A company produces circular drink coasters. the equation x2 y2 = 18.0625, with units in inches, represents the size of a coaster. each coaster is cut from a square piece of cardboard. what is the minimum possible area of each cardboard piece? 4.25 in2 8.5 in2 18.0625 in2 72.25 in2

Answer:

A. 1.99 ounces

Step-by-step explanation:

Ramsey's weights is less than gerbil so if gerbil weights is 2.04 so  B is 2.3 is not correct C and D are not less than Ramsey's weights so the answer is A

Step-by-step explanation:

How to rethink the way you choose people in a group is to figure out if they like you or not. Don't chose people that do not like you because they will not work well with you. Pick the people you feel will help you succeed in the group. And sometimes the people you pick in your group aren't even your friend, but they can help you succeed by staying on task and focusing on the task at hand.

Step-by-step explanation:

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Answer:

See below ↓

Step-by-step explanation:

Missing values (a)

Curve which matches the equation

Using the two given solutions and the general absolute value function we will get:

|x + 9|  = 27

The two solutions are:

x = 0 and x = -18.

Remember that the absolute value equation is something like:

|x - a| = b

If we want to have these solutions, then:

|0 - a| = b

|-18 -a| = b

From the first one, we have:

|-a| = b

Replacing that on the second equation we get:

|-18 -a| = |-a|

Notice that if we take a = -9, then we have:

|-18 + 9| = |+9|

|-9| = |+9|

This is true, so a = -9.

Then we find the value of b:

|18 + 9| = b = 27

Then the absolute value equation is:

|x + 9|  = 27

If you want to learn more about absolute value equations, you can read.

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Explanation:

Focus on one of the points in the figure on the left. Let's say we go for the upper left corner point (-7, 4)

Notice it moves to the corresponding image point (2,4). It has shifted 9 units to the right to follow the translation rule [tex](x,y) \to (x+9, y)[/tex]. We've added 9 to the x coordinate, and the y coordinate stays the same.

This notation can be shortened to <9, 0>

In general, the notation [tex](x,y) \to (x+a, y+b)[/tex] is shortened to the translation vector notation [tex]< a, b >[/tex]. In this case, a = 9 and b = 0.

Answer:

14

Step-by-step explanation:

To find the diameter you can just multiply the radius by 2:

7 x 2 = 14
Hope this helps :)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here's we go ~

We know that diameter of a circle is two times it's radius, that's a basic relation among diameter and radius, so let's use this to find the value of diameter :

[tex]\qquad \sf  \dashrightarrow \:d = 2r[/tex]

[tex]\qquad \sf  \dashrightarrow \:d = 2 \times 7[/tex]

[tex]\qquad \sf  \dashrightarrow \:d = 14 \: cm[/tex]

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Answer:

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Answer:

34.54

Step-by-step explanation:

you do 2 * 3.14 * 5.

to find the area 2pie r the 3.14 comes from the directions, the 2 comes from the circle because the full length of the circle is 10 but you divide by 2 to get 5 and the 5 also comes from the circle and that is the radius.

Answer:

Area=½b×h

Area =½×20×8=80m²

hope it helps!

Given is an A.P. in which -

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = a_2-a_1[/tex]

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 7-2 [/tex]

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 5[/tex]

nth term of an A.P ,is given by-

[tex]\green{ \underline { \boxed{ \sf{a_n =a+(n-1)d }}}}[/tex]

where

Putting n = 46

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + (46-1)\times 5 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 45\times 5 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 225 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 227 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Therefore, the 46th term is 227

Hence, the [tex]46th[/tex] term is [tex]227[/tex].

What is the sequence?

A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.

Here given sequence is

[tex]2,7, 12,...[/tex]

Here,

[tex]a=2[/tex]

[tex]d=a_2-a_1\\d=7-2\\d=5[/tex]

The general formula of the sequence is

[tex]a_n=a+(n-1)d[/tex]

where,

[tex]a_n=[/tex] nth term

[tex]a[/tex] is the first term

[tex]d[/tex] is the common difference

[tex]n[/tex] is the number of terms

Now substituting the values in general formula is

[tex]a_{46}=2+(46-1)5\\\\a_{46}=2+(45)5\\\\a_{46}=2+225\\\\a_{46}=227\\[/tex]

Hence, the [tex]46th[/tex] term is [tex]227[/tex].

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Answer:

3

Step-by-step explanation:

adding subtraction multiplication and division

Hello!

Plug in the value of x:

f(x)=5(x-3)+17

f of x is 5 times the difference of x and 3 plus 17

plug in 2:

f of 2 is 5 times the difference of 2 and 3 plus 17

f(2)=5(2-3)+17

f(2)=5(-1)+17

f(2)=-5+17

f(2)=12

[tex]\huge\boxed{\mathfrak{Answer:{\boxed{\rm{f(2)=12\star\star}}}}}[/tex]

Hope everything's clear.

Let me know if you have any questions!

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[tex]\boxed{An~Emotional~Helper!} :-)[/tex]

Answer: 2.83

Step-by-step explanation:

2.66+1.85+2.66 = 7.17

10.00 - 7.17 = 2.83

The area of the vase lies between the area [tex]135\ cm^2[/tex] and [tex]155\ cm^2[/tex] will be [tex]153.86\ cm^2[/tex].

As we know that the area of the circle is given by the formula

[tex]A=\pi r^2[/tex]

So now from the question, we will find the radius for both the given areas.

Radius for the first area

[tex]r=\dfrac{A}{\pi} =\dfrac{135}{\pi} =6.56\ cm[/tex]

Radius for the second area

[tex]r=\dfrac{A}{\pi} =\dfrac{155}{\pi} =7.03\ cm[/tex]

Now we can see the range of the radius lies

[tex]6.56\leq r\leq 7.03[/tex]

The radius must be r=7 cm lie between two quantities.

Then the area at r= 7cm will be

[tex]A=\pi r^2[/tex]

[tex]A=\pi\times 7^2=153.86\ cm^2[/tex]

Thus the area for the vase will be [tex]A=153.86\ cm^2[/tex] ar radius r= 7 cm

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Answer:

a = 1/2 • c

b = (root3)/2 • c

Step-by-step explanation:

30°-60°-90° triangle is a Special Right Triangle. There's a great short cut to find the sides if you know any one side. No trig or Pythagorean Theorem necessary (but that is where the short cut comes from)

The hypotenuse is double the short leg OR the short leg is half the hypotenuse. The long leg is the short leg times the sqroot3. Your question asked for everything in terms of c (the hypotenuse) see image. We can use these shortcuts to find your answer. See image.

Answer:

6(3x-2)

You can use the fact that the value which is outside of the bracket and in multiplication will be distributed to all terms inside with addition or subtraction( this is by distributive property of multiplication over addition).The expression which is equivalent to the given expression isWhat are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.The given expression is It can be seen that 18 is a multiple of 6 and 12 too is multiple of 6 Thus,we can write it as (since when bracket will be opened, the 6 value will distribute inside the bracket to each term joined by either addition or subtraction(which is negative addition).This expression is obtained by doing operations on given expression which didn't changed its value, so this expression obtained is equivalent to the given expression.(The given options are not correct, or it might be that the given expression is not written correctly).Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in Thus,The expression which is equivalent to the given expression is

6(3x-2)

After 23 years $125.32 will be matured to $46,683.28.

The formula for Recurring maturity is given by:

[tex]A=P_n\dfrac{p\times n \times(n+1)}{24}\times \dfrac{r}{100}[/tex]

Where A=matured amount

P =Principal value

n=Number of months

r=Interest rate(annual)

We have P= $125.32

n=23*12 = 276 months

r=2.5*12 =30%

Put these values in the above formula

we get A= $46,683.28

Therefore, After 23 years $125.32 will be matured to $46,683.28.

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Answer:

Step-by-step explanation:

Area = 1/2 b h

= 1/2 * 4 * 5

= 10 unit^2.

Answer:

10.50

Step-by-step explanation:Harold deposited $70 in an account earning 5% interest compounded annually. To the nearest cent, how much interest will he earn in 2 years? Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

The area of the ground floor after it has been reduced to the nearest tenth is 10,681,800 square foot.

In order to determine the area of the ground floor after it has been reduced, the area of the floor has to reduced by 6.3%.

Area that was reduced = 6.3% x 11,400,000 = 718,200

New area = 11,400,000 - 718,200 = 10,681,800 square foot

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Answer:

A.  168 units³

Step-by-step explanation:

volume = area of bas × height

volume = (6)(7)/2 × 8

volume = 168 units³

Answer:

We know that the slope or rate of change of the function can be:

positive

negative

zero, or

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Function 1

From the function 1 graph, it is clear that the graph is a horizontal line. We must note that the horizontal line has a slope or rate of change zero. The reason is that the horizontal line can not rise vertically. i.e. y₂-y₁=0

so using the slope formula

Rate of change = m = y₂-y₁ / x₂-x₁

Taking two points (x₁, y₁) = (0, 4), (x₂, x₁) = (1, 4)

Rate of change = m = 4-4 / 1-0

Rate of change = m = 0/1

Rate of change = m = 0

Thus, the rate of change of function 1 is zero.

Function 2

We know the slope-intercept form of linear equation is

where m is the rate of change or slope of the function and b is the y-intercept

Given the function

comparing with the slope-intercept form i.e. y = mx+b

Therefore, the rate of change of function 2 = m = 8

Conclusion

The rate of change of function 1  = 0

The rate of change of function 2  = 8

as

8 - 0 = 8

Therefore, function 2 has 8 more rate of change of function than the rate of change of function 1.

We know that the slope or rate of change of the function can be:

positive

negative

zero, or undefined

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Function 1

From the function 1 graph, it is clear that the graph is a horizontal line. We must note that the horizontal line has a slope or rate of change zero. The reason is that the horizontal line can not rise vertically. i.e. y₂-y₁=0

so using the slope formula

Rate of change = m = y₂-y₁ / x₂-x₁

Taking two points (x₁, y₁) = (0, 4), (x₂, x₁) = (1, 4)

Rate of change = m = 4-4 / 1-0

Rate of change = m = 0/1

Rate of change = m = 0

Thus, the rate of change of function 1 is zero.

Function 2

We know the slope-intercept form of linear equation is  y = mx+b

where m is the rate of change or slope of the function and b is the y-intercept

Given the function

comparing with the slope-intercept form i.e. y = mx+b

Therefore, the rate of change of function 2 = m = 8

Conclusion

The rate of change of function 1  = 0

The rate of change of function 2  = 8

as

8 - 0 = 8

Therefore, function 2 has 8 more rate of change of function than the rate of change of function 1.

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Step-by-step explanation:

mean = sum of all data points / number of data points

(1.3+1.5+2.2+2.2+2.8)/5 = 10/5 = 2

median is the number where half of the other data points are smaller or equal, and the other half are larger or equal.

median = 2.2

mode is the data point occurring most often = 2.2

range is the difference between largest and smallest data point : 2.8 - 1.3 = 1.5

The probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is 32.22%

Given here,

Mean (μ) = 3 years 6 months

= (3×12)+6 = 42 months

Standard deviation (σ) = 9 months

We will find the z-score using the formula: z = (X - μ)/σ

Here X₁ = 2 years 3 months

= (2×12)+3 = 27 months

and X₂ = 3 years 3 months

= (3×12)+3 = 39 months

So, z (X₁ =27) =

and z (X₂ =39) =

According to the standard normal table,

P(z> -1.666...) = 0.0485 and P(z< -0.333...) = 0.3707

So, P(27 < X < 39)

= 0.3707 - 0.0485

= 0.3222

= 32.22 % [Multiplying by 100 for getting percentage]

The probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is approximately 0.279 or 27.9%.

A normal distribution is a continuous probability distribution that describes a symmetric, bell-shaped curve of data.

It is also known as a Gaussian distribution or a bell curve.

The normal distribution is used to model many real-world phenomena, such as measurements of height, weight, blood pressure, and IQ scores, among others.

We have,

To solve this problem, we first need to standardize the values of 2 years 3 months and 3 years 3 months, using the mean and standard deviation of the distribution.

The mean of the distribution is 3 years 6 months, which is equivalent to 3.5 years, and the standard deviation is 9 months, which is equivalent to 0.75 years.

The standardized value of 2 years 3 months is:

z1 = (2 + 3/12 - 3.5) / 0.75 = -1.33

The standardized value of 3 years 3 months is:

z2 = (3 + 3/12 - 3.5) / 0.75 = -0.33

We can now use the standard normal table to find the probability of a randomly selected hard drive lasting between 2 years 3 months and 3 years 3 months.

P (-1.33 ≤ Z ≤ -0.33) = P(Z ≤ -0.33) - P(Z ≤ -1.33)

From the standard normal table, we find that:

P(Z ≤ -0.33) ≈ 0.3708

P(Z ≤ -1.33) ≈ 0.0918

Now,

P(-1.33 ≤ Z ≤ -0.33) ≈ 0.3708 - 0.0918 = 0.279

Thus,

The probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is approximately 0.279 or 27.9%.

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Answer:   If you sketch this out, you should be able to convince yourself that if you drew a line parallel to the bases and halfway between them, and a vertical at the end of that line, there would be an extra triangle on the longer base that would just fit into the space at the end of the shorter base, if you cut and pasted it.

You should also be able to convince yourself by what you know about similarity that the length of that parallel halfway line is just halfway between the lengths of the bases (you can add them and divide by two).

So your trapezoid (trapezium, we call ’em this side of the pond) has the same area as a rectangle with an altitude equal to the trapezoid’s and a width equal to the sum of those bases divided by two. And since you know about rectangles, you’re home and dry. I suggest you do the sketch, fill in the numbers, and then you’ve completed a model piece of homework that should earn full marks and the teacher’s approval.

Step-by-step explanation:

Answer: 147 Degrees

Step-by-step explanation

The size of the final unknown interior angle in a polygon is 147 degrees.

Given that,

The other interior angles are 162°, 115°, 120°, 148° and 85°.

We assume that there is an equation (2n - 4) 90.

Here n be 7.

Based on the above information, the calculation is as follows:

= (2n - 4) 90

= ((2) (7) - 4) 90

= 10 (90)

= 900

Now the size of the unknown interior angle is  

= 900-(162+125+148+105+98+115)

= 900 - 753

= 147°

Therefore we can conclude that the size of the final unknown interior angle in a polygon is 147 degrees.