What does the ratio 4: 18 represent in this situation?

The value of e³ = 20.079.

e is an irrational number , It is a numerical constant used in mathematical constant .

The value of e = 2.718

It is asked in the question to determine the value of e³

Therefore

e³ = ( 2.718)³

e³ = 20.079

Therefore the value of e³ = 20.079.

The image of the calculation is attached with the answer.

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Answer:

Area = 180 cm^2

Step-by-step explanation:

See attached image.  The width of the rectangle, a , is the hypotenuse of a right triangle with legs 15 and 20.

Use the Pythagorean Theorem: leg^2 +leg^2 = hypotenuse^2

[tex]a^2=15^2+20^2\\\\a^2=225+400\\\\a^2=625\\\\a=\sqrt{625}=15[/tex]

The width, w, is one leg of a right triangle that has hypotenuse 20 and one leg 16.

[tex]w^2+16^2=20^2\\\\w^2+256=400\\\\w^2=144\\\\w=\sqrt{144}=12[/tex]

The rectangle has length 15 cm and width 12 cm so its area is 12 x 15 = 180 cm^2

Answer:

AREA RECTANGLE =300 cm²

Step-by-step explanation:

If 2 of the 3 vertices of a triangle match up with 2 of the 4 vertices of a rectangle,then the area of the triangle will be exactly half of the area of the rectangle

(Or the area of the rectangle  will be exactly double  of the area of the triangle)

  Area right triangle  = ½ × base × height.

A = 1/2(15X20)

A=1/2( 300)

Area triangle =150  

Area of rectangle is DOUBLE as the  area of triangle

AREA RECTANGLE = 300

The number of fowls is 9, and the number of goats is 12 if there were 42 eyes and 66 legs in her backyard.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of fowls and

y be the number of goats

Then total eyes = 2x + 2y  

Because both have two eyes

2x + 2y = 42 ..(1)

Total legs = 2x + 4y

fowl has two legs and a goat has 4 legs

2x + 4y = 66 ..(2)

After solving two linear equation:

-2y = -24

y = 12

x = 9

Thus, the number of fowls is 9, and the number of goats is 12 if there were 42 eyes and 66 legs in her backyard.

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Answer:

A. is the answer

Answer:

1500

Step-by-step explanation:

3/7 of 3500

=3/7 × 3500

=150

find hourly rate:

96 / 16 = 6 pounds per hour

6 x 1.5 = 9 pounds per hour for overtime.

9 x 4 = 36 pounds

96 + 36 = 132 pounds total

There will be 354087.24 mosquitoes on the 19th of May.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

.

Using the relation :

y = 180000(1.07)^x

x = Number of days since May 6 ;

y = Number of mosquitoes after x days

x = May 9 May 19  = 10 days

Therefore, a number of mosquitoes inhabiting the city on May 19 will be :

y = 180000(1.07)^10

y = 180000  x  1.96715136

y = 354087.24

y = 354087.24  (nearest whole number).

Therefore there will be 354087.24 mosquitoes on the 19th of May.

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The expected number of M&M's in the bag is 308

The parameters that complete the question are:

Number of blue pieces = 4

Total = 15

From the question, the number of blue pieces is:

Blue = 82

Let the total number of M&M be M.

So, we have:

Blue = Number of blue/Total * M

This gives

82 = 4/15 * M

Multiply both sides by 15/4

15/4 * 82 = M

Evaluate

M = 307.5

Approximate

M = 308

Hence, the expected number of M&M's in the bag is 308

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The area of a circle to derive the formula for the area of a sector will be (θ/2π) x (area of the circle).

Let r be the radius of the circle. Then the area of the circle will be

Area = πr²

Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be

Area = (θ/2π) πr²

Area = (θ/2π) x (area of the circle)

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The water level increases by 0.608 meters per minute when the water is 3.5 m deep

The given parameters are:

The relationship between the radius and height is:

r/h = 3/7

Make r the subject

r = 3h/7

The volume of a cone is;

[tex]V = \frac 13\pi r^2h[/tex]

This gives

[tex]V = \frac 13\pi (\frac{3h}{7})^2h[/tex]

Expand

[tex]V = \frac{3h^3}{49}\pi[/tex]

Differentiate

[tex]V' = \frac{9h^2}{49}\pi h'[/tex]

Make h' the subject

[tex]h' = \frac{49}{9\pi h^2}V'[/tex]

When the water level is 3.5.

We have:

[tex]h' = \frac{49}{9\pi * 3.5^2}V'[/tex]

Also, we have:

V' = 4.3

So, the equation becomes

[tex]h' = \frac{49}{9\pi * 3.5^2} * 4.3[/tex]

Evaluate the products

[tex]h' = \frac{210.7}{346.36}[/tex]

Evaluate the quotient

h' = 0.608

Hence, the water level increases by 0.608 meters per minute

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Answer:

6

Step-by-step explanation:

The requried number of passes to reach the maximum is given as 10 passes.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,

We have 5 coins in your purse,
We Gain 1.5x the number of coins in your purse every time you pass the start. The maximum number of coins is 300.

According to the quesiton,
5 . 1.5ˣ = 300

Where x is the number of passes,
1.5ˣ = 60
x ≈ 10

Thus, the requried number of passes to reach the maximum is given as 10 passes.

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Probability helps us to know the chances of an event occurring. The probability of tossing heads and rolling a number less than 3 is 1/6.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The number of cases where coins land on heads and a number less than 3 are rolled is 2, which are H1 and H2.

The probability of tossing heads and rolling a number less than 3 is,

Probability = (Outcomes where coins land on heads and a number less than 3 are rolled)/(Total number of cases)

Probability = 2/12 = 1/6

Hence, the probability of tossing heads and rolling a number less than 3 is 1/6.

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The rate of the passenger train is 81.67 MPH and the rate of the freight train is 66.67 MPH.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

The distance traveled by passenger train = 245 miles

The distance traveled by freight train = 245 miles

The time takes for both trains is the same.

Let's suppose the rate of the passenger train is x and the rate of the freight train is y;

As we know,

Distance = speed×time

245/x = 200/y

200x = 245y

200x - 245y = 0 ..(1)

x = 15 + y ..(2)

Equations (1) and (2) represent the situation.

After solving equations (1) and (2):

[tex]\rm x=\dfrac{245}{3}= 81.67\\\\\\\:y=\dfrac{200}{3}=66.67[/tex]

Thus, the rate of the passenger train is 81.67 MPH and the rate of the freight train is 66.67 MPH.

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The surface area of the given composite figure is; 528 ft²

To get the surface area of the attached composite shape, we will have to break the object down into smaller shapes to get;

Surface area 1 = 2(15 * 4) = 120 ft²

Surface area 2 = 2(9 * 4) = 72 ft²

Surface area 3 = 2(6 * 4) = 48 ft²

Surface area 4 = 2((15 * 15) - (9 * 9)) = 288 ft²

Thus;

Total surface area = 120 + 72 + 48 + 288

Total surface area = 528 ft²

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Answer:

6190

Step-by-step explanation:

you multiply 4 days by 24 because a day have 24 hrs,then you will multiply the answer by 60 ,then after multiplying by 60 you will add 16 minutes and if you want to put is in seconds you multiply by 60 again that's what I know

1) [tex]V=lwh=5(x)(8)=\boxed{40x}[/tex]

2) [tex]V=\pi r^{2}h=(\pi)(3^{2})(8)=\boxed{72}\pi[/tex]

3) [tex]40x=72\pi\\\\x=\frac{72\pi}{40} \approx \boxed{5.7}[/tex]

If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.

Let be f and g two functions, h is a composition of f with respect to g when the input variable of f is equal to g.  The composed function is h(x) = √x + 5 and there may be more than a solution. One of these solutions are f(x) = x + 5 and g(x) = √x.

If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.

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We conclude that the interval in which the function decreases is (1.5, 3]

The ball is decreasing when the graph, reading from left to right, is going downwards.

Particularly, in this parabola that opens downwards, the graph will decrease after the vertex.

And we can see that the vertex is at x = 1.5

And we also see that the graph of the function ends at x = 3.

Then we conclude that the interval in which the function decreases is (1.5, 3]

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Answer:

It is arithmetic progression

Step-by-step explanation:

If wwe see, the numbers are going down by 3 each time, therfore the common difference is 3

Hii!

_________________________________________________________

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]

1. This sequence is arithmetic

2. The common ratio is 3.

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation.}}}\circ\leftharpoonup[/tex]

[tex]\bullet[/tex] Difference between arithmetic and geometric sequences

[tex]\twoheadrightarrow\sf Arithmetic\quad sequences[/tex] - In arithmetic sequences, we add the same amount to obtain the next term.

[tex]\twoheadrightarrow\sf Geometric\quad sequences[/tex] - In geometric sequences we multiply times the same amount to obtain the next term.

[tex]\bullet[/tex] Since we add the same amount to get the next term, the given sequence is arithmetic

[tex]\twoheadrightarrow\sf Common\;difference:-3[/tex]

[tex]\bullet[/tex] In the given sequence we add -3, or subtract 3, to obtain the next term

--

Hope that this helped! Best wishes.

[tex]\stackrel\ast{\textsl{Reach far. Aim high. Dream big.}}[/tex]

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Answer:

See below

Step-by-step explanation:

When you multiply or divide both sides of an inquality equation by a NEGATIVE number , it reverses the symbol to see this in action:

- 4n >36       Instead of dividing by -4   let's ADD - 4n to both sides

0 > 36 + 4n    now SUBTRACT 36 from both sides

-36 > 4n       re-arrange just a little

4n < -36       <======== see how the symbol has reversed ???

n < -9        

Hii!

___________________________________________________________

Answer:

'Cause both sides were divided by a negative number! ^^

Step-by-step explanation:

The sign of the inequality was flipped because you divided both sides of the inequality by -4, which is a negative number.

When we divide, or multiply, both sides of an inequality by a negative number, we flip the inequality sign.

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Hope that this helped! Best wishes.

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The income statement illustrates that the net income will be $3530.

The income statement will be:

Revenue

Consulting revenue 18350

Expenses

Miscellaneous expenses 720

Rent expense 4820

Salaries expense 8370

Telephone expenses 910

Total expenses 14820

Net income = 18350 - 14820 = 3530

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The correct answer is option A which is the pattern {prime, prime, prime, composite, prime, prime} is followed by 1, 5, 7, 9, 11, 13.

Prime numbers:-

The prime number is defined as the number which is divided by 1 and itself.

Composite numbers:-

The number is defined as the composite number when the number is divided by 1 itself and any other numbers also.

From the given options we need to choose the pattern of the series { prime, prime, prime, composite, prime, prime } so we can see that in option A correct pattern is followed.

Pattern { 1, 5, 7, 9, 11, 13 }

1   → prime

5  → prime

7  → prime

9  → composite

11  → prime

13 → prime

Therefore the correct answer is option A which is the pattern {prime, prime, prime, composite, prime, prime} is followed by 1, 5, 7, 9, 11, 13.

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Answer:

6x + 7y = 14

7x + 8y = 27

6 7. x = 14

7 8. y = 27

option B

Answer:

Step-by-step explanation:

Given:

Find: p

Formula: p=k²w

Solution:

p=k2w

➡️ p= (5)²(-3)

➡️ p= 25(-3)

➡️ p= -75

Answer:

Hope it helps

Answer: [tex]-4\left(\frac{1}{2} \right)^{x}[/tex]

Step-by-step explanation:

To reflect the graph of a function across the x-axis,

[tex]y=f(x) \longrightarrow y=-f(x)[/tex]

Answer:

c

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

The other graphs answers have a point at (3, 1) which is not on the graph.

Answer: [tex]3\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\tan 60^{\circ}=\frac{x}{3}\\\\\sqrt{3}=\frac{x}{3}\\\\x=\boxed{3\sqrt{3}}[/tex]

The least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold.

Let x be the number of sweaters that must be produced each hour to earn a profit of at least $100

Total selling price if earns $4 profit for each one sold = 4x

The expenses for running the machine are $45 per hour.

4x - 45 ≤ 100

4x ≤ 145

x ≤ 145/4

x ≤ 36.25

Number of sweater(estimate value) = 37

Thus, the least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.

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An equation is formed of two equal expressions. The number of infections in 6 weeks is 456.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The general equation of an exponential function is written as,

y = A(B)ˣ

Since the infection is increasing at a rate of 50%, therefore, the rate of growth will be,

B = 1.50

Substitute any value then we will get,

40 = A(1.50)⁰

A = 40

Thus, the exponential equation of the growth will be,

y = 40(1.50)ˣ

Now, the number of infections in 6 weeks will be,

y = 40(1.50)⁶

y = 455.625 ≈ 456

Hence, the number of infections in 6 weeks is 456.

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