Solve each equation, and write the algebraic reason for each step.
1. 3y+5=2y-8
2. -2(x-1)=3x-13
3. 3b+4+b=16

Answer:

Step-by-step explanation:

The equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane can be found by using the distance formula in three dimensions.

Let (x, y, z) be a point P on the surface. The distance from P to the x-axis is |x|, and the distance from P to the yz-plane is sqrt(y^2 + z^2). Setting these two distances equal and solving for x, we get:

|x| = 2 * sqrt(y^2 + z^2)

x = 2 * sqrt(y^2 + z^2) if x >= 0

x = -2 * sqrt(y^2 + z^2) if x < 0

This is the equation for a hyperboloid of one sheet. The hyperboloid of one sheet is a three-dimensional surface with two connected components that are mirror images of each other across the x-axis.

The total amount of liquid Bobby put in the bucket is [tex]$\frac{11}{12}[/tex]

As per the given data, Bobby filled a bucket with [tex]$\frac{5}{6}[/tex] of gallon of water.

Also, he filled the bucket with a [tex]$\frac{1}{12}[/tex] of a gallon of juice.

Here we have to determine that the total amount of the liquid that Bobby put in the bucket.

The amount of the liquid that Bobby put in the bucket is the sum of [tex]$\frac{5}{6}[/tex] of a gallon of water and [tex]$\frac{1}{12}[/tex] of a gallon of juice.

=  [tex]$\frac{5}{6}[/tex] + [tex]$\frac{1}{12}[/tex]

To add the two fractions, they must have the same denominator.

Find the LCM of both the denominators

The LCM of the denominators 6 and 12 = 12

= [tex]$\frac{10}{12}[/tex] + [tex]$\frac{1}{12}[/tex]

As both the fractions have the same denominator we can add them directly.

= [tex]$\frac{10+1}{12}[/tex]

= [tex]$\frac{11}{12}[/tex]

Therefore the total amount of liquid is [tex]$\frac{11}{12}[/tex].

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Nanometer is a more easier way to represent the length of a virus as it can be represented the length in integer form.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

One nanometer is equal to 1 x 10⁻⁶ mm, which means that in 1 millimeter there are 1,000,000 nm

A length measurement using the metric system. One billionth of a meter is known as a nanometer. The thickness of a typical human hair is 60,000 nanometers. Light wavelengths and the separations between atoms in molecules may both be measured using nanometers.

1 nanometer = 10⁻⁶ mm

30 nanometer = 30 * 10⁻⁶ mm = 3* 10⁻⁵ mm

Nanometer is a more easier way to represent the length of a virus as it can be represented the length in integer form.

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The running time of the algorithms of addition, multiplication and division of two numbers are O(N), O(N^2), and O(N^2) respectively.

For the typical algorithms used to perform calculations by hand:

A. Adding two N-digit integers typically takes O(N) time. This is because each digit of the larger number needs to be added to the corresponding digit of the other number and the carry over needs to be taken into account.

B. Multiplying two N-digit integers typically takes O(N^2) time. This is because each digit of one number needs to be multiplied by each digit of the other number, and the intermediate results need to be summed.

C. Dividing two N-digit integers typically takes O(N^2) time. This is because the process of long division involves repeatedly dividing, multiplying, and subtracting the digits of the dividend and the divisor until the result is obtained.

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After deducting this tax amount, his take-home pay would be $3250.

The determination of the take-home pay after deducting the income tax can be calculated using the following formula:

Take-home pay = Total salary - (Total salary x Tax rate)

In this case, the total salary is S$5000 and the tax rate is 35%, so the calculation would be:

S$5000 - (S$5000 x 35%) = S$5000 - S$1750 = S$3250

The formula used to calculate the take-home pay (Total salary - (Total salary x Tax rate)) is a general formula that can be applied to calculate the take-home pay for most individuals who have income tax deducted from their salary.

However, it may not be applicable in all cases as the amount of tax deducted and the tax rate may vary based on the individual's salary, country, tax laws, and other factors. It is always recommended to consult with a tax professional or financial advisor for a more accurate calculation of take-home pay.

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Graphs represents a one-to-one function is graph A.

Graphics is as a combination of

numbers, letters, symbols, pictures, emblems, sayings, paintings, which are presented in one medium to convey concepts and ideas from the sender to the target in the process of conveying information.

There is also another understanding of graphics, which is a framework for forming table visualization objects. Tables consisting of numbers can be presented or can be displayed in the form of images, can be in the form of lines, circles, bars etc. And the third definition is a description of the ups and downs of a situation or existing data with lines or pictures. Graphs are divided into 3 "three" types, including graphs: bars, lines and circles.

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The correct value is 10. The solution has been obtained by using algebra.

What is algebra?

In the field of mathematics known as algebra, variables' values are determined by solving equations.

In the question, the student made mistake in the third step wherein, on the left hand side  there was -5 + (-5) which is equal to (-10) but the student calculated it to be 0.

This is why the student got the answer wrong.

The correct solution is that we will first arrange the like terms on one side.

On rearranging, we get

⇒2x = 15 + 5

⇒2x = 20

⇒x = 10

Hence, the correct value is 10.

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The question has been attached below

Answer:

x = -1

y = 3

Step-by-step explanation:

Equation 1: x=2y-7

Equation 2: 3x-8y=-27  ==> isolate x

Equation 3: 3x = 8y - 27  ==> isolate 3x by adding 8y on both sides

3 * (x = 2y - 7) ==> multiply 3 by equation 1 to get 3x

Equation 4: 3x = 6y - 21

  3x = 8y - 27

- (3x = 6y - 21)

3x-3x = 8y-6y - 27-(-21)  ==> subtract equation 4 from equation 3 to cancel x

0 = 2y - 27 + 21  ==> simplify

0 = 2y - 6  ==> solve for y

6 = 2y  ==> add 6 on both sides to isolate y

y = 3  ==> divide 2 into both sides

Solve for x:

x=2(3) - 7  ==> plug in 3 for y in x=2y-7

x = 6 - 7

x = -1

The equation of the plane determined by the intersecting lines is:

0x + 7y + 9z - 19 = 0

What is the equation of the plane?

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely in all directions. It is defined by an equation of the form Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the normal vector to the plane and D is a constant. The coefficients A, B, and C determine the orientation of the plane in 3-dimensional space, and the constant D determines the distance of the plane from the origin.

The equation of the plane can be found by finding the cross product of the direction vectors of the two lines.

Let's start by finding the direction vectors of the two lines:

For line L1, the direction vector is:

d = <3, 2, -1>

For line L2, the direction vector is:

d = <-3, 1, -2>

Now, we can find the cross product of these two direction vectors:

n = d1 x d2 = <3, 2, -1> x <-3, 1, -2> = <0, 7, 9>

So the normal vector to the plane is <0, 7, 9>.

Next, we can find a point on either line to substitute into the general equation of a plane to find the equation of the plane:

Let's use the point from line L1:

x = -1 + 3 * 0 = -1

y = 2 + 2 * 0 = 2

z = 1 - 0 = 1

Now, we have a point (-1, 2, 1) and the normal vector <0, 7, 9>, which we can substitute into the general equation of a plane:

Ax + By + Cz + D = 0

where A, B, C are the components of the normal vector, and D is a constant.

Plugging in the values, we get:

0x + 7y + 9z - 19 = 0

So, the equation of the plane determined by the intersecting lines is:

0x + 7y + 9z - 19 = 0

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For a normally distributed variable x with a mean of 60 and a standard deviation of 15, theprobability P(x < 75) is 0.3173

Here, a variable x is normally distributed a mean of 60 and a standard deviation of 15.

This means, mean (μ) = 60

and the standard deviation (σ) = 15

To find:  P(x < 75) .

First we find the z-score.

Using the formula for the z-score,

[tex]z=\frac{75-60}{15}[/tex]

z = 1

Using standard normal table, the p-value corresponding to z = 1 is:

p = 0.3173

Thus the probability P(x < 75) is 0.3173

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The complete question is:

if a variable x is normally distributed with a mean of 60 and a standard deviation of 15, what is the probability P(x < 75) .

Answer:

Opposite sides are parallel.

Opposite sides are congruent.

All angles are right angles and congruent.

Diagonals are congruent.

Diagonals bisect each other.

Answer:We got 0.56 as the answer when you convert 5/9 to a decimal.

The total number of visitors is 148 + 107 + 3 = 258.

The number of visitors who purchased no more than one costume is 148 + 107 = 255.

The probability that the next person will purchase no more than one costume is 255/258.

In simplest form, the probability is 255/258 = (255 ÷ 3) / (258 ÷ 3) = 85/86.

Probability is a branch of mathematics that deals with the chance or likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.

The formula for calculating probability is:

P(event) = Number of favorable outcomes / Total number of possible outcomes

The result is always between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain to occur.

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Dividing the sum above by the total number of values in the data set.

Take the absolute value of each integer in the data collection and remove the mean. Then add the absolute values together. Divide the total number of values in the data set by the sum above to get the mean absolute deviation. Finally, round up to the tenth.

A collection of data’s Mean Absolute Deviation (MAD) is the average distance between each data item and the mean. The mean absolute deviation is the “average” of each point’s “positive distances” from the mean. The bigger the MAD, the greater the variability in the data (the data is more spread out).

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Answer: Measure of CED is: 212°

The median divides the data into half so that 50% of the measurement lies below the median and 50% lies above it, the quartile breaks down the data into quarters so that 25% of the measurements are less than the lower quartile, 50% are less than the median, and 75% are less than the upper quartile.

Now, According to the question:

The interquartile range and semi-interquartile range give a better idea of the dispersion of data. To calculate these two measures, you need to know the values of the lower and upper quartiles. The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order. The median is considered the second quartile (Q2). The interquartile range is the difference between upper and lower quartiles. The semi-interquartile range is half the interquartile range.

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The complete question is this:

What percent of data is between Q1 and Q2?

Arc length of a given circle with a radius of is π/.

According to the given diagram,

The angle subtended by arc AED or central angle

= 360°-120°-45°-30°

= 165°

The radius of the circle = 3 units

, ?

= Central angle(in radians) * Radius

So, arc length

= 165 *π/180 * 3

Arc length

= 11π/12 * 3 = 11π/4

Therefore, the Arc length of a given circle with a radius of 3 units is π/

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In circle f, segment eb is a diameter that divides the circle into two equal sectors. The length of segment fb is 3 units, so the radius of the circle is 3 units.

To find the area of one of the sectors in circle f, we need to know the radius of the circle. Since a diameter of the circle is segment eb, and the length of segment fb is 3 units, then the radius of the circle is 3 units. To find the area of one sector, we can use the formula A = (1/2)r^2, where r is the radius. In this case, the radius is 3 units, so the area of one sector is A = (1/2)(3^2), or A = 4.5 units^2. To find the area of the whole circle, we can multiply the area of one sector by 2, since there are two equal sectors in the circle. Thus, the area of the whole circle is A = 2(4.5) = 9 units^2.

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Use the information in provided in each part of the question to analyze the probability is 42.

Use the information in provided in each part of the question to analyze the probability.

A dealer deals a hand consisting of 3 spades, 4 diamonds. 6 clubs and 5 hearts. If two cards are picked at random from that hand without replacement,

The two types of compound events are calculated using several formulas: If two occurrences, A and B, are mutually exclusive, then P(A or B) = P (A) + P (B). P (A or B) = P(A) + P(B) - P for mutually inclusive occurrences (A and B).

Once the first event has occurred, multiply the likelihood of the subsequent event by the previous event's probability to arrive at the compound probability of dependent events.

P (A) + P (B)

3(4) + 6(5) = 12 + 30 = 42.

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Assuming the side lengths in the new phone are proportional to the old phone, the width of the new phone would be equal to 3.23 inches.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following mathematical expression:

1.2 inches = 3.4 inches

1.14 inches = w inches

Cross-multiplying, we have the following:

1.2w = 3.4 × 1.14

1.2w = 3.876

w = 3.876/1.2

w = 3.23 inches.

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To divide powers that have the same base and different​ exponents, keep the​ base and​ subtract the exponents.

When dividing two powers that have the same base but different exponents, you keep the base and subtract the exponents.

For example, if you want to divide a^m by a^n,

you can write it as a^m / a^n

= a^(m-n).

The new exponent is the result of subtracting the exponents of the two powers.

hence the division will result to a^(m-n).

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The correct equation to represent "Ehren worked 36 hours last week and earned a total of $500" is,

⇒ 36x = 500

Where, x represent the amount earn in per hour.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

"Ehren worked 36 hours last week and earned a total of $500"

Let the amount earn in per hour = x

Hence, For Ehren worked 36 hours last week and earned a total of $500, the correct equation is,

⇒ 36x = 500

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Yes, increasing the voltage of an electric motor will cause it to turn faster. Voltage is the difference in electrical potential between two points, and is measured in volts.

When voltage is increased, the electric motor is able to draw more power from the power source, which will result in a faster rotation speed. The independent variable in example B is the voltage supplied to the electric motor.

This is the variable that will be changed in order to test the effect on the motor's speed. By increasing the voltage supplied to the motor, we can see how the speed of the motor changes in relation to the change in voltage. By doing this, we can determine the motor's speed at various voltages, and can determine how the voltage affects the motor's speed.

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We can write {x} as follows -

{x} = (4/3) - (c/3)

An function in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). Example -

y = f{x} = ax + b

Given is a equation as -

3x + c = 4

The given equation is -

3x + c = 4

3x = 4 - c

x = (4 - c)/3

x = (4/3) - (c/3)

Therefore, we can write {x} as follows -

{x} = (4/3) - (c/3).

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500 m is equal to 0.310686 mi. This is due to the fact that one mile is equal to the errant total of 1,609.344 meters.

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As per the concept of standard deviation the statement that is not true is "f) None of the above".

The term standard deviation in math is known as the process of measure the spread of the data about the mean value and it is useful in comparing sets of data which may have the same mean but a different range.

Here it is important to understand the concept of sampling distribution, particularly the sampling distribution of the sample mean.

Statement (a) is true. The sampling distribution of the sample mean is often reasonably similar to the distribution of the population from which the sample is taken.

Statement (b) is also true. As the sample size increases, the normal approximation to the sampling distribution of the sample mean becomes better.

Statement (c) is true as well. The standard deviation of the sampling distribution of the sample mean can be calculated using the formula σ/√n, where σ is the standard deviation of the population and n is the sample size.

Statement (d) is somewhat true. The sampling distribution of the sample mean is indeed approximately normal, mound-shaped, and symmetric for sample sizes greater than 30, but this rule of thumb is not strict.

Statement (e) is true. The expected value of the sample mean is always the same as the expected value of the population mean.

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The distance to school, and therefore home, is d Thus, the student rides d+d miles in one day. so, she rides (2d) miles in one day.

Expression- 1 : she travels( 10d) long hauls in a normal rain free week. In a 4 week period she'd typically lift( 10d 10d 10d 10d) long hauls, but we need to abate the long hauls for the stormy days. For each rain day we've to abate 2d long hauls. thus, she traveled( 10d 10d 10d 10d∠′ 2d∠′ 2d∠′ 2d∠′ 2d) or( 10d 10d 10d 10d∠′( 2d 2d 2d 2d)). Equally 4( 10d) ∠′ 4( 2d) = ( 40d∠′ 8d).

Expression- 2 : If we decide to combine the stormy day long hauls with the daily long hauls traveled ahead of time also the expression for one academy week with one rain day looks like( 10d∠′ 2d) or( 8d) and the four week aggregate is( 8d 8d 8d 8d). Equally we can write 4( 8d).

The original expressions will vary greatly. Comparing the cases above we see that( 40d∠′ 8d) and 4( 8d) represent the same distance traveled and thus are original expressions.

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Answer:

see below

Step-by-step explanation:

length to width ratio is 2

so 5 1/2 ÷ 2 = 11/2 ÷ 2 , simplify  = 11/4 = 2 3/4

6 2/5 *2 = 32/5 *2 = 64/5 =12 4/5

The factorization of 21+39 is 3(7+13)

The process of finding two or more expressions whose product is the given expression is called the factorization of algebraic expressions. Thus, the factorisation of algebraic expressions is the reverse process of multiplication.

to factorize, we find a common factor between the two terms

The common factor between 21 and 39 is 3 .

3 in 21 is 7 and 3 in 39 is 13

therefore 21+39 can be written as 3(7+13)

we can therefore be say that 21+39 = 3(7+13) and 3 is the missing number in the question

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Answer:

1/6 and 1/6^1 so the second and 4th one.

Step-by-step explanation:

Look it up bud

(a) If the current distribution is Ps all other Pa 0.2, then in the next period, all states will have the same probability of 0.2, because the frog has a 0.2 probability of moving to any state.

(b) If the current distribution is Pz 0.5, Ps 0.5 all other Pa 0.2, then in the next period, the probabilities of being in state z and state s will each be 0.5 * 0.5 = 0.25, and the probabilities of being in all other states will be 0.2.

(c) If the current distribution is Pz 0.225, Pa 0.25, Pa 0.5, all other P; 0.2, then in the next period, the probabilities of being in each state will be the sum of the products of the current probability of being in that state and the transition probabilities from that state.

(d) If the current distribution is P: Pz 0.22, Pa 0.22, Pa 0.22, Ps 0.22. P6 0.2, then in the next period, the probabilities of being in each state will be the same as in the current period, because the frog has an equal probability of moving to any state.

Note that in each case, the probabilities must add up to 1, as they represent the entire possible states of the frog.

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