11. If the perimeter of ABCD is 600 ft. and AD=2x-10 find AB.

The correct answer is option d. The theoretical Probability of spinning a multiple of 3 with one spin is 0.

The theoretical probability of an event, we need to identify the number of favorable outcomes (the desired event) and the total number of possible outcomes.

In this case, the event is spinning a multiple of 3 on the spinner. Let's examine the possible outcomes and identify the favorable outcomes:

Possible outcomes on the spinner: {1, 2, 3, 4, 5, 6}

Favorable outcomes (multiples of 3): {3, 6}

The total number of possible outcomes is 6, and the number of favorable outcomes is 2.

The theoretical probability of spinning a multiple of 3 can be calculated as:

P(multiple of 3) = (Number of favorable outcomes) / (Total number of possible outcomes)

P(multiple of 3) = 2 / 6

Simplifying the fraction, we get:

P(multiple of 3) = 1 / 3

Therefore, the correct answer is option d. The theoretical probability of spinning a multiple of 3 with one spin is 0.

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Answer:

Around 2

Step-by-step explanation:

The value of the iterated integral 5∫_(-5)^(5) ∫_0^(π/2) (y + y^2 cos x) dx dy is 5π^2/4 + (π^3/12) sin 5.

To calculate the iterated integral ∬_S (y + y^2 cos x) dA over the given region S, where S is the rectangle defined by -5 ≤ x ≤ 5 and 0 ≤ y ≤ π/2, we will evaluate the integral in two steps: first integrating with respect to x and then integrating with respect to y.

Let's start by integrating with respect to x:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) ∫_(-5)^5 (y + y^2 cos x) dx dy

To integrate with respect to x, we treat y as a constant and integrate the expression (y + y^2 cos x) with respect to x over the range -5 to 5:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [(y * x + y^2 sin x)]|_(-5)^(5) dy

Now we have an expression in terms of y only. We substitute the limits of integration for x, which are -5 and 5, into the expression (y * x + y^2 sin x) and evaluate it:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [5y + y^2 sin 5 - (-5y - y^2 sin(-5))] dy

Simplifying further:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [10y + 2y^2 sin 5] dy

Now we integrate the expression [10y + 2y^2 sin 5] with respect to y over the range 0 to π/2:

∫_S (y + y^2 cos x) dA = [5y^2 + (2/3)y^3 sin 5] |_0^(π/2)

Evaluating the expression at the limits:

∫_S (y + y^2 cos x) dA = [5(π/2)^2 + (2/3)(π/2)^3 sin 5] - [5(0)^2 + (2/3)(0)^3 sin 5]

Simplifying:

∫_S (y + y^2 cos x) dA = [5(π^2/4) + (2/3)(π^3/8) sin 5] - [0]

Finally, we simplify the expression:

∫_S (y + y^2 cos x) dA = 5π^2/4 + (π^3/12) sin 5

Therefore, the value of the iterated integral 5∫_(-5)^(5) ∫_0^(π/2) (y + y^2 cos x) dx dy is 5π^2/4 + (π^3/12) sin 5.

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The original polynomial, \(x^2 + 7x + 12\), it can be seen that the two are the same, thus confirming that the polynomial was correctly factored.

To check the result after factoring a polynomial, one can use the FOIL method to ensure that the factored polynomial is equivalent to the original polynomial. The FOIL method stands for First, Outer, Inner, Last, and is used to multiply two binomials. To check the result, one would use the FOIL method to multiply the factored polynomial, and compare the result to the original polynomial. For example, let’s consider the polynomial\(x^2+7x+12\). After factoring, this can be written as (x+4)(x+3). To check the result, one would multiply the two binomials together, (x+4)\((x+3) = x^2 + 3x + 4x + 12\). Comparing this to the original polynomial, \(x^2 + 7x + 12\), it can be seen that the two are the same, thus confirming that the polynomial was correctly factored.

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Answer:

1

Step-by-step explanation:

Raise -2 to the power of 3 = -8

9-8= 1

Answer:

1

Step-by-step explanation:

A number raised to the 3rd power is equal to that number multiplied by itself twice. Below I have expanded the expression to visualize this process. If this makes it more confusing, the main way is just to go from line 1 to line 4.

9 + (-2)³                          <---- Original expression

9 + (-2 x -2 x -2)             <---- (-2)³ expanded

9 + (4 x -2)                     <---- -2 times -2

9 + (-8)                           <---- 4 x -2                    

1                                     <---- 9 - 8

The  solution to the system is x is 1.4 and y is -3.6.

Two or more expressions with an Equal sign is called as Equation.

The given system of equations  are -9.5x - 2.5y = -4.3 and 7x + 2.5y = 0.8

Add both the equations to eliminate y variable

-9.5x+7x=-4.3+0.8

-2.5x=-3.5

Divide both sides by 2.5

x=1.4

Substitute the value of the variable into either original equation to solve for the other variable.

-9.5(1.4)-2.5y=-4.3

-13.3-2.5y=-4.3

-2.5y=-4.3+13.3

-2.5y=9

Divide both sides by 2.5

y=-3.6

Hence, the  solution to the system is x is 1.4 and y is -3.6.

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Answer:

8(3y-4)

hope this help :)

Answer:

√[(5-1)² + (5-5)²]

√[16+0]

√(16)

+4 or -4 units

I hope this helped :D

Step-by-step explanation: for your other question

((

−

4

,

7

)

(

−

4

,

5

)

Answer:

4

Step-by-step explanation:

Answer:

1. 37°

2. 54°

3. 84°

Step-by-step explanation:

1. 180-(66+77)=37°

2. 180-(90+36)=54°

3. 360- (144+84+48)

The region enclosed by the graphs of y = e^x, y = x^2 - 1, x = -1, and x = 1 is more naturally integrated with respect to y. The area of the region is approximately 1.24 square units.



To sketch the region enclosed by the graphs of the functions y = e^x, y = x^2 - 1, x = -1, and x = 1, we can plot these functions on a coordinate plane. The region is bounded by the curves of the two functions and the vertical lines x = -1 and x = 1. To determine whether it is more natural to integrate with respect to x or y, we can look at the shape of the region. In this case, it is more natural to integrate with respect to y because the region is horizontally oriented.

To find the area of the region, we integrate with respect to y. The height of the approximating rectangle is the difference between the y-values of the functions e^x and x^2 - 1. The width is the difference between the x-values, which is 2.

Integrating y = e^x - (x^2 - 1) with respect to y from e to 0 gives the area of the region. Evaluating the integral, we get the area as approximately 1.24 square units.

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Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.

Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

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Answer:

option c

Step-by-step explanation:

The angles are 30° , 60° , 90° . So its a right angled triangle . We can use trigo.

⇒ sin 30 = p/h

⇒ 1/2 = p/10

⇒ p = 10/2

⇒ p = 5

Using Cosine now ,

⇒ cos 30° = b/h

⇒ √3/2 = b/10

⇒ b = √3/2 × 10

⇒ b = 5√3

Answer:

c) short leg = 5; long leg = 5 √3

Step-by-step explanation:

How long are the other sides?

short leg = 5; long leg = 5 √3

The histogram showing the number of events with the events cost is

misleading because;

Please find attached a possible diagram of the histogram in the question

created with MS Excel;

The data in the histogram is presented as follows;

\(\begin{array}{|c|c|c}Event \ Cost&Number \ of \ Events\\1000- 1499&2\\1500-1999&4\\2000-2499&3\\3000-3499&1\end{array}\right]\)

From the above table, we have that the class with event cost of 2000 to

2499 is left out, therefore, the data is more clustered.

The correct option is therefore;

The x-axis scale shows the data is more clustered than it actually is

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Answer:

its a

Step-by-step explanation:

got it right on edge

Answer:

how are you supposed to solve that??? I'm confused ://

The expected value for the complete pairs of socks that make it out alive from the washing machine is calculated based on the probability of losing a sock and the number of pairs. The expected value for the complete pair of socks is 2.

Let's denote the random variable X as the number of complete pairs of socks that make it out alive. To calculate the expected value of X, we need to consider the probability of losing a sock and the total number of pairs.

In this case, there are 20 pairs of socks, which means there are a total of 40 socks. The washing machine eats four socks at random, which means there will be 36 socks remaining.

The probability of losing a sock can be calculated by dividing the number of socks lost by the total number of socks. In this scenario, four socks are lost out of 40 socks, so the probability of losing a sock is 4/40 = 1/10.

To calculate the expected value, we multiply the probability of losing a sock by the total number of pairs. In this case, the expected value is (1/10) * 20 = 2.

Therefore, the expected value for the number of complete pairs of socks that make it out alive from the washing machine is 2.

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Answer:

m = 7 can also be y=7x+1 is positive and shows acceleration or ascending lines steep y axis 1 and x axis 0 ascending to 1 or above and when y = 7  x =1 see attached.

m = -7 is negative and shows deceleration of 1 as we add 1 here too. Or can be any number for y intercept see attached.

Step-by-step explanation:

it takes 2.25 seconds

oh, and it's 18 seconds for the next question assuming we had the same test.

Answer:

a= 126 degrees

b= 54 degrees

r= 54 degrees

s= 126 degrees

Step-by-step explanation:

Option C. Between 1982 and 2012, there were fewer House members who fell between the most liberal Republican and the most conservative Democrat. represents a trend supported by the data in the bar graph

What is bar graph?

A bar graph, also known as a bar chart, is a graphical representation of categorical data using rectangular bars. It is used to compare and display the values of different categories or groups.

In a bar graph, each category or group is represented by a separate bar. The length or height of each bar corresponds to the value or frequency of the category it represents. The bars are typically drawn vertically or horizontally, with the length or height proportional to the data being represented.

The horizontal axis of a bar graph represents the categories or groups, while the vertical axis represents the values or frequencies. Labels or values are often placed along the axes to provide additional information.

Bar graphs are commonly used to visualize and compare data in various fields, including statistics, economics, market research, and social sciences. They provide a clear visual representation of data, making it easy to interpret and understand comparisons between different categories or groups.

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Answer:

-50 + -50 = -100

Step-by-step explanation:

try that

Answer:

\( = \sqrt{100} \times \sqrt{ - 1} = 10i = 0 + 10i\)

The possible values of k are -11 and 11.

Given that equation is: x²-kx+28

Roots are: \(\alpha ,\alpha +3\)

To find: the value of x:

The general quadratic equation is:

ax²+bx+c

Product of roots=c/a

sum of roots=-b/a

From given,

x²-kx+28=0

a = 1

b = -k

c = 28

Therefore,

Product of roots=28/1=28

sum of roots=-k/1=-k

Given roots are:

\(\alpha ,\alpha +3\)

Therefore,

The two roots are two numbers whose difference is 3 and whose product is 28

Those two roots are 4 and 7 or -4 and -7

Then, the sum of roots is:

4 + 7 = 11

-4 - 7 = -11

Therefore, the possible values of k are -11 and 11.

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Answer: b= 45

Step-by-step explanation:

Step 1: Subtract 5b from both sides.

2b+23−5b=5b−112−5b

−3b+23=−112

Step 2: Subtract 23 from both sides.

−3b+23−23=−112−23

−3b=−135

Step 3: Divide both sides by -3.

−3b /-3 = -135/-3

Answer:

infinite solutions

Step-by-step explanation:

2x-6 = 3x+1-X-7

Combine like terms

2x-6 = 3x-x +1-7

2x-6 = 2x -6

subtract 2x from each side

-6 = -6

Since this is a true statement, x can be any real number

The given sequence does not have a common difference (d) as it is a geometric sequence. The recurrence relation is aₙ = aₙ₋₁ * 2, and the closed-form solution is aₙ = 3 * 2^(n-1). This solution is proven using induction.

To find the common difference (d) in the given sequence, we need to observe the pattern between consecutive terms.

The given sequence is: 3, 6, 12, 24, 48

To go from one term to the next, we can see that each term is obtained by multiplying the previous term by 2. This suggests that the sequence is a geometric sequence with a common ratio of 2.

Let's calculate the common difference (d) using the formula for the common ratio in a geometric sequence:

Common Ratio (r) = (second term) / (first term)

r = 6 / 3 = 2

Since the common difference (d) is the difference between consecutive terms in an arithmetic sequence, and we have identified the given sequence as a geometric sequence, we can conclude that there is no common difference (d) in this sequence. Instead, we have a common ratio (r) of 2.

To write the recurrence relation for this sequence, we can use the formula:

aₙ = aₙ₋₁ * r

where aₙ represents the nth term of the sequence and r is the common ratio.

In this case, the first term (a₁) is 3 and the common ratio (r) is 2. Therefore, the recurrence relation is:

aₙ = aₙ₋₁ * 2

To find the closed-form solution for this geometric sequence, we can use the formula:

aₙ = a₁ * r^(n-1)

where aₙ represents the nth term, a₁ is the first term, r is the common ratio, and n is the position of the term.

In this case, the first term (a₁) is 3, the common ratio (r) is 2, and n represents the position of the term.

The closed-form solution for this geometric sequence is:

aₙ = 3 * 2^(n-1)

To prove this closed-form solution using induction, we need to show that it holds true for the base case (n = 1) and then demonstrate that if it holds true for any arbitrary term, it also holds true for the next term.

Base case (n = 1):

Using the closed-form solution, when n = 1, we have:

a₁ = 3 * 2^(1-1) = 3 * 2^0 = 3 * 1 = 3

This matches the first term of the given sequence, which is 3. Therefore, the closed-form solution holds true for the base case.

Inductive step:

Assume that the closed-form solution holds true for an arbitrary term, let's say, aₖ, where k ≥ 1. In other words, assume that:

aₖ = 3 * 2^(k-1)

Now, let's consider the next term, aₖ₊₁. Using the recurrence relation, we have:

aₖ₊₁ = aₖ * 2

aₖ₊₁ = (3 * 2^(k-1)) * 2

aₖ₊₁ = 3 * 2^k

This matches the closed-form solution when n = k + 1. Therefore, if the closed-form solution holds true for aₖ, it also holds true for aₖ₊₁.

We can conclude that the closed-form solution, a = 3 * 2(n-1), is proven by induction for the given geometric sequence since the base case holds true and the inductive step has been shown.

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Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

Answer:

96 baceballs

Step-by-step explanation:

Hope this helps!

Answer:

graph A

Step-by-step explanation:

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Here we go ~

\(\qquad \tt \dashrightarrow \: \sin(x) = 0.6\)

\(\qquad \tt \dashrightarrow \: \sin(x) = \dfrac{6}{10} \)

\(\qquad \tt \dashrightarrow \: \sin(x) = \dfrac{3}{5} \)

\(\qquad \tt \dashrightarrow \:x = \sin {}^{ - 1} ( \dfrac{3}{5} ) \)

\(\qquad \tt \dashrightarrow \:x = 37 \degree\)

Now, since we have to find the value of x in quadrant 2, we have to subtract the given value from 180°

that is :

\(\qquad \tt \dashrightarrow \:x = 180 - 37\)

\(\qquad \tt \dashrightarrow \:x = 143 \degree\)