Name the vertex of angle 2

Answer:

3/2= 1 1/2

Step-by-step explanation:

simply 3/2 as a decimal

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer:

17/3 feet

Step-by-step explanation:

Area of a rectangle is length times width

The length is 3, so the width is area over length=17/3

Answer:

The answer is 5 1/4.

Step-by-step explanation:

You have to divide 17 23/32 from 3 3/8 to get 5 1/4. Hope this helps!

Answer:

The Answer is 6

After find the value of one ounce price compare the values then the cheaper one is 25 ounces for $8.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the data provided in the question,

Case 1:

20 ounces of $5

Then 1 ounce will cost = 20/5 = $4

Case 2:

25 ounces for $8

Then 1 ounce will cost = 25/8 = $3.125

Case 3:

40 ounces for $12

Then 1 ounce will cost = 40/12 = $3.33

Case 4:

100 ounces for $20

Then 1 ounce will cost = 100/20 = $5

After comparing all the values, it is clear that 25 ounces for $8 is cheaper.

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Answer: E

Step-by-step explanation:

Answer:

the solution to the trigonometric inequality cos(0.65x) > 0.44 over the interval 0 ≤ x < 4.834.

Step-by-step explanation:

The given inequality is:

cos(0.65x) > 0.44

To solve this inequality, we need to isolate the variable x.

First, let's take the inverse cosine (arccos) of both sides to remove the cosine function:

arccos(cos(0.65x)) > arccos(0.44)

Since the range of the inverse cosine function is limited to [0, π], we can rewrite the inequality as:

0 ≤ 0.65x < π

Now, let's solve for x by dividing each part of the inequality by 0.65:

0/0.65 ≤ x < π/0.65

Simplifying, we have:

0 ≤ x < π/0.65

Now, let's calculate the approximate value of π/0.65 to determine the interval for x:

π/0.65 ≈ 4.834

i hope i helped!

Step-by-step explanation:

Hey there!

Your required answer is option B.

Here,

Given,

The figure is an equilateral triangle with, side (7x+9) and (x+27).

By the defination of equilateral triangle we have,

All sides of equilateral triangle are equal.

So,

\(( 7x+ 9) = x + 27\)

Simplify them to get answer.

\(7x - x = 27 - 9\)

\(6x = 18\)

\(x = \frac{18}{6} \)

Therefore the value of x is 3.

Hope it helps...

The value of x in the figure is:

B) x = 3

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The signs on the three sides of the triangle indicate that all the sides of the figure are equal. Thus, we can say:

7x + 9 = x + 27

7x - x = 27 - 9

6x = 18

x = 18/6

x = 3

Therefore, the value of x is 3.

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Answer:

17

Step-by-step explanation:

the answer above me is wrong and silly how are you supposed to get a 17.6 rides makes no sense

The greatest number of rides you can go on at the carnival will be 17.6.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A carnival charges $6 for admission and $2.50 per ride. You have $50 to spend at the carnival.

Let x be the number of rides.

Then the equation is given as,

2.50x + 6 = 50

Simplify the equation, then we have

2.5x + 6 = 50

2.5x = 44

x = 17.6

Thus, the greatest number of rides you can go on at the carnival will be 17.6.

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Blake needs a wooden dowel that is 2 1/6 feet long. Blake needs to cut off 7.4167 feet from the dowel.

What are arithmatic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

To find out how much Blake should cut off the dowel, we need to subtract the length of the dowel from the required length.

The length of the dowel is -5 1/4 feet, which can be written as -5.25 feet.

The required length is 2 1/6 feet, which can be written as 2.1667 feet (rounded to four decimal places).

To find out how much needs to be cut off, we can subtract the length of the dowel from the required length:

2.1667 ft - (-5.25 ft) = 7.4167 ft

Therefore, Blake needs to cut off 7.4167 feet from the dowel.

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Answer:

The first one because it is matching the numbers correctly

Answer:

a

Step-by-step explanation:

175L of water is in the first tank while water is being added at a rate of 7 L per minute

550L is in the second tank while 8L of water is being drained per min

Knowing this we can create the two sides of the equation

175 + 7x = 550 - 8x

BONUS

The question asks when they will have the same amount

rearrange

8x+7x= 550-175

15x=375

x=25

The steps to create a bar graph are explained below.

To match the two-way table to the segmented bar graph, we need to create a segmented bar graph that represents the data in the table. The table shows the percentage of students in each grade who voted for each mascot option.

Here is how we can match the two-way table to the segmented bar graph:

By creating a segmented bar graph that represents the data in the two-way table, we can visually compare the percentage of students who voted for each mascot option across different grade levels.

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288 ounces of water are left in the water tank.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots

Here, we have

Given: Tom has a water tank that holds 5 gallons of water. tell me this is water for my footing to fill six bottles they each hold 16 ounces and a picture that holds one over 2 gallons.

1 gallon = 128 ounces, 2 gallon = 256 ounces

6 bottles × 16 ounces = 96 ounces

2 gallon + 96 ounces = 256 + 96 ounces = 352 ounces

5 gallon = 5 × 128 = 640 ounces

= 640 - 352 = 288 ounces

Hence,  288 ounces of water are left in the water tank.

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It will take roughly 15.7 months to drop in value to less than £1200 if the current value of the bike is £2550.

You can use the following formula to calculate how many months it will take for a motorbike with a value of £2550 value to drop to under £1200:

n = (1200 - 2550) ln / ln (1 - 0.05)

Where 0.05 denotes the 5% monthly depreciation rate, ln is indeed the natural logarithm function, and n refers to the number of months.

When we enter the values, we will get:

n = (1200 - 2550 - 1 - 0.05) / ln(1 - 0.05) = about 15.7 months

The motorcycle will take approximately 15.7 months to drop in value to less than £1200.

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The equation of the line is y = 800x + 294000 and the average price of a new home in 2014 is $302000.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

The line passes through the points:

(0, 294000) and (7, 288400)

The equation of the line:

y - 294000 = (288400 - 294000)/(7)[x]

y - 294000 = 5600/7 (x)

y = 800x + 294000

x = 2014 - 2004 = 10

Plug x = 10 in the above equation:

y = 800(10) + 294000

y = 302000

Thus, the equation of the line is y = 800x + 294000 and the average price of a new home in 2014 is $302000.

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The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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The ratios are;

Sin θ =  5/6

Cos θ = √11/6

Tan θ =  5√11/11

Sec  θ =  6√11/11

Cosec  θ = 6/5

Cot θ =  √11/5

These trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides

We can see that the hypotenuse is obtained from;

x =√\((10)^2 + (2\sqrt{} 11)^2\)

x = √100 + 44

x = 12

Then;

Sin θ = 10/12 = 5/6

Cos θ =  2√11/12

= √11/6

Tan θ = 10/2√11

= 20√11/44

= 5√11/11

Sec  θ =  1/Cos  θ

=  6/√11

= 6√11/11

Cosec  θ = 1/Sin

 θ = 6/5

Cot θ = 1/tan θ

= 11/ 5√11

= 55√11/275

= √11/5

Sinβ = 2√11/12

= √11/6

Cos β = 10/12

= 5/6

Tan β = 2√11/10

= √11/5

Sec β = 6/5

Cosec β = 6√11/11

Cot β = 5√11/11

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The last boxplot is the one that displays the values range  of the distribution that is given.

The range of a function in mathematics can refer to one of two ideas that are connected in some way: Codomain for the function an illustration of the action If there is precisely one y in Y and there are two sets X and Y, then a binary relation f between X and Y is a function that connects x and y.

Here ,Given information:

6,7,9,9,20,22,26,28,29,30

N = 10 observations were made.

The base number is 6. ( least value)

Quartile lower= n+1(0.25)

term = 0.25(13) = 3.25term = 13

Median equals 0.5 (n + 1)

term = 0.5(13) = 6.5 term = (20 + 24) /2 = 22

Upper quartile: 0.75 (13)

A term equals 9.75 a term equals 26.5

Interquartile Range (IQR) is equal to= Q3 - Q1= (26.5 - 13) = 13.5

The highest value is 30. (highest value in the distribution)

As a result, the Last boxplot is the one that shows the distribution that is given.

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Answer:

Step-by-step explanation:

Let's denote the amount Azarias pays for rent as "x." According to the given information, Kehinde pays $80 more than twice Azarias' rent. Therefore, we can set up the following equation:

2x + $80 = $1870

To solve for x, we can subtract $80 from both sides of the equation and then divide by 2:

2x = $1870 - $80

2x = $1790

x = $1790 / 2

Evaluating the expression:

x = $895

Therefore, Azarias pays $895 for rent.

Answer:

43.6 has 3 significant figures.

Answer:

3). (3,-3)

Step-by-step explanation:

reflection in the x-axis : (-2,-4) → (-2,+4)

five units to right : (-2+5,+4) = (3,4)

seven units to downward : (3,4-7) = (3,-3)

Answer:

3)   (3, -3)

Step-by-step explanation:

If a point is reflected in the x-axis, the x-coordinate remains the same and the sign of the y-coordinate is changed.

Therefore, (-2, -4) reflected in the x-axis ⇒ (-2, 4)

If the point is translated 5 units right and 7 units down, add 5 units to the x-coordinate and subtract 7 units from the y-coordinate:

Therefore, (-2, 4) ⇒ (-2 + 5, 4 - 7) = (3, -3)

Answer: The expected value of each warranty sold can be calculated as the sum of the product of the probability of a product failing after the original warranty period and the replacement cost, and the cost of the extended warranty:

Expected value = (0.8% of $300) + ($47)

Expected value = (0.008)($300) + ($47)

Expected value = $2.40 + $47

Expected value = $49.40

Therefore, the company's expected value of each warranty sold is $49.40.

Step-by-step explanation:

Answer:

hope you can understand

Answer:

There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.

Step-by-step explanation:

29 years from now, the father will be 49 years old.

Let's start by setting up the given information:

Currently, the father is 20 years old, and the son is 5 years old.

In 10 years, the father will be twice as old as the son.

The father is currently four times as old as the son.

Determine the age of the father and son in 10 years:

In 10 years, the father's age will be 20 + 10 = 30 years.

In 10 years, the son's age will be 5 + 10 = 15 years.

Write equations based on the given information:

The father's age in 10 years will be twice the son's age in 10 years: 30 = 2 × 15.

The father's current age is four times the son's current age: 20 = 4 × 5.

Solve the equations:

From the second equation, we find that the son's current age is 5 years.

Plugging this value into the first equation, we get: 30 = 2 × (5 + 10).

Simplifying further, we have: 30 = 2 × 15, which is true.

Determine the current age of the son in 29 years:

The son's current age is 5 years.

Adding 29 years to the son's current age, we find that the son will be 5 + 29 = 34 years old.

Determine the current age of the father in 29 years:

The father's current age is 20 years.

Adding 29 years to the father's current age, we find that the father will be 20 + 29 = 49 years old.

Therefore, 29 years from now, the father will be 49 years old.

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\(\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}\)

Speed of Carmen = 40km/h

and speed of Carmella = 60km/h

Step-by-step explanation:

Let the speed of Carmen = x km/h

Carmella speed will be (x + 20)km/h

Distance = 120 km

Time between Carmen and Carmella = 1 hour

\( \sf Time= \frac{distance}{speed} \)

Let the time taken by Carmen be T1

and Carmella be T2

\( \sf So \: T_1 = \frac{120}{x} \: and \: T_2 = \frac{120}{x + 20} \)

As there is 1 hour difference so

\( \sf T_2 - T_1 = \: 1 hour \\ \\ \\ \sf \implies \frac{120}{x } - \frac{120}{x + 20} = 1 \\ \\ \\ \sf \implies \frac{120(x + 20) - 120x}{x(x + 20)} = 1 \\ \\ \\ \sf \implies 120x + 2400 - 120x = {x}^{2} + 20x \\ \\ \\ \sf \implies 2400 = {x}^{2} + 20x \\ \\ \\ \sf \implies 0 = {x}^{2} + 20x - 2400 \\ \\ \\ \sf \implies 0 = {x}^{2} + 60x - 40x - 2400 \\ \\ \\ \sf \implies0 = x(x + 60) - 40(x + 60) \\ \\ \\ \sf \implies 0 = (x + 60)(x - 40) \\ \\ \\ \sf \implies \red{\boxed{x = 40km}}\)

We have not considered 60 as it will become negative value and negative value is not possible in distance

Speed of Carmen = 40km/h

Speed of Carmella = 40 + 20 = 60km/h

Answer:

17,680 ft²

Step-by-step explanation:

Shaded area = entire shaded rectangle area - unshaded rectangle area - square area

A = 200(100) - 24(30) - 40²

A = 20,000 - 720 - 1600 = 17,680

Answer:

  (2)  (-2, 4), (3, 9)

  (3)  (-2, 4), (1, 1)

Step-by-step explanation:

My favorite way to answer questions like this is to use a graphing calculator to find the points of intersection. The attached shows the points of interest.

If you want to solve this by hand, equate the expressions for y, then solve the resulting quadratic using any of the methods you know. Once you find the x-values, put those in either equation to find the y-value.

__

(2) x^2 = y = x+6

  x^2 -x -6 = 0 . . . . put in standard form

  (x -3)(x +2) = 0 . . . . factor

  x = 3 or -2 . . . . . find the x-values that make the factors zero

  y = x^2 = 9 or 4

The points are (3, 9) and (-2, 4).

__

(3) x^2 = -x +2

  x^2 +x -2 = 0 . . . . standard form

  (x +2)(x -1) = 0 . . . factored

  x = -2 or 1 . . . . . . .zeros

  y = x^2 = 4 or 1

The points are (-2, 4) and (1, 1).

_____

Comment on factoring

When you consider the factored form and its expanded equivalent, ...

  (x +a)(x +b) = x^2 +(a+b)x +ab

you see that the coefficient of the linear term (a+b) is the sum of factors of the constant term (ab). Your knowledge of multiplication tables will often help you factor equations easily. You need to pay attention to signs.

In problem 2, we want factors of -6 that have a sum of -1:

  -6 = (-1)(6) = (-2)(3) = (-3)(2) = (-6)(1)

These factor pairs have sums of 5, 1, -1, -5. The pair whose sum is -1 is the one we're looking for: -3 and 2. So, the factors in problem 2 are (x-3)(x+2).

__

In problem 3, we want factors of -2 that have a sum of +1:

  -2 = (-1)(2) = (-2)(1)

These factor pairs have sums of 1, -1. So, the second pair is the one of interest: -2 and 1. That makes the factors be (x-2)(x+1).