x÷3 - 9 = 0 what is the value of x

The dimensions that will admit the most light are, the breadth of the rectangular window is  \(2b = \frac{20+10\pi }{4+3\pi }\), the length of the window is \(2l = \frac{40}{4+3\pi }\) and the radius of the semicircular arc is  \(l= \frac{20}{4+3\pi }\).

In the given question,

Let the length and breadth of the rectangular part of the window be 2l and 2b respectively. So the radius of the semicircular arc will be l.

The total perimeter of the window will be 1 length of the rectangle, 2 breadths of the rectangle, and the length of the semicircular arc.

l+2b+πl = 10

(1+π)l+2b = 10

\(b = \frac{1}{2} [10-(1+\pi )l]\)

To admit maximum light through the window implies that the area of the window is maximized.

The area of the window will be:

\(A = (2l)(2b)+\frac{\pi l^{2} }{2}\)

\(= 4lb+\frac{\pi l^{2} }{2} \\= 2l[10-(1+\pi )l] +\frac{1}{2} \pi l^{2}\)

\(= 20l-2l^{2} -2\pi l^{2} +\frac{1}{2} \pi l^{2}\)

\(= 20l-2l^{2} - \frac{3}{2} \pi l^{2}\)

For the area to be maximum,

\(\frac{dA}{dl} =0\\20 -4l -3\pi l = 0\\l= \frac{20}{4+3\pi }\)

\(b = \frac{1}{2} [10-(1+\pi )\frac{20}{4+3\pi }\\b = \frac{10+5\pi }{4+3\pi }\)

Therefore, the breadth of the rectangular window is \(2b = \frac{20+10\pi }{4+3\pi }\), the length of the window is \(2l = \frac{40}{4+3\pi }\) and the radius of the semicircular arc is \(l= \frac{20}{4+3\pi }\).

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The graph of the equation that is parallel to 4x – 3y = –12 is determined as: A. y = 4/3x - 3/2.

If two lines are parallel to each other, their graph will have the same slope value, m. This means if their equations are expressed as y = mx + b in slope-intercept form, they will both have the same value of m.

Given the equation of a graph as 4x - 3y = -12, rewrite it in slope-intercept form to determine the slope value:

4x - 3y = -12

-3y = -4x - 12

-3y/-3 = -4x/-3 - 12/-3

y = 4/3x + 4

This means the slope, m is 4/3. The slope of the graph that is parallel to it will also have a slope of 4/3.

The slope of y = 4/3x - 3/2 is also 4/3, therefore, the answer is: A. y = 4/3x - 3/2.

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Complete Question:

The graph of which of the following will be parallel to the graph of 4x – 3y = –12?

A. y = 4/3x - 3/2

B. 6x - 4y = -8

C. y = 3/4x +1

D. 4x – 2y = –12

Answer:

147 purple jelly beans

Step-by-step explanation:

15% of 980 is 147

The probability of obtaining a value between two points will always be a positive value between 0 and 1.

If the measurements of a quantity are governed by the Gaussian distribution function (also known as the normal distribution), we can calculate the probability of obtaining a value between two specified points using the cumulative distribution function (CDF) of the normal distribution.

The CDF of the Gaussian distribution represents the probability that a random variable takes on a value less than or equal to a given point. To find the probability of obtaining a value between two points, we can subtract the CDF values corresponding to the lower and upper bounds.

Mathematically, the probability of obtaining a value between a lower bound (let's call it 'a') and an upper bound (let's call it 'b') can be calculated as follow

P(a < x < b) = Φ(b) - Φ(a)

Here, Φ represents the CDF of the Gaussian distribution.

To calculate this probability, we need to know the mean (μ) and standard deviation (σ) of the Gaussian distribution. These parameters define the shape and characteristics of the distribution.

Given the mean (μ) and standard deviation (σ), we can use statistical software, tables, or programming languages to find the values of Φ(b) and Φ(a) and then subtract them to obtain the probability.

It's important to note that the Gaussian distribution is symmetric, and the total area under the curve is equal to 1.

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Answer:

  2b +7

Step-by-step explanation:

We assume you want to simplify this expression. It can be helpful, though is not required, to group like terms near each other.

  = 3b -1b +4 +3

  = b(3 -1) +(4 +3) . . . combine like terms

  = 2b +7

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

On solving the provided question, we can say that  - he need 56  answers he need to get correct if he want a grade of 80 percent on a test with 70 questions

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56

Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.

\(70-56=14\)

So, the maximum number of questions you may omit is 14.

As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.

20% of 70 \(= .20)(70) = 14\)

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Marcie's monthly payment will be $360.88.

To calculate the monthly payment, we can use the formula for the present value of an annuity:

PV = Pmt  [(1 - (1 + r)⁻ⁿ) / r]

where PV is the present value of the loan, Pmt is the monthly payment, r is the monthly interest rate, and n is the number of months.

First, we need to convert the annual interest rate to a monthly rate:

r = 0.0875 / 12 = 0.007292

Next, we need to calculate the total number of payments:

n = 5 x 12 = 60

Now, we can solve for Pmt:

PV = 18000

Pmt = PV x r / (1 - (1 + r)⁻ⁿ)

Pmt = 360.88

Therefore, Marcie's monthly payment will be $360.88.

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This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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Answer:

The height in feet of the pine tree is 36 feet

Step-by-step explanation:

Please see the attachment below for an illustrative diagram.

In the diagram,

/AB/ represents the height of the pine tree

/BD/ represents the length of the shadow cast by the pine tree

/EC/ represents the length of the ruler ( one foot)

/CD/ represents the length of the shadow cast by the one-foot ruler

Consider triangle ADB and triangle EDC

Triangles ADB and EDC are similar triangles.

Hence, we can write that

\(\frac{/AB/}{/EC/} = \frac{/BD/}{/CD/}\)

/AB/ = ??

/EC/ = 1 ft

/BD/ = 24 ft

/CD/ = 8 inches

First we will convert 8 inches to feet

Since, 12 inches = 1 foot

Then, 8 inches = \(x\)

\(x = \frac{8}{12} \\\) ft

\(x = \frac{2}{3}\\\) ft

Hence.

/CD/ = \(\frac{2}{3}\) ft

Now, putting the values into

\(\frac{/AB/}{/EC/} = \frac{/BD/}{/CD/}\)

\(\frac{/AB/}{1} = \frac{/24/}{/\frac{2}{3} /}\)

\(/AB/= \frac{/24/}{/\frac{2}{3} /}\\\)

\(/AB/ = 36\) ft

Hence, the height in feet of the pine tree is 36 feet.

Answer:

3

Step-by-step explanation:

The minimum percentage of commuters in Tulsa within 2 standard deviations of the mean is approximately 95%.  within 1.5 standard deviations of the mean is approximately 68%.the minimum percentage of commuters who have commute times between 3.9 minutes and 39.1 minutes is approximately 100%.

To solve this problem, we'll use the properties of the normal distribution and the empirical rule.

Given:

Mean (μ) = 21.5 minutes

Standard deviation (σ) = 4.4 minutes

a. To find the minimum percentage of commuters in Tulsa with a commute time within 2 standard deviations of the mean, we can use the empirical rule. According to the empirical rule, approximately 95% of the data falls within 2 standard deviations of the mean in a normal distribution.

So, the minimum percentage of commuters in Tulsa within 2 standard deviations of the mean is approximately 95%.

b. To find the minimum percentage of commuters in Tulsa with a commute time within 1.5 standard deviations of the mean, we again use the empirical rule. According to the empirical rule, approximately 68% of the data falls within 1 standard deviation of the mean in a normal distribution.

Since 1 standard deviation is equal to 4.4 minutes, 1.5 standard deviations would be 1.5 * 4.4 = 6.6 minutes.

Therefore, the minimum percentage of commuters in Tulsa within 1.5 standard deviations of the mean is approximately 68%.

The commute times within 1.5 standard deviations of the mean are between μ - 1.5σ and μ + 1.5σ. Plugging in the values, we get:

μ - 1.5σ = 21.5 - 1.5 * 4.4 = 21.5 - 6.6 = 14.9 minutes

μ + 1.5σ = 21.5 + 1.5 * 4.4 = 21.5 + 6.6 = 28.1 minutes

So, the commute times within 1.5 standard deviations of the mean are between 14.9 minutes and 28.1 minutes.

c. To find the minimum percentage of commuters with commute times between 3.9 minutes and 39.1 minutes, we can calculate the z-scores for these values and use the z-table.

The z-score formula is:

z = (x - μ) / σ

For 3.9 minutes:

z1 = (3.9 - 21.5) / 4.4 = -4.0

For 39.1 minutes:

z2 = (39.1 - 21.5) / 4.4 = 3.99 (approximately)

Using the z-table, we can find the area under the curve between these two z-scores. Subtracting the area from 0.5 (to account for both tails), we can find the minimum percentage.

Looking up z1 = -4.0, we find that the area to the left is practically 0, so we'll approximate it as 0.

Looking up z2 = 3.99, we find that the area to the left is practically 1, so we'll approximate it as 1.

The area between -4.0 and 3.99 is essentially 1 - 0 = 1.

Therefore, the minimum percentage of commuters who have commute times between 3.9 minutes and 39.1 minutes is approximately 100%.

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Answer:

x=-7

Step-by-step explanation:

5x-2x+1=3x-6-x first combine like terms

3x+1=2x-6     combine like terms by subtracting 2x from both sides

x+1=-6           subtract 1 from both sides

x=-7

Answer: $66

Step-by-step explanation:

Given

The original price of shoes is \(\$120\)

Also, there is a discount of \(45\%\)

Price after discount is

\(\Rightarrow P=120-120\times 0.45\\\Rightarrow P=120(0.55)=\$66\)

Thus, Travis paid $66 after discount

2b

Step-by-step explanation:

-2bc-3c² -2ac+a+a²b+2ab²+2+b³

Answer:

the number of parts is going to be

= 15 parts

Step-by-step explanation:

A basketball pitch can be divided into twelve(12) parts , each part of equal length of twenty five (25) centimeters.

The initial and total length of the basketball pitch = 12*25

The initial and total length of the basketball pitch = 12*25

The initial and total length of the basketball pitch = 300 cm

So if it's now divided into parts of each 20 cm ,

the number of parts is going to be

= 300/20

the number of parts is going to be

= 15 parts

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

add the exponents

(7+(-6)

=7-6

=1

and let the same base =4^1 =4

The number line shows the value of 5 - (-8) = 13.

Addition:

Subtraction:

Here the given operation is subtraction. Where a subtrahend is a negative number i.e., -8.

Step1: Start from '5' on the number line.

Step2: Since the subtrahend is a negative number, move to the right side on the number line from '5'.

Step3: Thus, the number obtained on the line is 13.

Step4: Algebraically the result is 5 - (-8) = 5 + 8 = 13.

The number line for this operation is shown below.

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Step-by-step explanation:

in a triangle, if the hipotenus is 17, the other edges' lenghts are multiples of 8 and 15.

so the Man walked 23km.

subtract 7km

16km left

so he goes 8km north and 15km east

Answer:

138

Step-by-step explanation:

You take the measure from <1 and subtract it from 160 and that give you <2.<2 and <6 are corresponding angles so they have to have the same measure.

The required measure of angle ∠6 is 138°.

Given that,
x∥y and m∠1 = 42°. what is m∠6 is to be determined.

The angle can be defined as one line inclined over another line.

In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.

Here,
Since line x and y is parallel,
∠1 = ∠5
Now,
∠6 + ∠5 = 180
∠6 + ∠1 = 180
∠6 + 42 = 180
∠6 = 180 - 42
∠6 = 138°

Thus, the required measure of angle ∠6 is 138°.

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Answer:

i think its possibly 4

Step-by-step explanation:

Answer:

I think the answer would be 4

The inequality to determine how much more money he needs to save so he can buy the shoes is x ≥ $45

Let x be the amount of money Jordan still needs to save to buy the shoes.

The total cost of the shoes is $75, and Jordan has already saved $30. Therefore, the amount of money he still needs to save is:

x = $75 - $30

Simplifying the right side:

x = $45

So, the inequality that represents how much more money Jordan needs to save is:

x ≥ $45

This means that Jordan needs to save at least $45 more to be able to buy the shoes.

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Answer:

Step-by-step explanation:

\(\dfrac{x^2-8x+12}{x^2-7x+10}\\\\x^2-7x+10\ne0\ \iff\ x=\frac{7\pm\sqrt{49-40}}{2}\ne0\ \iff\ x\ne5\ \wedge\ x\ne2\\\\\\\dfrac{x^2-8x+12}{x^2-7x+10}=\dfrac{x^2-2x-6x+12}{x^2-2x-5x+10}=\dfrac{x(x-2)-6(x-2)}{x(x-2)-5(x-2)}=\\\\\\ =\dfrac{(x-2)(x-6)}{(x-2)(x-5)}=\dfrac{x-6}{x-5}\\\\\\f(x)=x-6\\\\g(x)=x-5\)

In regression analysis, the variable that is used to explain the change in the outcome of an experiment, or some natural process, is called independent variable

It is a branch of mathematics that deals with the occurrence of a random event.

The variable that is used to explain the change in the outcome of an experiment or some natural process in regression analysis is called the independent variable or predictor variable.

This variable is used to predict or explain the values of the dependent variable, which is the outcome variable being studied.

In other words, the independent variable is the variable that is manipulated or controlled by the experimenter or researcher, and its effect on the dependent variable is measured.

Hence, in regression analysis, the variable that is used to explain the change in the outcome of an experiment, or some natural process, is called independent variable

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The solution is, Dependent variable.

A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables.

The outcome variable (usually Y) in a regression analysis is called the

c) dependent variable

as, we know,

If there are two variables and there is a linear correlation between them we try to find the regression line by using least squares method.

X the variable which is input or which is first found out is called independent variable.

The outcome variable is the dependent variable

Dummy variable is one which takes only values 0 or 1 depending on whether not present or present.

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Answer:

2π(1.4)2 + 2.8π(3.7)

Step-by-step explanation:

A cylinder's surface is a rectangle and 2 circles

the circumference is 2.8pi, which is also the side length of the rectangle, so the surface area of the rectangle is 2.8pi*3.7

The area of the circle is simply pi*(1.4)^2, and there are 2 circles.

So the answer is 2π(1.4)2 + 2.8π(3.7)

The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office

Given data

Zarah's office is 2 cm wide and 4 cm long

Another office is 8 cm long and 4 cm wide

Area of an office = length * width = long * wide

Area of Zarah's office = 4 cm * 2 cm = 8 cm2

Area of another office = 8 cm * 4 cm = 32 cm2

comparing the two areas

say by how much is 32 cm2 greater than 8 cm2

32 cm2 / 8 cm2 = 4

The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office.

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Answer:

4.5

Step-by-step explanation:

find the difference,square them,add and find the square root

-1-1=-2

4-(-1)=4

2^2+4^2=4+16

=20

square root of 20=4.5(2dp)

All the real numbers x which satisfy the given inequality x²<4 , in  interval form is (-2, 2).

As given in the question,

Given inequality is given by :

x²< 4

Simplify the given inequality  x² < 4 to get all the real numbers x we have,

x² < 4

⇒ x² - 4 < 0

⇒ x² - 2² < 0

Apply a² - b² = ( a - b ) ( a + b ) we get,

⇒ ( x - 2 ) ( x + 2 ) < 0

⇒ x ∈ ( -2 , 2 ) as less than symbol represent open interval.

Therefore, all the real numbers x which satisfy the given inequality x²<4 , in  interval form is (-2, 2).

The complete question is :

Find all real numbers x such that x^2 < 4. Give your answer in interval notation.

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