Convert 81.3 to a fraction in simplest form

we have

4P2

the formula is equal to

n!/(n-r)!

n=4

r=2

substitute

4!/(4-2)!

4!/2!=(4*3*2!)/2!

simplify

4*3=12

A quadratic function is a function in the form,

Option A is a quadratic function,

Option B, is not a quadratic function because it is not the form of the equation written above and also,

Option C is also not a quadratic function because it has the highest degree of x to be 3.

In option D the function is given by the function is defined by

This implies that the function in option D is a quadratic function

Option E is not a quadratic function

Answer: there is a 0.095% chance that one of the adults tests positive

Step-by-step explanation:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given probabilities

STEP 2: Write the formula for calculating the required probability

STEP 3: Find P(Z=1)

STEP 4: Find P(Z=2)

STEP 5: Find the P(Z<3)

Hence, the answer is 0.7

The square roots for each side of the equation are not correct, as the square root of 36 is of -6 or 6, not -36 or 36, hence the correct solutions are:

x = -3 or x = 9.

The equation in Step 6 is given as follows:

[tex]\sqrt{(x - 3)^2} = \sqrt{36}[/tex]

Simplifying the square roots, the variable x can be isolated, as follows:

Both -6 and 6 are correct results for the square root of 36, because:

His mistake when removing the square root is that he did not calculate the root, he just removed the square root from the 36, hence the correct solutions will be found as follows:

From the (x - 3)² term, the square root is removed along with the square. However 36 = (6)² or (-6)², hence sqrt(36) = 6 or sqrt(36) = -6.;

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Given -

15 decreased by -7 is 22

To Find -

True or false

Step-by-Step Explaation -

15 decreased by -7 is 22

can be written as -

= 15 - (-7)

[as -(-a) = +a]

= 15 + 7

= 22

Final Answer -

Statement is True

the initial equation is:

So we can add bout of the equation so:

and we simplify it so:

now we solve for x so:

and with the value of x we can replace it in the first equation so:

and we solve for y:

So the solution is x equal to 3 an y equal to 2

If the point O is on the line segment NP, then:

Replace for the given values and find the length of OP:

The length of OP is 15.

Given the equation :

Make all terms at one side:

Factor the equation :

( x - 4 ) ( x - 3 ) = 0

Using the zero product to find x

So,

x - 4 = 0 OR x - 3 = 0

x = 4 OR x = 3

so, the answer is option 4. x = 3 or x = 4

Answer:

See below

Step-by-step explanation:

LCM of 7 9 13    

Prime factorization

9    =   3 x 3

7     =             7

13   =                  13

LCM = 3 x 3 x 7 x 13 = 819 in

LCM   of 6 and 13    is   similarly   78 min    

Step 1. Since Lana Pays the rent monthly, and the lease is for a 3 year period, the first step will be to calculate the number of months that are in 3 years.

Since there are 12 months in just 1 year, we multiply 12 by 3 to get the number of moths in 3 years:

There are 36 months in 3 years.

Step 2. Multiply the number of months by the monthly payment of the rent.

We multiply $395 by the 36 months:

And the result is:

$14,220 is the total amount she will pay for rent during the term of her lease.

Answer:

b. $14,220

A rectangle has 4 right angles.

A rhombus does not have 4 right angles,

So, A rhombus is sometimes a rectangle

The most appropriate choice for inverse of a  function will be given by-

[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]

What is inverse of a function?

At first, it is important to know about function

A function from A to B is a rule that maps to each element of A a unique element of B.

A is called the domain of the function and B is called the co domain of the function.

[tex]f^{-1}[/tex]  is said to be the inverse of [tex]f[/tex] if [tex]f[/tex] [tex]o[/tex] [tex]f^{-1}[/tex] = [tex]f^{-1} o[/tex] [tex]f[/tex] =  [tex]I[/tex], I is the identity function.

Let g(x) = y

[tex]\frac{10-5x}{2} = y\\10 - 5x = 2y\\5x = 10-2y\\x = \frac{10 - 2y}{5}[/tex]

[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]

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The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)

Define Volume of cone?

A pyramid having a circular cross section is called a cone. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly get the volume of a cone. Formula is , V =  1/3 πr²h

We have, dV/dt = 40 ft³/min

h = diameter where, h = 2r

so r = 1/2h

The formula for regular circular cone is,

V =  1/3 πr²h

put the value of r,

V = 1/ 3 * π * (1/2h)² * h

   = 1/12 * π * h³

differentiate it, we get

dV/dt = 3/12 * π * h² * dh/dt

dh/dt = (dV/dt)/(3/12*π*h²)

we have, dV/dt = 40 ft³/min and h = 6

Put these values,

dh/dt = 40 / (3/12 * 22/7 * 6²)               (∵ π = 22/7)

After solving, we get

dh/dt = 1.41 ft/min

Therefore, The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)

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Answer: a) The volume of the pyramid 440.44 cube units

(b) No she doesn't

(c) The volume of the larger pyramid is 1,486.485 cube units

Step-by-step explanation: The given parameters are;

The scale factor of the pyramids, S.F. = 2:3

The base area of the small pyramid,  = 110.11 square units

The height of the small pyramid, h₁ = 12 units

(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid

Therefore;

The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units

V₁ = 440.44 cube units

The volume of the small pyramid, V₁ = 440.44 cube units

(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid

She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid

The volume scale factor = (The linear scale factor)³

(c) The linear scale factor of the pyramids = 2:3 = 2/3

Therefore;

The volume scale factor of the pyramids = (2/3)³ = 8/27

To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁,  by 27/8 as follows;

V₂ = V₁ × (27/8)

Therefore;

The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units

The volume of the larger pyramid, V₂ = 1,486.485 cube units.

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Answer:

Population

Explanation:

A population is a complete group that has a common feature. A Sample is a part of that population and a statistic or parameter are measures of the sample or population.

In this case, we have the ages of all the country's vice presidents, so it is a population.

Answer:

1.  Choice (2)     13

2.  Choice (3)    8.1

3.  Choice (3)    95 to 105 ft

4. Choice (3)     96 in

Step-by-step explanation:

All the problems use the Pythagorean theorem
The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.

[tex]c^{2} = a^{2} + b^{2}[/tex]

or

[tex]c = \sqrt{a^{2} + b^{2}}[/tex]

where c is the hypotenuse and a, b the shorter sides.

This means that given any two of the three sides of a right triangle we can compute the length of the third side

For example if we were given the hypotenuse c and side b, we can solve for side a by:

[tex]a = \sqrt{c^{2} - b^{2}}[/tex]

If we were given side a and asked to solve for side b then
b = \sqrt{c^{2} - a^{2}}

Frankly it does not matter which you choose as side a and side b.

Question 1
The distance from the foot of the ladder to the wall can be taken to be side a and is equal to 8ft

So b = 8ft

The length of the ladder is the hypotenuse c = 15 feet
[tex]a = \sqrt{c^{2} - b^{2}} \\\\a = \sqrt{15^{2} - 8^{2}}\\\\a = \sqrt{225 - 64}\\\\a = \sqrt{161}\\\\a = 12.68857754045 \\\\[/tex]

Rounded to nearest foot, that would be 13 feet So choice (2)

Question 2

The points J and K have the following coordinates as indicated on the graph.

J(-3, 2)

K (1, -5)

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

For:

(X1, Y1) = (-3, 2)

(X2, Y2) = (1, -5)

[tex]d = \sqrt {(1 - (-3))^2 + (-5 - 2)^2}\\\\d = \sqrt {(4)^2 + (-7)^2}\\\\d = \sqrt {{16} + {49}}\\\\d = \sqrt {65}\\\\d = 8.062258\\\\\text{Rounded to the nearest 10th it would be \boldsymbol{8.1}}\\\\[/tex] So choice (3)

Question 3

This again involves a right triangle as shown in the figure
The sides are a = AC = 60 and b = BC = 80 and we are asked to find the length of AC which is the hypotenuse of ΔABC

Use the Pythagorean Theorem directly
[tex]c = \sqrt{a^{2} + b^{2}}}\\\\a = \sqrt{60^{2} + 80^{2}}\\\\c = \sqrt{3600 + 6400}}\\\\c = \sqrt{10000}}\\\\c = 100}\\\\[/tex]

Answer 100 feet so choice (3): from 95 to 105 ft

Question 4

The brace is one of the shorter sides, with the platform top as the hypotenuse.

Let's use a for the brace, b for the 40 in side and c for the hypotenuse = 104 in

So we have to compute for b using the formula:

[tex]b = \sqrt{c^{2} - a^{2}}[/tex]

Using the given values, this would be:

[tex]b = \sqrt{104^{2} - 40^{2}}\\\\b = \sqrt{10816 - 1600}\\\\b = \sqrt{9216}\\\\b = 96\\\\[/tex]

which would be choice (3)

Answer:

$7209.78

Explanation:

To find the amount in the account after 6 years, we will use the following equation

Where P is the initial amount, r is the interest rate and t is the time in years.

So, replacing P = $5000, r = 6.1% = 0.061, and t = 6 years, we get

Therefore, the answer is $7209.78

Answer: 1

Step-by-step explanation:

If the equation is a function there is one y-value for every x-value

EXPLANATION

As we can see in the graph, we need to take two ordered pairs in order to calculate the slope with the following equation:

Let's consider either one ordered pair, as (x1,y1)=(60,0) and (x2,y2)=(100,100), then the slope will be:

Answer: the slope is equal to 5/2.

The Standard form of the ellipse is given as,

The length of the major axis is given as,

The length of the minor axis is given as,

Therefore the required equation is calculated as,

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r = 7\\ \theta = 6 \end{cases}\implies s=\cfrac{(6)\pi (7)}{180}\implies s=\cfrac{7\pi }{30}\implies \underset{\textit{about 9 inches}}{s\approx \stackrel{ft}{0.73}}[/tex]

False

For the Left Hand side of the expression:

This can be simplified as:

For the Right Hand Side of the expression:

Since the Left Hand Side does not equal the Right Hand Side after simplification, the expression is not true

the answer would be 3

The value of the first proportion is 1.6 and the value of the second proportion is 2.78.

A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. A formula or claim shows that two ratios or fractions are equivalent.

According to the question,

The first proportion will be :

4/5 = n/2

n = 8/5

n = 1.6

The second proportion will be :

5/b = 9/5

b = 25/9

b = 2.78

Hence, the value of n will be 1.6 and the value of b will be 2.78 respectively.

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One line is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone.

A rhombus's three-dimensional surface of rotation around one of its symmetry axes is known as a bicone or dicone in geometry. A bicone is a surface made by uniting two right circular cones that are congruent at their bases.

A 3D representation of a double cone {not shown indefinitely stretched). A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.

The part that intersects the plane is only the bus of the cone.

As a result, when a double cone's apex is cut by a plane parallel to the cone's slant edge, one line is created.

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Answer: one line

Step-by-step explanation:

The probability of surviving is given as 20%.

It is required to find the odds of surviving.

Let the event "surviving a certain type of cancer" be X.

It follows that the probability can be written as:

Recall that for an event X, the odds in favor of the event happening are given by the ratio:

The probability of event X not happening is given as:

Substitute the probabilities into the odds formula:

The odds of surviving is 1:4.

The odds of surviving in the ratio from is 4 : 1.

The odds in favor is the ratio of the number of ways that an outcome can occur compared to how many ways it cannot occur.

The odds against is the ratio of the number of ways that an outcome cannot occur compared to in how many ways it can occur.

Given, An insurance company claims the probability of surviving a certain type of cancer is 20%.

So, The probability of not surviving a certain type of cancer is 80%.

∴ The odds of surviving is 2/8 = 1/4.

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Given equation:

Re-arranging:

Using quadratic formula:

a = 5, b = -7, c= -2

Substituting into the formula:

Writing as a decimal:

Answer:

x = -0.24, 1.64