Write 3.1405 x 10° in standard form

Answer:

The solution to the system of equations is \(\displaystyle \big(\frac{56}{29}, -\frac{16}{29}\big)\).

Step-by-step explanation:

We are given a system of equations:

\(\displaystyle \left \{ {{-3x+4y=-8} \atop {8x-y=16}} \right.\)

\(\displaystyle 8x - y = 16\\\\-y = -8x + 16\\\\\frac{-y}{-1}=\frac{-8x+16}{-1}\\\\y = 8x - 16\)

Now, we've solved for y. So, we can substitute this into either equation and solve for x.

\(\displaystyle -3x + 4(8x -16)=-8\\\\-3x + 32x - 64 = -8\\\\29x - 64 = -8\\\\29x = 56\\\\\frac{29x}{29}=\frac{56}{29}\\\\x = \frac{56}{29}\)

Now, we substitute our value for x into one of the original equations and solve for y.

\(\displaystyle 8\big(\frac{56}{29}\big)-y=16\\\\-y = 16 - 8\big(\frac{56}{29}\big)\\\\-y=\frac{16}{29}\\\\\frac{-y}{-1}=\frac{\frac{16}{29}}{-1}\\\\y = -\frac{16}{29}\)

Therefore, the solution to our system of equations is:

The estimate of ∫e^x dx using rectangles with heights given by right-hand endpoints and four subintervals (n = 4) can be determined by evaluating the function at those endpoints and multiplying by the width of each rectangle.

Among the given options, the correct representation of the estimate is:

∫e^x dx is approximately (0.5)e^0.5 + (0.5)e^1 + (0.5)e^1.5 + (0.5)e^2.

This is because we divide the interval [0,2] into four subintervals of equal width, each with a width of 0.5. For the right-hand endpoint approximation, we evaluate the function e^x at those endpoints.

The height of each rectangle is given by e^x evaluated at the right-hand endpoint of each subinterval. The width of each rectangle is 0.5.

By multiplying the height and width of each rectangle and summing them up, we obtain the estimate of the integral.

Therefore, the correct representation is (0.5)e^0.5 + (0.5)e^1 + (0.5)e^1.5 + (0.5)e^2 as an estimate of ∫e^x dx using rectangles with right-hand endpoints and four subintervals.

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The simplified value of √12 . √20 is 4√15.

To calculate this, we can break down the numbers under the square roots into their prime factors.

The prime factorization of 12 is 2^2 * 3, and the prime factorization of 20 is 2^2 * 5.

Taking the square root of 12, we can simplify it as √(2^2 * 3), which becomes 2√3.

Similarly, the square root of 20 can be simplified as √(2^2 * 5), which becomes 2√5.

Now, we can multiply the simplified values together: 2√3 * 2√5.

When multiplying two square roots, we can combine the numbers outside the square root and the numbers inside the square root separately.

Multiplying the numbers outside the square root, we have 2 * 2 = 4.

Multiplying the numbers inside the square root, we have √3 * √5 = √(3 * 5) = √15.

Therefore, the final simplified value is 4√15

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Answer:

y = 1/3x + 8/3

Step-by-step explanation:

The slope of a line that is perpendicular to the line y = -1/3x + 7 is the negative reciprocal of the slope of the given line, which is -3. So, the slope of the perpendicular line is 1/3.

The point where the perpendicular line intersects the given line is also the point where the two lines intersect, which is (4,2) in this case. So, we can use this point to find the equation of the perpendicular line using the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1,y1) is a point on the line.

In our case, the equation of the perpendicular line is:

y - 2 = 1/3(x - 4)

We can simplify this equation to obtain:

y = 1/3x + 8/3

Therefore, the equation of the perpendicular line is y = 1/3x + 8/3.

Let r be a partial order on set S, and let t be a subset of S. If a and a' are both elements of t, where a is the greatest element and a' is a maximal element, then it can be proven that a = a'.

To prove that a = a', we consider the definitions of greatest and maximal elements. The greatest element in a set is an element that is greater than or equal to all other elements in that set. A maximal element, on the other hand, is an element that is not smaller than any other element in the set, but there may exist other elements that are incomparable to it.

Given that a is the greatest element in t and a' is a maximal element in t, we can conclude that a' is not smaller than any other element in t. Since a is the greatest element, it is greater than or equal to all elements in t, including a'. Therefore, a is not smaller than a'.

Now, to prove that a' is not greater than a, suppose by contradiction that a' is greater than a. Since a' is not smaller than any other element in t, this would imply that a is smaller than a'. However, since a is the greatest element in t, it cannot be smaller than any other element, including a'. This contradicts our assumption that a' is greater than a.

Hence, we have shown that a is not smaller than a' and a' is not greater than a, which implies that a = a'. Therefore, if a is the greatest element and a' is a maximal element in t, then a = a'.

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Thus, there would be no-static change if the length of the jumps is measured in feet instead of inches.

Now, According to the question:

What is a statistic?

A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer.

Given the data is:

The mean is 41 inches

The median is 39 inches

The standard deviation is about 9.6 inches

The IQR is 5.5 inches

For the conversion of the length from inches to feet would not affect the static data but the values of observation will change with respect to the standard of conversion which is for 1 foot = 12 inches or  1 inch = 1 / 12 feet.

Thus, there would be no-static change if the length of the jumps is measured in feet instead of inches.

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(a) The curve defined by the parametric equations x = t^2, y = -1/4t (t > 0) represents a parabolic trajectory, the point of intersection between the curve and the hyperbola is (4∛2, -1/(4∛2)).

To find the points on the curve where the tangent line is parallel to the line y = x, we need to determine when the slope of the tangent line is equal to 1.

The slope of the tangent line is given by dy/dx. Using the chain rule, we can calculate dy/dt and dx/dt as follows:

dy/dt = d/dt(-1/4t) = -1/4

dx/dt = d/dt(\(t^2\)) = 2t

To find when the slope is equal to 1, we equate dy/dt and dx/dt:

-1/4 = 2t

t = -1/8

However, since t > 0 in this case, there are no points on the curve where the tangent line is parallel to y = x.

(b) To determine the points on the curve where it intersects the hyperbola xy = 1, we can substitute the parametric equations into the equation of the hyperbola:

\((t^2)(-1/4t) = 1 \\-1/4t^3 = 1\\t^3 = -4\\\)

Taking the cube root of both sides, we find that t = -∛4. Substituting this value back into the parametric equations, we get:

x = (-∛4)^2 = 4∛2

y = -1/(4∛2)

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Recurrence relations are linear if the terms of the sequence only depend on the previous terms, and are homogeneous if the terms of the sequence are multiples of a constant. Recurrence relations with constant coefficients have the same coefficient for each term.

The Question is Incomplete. The following is generalised solution.

a_n = 3a_{n-1} + 4a_{n-2} - 5a_{n-3}

This is a linear homogeneous recurrence relation with constant coefficients. The degree of the recurrence relation is 3.

a_n = 5a_{n-1} - 6a_{n-2}

This is a linear homogeneous recurrence relation with constant coefficients. The degree of the recurrence relation is 2.

a_n = 3a_{n-1} + 4

This is not a linear homogeneous recurrence relation with constant coefficients, as the coefficient of a_{n-1} is a constant but the coefficient of the constant term (4) is not.

a_n = 2a_{n-1} - 6a_{n-2} + a_{n-3}

This is not a linear homogeneous recurrence relation with constant coefficients, as the coefficient of a_{n-3} is not a constant.

Thus, we have above conclusions that Recurrence relations are linear if the terms of the sequence only depend on the previous terms, and are homogeneous if the terms of the sequence are multiples of a constant. Recurrence relations with constant coefficients have the same coefficient for each term.

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With reference to X-linked recessive traits in human beings b. they express more in males than in females

Recessive traits that are linked to the X chromosome and are more common in men are known as X-linked recessive traits. In males, a single copy of the allele is enough to cause the disease because they have just one X chromosome, but in females, two copies of the allele are necessary to cause the disease because they have two X chromosomes.

Hemophilia and red-green color blindness are two common X-linked recessive conditions found in humans. The human X chromosome carries more than 1,000 genes, the majority of which are not associated with sex determination but have other critical functions in the body. The X chromosome has a high number of genetic disorders linked with it, but these disorders are not X-linked for the most part. As a result, the inheritance pattern for these diseases is not predictable.

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Answer:

30

Step-by-step explanation:

- A number is divisible by 2 if its last digit is 2, 4, 6, 8 or 0

- A number is divisible by 3 if ist sum of digits is divisible by 3.

- A number is divisible by 5 if its last digit is a 5 or a 0.

_

The least 3 digit number divisible by 30 is 120 and the greatest is 990.

Answer: 30

Step-by-step explanation:

Divisible by 2,3 and 5 means divisible by 2*3*5=30

So we require to calculate number of multiples of 30 in the range 100 to 999.

The least 3 digit number divisible by 30 is 120 and greatest is 990.

This is an AP series with common difference 30.

First number is 120 and n'th number is 990.

We need to find n.

Using the AP series formula

120 + (n-1)*30= 990

or n= 30

There are 30 3-digit numbers divisible by 2,3 and 5.

Answer:

598

Step-by-step explanation:

800x0.93^4

Answer:

red, yellow, blue, brown, orange, green, violet, black, carnation pink, yellow orange, blue green, red violet, red orange, yellow green, blue violet, white, violet red, dandelion, cerulean, apricot, scarlet, green yellow, indigo and gray, canary yellow, unmellow yellow, emerald, jade, green earth, champagne pink, pink lace, piggy pink, magenta,

Step-by-step explanation:

Answer:

1/100, or 0.01, or 10^-2

Step-by-step explanation:

Simplify to get 1/10^2

and evaluate to get 1/100 or some the alternative forms (see above)

Answer:The unit cost per hour

Step-by-step explanation:

Answer:

the unit cost per item.

Step-by-step explanation:

Answer:

Net Earnings = $65

Step-by-step explanation:

Money deposited in saving account = $2500

Interest rate = 5% pa = 5% of 2500 = $125

Fee = $5 (monthly). So annual fee = 12 x 5 = $60

So, net earning = Interest Earning - Annual Fee

= $125 - $60 = $65

Choose C.

x^2 = a/b must be true.

Answer:

A plate costs £4

Step-by-step explanation:

Let us represent the cups by c and the plates by variable p

Thus mathematically from the statements;

2c + 3p = 18. ••••••• (i)

secondly

5c + p = 19 •••••••••(ii)

so we want to find the value of p

Let’s multiply equation i by 5 and ii by 2

we have;

10c + 15p = 90

10c + 2p = 38

Now subtract equation ii from i

13p = 52

p = 52/13

p = 4

Answer:

<C = 54 degrees

b = 123.6

a = 72.6

Step-by-step explanation:

<C = 180 - 90 - 36 = 54 degrees

b = 100/sin54 = 123.6

a = sqrt (123.6^2 - 100^2) = 72.6

Answer: x = 4ooo sin 340 x = 223627 ft.

Step-by-step explanation: The angle between the waterline and the submarine is 34°. How deep is the submarine?

The volume of the empty space inside Container A is given as follows:

703.4 ft³.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

For Container A, the dimensions are given as follows:

r = 8 feet, h = 8 feet.

(radius is half the diameter)

Hence the volume is given as follows:

V = 3.14 x 8² x 8

V = 1607.7 ft³.

For Container B, the dimensions are given as follows:

r = 4 feet, h = 18 feet.

Hence the volume is given as follows:

V = 3.14 x 4² x 18

V = 904.3 ft³.

Then the volume of the empty space is given as follows:

1607.7 - 904.3 = 703.4 ft³.

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Answer:

m=48

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

m = 48

▹ Step-by-Step Explanation

Rewrite:

m/8 = 6

Use the inverse operation:

8 * 6 = 48

m = 48

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

The required probability of a sum of 5 or sum of 7 and the first die shows a 3 or the sum of the result is 6 or 8 are 5/18 and 1/18 receptively.

Probability is just the way that logical something is to occur. Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions administered by likelihood is called statistics.

Two fair dice are thrown then the number of  possible way is 6×6 = 36

a) a sum of 5 or sum of 7 :-

The total possible way for dice occurs sum 5 or sum 7 is (1, 4), (2, 3), (3, 2), (4, 1), (1, 6), (2, 4), (3, 4), (4, 3), (5, 2), (6, 1).

So, the total number possible way for dice occurs sum 5 or sum 7 = 10.

Probability = 10/36 = 5/18

Hence, the probability is 5/18.

b) The first dice shows 3 or the sum of the result is 6 or 8 :-

As, first dice shows 3 we have fixed 3 in first dice or results sum is 6 or 8 then second dice possibilities only consist two number either 3 or 5,

So, total possible ways for first dice shows 3 or sum of result is 6 or 8 is (3, 3), (3, 5).

There are only two ways,

Therefore, probability = 2/36 = 1/18

Hence, the probability is 1/18.

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The additional time it will take for the liquid's temperature to decrease from 64°F to 32°F is 2 minutes, considering a rate of temperature decrease of 16°F per minute.

To find the additional time it will take for the liquid's temperature to decrease from 64°F to 32°F, we can consider the rate at which the temperature is decreasing.

From the given information, we know that the liquid's temperature decreases from 160°F to 64°F in 6 minutes. This means that the temperature decreases by 160°F - 64°F = 96°F in 6 minutes.

Therefore, the rate of temperature decrease is 96°F / 6 minutes = 16°F per minute.

To find the additional time it will take for the temperature to decrease from 64°F to 32°F, we can calculate the difference in temperature and divide it by the rate of temperature decrease

Temperature difference = 64°F - 32°F = 32°F

Additional time = Temperature difference / Rate of temperature decrease

Additional time = 32°F / 16°F per minute = 2 minutes

Therefore, it will take an additional 2 minutes for the temperature to decrease from 64°F to 32°F.

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Answer:

System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0

Step-by-step explanation:

Given:

To Find:

Formula used:

According to question, we have

Inequality for dotted line :

(y-1) > (0-1)/(-1-0) * (x-0)

y - 1 > x

x - y + 1 < 0...(1)

Inequality for solid line:

(y-(-3)) < (0-(-3))/(-6-0) * (x-0)

y + 3 < -x/2

x + 2y +6 < 0...(2)

Using (1) and (2), we get

System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0.

Answer:

short answer Yes and No

Step-by-step explanation:

long answer

let's say he drives to and from work 5 days a week that's 110 hours driving to and from work. But let's say he only drives to work and from work 2 days a week that only 44 hours driving to and from work. But now let's say he only drives 2 days a week but has to keep driving to and back from work because he forgets something at his house or at work and say he hasto drive and extra 77 hours because he forgot something that's now 99 hours he drove to and from work but only worked 2 days out of the week

Hope this helped :)

The equation of the horizontal asymptote is  y=0, as mentioned in the graph.

The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator. If N is the degree of the numerator and D is the degree of the denominator, and… N < D, then the horizontal asymptote is y = 0.

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The volume of the solid obtained by rotating the region bounded by the curves y = ln(x), y = 1, and x = 1 about the x-axis is V = π ∫[1² - (ln(x))²] dx from 1 to e.

To find the volume, follow these steps:

1. Sketch the region: Plot y = ln(x), y = 1, and x = 1 on the coordinate plane.

2. Identify the method: Use the washer method since we're rotating around the x-axis.

3. Set up the integral: The outer radius is 1, and the inner radius is ln(x). So, the volume is V = π ∫[1² - (ln(x))²] dx.

4. Determine the limits of integration: The intersection points of y = ln(x) and y = 1 are x = 1 and x = e.

5. Evaluate the integral: V = π ∫[1² - (ln(x))²] dx from 1 to e.

By following these steps, you can find the volume of the solid formed by rotating the given region about the x-axis.

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The distribution does not represent a probability distribution. The correct option is b.

A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).

In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.

Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.

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You would use the CHARINDEX string function to locate the index of the first character of the first occurrence of a substring within another string.

The CHARINDEX() function is defined as returning the substring's location within the given string. Like the SUBSTRING function, it operates in reverse.

⇒ Syntax of CHARINDEX() function is CHARINDEX (substring, input_string)

Substring: Here, we specify the substring within the input string that we wish to look for. A maximum of 8000 characters may be used in this argument.

Input_string: The input string is defined in this argument.

Therefore, You would use the CHARINDEX string function to locate the index of the first character of the first occurrence of a substring within another string.

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