How can you find 40% of 150 using mental math? Explain.

Answer:

B

Step-by-step explanation:

s = \(\frac{1}{2}\) a²v + c ( subtract c from both sides )

s - c = \(\frac{1}{2}\) a²v ( multiply both sides by 2 to clear the fraction )

2(s - c) = a²v ( isolate v by dividing both sides by a² )

\(\frac{2(s - c)}{a^2}\) = v

Answer:

\(y = - \frac{5}{4} x - \frac{1}{2} \)

Step-by-step explanation:

Slope-intercept form: y= mx +c, where m is the slope and c is the y-intercept.

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

Slope

\( = \frac{ - 3 - \frac{1}{8} }{2 - ( - \frac{1}{2}) } \)

\( = - \frac{5}{4} \)

Substitute the value of m into the equation:

\(y = - \frac{5}{4} x + c\)

To find the value of c, substitute a pair of coordinates the line passes through into the equation.

When x= 2, y= -3,

\( - 3 = - \frac{5}{4} (2) + c\)

\( - 3 = - \frac{5}{2} + c\)

\(c = - 3 + \frac{5}{2} \)

\(c = - \frac{1}{2} \)

Thus, the equation of the line is \(y = - \frac{5}{4} x - \frac{1}{2} \).

For a normal distribution, we can use the empirical rule to estimate the percentage of data within certain intervals.So, about 95% of the midexam scores lie between 29 and 91.

(a) About 68% of the data lies within one standard deviation of the mean. Therefore, for the midexam scores in the Business class at PMBS:

One standard deviation = 15.5
Lower bound = Mean - One standard deviation = 60 - 15.5 = 44.5
Upper bound = Mean + One standard deviation = 60 + 15.5 = 75.5

So, about 68% of the midexam scores lie between 44.5 and 75.5.

(b) About 95% of the data lies within two standard deviations of the mean. Therefore, for the midexam scores in the Business class at PMBS:

Two standard deviations = 2 * 15.5 = 31
Lower bound = Mean - Two standard deviations = 60 - 31 = 29
Upper bound = Mean + Two standard deviations = 60 + 31 = 91

So, about 95% of the midexam scores lie between 29 and 91.

 To  learn more about deviation click here:brainly.com/question/31835352

#SPJ11

A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.

Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.

To know more about research,

https://brainly.com/question/24250717

#SPJ4

There are approximately 63,063 ways to choose 16 croissants from the selection of 6 different types offered by the croissant shop.

To find the number of ways to choose 16 croissants from a selection of 6 different types, we can use the concept of combinations.

The formula for combinations is:

nCr = n! / (r! * (n-r)!)

where n is the total number of items to choose from, and r is the number of items to choose.

In this case, there are 6 different types of croissants, and we want to choose 16 of them. Therefore, we can calculate the number of ways to choose 16 croissants as follows:

6C16 = 6! / (16! * (6-16)!) = 6! / (16! * (-10)!) = 6! / (16! * 10!) ≈ 63,063

To learn more about combinations click on,

https://brainly.com/question/29291864

#SPJ4

Answer:

( 20 × 10 ) + ( 20 × 7 ) + ( 2 × 10 ) + ( 2 × 7 )

Step-by-step explanation:

To create partial products when multiplying two numbers, first break the numbers up into a sum of two numbers. The order that these numbers are multiplied does not necessarily matter as long as they are multiplied with the correct numbers.

22 × 17 = (20 + 2)(10 + 7) = 20 (10 + 7) + 2 (10 + 7) =

( 20 × 10 ) + ( 20 × 7 ) + ( 2 × 10 ) + ( 2 × 7 )

= 374

You can check this method works by using your calculator, and multiplying 22 by 17 to get 374 again!

Then just add like you would if when you distribute.

Remember FOIL (First, Outer, Inner, Last)

when multiplying two binomials(2 terms) or distributing factors with two terms.

For example:

(a + b)(c + d) =

F F

O O

I I

L L

(a × c) + (a × d) + (b × c) + (b × d)

a. The coordinates of the new triangle's points after a dilation with a scale factor of 2 are A'(-5, -9), B'(13, 7), and C'(-13, 5).

b. The coordinates of the new triangle's points after a dilation with a scale factor of 1/2 are A"(-1/2, 0), B"(4, 4), and C"(-5/2, 7/2).

a. If the scale factor is 2, the coordinates of the new triangle's points A', B', and C' can be found by applying the dilation formula:

For point A:

x-coordinate of A' = (scale factor) * (x-coordinate of A) + (1 - scale factor) * (x-coordinate of center)

y-coordinate of A' = (scale factor) * (y-coordinate of A) + (1 - scale factor) * (y-coordinate of center)

Using the given values:

x-coordinate of A' = 2 * (-2) + (1 - 2) * 1 = -4 + (-1) = -5

y-coordinate of A' = 2 * (-3) + (1 - 2) * 3 = -6 + (-3) = -9

So, the coordinates of point A' are (-5, -9).

Following the same formula, we can find the coordinates of B' and C':

For point B:

x-coordinate of B' = 2 * 7 + (1 - 2) * 1 = 14 + (-1) = 13

y-coordinate of B' = 2 * 5 + (1 - 2) * 3 = 10 + (-3) = 7

So, the coordinates of point B' are (13, 7).

For point C:

x-coordinate of C' = 2 * (-6) + (1 - 2) * 1 = -12 + (-1) = -13

y-coordinate of C' = 2 * 4 + (1 - 2) * 3 = 8 + (-3) = 5

So, the coordinates of point C' are (-13, 5).

b. If the scale factor were 1/2, the coordinates of the new triangle's points A", B", and C" can be found using the same dilation formula:

For point A:

x-coordinate of A" = (scale factor) * (x-coordinate of A) + (1 - scale factor) * (x-coordinate of center)

y-coordinate of A" = (scale factor) * (y-coordinate of A) + (1 - scale factor) * (y-coordinate of center)

Using the given values:

x-coordinate of A" = (1/2) * (-2) + (1 - 1/2) * 1 = -1 + 1/2 = -1/2

y-coordinate of A" = (1/2) * (-3) + (1 - 1/2) * 3 = -3/2 + 3/2 = 0

So, the coordinates of point A" are (-1/2, 0).

Following the same formula, we can find the coordinates of B" and C":

For point B:

x-coordinate of B" = (1/2) * 7 + (1 - 1/2) * 1 = 7/2 + 1/2 = 4

y-coordinate of B" = (1/2) * 5 + (1 - 1/2) * 3 = 5/2 + 3/2 = 4

So, the coordinates of point B" are (4, 4).

for such more question on coordinates

https://brainly.com/question/23907194

#SPJ8

The general solution of the differential equation y"-8y+15y=0 is \(y(t) = C_{1}sinh(\sqrt{3}t) + C_{2}sinh(\sqrt{5}t)\), where \(C_{1}\) and \(C_{2}\) are constants of integration

The characteristic equation for this differential equation is r^2 - 8r + 15 = 0, which factors as (r-3)(r-5) = 0. Therefore, the roots are r=3 and r=5.

The general solution of the differential equation is \(y(t)= C_{1}e^{3t}+C_{2}e^{5t}\), where \(C_{1}\)  and \(C_{2}\) are constants of integration.

we can write this as: \(y(t)= C_{1}sinh(at)+  C_{2} sinh(bt)\), where a and b are the square roots of the roots of the characteristic equation, i.e. \(a=\sqrt{3}\) and \(b=\sqrt{5}\).

Therefore, the general solution of the differential equation y"-8y+15y=0 is \(y(t) = C_{1}sinh(\sqrt{3}t) + C_{2}sinh(\sqrt{5}t)\), where \(C_{1}\) and \(C_{2\) are constants of integration.

To know more about "Differential equations" refer here:

https://brainly.com/question/25731911#

#SPJ11

Answer:

50 m.

Step-by-step explanation:

It's a 5m x 17m rectangle plus two "rouge" sides of 3m.

Required probability = 120 * 0.0010819 =  0.1298

total number of outcomes of 7 from 10 = 10*9*8 / 3*2*1  = 120

probability of each outcoe is 0.85^7* (0.15)^(3)  = 0.0010819

Required probability = 120 * 0.0010819 =  0.1298

Probability is simply how likely something is to happen.

Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?P(H)=?P, left parenthesis, H, right parenthesis, equals, question mark.

For more information on probability click on the link below:

https://brainly.com/question/24756209

#SPJ4

Answer:

mode is 39

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

  -1 ≤ x ≤ 2

Step-by-step explanation:

You want the solution to |x +1| +|x -2| = 3.

We find it convenient to solve these absolute value equations using a graphing calculator. When we subtract 3 from both sides, we have ...

  |x +1| +|x -2| -3 = 0

The solutions will show on the graph as places where the expression has a value of 0, that is, the x-intercepts.

The left-side expression has a value of 0 for all values of x between -1 and +2, inclusive. That is, the solution is ...

  -1 ≤ x ≤ 2

The absolute value function is piecewise defined:

  |x| = x . . . . for x ≥ 0

  |x| = -x . . . . for x < 0

That is, the behavior of the function changes at x=0.

In the given equation the absolute value function arguments are zero at ...

  x +1 = 0   ⇒   x = -1

  x -2 = 0   ⇒   x = 2

These x-values divide the domain of the equation into three parts.

In this domain, both arguments are negative, so the equation is actually ...

  -(x +1) -(x -2) = 3

  -2x +1 = 3

  -2x = 2

  x = -1 . . . . . . not in the domain

In this domain, the argument (x+1) is positive, but the argument (x-2) is negative. That means the equation is ...

  (x +1) -(x -2) = 3

  1 +2 = 3

True for all x in this domain.

In this domain, both arguments are positive, so the equation is ...

  (x +1) +(x -2) = 3

  2x -1 = 3

  2x = 4

  x = 2 . . . . in the domain (this point was excluded from x < 2).

The solution is -1 ≤ x ≤ 2.

The equation of the line passing through the given points is y = 3x-1.

Given that is a line passing through two points (0, 2) and (-1, -1) we need to find the equation of the line using them,

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (0, 2) and (-1, -1),

Therefore, the required equation is =

y+1 = -1-2/-1 (x-0)

y+1 = 3x

y = 3x-1

Hence, the equation of the line passing through the given points is y = 3x-1.

Learn more about equation of the line click

brainly.com/question/21511618

#SPJ1

A 2 x 2 matrix has 2 rows and 2 columns

A specific 2 x 2 matrix a with no zero entries at all is \(\left[\begin{array}{cc}1&-2\\-3&6&\end{array}\right]\)

From the question, we understand that the matrix is a 2 x 2 matrix.

A 2 x 2 matrix is represented as:

\(\left[\begin{array}{cc}a&b\\c&d&\end{array}\right]\)

Also from the question we understand that the elements of the matrix are non-zero.

This means that:

\(a \ne 0\ , b \ne 0, \ c \ne 0, \ d \ne 0\)

An example of such matrix is:

\(\left[\begin{array}{cc}1&-2\\-3&6&\end{array}\right]\)

Note that there are several matrices that fit the given construction requirement

Read more about matrix at:

https://brainly.com/question/1821869

Sierra needs 9/4 cups of orange juice to make 6 bars.

To determine how many cups of orange juice Sierra needs to make 6 bars, we can set up a simple multiplication problem.

Given that Sierra uses 3/8 cup of orange juice for each bar, we can multiply the amount per bar by the number of bars:

(3/8 cup) x (6 bars) = 18/8 cups

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2:

(18/8 cups) ÷ 2 = 9/4 cups

Therefore, Sierra needs 9/4 cups of orange juice to make 6 bars. Visually, you can represent this with a model by drawing 6 equal-sized bars, and for each bar, fill in 3/8 of a cup to represent the amount of orange juice used.

Learn more about cups

brainly.com/question/945283

#SPJ11

Answer:

-1/2

Step-by-step explanation:

-3/4= -.75

1  1/2= 1.5

-.75/ 1.5= - .5

-.5= -1/2

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

Basic fact:

all sides of a square are equal

Step-by-step explanation:

1 side is x+1 so all sides are x+1

there are 4 sides so times everything by 4

4(x+1) which is 4x+4

Answer:

Step-by-step explanation:

What we do is to divide 1500 by 4 = $1500/4 = $375

Answer:375

Step-by-step explanation:

1500/4=375

He have to pay $3.25.

Let the number of miles traveled by a driver be x

The toll paid by the driver is then represented as y. (in dollar)

Linear equation : an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.

Since there is a linear relation between the two, we can assume the equation can be written as:

y = mx + c

From the given data, we get

0.24 = m(0) + c

c = 0.25

Using the second point:

1 = m(1) + 0.25

m = 1 − 0.25 = 0.75

Hence, the equation is y = 0.75x + 0.25.

If  x = 4, then:

y = 0.75 × 4 + 0.25

y = 5.50

Hence, He have to pay $3.25.

Learn more about linear equations from here : brainly.com/question/28450464

#SPJ4

Answer: Your answer is B! Hope you have an awesome day, and be kind be You!!! <3

Step-by-step explanation: Also, I'm 3D printing the Tesla Cyber truck, and this is the design I have so far. What do you think?

Answer:

Point A is -2, 1

Point B is -4, -2

Point C is -4, -6

and D is -1, 3.

Step-by-step explanation:

Irdk if this is all right bcz its kinda hard to see the exact points. Hope it is tho, and hope it helps you out! Good luck :P

Answer:

x-y=-6

Step-by-step explanation:

hope this helps and I hope you have a good day

The missing term is "zero" for the given equation.

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles. There are two types of supplementary angles.

As per the given figure, the required solution would be as:

8x - 3 + 4x + 3 = 180

Rearrange the likewise terms and apply the arithmetics operation,

12x + 0 = 180

We know that the sum of 3 and -3 is 0.

Compared to the given equation, we get the missing term as zero.

Thus, the required value is 0.

Learn more about supplementary angles here:

brainly.com/question/3027144

#SPJ1

Answer:

29.88953

Step-by-step explanation:

x = 20*sin(90)/sin(42) = 29.88953

Answer:  b

Step-by-step explanation:

I think

The explicit formula for an arithmetic sequence calculator is a_n = a_1 + (n-1)d.

The formula for an arithmetic sequence is:

a_n = a_1 + (n-1)d

where a_n is the value of the nth term in the sequence, a_1 is the value of the first term in the sequence, n is the position of the term you want to find, d is the common difference between consecutive terms in the sequence, To use this formula to find a specific term in the sequence, simply substitute the values of a_1, n, and d into the formula and evaluate.

For example, if you wanted to find the 10th term in an arithmetic sequence with a first term of 3 and a common difference of 4, you would use the formula

a_10 = 3 + (10-1)4

a_10 = 3 + 36

a_10 = 39

Therefore, the 10th term in this sequence is 39.

To know more about arithmetic sequence:

https://brainly.com/question/11764572

#SPJ4

The Law of Cosines can be used to solve a triangle in the following cases: A. SAA (side, angle, angle), B. ASA (angle, side, angle), and E. SAS (side, angle, side).

The Law of Cosines is a mathematical equation that relates the lengths of the sides of a triangle to the cosine of one of its angles. It can be used to solve a triangle when certain information about the triangle is known.

A. In the SAA case, if the lengths of two sides and the measure of the included angle are known, the Law of Cosines can be used to find the remaining side or angles.

B. In the ASA case, if the measures of two angles and the length of the included side are known, the Law of Cosines can be used to find the remaining sides or angles.

C. In the SSS case, where the lengths of all three sides are known, the Law of Cosines is not needed since the Law of Sines or other methods can be used to solve the triangle.

D. In the SSA case, where the lengths of two sides and the measure of an angle not between them are known, the Law of Cosines alone is insufficient to solve the triangle.

E. In the SAS case, if the lengths of two sides and the measure of the included angle are known, the Law of Cosines can be used to find the remaining side or angles.

Therefore, the Law of Cosines can be used in cases A (SAA), B (ASA), and E (SAS) to solve a triangle.

To learn more about law of cosines visit:

brainly.com/question/30766161

#SPJ11

Solution: 25 × $9.85= $246.25 purchase price

25 × $11.22 = $280.5 sale price

$280.5 – $246.25 = $34.25 profit in dollars

$34.25 ÷ $246.25 = 0.139 = 13.9% ROI

Purchase price of the share is equals to 246.25dollars.

Profit percentage is equals to 13.9 percentage ( nearest tenth).

" Purchase price is defined as the total amount paid to buy any product."

Formula used

Profit = Selling price - Purchase price

Profit percentage = \(\frac{profit}{cost price} (100)\)

According to the question,

Total number of shares = 25

Purchase price of one share =  9.85 dollars

Selling price of 1 share = 11.22 dollars

Therefore,

Purchase price of 25 shares = (9.85 × 25 )dollars

                                               = 246.25 dollars

Selling price of 25 shares = (11.22 × 25) dollars

                                           = 280.5 dollars

Selling price > Purchase price

Therefore,

Profit = Selling price - Purchase price

         = 280.5 - 246.25

         = 34.25 dollars

Substitute the value in the formula we get,

Profit percentage = \(\frac{34.25}{246.25} (100)\)

                              = 13. 9 percentage ( nearest tenth)

Hence, purchase price of the share is equals to 246.25dollars.

Profit percentage is equals to 13.9 percentage ( nearest tenth).

Learn more about purchase price here

https://brainly.com/question/15623552

#SPJ2