A clothing store offers a 20% discount on every item. The original price of a t-shirt was $18. What is the discount price?

The number of agent arrangements where order is important can be calculated using the concept of permutations. The number of agent arrangements can be calculated as 12P6 = 665,280.

To find the number of agent arrangements where order is not important, we need to use the concept of combinations. In this case, the order of assigning customers to agents does not matter. We still have 12 sales agents and 6 customers to assign. The number of agent arrangements where order is not important can be calculated using combinations. We can use the formula 12C6 to determine the number of ways to choose 6 agents from a group of 12. The calculation would be 12C6 = 924.

In this case, we are only concerned with selecting the agents, not the order in which they are assigned to customers. For example, if agents A, B, C are assigned to customers 1, 2, 3, respectively, it is considered the same arrangement as if agents B, C, A are assigned to customers 1, 2, 3, respectively.

To summarize, the number of agent arrangements where order is important is 665,280, calculated using permutations (12P6). The number of agent arrangements where order is not important is 924, calculated using combinations (12C6).

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The fourth vertex's coordinates are as follows: ( 2.1, -3.6)

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

So, let the missing coordinates be (a,b).

Let's now utilize the midpoint formula to locate the erroneous coordinate.

Let the reference point be (-2.3, 3.6) A.

Let point B be (2.3, 2.2).

(2.1, 2.2) Let C be the point.

The center of AC should be at BD.

Step 1: Locating the AC's midpoint

Middle pint of AC:

(-2.3 + 2.1/2), (-3.6 + 2.2/2)

(0.2/2), (1.4/2)

(-0.1, -0.7)

Let's equate the midpoints in step two.

The BD mid-point:

(a + -2.3/2), (b + 2.2/2) =  (-0.1, -0.7)

(a + -2.3/2) = -0.1

(a -2.3/2) = -0.1*2

a = -0.2+2.3

a = 2.1

(b + 2.2/2) = -0.7

b + 2.2 = -0.7*2

b + 2.2 = -1.4

b = -1.4 -2.2

b = -3.6

Therefore, the fourth vertex's coordinates are as follows: ( 2.1, -3.6)

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Complete question:

Freddy drew a plan for a rectangular piece of material that hehe will use for a blanket. Three of the vertices are ​( -2.3 and −3.6​), ​(−2.3​, and 2.2​), and ​(2.1​, and 2.2​). What are the coordinates of the fourth​ vertex?

Answer:

Step-by-step explanation:

\(C=2\pi r\)

\(1=2\pi\time r\)

\(r=\frac{1}{2\pi}\)           ( divided both sides of equation by \(2\pi\))

 \(r\approx 16cm\)

The wheel's radius is approximately 16cm.

Answer:

width is 5, length is 6

Step-by-step explanation:

5x6=30

From the given graph, the interval (0,6)g is not continuous at x=2

A graph is a visual representation of the change of one variable in relation to one or more other variables, such as a collection of points, lines, line segments, curves, or areas. It can also be defined as  a grouping of all locations whose coordinates meet a certain relation (such as a function).

For instance, a function is continuous if the graph can be drawn with a pen without having to remove it from the paper. If a function's graph is a continuous curve without any flaws, gaps, or breaks, it is said to be continuous. However, phrases like "unbroken curve" and "gaps" aren't strictly speaking mathematical words, and at best they only give the reader a description of continuity rather than a definition.

A function may be continuous at a specific location, continuously over a specified time period, or continuously throughout.

In the given graph, we can observe that the line is not a continuous line. Here, the break in the line is being observed at x=2.

Therefore, the given graph, in the interval (0,6)g is not continuous at x=2.

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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\([Hello,BrainlyUser]\)

Answer:

19.5

Step-by-step explanation:

Given that;

Recipe calls for 5.25 grams of chocolate

Question Ask;

If you have 102.375 grams of chocolate, how many batches,of the recipe can you make?

Note;

102.375 ÷ 5.25 = b

102.375 ÷ 5.25 = Solution

Solve;

\(\mathrm{Multiply\:the\:numerator\:and\:denominator\:by:}\:100\)

\(\frac{10237.5}{525}\)

\(\mathrm{Write\:the\:problem\:in\:long\:division\:format}\)

\(\begin{matrix}525\overline{|\smallspace10237.5}\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(Divide\;1023\;by\;525\;to\;get\;1\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 525\overline{|\smallspace10237.5}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace5\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace9\emptyspace8\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(Divide\;4987\;by\;525\;to\;get\;9\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace19\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 525\overline{|\smallspace10237.5}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace5\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace9\emptyspace8\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\:\:\:\:\:\:\:\:\:\underline{\emptyspace47\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace6\emptyspace2\emptyspace5\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(Divide\;2625\;by\;525\;to\;get\;5\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace19.5\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 525\overline{|\smallspace10237.5}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace5\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace9\emptyspace8\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\:\:\:\:\:\:\:\:\:\underline{\emptyspace47\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace6\emptyspace2\emptyspace5\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\:\:\:\:\:\:\:\:\:\underline{\emptyspace26\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\:\:\:\:\:\:\:\:\:\emptyspace\emptyspace\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{102.375}{5.25}\:\mathrm{is}\:19.5\)

[CloudBreeze]

Colorado and Boston have 263 and 219 days of sunshine respectively.

Let the number of days of sunshine in Colorado is x and the number of days of sunshine in Boston is y.

Total number of days of sunshine=482

Also, the number of days of sunshine in Colorado is 1.2 times the number of days of sunshine in Boston.

So, the equation is formed as follows:

x+y=482  -(1)

The other equation is formed as:

x=1.2y  -(2)

Substitute the value x from equation (2) in (1),

1.2y+y=482

2.2y=482

y=482/2.2

y=219

Substitute the value of y in equation (1),

x+219=482

x=482-219

x=263

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Jeremy walked around a football field.

Jeremy walked around a football field.Which statement explains whether the example describes area or perimeter?

Jeremy walked around the football field. Which keans that he covered only the boundaries and we know that perimeter is the sum of length of the boundary but area is the complete sum of shape including boundary...~

Explanation:

The 0.5+8 simplifies to 8.5

It might help to think of 8 as 8.0

So,

y(0.5+8)

y(8.5)

8.5y

Or you could say it like this

y(0.5+8)

0.5y+8y

8.5y

the second step results from the distributive property.

Given information: In the PGA, on par 3 holes, golfers hit the green in one shot 80% of the time. In fact, 20% of the time, they hit the green in one shot and then need only one putt to complete the hole. So 60% of the time, they hit the green in one shot but are unsuccessful on their putt.

Let G be the event that the golfer hits the green in one shot. Let P be the event that the golfer needs one putt to make the hole. Probabilities listed in the problem: Probability of hitting the green in one shot

.= 80% = P(G)Probability of hitting the green in one shot and needing only one putt = 20% = P(G ∩ P)Probability of hitting the green in one shot but are unsuccessful on the putt = 60% = P(G ∩ P')Where P' denotes not P or the complement of P. In other words, P' means that the golfer needs more than one putt to make the hole.

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The line tangent to f(x) = x + sin(x) is parallel to the secant line connecting the endpoints at x = π on the interval [-2π, 2π].

Let's begin by finding the slope of the secant line connecting the endpoints of the function. The endpoints of the function on the interval [-2π, 2π] are (-2π, -2π + sin(-2π)) and (2π, 2π + sin(2π)), which evaluate to (-2π, 0) and (2π, 0), respectively.

The slope of the secant line is

m = (0 - 0)/(2π - (-2π)) = 0

Since we want the tangent line to be parallel to the secant line, the slope of the tangent line should also be 0. We can find the equation of the tangent line using the point-slope form

y - (x + sin(x)) = 0

y = x + sin(x)

To find the points on the interval where the tangent line is parallel to the secant line, we need to find the values of x where the derivative of f(x) is equal to 0 (i.e., where the slope of the tangent line is 0). The derivative of f(x) is

f'(x) = 1 + cos(x)

Setting this equal to 0 and solving for x, we get

cos(x) = -1

x = π

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The given question is incomplete, the complete question is:

At how many points on the interval [-2pi, 2pi] is the line tangent to f(x)=x+sin x parallel to the secant line connecting the function endpoints?

The integer would be -250, since it is a decrease.

Step-by-step explanation:

Because it is a square, this means that all of the sides have to be the same measurement. To find this, you should divide 36 inches by four to get 9 inches. To find the area, you multiply height by width, in this case, nine times nine which would equal eighty one inches²

When adding, you only add the numerators. The denominator stays the same (Assuming the denominators are the same number). If not, then you will have to find a common denominator first. IN this case, the denominator is already the same. Add the numerator

2/3 + 2/3 = 4/3

Note that the answer gotten is an “improper fraction”, because the numerator is greater than the denominator. Simplify.

4/3 = 3/3 + 1/3

Divide: 3/3 = 1

1 + 1/3 = 1 1/3

1 1/3 is your mixed fraction answer (4/3 for improper fraction answer)

19 & 20  are the reqd. integers.

By what is given,  x + ( x + 1 ) = 39 .

∴ 2 x + 1 =39.

∴ 2 x = 39 − 1 = 38 .

∴ x = 19 ,  so,  x + 1 = 20 .

Thus,  19 & 20  are the reqd. integers.

Given:

The function is

\(f(x)=4x-8\)

To find:

The input of the function when the output is 20.

Solution:

We have,

\(f(x)=4x-8\)

Here, x is input and f(x) is output.

Put f(x)=20 in the given function to find the input of the function when the output is 20.

\(20=4x-8\)

\(20+8=4x\)

\(28=4x\)

Divide both sides by 4.

\(\dfrac{28}{4}=x\)

\(7=x\)

Therefore, the required input value is 7.

When performing a hypothesis test on the population mean (μ) when the population standard deviation (σ) is known, the null hypothesis (H0) can never be rejected if the sample mean falls within the acceptance range determined by the chosen significance level and the critical values.

In hypothesis testing for the population mean when the population standard deviation is known, the null hypothesis (H0) represents the claim or assumption that the population mean is equal to a specific value. The alternative hypothesis (Ha) states that the population mean is not equal to the specific value.

To determine whether to reject or fail to reject the null hypothesis, we compare the sample mean to the expected value under the null hypothesis. If the sample mean falls within the acceptance range determined by the chosen significance level and the critical values, we do not have sufficient evidence to reject the null hypothesis. The acceptance range is defined by the margin of error around the expected value, and it indicates the range of values that can be considered reasonably close to the expected value.

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Answer:

18/24 or 75%

Step-by-step explanation:

Okay so you already know that he got 16/24 which means that there were 8 questions that were wrong because 24-16= 8

So he has 16 points that we know of and 8 questions that he got wrong.

If he lost 1/4 of a point when he got it incorrect 1/4= 0.25

0.25 x 8 = 2points

So he got to points

16+ 2= 18 so now it is 18/24

If you have to show Out for 100% it would be 75%

Hope it helped!

The ant population will reach 38.2 thousand in about 3.25 years, assuming a growth rate of 5% per year.

To answer this question, we need to know the growth rate of the ant population. Let's say the growth rate is 5% per year. This means that each year, the population will increase by 5% of its current size. To calculate the population size after a certain number of years, we can use the formula:

P = P0 * (1 + r)^t

where P is the population size after t years, P0 is the initial population size, r is the growth rate as a decimal, and t is the number of years.

Assuming the initial population size is 30 thousand, we can plug in the values to find when the population will reach 38.2 thousand:

38.2 = 30 * (1 + 0.05)^t

Solving for t, we get t = 3.25 years. However, it's important to note that the actual growth rate may be different, so this calculation is just an estimate.

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Answer:

x - 4

Step-by-step explanation:

The difference means subtraction

The algebraic expression of the phrase is x-4.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given phrase:

The difference of x and 4.

Here, we have the phrase difference.

So, we will use the subtraction operation.

So, the algebraic expression,

x - 4.

Therefore, x -4 is the algebraic expression.

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Answer:

Its D

Step-by-step explanation:

Took on Ed

Answer:

9

Step-by-step explanation:

5^2 - 2 x 8 is the equation

first you do exponents so now the equation looks like this: 25 - 2 x 8

then (when following pemdas) you multiply to get this: 25 - 16

last, you should subtract to get your answer: 9

i hope this helps :))

The general form of the equation for the given circle centered at O(0, 0) is x² +y² - 41=0.

The correct option is (B).

The general equation for a circle is ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.

as, general equation for a circle is ( x - h )² + ( y - k )² = r²

Here,  centered at O(0, 0).

So,

a =0 and b = 0

now, r² = (BO)²

r² = (4-0)² +(5-0)²

r²  = 16+25

r² = 41

Hence, Center at the origin passing through B(4, 5) is x² +y² = 41.

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The number of aluminium balls with a radius of 4.5 in will be 200.

The amount of space that a sphere can occupy is measured by its volume. The three-dimensional shape of a sphere lacks vertices and edges.

Given that Amy's company makes solid balls out of scrap metal for various industrial uses. Her current task is to make a batch of aluminium balls with a radius of 4.5 in. The total volume of the aluminium is 76302 cubic inches.

The number of spheres with a radius of 4.5 inches will be calculated as:-

Number = ( Total volume of aluminium) / ( Volume of the small sphere)

The volume of small sphere = ( 4 / 3 ) πr³

The volume of small sphere = ( 4 / 3 ) π x 4.5³

The volume of the small sphere = 381.7 cubic inches

Number = ( Total volume of aluminium) / ( Volume of the small sphere)

Number = 76302 / 381.7

Number = 200

Hence, the number of spheres will be 200.

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Answer:

.......B......

Step-by-step explanation:

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