Evaluate the expression 5x + 3y - 2 when x = 2 and y = 5

Answer:

Step-by-step explanation:

We can use the concept of unit rate to find the constant of proportionality between the number of packets and the number of beads.

For the first case, with 3 packets and 36 beads, the unit rate is 36/3 = 12 beads per packet.

For the second case, with 4 packets and 48 beads, the unit rate is 48/4 = 12 beads per packet.

We can see that the unit rate is the same for both cases, so we can conclude that the relationship between the number of packets and the number of beads is proportional, and the constant of proportionality is 12 beads per packet.

Therefore, the equation that models this relationship is:

b = 12p,

where b is the number of beads and p is the number of packets.

Vaishyas were merchants and farmers, Shudras were manual laborers, and Dalits, also known as Untouchables, were considered outside the caste system and faced significant social and economic discrimination.

These are the traditional castes or social classes in Hinduism. The Brahmins were highly respected as they were members of this highest caste. Priest, scholars, and teachers were some of the jobs in this cast so I chose praying hands and a book to represent them.

The praying hands shows they were religious leaders who passed down oral and written traditions. The book represents the teachers in this caste, they would share knowledge and Information about their way of life.

Kshatriyas were warriors and rulers,

However, the caste system has been officially abolished in India, and discrimination based on caste is now illegal.

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Answer:

47

Step-by-step explanation:

a = número original de bolitas azules

r = número original de bolitas rojas

Al cabo de 5 días:

a + 5 × 2 = r - 5 × 3

Al cabo de 9 días:

a + 9 × 2 = 2(r - 9 × 3)

a + 10 = r - 15

a + 18 = 2r - 54

a = r - 25

a + 18 = 2r - 54

a = r - 25

r - 25 + 18 = 2r - 54

a = r - 25

-r = -47

r = 47

Answer: 47

Answer:

(26, ∞)

Step-by-step explanation:

(I am assuming the question has been copied and pasted properly because the answer is not as simple as computing inequalities. It also involves using triangle properties)

Let the sides of the triangle be
x, y and z where x is the base

Let y be the side which is 9cm shorter than x:
y = x - 9

Let z be the side which is17cm longer than x:
z = x + 17

Perimeter = x + y + z

= x + (x-9) + (x + 17)

= x + x + x -9 + 17

= 3x + 8

We are told that the perimeter should be at least 32 cm

So 3x + 8 ≥ 32

Subtract 8 from both sides of the inequality:
==> 3x + 8 - 8 ≥ 32 - 8

==>  3x ≥ 24

Divide by 3 both sides:
==> 3x/3 ≥ 24/3

==> x ≥ 8

If these were inequalities in x, then this would be the solution and the interval will be [8, ∞ ]

However, we can see that some of the values for x are impossible within this inequality

For example, for x = 8, y = -1
for x = 9 y = 0 and both these are not possible in a triangle

Since these are the sides of a triangle. In any triangle, the sum of any two sides must be greater than the third side

In this particular triangle, the shortest side is y=  x - 9 and the longest side is z = x + 17

So the shortest side + x > longest side

x + y > z

==> x + x -9 > x +17

2x - 9 > x + 17

Moving x to the left side and -9 to the right side

2x - x > 17 + 9

x > 26

So x must be greater than 26 and it can go all the way to infinity. Remember x need not be an integer

The interval is (26, ∞)

The most appropriate choice for dilation and vertical dilation will be given by:

Equation of new graph => C.y= -1/4 |x|

Dilation is the process of changing the dimension of an object by some scale factor.

Suppose the scale factor is K. Let the equation be y=f(x) . Then vertical dilation of  is y= K.f(x)

Here, we have,

y = |x| ,

is reflected across the x-axis

Equation after reflection from x - axis = - |x|

Now, y = - |x|, is  scaled vertically by a factor of 1/4

Equation of new graph => y= -1/4 |x|

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The "uncertain digit" is the final digit of a measured value whose precise value we are unsure about.

The total number of certain digits in a measurement plus one estimated or uncertain digit make up the significant figures.

Thus, the "uncertain digit" is the final digit of a measured value whose precise value we are unsure about.

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Answer:

Step-by-step explanation:

c

Answer:

5 feet

Step-by-step explanation:

Let's call the width of the rectangle "w". Then, the length would be "w + 7".

The perimeter of the rectangle is given as 34 feet, so we can set up an equation using the two sides of the rectangle:

2w + 2(w + 7) = 34

Expanding the second term and simplifying the equation, we get:

2w + 2w + 14 = 34

4w + 14 = 34

4w = 20

w = 5

Therefore, the width of the rectangle is 5 feet.

The vertex form of an equation is,

⇒ y = - 7 (x - 1)² + 2

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ y = - 7x² + 14x - 5

Now, We can solve the equation for the vertex form as;

⇒ y = - 7x² + 14x - 5

⇒ y = - 7 (x² - 2x + 1) + 7 - 5

⇒ y = - 7 (x - 1)² + 2

Thus, The vertex form of an equation is,

⇒ y = - 7 (x - 1)² + 2

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The orange straws make up 41.7 percent of the total straws in the box.

First, let's find the total number of blue straws:

Number of blue straws = Number of blue stricent + Number of blue straws = 6 + 0 = 6

Next, let's find the total number of pink straws:

Number of pink straws = 12

And finally, let's find the number of orange straws:

Number of orange straws = Total number of straws - (Number of blue straws + Number of pink straws + Number of white straws)

Number of orange straws = 36 - (6 + 12 + 3)

Number of orange straws = 36 - 21

Number of orange straws = 15

So, the orange straws make up 15 out of 36 total straws, or 15/36 of the total. To express this as a decimal, we can divide 15 by 36:

15/36 = 0.417

And to express this as a percentage, we can multiply the decimal by 100:

0.417 * 100 = 41.7%

So, the orange straws make up 41.7% of the total straws in the box.

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The XOR (exclusive or) of two events A and B can be defined as the set of all elements that are in either A or B but not both.

The probability of this event, P(AAB), can be calculated by summing the probabilities of A and B and subtracting twice the probability of the intersection of A and B, as follows:

P(AAB) = P(A) + P(B) - 2P(AnB)

This can be illustrated with a Venn diagram, where A and B are represented by two overlapping circles. The intersection of A and B, AnB, is represented by the overlapping region, and the symmetric difference, AAB, is represented by the non-overlapping regions of A and B.

The probability of AAB can then be calculated by adding the area of the two non-overlapping regions and subtracting twice the area of the overlapping region.

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Answer: To solve for x, we need to find the value of x that makes both equations equal to each other. We can do this by setting the two equations equal to each other and solving for x:

3x + 2 = 4x - 5

Subtracting 4x from both sides:

-x - 2 = -5

Adding 2 to both sides:

-x = -3

Finally, dividing both sides by -1:

x = 3

So x = 3 is the solution that makes both y = 3x + 2 and y = 4x - 5 equal to each other.

You can substitute x = 3 into either equation to find the corresponding y value:

y = 3x + 2, when x = 3, y = 3(3) + 2 = 9 + 2 = 11

y = 4x - 5, when x = 3, y = 4(3) - 5 = 12 - 5 = 7

So the solution is (x, y) = (3, 11) or (3, 7).

Step-by-step explanation:

Increasing the compounding interval from annual to daily has a positive impact on the future value of an investment and a negative impact on the present value of an investment.

The compounding interval refers to the frequency at which interest is calculated and added to the balance of an investment. Increasing the compounding interval from annual to daily will impact the future value and present value of an investment.

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To prove: If one angle of a triangle is 90°, then the sum of the other two angles is equal to 90°. is sum of angles on a triangle is 180 degrees

In a triangle, the sum of the interior angles in the triangle is 180 degrees

For right triangle, that is angle that has one side as 90 degrees, the sum of the other two sides will be 90 degrees

Assuming the other angles are x and y, then a side is 90 degrees

x + y + 90 = 180 (sum of interior angles on a triangle)

x + y = 180 - 90

x + y = 90 degrees

hence the sum of the interior angles is 90 degrees

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Step-by-step explanation:

[tex]14y + \frac{37}{5} - 8(2y - 1)[/tex]

BODMAS:

We deal with the brackets first

[tex]8(2y - 1) [/tex]

we multiply everything in the brackets with 8

[tex] - 8 \times 2y = - 16y[/tex]

[tex] - 8 \times - 1 = 8[/tex]

[tex]14y + \frac{37}{5} - 16y + 8[/tex]

Let's bring the like-terms together by rearranging the question

[tex]14y - 16y + 8 + \frac{37}{5} [/tex]

[tex]14y - 16y = - 2y[/tex]

[tex]8 + \frac{37}{5} = 15.4[/tex]

[tex] - 2y + 15.4[/tex]

Based on the doubling time and starting OD600, it can be estimated that the cultures will reach an OD600 of 0.7 in late afternoon, after 3:00 PM.

To determine the time when the S. cerevisiae culture will reach an OD600 of 0.7, we need to calculate the number of doublings that will occur.

First, we need to find the difference in OD600 between the current OD600 of 0.2 and the desired OD600 of 0.7:

0.7 - 0.2 = 0.5

Next, we can use the equation for a logarithmic growth curve to determine the number of doublings required to reach an OD600 of 0.7:

ln(0.7/0.2) / ln(2) = n

where n is the number of doublings required.

Next, we can multiply n by the doubling time of 90 minutes to determine the total time required to reach an OD600 of 0.7:

t = 90 * n

So, if it is currently 10 AM, the cultures will be ready for the experiment at

10 AM + t.

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Answer:

x = 4

Step-by-step explanation:

12x + 5 = 4x + 37

subtract 5 from both sides:

12x + 5 - 5 = 4x + 37 - 5

12x = 4x + 32

subtract 4x from both sides:

12x - 4x = 4x + 32 - 4x

8x =  32

divide both sides by 8:

8x/8 =  32/8

x = 4

Answer:

250 adult tickets

Step-by-step explanation:

s = number of student tickets

a = number of adult tickets

s = a - 56  ==> 56 fewer student tickets sold than adult tickets

s + a = 444   ==> 444 total tickets were sold

(a - 56) + a = 444  ==> plug in a - 56 for s to solve for one variable

a - 56 + a = 444

a + a - 56 = 444  ==> combine like terms

2a - 56 = 444

2a = 500  ==> add 56 on both sides

a = 250 adult tickets

s:

s + a = 444

s + 250 = 444 ==> plug in 250 for a

s = 194 student tickets sold

a - s = 56

250 - 194 = 56 √

Hence, the difference between the number of student and adult tickets is 56.

The painter takes 877.5 minutes to paint 75% of the pyramid.

A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.

Given:

base side= 40 feet

slant height = 50 feet.

So, the Surface area

= Base + 1/2 perimeter of the base x slant height

= (50x50) + 1/2 (50x4) (40)

= 2500 + 0.5 x 200 x 40

= 6500 ft²

Now, to paint 75% of the Pyramid

= 6500 / 100 x 75

= 4875

As, the painting rate 100 square feet

= 4875 /100 x 18

= 48.75 x 18

= 877.5 minutes

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Answer:

Step-by-step explanation:

Option B is correct. When researcher conducts a study, it is important to ensure that the groups being compared are well matched.

In this case, if the subjects were truly being randomly assigned to the two conditions, it is unlikely that 7 of the 8 subjects in each condition would be either all women or all men. This suggests that there might be some issue with the randomization procedure, such as bias in the selection of subjects or unequal allocation to the two conditions. This unequal representation of men and women in the two groups could potentially affect the validity of any conclusions drawn from the study, since the two groups are not well matched. Therefore, there is a problem with the design of the study.

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A. No, B. Yes, dimension is 2 and basis is y(x) = cos(2x), y(x) = sin(2x).

A. No, this set is not a vector space. The set of all skew-symmetric 3x3 matrices does not contain the zero matrix, which is a requirement for a vector space.

B. Yes, this set is a vector space. The dimension is 2, and the basis is the functions y(x) = cos(2x) and y(x) = sin(2x). To verify this is a vector space, we need to check that the set is closed under addition and scalar multiplication. For arbitrary real constants a and b, the function y(x) = a cos(2x) + b sin(2x) is a linear combination of the basis vectors. This means that it is closed under addition and scalar multiplication, so the set is a vector space

A. No, B. Yes, dimension is 2 and basis is y(x) = cos(2x), y(x) = sin(2x).

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the perimeter of the given triangles will be 119 inches and 73.5 inches.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Given a triangle that has two angles equal,

Since the isosceles triangle has both two equal sides and two equal angles.

Thus, the given triangle is an isosceles triangle

So,

7x - 13  = x + 29

6x = 42

x = 8

From the general formula of the perimeter:

The perimeter of a triangle = sum of all sides

In our case,

perimeter  = 7x - 13  + x + 29+ 3x + 5

perimeter = 11x +31

Substitute the value of x

Perimeter = 11 * 8 + 31

The perimeter of the triangle = 119 in.

The same process will be followed in question number 11

and the perimeter of the triangle in question 11 will be 73.5 inches

Therefore, the perimeter of the given triangles will be 119 inches and 73.5 inches.

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there are four factors, giving it a fourth degree. This is the polynomial function of least degree that has the zeros 3, 6, and √6.

f(x) = (x - 3)(x - 6)(x - √6)(x + √6)

We start by listing out the zeros

3, 6, √6

Now, we can write the polynomial function of least degree that has these zeros

f(x) = (x - 3)(x - 6)(x - √6)(x + √6)

Note that this is a fourth degree polynomial because it has four factors.

We can write a polynomial function of least degree that has the following zeros: 3, 6, and √6. This polynomial function is a fourth degree polynomial, which means it has four factors. We can write it as f(x) = (x - 3)(x - 6)(x - √6)(x + √6). This polynomial function has the zeros 3, 6, and √6, and any other x-value that makes the equation equal to 0. The degree of the polynomial depends on how many factors are in the equation, and in this case, there are four factors, giving it a fourth degree. This is the polynomial function of least degree that has the zeros 3, 6, and √6.

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a) The solution to the equation is y = ( 21,600 - 3.6x ) / 7.5 , where y is the number of trucks and x is the number of cars

b) when x = 1,000 cars , y = 2,400 trucks and

when x = 4,250 cars , y = 840 trucks

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of cars be x

Let the number of trucks be y

The total cargo the ship can hold = 21,600 tons

The weight of one car = 3.6 ton

The weight of one truck = 7.5 tons

Now , the equation will be

3.6x + 7.5y = 21,600

On simplifying the equation , we get

Subtracting 3.6x on both sides of the equation , we get

7.5y = ( 21600 - 3.6x )

Divide by 7.5 on both sides of the equation , we get

y = ( 21,600 - 3.6x ) / 7.5

The number of trucks y = ( 21,600 - 3.6x ) / 7.5

b)

Now , when x = 1000 cars

Substitute the value of x in the equation , we get

y = ( 21,600 - 3.6 ( 1000 ) ) / 7.5

y = 2,400 trucks

And , when x = 4250 cars

Substitute the value of x in the equation , we get

y = ( 21,600 - 3.6 ( 4250 ) ) / 7.5

y = 840 trucks

Hence , the equation is y = ( 21,600 - 3.6x ) / 7.5

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The ending balance on your account on November 15, 2004, was $142.72.

The ending balance is the arithmetic difference between the beginning balance, deposits, and withdrawals, including interest and finance charges.

To determine the ending balance, add all deposits to the beginning balance and deduct all charges against the account

Beginning balance                           $200.00

Nov. 13, 2004 Groceries Purchase    $42.63    $157.37

Nov. 14 Deposit                                   $20.45   $177.85

Nov. 15, 2004 Check for textbook     $35.10   $142.72

Thus, based on your beginning balance, deposits, purchases, and checks, the ending balance has been determined as $142.72.

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Indicate your remaining balance.​

The amount more that the cardholder will pay, given the amount owed and the monthly payment, is D. $ 1, 465. 96.

You can use a credit card repayment calculator to find the payment period when you have a credit card balance of $ 4, 528. 34, an interest rate of 22. 99 % and monthly payments of $ 200.

This repayment period would be 29. 97 or 30 months approx. which means that the total paid would be:

= 29. 97 x 200 per month

= $ 5, 994. 30

The amount that the credit card holder would pay over paying the current balance is:

= 5, 994. 30 - 4, 528. 34

= $1,465.96

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Answer: D- $1,465.96

Step-by-step explanation: I got it right on the test :)

The problem is asking to find the probability that in a sample of 300 children under the age of 6 years in the United States, 27% of them live in households that are at or below poverty income.

The first step is to calculate the standard deviation for the proportion of children in poverty in the sample. This can be done using the formula:

σ = sqrt(p * (1-p) / n)

Where p is the proportion of children in poverty in the population (0.22) and n is the sample size (300).

Next, we can standardize the difference between the sample proportion and the population proportion using the z-score formula:

z = (p_sample - p_population) / σ

Finally, we can find the probability that the z-score is less than or equal to the z-score corresponding to a 27% sample proportion using a standard normal table or calculator. This probability can be interpreted as the probability that 27% or fewer children in the sample are living in households below poverty income.

Answer choice C, (0.27 - 0.22) * (0.73), does not seem to be related to the steps outlined above and does not provide an accurate answer for the problem.

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The number of words with two A's and the number of words with one A, which you have already counted Twice.

a). There are 3 words with 2 as well as (62) 3 words with 1 as, for a total of 8 7 6 3 6 15 6

Consider dividing 8-letter words into cases according to how many A's are present in the word:

1) You need to arrange the letters AAPRRMTT if there are two As.

2) If there are three A's, you can subdivide this based on the letter that is missing. (The examples P and M, as well as R and T, ought to have comparable counts.)

3) If there are 4 A's, then you break this into subcases based on the 2 letters omitted: RR, TT, PR, PM, PT, MR, MT.

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The graph of the equation shown above has infinite number of solutions.

In Mathematics, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

In Mathematics, an equation is said to have an infinitely many solution (infinite number of solutions) when the left hand side and right hand side of the equation are the same or equal.

Since the line representing this equation extends infinitely, we can reasonably infer and logically deduce that it has infinitely many solution (infinite number of solutions). Therefore, every point located on this line would satisfy the equation.

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