the annual rainfall in a certain region is approximately normally distributed with mean 41.4 inches and standard deviation 5.5 inches. round answers to the nearest tenth of a percent. a) what percentage of years will have an annual rainfall of less than 43 inches?

The equation of the circle C is x² + y² = 80 when it passes through the tangent points (-20, 0) and (0, 10).

Equation of circle:

Equation of the circle refer the position of a circle on a cartesian plane.

Given,

C is a circle with center the origin.

A tangent to C passes through the points (-20, 0) and (0, 10)

Here we need to find the equation of the circle C.

In order to find the equation of our line:

We have to identify the y-intercept which is (0,10).

Now, we need to find the gradient of our line which is:

Than can be calculated by,

=> (10 - 0) / (0- (-20))

=>  10/20 = 0.5

Now, the equation of our line is written as,

y = 0.5x + 10

But, here we know the center of our circle is the origin:

Which is in the following form:

=> x² + y² = r²

where r refers the radius

So, here we need the line to meet our circle at one point, we can substitute the equation for our straight line in for y.

Then the equation of the circle is written as,

=> x² + (0.5x + 10)² = r²

When we simplify it, then we get,

=> x² + (0.5x + 10)(0.5x + 10) = r²

Now, we can expand and simplify the brackets to leave us with:

=> 1.25x² + 10x + 100 = r²

=> 1.25x² + 10x + 100 - r² = 0

Here we know that this is a tangent and so it only meets the circle at one point.

So, this equation should only have one solution.

Then it can be written as,

=> b² - 4ac = 0

=> 10² - 4(1.25)(100 - r²) = 0

When we simplify this one then we get the value of

=> r² = 90

Therefore the equation of the circle is x^2 + y^2 = 80.

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The given statement is FALSE.

If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.

When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.

When you have a skewed distribution, the median is a better measure of central tendency than the mean

The median and mean can only have one value for a given data set. The mode can have more than one value

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The rule that describes the function is (c) Output = (0.5)(Input) + 1.5

The points on the coordinate plane are given as

(negative 1, 1), (1, 2), (3, 3), (5, 4)

Express as numbers

So, we have

(-1, 1), (1, 2), (3, 3), (5, 4)

Divide the input values by 2

So, we have

0.5(Input) => (-1/2, 1), (1/2, 2), (3/2, 3), (5/2, 4)

Add 1.5 to the input values

So, we have

0.5(Input) + 1.5 => (1, 1), (2, 2), (3, 3), (4, 4)

So, we have

Output = 0.5(Input) + 1.5

Hence, the equation is (c)Output = 0.5(Input) + 1.5

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Answer:

Step-by-step explanation:

Given is a kite because:

Since MQ and QP are congruent, set equation and solve for y:

Answer:

y = 3

Step-by-step explanation:

Forming the equation,

→ 12y + 7 = 43

Now the value of y will be,

→ 12y + 7 = 43

→ 12y = 43 - 7

→ 12y = 36

→ y = 36/12

→ [ y = 3 ]

Hence, the value of y is 3.

The length of the third side is 9

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) in familiar algebraic notation, a2 + b2 = c2

Given that

By using Pythagoras' theorem.

A^2+B^2=C^2

13 is c because it is the hypotenuse and across from the right angle

a is unknown and b is 15

A^2+12^2=15^2

A^2 +144 = 225

A^2 = 225- 144

A^2= 81

A = 9

Therefore the length of the third side is 9

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Answer:

Step-by-step explanation:

Let the number of weeks be x after which both boys have same weight.

Mike's weight after x weeks:

Tom's weight after x weeks:

Equate both expressions and solve for x:

Answer:

After 8 weeks, both boys weigh same.

Step-by-step explanation:

Forming the equation,

→ 200 - 2x = 160 + 3x

Now the value of x will be,

→ 200 - 2x = 160 + 3x

→ -2x - 3x = 160 - 200

→ -5x = -40

→ x = -40/-5

→ x = 40/5

→ [ x = 8 weeks ]

Hence, the value of x is 8.

Z in terms of m and n is z = [tex]3^{m} -2^{n}[/tex]

Exponentiation is the process of expressing large numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself. For example, 6 is multiplied by itself four times, yielding 6 6 6 6. This is written as [tex]6^{4}[/tex]. The exponent is 4 and the base is 6.

Given that 1000 to the power of m divided by 100 to the power of n

When powers of the equal base are divided, the same base is placed and the exponents are subtracted, which is an important mathematical property of powers.

Then, as powers of the same base, we can write 1000m and 100n:

1000m = [tex](10^{3})^{m}[/tex] = [tex]10^{3m}[/tex]

100n= [tex](10^{2)^{n} }[/tex] = [tex]10^{2n}[/tex]

Now we perform the division of powers of the same base (10)

103m/102n

= 103m-2n

Finally

103m-2n = 10z

z = 3m-2n

Therefore Z in terms of m and n is z = [tex]3^{m} -2^{n}[/tex]

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The numerical expression to model the situation when Kristen read her book is 2 + 1.

A numerical expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, Kristen read her book for 2 hours after school, then she read for another hour before she went to sleep. The expression will be:

= 2 + 1

= 3

She read for 3 hours.

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Answer:

27 miles, 40.5 miles, and 47.25 miles

Step-by-step explanation:

9 miles in 2/3 hours. To get to a whole number, we can multiply by the reciprocal of 2/3, which is 3/2. 2/3*3/2=1. Now lets multiply 9 by 3/2. 9*3/2=13.5

We now have a unit rate which is 13.5 miles each hour.

Now lets solve for 2 hours.

13.5*2= 27 miles

Now lets solve for 3 hours.

13.5*3=40.5 miles

Now lets solve for 3.5

13.5*3.5= 47.25 miles

Answer:

Step-by-step explanation:

Area of circle equation:

Circumference of circle equation:

Use circumference equation to find the radius:

Find the area:

Answer:

Step-by-step explanation:480/3000

There are 8 small rooms and 6 large rooms.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Let s be the number of small rooms reserved.

Let l be the number of large rooms reserved.

Each small room can accommodate 3 guests, hence s small rooms can hold 3s guests.

Each large room can accommodate 4 guests, so all large rooms can hold 5l guests.

Thus, the total number of guests

48 =3s+4l

3s+4l=48

3s+4l=48

as,  Khadija reserved 2 more small rooms than large rooms,

So, s=l+2

s=l+2

Now, solving the equations

3s+5l= 54

s=l+2

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Answer:

There are 54 Republicans, and 58 Democrats

Step-by-step explanation:

See the attached image

The shopper bought a watermelon costing $4.45.

Let x represent the cost of watermelon

y = cost of napkin + cost of paper plates

The tax rate on non-food items is 5%, hence:

5% of y = 0.19

0.05y = 0.19

y = $3.8

The total for the three items he bought was $8.25 before tax,

x + y = 8.25

x + 3.80 = 8.25

x = 4.45

The shopper bought a watermelon costing $4.45.

A tax is a compulsory monetary charge or a few other sorts of levy imposed on a taxpayer (a man or woman or criminal entity) by using a governmental agency if you want to fund authorities' spending and numerous public expenses (regional, neighborhood, or countrywide), and tax compliance refers to coverage movements and character behavior geared toward making sure that taxpayers are paying the right amount of tax on the proper time and securing the right tax allowances and tax reliefs. the first known taxation passed off in historical Egypt around 3000–2800 BC. A failure to pay in a well-timed way (non-compliance), together with evasion of or resistance to taxation, is punishable by means of regulation. Taxes consist of direct or oblique taxes and may be paid in cash or as its labor equivalent.

Maximum nations have a tax system in the region, so as to pay for public, common societal, or agreed-on country-wide needs and for the capabilities of the presidency. a few levies a flat percentage rate of taxation on private annual profits, however, maximum scale taxes are modern and based on brackets of annual earnings amounts. most nations charge a tax on a character's profits as well as on corporate earnings. nations or subunits regularly additionally impose wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, use taxes, payroll taxes, duties, and/or tariffs.

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Sides XY and YZ are both equal to √45 units, therefore, triangle XYZ is an isosceles triangle.

If a triangle has two side lengths that are equal to each other, the triangle is called an isosceles triangle. Therefore, two of the sides of an isosceles triangle must be equal.

Given the vertices of triangle XYZ as:

X(0, 2)

Y(3, 8)

Z(6, 2).

Find the length of each side using the distance formula, [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

XY = √[(3−0)² + (8−2)²]

XY = √45

XZ = √[(6−0)² + (2−2)²]

XZ = √36

XZ = 6

YZ = √[(6−3)² + (2−8)²]

YZ = √45

The triangle has two equal sides YZ and XY, therefore it is an isosceles triangle.

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The set of scores has a mean of 5 and a standard deviation of 2. The score which corresponds to a z score of -2.0 is 1.

Given in the question,

Mean (m) = 5

Standard deviation σ =2

Z-score = -2

The score x,

= Z = x - m / σ

= -2 = x - 5 / 2

= -4 = x - 5

= x = 1

Standard deviation in statistics means the amount of dispersion or variations in the set of values. A lower standard deviation means the value is closer to the mean while a higher standard deviation means the value is farther away from the mean.

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Answer:

The rate of change, or slope, is 1/2.

To find the slope of a line, first, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!

Answer: 15 minutes

Step-by-step explanation:

Let's make a proportion

16  miles    -    20 minutes

12  miles    -      х  minutes

Hence,

[tex]\displaystyle\\x=\frac{12(20)}{16} \\\\x=\frac{3(4)(4)(5)}{4(4)} \\\\x=3(5)\\\\x=15\ minutes[/tex]

Yes, the graphs of a power function and its inverse are symmetric about the line y=x.

What is an inverse function?

A function that "undoes" another function is called an inverse. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

What is a power function?

Any function where y = xⁿ, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions.

Here,

The graphs of self-inverse functions are symmetrical about the line y=x. The domain of a one-to-one function f is the same as the range of its inverse f⁻¹ and the range of f is the same as the domain of f⁻¹.

Hence, the graphs of a power function and its inverse are symmetric about the line y=x.

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Answer:

- 3/4

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The smallest possible perimeter of the triangle is, 72.4 inches.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

As given the longest side of an acute triangle measure 30 inches.

The two remaining sides' combined length must be longer than the opposite side.

The sum of the two remaining sides should be greater than 30 inches if the side is 30.

Assume the other two sides add up to 31 inches.

So, The perimeter of a triangle is equal to the sum of its three sides, which comes to 30 + 31 = 64 inches.

Consequently, the circumference must be greater than 64 inches.

Hence, based on the possibilities, the triangle's smallest conceivable perimeter is 72.4 inches.

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Answer:

63.75 litres

Step-by-step explanation:

the original amount of water is 100%

then a reduction of 15% = 100% - 15% = 85% of original

multiply 75 litres by 85% to obtain reduction

75 × 85%

= 75 × [tex]\frac{85}{100}[/tex] = 75 × 0.85 = 63.75

75 litres reduced by 15% = 63.75 litres

Answer: 6 units^3

Step-by-step explanation:
using the volume of a rectangular prism formula:

L*W*H

We are already given the AREA which is the part L*W of the previous formula.

Now we multiply:

1 1/3 units * 4 1/2 units^2

Convert the fractions into 4/3 * 9/2 for an easier multiplication.

Resulting in 36/6 which is equivalent to 36 divided by 6.

Which gives us our answer of 6.

[tex]y = \cfrac{2}{5}x + 0\implies y=\cfrac{2}{5}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

Step-by-step explanation:

Answer: I Can't Read it

Step-by-step explanation: Its to far

Answer:

[tex]5x-4y=-3[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

We can write z = x + y using thee Exterior Angle Property of a Triangle

What is Exterior Angle Property of a triangle?

If a triangle side is constructed, the outside angle formed is equal to the sum of the two inside opposing angles.

Solution:

Using the Exterior Angle Property of a Triangle it can be observed that z = x + y

Sum of angles in a triangle is 180 degrees

w + x + y = 180 degree -----(1)

Also, using linear angle sum property

w + z = 180 degree -----(2)

From equation 1 and 2

w + x + y = w + z

Therefore, x + y = z

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