what is the answer of 20 plus 12

Answer:

X+2

Step-by-step explanation:

A number is x plus 2

X+2

Answer:

\(\left(3m+5n\right)\left(9m^2-15mn+25n^2\right)\)

Step-by-step explanation:

\(27m^3+125n^3=\left(3m\right)^3+\left(5n\right)^3\)

Apply sum of cubes formula: \(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)\)

\(\left(3m\right)^3+\left(5n\right)^3=\left(3m+5n\right)\left(3^2m^2-3m\times 5n+5^2n^2\right)\)

\(\left(3m+5n\right)\left(9m^2-15mn+25n^2\right)\)

The factored form of 27 m³ + 125 n³ will be ( 3m + 5n ) [ 9m² - 15mn + 25n²]

An expression is given which is 27 m³ + 125 n³.

We have to find out the factored form of the above expression.

What is the formula for a³ + b ³ ?

The formula for a³ + b³ is a³ + b³ = ( a + b ) ( a² - ab + b² ).

As per the question ;

Expression given is ; 27 m³ + 125 n³

here , a = 3m and b = 5n

The factored form of the above expression will be ;

∵ a³ + b³ = ( a + b ) ( a² - ab + b² )

⇒ (3m)³ + (5n)³ = ( 3m + 5n ) [ (3m)² - ( 3m × 5n ) + (5n)²]

                        =  ( 3m + 5n ) [ 9m² - 15mn + 25n²]

Thus , the factored form of 27 m³ + 125 n³ will be ( 3m + 5n ) [ 9m² - 15mn + 25n²]

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Answer:

12.1

Step-by-step explanation:

A^2+b^2=c^2

a^2+49=196

196-49=a^2

sqrt147=a

12.1=a

Answer:

x = 12.1 in.

Step-by-step explanation:

a² + b² = c²

7² + x² = 14²

49 + x² = 196

x² = 147

x = sqrt(147)

x = 12.1 in.

There are 144 combinations of 1 entree, 2 vegetables, and 1 dessert that can be selected from 4 entrees, 6 vegetables, and 6 desserts.

To determine the number of combinations, we multiply the number of options for each category.

For the entree, we have 4 options to choose from.

For the vegetables, we need to select 2 out of 6, which can be done in 6 choose 2 ways.

This is calculated as 6! / (2!(6-2)!), which simplifies to

6! / (2!4!)

Similarly, for the dessert, we have 6 options to choose from.

To calculate 6 choose 2, we can use the formula for combinations:

n choose r = n! / (r!(n-r)!).

Plugging in the values, we have

6! / (2!4!) = (6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (4 × 3 × 2 × 1)] = 15.

Therefore, we have 4 options for the entree, 15 options for the vegetables, and 6 options for the dessert.

Multiplying these numbers together, we get 4 × 15 × 6 = 144.

Therefore, there are 144 possible combinations of 1 entree, 2 vegetables, and 1 dessert, given the options of 4 entrees, 6 vegetables, and 6 desserts.

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9514 1404 393

Answer:

  D.  AC ⊥ BD

Step-by-step explanation:

Given that  ABCD is a parallelogram, we already know A (BD bisects AC) and B (AB ║ CD). Statement C (AC ≅ BD) will not be true for a parallelogram or rhombus.

Statement D (AC ⊥ BD) guarantees the parallelogram is a rhombus.

Therefore, the required answer is 0.7565,  csc(x) = 27/8Let us first find sin(x):We know that, csc(x) = 1/sin(x)csc(x) = 27/8, we can write,1/sin(x) = 27/8sin(x) = 8/27

Now, we can find the value of cos(x) by using the Pythagorean identity: cos(x) = sqrt(1 - sin^2(x))= sqrt(1 - (8/27)^2)= sqrt(605/729)Therefore, cos(x) = 0.8726 (approx)

Now, let's find the value of cos(2x):cos(2x) = cos^2(x) - sin^2(x)= (cos(x))^2 - (sin(x))^2We know the value of sin(x) and cos(x) from above,

substituting the values,cos(2x) = (0.8726)^2 - (8/27)^2= 0.7565Therefore, cos(2x) = 0.7565 (approx)Therefore, the required answer is 0.7565,

which is accurate to 4 decimal places. Note: We have to write a solution of at least 250 words for questions which are descriptive.

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Randy needs 8 loads.

To find the answer on the question we have to follow the method of multiplication and division .

A washing machine can hold \(\frac{3}{4}\) kg of laundry in each load.

\(\frac{3}{4}\) kg of laundry is equal to 1 load.

\(\frac{3}{4}\) kg of laundry =  1 load

1 kg of laundry  =  \(\frac{1 * 4}{3}\) load ( following the method of division )

1 kg of laundry = \(\frac{4}{3}\) load

Randy has 6kg of laundry.

So, 1kg of laundry i.e \(\frac{4}{3}\) load is to be multiplied by 6.

6kg of laundry = \(\frac{4 * 6}{3}\) load ( following the method of multiplication)

                         = 8 loads

Hence, Randy needs 8 loads.

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Answer: Q=(9,5)

Step-by-step explanation: this is because 3 went to 6 and if you add 3 more it would be 9 and plus 3 and 4 so it would e five

Answer:

-2.5

Step-by-step explanation:

-36= -12y+(-48)+(-12y)+(-48)

-36= (-24y)+(-96)

+96             +96

60= -24y

divide 60 by -24y and you get -2.5

Answer:

x ≈ 31.0°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanx = \(\frac{opposite}{adjacent}\) = \(\frac{9}{15}\), then

x = \(tan^{-1}\) (\(\frac{9}{15}\) ) ≈ 31.0° ( to 1 dec. place )

The solution of the quadratic equation x² + 7x - 18 = 0 will be 2 and negative 9.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The quadratic equation is given below.

x² + 7x - 18 = 0

Factorize the quadratic equation, then we have

x² + 7x - 18 = 0

x² + 9x - 2x - 18 = 0

x(x + 9) - 2(x - 9) = 0

(x + 9)(x - 2) = 0

x = 2, -9

The arrangement of the quadratic condition x² + 7x - 18 = 0 will be 2 and negative 9.

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The sum of the infinite geometric series –288 –216 –144 –72 is -1152.

The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.

Given series, -288, -216, -144, -72, ...

The sum of the infinite geometric series can be calculated as:

Sum = \(\dfrac{a}{1 -r}\)

Here, 'a' is the first term of the series and 'r' is the common ratio.

a = -288

The common difference can be calculated as:

r = \(\dfrac{(-216)}{(-288)}\)

= \(\dfrac{3}{4}\)

Substitute the values in the sum formula:

Sum = \(\dfrac{-288}{1 - \dfrac{3}{4}}\)

It can be simplified as:

Sum =  -288 \(\times\) 4

             = -1152

So, the sum of the infinite geometric series is -1152.

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The area to the left of the z-score corresponds to the cumulative probability up to that point. The correct answer is b. z=0.84.

To find the z-score that separates the top 70% from the bottom 30%, we need to look up the corresponding percentile in a standard normal distribution table.

The area to the left of the z-score corresponds to the cumulative probability up to that point. For example, if we look up a z-score of 0.84 in the table, we find that the area to the left of that value is 0.7995, or 79.95%.

Since we want to find the value that separates the top 70% from the bottom 30%, we subtract 0.30 (or 30%) from 1.00 to get 0.70 (or 70%). We then find the z-score that corresponds to that area, which is approximately 0.84.

Therefore, the answer is b. z=0.84.

To find the Z-score value that separates the top 70% of a normal distribution from the bottom 30%, you need to look for the Z-score corresponding to the 70th percentile. In this case, the correct answer is:

b. z=0.52

Here's a step-by-step explanation:

1. Determine the percentile you're looking for, which is the 70th percentile (separating the top 70% from the bottom 30%).
2. Consult a Z-score table or use a calculator to find the Z-score corresponding to the 70th percentile.
3. The Z-score for the 70th percentile is approximately 0.52.

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a)  the vectors in b are linearly independent and span R^2, we can conclude that b is a basis for R^2.

(a) To prove that the set of vectors b = {(3, 4), (1, 2)} is a basis for R^2, we need to show two things: linear independence and spanning.

Linear independence: We need to show that the vectors in b are linearly independent, which means that there is no non-trivial linear combination of the vectors that equals the zero vector.

Let's assume that we have scalars a and b such that a(3, 4) + b(1, 2) = (0, 0). This leads to the following system of equations:

3a + b = 0

4a + 2b = 0

Solving this system, we find that a = 0 and b = 0. Since the only solution to the system is the trivial solution, the vectors (3, 4) and (1, 2) are linearly independent.

Spanning: We need to show that any vector in R^2 can be expressed as a linear combination of the vectors in b. In other words, we need to show that for any vector (x, y) in R^2, there exist scalars a and b such that a(3, 4) + b(1, 2) = (x, y).

Solving this system of equations, we find a = (2x - y)/5 and b = (3y - x)/5. This shows that any vector (x, y) in R^2 can be expressed as a linear combination of (3, 4) and (1, 2).

(b) To perform the Gram-Schmidt orthonormalization process on the set of vectors b = {(3, 4), (1, 2)}, we can follow these steps:

Step 1: Normalize the first vector:

u1 = (3, 4) / ||(3, 4)|| = (3, 4) / 5 = (0.6, 0.8)

Step 2: Subtract the projection of the second vector onto the first vector:

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The sum of infinite geometric series is

\(25 - 10 + 4 - \frac{8}{5}\)

is \(\frac{125}{7}\)

What is geometric series?

The series where the ratio between the consecutive terms of the series are same is called geometric series.

The sum of infinite geometric series is

\(25 - 10 + 4 - \frac{8}{5}\)

Here

common ratio (r) = \(-\frac{10}{25} = -\frac{2}{5}\)

Here r lies between -1 and 1

So the given geometric series converges

First term is 25

Sum =

\(\frac{25}{1 -(-\frac{2}{5})}\\\\\frac{25}{\frac{5+2}{5}}\\\\\frac{25}{\frac{7}{5}}\\\\\frac{25 \times 5}{7}\\\\\frac{125}{7}\)

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the following expression i.e. (1.8x10⁹) (6.7 x 10¹²) in Scientific Notation is 120.6×\(10^{20}\) and a=120.6 and b=20

Scientific notation:

Scientific notation is a method of presenting very large or very small numbers in a more simplified format. We know that whole numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers found after the decimal point needed to be represented in a more straightforward manner.

(1.8x10⁹) (6.7 x 10¹²) = 120.6×\(10^{20}\)

Given (1.8x10⁹) (6.7 x 10¹²) =a x \(10^{b}\)

a x \(10^{b}\)= 120.6×\(10^{20}\)

a=120.6 and b=20

Therefore,the following expression i.e. (1.8x10⁹) (6.7 x 10¹²) in Scientific Notation is 120.6×\(10^{20}\) and a=120.6 and b=20

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The value of x from the solution =4
The value of y from the solution =7

Equation 1: 2x + y = 15
Equation 2: y + 5 = 3x

Let's solve for y in Equation 1:

y = 15 - 2x

Now, substitute this expression for y in Equation 2:

(15 - 2x) + 5 = 3x

Simplify and solve for x:

15 - 2x + 5 = 3x
20 = 5x
x = 4

Now that we have the value of x, substitute it back into the expression for y:

y = 15 - 2(4)
y = 15 - 8
y = 7

So, the solution for the system of equations is x = 4 and y = 7.

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The drawer contains 11 identical red socks and 8 identical black socks. Here are the answers to the questions below

a. What is the probability that you get a pair of red socks?The probability of getting a pair of red socks is the probability of selecting two red socks, which is: P(Red and Red) = P(Red) × P(Red | Red was first) = (11/19) × (10/18) = 55/171.

b. What is the probability that you get a pair of black socks?The probability of getting a pair of black socks is the probability of selecting two black socks, which is: P(Black and Black) = P(Black) × P(Black | Black was first) = (8/19) × (7/18) = 28/171.

c. What is the probability that you get 2 unmatched socks?The probability of getting two unmatched socks is the sum of the probability of selecting a red sock first and a black sock second and the probability of selecting a black sock first and a red sock second: P(Red and Black or Black and Red) = P(Red) × P(Black | Red was first) + P(Black) × P(Red | Black was first) = (11/19) × (8/18) + (8/19) × (11/18) = 88/171.

d. Where did the other red sock go? It's not clear from the information given. It could be missing or misplaced, or it could be in the drawer, but the problem doesn't provide enough information to determine what happened to it.

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The probability that a girl answers the door when the Smiths' children open depends on the gender distribution of their children. The probability that a girl answers the door is 1/3 or approximately 33.33%.

Without any additional information about the Smiths family, we cannot determine the exact probability. However, if we assume that the probability of having a boy or a girl is equal (i.e., a 50% chance for each), we can make an estimate.

Under this assumption, let's consider the possible outcomes for the Smiths' children: BB (both boys), BG (one boy and one girl), and GG (both girls). Since we know that one of their children will answer the door, the outcomes BB and BG are possible scenarios in which a boy answers. The only scenario in which a girl answer is GG. Therefore, the probability that a girl answers the door is 1/3 or approximately 33.33%.

It is important to note that this estimation assumes an equal probability for each gender and that the gender of one child does not affect the gender of the other. In reality, the probability could differ depending on the specific circumstances and family dynamics of the Smiths.

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Answer:

hjyfgtuygtfvfvhjkoijuhgytfrdetrft

Step-by-step explanation:

dcfgvhbjnkiouytrfdr

Answer:

-2.94

Step-by-step explanation:

I got the answer correct on edge

Answer:

.30 cents

Step-by-step explanation:

11-5=6

6 divided by 20

The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

What is the intermediate value theorem?

Intermediate value theorem is theorem about all possible y-value in between two known y-value.

x-intercepts

-x^2 + x + 2 = 0

x^2 - x - 2 = 0

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

x = -1, x = 2

y intercepts

f(0) = -x^2 + x + 2

f(0) = -0^2 + 0 + 2

f(0) = 2

(Graph attached)

From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3

For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.

Your question is not complete, but most probably your full questions was

Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?

Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

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The new coordinates of the given rectangle after the dilation are:

J'(3, 12)

K'(18, 12)

L'(18, 3)

M'(3, 3)

Dilation is defined as a transformation, that is used to resize the object. Dilation is used to make the objects either larger or smaller.

The coordinates of the given rectangle are given as:

J(1, 4)

K(6, 4)

L(6, 1)

M(1, 1)

Thus, a dilation of (x, y) → (3x, 3y) will be:

J'(3, 12)

K'(18, 12)

L'(18, 3)

M'(3, 3)

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Answer:

\(x = -2\) and \(y = \frac{5}{3}\)

Step-by-step explanation:

Given

\(y = \frac{2}{3}x + 3\)

\(x = -2\)

Required

Determine the solution to the equations

From the second equation, we have the value of x already;

The next step is to substitute -2 for x in the first equation

\(y = \frac{2}{3}x + 3\) becomes

\(y = \frac{2}{3}(-2) + 3\)

\(y = \frac{-4}{3} + 3\)

\(y = -\frac{4}{3} + 3\)

Take LCM

\(y = \frac{-4 + 9}{3}\)

\(y = \frac{5}{3}\)

Hence,

\(x = -2\) and \(y = \frac{5}{3}\)

Answer:

The student would walk 205 feet

Step-by-step explanation:

Since Street A would represent a hypotenuse, use Pythagorean Theorem to solve:

a^2 + b^2 = c^2

156^2 + 133^2

24336 + 17689 = square root of 42025

square root of 42025 = 205

Answer:

\(y=-\frac{4}{3} x+\frac{10}{3}\)

Step-by-step explanation:

First, we need to get this in y=mx+b form.

m=slope

b=y axis intercept

8x+6y+1=0

8x+6y=-1

6y=-8x-1

\(y=-\frac{4}{3}x-\frac{1}{6}\)

now that we have it in y=mx+b form, we know the slope. For the new equation, the slope will be the same and the only thing we don't know is the y axis intercept, so we'll have to solve for it.

\(6=-\frac{4}{3}(-2)+b\\6=\frac{8}{3} +b\\\frac{10}{3}=b\)

Now that we know b, we just put it with the rest of the equation.

\(y=-\frac{4}{3} x+\frac{10}{3}\)

Answer:

The value needed now is $102,296.60

Step-by-step explanation:

Here, we want to calculate the present value needed.

We shall be using the formula for compound interest here

Mathematically;

A = I(1 + r/n)^nt

According to the question;

I is the initial amount which is what we want to calculate

A is the accumulated amount with interest = 140,000

r is the interest rate = 8% = 8/100 = 0.08

n is the number of times interest is compounded which is 4, since it is quarterly

t is the number of years = 2

Substituting these values, we have ;

140,000 = I(1 + 0.08/2)^(4 * 2)

140,000 = I(1.04)^8

I = 140,000/(1.04)^8

I = 102,296.62870027774

Which is I = $102,296.60 to the nearest cent

Answer:

Yes, it's 30.

Step-by-step explanation:

50% means half.

60 x 0.5 = 30

By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on.

The dotplot that displays the data correctly is the one titled "Roger's Training" with a number line labeled "Miles Run" that goes from 0.5 to 5 in increments of 0.5. The dotplot should have the following data points:
0.5, 4
1, 1
1.5, 2
2, 2
2.5, 3
3, 2
3.5, 0
4, 3
4.5, 2
5, 1
This dotplot accurately represents the number of miles Roger ran each day over a 20-day period. Each dot represents a data point from the given list of miles run. The number line indicates the range of miles run, starting from 0.5 and ending at 5, with increments of 0.5.
By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on. This visual representation allows you to easily interpret the data and observe any patterns or trends in Roger's training.

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Answer:  greatest number of bunches using all balloon is 48, using purple ballon is 27

Step-by-step explanation: