The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Suppose that V= 70 cm^3 when T = 420 kelvin and P = 18 kg/cm^2 . Find the pressure when T = 140 kelvin and V = 60 cm^3.

Answer:

$1.70 per share

Step-by-step explanation:

37.90-36.20=1.70

Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.

As given in the question,

Conversion of quarter into dollars is :

1 quarter = 0.25 dollars

Amount of money with Lee in his pocket is equal to :

= ( 7 × 5) dollars + ( 6 × 0.25) dollars

= (35 +1.5) dollars

=$ 36.5

Cost of leather jacket buy by Lee = $35.20

Amount of money left in lee's pockets after purchasing jacket

= $( 36.5 - 35.20)

= $ 1.3

Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.

The complete question is :

Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket

worth $35.20?

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Answer:

20 miles

Step-by-step explanation:

1.6km is equivalent to 1 mile

so 30km / 1.6 = 18.75 miles

therefore 20 miles is the closest to 30km

The rate of change of the equation, y = 2/3x - 18, is: 2/3.

The rate of change of a linear equation that is expressed in slope-intercept form as y = mx + b is represented by the value of m in the equation. It is also referred to as the slope of the equation.

For example, if we are given the equation, y = 4x + 5, the value of m is 4. This implies that the rate of change, which is the slope, is equal to 4.

In the same vein, we are given the equation, y = 2/3x - 18.

The value of m, which is the slope or rate of change in the equation y = 2/3x - 18 is equal to 2/3.

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Option A is correct. The value of function (f/g)(x) is found to be  [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that  x ≠  -2/3.

In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

The new function obtained by performing f first and then g is the combination of two functions g and f.

Given:

f(x) = [tex]\sqrt[3]{3x}[/tex]

g(x) = 3x + 2

(f/g)(x) =  [tex]\sqrt[3]{3x}[/tex]/(3x+2)

Also, the denominator should not be equal to 0.

So, 3x + 2 ≠ 0

     x ≠  -2/3

Therefore, the value of function  is found to be  [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that  x ≠  -2/3. So, Option A is correct

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The conditional probability that a camper entering the Luray Caverns has Canadian license Plates is given by:

0.3214 = 32.14%.

Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is given by the rule presented as follows:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

The probabilities that compose the formula are listed as follows:

The events in this problem are given as follows:

The probabilities are given as follows:

P(A) = 0.28, P(A and B) = 0.09.

Hence the conditional probability is obtained as follows:

P(B|A) = P(A and B)/P(A) = 0.09/0.28 = 0.3214 = 32.14%.

The probability asked is that a camper entering the Luray Caverns has Canadian license Plates.

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Answer:

Step-by-step explanation:

1. Put the words into math

3  3 1/4 divided by 2 3/8 equals a b/c.= 3 1/4/2 3/8

3 1/4/2 3/8=

1 7/19

2. Answer: 1 7/19

Answer: 1.367

Step-by-step explanation:

csc47° = 1.3673 ≈ 1.367

The value of cosec 47° is 1.367.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

cosec 47°

The value of cosec 47°.

= 1.367334

Rounding to the nearest thousandth.

= 1.367

Thus,

The value of cosec 47° is 1.367.

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Answer:

18.0833333333

Step-by-step explanation:

online calculator

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+7\qquad \impliedby \qquad \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]

so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (-2 , 5.5)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5.5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5.5}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -5.5= -\cfrac{1}{3} (x +2)[/tex]

[tex]y-5.5=-\cfrac{1}{3}x-\cfrac{2}{3}\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+5.5\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{55}{10} \\\\\\ y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{11}{2}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x+\cfrac{29}{6} \end{array}}[/tex]

The expected change in the dividend of a 6% preferred stock is $75.

Given that, the required rate of return drops instantly from 8% to 6%.

A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time.

The value of preferred stock = $100

Annual dividend = 100 × 6% = $6

Price of preferred stock when required return is 8% = Annual dividend / Required rate of return

= 6/8%

= 6 ×100/8

= $75

Therefore, the expected change in the dividend of a 6% preferred stock is $75.

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The Mathematical Expression formed is 4(10-8)

What is a Mathematical Expression?

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations.

Solution:

The mathematical expression formed frrom the statement;

Multiply the difference of 10 and 8 by 4

is as follows,

4(10-8)

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The percent that Desmond average speed increase is 25%.

From the information, with his old trainer, Desmond averaged a pace of 24 MPH and with his new trainer, he rode at an average speed of 30 MPH.

It should be noted that the percentage increase in speed will be:

= Change in speed / Initial speed × 100

= (30 - 24) / 24 × 100

= 6/24 × 100

= 25%

The percentage is 25%.

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Answer:

Step-by-step explanation:

area=10×5+[(15-5)+7]/2×(10-6)

=50+(17)/2×4

=50+34

=?

The simple interest is $420 and the maturity value is $$6,720

Using this formula to find the simple interest

Simple interest = Principal  × Interest rate × Time

Where:

Principal = $6300

Interest rate =4% or 0.04

Time = 20 month = 20/12 = 1.6666666

Let plug in the formula

Simple interest = $6,300 × 0.04 × 1.6666666

Simple interest = $420

Using this formula to find the maturity value

Maturity value = Principal + Interest

Maturity value = $6,300 + $420

Maturity value = $6,720

Therefore the interest is $420.

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The measure of an obtuse angle is greater than 90° but less than 180°

An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

An angle is the space between two intersecting lines or surfaces at or close to the point where they meet.

Angles are mostly measured in degrees. But it can also be measured in radian. Examples of obtuse angle are 91°, 100°, 150° e.t.c

Other examples of angles are acute angle, reflex angle , right angle.

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Answer: 13

Step-by-step explanation:

Answer:

y = 8 [tex](\frac{1}{2}) ^{x}[/tex]

Step-by-step explanation:

an exponential function can be expressed in the form

y = a [tex]b^{x}[/tex]

to find a and b use points that lie on the graph

using (0, 8 ) , then

8 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then a = 8

y = 8[tex]b^{x}[/tex]

using (1, 4 ) , then

4 = 8[tex]b^{1}[/tex] = 8b ( divide both sides by 8 )

[tex]\frac{4}{8}[/tex] = b , that is b = [tex]\frac{1}{2}[/tex]

y = 8 [tex](\frac{1}{2}) ^{x}[/tex] is the exponential function

Answer:

depends on how many sections there are

Step-by-step explanation:

if there were 2 then it would be one foot 4 sections equal 2 and so on. the ratio for this 2:1 meaning there has to be 2 sections for there to be one foot.

The correct interpretation is Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.

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.

Given:

Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells.

So, for x= 3 them Q(3)

Q(3)= 8.25 (3) - 24.75

Q(3) = 24.75 - 24.75

Q(3) = 0

Hence, Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.

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Answer:

Scientific notation: 5.2516 x [tex]10^{7}[/tex]

Standard notation 52,516,000

Step-by-step explanation:

Are you asking for the answer to be in scientific notation?

5.2516 x [tex]10^{7}[/tex] or 52,516,000

(1.8066 x [tex]10^{7}[/tex]) + (3.445 x [tex]10^{7}[/tex])

(1.8066 + 3.445) x [tex]10^{7}[/tex]

5.2516 x [tex]10^{7}[/tex]

Answer:

Step-by-step explanation:

You have a total of 114 legs among hippos and birds, of which there are a total of 42. You want the number of each kind of animal.

Let h represent the number of hippos. Then 42-h is the number of birds, and the total number of legs is ...

  4h +2(42 -h) = 114

Simplifying the equation gives ...

  2h +84 = 114

  2h = 30 . . . . . . subtract 84

  h = 15 . . . . . . . . number of hippos

  42 -h = 27 . . . . number of birds

There were 15 hippos and 27 birds.

Applying the area of square and triangle, the amount of paper needed is:  180 inches².

The area of a square shape = (side length of the shape)².

The area of a triangular shape = 1/2(base)(height)

The diagram that illustrates the problem given is shown in the image attached below, where the triangular paper to cover the triangular plank and the square paper for the square plank are shown also with their dimensions.

Therefore, the amount of paper that would cover the piece of art = area of the square shape + area of the triangular shape.

Area of the square shape = 12² = 144 inches²

Area of the square shape = 144 inches²

Area of the triangular shape = 1/2(12)(6)

Area of the triangular shape = 36 inches²

Amount of paper needed = 36 + 144

Amount of paper needed = 180 inches²

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Complete Question:

Theresa created a piece of art by attaching a square plank to a triangular plank. The square plank has a perimeter of 48 inches. The triangular plank has a base length of 12 inches and a height of 6 inches. She wants to cover the piece of art with colored paper.

How many square inches of paper are needed to cover Theresa's art piece?

The length of one sides of the square Tito's Kitchen is 13 feet.

A square is a quadrilateral with 4 sides equal to each other. The opposite sides of a square is parallel to each other.

The sum of angles in a square is 360 degrees. Each angle is 90 degrees.

The kitchen is a square and has an area of 169 square feet.

The length of one side of the kitchen can be calculated as follows:

area of the square kitchen = l²

where

Therefore,

area of the square kitchen = 169 ft²

169 = l²

square both sides of the equation

√169 = √l²

l = 13 ft

Therefore,

length of the square kitchen = 13 feet.

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The number of ways to select 3 position out of 10 applicant is 120 ways

Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Combination formula is illustrated as:

nCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

Since there are 10 applicants applying for 3 positions. This will be:

= 10! / (10 - 3)!3!

= 10! / 7!3!

= 10 × 9 × 8 / 3 × 2

= 120

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Option C: The relationship between the statement cannot be determined.

What is Conditional statement?

Two independent statements can be related to each other in a logic structure called a conditional statement.

The first statement is presented with “if,” and is referred to as the hypothesis.

The second statement is linked with “then”, and is known as the conclusion.

The notation associated with conditional statements typically uses the variable p for the hypothesis statement, and q for the conclusion.

                                     p → q

Explanation for the answer:

So, from the above we can clearly see that the both the statement 1 and statement are not start with "if" and "then".

Therefore, their relationship cannot be determined.

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The features of the functions when a quadratic function is given in the form: y = a (x − p) (x − q)

y = value in the y coordinates

a = constant in the equation

p and q = zeros or roots

x = value in the x coordinates

When quadratic equation is written of the form y = a (x − p) (x − q), it is called the factored form of quadratic equation

The other form is ax^2 + bx + c and called standard form of quadratic equation

a in both cases are same and it helps to da if the curve opens upward or downward

when a is positive the curve opens upward but when it is negative the curve opens downward

Expanding the factored form of quadratic equation brings the equation to the standard form

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The arithmetic sequence has the 73rd term of 306

The sequence is given as:

18,22,26,30,....

The above sequence has the following parameters

This means that the sequence is an arithmetic sequence

The nth term of an arithmetic sequence is calculated as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation

So, we have the following equation

f(73) = 18 + (73 - 1) * 4

Evaluate

f(73) = 306

Hence, the 73rd term for the arithmetic sequence is 306

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