Which solution for the value of x is right? 4x - 2 = 3x + 6 or 4x - 2 +3x+6=180

Answer:

y = 3x + 5

Step-by-step explanation:

y = 3x + 5

y = 3x + 9 - 4

y = 3x + 5

If you need more help, comment on my answer. K? feel free to comment. lol.

When a solute does not dissolve in a solvent on further mixing, it is a saturated solution. An alloy is an example of solid/solid solution.

A saturated solution means a solution which has maximum solute concentrate. It cannot dissolve more solute in normal temperature. In such a solution system, if we add further crystals of solid, it will not dissolve. It has attained an equilibrium state. The amount of solute that dissolves will be equal to the amount which precipitates.

An alloy is a mixture of solid with solids. It can be two metals or a metal and  a non-metal. It is a homogenous mixture of solid substances, so it is also called as solid solution. The metal in higher concentration acts as the solvent and the one with lower concentration acts as solute.

So saturated solutions does not dissolve further solute particles. Alloy are solid/solid solutions.

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Answer:

The critical point of the function F(x) = 2x^2 + 4 is x = 0.

Step-by-step explanation:

A. x=0

The critical point of a polynomial function is the value of x at which the function changes from increasing to decreasing or vice versa. To find the critical point of a polynomial function, we need to find the value of x that makes the first derivative of the function equal to zero.

The first derivative of F(x) = 2x^2 + 4 is F'(x) = 4x

Setting F'(x) = 0, we get:

4x = 0

x = 0

Therefore, the critical point of the function F(x) = 2x^2 + 4 is x = 0.

4 cm Equals 1 day on the x axis

2 cm = 5 0 C on the y axis

To determine the temperature on a specific day:

Trace the vertical line parallel to the y axis from the position on the x axis to the point where this vertical line crosses the graph.

Trace a horizontal line parallel to the x axis from that point until it meets the y axis at the desired location.

To locate the day at a specific temperature, trace a horizontal line parallel to the x axis from the temperature point on the y axis to the point where this horizontal line meets the graph.

Now, trace a vertical line parallel to the y axis from that position until it crosses the x axis at the desired location.

Now, a) the forecast and actual temperatures are the same where the graphs of Both intersect on Tuesday, Friday, and Sunday.

b) Repeat step 1 to obtain the temperature for the graph forecast for the days of the week.

Mon 15 0 C Tuesday 20 0 C Wednesday 25 0 C

Thu −22.5 \s0\s C

Friday 15 0 C Saturday 30 0 C

Sun −35 \s0\s C

As a result, the highest expected temperature for the week is 35 0 C.

c) Repeat step 1 to determine the temperature for the real graph based on the days of the week.

Mon−17.5 \s0\s C

Tuesday 20 0 C Wednesday 30 0 C

Thu −15 \s0\s C

Friday 15 0 C Saturday 25 0 C

Sun −35 \s0\s C

So the week's minimum real temperature is 15 0 C.

d) The difference between actual and predicted temperatures for the week

Mon, 17.5−15=2.5 \s0 C

Tue, 20−20=0 \s0\s C

Wed, 30−25=5 \s0\s C

Thu, 15−22.5=−7.5 \s0\s C

Fri, 15−15=0 \s0\s C

Sat, 25−30=−5 \s0\s C

Sun, 35−35=0 \s0\s C

The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday.

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The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday. 4 cm Equals 1 day on the x axis. 2 cm = 5 0 C on the y axis

To determine the temperature on a specific day:

Trace the vertical line parallel to the y axis from the position on the x axis to the point where this vertical line crosses the graph.

Trace a horizontal line parallel to the x axis from that point until it meets the y axis at the desired location.

To locate the day at a specific temperature, trace a horizontal line parallel to the x axis from the temperature point on the y axis to the point where this horizontal line meets the graph.

Now, trace a vertical line parallel to the y axis from that position until it crosses the x axis at the desired location.

Now, a) the forecast and actual temperatures are the same where the graphs of Both intersect on Tuesday, Friday, and Sunday.

b) Repeat step 1 to obtain the temperature for the graph forecast for the days of the week.

Mon 15 0 C Tuesday 20 0 C Wednesday 25 0 C

Thu −22.5

Friday 15 0 C Saturday 30 0 C

Sun −35

As a result, the highest expected temperature for the week is 35 0 C.

c) Repeat step 1 to determine the temperature for the real graph based on the days of the week.

Mon−17.5

Tuesday 20 0 C Wednesday 30 0 C

Thu −15

Friday 15 0 C Saturday 25 0 C

Sun −35

So the week's minimum real temperature is 15 0 C.

d) The difference between actual and predicted temperatures for the week

Mon, 17.5−15=2.5

Tue, 20−20=0

Wed, 30−25=5

Thu, 15−22.5=−7.5

Fri, 15−15=0

Sat, 25−30=−5

Sun, 35−35=0

The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday.

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Answer:

The probability of getting unsatisfactory piston of machine 1 and satisfactory machine of piston 2 is 0.072

Step-by-step explanation:

p(E) = p(unsatisfactory Pistons of machine 1) = 84/700

p(F) = p(Satisfactory Pistons of machine 2) = 414/690

p(E and F) =

p(unsatisfactory piston of machine 1 and satisfactory machine of piston 2)

p(E and F) = p(E) . p(F)

= 84/700 . 414/690

= 0.072

Answer: 8.24%

Step-by-step explanation:

To calculate the annual percentage rate (APR) and the effective annual rate of interest on Aruna's investment, we need to know the following information:

The initial investment amount (Rs 150,000)

The final investment amount (Rs 168,925)

The time period of the investment (18 months)

The frequency of interest payments (every 3 months)

The interest earned on the investment is the difference between the final investment amount and the initial investment amount. In this case, the interest earned is:

Rs 168,925 - Rs 150,000 = Rs 18,925.

Calculate the interest rate per period: To find the interest rate per period, divide the interest earned by the initial investment amount and multiply by the number of periods per year. In this case, the interest rate per period is:

(Rs 18,925 / Rs 150,000) * (4 periods per year) = 0.08%.

Calculate the APR: The APR is the interest rate per period multiplied by the number of periods in the investment. In this case, the APR is:

0.08% * 18 months = 8%.

The effective annual rate of interest takes into account the compounding of interest over time. To calculate the effective annual rate of interest, we use the formula:

(1 + r/n)^n - 1, where r is the interest rate per period and n is the number of compounding periods per year.

In this case, the effective annual rate of interest is:

(1 + 0.08%/4)^4 - 1 = 8.24%.

So the annual percentage rate (APR) is 8% and the effective annual rate of interest is 8.24%

Probability is a measure of how likely something is to occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. For example, if there is a 20% chance of rain, the probability of rain is 0.2. Probability is often used to calculate the likelihood of different outcomes in a situation.

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The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).

In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :

We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)

applying quotient rule,

=> f(x) = ln(1) - ln( gᵏ)

Appling power rule,

=> f(x) = ln(1) - k ln( g)

Applying Zero Exponent Rule,

=> f(x) = 0 - k × ln( g)

Hence, the required expansion is f(x) = - k × ln( g).

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The population density in city B is 6000 people per square mile considering it has 3/5 of the population in city A.

The population density in city A is 6,000.

It is known that city B, is bigger than city 1.2 times bigger than city A, so this means:

1 mile in city A = 1.2 miles in city B

Using this, and knowing that the population in city B is 0.6 times that of the one in city A, let's calculate the density:

0.6 x 6000 / 1.2 = 3,000 people per square mile

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When investing, the principal is the money that is kept in an investment account.

Cash held in an investment account serves as the principal while investing. The amount you really borrow when you take out a loan—before interest is applied—is known as the principle.

Senior employees at venture capital firms, principals are ranked above associates and analysts. They are less senior than partners, but they could be on the partner track. Principals can assist the company in sourcing and carrying out deals, much like an associate.

When you sell an investment, you normally only need to pay taxes if you make a profit. To determine whether you made a profit or loss, you must deduct the cost basis of your investment—typically, the price you paid—from the sale price.

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The principal for amount $2496.76 at 1% compound interest annually for 3 years is $ 2420.03.

When investing, the principal is the money that is kept in an investment account. The principle of a loan is the amount that you actually borrow when you apply for one, before interest is added.

Principals are the most senior personnel in venture capital firms, ahead of associates and analysts. They are not as senior as partners, but they might be moving toward becoming partners. Similar to an associate, principals can help the business find and close deals.

You typically only have to pay taxes on an investment sale if you make a profit. You must subtract the cost basis of your investment, which is often the price you bought, from the sale price to establish if you made a profit or a loss.

Using the formula,

Amount  = P(1 + R/100)ⁿ

Where P = principle amount,

R = rate of interest,

n = time period,

It is given that

Amount = $2496.79

Rate of interest (R ) = 1%

(n) time period = 3,

Putting the above values in the formula,

2496.76 = P (1 + 1/100)³

⇒ 2496.76 = P (101/100)³

⇒ 2496.76 / (101/100)³ = P

⇒ P = 2496.76 / 1.03

⇒ P = $ 2420.03

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Answer:

X + 9

Step-by-step explanation:

sum is addition

Answer: 200 miles

Step-by-step explanation: First divide 150 by 3 = 50, then multiply by 4 = 200 miles.

You can drive 200 miles with one tank of gas.

3/4 of a tank ---> 150 miles

1 full tank ---> x amount of miles

x = (1 full tank * 150 miles) / 3/4 of a tank

x = (1 * 150) / 3/4=  200 miles.

Check the attached image to better understand how a rule of 3 is solved. Beware that this procedure only applied when there is direct proportionality between the variables.

You can drive 200 miles with one tank of gas.

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The cost allocation to each inventory is:

We can use the ratio of warehouse space usage to calculate the cost allocation to each inventory. Let's first calculate the warehouse space usage for each inventory.

Raw materials: 1/3 * 9.6 million square metres = 3.2 million square metres

Work-in-process: 1/6 * 9.6 million square metres = 1.6 million square metres

Finished goods: 3/8 * 9.6 million square metres = 4.8 million square metres

Next, we can calculate the cost allocation for each inventory by dividing the total cost by the corresponding warehouse space usage.

Raw materials: $11.55 million / 3.2 million square metres = $3.6 million/million square metres

Work-in-process: $11.55 million / 1.6 million square metres = $7.2 million/million square metres

Finished goods: $11.55 million / 4.8 million square metres = $2.4 million/million square metres

Finally, we can multiply the cost per million square metres by the warehouse space usage for each inventory to find the total cost allocation.

Raw materials: $3.6 million/million square metres * 3.2 million square metres = $11.52 million

Work-in-process: $7.2 million/million square metres * 1.6 million square metres = $11.52 million

Finished goods: $2.4 million/million square metres * 4.8 million square metres = $11.52 million

So, the cost allocation to each inventory is:

Raw materials: $11.52 million

Work-in-process: $11.52 million

Finished goods: $11.52 million

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The shape of the histogram for the first digit of a randomly chosen legitimate record following Benford's law is a logarithmic curve, with the first digit "1" appearing most frequently, followed by "2," and so on, with the frequency of each digit decreasing as the digit increases.

A tax return is a document filed with a tax authority (such as the IRS) that reports an individual's or a business's taxable income, expenses, and other information for a given tax year. The purpose of a tax return is to determine how much tax an individual or business owes or to claim a refund if they overpaid their taxes during the year.

Benford's law is a mathematical principle that predicts the frequency of occurrence of digits in many real-life sets of data. According to the law, in such datasets, the first digit is likely to be a "1" more often than any other digit, followed by "2", and so on, with "9" being the least likely first digit. The law has been shown to hold true for many types of data, including population sizes, stock prices, and physical constants.

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The probability that all six dice show a one is 1/46656

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

Number of dices = 6

Outcome = all 1

The probability of rolling a one on one die is 1/6.

So the probability of rolling a one on all six dice is:

(1/6) * (1/6) * (1/6) * (1/6) * (1/6) * (1/6) = (1/6)^6

So the probability of all six dice showing a one is 1/46656

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The standard matrix A is [ (1/2, √3/2) (√3/2, -1/2) ]

To find the standard matrix of a linear transformation, we need to find the images of the standard basis vectors under the transformation.

The standard basis vectors in R2 are (1,0) and (0,1). Let's find their images under T.

The image of (1,0) under a 30∘ clockwise rotation is (√3/2, 1/2). The image of this under reflection through the line y=x is (1/2, √3/2).

The image of (0,1) under a 30∘ clockwise rotation is (-1/2, √3/2). The image of this under reflection through the line y=x is (√3/2, -1/2).

The standard matrix of T is then the matrix whose columns are the images of the standard basis vectors:

A = [ (1/2, √3/2) (√3/2, -1/2) ]

= [tex]\left[\begin{array}{cc}1/2&\sqrt{3} /2\\\sqrt{3} /2&-1/2\end{array}\right][/tex]

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The circle's A and C are similar because A can be mapped onto C by a translation of 3 units to the left and 5 units down, followed by a dilation about its center by a scale factor of 2.5. Option D is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Here,

To prove that the two circles are similar, circle A can be mapped onto C by a translation of 3 units to the right and 5 units up, followed by a dilation about its center by a scale factor of 2.5.

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The mean of the sampling distribution is the average value of the mean of a large number of samples of the same size, taken from the same population. The symbol for the mean of the sampling distribution is usually represented by the Greek letter "mu" (μ). It is calculated as the sum of all the sample means divided by the number of samples.

The equation for the mean of the sampling distribution is given as:

μ = (1/n) * Σ x

where:

μ = mean of the sampling distribution

n = number of samples

Σ x = sum of the sample means

x = mean of each individual sample

The mean of the sampling distribution represents the center of the distribution and provides an estimate of the population mean. In this equation, the mean of each individual sample (x) is calculated first, and then those sample means are summed and divided by the number of samples (n) to find the mean of the sampling distribution (μ).

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The wind speed of a hurricane with an air pressure of 937 kPa is 203, hence option C is correct answer.

A straight line is represented using its slope and a point on the line using point slope form. This indicates that the point slope form is used to get the equation of a line whose slope is'm' and which passes through a point. The equation of a straight line can be expressed in several ways. Point slope shape is one of them. The point slope form's equation is as follows: y - y1 = m (x - x1)

From the given graph we can observe that the two coordinates of the wind and pressure are:

(x1, y1) = (934, 206)

(x2, y2) = (922, 218)

The slope of the line is given by:

m = (y2 - y1) / (x2 - x1)

m = (218 - 206) / (922 - 934)

m = - 12/ 12

m = - 1

Using the point-slope form we have:

y - y1 = m (x - x1)

Substituting the values:

y - 206 = -1 (x - 934)

y - 206 = -x + 934

y = -x + 934 + 206

y = -x + 1140

Substitute the value of x = 937kPa:

y = -x + 1140

y = -937 + 1140

y = 203

Hence, the wind speed of a hurricane with an air pressure

of 937 kPa is 203, hence option C is correct answer.

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To solve this problem using polar coordinates, we need to change from rectangular coordinates to polar coordinates, which represent points in the plane as pairs of polar coordinates (r,θ).

Given that Y1 = rcos(θ) and Y2 = rsin(θ), the condition Y1 ≤ Y2 is equivalent to 0 ≤ θ ≤ π/2. Hence, the required probability can be expressed as:

P(Y1 ≤ Y2) = ∫∫_{0<=θ<=π/2, 0<=r<=1} f(r,θ) dr dθ

where f(r,θ) = 1/π, 0 <= r <= 1.

The integration yields P(Y1 ≤ Y2) = 1/2.

Therefore, the probability that Y1 is less than or equal to Y2 for a point chosen randomly inside the unit circle is 1/2.

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Answer:

1) A and B = {1, 3, 5, 7, 9, 0, 2, 4, 6, 8}

2) Yes, A and B are disjoint.

Step-by-step explanation:

The set union of A and B is the set containing all the elements of Set A and Set B. So it would be:

Set A U B = {1, 3, 5, 7, 9, 0, 2, 4, 6, 8}

The set intersection of A and B is the set containing all the elements that are common to both Set A and Set B. So it would be:

Set A ∩ B = {} (empty set)

Yes, A and B are disjoint because they have no elements in common.

Distance is the number of units between two points.

Shakil's  distance was 15 km shorter than Omar's

How to interpret the graphs

Calculate the difference between these distances

d=25km-10km

Evaluate the differences

d=15km

Hence, Shakil's distance was 15 km shorter than Omar's

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Answer:C

Step-by-step explanation:Basically time goes on and it starts off with a less percentage based off the amount of weeks later to add up to the most

Using Compound Interest, The largest balance is $780255, so the option A will give them the largest balance after 5 years.

Even though there are several ways to define an investor, compound interest helps investors. When banks lend money and utilize the income they earn to finance other loans, for instance, they profit from compound interest. When depositors earn interest on their bank accounts, bonds, or other investments, compound interest benefits them.

It's crucial to remember that although while "compound interest" includes the word "interest," the idea extends beyond the contexts in which the expression is typically employed, such as bank accounts and loans.

We will calculate compound interest in every case:

Using formula

[tex]Amount = P(1 + \frac{r}{m})^{t}[/tex]

option A: balance after 5 years:

[tex]5,000 (1+ 2 \frac{1}{4}\%) ^{4\times 5} = $7802.55[/tex]

option B:

balance after 5 years:

[tex]5000 (1+ 3\%)^{3\times 5} = $7789.84[/tex]

option C:

balance after 5 years:

[tex]5,000 (1+ 4\frac{1}{2}\%) ^{3\times 5} = $7764.85[/tex]

The largest balance is $780255, so the option A will give them the largest balance after 5 years.

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Refer to the attached images.

The polygons are classified as;

33. 3 sides

34. 23 sides

A polygon can be defined as a plane figure that is described by a finite number of straight line segments which are all connected to form a closed polygonal chain.

The different types of polygons are;

From the information given,

The polygon has a measure of 180 degrees

The formula for calculating the sum of the angles of a polygon is;

(n-2) 180

(3-2)180

180. It is a triangle

(23--2) 180

21(60)

3960. It has 23 sides

Hence, the values are 3 and 23

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Answer:

To find an ordered pair (x, y) that is a solution to the equation -x + 2y = 7, we can substitute any values of x and y that satisfy the equation. For example, let x = 3, then we can solve for y:

-3 + 2y = 7

2y = 10

y = 5

So (3, 5) is an ordered pair that is a solution to the equation.

If matrix c equals matrix d, then matrix d is [tex]\left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-1&11\end{array}\right][/tex], hence option B is the correct answer.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the sectors of engineering, physics, business, and statistics.

Given the elements of the matrix C.

The matrix c is represented by its rows and columns element, and the arrangements are:

C11 = 3    C12 = 1   C13=-9   C14 = 8

C21 = 2   C22=2   C23 =0   C24 = 5

C31 = 16   C32 = 1  C33=-3   C34=11

Hence, the matrix C is:

[tex]\left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-1&11\end{array}\right][/tex]

From the given option we observe that the matrix d that is similar to matrix c is option B.

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The correct question is:

Answer: 116.7 yards.

Step-by-step explanation: The length of the diagonal of a rectangular soccer field with a length of 100 yards and a width of 60 yards can be found using the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the triangle are 100 yards and 60 yards.

So, the diagonal can be found by:

d = √(100^2 + 60^2)

d = √(10000 + 3600)

d = √(13600)

d = 116.74 yards

Rounding to the nearest tenth, the length of the diagonal is 116.7 yards.

The length of the diagonal of the rectangular soccer field is 116.7 yards.

The line from one corner of a rectangle to the opposite center through the center is called a diagonal.

Here given that,

Length of the  rectangular soccer field, l = 100 yards

Width of the rectangular soccer field, w = 60 yards

To find the length of the diagonal d,

The formula is

d = sqrt(l^{2} + w^{2} )

d = sqrt(100^2 + 60^2)

= sqrt(10,000 + 3600)

=sqrt (13,600)

= 116.61

=116.7 yards

Therefore, the length of the diagonal of a rectangular soccer field = 116.7 yards

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