In a circle, a central angle whose measure is pi/2 radians intercepts an arc whose length is 3pi/2 centimeters. How many centimeters are in the radius of the circle?

There are 9 hours between 8:30 am to 5:30 pm

From the question, we have the following parameters that can be used in our computation:

Initial time  = 8:30 am

Final time = 5:30 pm

using the above as a guide, we have the following:

Number of hours = Final time - Initial time  

substitute the known values in the above equation, so, we have the following representation

Number of hours = 5:30 pm - 8:30 am

Evaluate

Number of hours = 9 hours

Hence, there are 9 hours between 8:30 am to 5:30 pm

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Answer:

They are both correct.

Step-by-step explanation:

SInce they both are saying the same amount of pages just in different ways, Kim is saying a thousand plus five hundred, that is 1500, and Kim says 15 hundred, which is basically 1500, so they are both rounding up the number to the nearest cent correctly just are expressing the number in different ways.

The integer represents the change in balance from Monday to Tuesday is -34

Zero, a positive natural number, or a negative integer are all considered integers. The equivalent positive numbers' additive inverses are represented by the negative numbers. The boldface Z or blackboard bold is frequently used to represent the set of all numbers.

Based on the question, there is a change in balance from Monday to Tuesday , then

monday=-21

Tuesday = -55

The change =-55 - (-12)

=-55+12

=-34

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Answer:

Step-by-step explanation:

4x+7(0.75)=13.25

4x+5.25=13.25

4x=13.25-5.25

4x=8

X=$2 each

The amount of fluorine (in grams) on second sample is,

⇒ 2062.5 g.

Here,

On Sample one, 1.65 kg Magnesium and 2.57 kg Fluorine.

And, On second sample, 1.37 kg of magnesium and let x kg of fluorine.

We have to find the amount of fluorine (in grams) on second sample.

What is Ratio?

Ratios compare two numbers, usually by dividing them.

Now,

On Sample one, 1.65 kg Magnesium and 2.57 kg Fluorine.

And, On second sample, 1.37 kg of magnesium and let x kg of fluorine.

Hence,

The ratio from sample one,

⇒ 1.65kg / 2.57kg = 0.64

The ratio of second sample,

⇒ 1.3 kg / x kg

Now, Using Law of define properties of ratio, the first and second should have the same ratio.

Hence,

1.3 kg / x kg F = 0.64

x = 2.0315 kg F

x = 2031.2 g F

Therefore, The amount of fluorine (in grams) on second sample is,

⇒ 2062.5 g.

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Final answer:

A decimal written in word form represents a mixed number if there's a whole number followed by 'and', then the fractional part, such as 'two and three tenths' for 2.3.

Explanation:

When a decimal is written in word form, the indication that the equivalent form is a mixed number rather than a fraction is the presence of a whole number followed by the word 'and', then the fractional part.

For example, 'two and three tenths' (2.3 in numeric form) is a mixed number, as it has a whole number 'two' and the fractional part 'three tenths'. In contrast, a number written solely as 'three tenths' would represent just a fraction (0.3 in numeric form).

An indifference curve is used in economics to show different combinations of goods that provide equal satisfaction to a consumer. Ambrose's indifference curve equation and marginal rate of substitution are given, representing his willingness to trade one good for another while holding utility constant.

An indifference curve is a graphical representation used in economics to show the different combinations of two goods that provide equal satisfaction or utility to a consumer. In this case, Ambrose has an indifference curve with the equation x2 = 20 - 4x1/21. To find his marginal rate of substitution (MRS), we need to calculate the slope of the indifference curve at the point (4, 16). The MRS is given as 25/4, which means that Ambrose is willing to give up 25/4 units of x1 in exchange for 1 unit of x2, while keeping his utility constant.

Final answer:

Dustin is currently 9 years old.

Explanation:

The question is asking us to solve for Dustin's current age given a relationship between his age and Elias's. To solve the problem, we need to set up an equation where Dustin's current age is represented by D and Elias's current age is represented by E.

We are told that Dustin is 11 years younger than Elias, which gives us the first equation:

E = D + 11

In two years, Dustin will be half as old as Elias. We can represent this future scenario with another equation:

D + 2 = (E + 2) / 2

To find Dustin's age, we will solve these two equations simultaneously. By substituting the expression for E from the first equation into the second equation, we get:

D + 2 = (D + 11 + 2) / 2

The equation simplifies to:

D + 2 = (D + 13) / 2

Now, we simplify and solve for D:

Therefore, Dustin is currently 9 years old.

There are 10 spaces then the first space will be (3,1), the second one cannot be the same as the first one so it will have to be (2,1).

So it will come down to 3×2^9

There are 1536 ternary sequences of length 10 with no pair of consecutive digits the same.

The question is asking about how many ternary sequences of length 10 there can be without any pair of consecutive digits being the same. In a sequence of length 10, each digit has 3 possible values (0, 1, 2) but cannot be the same as the digit before it. Therefore, the first digit has 3 choices, and each subsequent digit has 2 choices (since it can't be the same as the previous one). Using the multiplication principle of counting, there would be 3*2^9 = 1536 such sequences.

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Final answer:

The term 'trapezoid' refers to a four-sided figure with at least one pair of parallel sides in American English, while 'trapezium' is the equivalent term in British English.

Explanation:

Other names for a trapezoid include trapezium in British English. The term trapezoid is commonly used in American English to describe a four-sided figure with at least one pair of parallel sides. In contrast, British English refers to the same shape as a trapezium. It is important not to confuse these terms with trapezius, which is a muscle in the human body, or other unrelated terms such as triad or tricarboxylic acid cycle (TCA).

Answer:

gross pay = $552.50

Step-by-step explanation:

Kenneth earns a commission on his total sales = [tex]4\frac{1}{2}[/tex] %

                                                                              = [tex]\frac{9}{2}[/tex] %

                                                                              = 4.5%

If his sales are 4500 this week.

His commission would be = 4.5% × 4500

                                           =  [tex]\frac{4.5}{100}\times 4500[/tex]

                                           = 0.045 × 4500

                                           = $202.50

His weekly salary is $350

Gross pay = 350 + 202.50 = $552.50

Kenneth's gross pay would be $552.50 this week.

Final answer:

To factor the expression 10x + 40, we can factor out the greatest common factor (GCF) of 10 from both terms, resulting in 10(x + 4).

Explanation:

To factor the expression 10x + 40, we can first find the common factor for both terms, which is 10. Factoring out 10, we get 10(x + 4). This expression represents the original 10x + 40. In simpler terms, we've taken out the common factor of 10 from both terms, leaving us with 10 multiplied by the quantity (x + 4). This factored form is useful for simplifying expressions or solving equations. Essentially, factoring helps us break down a more complex expression into simpler parts, making it easier to work with and understand in various mathematical contexts.

the solution is[tex]\( n \geq -9 \).[/tex]

Sure, let's break down the problem step by step.

1. The inequality given is[tex]\( 6 \leq n + 15 \).[/tex]

2. To find the value of ( n ), we'll start by isolating ( n ) on one side of the inequality.

[tex]6 &\leq n + 15 \\6 - 15 &\leq n \\-9 &\leq n[/tex]

So, the solution is[tex]\( n \geq -9 \).[/tex]

Now, let's explain the steps and the final answer in more detail.

The inequality[tex]\( 6 \leq n + 15 \)[/tex] states that "six is less than or equal to the sum of a number ( n ) and fifteen."

To solve for ( n ), we first subtract 15 from both sides of the inequality to isolate ( n ):

[tex]\[ 6 - 15 \leq n \][/tex]

This simplifies to:

[tex]\[ -9 \leq n \][/tex]

So, the solution to the inequality is[tex]\( n \geq -9 \),[/tex] which means that any number greater than or equal to -9 will satisfy the original inequality [tex]\( 6 \leq n + 15 \).[/tex]

In conclusion, the correct answer is[tex]\( n \geq -9 \)[/tex], and this means that any number greater than or equal to -9 makes the statement "six is less than or equal to the sum of that number and fifteen" true.

complete question

Six is less than or equal to the sum of a number n and 15

Answer:

1500 g.

Step-by-step explanation:

So i'll start by converting 6 kg to grams. Which is 6000 g.

There are four bags so i will do 6000 divided by 4 which equals 1500.

So the answer is 1500. each bag weighs 1500 g.

Your welcome hope this was helpful!

Answer:

yes

Step-by-step explanation: