Write an algebraic expression to model this word phrase: The quotient of the sum of 6 and a number, x, and 4

Let's begin by listing out the information given to us:

3 treasure chests contain: 34 jewels, 48 jewels & 18 jewels

Total jewels = 34 + 48 + 18 = 100 jewels

Five explorers plan to share them equally:

To know how many jewels does each get, we divide the total number of jewels by the number of explorers

Total jewels / number of explorers = 100/5 = 20 jewels

Therefore each explorer gets 20 jewels

Answer

The triangle might be an equilateral triangle.

False

The triangle must be a right triangle.

False

The triangle might be an acute triangle.

True

Explanation

First of, we will explain the different types of triangles that exist based on side lengths and angle measures respectively,

Based on side lengths,

- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.

- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.

- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.

Based on angle measures,

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

So, a sketch of the triangle described would look like

So, we can see that the triangle has two sides equal, hence, the two base angles will be equal to.

If we call those base angles, x,

x + x + 45° = 180°

2x = 180° - 45°

2x = 135°

Divide both sides by 2

(2x/2) = (135°/2)

x = 67.5°

Three angles of the triangle are 45°, 67.5° and 67.5°

So, taking the statements one at a time now

The triangle might be an equilateral triangle.

This statement is False since it is evident that all the angles of this triangle are not equal to one another, hence, the sides cannot all be equal too.

The triangle must be a right triangle.

This statement too, is False. None of the angles of the triangle is equal to 90°.

The triangle might be an acute triangle.

This statement is True. All of the angles of the triangle are less than 90°.

Hope this Helps!!!

The probability that the person smoked 11 to 20 cigarettes per day is 15273/100450.

The likelihood of choosing at random one study participant who smoked between 11 and 20 cigarettes per day is equal to the frequency of those who smoke between 11 and 20 cigarettes divided by the total number of study participants.

1. People smoking at most ten cigarettes per day,

African American: 9886

Native Hawaiians: 2745

Latinos: 12831

Japanese Americans: 8378

Whites: 7650

2. People who smoke 11 to 20 cigarettes per day.

African Americans: 6514

Native Hawaiians: 3062

Latinos: 4932

Japanese Americans: 10680

Whites: 9877

3. People smoking 21 to 30 cigarettes per day,

African Americans: 1671

Native Hawaiians: 1419

Latinos: 1406

Japanese Americans: 4715

Whites: 6062

4. People smoke at least 31 cigarettes per day.

African Americans: 759

Native Hawaiians: 788

Latinos: 800

Japanese Americans: 2305

Whites: 3970

Therefore, the total will be:

Group                       Total

[0 - 10]                      41,490

[11 - 20]                     35,065

[21 -30]                     15,273

[31 and more]            8,622

Total           100,450

Therefore, the probability that a person smoked 11 to 20 cigarettes per day will be:

P = 15,273/100,450

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The complete question is mentioned below:

An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 Whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 Whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 Whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 Whites. Suppose that one person from the study is randomly selected. Find the probability that person smoked 11 to 20 cigarettes per day. (Enter your probability as a fraction.)

Answer:

9 bases were stolen by elena

Step-by-step explanation:

Let n = number of bases stolen by Natasha

    e = number of bases stolen by Elena

So, n = 2e -3

So, if n=15,   15 = 2e-3   >>

e=9 bases stolen by Elena

If Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases, Then 9 bases did Elena steal

Two or more expressions with an Equal sign is called as Equation.

Given,

Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases, we need to find bases stolen by Elena.

Let N be the number of bases stolen by Natasha

E be the number of bases stolen by Elena

Natasha stole three fewer bases than twice the number Elena stole.

We can write this sentence as expression.

So, N= 2E -3

When Natasha stole 15 bases, then we need to find E

15=2E-3

Add 3 on both sides

18=2E

Divide both sides by 2

9=E

Hence 9 bases were Elena steal when Natasha steals 15.

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Area of standard football pitch is 7140 square m.

What is the area and perimeter of the rectangle?

Perimeter  is the total distance of the rectangle moves outside of it. The Perimeter  basically indicates the length of the shape. A rectangle has four sides, so the perimeter of the rectangle is the sum of all four sides. Perimeter is a linear measure, so rectangle perimeter units are meters, centimeters, inches, feet, and so on.

perimeter, P = 2 ( a+b) units

area = length × width = a × b

Area can be defined as the region covered by the rectangle in two-dimensional space. The area of ​​a rectangle can also be defined as the number of square units required to completely fill the rectangle.

Length of the standard football pitch = 105 m

Breadth of the standard football pitch = 68 m

Using, area of rectangle = Length × breadth

Area of standard football pitch = 105 × 68 = 7140 square m.

Hence, area of standard football pitch is 7140 square m.

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%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

When expressing a proportionate share of a total, percentages are frequently utilized. (Similarly, the term "per mile" or the sign "" can be used to denote a number as a fraction of 1,000.)

Answer:

The percentage of water in a 64-ounce bottle of orange juice is higher.

Detailed explanation:

Case 1: There are 32 ounces of water in an 80-ounce container of apple juice.

80 ounces total are contained in the bottle.

32 ounces of water, please.

Therefore, Percent of Water =32/80x100

                                                = 40%

Case 2) There are 48 ounces of water in a 64-ounce bottle of orange juice.

64 ounces total are contained in the bottle.

Water measurement is 48 ounces.

Therefore, Percent of Water =48/64x100

                                              =75%

The percentage of water in a 64-ounce bottle of orange juice is therefore higher.

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We are given the following system of equations:

we are asked to determine if the point (0, 3) is a solution of the equation. To do that, we will replace the points x = 0 and y = 3 in each of the equations to see if they are both satisfied:

Replacing in equation (1):

Since equation (1) is not satisfied by the point this means that this is not a solution.

√664 is the perimeter of the triangle .

What is a perimeter in math?

In this graph three points are given .

Let A = ( -9 , 3)

     B = ( 5 , 7 )

     C = ( -4 , -8 )

Distance between point AB = [tex]\sqrt{( 5 + 9 )^{2} + ( 7 - 3 )^{2} }[/tex]

                                             = [tex]\sqrt{( 14)^{2} + ( 4)^{2} }[/tex]

                                             = [tex]\sqrt{196 + 16}[/tex]

                                              = √212

Distance between point BC = [tex]\sqrt{( -4 -5)^{2} + ( -8 -7 )^{2} }[/tex]

                                               = [tex]\sqrt{( -9)^{2} + ( -15)^{2} }[/tex]

                                               = [tex]\sqrt{ 81 + 225}[/tex]

                                               = √306

Distance between point CA = [tex]\sqrt{ ( -4 + 9)^{2} + ( - 8 - 3 )^{2} }[/tex]

                                               = [tex]\sqrt{(5)^{2} + ( - 11 )^{2} }[/tex]

                                               = [tex]\sqrt{25 + 121}[/tex]

                                               = √146

Perimeter of triangle = AB + BC + CA

                                  = √212 +  √306  +  √146

                                 = √664

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Answer:

1. n + 7 ≤ 9

2. 3w < 18

3. 3 < s + 4

4. 4 ≥ x/2.1

Correct answers are B, C , E & F.

Step-by-step explanation:

Part A) sin(X)

we know that

The sine of angle X is equal to dividing the opposite side angle X by the hypotenuse

so

Sin (X) = ZY/ZX

substituting the values
Sin (X) = 5/13

Part B) tan(Z)

we know that

The tangent of angle Z is equal to dividing the opposite side angle Z  by the adjacent side to angle Z

so

Tan(Z) = XY/YZ

substituting the values

Tan(Z) = 12/5

Part C) Cosec(Z)

we know that

The cosecant of angle Z is equal to dividing the adjacent side angle Z by the  perpendicular

so

Cosec(Z) = ZX/YX

substituting the values

Cosec(Z) = 13/12

Part D) Sec(X)

we know that

The secant of angle X is equal to divide the adjacent side angle X by the  base

so

Sec(X) = ZX/ZY

substituting the values

Sec(X) = 12/13

Part E) cos(Z)

we know that

The cosine of angle Z is equal to divide the adjacent side angle Z by the  hypotenuse

so

Cos(Z) = ZY/ZX

substituting the values

Cos(Z) = 5/13

Part F) Cot(X)

we know that

The cotangent of angle X is equal to dividing the adjacent side of angle X  by the opposite side to angle X.

so

Cot(X) = XY/YZ

substituting the values

Cot(X) = 12/5

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The probability of getting exactly four heads when a fair coin is flipped 10 times is 20.51%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

A coin is filliped 10 times. Each of the flips is independent.

Let's say X is the number of heads in 10 tosses.

Then X is distributed as n = 10 and the probability that the head comes after a single flip is 1/2.

Therefore, the probability of X being exactly 4 will be:

P( X = 4 ) = ₁₀C₄ ( 1/2 )⁴ ( 1 - 1/2 )⁶

P( X = 4 ) = 210 × ( 1/16 ) × ( 1/2 )⁶

P( X = 4 ) = 210 × ( 1/16 ) × ( 1/64 )

P( X = 4 ) = 210/1024

P( X = 4 ) = 105/512

P( X = 4 ) = 0.2051

Hence, the probability is 20.51%.

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60 liters of 50% and 20 liters of 90% solution should be used.

By mixture and allegation

90                 50

          60

10                  30

10:30 = 1:3

We must mix the acid solution in a 1:3 ratio.

For 1 liter of 60% acid solution, we must use 1l 90% acid solution and 3l  50% acid solutions.

Then for 20 l of 60% acid solution, 1*20 = 20 l of 90% acid solution and 3 * 20 = 60 l of 50% acid solution should be used.

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Answer: 78.3 ft.

Step-by-step explanation: If I am looking at it right, it would be 8.7 ft x 9 ft because A= L x W. Hope this helps.

The time taken for the mixture to find the right amount of additive per gallon is 12.869 minutes.

The total amount of diesel into the tank = 1700 gallons

The mixture is added at the rate of 0.28 ounces per gallon.

The mixture is added at the rate of 25 gallon per minute.

Let us consider that the time taken is t minutes.

A mixture is a substance made up of two or more distinct chemical components that are not chemically bonded together. A mixture is a mixture of two or more substances that retain their identities while being mixed in the form of solutions, suspensions, and colloids.

Now in t minutes the mixture = 25 × .28 ×t = 7t

Now we will use the second part of the equation as:

The rate of 20gal/min. if there should be 14oz of additive for every 120 gallons of diesel fuel, how long will it take to reach the right mixture

Now we will use the mixture formula to calculate the e amount of diesel in the mixture.

Hence 0.20 × 14×120=336  × 65.11 = 21877.3

Now the diesel mixture will have

Therefore the equation formed is :

336t +7t = 21877.3

Solving we get t=21877.3.

Hence the time taken for the mixture to find the right amount of additive per gallon is 12.869 minutes.

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Answer:

f(x) is -1 and g(x) is 2 this is because f(x) intersect at -1 which is x axis and g(x) intersect 2 which is y axis

Part a: There are 4735 ways in which the event planner can choose 9 dishes if the number of hot dishes must be greater than or equal to 7

Part b: There are 91963 ways in which the event planner chooses 9 dishes if the number of hot dishes must be less than 7

Number of cold dishes = 9

Number of hot dishes = 10

Total number of dishes = 19

Part a:

The number of ways 9 dishes can be chosen, given the number of hot dishes, must be greater than or equal to 7:

= (¹⁰C₇*⁹C₂) + (¹⁰C₈*⁹C₁) + ¹⁰C₉

= 4320 + 405 + 10

= 4735 ways

Part b:

Choosing 9 dishes, when the number of hot dishes must be less than 7

= (¹⁰C₇*⁹C₂) + (¹⁰C₆*⁹C₃) + (¹⁰C₅*⁹C₄) + (¹⁰C₄*⁹C₅) + (¹⁰C₃*⁹C₆) + (¹⁰C₂*⁹C₇) + (¹⁰C₁*⁹C₈) + (¹⁰C₀*⁹C₉)

= 4320 + 17640 + 31752 + 26460 + 10080 + 1620 + 90 +1

= 91963 ways

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Julia paid a total of $94.07 for the service she received at the salon

Service tax: Service tax is a type of indirect Tax that you are liable to pay to the government once you. The consumer pays the service tax to the service provider while paying the bill (for example, your restaurant bill has a component of service tax). The government in turn collects the tax from the service providers.

Service charge for Julia at a beauty salon = $72.60

The rate of sales tax taken = 8%

Percentage of tips she added to the service charge before sales tax= 20%

Then amount of tips given by Julia = (20/100)x72.60

                                                      = (1/5)x72.60

                                                      = 14.52 dollars

Then the amount in total paid by Julia before adding service tax =

(72.60 + 14.52) dollars=87.12dollars

Now the sales tax of 8% has to be calculated on the amount of $87.12

Then

Amount of sales tax given by Julia = (8/100)x87.12

                                                      = 696.96/100

                                                      = 6.969

                                                      = 6.97 dollars

So the total amount paid by Julia for the service at the salon =

(87.12 + 6.97) dollars = 94.07 dollars

Julia paid a total of $94.07 for the service received by her at the salon

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Answer:

3.46410

Step-by-step explanation:

Answer:

Option D is right

Step-by-step explanation:

It is correct .

Answer: x = 4

Step-by-step explanation:

4x = 16

Divide both sides by 4

x = 4

Answer:

4

Step-by-step explanation:

Because 4x=16, then divided both sides by 4.4÷4=1 times x =x and 16 ÷4=4. so the value of x is 4.

The relative rate of population change after seven years from now is a) 1.7 % (rounded off to 1 decimal place) b) Yes, the relative rate of population change will reach 2.3% in 19.21 years

The function for population t years from now is P(t)= 2+ 1.2e^(0.04t)

a) relative rate of change of population

= P'(t) / P(t)

= (0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(.04t) )

= 0.048 e ^(0.04t) / (2 + 1.2e^(0.04t) )

Relative rate of change of population 7 years from now

= 0.048 e ^(0.04 * 7) / (2+ 1.2e^(0.04*7))

=0.0177 = 0.177 * 100 = 1.7 % per year (rounded off to one decimal place

b) For the relative rate of change to reach 2.3 %

P'(t) / P(t) = 2.3 % = 0.023

⇒(0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(0.04t) ) = 0.023

⇒0.048e ^(0.04t) = 0.046 + 0.0267e^(0.04t)

⇒e ^(0.04t) = 0.958 + 0.556e ^(0.04t)

⇒e ^(0.04t) ( 1 - 0.556) = 0.958

⇒e ^(0.04t) ( 0.444) = 0.958

⇒e ^(0.04t) = 2.157

⇒0.04t = ln(2.157)           (applying ln on both sides)

⇒t = 19.21 years

The relative rate of population change is 2.3% in 19.21 years

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Yes, the equation 6x²-2y=7 will give a straight line.

Let's put the some values in equation for proof,

put x = 0, find y

6x² - 7 = 2y

6(0)² - 7 = 2y

y = -3.5

put x = 1, find y

6(1)² - 7 = 2y

y = -1/2 or -0.5

put x = 2, find y

6(2)² - 7 = 2y

y = 8.5

we get the some of the points to plot in graph,

The points are (0, -3.5) (1, -0.5) (2, 8.5)

Plot these points on graph you'll get a straight line.

Therefore, we can say that 6x²-2y=7 will give a straight line.

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The distance that should be drwan on a scale plan of 1:100000 is = 32m

Distance can be defined as the area that is covered by the movement of an object without reference to its direction.

From the scale given,

1cm : 100000cm on the scale plan of the map

The given distance = 32km

Convert km to cm by multiplying by 100000

32km = 32× 100000 = 3,200,000

To determine the equivalent ratio,

1 cm = 100000

n cm = 3,200,000

n cm= 3,200,000/100000

n cm= 32cm

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The statement that is true about the function f(x)=4[tex]x^{5}[/tex] is that the function is odd because f(-x)=-f(x).

Given that the function is f(x)=4[tex]x^{5}[/tex].

We are required to choose which statement is true for the given function.

Function is basically the relationship between two or more variables that are expressed in equal to form. The values that enter in the function are known as part of domain of the function and the values that we get from the function are known as part of range of the function.

f(x)=4[tex]x^{5}[/tex]

f(-x)=4[tex](-x)^{5}[/tex]

Since the power of negative x is odd so the result which we will get will be negative. So,

f(-x)=-4[tex]x^{5}[/tex]

f(-x)=-f(x)

So, the function is odd.

Hence the statement that is true about the function f(x)=4[tex]x^{5}[/tex] is that the function is odd because f(-x)=-f(x).

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Answer:  The correct answer is y= -8

Step-by-step explanation:  A line with a slope of zero is a horizontal line. In this case, the horizontal line intersects the y-axis at -8 and includes all values of x.

There are 2 parallel lines with the intersection. The angles of x=171° and y=9°.

Given that,

In the picture there is a diagram and we have to find the angle of x and y.

There are 2 parallel lines with the intersection.

If a transversal cuts two parallel lines, then the equivalent angles in the pair are equal.

The pair of corresponding angles are equal

x=19y

So,

We can say x and y are on the line

Then,

x+y=180°

19y+y=180°

20y=180°

y=180/20

y=9°

Now,

x=19y

x=19×9

x=171°

Therefore, the angles of x=171° and y=9°.

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Taking into account the definition of a system of linear equations, there were 4 adult dinosaurs and 12 baby dinosaurs.

A system of linear equations is a set of linear equations that have more than one unknown, related by the equations and that can appear in all of them or only in some of the equations.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. This is, ystems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

15b + 7a= 208

b= 3a

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

15×3a + 7a= 208

45a + 7a= 208

52a= 208

a= 208÷ 52

a= 4

Remembering that b= 3a, you get

b=3×4

b= 12

Finally, there were 4 and 12 adult dinosaurs and baby dinosaurs respectively.

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The population of bacteria in 8 hours will be 27,437.

It is given in the question that:-

Current population of bacteria = 12,800

Growth rate of bacteria = 10 % per hour

We have to find the population of bacteria in 8 hours.

As the growth of bacteria will be compounded per hour we can use the formula of compound amount to evaluate the population of bacteria in 8 hours.

Hence,

Amount of bacteria = Current population of bacteria(1 + Rate of growth/100)^(number of hours)

Let Amount of bacteria = A

Hence,

[tex]A=12800(1+10/100)^8[/tex]

[tex]A=12800(1+0.1)^8=12800(1.1)^8[/tex]

A = 12800*(2.14358881)

A = 27437.936768 ≈ 27438 bacteria.

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In the standard conversion unit, 24 m/s equals 54 mph in mph

The conversion equation is given as

8 km/h = 5 mph

Convert 8 km to meters

So, we have the following equation

8 x 1000 m/h = 5 mph

Evaluate the products

So, we have the following equation

8000 m/h = 5 mph

Convert 1 hour to seconds

So, we have the following equation

8000 m/3600 s = 5 mph

Evaluate the quotient

So, we have the following equation

20/9 m/s = 5 mph

Multiply both sides by 9/20

1 m/s = 9/20 * 5 mph

Multiply both sides by 24

24 * 1 m/s = 24 * 9/20 * 5 mph

Evaluate the products

24 m/s = 54 mph

Hence, the equivalent of 24 m/s in mph is 54 mph

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