A triangle with exterior angles is shown. A horizontal line intersects with a diagonal line. Another line connects the horizontal line to the diagonal line to form a triangle. The exterior angle at the top left of the triangle is 130 degrees. The exterior angle at the top right of the triangle is x degrees. The exterior angle at the bottom of the triangle is 134 degrees.
The value of x is _____.

Answer:

[tex]2\sqrt{10}[/tex]

Step-by-step explanation:

we can take 4 out of 40 and when you take it out it gets turned into a 2 so its 2 sqrt 10

60 pounds when converted to dollars is 81.97 US dollars.

Countries like the United Kingdom, the South Sandwich Islands, the British Overseas Territories of South Georgia, and the British Antarctic Territory all use pounds as their official currency. Penny sterling, which is one-tenth of a pound, is the name for the lesser units that make up the pound.

The conversion rate of pounds to dollars can vary depending on the current exchange rate. However, as of February 20, 2023, the conversion of 60 pounds to dollars would be:

1 pound = 1.37 US dollars

Hence,

60 pounds = 60*1.37 dollars

                  = 81.97 dollars

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Answer:

The similar figures have dimensions equal in proportion. But in the case of congruent, the transformation of objects is done by using rotation, reflection or translation. The shape is turned or flipped to transform into another shape.

Step-by-step explanation:

Yes, since this 100 adults demonstrate just under 5% of the adult American population, the trials are considered independent.

We have n=100 and p=0.15 here.

np=100*0.15=15 ≥ 10,

nq=100*(1-0.15))=85 ≥ 10

The normality assumption can be used to approximate the binomial distribution.

Option A) is the correct answer.

The probability of seeing a specific value of such a continuous probability distribution is 0 percent.

Determine the prerequisites since a distinct distribution of probabilities.

The probability sum must equal one. So every probability should be between 0 and 1.

Describe how to determine the median of a separate random variable. To calculate the men of such a stochastic process, divide the total each value by it's own probability and afterwards add the results.

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Answer:

$7500

Step-by-step explanation:

So to find mean the formula is total divided by no. of items or values so therefore the total no. of people is 310+390+380+420 which is 1500 people and if one ticket is $20 ,1500 tickets is 1500 multiplied by 20 which is $30,000 and the mean of one night would by 30,000 divided by 4 nights which is $7500 per night.Hope this helped!

The sum of the expressions 8x - 2 and - 3x² - 7 is, - 3x² + 8x - 9.

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.

Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.

Given, Two expressions, 8x - 2 and - 3x² - 7.

Now, Sum implies adding.

Therefore, The sum of 8x - 2 and - 3x² - 7 is,

(8x - 2) + (- 3x² - 7).

= - 3x² + 8x - 2 - 7.

= - 3x² + 8x - 9.

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The constant function, reciprocal function, exponential function, natural log function, and cos function have the property of f(0) ≠ 0.

There are 12 basic functions

Now here we are asked those 5 basic functions where f(0) ≠ 0

Here if we see serial wise

the constant function will always be a constant irrespective of the value of x. Now f(0) here, will not be provided the constant is not 0.

Then we have the reciprocal function where f(0) = 1/0 which is undefined.

The next function is the exponential function

here f(0) will be e⁰ = 1

Then there is the natural log function where ln0 is undefined.

Last we have the cos function where f(0) = cos0 = 1

Hence, the constant function, reciprocal function, exponential function, natural log function, and cos function have the property of f(0) ≠ 0.

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The value of the expression is found to be 1 0 when the value of x is equal to 2.

The expression provided to us is 5.x³/x² for x = 2.

Now, in order to evaluate this expression, we will follow the simple,

5.x³/x² = 5x.

First as we can see, x³ can be divided by x²and then we will get x as the outcome of the simple division operation,

So, we will get,

5x

Now, we have to put the value of x equal to 2 so that we get to know about the exact value of the expression,

x = 2,

= 5(2)

= 10

So, the value of the expression is found to be 10 when the value of x was 2.

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Complete question - Evaluate the expression 5.x³/x² for x equals to 2.

the unit rate for cranberries is $3 per pound.

How did we get?

The unit rate for raisins is the cost per pound. Since the cost for x pounds of raisins is y=2.5x, the unit rate for raisins is:

$$\frac{y}{x}=\frac{2.5x}{x}=2.5$$

Therefore, the unit rate for raisins is $2.5 per pound.

The unit rate for cranberries is also the cost per pound. Since the cost for 4 pounds of dried cranberries is $12, the unit rate for cranberries is:

$$\frac{\text{cost}}{\text{quantity}}=\frac{12}{4}=3$$

Therefore, the unit rate for cranberries is $3 per pound.

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Answer:

4b

Step-by-step explanation:

To solve this division problem, you need to divide 44b2−22b by 11b. To do this, you can use the long division method. Begin by dividing the first term of the dividend (44b2) by the divisor (11b). The quotient will be 4b and the remainder will be 0. Then, subtract the remainder from the next term of the dividend (22b). This will give you a difference of 22b. Divide this by the divisor (11b), and you will get a quotient of 2b and a remainder of 0. Since the remainder is 0, the final answer is 4b.

52 cm is equivalent to nearly 20.47 inches, rounded to two decimal places.

The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.

It is the unit of length.

Furthermore, length is measured in centimeters,

Used in the International System of Units,

This is the metric system's present configuration.

52 centimetres equal 20.47 inches (centimeters).

To convert centimeters to inches,

We can use the following conversion:

1 inch = 2.54 cm

Therefore,

To convert 52 cm to inches,

You can divide 52 by 2.54:

52 cm / 2.54 = 20.47 inches

So, 52 cm is equivalent to nearly 20.47 inches,

rounded to two decimal places.

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The area of the given parallelogram is 421 7/8 ft² [option 2]

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, a parallelogram, with height 18 3/4 ft and base length 22 1/2 ft,

The area of a parallelogram = base x height

Area = 18 3/4 x 22 1/2

= 421 7/8 ft²

Hence, the area of the given parallelogram is 421 7/8 ft² [option 2]

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Answer:

h ≈ 29.98

Step-by-step explanation:

diameter = 12m

volume = [tex]1130m^{3}[/tex]

radius = 6m

The equation to find the height given radius and volume:

[tex]h = \frac{3(V)}{\pi r^2}[/tex]

Plug in values

Answer:

Given:-

Diameter=12m

Volume=1130m³

Takeπ=3.14

To find:-

Height of cone=?

Step-by-step explanation:

Solution:-

Radius=d/2

= 12/2

=6m

Volume of cone=1/3πr²h

h= 3v/πr²

= 3×1130/3.14× 6²

= 3390/113.04

= 29.98m

hence, the height of cone is 30m.

Answer:

Q1: [tex]y\leq -x^2+5x-4[/tex]

Q2: [-3/2,1/4]

Q3: [-4,3]

Step-by-step explanation:

Answer:

Peyton = 45.69 seconds to run the race

Step-by-step explanation:

Karen = 43.52 seconds

Peyton = k + 2.17

Peyton = 43.52 + 2.17

Peyton = 45.69 seconds

Answer:

45.69

Step-by-step explanation:

If Peyton's time running the race was 2.17 seconds more than Karen's time, then we can calculate Peyton's time by adding 2.17 seconds to Karen's time.

Karen's time: 43.52 seconds

Peyton's time: 43.52 + 2.17 = 45.69 seconds

Therefore, Peyton's time running the race was 45.69 seconds...

Based on the information, the probability that the next buyer did not buy apples last week is: 0.23

To calculate the probability that the next buyer did not buy apples last week we must carry out the following mathematical procedure:

Add up all the values.

Now we add the number of buyers who bought apples

Finally, to find the probability we must divide the number of people who bought apples by the total number of buyers.

However, to find the value of those who did NOT buy apples we must subtract this value from 1.

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Answer:

Below

Step-by-step explanation:

For the x distance   -2 to 5   is 7 units

for the y distance   2 to 8 = 6 units

Pythagorean Theorem

 7^2 + 6^2 = d^2

  49 + 36 = d^2

  d^2 = 85       d = [tex]\sqrt{85}[/tex]   =~ 9.2  units  

The solution is, the correct option is, A.) tan 37 = x/12.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

now, from the given figure we get,

tan 37 = x/12

Hence, The solution is, the correct option is, A.) tan 37 = x/12.

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If the cross-price elasticity of demand for two goods is 1.25, then the two goods are substitutes.

Cross Price Elasticity of Demand:

The cross elasticity of demand is an economic concept that measures the response of the quantity demanded of one good to changes in the price of another good. Also known as the cross-price elasticity of demand, this measure is calculated by dividing the percentage change in quantity demanded for one good by the percentage change in price of another commodity.

[tex]E_X_Y[/tex] = [tex]\frac{Percentage change in Quantity of X }{Percentage Change in Quantity of Y}[/tex]

[tex]E_X_Y[/tex] = ΔQ/Q ÷ ΔP/P

       = ΔQ/Q × P/ΔP

       = ΔQ/ΔP × P/Q

where:

Q = Quantity of good X

P = Price of good Y

Δ = Change

​The cross elasticity of demand for a substitute is always positive because an increase in the price of a substitute increases the demand for one good. For example, when the price of coffee rises, the demand for tea (alternative beverage) increases as consumers switch to cheaper but alternative beverages. This is reflected in the formula for the cross-elasticity of demand, as the numerator (the percentage change in demand for tea) and the denominator (the price of coffee) represent positive increases.

Items with a coefficient of 0 are unrelated and independent products. Commodities can be weak substitutes for which both products are positive but have a low cross-elasticity of demand. This is often the case with various alternative products such as tea or coffee. Commodities that are strong substitutes have a higher cross-elasticity of demand. Consider a different brand of tea. An increase in the price of green tea from one company has a greater impact on the demand for green tea from the other company.

The cross elasticity of demand is 1.25. Positive cross elasticity means that when the price of one good changes, the quantity demanded of another good changes in the same direction. For example, when the price of one good increases, the demand for another good increases.

This indicates that the two products are fungible. When the price of a product rises, consumers will prefer the cheaper product. As a result, the demand for alternatives will increase.

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Minimum and Maximum Calculator is an online widget that helps you find the max and min values ​​of a function.

The maximum value is the point at which the function has the highest value of all other values, while the minimum value is the lowest value in the entire function.

The calculator returns the global maximum and minimum of the function along with a graph on the Cartesian plane as the solution. A min-max calculator is an online calculator that can be used to find the maximum and minimum values ​​of a mathematical function.

Finding the extreme values ​​of a function is also known as optimization. Feature optimization is a central concept in engineering, business, and machine learning.

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Answer:

172.72 cm

Step-by-step explanation:

5 feet 8 inches in cm = [(5×12)+8] x 2.54 = 68 x 2.54 = 172.72 cm

The answer is that there are 8 green pins and 12 yellow pins remaining in the bag after Yaqub gives a green pin to his sister.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is used to measure the likelihood or chance of an event occurring. Probability is represented as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if a fair coin is flipped, the probability of getting heads is 1/2, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

There are two main types of probability: theoretical probability and empirical probability.

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. For example, the theoretical probability of rolling a six on a fair die is 1/6, since there is one favorable outcome out of six possible outcomes.

Empirical probability is based on observations and experiments and reflects the actual frequency of an event occurring. For example, the empirical probability of rolling a six on a particular die after many rolls may be different from the theoretical probability due to factors such as bias or chance.

Probability is used in many real-life situations, such as in games of chance, insurance, stock market analysis, and weather forecasting. It is also used in various fields of science, such as physics, biology, and chemistry, to model and analyze the behavior of complex systems.

Let's start by using algebra to represent the information given in the problem.

Let G be the number of green pins in the bag, and Y be the number of yellow pins in the bag. We know that:

G + Y is the total number of pins in the bag.

G/(G + Y) = 3/7, since 3/7 of the pins are green.

(G - 1)/[(G - 1) + Y] = 2/5, since after Yaqub gives a green pin to his sister, there are (G - 1) green pins remaining out of (G - 1 + Y) total remaining pins.

To solve for G and Y, we can use algebra to manipulate the equations:

G/(G + Y) = 3/7 can be simplified to 7G = 3(G + Y), which gives us 4G = 3Y.

(G - 1)/[(G - 1) + Y] = 2/5 can be simplified to 5(G - 1) = 2(G - 1 + Y), which gives us 3G - 2Y = 3.

We now have two equations with two variables, so we can solve for G and Y using substitution or elimination. For simplicity, we will use substitution.

From 4G = 3Y, we can solve for Y in terms of G:

Y = (4/3)G

Substituting this into 3G - 2Y = 3, we get:

3G - 2(4/3)G = 3

Simplifying, we get:

G = 9

Therefore, there are 9 green pins in the bag. Using the equation Y = (4/3)G, we get:

Y = (4/3)(9) = 12

So there are 12 yellow pins in the bag. After giving one green pin to his sister, Yaqub has 8 green pins and 12 yellow pins remaining in his bag. To check that 2/5 of the remaining pins are green, we can calculate:

8/(8+12) = 4/10 = 2/5

Therefore, the answer is that there are 8 green pins and 12 yellow pins remaining in the bag after Yaqub gives a green pin to his sister.

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A = ( θ/360)πr² is used to find area of sector and L = ( θ/360)2πr used to find  length of the arc.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

To find the area of a sector:

Find the fraction of the circle represented by the sector by dividing the central angle  θ by 360 degrees.

Multiply this fraction by the total area of the circle, which is given by πr².

The result is the area of the sector, which can be expressed as A = ( θ/360)πr².

To find the length of an arc:

Find the fraction of the circle represented by the arc by dividing the central angle  θ by 360 degrees.

Multiply this fraction by the circumference of the circle, which is given by 2πr.

The result is the length of the arc, which can be expressed as L = ( θ/360)2πr.

Hence, A = ( θ/360)πr² is used to find area of sector and L = ( θ/360)2πr used to find  length of the arc.

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The equation of the points is y + 4 = -7(x = 24)

From the question, we have the following parameters that can be used in our computation:

(-4,24) and (7,-53)

The slope is calculated as

m = (-53 - 24)/(7 + 4)

m = -7

The equation is then calculated as

y - y1 = m(x - x1)

Substitute the known values in the above equation, so, we have the following representation

y + 4 = -7(x = 24)

Hence, the equation is y + 4 = -7(x = 24)

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The solution for the system of equations is Ax = b as the matrix is invertible (or non-singular) if and only if its determinant is not zero.

To solve a system of equations, we can use matrix algebra. We can write the system of equations in matrix form as follows:

Ax = b

where A is the matrix of coefficients, x is the vector of unknowns (the concentrations), and b is the vector of right-hand sides (the mass inputs).

To solve for x, we can multiply both sides by the inverse of A:

x = [tex]A^{-1}b[/tex]

where [tex]A^{-1}[/tex] is the inverse of A.

However, not all matrices have inverses. A matrix is invertible (or non-singular) if and only if its determinant is not zero. So, before we can solve for x, we need to check if A is invertible by calculating its determinant.

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a) The square root of complex number, 2i is equals to the ±( 1 + i).

b) The square root of complex number, (1 - √3i) is equals to the ±1/√2(√3 - 1). The rectangular coordinates plane of both present in above figure.

Square root of a number is defined as a value which on multiplication by itself, results the original number. If p is the square root of q then it is denoted as p=√q. We have to determine the square root of complex numbers and express them in rectangular coordinates. For a nonzero complex number z, its square roots are √z =√r exp( i(2πk + θ)/2), k = 0,1

(a) The magnitude of 2i is r =√(2² + 0) = 2, and the principal argument is θ = π/2. So, (2i)½ = r½ exp(i (2πk + π/2)/2) , k = 0, 1

For first root, substuting, k = 0

=> (2i)½ = 2½ exp(i (2π×0 + π/2)/2)

=> (2i)½ = √2 exp(i (π/2)/2)

=> (2i)½ = √2 exp(i π/4) = √2(cos(π/4) + i sin(π/4)

=> (2i)½ = √2( 1/√2 + i(1 /√2)) = 1 + i

For second root substuting, k = 1

=> (2i)½ = 2½ exp(i (2π×1 + π/2)/2)

=> (2i)½ = √2 exp(i (5π/2)/2)

=> (2i)½ = √2 exp(i (5π/4) = √2( cos(5π/4) + i sin(5π/4)

=> (2i)½ = √2(- 1/√2 + i(-1 /√2)) = - (1 + i)

Hence, square root of 2i is ±( 1 + i).

b) 1 -√3i

The magnitude and principal argument of 1 −√3i are respectively, r = √(1² + (√3)²) = 2 and θ = tan⁻¹ ( -√3/1) = - π/3. Similar to part(a), square root of (1 - √3i) is written as (1 - √3i)½ = r½ exp(i (2πk - π/3)/2), k= 0, 1

For first root , k = 0

(1 - √3i)½ = √2 exp(i (2π×0 - π/3)/2)

=> (1 - √3i)½ = √2 exp(i (- π/6) )

=> (1 - √3i)½ = √2( cos(-π/6) - i sin(π/6))

=> (1 - √3i)½ = √2( cos(π/6) - i sin(π/6))

=> (1 - √3i)½ = √2( √3/2 - i (1/2)) = 1/√2(√3 - 1)

For second root, k = 1

(1 - √3i)½ = √2 exp(i (2π×1 - π/3)/2)

=> (1 - √3i)½ = √2 exp(i (5π/3)/2)

=> (1 - √3i)½ = √2 exp(i (5π/6))

=> (1 - √3i)½ = √2 (cos(5π/6) + i sin(5π/6))

=> (1 - √3i)½ = √2 (- √3/2 + i(1/2) ) = - 1/√2(√3 - i)

so, (√1- √3i ) is ± 1/√2(√3 - 1). Hence, we got all required square roots.

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Complete question:

1. Find the square roots of (a) 2i; (b) 1 - √3i and express them in rectangular coordinates.

The total cost of the bill and tip for Tyler is $71.46. This means that Tyler paid $58.6 for the food and drinks, and an additional $12.86 as a tip for the service.

To calculate how much the bill and tip cost Tyler, we first need to calculate the amount of the tip. We can do this by multiplying the total bill by the percentage of the tip, which is 18% or 0.18 as a decimal.

Tip amount = $71.46 x 0.18 = $12.86

Once we know the tip amount, we can add it to the total bill to find the final cost.

Bill and tip cost = $71.46 - $12.86 = $58.6

Therefore, total bill is $84.32 with tip as $12.86 and bill as $58.6

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Take into consideration the solid that results from rotating the area enclosed by the provided curves about the x-axis. y = 2/7 x^2, y = 9/7 - x^2 . the volume of the solid is approximately 1.412 cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y = 2/7 [tex]x^{2}[/tex] and y = 9/7 - [tex]x^{2}[/tex] about the x-axis, we can use the method of disks or washers.

First, we need to find the limits of integration. The curves intersect when:

2/7[tex]x^{2}[/tex] = 9/7 - [tex]x^{2}[/tex]

Multiplying both sides by 7, we get:

2[tex]x^{2}[/tex] = 9 - 7[tex]x^{2}[/tex]

9[tex]x^{2}[/tex] = 9

[tex]x^{2}[/tex] = 1

x = ±1

Therefore, the limits of integration are x = -1 and x = 1.

Next, we need to express the curves in terms of y. Solving for x in each equation, we get:

x = ±√(7/2 y)

x = ±√(9/7 - y)

Using the method of disks, we can find the volume of the solid by integrating the areas of circular disks with radius y from y = 0 to y = 9/7.

The radius of each disk is given by the difference between the upper and lower curves evaluated at y:

r = √(9/7 - y) - √(7/2 y)

The area of each disk is given by:

A = π[tex]r^{2}[/tex]

Substituting for r, we get:

A = π [√(9/7 - y) - √(7/2 y)]

Expanding and simplifying, we get:

A = π [9/7 - y + 7/2 y - 2√(9/7 y)]

A = π [9/7 + 3/2 y - 2√(9/7 y)]

Integrating with respect to y, we get:

V = ∫[0, 9/7] π [9/7 + 3/2 y - 2√(9/7 y)] dy

V = π [(9/7) y + (3/4) - (4/9) [tex]9/7^{3/2}[/tex] [tex]y^{3/2}[/tex]] [0, 9/7]

V = π [81/28 - (64/81)  [tex]9/7^{3/2}[/tex]]

V ≈ 1.412

Therefore, the volume of the solid is approximately 1.412 cubic units.

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