Please help ASAP! thank you! 15 points
Choose the correct inequality for this real-world situation: a corvette’s maximum speed is 195 mph. Let S represent speed.

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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If 25% of Paul's cookies are chocolate chip, then 75% of his cookies are not chocolate chip. Let's call the total number of cookies Paul has "x".

So, 25% of x is equal to 6:

0.25x = 6

To solve for x, we can divide both sides by 0.25:

x = 24

So Paul has 24 cookies altogether.

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.

1000 hours in day can be converted in to by a formula dividing the the 1000 hours by 24 is 41.66 days.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

As 1 Hour is equal to 0.0416666666667 Days, you must multiply 1000 by 0.041666666666667 to convert hours to days. The outcome is as follows:

1000 hr × 0.041666666666667 = 41.667 d

1000 hr = 41.667 d

We come to the conclusion that one thousand thousand hours is equal to 41.7667 days:

41.667 days are equivalent to 1000 hours.

Hence, using the conversion method above, you can figure out how many days there are in 1000 hours.

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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  

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.

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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The volume of a right circular cone is given by the formula V = (1/3)*pi*r²*h, where r is the radius, h is the height, and pi is the constant 3.14. When the radius is multiplied by a factor of x, the volume will be multiplied by a factor of x².

Therefore, when the radius is multiplied by a factor of x. The volume changes by x².

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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:

Answer:A

Step-by-step explanation:

they are alternate exterior angles so, x+y=180

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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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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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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Based on the information provided, the greatest weight of a baby walrus in ounces is 2560 ounces.

According to the information provided, the weight of a baby walrus is between 100 and 160 pounds, which means 160 is the maximum weight for these animals.

Now, let's convert the pounds to ounces to know the maximum weight in ounces. For this, let´s consider that 1 pound = 16 ounces.

160 x 16 = 2560 ounces

Based on this, it can be concluded that the maximum weight is 2560 ounces.

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The required converting value into kilograms of the given 116 pounds is equal to 52.62 kilograms ( round up to two decimals ) .

Converting factor used to convert pounds to kilograms is equal  to:

1 pound = 0.453592 kilograms

Now to get the value of 116 pounds we have,

116 pounds = 116 × converting factor

Substitute the value of converting factor we have,

⇒ 116 pounds = 116 × 0.453592 kilograms

⇒ 116 pounds = 52.6167 kilograms

⇒ 116 pounds = 52.62 kilograms ( round up to two decimals )

Therefore, the converted values of the required 116 pounds is equal to 52.62 kilograms ( round up to two decimals ) .

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Answer:

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

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

Q3: [-4,3]

Step-by-step explanation:

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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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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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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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

If you  deposit $5,000 in a savings account and will earn 6. 5% simple interest over the first 10 years, then will earn $3,250 in interest over the 10-year period

Simple interest is a type of interest that is calculated only on the principal amount of an investment, and not on any interest that has been earned previously. It is typically expressed as a percentage of the principal amount and is applied over a fixed period of time.

To calculate the interest earned on the account over the 10-year period, we can use the formula for simple interest:

Interest = Principal x Rate x Time

Here, the principal is $5,000, the interest rate is 6.5%, and the time is 10 years.

Plugging in the values, we get:

Interest = $5,000 x 0.065 x 10

Interest = $3,250

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The given question is incomplete, the complete question is:

Big Money Bank has an offer for new customers: if you deposit $5,000 in a savings account, you will earn 6.5% simple interest over the first 10 years. How much interest will the account earn over this period?

Answer: There are infinitely many fractions that are greater than 3/4. Any fraction whose numerator is greater than three and whose denominator is greater than four will be greater than 3/4. Here are a few examples:

4/5 is greater than 3/4

5/6 is greater than 3/4

6/8 (which simplifies to 3/4) is not greater than 3/4, but any fraction greater than 6/8 will be greater than 3/4. For example, 7/8, 8/9, 9/10, and so on.

In general, to determine whether a fraction is greater than 3/4, you can compare its numerator and denominator. If the numerator is greater than the denominator times 3/4 (which is the same as multiplying the denominator by 3/4 and comparing it to the numerator), then the fraction is greater than 3/4.

Step-by-step explanation:

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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To find all real solutions of the equation 8x²3 - 27x²2 - 50x + 75 = 0, we can factor it by grouping

How to do that?

8x²3 - 27x²2 - 50x + 75 = 0

=> (8x²3 - 50x) - (27x²2 - 75) = 0

=> 2x(4x²2 - 25) - 3(9x²2 - 25) = 0

=> (2x - 3)(4x²2 - 9x + 15) = 0

Using the quadratic formula to solve the quadratic factor, we get:

4x²2 - 9x + 15 = 0

=> x = [9 ± sqrt(81 - 4(4)(15))] / (2(4))

=> x = [9 ± sqrt(-191)] / 8

Since the discriminant of the quadratic factor is negative, it has no real roots, and therefore, the only real solution of the equation is:

x = (2x - 3) = 0

=> x = 3/2

Therefore, the only real solution of the equation 8x²3 - 27x²2 - 50x + 75 = 0 is x = 3/2.

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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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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 scale factor produced in Figure 2 from Figure 1 is 3 over 7.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Given, Two right triangles Δ₁ and Δ₂, where the legs of Δ₂ is 7 units long and the legs of  Δ₁ is 3 units long.

Therefore, The scale factor produces in Figure 2 from Figure 1 is Δ₂/Δ₁,

= 3/7.

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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:

z ÷ 2 = ≥ -6

Step-by-step explanation:

The expression to represent this problem is:

z ÷ 2 = ≥ -6