A baseball pitcher won 65% of the games he pitched in his career If he pitched 120 games, how many games did he win?​

The limits are evaluated as limₓ→∞ (3x + 15)/(x² + 2) = 0, limₓ→-∞ (9x² + 2)/(3x + 17) = -∞, and limₓ→∞ ln[(3x³ + 4)/(5x⁴ + 23x)] = ln(3/5).

We need to sketch a function given the conditions: f(x) is continuous on its domain (x ≠ 3), f(1) = 0, limₓ→3 f(x) = -∞, limₓ→∞ f(x) = 1, limₓ→-∞ f(x) = -2.

So, let us summarize all the given conditions:At x = 1, f(x) = 0limₓ→3 f(x) = -∞limₓ→∞ f(x) = 1limₓ→-∞ f(x) = -2.

Now, we can make the following graph with the help of these conditions:Figure 1: Sketch of function f(x)Note: The sketch may not be perfect but it should give a rough idea about how the function may look like.

We are given the following limits: limₓ→∞ (3x + 15)/(x² + 2), limₓ→-∞ (9x² + 2)/(3x + 17), limₓ→∞ ln[(3x³ + 4)/(5x⁴ + 23x)].We need to determine these limits one by one. (a) limₓ→∞ (3x + 15)/(x² + 2).

We can use the method of division by highest power of x to determine this limit. So, the numerator and denominator should be divided by the highest power of x, i.e., x². We get, limₓ→∞ (3x + 15)/(x² + 2) = limₓ→∞ (3/x + 15/x²)/(1 + 2/x²).

Now, taking the limit on both sides, we get, limₓ→∞ (3x + 15)/(x² + 2) = 0. (b) limₓ→-∞ (9x² + 2)/(3x + 17)We can again use the method of division by highest power of x to determine this limit.

So, the numerator and denominator should be divided by the highest power of x, i.e., x. We get, limₓ→-∞ (9x² + 2)/(3x + 17) = limₓ→-∞ (9 - 2/x)/(3/x + 17/x²).

Now, taking the limit on both sides, we get, limₓ→-∞ (9x² + 2)/(3x + 17) = -∞. (c) limₓ→∞ ln[(3x³ + 4)/(5x⁴ + 23x)].

We can write this limit as the difference of two logarithmic limits.

We get, limₓ→∞ ln[(3x³ + 4)/(5x⁴ + 23x)] = limₓ→∞ [ln(3x³ + 4) - ln(5x⁴ + 23x)]Now, applying the logarithmic limit rule, we get, limₓ→∞ ln[(3x³ + 4)/(5x⁴ + 23x)] = ln(3/5).

Hence, the main answer is,limₓ→∞ (3x + 15)/(x² + 2) = 0limₓ→-∞ (9x² + 2)/(3x + 17) = -∞limₓ→∞ ln[(3x³ + 4)/(5x⁴ + 23x)] = ln(3/5).

In conclusion, we sketched the function given the conditions and determined the following limits: limₓ→∞ (3x + 15)/(x² + 2), limₓ→-∞ (9x² + 2)/(3x + 17), limₓ→∞ ln[(3x³ + 4)/(5x⁴ + 23x)]. The limits are evaluated as limₓ→∞ (3x + 15)/(x² + 2) = 0, limₓ→-∞ (9x² + 2)/(3x + 17) = -∞, and limₓ→∞ ln[(3x³ + 4)/(5x⁴ + 23x)] = ln(3/5).

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The normal stress and shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ 11 are σn = 16−15√3 and τ = 2+15√3/4. The maximum shear stress is 17.5.

The stress tensor σ given in the problem is:

σ = 201504−400−1500−1010

The normal stress is given by

σn = σ11cos²θ+σ22sin²θ−2σ12sinθcosθ

where

θ = 30°

θ = 30° is the angle between the direction perpendicular to the plane and the direction of σ11

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
σn = 20cos²(30)+(-15)sin²(30)-2(-4)sin(30)cos(30)

σn = 20cos²(30)+(-15)sin²(30)+4sin(30)cos(30)

σn = 20(3/4)+(-15)(1/4)+4(1/2)(√3/2)

σn = 12−15√3+4√3

σn = 16−15√3

The normal stress is σn = 16−15√3

The shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ11

σ11 is given by:
τ = σ12(sin²θ−cos²θ)+0.5(σ11−σ22)sin2θ

where

θ = 30°

θ=30° is the angle between the direction perpendicular to the plane and the direction ofσ11.

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
τ = −4(sin²(30)−cos²(30))+0.5(20−(−15))sin(60)

τ = −4((1/4)−(3/4))+0.5(20+15)(√3/2)

τ = 4(1/2)+0.5(35)(√3/2)

τ = 2+15√3/4

The shear stress is τ = 2+15√3/4

Maximum shear stress
The maximum shear stress is given by

τmax = 0.5(σ1−σ2)

whereσ1σ1 andσ2σ2 are the first and second principal stresses.

The eigenvalues of the stress tensor σ are found by solving the characteristic equation:

det(σ−λI)=0

Here is a detailed calculation:
σ−λI = [20150−λ−400−1500−λ0−400−15−λ10−λ]

σ−λI = 0(20150−λ)[(−λ)(−λ−15)+0(−400)]−(−4)[0(−λ−15)+(−400)(−λ)]+0[0(−400)+(20150−λ)(−λ)]

σ−λI = 0λ³+35λ²−605λ−1875

σ−λI = 0

λ = −25,5,3

The maximum shear stress occurs on the plane of maximum shear stress which is at 45° 45° to the coordinate axes.

The maximum shear stress is found to be

τmax = 0.5(σ1−σ2)

τmax = 0.5(20−(−15))

τmax = 17.5.

Therefore, the maximum shear stress is τmax = 17.5.

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The length of Alice’s step is 0.6 m.

The length of Basil’s step is 0.8 m.

Since Basil takes 100 fewer steps than Alice to walk 240 m;

the number of steps Basil takes = (240/A) - 100.

Basil's step is 20 cm longer than Alice's step;

B = A + 0.2

The distance each person walks is calculated as;

A(240/A) = (A + 0.2) [(240/A) - 100]

240 = 240 - 100A + 48/A - 20

0 =  - 100A + 48/A - 20

100A - 48/A = -20

100A² - 48 = -20A

100A² + 20A - 48 = 0

Solve for A using formula method;

A = 0.6 m

Basil's step length:

B = 0.6 + 0.2

B = 0.8 m

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Answer:

3/4 or 1/4 stays

Step-by-step explanation:

On solving the provided question, we can say that equation is w+y = 27 and There are 16 yellow and 11 white sweatshirts.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

count of yellow sweatshirts = y

count of white sweatshirts = w

equation is

w+y = 27

w = 27 - y........(equation 1)

we have;

w×11.95 + y×12.50 = 331.45......2 now from equation 1 and 2

(27-y)×11.95 + 12.50y = 331.45

322.65 + 0.55y = 331.45

0.55 y = 8.8

y = 16

w = 11

so, There are 16 yellow and 11 white sweatshirts

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Answer: x=4+2i , x=4-2i hope this helps tho :>

Step-by-step explanation

The solutions to the equation x 2 −8x+20=0 are x= 10,-2.

The equation  x 2 −8x+20=0  can be written as (x-10) (x+2) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-10=0

x+2=0

so, the solution to the equation x 2 −8x+20=0 are x=10 and x=-2.

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At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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Answer:

A B D

Step-by-step explanation:

The solutions of the given cubic equation are (x = -8), (x = -4), and (x = 6) and this can be determined by using the factorization method.

Given :

Equation is \(x^3+6x^2-40x=192\).

The following steps can be used in order to determine the solution(s) to the given equation:

Step 1 - Write the given equation.

\(x^3+6x^2-40x=192\)

Step 2 - Rewrite the above equation.

\(x^3+6x^2-40x-192=0\)

Step 3 - Now, factorize the above equation.

\(\begin{aligned}\\x^3-6x^2+12x^2-72x+32x-192&=0\\(x^2+12x+32)(x-6)&=0\\\end{aligned}\)

Step 4  -Again factorize the above equation.

\(\begin{aligned}\\(x-6)(x^2+8x+4x+32)&=0\\(x-6)(x+8)(x+4)&=0\\\end{aligned}\)

Therefore, the correct options are A), B), and C).

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Answer:

114 pies

Step-by-step explanation:

If the pie get together only had 20 people with 15 pies, then each person had a portion of 3/4 (divide them). The pie party has 152 people with 3/4 portions each, which means there has to be 114 pies at the party (multiply them).

:)

Answer:

152÷20=7.6

7.6×15=114

114 pies

• Answer:

x = 2

• Step-by-step explanation:

AB = AC/2 = 16/2 = 8

AB = 2x + 4

8 = 2x + 4

2x = 8 - 4

2x = 4

x = 4 : 2

x = 2

Answer:

I believe they are 5 and 7

Step-by-step explanation:

Answer:

5 and 7

Step-by-step explanation:

those numbers are used with the variable 5x and 7x

Answer: The Answer is 3rd

Answer:

I currently have $-68

Step-by-step explanation:

Answer:

\(2r-2s\)

Step-by-step explanation:

Start by removing the parentheses:

\((r-s)-(s-t)-(t-r)\\r-s-(s)-(-t)-t-(-r)\)

Note that two negatives make a positive.

\(r-s-s+t-t+r\)

Combine like terms

\(r+r-s-s+t-t\\2r-2s\)

Answer:

y = 3x - 2

Step-by-step explanation:

There is no graph so I'll explain with the slope intercept form

slope is m so m = 3

y-intercept is -2 so b = -2

then y = 3x - 2

whichever graph has slope of 3 and y-intercept of -2 is the right answer

Answer:

hope it helps...

have a great day!!

Answer:

Yes he will have enough.

Step-by-step explanation:

9 quarts = 2.25 gallons

22 pints = 2.27 gallons

2.25 + 2.27 is 5 gallons : He will have enough to paint the fences w/ 3 leftover gallons

STEP 1

Interpret question to make sense geometrically.

We have circular shapes, thus, we are dealing with circles and these circles have their area, however, we seek the angle with which when used to cut the circle will give us an area of 220 sq cm.

Note that this is a fraction of the total area of the circle.

This will be illustrated diagrammatically below

Area of a sector is given as:

STEP 2

Find unknown

The ci

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

18 is less than 34

16 ≤ 2x

x minus 13 multiplied by 5 is greater than or equal to 24

7> -15

Answer: $3.32

Step-by-step explanation:

-0.3853 = (x - 3.4) / 0.2

Solving for x, we get:

X = 3.32

Therefore, the price for which only 35% of milk vendors is lower than $3.32.

Answer:

step 2

Step-by-step explanation:

from -8(a+6) to -80 - 48 is incorrect

when you multiply -8 x a it's -8a not -80

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.

The mean of a probability distribution, also known as the expected value, is a measure of central tendency that represents the average value of a random variable in the long run. It is calculated by taking the weighted average of all possible values that the random variable can take, with the weights being the probabilities of each value occurring.

In the case of a discrete random variable, the mean is calculated by multiplying each possible value by its probability and then summing the results. For a continuous random variable, the mean is calculated by integrating the product of the value and its probability density function over the entire range of possible values.

The mean is significant because it provides a measure of the central tendency of a probability distribution, which can be used to make predictions about future outcomes. It is also used in various applications, such as calculating the expected value of a financial investment or the expected number of occurrences of an event in a given time period.

It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.

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Answer:

Cylinder

....................................................................

In a research of investigating the effects of working in crowded versus uncrowded conditions on the job satisfaction of employees in a variety of work setting , working is a depending variable and crowding is an independent variable.

Given aim of the research is to investigate the effects of working in crowded conditions and uncrowded conditions.

We know that depending variable is a variable whose value is dependent on the other variable. Independent variable is a variable whose value does not dependent on the other variables.

In the given question working may be affected negatively in crowded environment means there will be less work in crowded environment and more work in uncrowded environment.

Hence the depending variable in research is working.

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Answer: first blank: jen

second blank: mean

Step-by-step explanation:

N/A

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

Given that,

We have to find why i squared is equal to negative 1.

We know that,

The imaginary numbers are denoted as i.

We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

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