation 1.

By Green's theorem,

[tex]\displaystyle\int_{x^2+y^2=16}(3y-e^{\sin x})\,\mathrm dx+(7x+y^4+1)\,\mathrm dy[/tex]

[tex]=\displaystyle\iint_{x^2+y^2\le16}\frac{\partial(7x+y^4+1)}{\partial x}-\frac{\partial(3y-e^{\sin x})}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]

[tex]=\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy[/tex]

The remaining integral is just the area of the circle; its radius is 4, so it has an area of 16π, and the value of the integral is 64π.

We'll verify this by actually computing the integral. Convert to polar coordinates, setting

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]

The interior of the circle is the set

[tex]\{(r,\theta)\mid0\le r\le4\land0\le\theta\le2\pi\}[/tex]

So we have

[tex]\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy=4\int_0^{2\pi}\int_0^4r\,\mathrm dr\,\mathrm d\theta=8\pi\int_0^4r\,\mathrm dr=64\pi[/tex]

as expected.

Answer:

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is 202500 swordfishes.

Step-by-step explanation:

Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)

First Derivative Test

[tex]f'(p) = -0.02\cdot p +9[/tex]

Let equalize the resulting expression to zero and solve afterwards:

[tex]-0.02\cdot p + 9 = 0[/tex]

[tex]p = 450[/tex]

Second Derivative Test

[tex]f''(p) = -0.02[/tex]

This means that result on previous part leads to an absolute maximum.

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is:

[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]

[tex]f(450) =2025[/tex]

The maximum sustainable yield is 202500 swordfishes.

Answer:

The answer is "[tex]\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}[/tex]"

Step-by-step explanation:

Given:

[tex]\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}[/tex]   [tex]_{where} \ \ n \geq 1[/tex]

In the above-given value, [tex]S_n[/tex] is required for the monotone decreasing so, [tex]S_2 :[/tex]

[tex]\to \sqrt{4k-1} \leq \ k=S_1\\\\[/tex]

square the above value:

[tex]\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\[/tex]

[tex]\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}[/tex]

Answer:

4). 27V

Step-by-step explanation:

Let the edge of the cube A be x

Volume of Cube A= V

Volume= x*x*x= x³

so V = x³

Edge of cube B = 3 times edge of cube A

Edge of cube B = 3x

Volume of cube B =( 3x)³

volume of cube B = 27x³

But x³= V

So volume of cube B = 27v

Answer:

x  ≤ 9

Step-by-step explanation:

x − 6 ≤ 3

Add 6 to each side

x − 6+6 ≤ 3+6

x  ≤ 9

Answer:

x ≤ 9

I hope this helps!

Answer:

169 [tex]cm^{2}[/tex]

Step-by-step explanation:

Surface area (SA) = 2B + PH

                       SA = 2 ([tex]\frac{1}{2}[/tex] x 9 x 6) + (7+7+9) 5

                             = 2 (27) + (23) 5

                             = 54 + 115

                        SA = 169 [tex]cm^{2}[/tex]

Answer:

Step-by-step explanation:

50 : 10 = 5 speaks French only

50 -5= 45 the remainder

4/5 * 45= 36 speaks French and English

45 - 36= 9 speaks English only

The number of students who speak:

i) French only = 5 students,

ii) both French and English = 36 students,

iii) English only = 9 students.

Step 1: Find the number of students who speak French only.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Step 3: Find the number of students who speak both French and English.

Step 4: Find the number of students who speak English only.

Let's calculate it step by step:

Step 1: Find the number of students who speak French only.

1/10 of 50 pupils speak French only:

French-only speakers = (1/10) * 50 = 5 students.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Remaining students = Total students - French-only speakers

Remaining students = 50 - 5 = 45 students.

Step 3: Find the number of students who speak both French and English.

4/5 of the remaining students speak both French and English:

Both French and English speakers = (4/5) * 45 = 36 students.

Step 4: Find the number of students who speak English only.

To find the English-only speakers, subtract the total number of French-only speakers and both French and English speakers from the total number of students:

English-only speakers = Total students - (French-only speakers + Both French and English speakers)

English-only speakers = 50 - (5 + 36) = 50 - 41 = 9 students.

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#SPJ2

Complete question is:

There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only, find the number of students who speak​

i) French only,

ii) both French and English,

iii) English only,

Answer:

C. x = 2, y = -2

Step-by-step explanation:

y = -3x + 4

x + 4y = -6

x + 4(-3x + 4) = -6

x - 12x + 16 = -6

-11x = -22

x = 2

y = -3(2) + 4 = -2

Answer: i don’t kno I’m 6 years old

Step-by-step explanation:

Answer:

  x < -1

Step-by-step explanation:

Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.

  all real values of x where x < -1

Answer:

Base area (B) should not be added.

Step-by-step explanation:

Base area should not be added as cone is not solid. Only Lateral surface area is sufficient in order to find the required paper.

Answer:

Calculated value of F = 0.0535

The critical region is F >F ₀.₀₅ (6,21) = 2.575

Reject H0

Step-by-step explanation:

1. Null hypothesis

H0: µ Nitrogen = µ Phosphorus = µ Both = µ Neither

2. Alternative hypothesis

H1: Not all means are equal.

3. The degrees of freedom for the numerator of the F-ratio = k- 1= 7-1=6

4.The degrees of freedom for the denominator of the F-ratio = n-k= 28-7

= 21

5. The significance level is set at α-0.05

The critical region is F >F ₀.₀₅ (6,21) = 2.575

The test statistic to use is

F = sb²/ sw²

Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom

Correction Factor = CF = Tj²/n = (410)²/28= 6003.57

Total SS ∑∑X²- C. F = 6108- 6003.57= 104.43

Between SS ∑T²j/r - C.F = 42036/ 7 - 6003.57 =  1.57286

Within SS = Total SS - Between SS= 104.43- 1.573= 102.86

The Analysis of Variance Table is

Source Of                 Sum of          Mean              Computed

Variation          d.f     Squares       Squares               F

Between

Samples          6         1.57286       0.2621               0.0535

Within

Samples         21       102.86           4.898

Calculated value of F = 0.0535

Pvalue = 2.575

Since it is smaller than 5 % reject H0.

Answer:

32. A

33. B

Step-by-step explanation:

32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is

33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end