Translate the following into an algebraic expression: If it would take Mark m hours to clean the house alone and with his brother Sam they can clean the house together in t hours. How many hours would it have taken Sam if he was working alone

Answer:

$ 1220.00

Step-by-step explanation:

1269.79 = A [tex]e^{.02 * 2}[/tex]

1269.79 /A = [tex]e^{.04}[/tex]

ln(1269.79 /A) = .04 ln(e)

ln(1269.79 /A) = .04

1269.79 /A = [tex]e^{.04}[/tex]

1269.79 /A = 1.0408

A =  1269.79 / 1.0408

$ 1220.00

Answer: No, it fails the vertical line test.

Step-by-step explanation:

9514 1404 393

Answer:

  (1, -1)

Step-by-step explanation:

The three transformations are ...

  (x, y) ⇒ (-x, y) . . . . . reflection over the y-axis

  (x, y) ⇒ (x, -y) . . . . . reflection over the x-axis

  (x, y) ⇒ (-x, -y) . . . . . rotation 180°

Then the composition of the three transformations is ...

  (x, y) ⇒ (x, y) . . . . . . back to the original position

  A(1, -1) ⇒ A'(1, -1)

Answer:

Step-by-step explanation:

Step-by-step explanation:

Let us take a nominal square of area 25 cm².

So, in this question, we can say that:-

a. The length of one of its sides will be less than 5 cm.

b. Its perimeter will be less than 20 cm.

Hope it helps :)

Step-by-step explanation:

area= 25cm squared

length of one side = 5cm as 5*5 =25

perimeter= 5*4= 20cm

But since the area is less than 25cm squared

we can say that the length of one side is less than 5cm and we can also say that the length of the perimeter is less than 20cm.

Hope this helps.

9514 1404 393

Answer:

  a-b

Step-by-step explanation:

Add the two equations together:

  (ax +by) +(bx +ay) = (a² -b²) +(0)

  x(a +b) +y(a +b) = (a +b)(a -b)

  x + y = a - b . . . . . divide by (a+b), assuming a+b ≠ 0

Answer:

The answer is below

Step-by-step explanation:

a) A cube is a three dimensional solid with 6 square faces.

A cube has 8 vertices

b) A rectangular prism is a three dimensional solid with two parallel rectangular bases.

A rectangular prism has 6 faces.

c) A rectangular prism is a three dimensional solid with two parallel rectangular bases.

A rectangular prism has 12 edges.

d) A square-based pyramid is a pyramid with a square base.

A square-based pyramid has 8 edges

e) A triangular prism is a three dimensional solid with two parallel triangular bases.

A triangular prism has 5 faces.

f) A triangular prism is a three dimensional solid with two parallel triangular bases.

A triangular prism has 6 vertices.

Answer:

Logistic model

Step-by-step explanation:

A scatter plot is a mathematical representation or diagram which is used to shoe the relation between two given variables. It uses the Cartesian coordinates which is used to display the values for a typically two variables for the given set of data.

In the context, a scatter plot is made between two variables. The two variables are the total number of hours and the number of weeks.

From the graph shown, we can say that model is a logistic model as the shape of the graph is S shaped.

Therefore, the appropriate model for the data given is logistic model.

Answer:

30 additional teachers will have to be hired to reduce the ratio to 1:20.

Step-by-step explanation:

Given that Jefferson School has 1800 students, and the teacher-pupil ratio is 1:30, to determine how many additional teachers will have to be hired to reduce the ratio to 1:20, the following calculation must be performed:

30 = 1800

1 = X

1800/30 = X

60 = X

20 = 1800

1 = X

1800/20 = X

90 = X

90 - 60 = 30

Therefore, 30 additional teachers will have to be hired to reduce the ratio to 1:20.

Answer:

21

Step-by-step explanation:

7+7+7=21

Answer:

f(h(x)) = 2•(x²-1)² -4•(x²-1)

Answer:

C.

Step-by-step explanation:

The function shifted left five units instead of right five units.

There's no vertical compression in the equation provided, but that's probably just a typo since there's a random bracket that I assume was supposed to be a fraction.

Answer:

obtuse cant be a right angle

Step-by-step explanation:

in order to be  obtuse you  have to be more than 90 dagrees

Answer:

[tex]\frac{(2/36)}{(1-(28/36))} = 1/4[/tex]

Step-by-step explanation:

Answer:

80 seconds

Step-by-step explanation:

10/10 = 1

now it takes 1 seconds to count 1 sheet

80 x 1 = 80 seconds to count 80 sheets

Step-by-step explanation:

10sheets=10seconds

1sheet=1sheet÷10sheets x 10seconds

=1second

80sheets=80sheets÷1sheet x 1second

80seconds

hope this is helpful

Answer:hello

Step-by-step explanation:

1+1

Answer:

A is that answer

A) y<2x-3

Answer:

The correct answer is 3x-2

Step-by-step explanation:

It gives you the expression for JM and LM, and it asks for JL. Therefore, if you take away LM from JM, you are left with JL. You must subtract 2x-6 from 5x-8.

∴5x-8-(2x-6)

Do not forget to distribute the negative since you are subtracting, so instead of subtracting 6 from 8, you will be adding 6 to 8 because two negatives make a positive.

the answer Is 95.61465. If you approximate you get 10.

Answer:

65 km/hr

Step-by-step explanation:

The average of numbers can be calculated by adding them up and dividing that by how many numbers there are.

Here, we have two numbers. Therefore, we first add them (55+75 = 130) and then divide by 2 because there are 2 numbers, so 130/2 = 65

Answer:

∠DFE

Step-by-step explanation:

Complementary angles are angles that have a sum of 90°. Since there is a box on angle ∠CFB, we can infer that ∠CFE is also 90°. This is because the two are supplementary (equal 180°). Therefore, ∠DFE is the other part of ∠CFD that would complete the 90° pair.

Answer:

Problem 17)

[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]

Problem 18)

[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]

Step-by-step explanation:

Problem 17)

We have the curve represented by the equation:

[tex]\displaystyle 4x^2+2xy+y^2=7[/tex]

And we want to find the equation of the tangent line to the point (1, 1).

First, let's find the derivative dy/dx. Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}\left[4x^2+2xy+y^2\right]=\frac{d}{dx}[7][/tex]

Simplify. Recall that the derivative of a constant is zero.

[tex]\displaystyle \frac{d}{dx}[4x^2]+\frac{d}{dx}[2xy]+\frac{d}{dx}[y^2]=0[/tex]

Differentiate. We can differentiate the first term normally. The second term will require the product rule. Hence:

[tex]\displaystyle 8x+\left(2y+2x\frac{dy}{dx}\right)+2y\frac{dy}{dx}=0[/tex]

Rewrite:

[tex]\displaystyle \frac{dy}{dx}\left(2x+2y\right)=-8x-2y[/tex]

Therefore:

[tex]\displaystyle \frac{dy}{dx}=\frac{-8x-2y}{2x+2y}=-\frac{4x+y}{x+y}[/tex]

So, the slope of the tangent line at the point (1, 1) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=-\frac{4(1)+(1)}{(1)+(1)}=-\frac{5}{2}[/tex]

And since we know that it passes through the point (1, 1), by the point-slope form:

[tex]\displaystyle y-1=-\frac{5}{2}(x-1)[/tex]

If desired, we can simplify this into slope-intercept form. Therefore, our equation is:

[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]

Problem 18)

We have the equation:

[tex]\displaystyle y=\tan^{-1}\left(x^3\right)[/tex]

And we want to find the equation of the tangent line to the graph at the point (1, π/4).

Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\tan^{-1}(x^3)][/tex]

We can use the chain rule:

[tex]\displaystyle \frac{d}{dx}[u(v(x))]=u'(v(x))\cdot v(x)[/tex]

Let u(x) = tan⁻¹(x) and let v(x) = x³. Thus:

(Recall that d/dx [arctan(x)] = 1 / (1 + x²).)

[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2[/tex]

Substitute and simplify. Hence:

[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2=\frac{3x^2}{1+x^6}[/tex]

Then the slope of the tangent line at the point (1, π/4) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{x=1}=\frac{3(1)^2}{1+(1)^6}=\frac{3}{2}[/tex]

Then by the point-slope form:

[tex]\displaystyle y-\frac{\pi}{4}=\frac{3}{2}(x-1)[/tex]

Or in slope-intercept form:

[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]

Answer:

[tex]P(x=4) = 0.200[/tex]

Step-by-step explanation:

Given

[tex]n=10[/tex] --- selected customers

[tex]x = 4[/tex] --- those that are expected to use the restroom

[tex]p =30\% = 0.30[/tex] --- proportion that uses the restroom

Required

[tex]P(x = 4)[/tex]

The question illustrates binomial probability and the formula is:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]

So, we have:

[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (1 - 0.30)^{10 - 4}[/tex]

[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (0.70)^6[/tex]

[tex]P(x=4) = 210* (0.30)^4 * (0.70)^6[/tex]

[tex]P(x=4) = 0.200[/tex]

9514 1404 393

Answer:

  x = 22, y = 123

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  (2x +13)° +57° +3x° = 180°

  5x +70 = 180 . . . . . . . . . . . . . collect terms, divde by °

  5x = 110 . . . . . . . . . . . subtract 70

  x = 22 . . . . . . . . divide by 5

__

Angles in a linear pair are supplementary.

  y° + 57° = 180°

  y = 123 . . . . . . . . divide by °, subtract 57

Answer:

A

=

w

l

d

=

w

2

+

l

2

Solving for

d

d

=

l

2

+

(

A

l

)

2

=

11

2

+

(

110

11

)

2

≈

14.86607

The length of the diagonal of the rectangle is 14.9 units.

A diagonal is the longest line that divides a plane shape into two halves.

To calculate the diagonal of the rectangle, we use Pythagoras theorem.

Formula:

Where:

make w the subject of the equation

From the question,

Given:

Substitute these values into equation 2

Finally, to calculate the diagonal of the rectangle, we use the formula below

Given:

Substitute these values into equation 3

Hence, the length of the diagonal of the rectangle is 14.9 units.

Learn more about diagonal here: https://brainly.com/question/654982

#SPJ2

Answer:

option B is correct

interior angle of given polygon =156

exterior angle of polygon=180 - 156 =24

as we know that sum of exterior angle of any polygon is 360 degree

so number of sides of regular polygon=360/24=15

Answer:

option B. 15

Step-by-step explanation:

Sum of interior angles of a polygon with n sides  =  ( n - 2 ) x 180°

Therefore each interior angle,

                                  [tex]\frac{n - 2}{n} \times 180^\circ[/tex]

Given the interior angles = 156°

That is ,

                         [tex](\frac{n-2}{n}) \times 180 = 156\\\\\frac{n-2}{n} = \frac{156}{180}\\\\1- \frac{2}{n} = \frac{156}{180}\\\\1 - \frac{156}{180} = \frac{2}{n}\\\\\frac{180-156}{180} = \frac{2}{n}\\\\\frac{24}{180} = \frac{2}{n}\\\\24 \times n = 2 \times 180\\\\n = \frac{2 \times 180}{24} =\frac{180}{12} = 15[/tex]

Answer:

65000

Step-by-step explanation:

65x 1000

1000 because 1kg= 1000

Answer:

answer is in the picture above

Answer:

The choose (A)

y=(x-1)²-2