Bilquis owns a small business selling used books. She knows that in the last week 49 customers paid cash, 42 customers used a debit card, and 32 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a credit card as a decimal to the nearest hundredth.

Answer:

[tex]\dfrac{dy}{dx}=-y\left(4+\dfrac{1}{x}\right)[/tex]

or written in rational form:

[tex]\dfrac{dy}{dx}=\dfrac{-4xy-y}{x}[/tex]

Step-by-step explanation:

[tex]\ln(xy)+4x=45[/tex]

[tex]\textsf{Apply the product log law}\quad\ln(ab)=\ln(a)+\ln(b):[/tex]

[tex]\implies \ln(x)+\ln(y)+4x=45[/tex]

[tex]\textsf{Add}\:\dfrac{d}{dx}\:\textsf{in front of each term}:[/tex]

[tex]\implies \dfrac{d}{dx}\ln(x)+\dfrac{d}{dx}\ln(y)+\dfrac{d}{dx}4x=\dfrac{d}{dx}45[/tex]

[tex]\textsf{Differentiate the}\: x \: \textsf{terms and constant terms first}:[/tex]

[tex]\implies \dfrac{1}{x}+\dfrac{d}{dx}\ln(y)+4=0[/tex]

[tex]\textsf{When differentiating with respect to}\:y,\: \textsf{differentiate and add}\: \dfrac{dy}{dx}:[/tex]

[tex]\implies \dfrac{1}{x}+\dfrac{1}{y}\dfrac{dy}{dx}+4=0[/tex]

[tex]\textsf{Rearrange to make}\:\dfrac{dy}{dx}\:\textsf{the subject}:[/tex]

[tex]\implies \dfrac{1}{y}\dfrac{dy}{dx}=-4-\dfrac{1}{x}[/tex]

[tex]\implies \dfrac{dy}{dx}=y\left(-4-\dfrac{1}{x}\right)[/tex]

[tex]\implies \dfrac{dy}{dx}=-y\left(4+\dfrac{1}{x}\right)[/tex]

If you want it in rational form, then:

[tex]\implies \dfrac{dy}{dx}=-4y-\dfrac{y}{x}[/tex]

[tex]\implies \dfrac{dy}{dx}=\dfrac{-4xy-y}{x}[/tex]

[tex]~~~~~\ln(xy) +4x = 45\\\\\\\implies \dfrac{d}{dx} \left[\ln(xy) +4x \right] = \dfrac{d}{dx} ( 45)\\\\\\\implies \dfrac{1}{xy} \cdot \dfrac{d}{dx} (xy) + 4 = 0\\\\\\\implies \dfrac 1{xy} \left( x\dfrac{dy}{dx} + y \right) +4 =0\\\\\\\implies x\dfrac{dy}{dx} + y + 4xy=0\\\\\\\implies x \dfrac{dy}{dx} =-y-4xy\\\\\\\implies \dfrac{dy}{dx} = \dfrac{-y-4xy}x[/tex]

The material is needed to make the tent, assuming the tent has a floor would be equal to 36/√3.

Connect three rectangles edge to edge. Now close their triangular mouths from both ends. That shape is called a triangular prism.

Let the tent width be w and the given Length is 6 feet.

[tex]tan\theta = \dfrac{opposite }{adjecent} \\\\tan60 = \dfrac{h}{w/2} \\\\\sqrt{3} = \dfrac{6}{w/2} \\\\\sqrt{3} = \dfrac{12}{w} \\\\w = \dfrac{12}{\sqrt{3} }[/tex]

[tex]sin60 = \dfrac{opposite }{hypotenuse} \\\\sin60 = \dfrac{6}{x}\\\\x = \dfrac{6}{\sqrt{3}/2 }\\\\x = \dfrac{12}{\sqrt{3} }[/tex]

The area of the front tent =

[tex]\dfrac{1}{2} \times base \times height\\\\\dfrac{1}{2} \times w\times h\\\\\\\dfrac{1}{2} \times 12/\sqrt{3} \times 6\\\\\dfrac{36}{\sqrt{3} }[/tex]

The area of the back tent is also the same.

Learn more about triangular prisms here:

https://brainly.com/question/16261758

#SPJ1

Answer:

The green would take 4 and the blue would take 16 times respectivly.  I did it by finding the volumes of the cups in terms of pi, then dividing it by the volume of the sink.

Step-by-step explanation:

So the volume of the whole half sphere is 512pi.

Now we have to find the volumes of the cup.

Equation: [tex]\pi r^2h[/tex]

Blue cup:

[tex]\pi 2^2(8)\\\pi 4(8)\\\pi 32[/tex]

It would take 16 times to drain it completly.

Green cup:

[tex]\pi 4^2(8)\\\pi 16(8)\\\pi 128[/tex]

It would take 4 times to drain it completly.

Answer:

option C is the answer

Step-by-step explanation:

I think it will help you

Answer:

  Bulawayo

Step-by-step explanation:

Proportions can be compared numerous ways. Here, we find it convenient to look at the difference between girls and boys relative to the number of boys.

__

With 35 girls and 25 boys, there are 10 more girls than boys. 10 is less than half of the number of boys, so the ratio of girls to boys is less than 1.5.

With 35 girls and 15 boys, there are 8 more girls than boys. 8 is more than half of the number of boys, so the ratio of girls to boys is more than 1.5.

"More than 1.5" is greater than "less than 1.5", so Bulawayo has the greatest proportion of girls.
_____

Additional comment

As a fraction of the total, the proportions of girls are ...

  Harare: 35/(35+25) = 35/60 = 7/12 = 21/36

  Bulawayo: 22/(22+14) = 22/36 . . . . . . greater than 21/36.

Answer:

The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?

The vertex of the graph of g is 1.5 units to the left of

the vertex of the graph of f.

B

The y-intercept of the graph of g is 1.5 units above the

y-intercept of the graph of f.

The graph of g is a reflection of the graph of f across

the y-axis.

The graph of g is a reflection of the graph of f across

the x-axis.

Step-by-step explanation:

Answer: The slope is 1/2

Step-by-step explanation:

Calculate the rise (change in y-component) divided by the run (change in x-component).

rise = 0 - (-5) = 5

run = 12 - 2 = 10

slope = 5/10 = 1/2

Answer:

20% probability

Step-by-step explanation:

First, we need to calculate the area of all the figures inside the rectangle.

Area of triangle= 1/2 BH

So, 3x2=(6)

Area of Square= L^2

3x3=(9)

Area of rectangle= LxW

=60.

60+9+6= 75.

75 is the total area.

Now, lets find the added area of only the triangle and square.

9+6= 15

The probability will be 15/75=

Convert into percent form

= 20%

Hope this helps and please mark me brainliest :)

Answer:

20% probability

Step-by-step explanation:

20% probability

20% probability

20% probability

20% probability

Answer:

the answer is in the picture

#a

P and B are sides of square

#b

Apply cosines

Answer:

First Find the Radius of Cake by dividing 40/2

Now Find Area of the cake of Bottom

And Then Use the Formula to calculate volume of Circle

Cross Section Area=π Square

Bole of Circle 4/3π× radius cube

Answer:

24,727.5 cm³

Step-by-step explanation:

Information to keep in mind

Formula of a cylinder

Volume (total)

Answer:

to you in 1980 is the lol in lol1234in lol to you in the kids in the lero girl

Answer:

8

Step-by-step explanation:

y = 4 and n = 3

5y - 4n = 5(4) - 4(3)

= 12

Answer:

−4n+5y

Step-by-step explanation:

Larry had 778 automobiles before he had the shipment.

The length of the railing that will fit completely around the deck is 54 feet. The area of the triangular deck is approximately 164.25 square feet.

To find the length of the railing that will fit completely around the triangular deck, we need to calculate the perimeter of the triangle. The perimeter of a triangle is the sum of the lengths of all three sides.

Since each side of the triangular deck is 18 feet long, the perimeter (P) can be calculated as:

P = 18 feet + 18 feet + 18 feet

P = 54 feet

So, the length of the railing that will fit completely around the deck is 54 feet.

Next, let's find the area of the triangular deck. The area of a triangle can be calculated using the following formula:

Area (A) = (1/2) * base * height

Since the triangle is equilateral (all sides have the same length), any side can be considered as the base, and the height can be drawn from any vertex to the midpoint of the opposite side.

Let's consider one of the sides (18 feet) as the base. Now, to find the height, we can draw a perpendicular line from the vertex to the midpoint of the base, creating two right-angled triangles.

The height (h) of one right-angled triangle can be found using the Pythagorean theorem:

[tex]h^2 = (18 feet / 2)^2 + (18 feet)^2\\h^2 = 9 feet^2 + 324 feet^2\\h^2 = 333 feet^2\\[/tex]

h ≈ √333 feet

h ≈ 18.25 feet (rounded to two decimal places)

Now, we can find the area (A) of the triangular deck:

A = (1/2) * base * height

A = (1/2) * 18 feet * 18.25 feet

A ≈ 164.25 square feet (rounded to two decimal places)

So, the area of the triangular deck is approximately 164.25 square feet.

To know more about length:

https://brainly.com/question/27976550

#SPJ2

Answer:

Coefficient 1.2. Exponent 1.3. Variable or Base

Step-by-step explanation:

Answer:

I have got an answer it is false for explanation go to picture

Answer:

I don’t know

Step-by-step explanation:

Answer:

533.3mph

Step-by-step explanation:

The value of (k ○ r) (x) from the given parameters in the task content is; 5 ln(2x³ -14)

If follows from the task content that;

It therefore follows that;

(k ○ r) (x) = k(r(x)) = 5 ln (2(x³-7)).

On this note, the expression which represents (k ○ r) (x) is; 5 ln(2x³ -14).

Read more on nested functions;

https://brainly.com/question/15855840

#SPJ1

Answer: 1 3/10

Step-by-step explanation:

first turn it into a fraction 13/10 then how many times does 13 fit into 10. It fits once with 3 remaining. So you get 1 and 3/10

Answer:

  1 3/10

Step-by-step explanation:

When you read the decimal number, it reads the same as the equivalent mixed number:

  1.3 = "one and three tenths" = 1 3/10

__

Additional comment

This will generally be the case. Some mixed numbers found this way can have their fractions reduced:

  1.2 = "one and two tenths" = 1 2/10 = 1 1/5

Answer:56 bags

Step-by-step explanation:

you are dividing 40 into 5/7 so its technically 40*7 divided by 5, which equals 56. double check by doing 56*5 divided by 7 and you get 40 pounds,

[tex]\frac{40(7)}{5}[/tex]Answer:

To find out how many can be filled, divide the number of pounds of candy by the number of pounds a single bag can hold.

40 can be considered 40/1.

So,

40/1 ÷ 5/7

Make 5/7 a reciprocal(basically flipping the fraction upside down):

40/1 ÷ 7/5

Convert the division symbol into a multiplication symbol:

40/1 × 7/5

Solve!

[tex]\frac{40(7)}{5}[/tex]

Cancel:

[tex]\frac{8(7)}{1}[/tex]

= 56 bags can be filled.

Answer:

-1

Step-by-step explanation:

Formula to the determinant is:

[tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc[/tex]

0(0)–1(1)

0-1

-1

Answer:

-1

Step-by-step explanation:

Formula: ad-bc

0(0) - 1(1)

0-1

-1

Answer:

A=10240033.0/pift /ft

Step-by-step explanation:

Calculate the area of circle:

Round the number: A=10240033.0/pift /ft

Answer: A=10240033.0/pift /ft

The radius of the sphere is 4.2 feet.

A sphere is a geometrical shape in three dimension which has every point on the surface of it at an equal distance from a common point called the center of the sphere.

Volume of a sphere is given by the equation,

Volume = [tex]\frac{4}{3}[/tex]πr³, where r is the radius.

We have volume of the given sphere = 320 feet³

Substituting this value in the main equation, we get,

320 =  [tex]\frac{4}{3}[/tex]πr³

320 × 3 = 4πr³

960 / 4π = r³

960 / (4 × 3.14) = r³

r³ = 76.43

r = 4.24 ≈ 4.2

Hence, the radius of the sphere with a volume of 320 feet³ has a radius of 4.2 feet, to the nearest tenth of a foot.

To learn more about spheres, click:

https://brainly.com/question/11374994

#SPJ2

Answer:

Step-by-step explanation:

C(t)=30+3.5t

hope this help yw and can i get brainly pls

Answer:

option C, 6

Step-by-step explanation:

If we subtract 252 - 126

we get 126 then divide by 21 to get 6.

therefore 6 hours

edit: If you liked my answer Brainlist Please.

Answer: C) P(blue) = 70%, P(green) = 30%, P(blue and green) = 21%

Step-by-step explanation:

Given probabilities P(A) AND P(B) are independent, the probability that both events to occur is given by:

P(A)∩P(B)

thus from the example, independent events will be:

P(blue)=70%, P(green)=30%, P(blue and green)=21%

Because:

P(blue)∩P(green)=0.7×0.3=0.21=21%

Answer:

[tex]\huge\boxed{\sf Option \ 1}[/tex]

Step-by-step explanation:

People surveyed = 42

People who approved = 25

So, the sample is:

25 residents who approve.

And population:

42 residents surveyed.

[tex]\rule[225]{225}{2}[/tex]

Answer:

it is 113*

Step-by-step explanation:

hat is the measure of XYZ?