The price of widgets has increased from $6 to $12, causing the quantity supplied to increase from 100 to 300 units. Use the midpoint method to calculate the price elasticity of supply.

Answer:

503.8

Step-by-step explanation:

Since the hundredths place is above 4, you round up.

Answer:

503.8

Step-by-step explanation:

Note the tenth place value.

5 (hundreds place value)

0 (tens place value)

3 (ones place value)

.

7 (tenths place value)

8 (hundredths place value)

2 (thousandths place value)

You are trying to solve for the tenths place value. In this case, locate the tenths place value. The value is a 7. Now look at the place value directly next to it (hundredths place value). It is a 8. Because 8 is greater than 4, round up.

503.782 rounded to the nearest tenths is 503.8

Note:

Note the rules of rounding. IF:

The number is 4 or less, round down.

The number is 5 or greater, round up.

~

The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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Answer:

Domain (-∞,∞)

Range (0, ∞)

Step-by-step explanation:

The domain of a function is always the set of all real numbers therefore the domain is going to be (-∞,∞). The range is (0, ∞) because 0 is one of the outputs for the function

A spurious correlation is a correlation between two variables that appears to be causally linked but is actually due to the influence of a third variable that is not considered. The correct answer is  spurious correlation.

Spurious correlations are correlations that exist between two variables, but they are not actually causally related to one another, despite the fact that they appear to be causally related at first glance. The relationship between two variables may be accounted for by a third variable that was previously overlooked or not considered, causing the original correlation to be explained away. Spurious correlations are commonly found in science and research, and they can lead to misleading results if not properly identified and accounted for. It is critical to account for all potential confounding variables in order to establish causal links between variables and avoid spurious correlations. Therefore, researchers must carefully consider all variables that might influence the relationship between two variables to avoid drawing inaccurate conclusions.

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The compound inequality which correctly represents the given number line graph as required is; x < -1 and x ≥ 2

It follows from the task content that the compound inequality which correctly represents the given number line graph be determined.

By observation; The solution set is a union of two set which do not have any elements in common.

Therefore, the required inequalities are;

x < -1 and x ≥ 2

Consequently, the required compound inequality is; x < -1 and x ≥ 2.

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Answer:

see explanation

Step-by-step explanation:

(a)

The area is calculated as length × breadth

area = 2x(2x + 6) ← distribute

       = 4x² + 12x

(b)

area = x(x + 4) ← distribute

       = x² + 4x

(c)

shaded area = 4x² + 12x - (x² + 4x)

                      = 4x² + 12x - x² - 4x ← collect like terms

                      = 3x² + 8x

Answer: 2046

Step-by-step explanation:

:)

The correct choice is within your skills and abilities.

Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.

It will also result in no or less time wasted in doing what you are less capable of.

Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.

Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.

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Answer:

Step-by-step explanation:

a you just had to say a

(a) The number of loads that can be expected to occur during a 2-year period can be found using the mean time between loads and the length of the time period. The mean number of loads that occur in a time period of length t can be found using the formula: mean number of loads = λt, where λ is the mean number of loads per unit time.

In this case, λ = 1/0.4 loads/year, so the mean number of loads that occur in a 2-year period is:

mean number of loads = λ * 2 years = 1/0.4 * 2 = 5

So, we can expect 5 loads to occur during a 2-year period.

(b) The probability that more than eight loads occur during a 2-year period can be found using the Poisson distribution. The Poisson distribution gives the probability of a specific number of events occurring in a given time period, given the average rate of events per unit time. In this case, the Poisson distribution can be used to find the probability that more than 8 loads occur in a 2-year period:

P(more than 8 loads) = 1 - P(8 or fewer loads) = 1 - (P(0) + P(1) + ... + P(8))

Where P(k) is the Poisson probability of exactly k loads occurring in a 2-year period. The Poisson probability of exactly k loads occurring can be found using the formula:

P(k) = (λt)^k * e^-λt / k!

So, substituting the values of λ = 1/0.4 and t = 2 into this formula, we can find the probability that more than 8 loads occur:

P(more than 8 loads) = 1 - (P(0) + P(1) + ... + P(8)) = 1 - (0.135 + 0.270 + 0.405 + 0.541 + 0.678 + 0.814 + 0.947 + 1.078 + 1.206) = 1 - 6.590 = -5.59

Since the probability of an event cannot be negative, this result is not meaningful. The probability that more than 8 loads occur during a 2-year period is greater than 1, which is not possible. This indicates that the assumption that the loads follow a Poisson process may not be valid.

(c) To find the time period for which the probability of no loads occurring is at most 0.2, we can solve for t in the equation:

P(0) = (λt)^0 * e^-λt / 0! = e^-λt = 0.2

Taking the natural logarithm of both sides:

-λt = ln(0.2)

And dividing both sides by -λ:

t = -ln(0.2) / λ = 3.5695 / (1/0.4) = 14.2780 years

So, the time period must be at least 14.2780 years in order for the probability of no loads occurring to be at most 0.2.

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The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2

We want to find the equivalent quotient of the given expression; √16 / √8

Now, we know that the square root of 16 is equal to 4 i.e. √16 = 4

Thus, applying that to our expression gives;

√16/√8 = 4/√8

Now, square root of 8 which is √8 can also be expressed as; 2√2

Thus;

4/√8  = 4/2√2 = 2/√2

The steps to rationalize the denominator, to get rid of all radicals that are in the denominator are as follows;

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

Step 2: Make sure all radicals are simplified.

Step 3: Simplify the fraction if needed.

If we rationalize the denominator of our expression, we have;

2/√2 × √2/√2 = 2√2/ 2 = √2

Also, 2/√2 can be expressed as √4 /√2

Therefore, The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2

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Answer:

Multiplication property of equality

Step-by-step explanation:

x/4=36/16

Cross product

16*x=36*4

16x=144

Divide both sides by 16

x=144/16

=9

What property allowed her to go from

x/4=36/16

To

x/4*4=36/16*4

Multiplication property of equality would allow her to go from

x/4=36/16

To

x/4*4=36/16*4

Answer:

multiplication property of equality

Step-by-step explanation:

It is not true that whenever  we add two irrational numbers we get an irrational number.

Since we know a rational number is a number in the form, p/q, where q ≠ 0. Let  take two numbers : 2 + √3 & 2 - √3

The sum of the two numbers be :

= 2 + √3 + 2 - √3

= 4

Here the number is rational, taking another irrational numbers :  2 + √5 & 2 - √3

= 2 + √5 + 2 - √3

= 4 + √5 - √3,  where it is an irrational number.

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n = 12 + 15 = 27

Probability of choosing girl,

p = 15/27

Probability of choosing boy,

q = 1 - 15/27 = 12/27

\(P(X = 1) = \binom{27}{1} { (\frac{15}{27}) }^{1} ( { \frac{12}{27} )}^{26} \\ = 1.045552364 \times {10}^{ - 8} \)

The probability that he will choose a girl will be equal to 15/27.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that there are 12 boys and 15 girls in Mr Fraioli’s math class. He will randomly call on one person to answer the problem of the day.

The probability that he will choose a girl,

n = 12 + 15 = 27

Probability of choosing a girl,

p = 15/27

Probability of choosing boy,

q = 1 - 15/27 = 12/27

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The number of marbles that Leah has is: 48 marbles

Information about the problem:

To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:

Solving the equation we have:

1/3 x = 4/5 (x-28)

Simplifying the equation we have:

5(1x) = 3*[4*(x-28)]

5x = 12(x-28)

5x = 12x-336

336 = 12x-5x

7x = 336

x = 336/7

x = 48

Leah = x

Leah = 48

Dan = x - 28

Dan = 48-28

Dan = 20

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points.

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

There are some steps of translating the triangle:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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Answer:

5.5 weeks

Step-by-step explanation:

180 = 80+(18)w

100= 18w

w=100/18

w = 5.5

The simplified value of the expression "27 superscript one-third" is 3 , the correct option is (a) .

In the question ,

it is given that ,

the statement for the exponential expression is "27 superscript one-third" ,

which can be written in numbers as

= \(27^{\frac{1}{3} }\)

the number 27 can be expressed as product of number "3" ,

27 = 3 × 3 × 3 = 3³ ,

Substituting the value of 27 in the expression ,

we get ,

= \(3^{3\times \frac{1}{3} }\)  

= 3¹        ....because 3 × (1/3) = 1

= 3

So ,  \(27^{\frac{1}{3} }\) = 3 .

Therefore , the simplified value is 3 .

The given question is incomplete ,the complete question is

What is the simplified value of the exponential expression 27 superscript one-third ?

(a) 3

(b) 9

(c) 2

(d) 18

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Answer:

20

Step-by-step explanation:

Find 30% of the class
then add it

30% x 14 / 70% = 6

6 + 14 = 20 kids
Hope it helped ! Have a nice day !

we know that 14 is 70%, how much will it be for 100%? or namely the whole class?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 14 & 70\\ x& 100 \end{array} \implies \cfrac{14}{x}=\cfrac{70}{100}\implies \cfrac{14}{x}=\cfrac{7}{10} \\\\\\ 140=7x\implies \cfrac{140}{7}=x\implies 20=x\)

Answer:

angle x  = 133 degrees

Step-by-step explanation:

A straight line has a angle of 180.

So you need to find the other angle of the triangle.

To do this add the known angles and subtract from 180 because that is the sum of all angles of a triangle.

91 + 42 = 133

180 - 133 = 47

Now subtract 47 from 180.

180 - 47 = 133

The answer is 133.

Answer:

3240 degrees? I guess. I'm sorry if its the wrong answer.

Answer: 170

Step-by-step explanation:

Let L be the sum of the degree measures of the 10 larger interior angles, and S be the sum of the degree measures of the 10 smaller interior angles. The angles in a convex 20-sided polygon add up to 180(20-2)=3240 degrees, which tells us that L+S=3240. The problem also tells us that L-S=160. Adding both equations together, we get $2L=3400, and by dividing by 2, we get L=1700. Therefore, the sum of the 10 larger interior angles is 1700 degrees, and the average measure of these angles is 1700/10

=170

Answer:

68 is the perimeter

the answer would be 48.17

Step-by-step explanation:

to find the perimeter you have to add all the sides

Hilbert axioms changed Euclid's theorem by identifying and explaining the concept of undefined terms

These were the sets of axioms that were proposed by the man David Hilbert in the 1899. They are a set of 20 assumptions that he made. He made these assumptions as a treatment to the geometry of Euclid.

These helped to create a form of formalistic foundation in the field of mathematics. They are regarded as his axiom of completeness.

Hilbert’s axioms are divided into 5 distinct groups.  He named the first two of his axioms to be the axioms of incidence and the axioms of completeness. His third axiom is what he called the axiom of congruence  for line segments. The forth and the fifth are the axioms of congruence for angles respectively.

Hence we can conclude by saying that Hilbert axioms changed Euclid's theorem by identifying and explaining the concept of undefined terms.

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complete question

Hilbert’s axiom’s changed Euclid’s geometry by _____.

1 disproving Euclid’s postulates

2 utilizing 3-dimensional geometry instead of 2-dimensional geometry

3 describing the relationships of shapes

4 identifying and explaining the concept of undefined terms

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

x=0,3

Step-by-step explanation:

a) The probability that a male passenger is randomly selected and can fit through the doorway without bending is 0.64. b) The probability that the mean height of the 100 men is less than 70 inches is 0.0002. c) The probability from part a is more relevant as it gives the probability that a single passenger can fit through the doorway without bending. d) Women are not considered in this case because the question only deals with men's height.

a) Since, The mean height of the men is 69.0 inches and the standard deviation is 2.8 inches.

Find the z-score of the height that can fit through the doorway.

70 - 69 / 2.8 = 0.357.

Using the z-tables, we get the probability of z-score less than 0.357 is 0.64.

Thus, the probability that a male passenger is randomly selected and can fit through the doorway without bending is 0.64.  

b)  If the mean height of the 100 men is less than 70 inches, then it can be said that most of the male passengers cannot fit through the doorway without bending.

Since the mean height of the men is 69.0 inches and the standard deviation is 2.8 inches.

Find the z-score of the height that can fit through the doorway.

70 - 69 / 2.8 = 0.357.

Using the z-tables, we get the probability of z-score less than 0.357 is 0.64.

Thus, the probability that a male passenger can fit through the doorway without bending is 0.64. If the mean height of the 100 men is less than 70 inches, then the mean z-score of the height of the 100 men is (70 - 69) / (2.8 / √100) = 3.57.

Using the z-tables, we get the probability of z-score more than 3.57 is 0.0002.

Thus, the probability that the mean height of the 100 men is less than 70 inches is 0.0002.

c) The probability from part a is more relevant as it gives the probability that a single passenger can fit through the doorway without bending.

d) Women are not considered in this case because the question only deals with men's height. The height of women does not matter in this situation as they are not considered.

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Given:

The cylinder with radius 17 ft. and height 17ft.

Required:

What is the surface are of cylinder?

Explanation:

The formula to calculate surface area of cylinder:iven:

We have radius(r) = 17 ft. and height(h) = 17 ft.

Answer:

Second option is correct.

Th

The largest angle in the pentagon with consecutive even interior angle sizes is 112 degrees.

Let's assume the smallest interior angle of the pentagon is x degrees. Since the angles are consecutive even numbers, the other four angles can be expressed as x + 2, x + 4, x + 6, and x + 8 degrees.

The sum of the interior angles of a pentagon can be calculated using the formula: (n - 2) * 180 degrees, where n is the number of sides of the polygon. For a pentagon, the sum of the interior angles is (5 - 2) * 180 = 3 * 180 = 540 degrees.

Now, let's add up the five angles of the pentagon:

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 540

Simplifying the equation:

5x + 20 = 540

5x = 540 - 20

5x = 520

x = 520 / 5

x = 104

So, the smallest interior angle, x, is 104 degrees. The largest interior angle is x + 8 = 104 + 8 = 112 degrees.

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Answer:

Just 19 is a factor of both.

GCF of 38 m and 57 n is :19.

Hope this helps!

The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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