Solve fraction 2/3x -1/2=1/6x-1/9

Answer:

\(x^2-10x+18=0\)

a = -10 and b = 18.

Step-by-step explanation:

Let w represent the width of the rectangle.

We are given that the perimeter of the rectangle is 20 cm, this means that:

\(20=2(x + w)\)

Let's put w in terms of x. Divide both sides by two:

\(10=x+w\)

And solve for w:

\(w=10-x\)

So, the rectangle measures x by (10 - x) cm.

According to the Pythagorean Theorem:

\(a^2+b^2=c^2\)

a and b are the legs and c is the hypotenuse.

Substitute x for a, w for b, and 8 for c:

\(x^2+w^2=8^2\)

Simplify and substitute:

\(x^2+(10-x)^2=64\)

Square:

\(x^2+(100-20x+x^2)=64\)

Isolate the equation. So:

\(2x^2-20x+36=0\)

Since the leading coefficient is one, divide both sides by two:

\(x^2-10x+18=0\)

Therefore, a = -10 and b = 18.

Answer:

0.6 servings

Step-by-step explanation:

division. divide 3/5.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

10=j

Step-by-step explanation:

i did the math and typed it in and clicked the "add answer" button

The solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

Linear inequalities are inequalities that have constant average rates of change, slope or gradient

A system of linear inequalities is a collection of at least two linear inequalities.

In this case, the system of linear inequalities is given as

7x+2y > 3

x-2y < 2

Rewrite the inequalities as equations

7x+2y = 3

x-2y = 2

Make x the subject in the second equation, by adding 2y to both sides of the equation

x - 2y +2y = 2 + 2y

This gives

x = 2 + 2y

Substitute x = 2 + 2y in 7x+2y = 3

7(2 + 2y) +2y = 3

Expand the brackets

14 + 14y + 2y = 3

Evaluate the like terms

16y = -11

Divide both sides by 16

y = -11/16

Substitute y = -11/16 in x = 2 + 2y

x = 2 - 2 * 11/16

Evaluate the product

x = 2 - 11/8

Evaluate the difference

x = 5/8

Hence, the solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

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Answer:

(C) 1/4 of the pie.

Step-by-step explanation:

Given that Fernando had 3/8 of a pumpkin pie left.

So, the remaining pie= 3/8 of a pie.

As Fernando ate 2/3 of the remaining pie, so,

the portion of a pie that Fernando ate = 2/3 x 3/8 of a pie = 1/4 of a pie.

So, Fernando ate 1/4 of a pie.

Hence, option (C) is correct.

To determine if triangle XYZ and triangle X'Y'Z' are the same shape and size, we need to compare their corresponding angles and side lengths.

Angle Comparison: Check if the corresponding angles in both triangles are equal. If all three angles of triangle XYZ are congruent to the corresponding angles of triangle X'Y'Z', then they have the same shape. However, this does not guarantee they have the same size.

Side Length Comparison: Compare the lengths of the corresponding sides. If all three sides of triangle XYZ are equal in length to the corresponding sides of triangle X'Y'Z', then they have the same size.

If both the angles and side lengths are equal for the corresponding parts of the triangles, then triangle XYZ and triangle X'Y'Z' are congruent, meaning they are the same shape and size.

It's important to note that without specific measurements or additional information about the triangles, it is not possible to definitively determine if they are the same shape and size.

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The expected value of the absolute value of the difference of two distinct integers chosen at random from the first six positive integers is 35/12.

To find the expected value, we need to consider all possible pairs of distinct integers and their corresponding absolute differences. There are a total of 15 pairs, and we can list them as (1,2), (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,4), (3,5), (3,6), (4,5), (4,6), and (5,6).

The absolute differences of these pairs are 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, and 1, respectively. The expected value is the sum of the products of each absolute difference and its corresponding probability, which is 1/15 for each pair, giving us:

(1/15) × (1+2+3+4+5+1+2+3+4+1+2+3+1+2+1) = 35/12.

Therefore, the expected value of the absolute value of the difference of these two numbers is 35/12.

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The best interest rate which banks can charge a customer is the prime rate.

Reasons:

The Annual Percentage Rate, APR = Prime + 5%

∴ APR = 10% + 5% = 15%

\(\displaystyle The \ periodic \ rate = \frac{15}{12} = 1.25 \%\)

The balance on June 1 = $2,550

Daily balance, June 1 — 3 = $2,550 × 3 = $7,650

June 4 borrowed $5,300

The new unpaid balance = $2,550 + $5,300 = $7,850

Daily balance from June 5 — 8 = $7,850 × 3 = $23,550

Chris made payment on June 9

Unpaid balance = $7,850 - $800 = $7,050

Daily balance from June 9 — 16= $7,050 × 8 = $56,400

June 17 borrowed $5,600

Unpaid balance = $7,050 + $5,600 = $12,650

Daily balance June 17 — 30 = $12,650 × 14 = $177,100

Sum of daily balance = 7,650 + 23,550 + 56,400 + 117,100 = 204,700

\(\displaystyle Average \ daily \ balance = \frac{204,700}{30} = 6,823.\overline 3\)

Finance charge = Average daily balance × Periodic rate

∴ Finance charge = $6,823.\(\overline 3\) × 0.0125 = $85.291\(\overline 6\)

New balance = Cash advance + Credits and payment + Previous balance + Finance charge

New balance = $2,550 + $5,300 - $800 + $5,600 + $85.291\(\overline 6\)

= $12,735.291\(\overline 6\)

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Answer:

\( {\boxed{x = \frac{1}{81} }}\)

Step-by-step explanation:

\( \\3x = \frac{1}{27} \)

\( \\ \longmapsto \: x = \frac{1}{27 \times 3} \)

\( \\ \longmapsto \: x = \frac{1}{81} \)

If the outdoor temperature were recorded every hour for 4 consecutive hours, the ordered pairs for each point would be different. Currently, the given ordered pairs represent the outdoor temperature recorded at every 2-hour interval.

However, if the temperature were recorded every hour, there would be a total of 4 temperature readings, each separated by an hour. This means that the ordered pairs would include an additional set of numbers, representing the additional temperature readings. For instance, the first ordered pair (1,61) indicates that the outdoor temperature was 61 degrees Fahrenheit at hour 1. If the temperature were recorded every hour for 4 consecutive hours, the ordered pairs would be (1,61), (2,?), (3,65), (4,?), (5,71), (6,?), (7,75), (8,?), (9-77). In this case, the temperature readings at hours 2, 4, 6, and 8 are unknown and would need to be recorded in order to generate the corresponding ordered pairs.
The difference in the ordered pairs would also reflect the changes in temperature over shorter intervals of time. By recording the temperature every hour, we would be able to track any fluctuations in temperature that might occur within the 2-hour interval between the given ordered pairs. For example, if the temperature rose from 61 to 64 degrees Fahrenheit within the first hour, the second ordered pair would be (2,64) instead of (3,65).

In conclusion, the ordered pairs would be different if the outdoor temperature were recorded every hour for 4 consecutive hours, as it would include additional temperature readings and reflect changes in temperature over shorter intervals of time.

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Answer:

Midpoint (-1,7)

Step-by-step explanation:

To find a midpoint, average the x's and then average the y's (add and divide by 2)

The x-coordinate of the midpoint is: (-4+2)/2

= -2/2

= -1

and the y-coordinate is:

(4+10)/2

= 14/2

= 7

So the midpoint is:

(-1,7)

Answer:

(-1, 7)

Step-by-step explanation:

Midpoint of a line segment

\(\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}\)

\(\textsf{let}\:(x_1,y_1)=(-4,4)\)

\(\textsf{let}\:(x_2,y_2)=(2,10)\)

\(\implies \textsf{Midpoint}=\left(\dfrac{2+(-4)}{2},\dfrac{10+4}{2}\right)=(-1,7)\)

Assuming that there are 365 possible birthdays (excluding leap years), the probability that no 2 people have the same birthday can be calculated as follows:

The first person can have any birthday, so the probability is 1.

The second person must have a different birthday than the first person. The probability of this is 364/365, since there are 364 possible birthdays that the second person could have, out of 365 total possible birthdays.

The third person must have a different birthday than the first two people. The probability of this is 363/365, since there are 363 possible birthdays that the third person could have, out of 365 total possible birthdays.

Continuing this process, the probability that the 25th person has a different birthday than the first 24 people is:

(365/365) * (364/365) * (363/365) * ... * (342/365)

Multiplying these probabilities together, we get:

(365/365) * (364/365) * (363/365) * ... * (342/365) ≈ 0.4313

Therefore, the probability that no 2 people have the same birthday among a group of 25 people is approximately 0.4313, or 43.13%.

Answer:

y = x²

Step-by-step explanation:

(Hint: Try typing y = x²)

Answer:

Blank 1: (-7,0)

Blank 2: (-1,0)

Step-by-step explanation:

Plug x=0 into the equation and solve the resulting equation y=7 for y

Plug y=0 into the equation and solve the resulting equation 0=(x+1)(x+7) for x

f-1(x) = 4x/(3 - x). The inverse function is denoted as f-1(x) and is obtained by interchanging x and y in the original function and solving for y.

The given function is f(x) = 3x/(x + 4). To find f-1(x), we need to determine the inverse of f (x).

To find f-1(x), we start by writing the equation y = 3x/(x + 4) and then solve for x in terms of y. This involves first multiplying both sides by (x + 4) to get rid of the denominator, which gives us:

y (x + 4) = 3x

Expanding the left-hand side, we get:

xy + 4y = 3x

Grouping the terms with x on one side and the rest on the other side, we get:

3x - xy = 4y

Factorizing x on the left-hand side, we get:

x (3 - y) = 4y

Dividing both sides by (3 - y), we get:

x = 4y/ (3 - y)

Therefore, the inverse function of f(x) = 3x/ (x + 4) is given by:

f-1(x) = 4x/(3 - x)

In summary, to find f-1(x) for the given function f(x), we first write the equation y = 3x/ (x + 4), solve for x in terms of y, and then interchange x and y to get f-1(x) = 4x/(3 - x).

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Answer:

19

Step-by-step explanation:

Plug in

Here, we are required to determine the point where point H lie on the number line.

The point H is at point 2.5 on the number line.

The distance between point F and G on the number line is:

4 - (-2) = 6 numbers on the number line.

And since the ratio of FH to HG is 3:9

Therefore; FH/HG = (4 - x)/(x - (-2))

i.e 3/9 = (4 - x)/ (x +2).

By cross multiplication, 3x + 6 = 36 - 9x.

Therefore, 12x = 30

and, x = 2.5

Therefore, the point H is at point 2.5 on the number line.

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Answer:

2.5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

PEMDAS means always do parenthesis first, which means subtract 10-6=4

Answer:

Remember PEMDAS!!!! The answer is the first box (20x3+4/8) I strongly suggest you read below because PEMDAS is a basic skill used throughout life.

Step-by-step explanation:

Parentheses

Exponents

Multiplication (left to right)

Division (left to right)

Addition (left to right)

Subtraction (left to right)

search it up and look for a mathisfun article for more info.

There are eight possible states, and the transition probabilities can be estimated based on historical data or observations.

To analyze the given weather system using a Markov chain, we need to identify the different possible states that the system can be in.

In this case, the states would correspond to the different combinations of weather conditions over the last three days. There are eight possible states, as each day can either be rainy or not rainy, resulting in 2^3 = 8 possible combinations.

Next, we would need to determine the probability of transitioning from one state to another. For example, if it rained for the past three days, the probability of it raining again tomorrow might be high,

while if it was sunny for the past three days, the probability of rain might be low. These transition probabilities can be estimated based on historical weather data or by observing the system for a period of time.

Once we have determined the transition probabilities, we can create a transition matrix that describes the probabilities of moving from each state to every other state. This matrix can then be used to calculate the long-term probabilities of being in each state, and to make predictions about the likelihood of rain in the future.

In summary, to analyze the given weather system using a Markov chain, we need to identify the possible states based on the weather conditions over the last three days,

determine the transition probabilities between states, create a transition matrix, and use it to calculate long-term probabilities and make predictions.

In this case, there are eight possible states, and the transition probabilities can be estimated based on historical data or observations.

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Answer:

I would assume you're referring to this test? if so the answer is

a, d and e

The expression that describes the slope properly are:

A. m = \(\frac{y_2 - y_1}{x_2 - x_1}\)

D. m = rise/run

E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

We have,

The slope of a line is a measure of its steepness or inclination.

It represents the rate of change between two points on the line, specifically the ratio of the vertical change (rise) to the horizontal change (run).

Mathematically, the slope (m) is calculated as:

m = change in vertical distance/change in horizontal distance

or

m = rise/run

or

m = \(\frac{y_2 - y_1}{x_2 - x_1}\)

Thus,

The expression that describes the slope properly are:

A. m = \(\frac{y_2 - y_1}{x_2 - x_1}\)

D. m = rise/run

E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

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When the significant figures are being calculated, the last digit of the result is always uncertain. If there are no remaining digits, it is significant. When multiplication or division is performed, the calculation's outcome is limited to the number of significant figures present in the number with the fewest significant figures.

To know how many significant figures are in the following calculation, (2.461 × 4.215) - 5.122, we need to follow the following steps;2.461 × 4.215 = 10.386915 (multiply first)10.386915 - 5.122 = 5.264915 (subtract next)To determine the final number of significant figures in the result, use the number with the least significant figures. So, 5.122 has the least number of significant figures, which is four (4), so the result is limited to four (4) significant figures. Therefore, the number of significant figures is four (4).This calculation has three (3) significant figures that are reliable. The trailing zeros to the right of the decimal place do not provide any additional information. So, the answer is:There are four (4) significant figures resulting from the given calculation.

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The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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Answer:

$43.64

Step-by-step explanation:

If the tax rate = 3.9% and the product u are buying is priced at $42

Then, the amount you will pay for the object will be,

$42 + 3.9/100 * 42

=> 42 + 0.039 * 42

=> 42 + 1.638

=> 43.638

43.638 when rounded to the nearest hundredth is,

43.64

Hope it helps :)

The F statistic for this data set is 1.93, with a p-value of 0.098. This means that we cannot reject the null hypothesis that there is no difference between the means of the cities at a significance level of 0.05.

Therefore, we cannot conclude that there is a significant difference in hotel costs per night between the five cities.

To find the value of the test statistic to test for a difference between cities, we need to perform a statistical test such as a one-way ANOVA (analysis of variance) test. This test compares the variation between the means of multiple groups to the variation within each group. The test statistic for a one-way ANOVA is F.

To calculate the F statistic, we need to first find the sum of squares within groups (SSW) and the sum of squares between groups (SSB). SSW measures the variation within each group and SSB measures the variation between groups.

SSW = ∑(xi – xj)² / df_within

where xi is the value of each observation, xj is the mean of each group, and df_within is the degrees of freedom within groups, which is equal to the total number of observations minus the number of groups.

SSB = ∑(xj – xbar)² / df_between

where xbar is the grand mean of all the observations, and df_between is the degrees of freedom between groups, which is equal to the number of groups minus one.

Once we have calculated SSW and SSB, we can calculate the F statistic as:

F = SSB / df_between / (SSW / df_within)

If the F statistic is greater than the critical value from the F distribution table, we can reject the null hypothesis that there is no difference between the means of the groups.

In this case, we have five cities: New York, Los Angeles, Atlanta, Houston, and Phoenix. We can use Excel or another statistical software to calculate the ANOVA test.

The F statistic of 1.93 and the associated p-value of 0.098 indicate that we cannot reject the null hypothesis at a significance level of 0.05. This suggests that there is no significant difference in hotel costs per night among the five cities: New York, Los Angeles, Atlanta, Houston, and Phoenix. The analysis was performed using a one-way ANOVA test, comparing the variation between the means of the cities to the variation within each city.

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Answer:

gifted and talaneted

Step-by-step explanation:

Answer:

r = 86

Step-by-step explanation:

23+71=94

180-94=86

The coordinates of point P which divides the line segment AB in the ratio 1:3 are ( -13.5, 0)

What is section formula for internal division?

If point P (x,y) lies on line segment AB and satisfies AP:PB = m:n, then we say that P divides AB internally in the ratio m:n. The point of division has the coordinates

(x, y) = \((\frac{mx_2 + nx_1}{m+n} }, \frac{my_2 + ny_1}{m+n} )\)

According to the given question:

Coordinates of the line segment AB are A(-18, -2) and B(0, 6).

This line segment is divided into 1:3 ratio by point P

Let coordinates of point P be (x, y)

Using Section Formula

(x, y) = \((\frac{mx_2 + nx_1}{m+n} }, \frac{my_2 + ny_1}{m+n} )\)

Clearly (x₁, y₁) = (-18, -2) and (x₂, y₂) = (0, 6). Also m:n = 1:3

Substituting in the above equation

(x, y) = \((\frac{1.0 + 3.(-18)}{1+3} }, \frac{1.6 + 3.(-2)}{1+3} )\\\)

(x, y) = ( -13.5, 0)

Hence the coordinates of point P which divides the line segment AB in the ratio 1:3 are ( -13.5, 0)

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