Factor the expression - 12b + 6C + 18 using the GCF. *
2(-2b + C +3)
3(-2b + c + 3)
4(-2b + c + 3)
6(-2b + C +3)
HURRY

Answer:

there is no solution

Step-by-step explanation:

x + y = 6 → (1)

x + y = 4 → (2)

subtract (2) from (1) term by term

(x - x) + (y - y) = 6 - 4

0 + 0 = 2

0 = 2 ← false statement

this false statement indicates the equations have no solution

Yes,  This is established by the Rank-Nullity Theorem, A counter-example would be a transformation that is not linear.

Yes, all linear transformations have a matrix representation. The theorem that establishes this is the Matrix Representation Theorem. This theorem states that given a linear transformation T : V → W where V and W are vector spaces over a field F, then there is a unique matrix A such that T(v) = Av for any v in V. This theorem proves that any linear transformation can be represented by a matrix.

A counter-example of a linear transformation that does not have a matrix representation is a transformation that maps a vector in one vector space to a vector in a different vector space. For example, if V is a vector space over the field F, and W is a vector space over another field K, then the linear transformation T : V → W does not have a matrix representation since the size of the matrix would need to be different for each vector in the different vector spaces.

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Answer:

x = 3

Step-by-step explanation:

The 2nd polygon is 1.5 times larger.

12 x 1.5 = 18

18-6 = 12

12/4 = 3

x = 3

Answer:

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

Step-by-step explanation:

An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating:

At the null hypothesis, we test if the mean is the same, that is:

\(H_0: \mu = 59.5\)

At the alternate hypothesis, we test that it is different, that is:

\(H_a: \mu \neq 59.5\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

59.5 is tested at the null hypothesis:

This means that \(\mu = 59.5\)

After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9.

This means that \(n = 250, X = 59.2, \sigma = 1.9\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{59.2 - 59.5}{\frac{1.9}{\sqrt{250}}}\)

\(z = -2.5\)

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a mean that differs from 59.5 by at least 0.3, which is P(|Z|>-2.5), which is 2 multiplied by the pvalue of Z = -2.5.

Looking at the z-table, Z = -2.5 has a pvalue of 0.0062

2*0.0062 = 0.0124

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

Answer:

5 each

Step-by-step explanation:

we will minus the coffee from the total

25 - 5 = 20

there's was 4 magazines so we do...

20 ÷ 4 = 5

Step-by-step explanation:

change graphic into alohabet so it is easier to see

solve easy equation with only a type of unknown first..

once you found the value of the unknownm , substitute it in any equation so you can find the value of other unknown.

Answer:

First choice

Step-by-step explanation:

Looking at the graph, as the line gets further to the right (positive x, also displayed as x-> infinity) the line continues downwards in the y (vertical) direction

Looking at the graph, as the line gets further to the left (negative x, also displayed as x-> -infinity) the line continues downwards in the y (vertical) direction

Thus, the end behavior is -infinity for both ends

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

The quadratic equation that describes the function is  

f(x) = x² + 4x + 1

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the table that describes the quadratic function h(x) as follows -

{x}                h{x}

−3               −2

−2               −3

−1                −2

0                  1

1                   6

2                  13

3                  22

The quadratic equation is of the form given -

y = ax² + bx + c

For the point (0, 1), we can write -

1 = c                                                      ..... Eq{1}

For the point (1, 6), we can write -

6 = a + b + 1

a + b = 5                                               ...... Eq{2}

For the point (2, 13), we can write -

13 = 4a + 2b + 1

4a + 2b = 12                                               ...... Eq{3}

From Eq{2}, we can write -

a = 5 - b

So, the equation 3 can be written as -

4(5 - b) + 2b = 12

20 - 4b + 2b = 12

20 - 2b = 12

2b = 8

b = 4                                    ...... Eq{4}

then

a = 1                                ...... Eq{5}

So, we can write the quadratic equation as -

f(x) = x² + 4x + 1

Therefore, the quadratic equation that describes the function is  

f(x) = x² + 4x + 1

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Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

1 day = 1440min

so 36min of a day = 36/1440 = 1/40

From the sampling distribution, the correct answer is: Both the center will remain the same, but the spread will decrease.

The center of the sampling distribution will remain the same, which is the expected proportion of even numbers showing on a single roll of the die, which is 1/2 or 0.5. This is because the probability of getting an even number on a single roll of the die does not change with the number of rolls in the experiment.

However, the spread of the sampling distribution will decrease as the number of rolls increases. This is because the larger the sample size, the more precise our estimate of the proportion of even numbers showing on each roll of the die will be. With more rolls, we will have a better idea of the true proportion of even numbers that the die produces.

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Answer:

Step-by-step explanation:

49255-1674.67=47580.33

Answer:

25/30

Simplified: 5/6

Step-by-step explanation:

Have a good day!

Please rate and mark brainliest!

Answer:

the answer is 25/30 or in a simple form 5/6

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

5 and 4 have no common factors until they are multiplied by each other. So if you were to convert your existing measurements, you would do the following.

(3/4) x (5/5)

(2/5) x (4/4)

Giving you 15/20 and 8/20

Answer:

12.14 feet

Step-by-step explanation:

16 inches = 1.4 feet

17/1.4 = 12.14 feet

Approximately, the amount of money, in cents, that Celine will save in 12 years is: B. 300

In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the money (in cents) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the years and the money (in cents), an equation for the line of best fit is given by

y = 26.9x - 18.5

when x = 12, the amount of money, in cents, that Celine will save in 12 years is given by;

y = 26.9(12) - 18.5

y ≈ 300 cents.

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Answer:

____ 1 _____ 2 ____ 3

1 __ 1, 1 ____ 1, 2 __ 1, 3

2 __2, 1 ____2, 2 __ 2, 3

Step-by-step explanation:

Given that :

Steps required for procedure One  : Either 1, 2, or 3

Steps required for procedure two  : Either 1 or 2

The first procedure has 3 possible steps

The second procedure has 2 possible steps

. The experimental outcome associated with performing the blood analysis is displayed in the table below :

____ 1 _____ 2 ____ 3

1 __ 1, 1 ____ 1, 2 __ 1, 3

2 __2, 1 ____2, 2 __ 2, 3

Answer:

x = 4

Step-by-step explanation:

Point (4, -1)

x = 4

Answer:

a. The circumference of the base is 2πr, where r is the radius of the cylinder. Therefore, the circumference of the base is:

2π(10) = 20π

So the circumference of the base is 20π.

b. The area of the base is πr^2, where r is the radius of the cylinder. Therefore, the area of the base is:

π(10)^2 = 100π

So the area of the base is 100π.

c. The lateral area of the cylinder is given by the formula 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the lateral area of the cylinder is:

2π(10)(2) = 40π

So the lateral area of the cylinder is 40π.

d. The total surface area of the cylinder is the sum of the lateral area and the areas of the two bases. The area of each base is πr^2, which we already calculated to be 100π. Therefore, the total surface area of the cylinder is:

2(100π) + 40π = 240π

So the total surface area of the cylinder is 240π.

e. The volume of the cylinder is given by the formula πr^2h, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the volume of the cylinder is:

π(10)^2(2) = 200π

So the volume of the cylinder is 200π.

Answer:

36

Step-by-step explanation:

7/6 - x = 1/2

x = 4/6 because beans

4 * 6 = 24

6 * 6 = 36

Babooshka

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The exchange rate between Japanese Yen and Nepali Rupees in this case is given by Rs 0.92 per Yen.

The exchange rate between Japanese Yen and Nepali Rupees is

1 JPY = 0.7184 NPR

Therefore, the exchange rate is  6,852 JPY = 6,320 NPR

Therefore, the exchange rate between Japanese Yen and Nepali Rupees is 0.7184 NPR per 1 JPY.

The exchange rate between Japanese Yen and Nepali Rupees is given by the following formula:

Exchange Rate = (Total Amount in Nepali Rupees/Total Number of Japanese Yen)

Exchange Rate = (Rs 6320/6852 Yens) = Rs 0.92 per Yen.

Therefore, the exchange rate between Japanese Yen and Nepali Rupees in this case is given by Rs 0.92 per Yen.

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The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

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Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

Answer:

53.65

Step-by-step explanation:

643.8 / 12 = 53.65

Answer:

Step-by-step explanation:

area of trapezium ABCD

=(16.5+12)/2 \times 15

=(28.5)/2 \times 15

=213.75 cm^2

\(\frac{PQ}{DC} =\frac{8}{12} =\frac{2}{3}\)

Area of PQRS

=213.75 \times (\frac{2}{3} )^2\\=213.75 \times\frac{4}{9} \\=95 ~cm^2

area of green portion=213.75-95=118.75 cm²

Answer:

t = 0

Step-by-step explanation:

(7t - 2) - (-3t + 1) = -3(1 - 3t)

because you can not do anything inside the parantheses, you distribute. there aren't any numbers on the left side of the parantheses on the left side of the equation so we just imagine the number 1. on the right side of the equation, just distribute normally

[ 1(7t - 2) -1(-3t + 1) = -3(1 - 3t) ]

will be

7t - 2 + 3t - 1 = -3 + 9t

add like terms

10t - 3 = -3 + 9t

subtract 9t from both sides

t - 3 = -3

add 3 to both sides

t = 0