Combining like terms: 5x^2−8x+10x^2−2x

By solving a percentage equation, we will see that the initial amount is $142.70

If we have an amount A, and we reduce it by X (where X is a percentage) then the new value is:

V = A*(1 - X/100%)

In this case, we know that the percentage reduced is 19.4%, and the new value is $115, replacing these values we will get:

$115 = A*(1 - 19.4%/100%)

Now we can solve that equation for A.

$115 = A*(1 - 19.4%/100%)

$115 = A*(0.806)

$115/(0.806) = A

$142.70 = A

The original value was $142.70

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The 99.7% confidence interval for the true proportion of teachers who provide extra credit is 0.21 to 0.33.

Number is a mathematical concept used to quantify a particular quantity or amount, or to name a specific object or entity. It is used in a variety of ways such as counting, measuring, comparing, estimating, and expressing mathematical relationships. Numbers are used for counting, measuring, and many other operations. Numbers can be expressed in numeric form, such as 1, 2, 3; in algebraic form, such as x^2-3x+2; or in symbolic form, such as √2. Numbers can also be used to represent functions or variables.

A 99.7% confidence interval for the true proportion of teachers who provide extra credit can be calculated as:

p′ ± 3σp′ = 0.27 ± (3 × 0.03) = 0.21 to 0.33

This confidence interval indicates that the true proportion of teachers who provide extra credit is between 0.21 and 0.33 with a 99.7% confidence level. That is, there is a 99.7% probability that the true proportion of teachers who provide extra credit is between 0.21 and 0.33.

The confidence interval for the true proportion of teachers who provide extra credit is determined by calculating the sample proportion (p′), sampling standard deviation (σp′), and the critical value of the normal distribution (Zc), which is the number of standard deviations from the mean that the sample proportion is likely to be. In this case, the critical value of the normal distribution is 3, because a 99.7% confidence level corresponds to a Z-score of 3. The confidence interval is calculated by adding and subtracting the critical value multiplied by the standard deviation from the sample proportion.

This confidence interval is an estimate of the true proportion of teachers who provide extra credit, and it can be used to make decisions or predictions about the population proportion. For example, a school administrator may use the confidence interval to determine the likely proportion of teachers who provide extra credit and make decisions about how to allocate resources.

In conclusion, the 99.7% confidence interval for the true proportion of teachers who provide extra credit is 0.21 to 0.33. This confidence interval is an estimate of the true proportion of teachers who provide extra credit, and it can be used to make decisions or predictions about the population proportion.

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The 99.7% confidence interval for the true proportion of teachers who provide extra credit is 0.21 to 0.33.

What is number?

Number is a mathematical concept used to quantify a particular quantity or amount, or to name a specific object or entity. It is used in a variety of ways such as counting, measuring. comparing, estimating, and expressing mathematical relationships. Numbers are used for counting, measuring, and many other operations. Numbers can be expressed in numeric form, such as 1, 2, 3; in algebraic form, such as x^2-3x+2; or in symbolic form, such as √2. Numbers can also be used to represent functions or variables.

A 99.7% confidence interval for the true proportion of teachers who provide extra credit can be calculated as:

p' ± 3op' = 0.27 ±(3 x 0.03) 0.21 to 0.33

This confidence interval indicates that the true proportion of teachers who provide extra credit is between 0.21 and 0.33 with a 99.7% confidence level. That is, there is a 99.7% probability that the true proportion of teachers who provide extra credit is between 0.21 and 0.33.

The confidence interval for the true proportion of teachers who provide extra credit is determined by calculating the sample proportion (p'), sampling standard deviation (op'), and the critical value of the normal distribution (Zc), which is the number of standard deviations from the mean that the sample proportion is likely to be. In this case, the critical value of the normal distribution is 3, because a 99.7% confidence level corresponds to a Z-score of 3. The confidence interval is calculated by adding and subtracting the critical value multiplied by the standard deviation from. the sample proportion.

This confidence interval is an estimate of the true proportion of teachers who provide extra credit, and it can be used to make decisions or predictions about the population proportion. For example, a school administrator may use the confidence interval to determine the likely proportion of teachers who provide extra credit and make decisions about how to allocate resources.

In conclusion, the 99.7% confidence interval for the true proportion of teachers who provide extra credit is 0.21 to 0.33. This confidence interval is an estimate of the true proportion of teachers who provide extra credit, and it can be used to make decisions or predictions about the population proportion.

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The perimeter of triangle ABC is approximately 50.9 units.

The perimeter of a triangle is the total distance around the outside of the triangle. It is defined as the sum of the lengths of all three sides of the triangle.

To find the perimeter of triangle ABC, we need to know the lengths of all three sides. We are given the measure of angle C (40 degrees), the length of side AC (13 units), and the measure of angle B (49 degrees).

To find the length of side BC, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides, and A, B, and C are the measures of the opposite angles.

Using this formula, we can write:

13/sin(40) = BC/sin(91)

Solving for BC, we get:

BC = (13 * sin(91)) / sin(40)

BC ≈ 21.12

To find the length of side AB, we can use the fact that the sum of the angles in a triangle is 180 degrees. We know the measures of angles B and C, so we can find the measure of angle A as follows:

A = 180 - B - C

A = 180 - 49 - 40

A = 91 degrees

Now we can use the law of sines again to find the length of side AB:

AB/sin(49) = 13/sin(91)

Solving for AB, we get:

AB = (13 * sin(49)) / sin(91)

AB ≈ 16.78

Finally, we can add up the lengths of all three sides to find the perimeter:

Perimeter = AB + AC + BC

Perimeter = 16.78 + 13 + 21.12

Perimeter ≈ 50.9 units

Therefore, the perimeter of triangle ABC is approximately 50.9 units.

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The correct option regarding the mean of X + Y is given as follows:

a. MX+MY.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

Hence, when two variables are added, we can add their means, as we add all the observations and divide by the number of observations, considering the two variables.

This means that the correct option is given by option A.

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Answer: 18:4

Step-by-step explanation:

Ez

Answer:

9 : 2

Step-by-step explanation:

length : Width = 18 : 4

                       \(\sf = \dfrac{18 \ \div \ 2}{4 \ \div \ 2}\\\\=\dfrac{9}{2}\)

                       = 9 : 2

Answer:

It took 16 days

Step-by-step explanation:

400/25=16

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Given:

The table showing data of Depth and Age.

Required:

To plot a graph using data given in the table.

Answer:

We will draw a graph with Depth on x-axis and Age on Y-axis.

The graph is shown in the image attached below:

Final Answer:

The graph using data given in the table is plotted and shown in the image attached.

Figure J is rotated 90° clockwise and then translated by 3 units toward the right.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

Figure J is rotated 90° clockwise and then translated by 3 units toward the right.

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Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

\(x + y = 5800\)

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

\(0.03x + 0.08y = 229\)

We now have two equations with two unknowns:

\(x + y = 5800\)

\(0.03x + 0.08y = 229\)

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

\(x = 5800 - y\)

Substitute this expression for x into the second equation and solve for y:

\(0.03(5800 - y) + 0.08y = 229\)

\(174 - 0.03y + 0.08y = 229\)

\(0.05y = 55\)

\(y = 1100\)

Now substitute this value of y into either equation to solve for x:

\(x + 1100 = 5800\)

\(x = 4700\)

Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.

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Hence, one serving weighs 3/5 kg

The total number of beads in the necklace is 40 beads.

Number of white beads:

2/5 of the beads are white.

Therefore, the number of white beads is:

Number of red beads:

The number of red beads is:

Ratio of red beads to white beads:

The ratio is given to be:

We can divide through by 8 to get the simplified form, such that:

The ratio is 3 : 2.

Answer: $536.40

Step-by-step explanation:

8.94 * 2 = 17.88

8.94(40) + 17.88(10)

357.60 + 178.80 = $536.40

To calculate the percentage,

75/250×100 = 30%

Answer:

30%

Step-by-step explanation:

75/250=0.3

0.3= 3/10

3/10=30%

1. The value of 312.6525° in 39°39'9" degrees-minutes-seconds is

2. The value

114°9'56" to degree 114.1656°

Degree is a unit of measurement for angles. and we can convert degrees to minutes and seconds

1° = 60'

1' = 60''

Therefore

1° = 3600"

1. Converting 312.6525° to degrees-minutes-seconds

= 312°

0.6525° = 0.6525 × 60 = 39.15'

0.15' = 0.15 × 60 = 9''

Therefore ;

312.6525° = 39°39'9"

2. converting

114°9'56" to degree

= 114° + (9/60)°+ 56/3600

= 114 + 0.15 + 0.0156

= 114.1656°

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Answer:

It's 3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

__________________________________________________________

According to Desmos,

\(\frac{45}{15}\) = \(3\)

Here's why.

__________________________________________________________

If you simplify the fraction, this happens.

\(\frac{45}{5}\) = \(9\)

\(\frac{15}{5}\) = \(3\)

__________________________________________________________

9 over 3 is equivalent to 9 divided by 3, or  \(\frac{9}{3}\).

__________________________________________________________

And \(9\div3\) = \(?\)

__________________________________________________________

__________________________________________________________

Hope this helps! <3

__________________________________________________________

Explanation

We are given the following:

We are required to determine the missing value μ.

This is achieved thus:

We know that the formula for z-score is given as:

Therefore, we have:

Hence, the answer is:

The rest wavelength of the emission line observed at 2148 nanometers in the galaxy 100 million light-years away is approximately 2103 nanometers.

The rest wavelength of an emission line can be determined by applying the concept of redshift, which is a phenomenon observed in astrophysics where light from distant objects is shifted towards longer wavelengths due to the expansion of the universe.

In this case, the emission line is observed at 2148 nanometers (or 2.148 micrometers) in a galaxy located 100 million light-years away. To calculate the rest wavelength, we need to consider the redshift factor. Redshift, denoted by z, is defined as the observed wavelength divided by the rest wavelength minus 1.

Given that the observed wavelength is 2.148 micrometers and the galaxy is located 100 million light-years away, we need to convert the distance into a redshift factor using the cosmological relationship between redshift and distance. Assuming a standard cosmological model, we can use the Hubble constant to estimate the redshift.

The Hubble constant represents the rate at which the universe is expanding. Taking a typical value of the Hubble constant as 70 kilometers per second per megaparsec, we find that the redshift factor, z, is approximately 0.021.

To determine the rest wavelength, we rearrange the redshift equation as \((observed wavelength) = (1 + z) \times (rest wavelength)\). Substituting the values, we get \((2.148 micrometers) = (1 + 0.021) \times (rest wavelength).\)

Simplifying the equation, we find the rest wavelength to be approximately 2.103 micrometers or 2103 nanometers.

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Answer:

Step-by-step explanation:

Step 1: Simplify

\(800m/12h = 66\frac{2}{3}m/h\) (66 2/3 miles per hour)

Step 2: Transform hours into minutes by dividing by 60

\(66\frac{2}{3}m/h / 60\\\)

\(1\frac{1}{9} m/m\) (1 1/9 miles per minute)

Step 3: Transform miles into feet by multiplying by 5280

\(1\frac{1}{9}*5280\)

\(5866\frac{2}{3}f/m\\\\\)

or  \(5866.667f/m\) (feet per minute)

Answer:

60mp/h hope this helped! ;D

Step-by-step explanation:

(Sorry my finger hurts)

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Answer:

(a) At 8,000 ft :

The air  temperature is 30.52  °F

The air pressure is 1574 lbs/ft²

The air density is 1.869 x 10⁻³ slug/ft³

(b)  At 18,000 ft :

The air temperature is -5.08  °F

The air pressure is 1059.2 lbs/ft²

The air density is 1.356 x 10⁻³ slug/ft³

Step-by-step explanation:

Given;

pressure at sea level, P₀ = 14.8 PSI

temperature, T' = 80 °F

At 8,000 ft (m) altitude

for altitude h, less than 36,152 ft, the following model is used to modify temperature and pressure;

T = 59 - 0.00356h

T = 59 - 0.00356(8,000)

T = 30.52  °F

The pressure is calculated as;

\(P = 2116[\frac{T+459.7}{518.6} ]^{5.256}\\\\P = 2116[\frac{30.52+459.7}{518.6} ]^{5.256}\\\\P = 1574.2 \ lbs/ft^2\)

The density is given by;

\(\rho = \frac{P}{1718*(T+459.7)}\\\\\rho = \frac{1574.2}{1718*(30.52+459.7)}\\\\\rho = 1.869*10^{-3} \ slug/ft^3\)

For 18,000 ft

T = 59 - 0.00356h

T = 59 - 0.00356(18,000)

T = -5.08 °F

The pressure is calculated as;

\(P = 2116[\frac{T+459.7}{518.6} ]^{5.256}\\\\P = 2116[\frac{-5.08+459.7}{518.6} ]^{5.256}\\\\P = 1059.2 \ lbs/ft^2\)

The density is given by;

\(\rho = \frac{P}{1718(T+459.7)} \\\\\rho = \frac{1059.2}{1718(-5.08+459.7)}\\\\ \rho = 1.356*10^{-3} \ slug/ft^3\)

The equation of the line containing coordinates (5, 3) that is perpendicular to the line y + 11 = 1/2(4x + 6) is y = (-1/2)x - 1/2.

What are coordinates of a line segment?

A line segment is a part of a line that is joined by two different endpoints. Each endpoint has its own coordinates, which are usually represented as an ordered pair (x,y).

For example, if one endpoint of a line segment has the coordinates (1,2) and the other endpoint has the coordinates (5,6), we can represent the line segment as the pair of points: {(1,2), (5,6)}.

Now,

To find the equation of a line that is perpendicular to the given line, we first need to find the slope of the given line.

Starting with the equation given:

y + 11 = 1/2 (4x + 6)

We can simplify it to slope-intercept form:

y = 2x - 5

So the slope of the given line is 2.

Since the line we want is perpendicular to the given line, its slope will be the negative reciprocal of 2, which is -1/2.

Using the point-slope form of a line

y - y1 = m(x - x1)

where (x1, y1) is the point (5, 3) and m is the slope we just found (-1/2).

Substituting in the values, we get:

y - 3 = (-1/2)(x - 5)

Simplifying and rearranging to slope-intercept form, we get:

y = (-1/2)x + 5/2 - 3

y = (-1/2)x - 1/2

Therefore, the equation of the line containing (5, 3) that is perpendicular to the line y + 11 = 1/2(4x + 6) is y = (-1/2)x - 1/2.

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The average speed over the entire two hours will be 25 miles per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

The speed will be:

= Total distance / Total time taken

= (30 × 1) + (40 × 0.5) + (0 × 0.5) / 1 + 0.5 + 0.5

= 50 / 2

= 25 miles per hour.

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After the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

Before the 2:30 stop, the bus let off 15 people and let on 9 people. The total change in the number of people at that stop is -15 (let off) + 9 (let on) = -6.

Therefore, there are 6 fewer people on the bus after the 2:30 stop compared to before that stop.

Ten minutes later, the bus makes another stop and lets off 4 more people. This additional change needs to be considered.

Since the previous calculation only accounted for the changes up until the 2:30 stop, we need to adjust the total change by including the subsequent stop.

Adding the change of -4 (let off) to the previous total change of -6, we get a new total change of -10.

Therefore, after the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

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