During the problem disaggregation process, the logic trees should have branches that are?.

Answer:

-3.2

Step-by-step explanation:

-5(x+1)-9=2

first simplify by distributiom

-5(x)-5(1)-9=2

simplify the multiplication

-5x-5-9=2

add the numbers

-5x-14=2

now to get x by itself on one side we undo in reverse order and move the -14 over to the other side so add 14 to both sides to cancel the -14

-5x=2+14

simplify

-5x=16

now divide both sides by -5 to get x by itself

-5x/-5=16/-5

simplify

x=-3.2 or as a fraction, [tex]-\frac{16}{5}[/tex]

The required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

The quadratic function is defined as a function containing the highest power of a variable is two.

The quadratic function is given in the question:

2y² + 2y - 5 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 2, b = 2 and c = -5

Using the quadratic formula to solve the above quadratic function

[tex]y = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of a = 2, b = 2 and c = -5 in the above formula

[tex]y=\dfrac{-2\pm \sqrt{2^2-4\cdot \:2\left(-5\right)}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-2\pm \:2\sqrt{11}}{2\cdot \:2}[/tex]

Separate the solutions as:

[tex]y=\dfrac{-2+2\sqrt{11}}{2\cdot \:2},\:y=\dfrac{-2-2\sqrt{11}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

Therefore, the required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

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The proportional relationship between the number of books on shelf and how much shelf space the books takes up is 1 inch

What is proportionality?

The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.

When two or more parameters are directly or indirectly proportional to one another, the relationship is written as a = kb or a = k/b, where k denotes the direction of the relationship between the two variables. The proportionality constant, k.

As we know [tex]\frac{y}{x}[/tex] = constant of proportionality

So, [tex]\frac{y}{x}[/tex] will be

[tex]\frac{2}{2} = \frac{11}{11} = \frac{13}{13} = \frac{16}{16}[/tex] = 1

∴ it is 1 inch per book

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Step-by-step explanation:

when we say "a/b of c", we mean mathematically :

a/b × c

so,

a)

x = 1/5 × 15 = 15/5 = 3

b)

x = 3/4 × 48 = 3×48/4 = 3×12 = 36

Answer:

Step-by-step explanation:

a) 1/5 of 15 = ?

→ 1/5 of 15

→ (1/5) × 15

→ 15/5 = 3

So, answer is 3.

b) 3/4 of 48 = ?

→ 3/4 of 48

→ (3/4) × 48

→ 144/4 = 36

So, answer is 36.

Answer:

x = -20

Step-by-step explanation:

x/4 + 8 = 3

subtract 8 from both sides:

x/4 + 8 - 8 = 3 - 8

x/4 = -5

multiply both sides by 4:

4(x/4) = 4(-5)

x = -20

The capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter are I, N, O and S.

It is possible to rotate clockwise or counterclockwise. If an item needs to be rotated, there are several methods for doing so:

When the capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter: I, N, O and S.

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Answer:  y  =  160/q   -a

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

x = 3.5 hours

y = 1.5 hours

Step-by-step explanation:

There are two unknowns, x and y, both in umits of hours.  We need at least two equations before we start trying to solve this with substitution.  Looking at the information, this should be possible.

First, we know that Speed x Time = Distance.  

The distance covered by the cyclyst would be the sum of (12km/h)*x and (16km/h)*y, where x is the time, in hours, for the slower speed and y for the faster.  Together, the student travels 66 km.

The total distance of 66 km would be comprised of the two distances 12x and 16y:

 12x + 16y = 66 km  

For the second equation, we know that the total time is 5 hours.  That would be the sum of x and y:

 x + y = 5 hours

We now have 2 equations, so we stand a good chance of finding the answer.  Pick one of the equations and isolate one of the variables to one side.  Let's choose x + y = 5 hours, since that is easy to rearrange:

     x = 5-y

Now take the first equation and substitute the definition of x from above (5-y):

12x + 16y = 66

12(5-y) + 16y = 66

60-12y + 16y = 66

4y = 66-60

4y = 6

y = (6/4) or 1.5 h

The time spent at 16 km/h was 1.5 hours.

Use this value of y in either equation to find x.  Let's use x+y=5, since that will be easier:

x+y = 5 for y = 1.5

x+1.5 = 5

x = 3.5h

The time spent at 12 km/h was 3.5 hours

Work Shown:

p * q = 3p + 2q - 5

3 * 2 = 3(3) + 2(2) - 5

3 * 2 = 9 + 4 - 5

3 * 2 = 13 - 5

3 * 2 = 8

The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.

According to the given information line using the slope and y-intercept is; y= 1/5x + 8

thus, the slope of this line is:

m = 1/5

And its y-intercept is: c= 8

The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.

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We utilize the z statistic to find the probability percentage. Calculating the z value and then looking up the p value using the common probability tables is the process to follow. The z score formula is:

Z = (x - )/ ( / sqrt(n)

where,

Standard deviation equals 2

sample size, n With n = 5, calculating the z and p values:

The tables show that p(5) = 0.8686.

For n = 6, calculate the z and p values as follows:

The tables show that p(6) = 0.8888.

If both days to occur, the probability that each day will last no more than 11 minutes is as follows:

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There is 2.1 miles distance between the last water stop and the end of the race.

Total miles Julio will run = 13.1 miles

Distance at which water stops are location = 2.75

Total number of water stops in full race of 13.1 miles = 13.1 / 2.75

=4.764

so , there are 4 stops in the runs for drinking water every 2.75 miles

Distance from starting point of race and last water stops = 4 × 2.75 = 11 miles

Distance between the last water stop and the end of the race = 13.1 - 11

= 2.1 miles

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The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.

Here,

When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).

Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.

As a result, 186 outcomes or triplets are possible and satisfy this property.

Hence, the required probability is 186/216=31/36.

The required probability is 31/36 for three dice rolls to produce triangle sides.

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The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.

A combination is a grouping of items where order does not matter. The formula of combination is

[tex]_{n}C_{r} = \frac{n!} {r! (n-r)!}[/tex]

Where

Given the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.

What is the probability that no two adjacent people will stand?

First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.

The number of arrangements according to the number of people standing.

Case 1: 0 people standing = 1 arrangement.

Case 2: 1 people standing = [tex]_{8}C_{1}[/tex] = [tex]\frac{8!} {1! 7!}[/tex] = 8 arrangements.

Case3: 2 people standing = [tex]_{8}C_{2}[/tex] = [tex]\frac{8!} {2! 6!}[/tex] = [tex]\frac{7 \times 8} {2}[/tex] = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.

Case 4: 3 people standing = [tex]_{8}C_{3}[/tex] = [tex]\frac{8!} {3! 5!}[/tex] = [tex]\frac{6 \times 7 \times 8} {6}[/tex] = 56 arrangements. In this case, three people standing are next to each other = [tex]_{8}C_{1}[/tex] = 8 arrangements. Two people standing are next to each other and the third person is not = [tex]_{8}C_{1} \times _{4}C_{1}[/tex] = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.

Case 5: 4 people standing but no two adjacent people = 2 arrangements.

The number of arrangements that no two adjacent people will stand.

n(A) = 1 + 8 + 20 + 16 + 2 = 47

The probability that no two adjacent people will stand is

P(A) = n(A)/n(S)

P(A) = 47/256

Hence, the probability that no two adjacent people will stand is 47/256.

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√14 feet, A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. A point in a plane has specific coordinates, as we are aware. Any point's location on a plane can be described by an ordered pair of numbers, or coordinates, which are written as ((x,y)).

A coordinate can be expressed in one of three ways. a coordinate with an integer for degrees, a real number for minutes, and an integer for seconds (DMS). a coordinate that contains minutes (a real number) and degrees (an integer) (MinDec). a coordinate that merely contains degrees (real number).

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Answer: [tex]f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x[/tex].

[tex]x=(2y+1)^2\\\\\pm \sqrt{x}=2y+1\\\\-1 \pm \sqrt{x}=2y\\\\y=-\frac{1}{2} \pm \frac{\sqrt{x}}{2}[/tex]

Since the domain of the original function is the same as the range of the inverse, the rate of [tex]f^{-1}(x)[/tex] is [tex]f^{-1}(x) \geq -1/2[/tex]. This means we consider the positive case.

[tex]\therefore f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]

a.  I would rather compound annually at 5 % interest

b.  I would increase the simple interest rate if i were to change my answer

Since you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually, we need to determine the amount of each type of interest after 10 years.

Since  you have $200 to invest for 10 years at  7% simple interest, using the simple interest formula for the amount, we have

A = P(1 + rt) where

Substituting the values of the variables into the equation, we have

A = P(1 + rt)

A = 200(1 + 0.07 × 10)

A = 200(1 + 0.7)

A = 200(1.7)

A = 340

Also, since  you have $200 to invest for 10 years at  5% interest compounded annually, using the compound interest formula for the amount, we have

A' = P(1 + r)ⁿ where

Substituting the values of the variables into the equation, we have

A' = P(1 + r)ⁿ

A' = 200(1 + 0.07)¹⁰

A' = 200(1.07)¹⁰

A' = 200(1.9672)

A' = 393.43

Since A' = $393.43 > A = $340, i would rather compound annually at 5 % interest

To change my answer, I would increase the simple interest rate if i were to change my answer

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The reflection of point produce an image at the same coordinates, (0, k) is a reflection of the point across the y-axis.

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting a figure in a line or a point.

Every point of a figure is translated to an image across a fixed line via a reflection. The fixed line is referred to as the reflection line.

Given:

A point has the coordinates (0, k).

The rule for a reflection of a point across the x-axis is:

(x, y) ----> (x, -y)

and, the reflection is (0 , -k)

The rule for a reflection of a point across the y-axis is:

(x, y) ----> (-x, y)

and, the reflection is (-0 , k) or (0, k).

The rule for a reflection of a point across the line y = x is:

(x, y) ----> (y, x)

and, the reflection is (k, 0).

and, The rule for a reflection of a point across the line y = -x is:

(x, y) ----> (-y, x)

and, the reflection is (-k, 0)

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Pieces of data such as $18,000 and $350,000 represent outliers in this chart in standard deviation .

How to interpret a standard deviation?

In this chart, there are outliers. The main outliers are $18,000 and $350,000. This is because we know the mean or average is $63,423, and therefore values that are too different from this average are considered outliers.

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Answer:

We may use the logarithm formula,

N = ln(EV/SV) ÷ ln(1+r), where (1+ r) is the value of 1 plus interest for 1 year.

EV is end value, SV is start value.

EV is 20000, SV is 12000, interest is 5.6% semi annual

(1+r) is obtained as,

Step-by-step explanation:

The percentage decrease of the population of a city is 19%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, the population of a city was 325,000 and several years later it was 263,250.

The percentage decrease will be:

= Decrease in population / Original population × 100

= (325000 - 263250) / 325000 × 100

= 61750 / 325000 × 100

= 19%

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Using the simple interest formula, Mr. Solo received $26 interest.

In the given question we have to find how much interest Mr. Solo received.

The investment(P) = $325.

Interest rate(R) = 8%

Time(T) = 1 year

Finding the interest using the simple interest formula.

I = PRT/100

where I = interest

P = Principal Amount

T = Time

R = Interest Rate

Putting the value

I = 325*8*1/100

I = 26

Hence, Mr. Solo received $26 interest.

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The completed statement with regards to Chang and Carlotta's methods used for solving the word problem is presented as follows;

A word problem in mathematics and science is the verbal presentation of the information in a scenario required to mathematically solve a problem.

The steps to solve the problem is presented as follows;

The amount in the bank account = $50

Amount made per hour by mowing lawns = $8

The number of hours put into mowing lawns in order to have a total of $130 in the account can be found by using the equation;

The amount in the account increases based on the number of hours used for mowing lawns, therefore;

130 = 50 + 8 × h

8·h = 130 - 50 = 80

h = 80/8 = 10

Ten hours of lawn mowing is required to have a total of $130 in the bank.

Chang's method involve the use of expressing the situation mathematically, by use of variables.

Carlotta's method involves the use of verbal expressions to outline the relationship between the variables, simplifying them to arrive at the determining variable that indicates the number of hours require.

Therefore;

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Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

now let's consider the white, "cut-out" triangle on the left side.

the purple one angles at the top and bottom corner are 45°.

the withe outer angles at the same corners (they are the inner angles for the white triangle) are complementary angles (together they have 90°) to the purple ones, because due to the equal angles at the top and bottom we know the connection between the 2 45° angles (the white baseline) is at a 90° angle to the 45° to 135° sides.

so the 2 baseline angles of the left white triangle are also 45° (45+45 = 90).

and that means that the third white angle is

180 - 45 - 45 = 90°.

and because a full circle around the 3x° point must have 360° (as any full circle), we know that both angles (90° and 3x°) together are 360°.

360 = 90 + 3x

270 = 3x

x = 90°

3x = 270°

The sum of the numerator and denominator of the decimal is found as 111.

As for the given question;

The decimal number is given as;

0.12 bar

Decimal to fraction conversion

100(0.12 bar) = 12(0.12 bar)

99.(0.12bar) = 100(0.12bar) - (0.12 bar)

99.(0.12bar) = 12 × 0.12bar - 0.12bar

99.(0.12bar) = 12

0.12 bar = 12/99 (lowest fraction)

Thus, in the result the numerator is found as 12 and the denominator is found as 99.

Add = 12 + 99

Add = 111

Thus, the sum of the numerator and denominator of the decimal is found as 111.

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Answer:

2.43

Step-by-step explanation:

The quotient is the answer to a division problem.

67.98/28 = ~2.42785714286

To round to the nearest hundredth, leave 2 decimal digits remaining. If the thousandth place (3rd decimal digit) is greater they or equal to 5, add 1 to the hundredths digits.

7 [tex]\geq[/tex] 5

2.42+0.01

2.43