Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0. Parallel lines are numbered up to pi/2 to the north and to the south. If we assume Earth is spherical, the length of any parallel of latitude is equal to the circumference of a great circle of Earth times the cosine of the latitude angle.
a. The radius of earth is about 6400 kilometers. Find the circumference of a great circle.
b. Write an equation for the circumference of any latitude circle with angle 0
c. Which latitude circle has a circumference of about 3593 kilometers?
d. What is the circumference of the equator?

a - 47 = more time spent

In this mathematical problem, Abby's time is represented as x and the difference in time between Abby's and Susanna's work can be modeled by the equation x-47=y, where y is the extra time Abby spends. A number line can be used to visualize this problem, but without knowing Abby's time, we cannot determine y.

The subject of this problem is mathematics and it discusses time spent by two individuals on their project. We know that Susanna spends 47 minutes on her project. However, we do not know how much time Abby spends on her project. We could represent the time Abby spends on her project as x.

To visualize the situation, we can draw a number line. Place a point at 47 which represents Susanna's time. Then place another point at x which represents Abby's time.

The difference in time between Susanna and Abby can be represented by the equation x - 47 = y, where y is the number of extra minutes Abby spends working on her project.

Without any additional information on how much time Abby spent on her work, it's impossible to give a specific answer.

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Answer:

The correct option is A.

Step-by-step explanation:

Total number of students at the school is 2,500.

In the given pi chart Pink, Yellow and Sky Blue color represent the percentage of students that under reported, accurately reported, and over reported their heights respectively.

From the graph we can conclude that the yellow portion is approximately one fifth of whole circle. It means the number of students that accurately reported their height is one fifth of total number of students.

[tex]2500\times \frac{1}{5}=500[/tex]

Therefore the number of students that accurately reported their height is 500. Option A is correct.

Answer:

Option A) 500

Step-by-step explanation:

We are given the following information:

Total number of students = 2500

From pie chart:

[tex]\text{Under Reported }= \displaystyle\frac{1}{5}\times 100\% = 20\%\\\text{Accurately Reported }= \displaystyle\frac{1}{5}\times 100\% = 20\%\\\text{Over Reported }= \displaystyle\frac{3}{5}\times 100\% = 60\%[/tex]

We have to find the number of students whose height were accurately reported =

[tex]\text{Number of students whose height were accurately reported }= \\\text{Number of students}\times \text{Percentage of students whose height were accurately reported}\\= 2500\times 20\%\\\\= 2500\times \displaystyle\frac{20}{100} = 2500\times \frac{20}{100} = 500[/tex]

500 students report their height accurately.

First multiply 5 on both sides to get rid of the five on the bottom.

[tex]\frac{1-7n}{5*5}[/tex][tex]>10*5[/tex]

[tex]1-7n>50[/tex]

Subtract 1 from both sides of the inequality.

[tex]1-1-7n>50-1[/tex]

[tex]-7n>49[/tex]

Divide -7 on both sides, and flip the inequality sign since we are dividing by a negative.

[tex]\frac{-7n}{7}[/tex][tex]>\frac{49}{-7}[/tex]

[tex]n<-7[/tex]

The solution to the inequality is n<-7.

[tex]Solution, \frac{1-7n}{5}>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\end{bmatrix}[/tex]

[tex]Steps:[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}5, \frac{5\left(1-7n\right)}{5}>10\cdot \:5[/tex]

[tex]\mathrm{Simplify}, 1-7n>50[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}, 1-7n-1>50-1[/tex]

[tex]\mathrm{Simplify}, -7n>49[/tex]

[tex]Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right), \left(-7n\right)\left(-1\right)<49\left(-1\right)[/tex]

[tex]\mathrm{Simplify}, 7n<-49[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}7, \frac{7n}{7}<\frac{-49}{7}[/tex]

[tex]\mathrm{Simplify}, n<-7[/tex]

The correct answer is n<-7

Hope This Helps!!!

Hey there,

Here is your answer:

10/1 = 10

X

5x1=5

5x2=10

5x3=15

5x4=20

5x5=25

Y

20-2=18

18-2=16

16-2=14

14-2=12

X Is by 5 and Y is subtracting by 2

Answer:

17%

Step-by-step explanation:

Final answer:

Ella owns 15% of Fitz Incorporated, and the remaining 85% is shared equally among 5 other shareholders. Thus, each of these shareholders owns an equal share of 17% of the corporation.

Explanation:

The question asks about corporate stock and how it relates to the percentage of ownership in a corporation. Ella owns 15% of Fitz Incorporated, and the remaining 85% is owned equally by 5 other shareholders. To find the percentage each of these shareholders owns, we divide the remaining percentage by the number of shareholders.

The calculation would be:

Subtract the percentage owned by Ella from the total, which is 100% - 15% = 85%.

Divide this remaining percentage (85%) by the number of other shareholders, which is 5.

85% / 5 = 17% ownership for each of the other shareholders.

So, each of the remaining 5 shareholders owns 17% of the corporation.

a single die being rolled to a number less or equal to 2

Final answer:

The complement of rolling a number greater than 2 on a single six-sided die is rolling a 2 or less, which has a probability of 1/3.

Explanation:

In the context of a single six-sided die roll, the complement of rolling a number greater than 2 would be rolling a number that is 2 or less, which in this case includes rolling a 1 or a 2. Each face of a fair six-sided die has an equal chance of landing face up, giving us a probability of 1/6 for landing on a specific number. Since there are two outcomes that are 2 or less (1 and 2), we simply add their probabilities to get the complement. Thus, the complement of rolling a number greater than 2 is:

P(rolling a 1 or 2) = P(rolling a 1) + P(rolling a 2)
= 1/6 + 1/6
= 1/3.

Therefore, there is a 1/3 chance of rolling a number that is 2 or less when rolling a single fair six-sided die.

The answer is D or -30

The value of the expression for the given values of the variables is -30.

The given expression is 4a+7b+3a-2b+2a, the values of the variables a=-5 and b=3.

We need to evaluate the expression for the given values of the variables.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Now, put a=-5 and b=3 in the given expression and simplify.

That is, 4a+7b+3a-2b+2a=4(-5)+7(3)+3(-5)-2(3)+2(-5)

=-20+21-15-6-10

=-30

Therefore, the value of the expression for the given values of the variables is -30.

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yes the answer is 12

                                                       hope it helps

Answer,

C.g-^m -^n

Hope this helps :-)

Pretty sure it is A - a parallel line to a given line from a point not on the line

I'm working on the same test :)

Answer:

The construction is a parallel line to a given line  from a point not on the line.

Step-by-step explanation:

For a given figure,

To construct a parallel line

Step 1 : Draw transversal line through any point not on line which is given.

Step 2: Using construction copy an angle, construct same angle formed by transversal line and given line.

Step 3: This is the last step in which when the copy of an angle completed draw a line parallel to the line.

Your answer (C, the line is vertical) is correct

Your line would have to be horizontal. A vertical line yields an undefined slope.

Slope is rise over run. For a horizontal line you would have 0 rise and X amount of run or 0/x. 0 divided by anything = 0

For a vertical line, you would have the opposite, X rise and 0 run or x/0. You cannot divide by 0. It is impossible.

Therefore, your answer is the second option.

2c - 5 < -21 - 2c     |add 5 to both sides

2c < -16 - 2c      |add 2c to both sides

4c < -16      |divide both sides by 4

c < -4

2 red / 4 blu

just semplify

1 red / 2 blu

so the probability is

1/2

Answer:

The answer is 50% Hope this helps!

Answer:

Kenya’s equation has infinitely many solutions

Step-by-step explanation:

we have

[tex]-6(x-2)+3x=-3(x+3)+21[/tex]

Solve for x

Eliminate the parenthesis

[tex]-6x+12+3x=-3x-9+21[/tex]

Group terms that contain the same variable

[tex]-6x+3x+3x=-9+21-12[/tex]

Combine like terms

[tex]0=0[/tex]  ---> is true for any value of x

therefore

Kenya’s equation has infinitely many solutions

Answer:

D

Step-by-step explanation:

Additive inverse: the additive inverse of a number a is the number that when added to a yields zero.It's also known  as the opposite sign change  and negation. For a real number  it reverses its sign: the opposite to a positive number is negative and the opposite to a negative number is positive

Integer:Any number that is positive negative or nuetral, intergers cannot have decimals or fractions

Negative number: A number that is below zero. For example, -1 or -2 2/3

Positive number: A number that is above 0. For example, 1 or 2 2/3. You can also write a positive number with a + sign infront of it. For example, +1 or +2

good luck

Answer:

Edison will be paid $15,112 for the first three months.

Step-by-step explanation:

We know that Edison receives an annual fixed pay of $45,448. Therefore, his fixed pay for each month will be [tex]\frac{45448}{12}=\$3787.33[/tex]

Therefore, his fixed pay for the 3 months will be [tex]3787.33*3=\$11362[/tex].

Now let us compute the commission that Edison received. For that we will compute the 15% of the total sales for those 3 months. Total sales for the 3 months is $25000. Therefore, his commission would be [tex]0.15*25000=\$3750[/tex]

Therefore, total pay that Edison received during first 3 months would be:

[tex]11362+3750=\$15,112[/tex]

Edison will be paid $48,862 for the first 3 months.

To calculate Edison's total payment for the first 3 months, we need to consider both his annual pay and the commission he earns from his sales.

First, let's calculate the commission Edison earns from his sales. He makes sales of $250,000 in the first 3 months, and the commission rate is 15% of the total sales. The commission can be calculated as:

[tex]\[ \text{Commission} = \text{Total Sales} \times \text{Commission Rate} \] \[ \text{Commission} = \$250,000 \times 0.15 \] \[ \text{Commission} = \$37,500 \][/tex]

Next, we need to calculate Edison's base salary for 3 months. Since his annual pay is $45,448, we divide this by 4 to get the quarterly pay (as there are 4 quarters in a year):

[tex]\[ \text{Quarterly Pay} = \frac{\text{Annual Pay}}{4} \] \[ \text{Quarterly Pay} = \frac{\$45,448}{4} \] \[ \text{Quarterly Pay} = \$11,362 \][/tex]

Now, we add the quarterly pay to the commission to find the total payment for the first 3 months:

[tex]\[ \text{Total Payment for 3 Months} = \text{Quarterly Pay} + \text{Commission} \] \[ \text{Total Payment for 3 Months} = \$11,362 + \$37,500 \] \[ \text{Total Payment for 3 Months} = \$48,862 \][/tex]

[tex]\vee=or\\\\therefore\\\\p:x < -3\ ; q:x > 3\\\\p\vee q\to x < -3\ or\ x > 3[/tex]

[tex]\wedge=and\\\\\Rightarrow=if\ ...,\ then\ ...\\\\\Leftrightarrow=if\ and\ only\ if[/tex]

Answer:

the one with or just got it right

Step-by-step explanation:

[tex]-11(9b-8)=(-11)(9b)+(-11)(-8)=-99b+88[/tex]

[tex]9^{\frac{1}{8} }[/tex]x

note that [tex]\sqrt[4]{9}[/tex] = [tex]9^{\frac{1}{4} }[/tex]

and all raised to the power [tex]\frac{1}{2}[/tex] x

multiply [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{2}[/tex] x = [tex]\frac{1}{8}[/tex] x

1. 1/9

2. 0

3. -9

4. -1

Reasoning: To get the opposite of a number just add a negative sign or take it away. This can be done to all numbers other than 0

p(10) is the profit, in dollars, from selling 10 books. Replace every copy of x with 10 and simplify

p(x) = 8x-10

p(10) = 8*10-10 .... every x is replaced with 10

p(10) = 80-10

p(10) = 70

So the profit is $70

For the function p(x) = 8x - 10, the profit for selling 20 books is $150.

Explanation:

In the problem, the function p(x) = 8x - 10 represents the profit, in dollars, for selling 'x' books. When it's stated that p(20) = 150, it means that by substituting the value of 'x' as 20 in the function, we get the value as 150. In terms of the problem, it means that the profit for selling 20 books is $150.

Let's break down the problem step by step.

1. You're given the function p(x) = 8x - 10, which represents the profit, in dollars, for selling x books. In this equation, p(x) is the profit, and \(x\) is the number of books sold.

2. You're asked to evaluate the function at x = 20, which means you want to find p(20). To do this, substitute x = 20 into the function and calculate the result.

  p(20) = 8(20) - 10

3. Perform the calculation:

  p(20) = 160 - 10

4. Complete the subtraction:

  p(20) = 150

So, p(20) = 150, which means that the profit for selling 20 books is $150. This is the interpretation of the statement "p(20) = 150" in terms of the problem.

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The probable question can be: The function p(x) = 8x - 10 shows the profit, in dollars, for selling x books.

p(10) = 70

p(20) = 150

What does p(20) = 150 mean in terms of the problem?

It costs $150 to make 20 books.

It costs $20 to make 150 books.

The profit for selling 150 books is $20.

The profit for selling 20 books is $150.

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Answer:

Option A.

Step-by-step explanation:

Machine to fill the balloons with helium will cost = $39.99

Cost of the balloons, helium and ribbons for each bouquet = $2.00

If b balloon bouquets are produced then cost of b balloon bouquets = $2b

Total cost for producing b balloon bouquets = cost of machine + cost of material

                                                                           = $(39.99 + 2b)

Therefore, cost to produce b bouquets will be $2.00b + $39.99

Hence option A is the answer.

Answer:

Step-by-step explanation:

[tex]-12-a=4a-7\qquad|\text{add 12 to both sides}\\\\-a=4a+5\qquad|\text{subtract 4a from both sides}\\\\-5a=5\qquad|\text{divide both sides by -5}\\\\\boxed{a=-1}[/tex]

I believe it would be x5 considering you must add exponents when you multiply.

Answer:

[tex]x^3\cdot x^2=x^5[/tex]

Step-by-step explanation:

The rule to multiply two powers with the same base consists in adding the exponents. The general form would be:

[tex]x^a\cdot x^b=x^{a+b}[/tex]

For verifying the previous rule, let's say that x=2, a=2 and b=3. The equation would be:

[tex]2^2\cdot 2^3=2^{5}[/tex]

[tex](4)\cdot (8)=2^{5}[/tex]

[tex]32=32[/tex]

We have obtained the result multiplying individually and applying the rule.

Now, for the [tex]x^3\cdot x^2[/tex] exercise, the result would be obtained by adding 3 and 2. It would be:

[tex]x^3\cdot x^2=x^{3+2}=x^5[/tex]

The solution is [tex]x^5[/tex]

It would have to be feet squared, it couldn't just be feet.