factoring trinomials with leading coefficient greater than 1. Learn how to factor quadratic expressions as the product of two linear binomials. For example, 2x²+7x+3=(2x+1)(x+3).

The size of the letters appear on the retina is 0.00289 cm

Given data:

To determine the size of the letters on the retina, use the concept of angular size and the relationship between object size, distance, and angular size.

Angular size is the measure of the angle subtended by an object as seen from a particular point, in this case, the eye.

Angular size = Object size / Distance

Object size = 1.0 cm

Distance = 6 meters

Angular size = 1.0 cm / 6 meters

To convert the distance to centimeters, multiply by 100:

Angular size = 1.0 cm / (6 meters * 100 cm/meter)

Angular size = 1.0 cm / 600 cm

Angular size = 0.0017 radians

The angular size of the letters is 0.0017 radians.

Now, to determine the size of the letters on the retina, calculate the linear size on the retina using the angular size and the distance from the lens to the retina.

Linear size on retina = Angular size * Distance from lens to retina

Angular size = 0.0017 radians

Distance from lens to retina = 1.7 cm

Linear size on retina = 0.0017 radians * 1.7 cm

Linear size on retina ≈ 0.00289 cm

Hence, the letters appear to be approximately 0.00289 cm in size on the retina.

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Answer:

3,6,9,12,etc

Step-by-step explanation:

In math, a multiple is the product of any quantity and an integer. In other words, for the quantities a and b, we say that b is a multiple of a if b = na for some integer n, which is called the multiplier. If a is not zero, this is equivalent to saying that b/a is an integer. 

The correct answer is a) the probability of precipitation is 72%. and b)  the probability of precipitation is 2%.

The given formula to determine the probability of precipitation (PoP) is PoP = (C * A) * 100 percent where C represents the confidence that precipitation will occur somewhere in the forecasted area and A represents the percentage of the area that will receive measured precipitation if it occurs.

(a) If a forecaster expresses confidence that there is an 80% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 90% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 80%A = 90%PoP = (80% * 90%) * 100%

PoP = 72%.

Therefore, the probability of precipitation is 72%.

(b) If a forecaster expresses confidence that there is a 20% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 10% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 20%A = 10%PoP = (20% * 10%) * 100%PoP = 2%

Therefore, the probability of precipitation is 2%.

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Answer:

77

Step-by-step explanation:

2:3:7.

A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

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Answer:

(6, 20) (8, 42)

Find the gradient:

(6 = x1, 20 = y1)

(8 = x2, 42 = y2)

Formula = m = y2 - y1 divided by x2 - x1

m = 42 - 20 divided by 8-6

m = 22/2

m = 11/1 which is the same as 11

Find the y-intercept:

Then, take one of the coordinates above. In this case, I'll take (6, 20).

Then we replace y and x from the coordinates.

y = 11x - 46

The final answer is: a = -6, b+ = √3/2, c = -3, and d = ∞

Given the unity feedback system with feedforward transfer function as G(s)= 2+2s+10 and the root locus is sketched in the -plane as below:

For this system, let's find the values of a, b, c, and d on the real axis and the imaginary axis using the root locus sketch.

The general equation of a straight line in the complex plane can be expressed as:

{}=+ ,

where

: real-axis intercept.

: slope.

For the given root locus plot, the  value is 0.382.

The angle of the asymptotes is given as:

θ=×360°±180°

where n is the number of open-loop poles minus the number of open-loop zeros.

Here,

n=2-1

=1.θ

=360°±180°

=±180°

For the locus to intersect the real-axis at =, we have to determine the value of .

This can be determined using the angle condition:

Angle condition:∑=2−1×180°

where  is the angle of departure (→∞) or the angle of arrival (→) of the th branch of the root locus.

For the given root locus plot, we have three branches.

Therefore, we will have three angles:

1

=π−π/3

=2π/32

=π+π/3

=4π/33

=−π

In the figure, there are 2 open-loop poles at =−1, and =−5, and no open-loop zeros.

Therefore, the number of branches in the root locus is 2 for this system.

The root locus plot has two branches that terminate on the real-axis at =1 and =2, respectively.

The angle condition gives:

∑

=2−1×180°

=(2×1−1)×180°

=180°.1+2+3

=2π/3+4π/3−π

=2π/3

Then, we have,

=180°−2π/3=60°

Slope (b) of the line joining =−5 and =1 is given by:

=()=tan(60°)=√3x=-(1+2)/2

where 1 and 2 are the  values of the two points in the real axis where the root locus intersects the real axis.

=−()=(−5+1)=(−5+1)√3/2

For the line joining =−1 and =2:

Slope (b) of the line joining =−5 and =1 is given by:

=()

=tan(−60°)

=−√3

=−()

=(−1+2)/2

=−(−1+2)√3/2

The transfer function of the given system is:

G(s)=2+2s+10=12/s+5+s

Let's write the transfer function using pole-zero form:

G(s)=12(1+s/6.67)/(1+s/5)/(1+s/1.5)

Now, we can use the breakaway and break-in points of the real-axis segments of the root locus to solve for the real-axis intercepts 1 and 2.

We have:

Breakaway point:

=−(/2)=−(√3/4)

Break-in point:

=−5

Let's compute the value of d (on the imaginary-axis) using the angle asymptotes.

Due to the two poles of the transfer function, the angle asymptotes intersect at:

θa

=180°/(n−z)

=180°/(2−0)

=90°

Therefore, we have,

=±tan(90°−60°)

=±∞

Finally, the values of a, b, c, and d are:

a=-5.99 (The value of a is approximately equal to -6)

+=+√3/2

c=-3.01 (The value of c is approximately equal to -3)

=∞The sign of b is positive as it intersects =1 on the right-hand side of the origin.

Therefore, the final answer is:

a=-6b+=√3/2c=-3d=∞

a = -6, b+ = √3/2, c = -3, and d = ∞

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Answer:

.68 Centiseconds

Step-by-step explanation:

A microsecond is exactly 1 x 10-6 seconds. 1 µs = 0.000,001 s. One millionth of a second.

and a centisecond is exactly 0.01 seconds. One hundredth of a second.

Im not really sure how to explain it. But I hope that I helped.

There are 0.68 Centiseconds in 6800 microseconds.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometres, or feet, or any other measure of length.

Given that, Convert 6800 microseconds to centiseconds

We know that 1 centisecond = 10000 microseconds

Thereforre, 6800 microseconds = 6800/10000 centiseconds

= 0.68 Centiseconds

Hence, There are 0.68 Centiseconds in 6800 microseconds.

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Answer:

Step-by-step explanation:

The rate of change is the slope of the line formed by connecting the two data points:

1.  (2010,1510). and   [enrollment for a school in 2010 was 1510 students]

2.  (2020, 860)         [In 2020, the enrollment was 860 students]

Slope is the Rise/Run of the line.  Lets go from the first point to the second.

The Rise:  (1510 - 860) = 650

The Run:   (2020-2010) = 10

The slope, or rate of change, is = 65

The interpretation is that "The enrollment at the school increase by an average of 65 students every year since 2010 until 2020."

In the ΔIJH, the value of the cosec (I) is \(1\frac{9}{56}\).

Given ΔIJH the length of the hypotenuse is 65,  the length of the base is 33, and the length of the opposite side is 56.

We have to find the value of the cosec (I).

A function of an arc or angle that is most easily represented in terms of the ratios of pairs of sides of a right-angled triangle, such as the sine, cosine, tangent, cotangent, secant, or cosecant.

We know cosec (I) = hypotenuse / opposite side

Substitute the values

cosec (I) = 65/56

              = \(1\frac{9}{56}\)

Hence the value of cosec (I) is \(1\frac{9}{56}\).

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The candidate that would make the company the most money in their first year of employment is Candidate B

The amount of profit that a candidate can make for the company is:

= ( Number of weeks in year x Profit per week ) - Salary for the year

We shall assume 48 working weeks in a year.

The amount of money made by Candidate A would be:

= ( 48 x 3, 000 ) - 80, 000

= $64, 000

The amount of money made by Candidate B is:

= ( 48 x 2, 400 ) - 45, 000

= $70, 200

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Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario. The formula is given to be:

where f is the number of times the data occurred and n is the total number of observations.

We have the frequency of the individual groups as shown below:

The total number of observations is 19.

Therefore, the relative frequencies are calculated below:

ANSWER

T

3-44x

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Answer:

Step-by-step explanation:

Emmanuel weighs 150 pounds. about 2 hours will it take him to metabolize one standard drink

Every hour, the body processes one normal drink. If you have 5 standard drinks, your body will take 5 hours to absorb the alcohol.

In general, the liver can digest one ounce of liquor (or one standard drink) in one hour. If you consume more than this amount of alcohol, your system will get saturated, and the excess alcohol will accumulate in your blood and physiological tissues until it can be metabolized.

It takes your liver around an hour to break down the amount of alcohol in a standard alcoholic drink (one beer, one glass of wine, or one shot).

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Answer:

x=-2

Step-by-step explanation:

5x - (3x + 2) = 8x + 10

5x-3x-2=8x+10 (Distribute to get rid of the parenthesis)

2x-2=8x+10 (Combine like terms)

-2=6x+10 (Subtract 2x from both sides to get the variable on one side)

-12=6x (Subtract 10 from both sides to get closer to isolating the variable)

-2=x (Divide by 6 on both sides to finish isolating the variable_

The output for the input by linearity property \(\(x(t) = 2u(t) + t\)\) is \(\(y(t) = te^{-t} + e^{-t}\)\). (Answer: B.\(\(y(t) = te^{-t} + e^{-t}\))\)

Find the output for the input \(x(t) = 2u(t) + t\), we can use the linearity property of the system.

Output\(\(y_1(t) = te^{-t}\)\) for input \(\(x_1(t) = t\)\)

Output \(\(y_2(t) = 0.5e^{-t}\)\) for input \(\(x_2(t) = u(t)\)\)

We can express \(\(x(t) = 2u(t) + t\)\) as a sum of\(\(x_1(t)\) and \(x_2(t)\):\)

\(\(x(t) = x_1(t) + 2x_2(t)\)\)

Using the linearity property, we can find the output \(\(y(t)\) for \(x(t)\):\(y(t) = y_1(t) + 2y_2(t)\)\)

Substituting the given expressions for \(y_1(t)\) and \(y_2(t)\):

\(\(y(t) = te^{-t} + 2(0.5e^{-t})\)\(y(t) = te^{-t} + e^{-t}\)\)

Therefore, the output for the input \(\(x(t) = 2u(t) + t\) is \(y(t) = te^{-t} + e^{-t}\).\)

B. \(\(y(t) = te^{-t} + e^{-t}\)\)

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Answer

7

Step-by-step explanation:

Using the rule of 72, startfraction 72 over t endfraction, Manuel will double his money first, in approximately 9 years. Option C is the answer.

The rule of 72 is a quick and simple way to estimate the number of years it takes for an investment to double given the

interest rate. It is calculated by dividing 72 by the interest rate.

For example, if an investment has an interest rate of 8%, it will take approximately 72 / 8 = 9 years to double the investment.

Applying this rule, we can estimate the time it will take for Sylvia's investment to double: 72 / 8 = 9 years.

And for Manuel's investment to double: 72 / 7.25 = 10 years.

Since Manuel's investment will double in approximately 9 years, he will double his money first.

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The missing vertex is (11, 7) with an area of 128 in2.

Answer:

380

Step-by-step explanation:

Answer:

x=11°

Step-by-step explanation:

opposite angles are equal

so 10x-7 is the same as 103

this looks like

10x-7=103

now you solve it

10x=110

x=11

The primary eight candles or oil lamps must be on a plane that is higher or lower than the shamash.

A nine-branched candelabrum known as a Hanukkah menorah, also known as a hanukkiah, is lighted during the eight-day Jewish festival of Hanukkah. Eight of the nine branches are held up by lights (candles or oil lamps), which stand throughout the eight nights of the festival. One additional light is lighted each night until all eight branches are illuminated on the last night. The candle on the ninth branch, known as the shamash (Arabic for "helper" or "servant"), is used to light the other eight branches.

The seven-branched menorah used in the first Temple in Jerusalem is commemorated by the Hanukkah menorah, which is separate from it. It's one of the most commonly manufactured pieces of Jewish ritual art, along with the Star of David and the menorah with seven branches.

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Answer:

J.  6.5

Step-by-step explanation:

Theorem:

In a triangle, a segment that has as endpoints the midpoints of two sides is parallel and half the length of the third side.

Here, BD is half the length of AE.

BD = AE/2 = 13/2 = 6.5

Let:

The slope m is given by:

Using the point-slope equation:

since the area is above the line, and the line is continuous:

(a)The range of the given set of measurements is 4.

(b)The sample mean of the given set of measurements is approximately 5.625.

(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.

(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.

To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.

Range = Largest value - Smallest value

Range = 8 - 4

Range = 4

The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.

(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.

To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.

Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45

Sample mean = Sum of measurements / Total number of measurements

Sample mean = 45 / 8

Sample mean ≈ 5.625

The sample mean represents the average value of the measurements and provides a measure of central tendency.

(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.

To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.

Squared difference for each measurement:

(4 - 5.625)^2 = 2.890625

(4 - 5.625)^2 = 2.890625

(7 - 5.625)^2 = 1.890625

(6 - 5.625)^2 = 0.140625

(4 - 5.625)^2 = 2.890625

(6 - 5.625)^2 = 0.140625

(6 - 5.625)^2 = 0.140625

(8 - 5.625)^2 = 5.390625

Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375

Sample variance = Sum of squared differences / (Total number of measurements - 1)

Sample variance = 16.364375 / (8 - 1)

Sample variance ≈ 2.337768

The standard deviation, denoted as s, is the square root of the sample variance.

Sample standard deviation = √(Sample variance)

Sample standard deviation = √(2.337768)

Sample standard deviation ≈ 1.529

These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.

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Answer:

x ≤ 15

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

See Below.

Step-by-step explanation:

The sum of an A.P. is given by:

\(\displaystyle S_n=\frac{n}{2}(a+x_n)\)

Where n is the number of terms, a is the initial term, and xₙ is the last term.

Therefore:

\(\displaystyle S_{30}=\frac{30}{2}\Big(a+x_{30}\Big)=15(a+x_{30})\)

And likewise:

\(\displaystyle S_{20}=\frac{20}{2}\Big(a+x_{20}\Big)=10(a+x_{20})\\\\ S_{10}=\frac{10}{2}\Big(a+x_{10}\Big)=5(a+x_{10})\)

Substitute:

\(15(a + x_{30}) = 3(10 (a + x_{20}) - 5(a + x_{10} ))\)

Distribute:

\(15a+15x_{30}=30a+30x_{20}-15a-15x_{10}\)

Simplify:

\(15x_{30}=30x_{20}-15x_{10}\)

Simplify:

\(x_{30}=2x_{20}-x_{10}\)

The nth term for an A.P. is:

\(x_n=a+d(n-1)\)

Where a is the initial term and d is the common difference.

So, it follows that:

\(x_{30}=a+d(30-1)=29d+a\\ x_{20}=a+d(20-1)=19d+a\\ x_{10}=a+d(10-1)=9d+a\)

Therefore:

\(29d+a=2(19d+a)-9d-a\)

Which follows that:

\(29d+a=38d+2a-9d-a\\ \\ 29d=29d \\\\ d\stackrel{\checkmark}{=}d\)

QED.