if x:y=3:5 find the ratio 3×+4y:8x +5y​

Answer:

x=31.67[by rounding]

Step-by-step explanation:

As

sin=p/h

Here,

p=2.1

h=4

\(solution \\ sin(x )= \frac{2.1}{4} \\ sin(x) = 0.525 \\ \sin(x) = sin(31.66824325 )\\ x = 31.66824325\)

Answer:

31.7°

Step-by-step explanation:

\(sin(x)=\frac{opposite}{hypotenus} \\x = sin^{-1} (\frac{2.1}{4} )\\x = 31.668 = 31.7(nearest\ tenth\ of\ a\ degree)\)

The cross product and dot product of the vectors ⟨2,−7,5⟩ and ⟨−8,−2,0⟩ are ⟨10, 40, −54⟩ and -2 respectively.

For the given vectors, ⟨−4,−2,1⟩ and ⟨−2,0,−5⟩, the angle between them can be obtained using the formula given below.θ = arccos((A.B)/|A| |B|) Where A and B are vectors, A.B is the dot product of A and B, |A| is the magnitude of A, and |B| is the magnitude of B.

According to the above formula, the angle between the given vectors is given by,

θ = arccos(((-4)*(-2) + (-2)*0 + (1)*(-5))/√((-4)² + (-2)² + (1)²) √((-2)² + 0² + (-5)²))

θ = arccos((-8 - 5)/√21 √29)

θ = arccos(-1.224)

θ = 116.8 degrees

Therefore, the angle between the given vectors, ⟨−4,−2,1⟩ and ⟨−2,0,−5⟩, is 116.8 degrees.

Find the cross product and dot product of the vectors ⟨2,−7,5> and ⟨−8,−2,0>.

Let the given vectors be A and B. The cross product of A and B is given by the formula,

A x B = |i j k| |A1 A2 A3| |B1 B2 B3|

Where i, j, k are the unit vectors along the x, y, z-axes respectively, and |A1 A2 A3| and |B1 B2 B3| are the components of vectors A and B respectively.

Using the above formula, the cross product of the given vectors can be found as follows.

A x B = |i j k| |2 -7 5| |-8 -2 0|

= i(-7*0 - 5*(-2)) - j(2*0 - 5*(-8)) + k(2*(-2) - (-7)*(-8))

= ⟨10, 40, -54⟩

Therefore, the cross product of the given vectors ⟨2,−7,5⟩ and ⟨−8,−2,0⟩ is ⟨10, 40, −54⟩.

The dot product of the given vectors is given by the formula,

A.B = (A1*B1 + A2*B2 + A3*B3)

Using the above formula, the dot product of the given vectors can be found as follows.

A.B = 2*(-8) + (-7)*(-2) + 5*0

= -16 + 14 + 0

= -2

Therefore, the dot product of the given vectors ⟨2,−7,5⟩ and ⟨−8,−2,0⟩ is -2.

Thus, the cross product and dot product of the vectors ⟨2,−7,5⟩ and ⟨−8,−2,0⟩ are ⟨10, 40, −54⟩ and -2 respectively.

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On solving the provided question, we can say that random sample the conditions for interference are met.

selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.

Yes, the conditions for interference are met.

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The largest integer less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13. is 1440

Given, a number less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13.

On using the Chinese remainder theorem. As, the numbers 7, 11, 13 are pairwise coprime.

Firstly, an integer  m  such that  m−5  is divisible by 7 and  m−10  is divisible by 11 .

The Chinese remainder theorem says that all integers that work will be of the form  54+7⋅11⋅k=54+77k  for any integer  k .

Next an integer  n  such that  n−10  is divisible by 13 and  n−54  is divisible by 77.

Then, by the Chinese remainder theorem, all the integers that also work are of the form  439+13⋅77⋅k=439+1001k .

Hence, the positive integers satisfying the condition are: 439, 439 + 1001 = 1440, 1440 + 1001 = 2441, and so on.

The largest integer less than 2010 is 1440.

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Rate of change

Option B

The key approach is to analyze the relationship between the number of solutions to the equation Ax = 0 and the result of Gaussian elimination.

Since the columns of A are linearly dependent, there exist scalars c1, c2, ..., cn (not all zero) such that c1a1 + c2a2 + ... + cnan = 0, where ai represents the columns of A. We can rewrite this equation as a system of linear equations: Ax = 0, where x = [c1, c2, ..., cn]T is a column vector.

The linear dependence of the columns implies that the system Ax = 0 has infinitely many solutions, as we can always find non-trivial combinations of the columns that yield the zero vector.

Now, let's consider applying Gaussian elimination to matrix A. Gaussian elimination transforms the matrix into reduced row echelon form. If the resulting matrix has at least one row of all zeros, it means that there is at least one free variable in the system Ax = 0. This indicates that the system has infinitely many solutions.

Since the system Ax = 0 has infinitely many solutions, and the result of Gaussian elimination with a row of all zeros indicates linear dependence, it follows that the rows of A must also be linearly dependent. Therefore, the linear dependence of the columns implies the linear dependence of the rows.

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Answer:

g

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

z2 - z1 = 7/3i

Step-by-step explanation:

Given the following complex number:

z1 = 9+i/3i

z2 =  2+i/3i,

Taking the difference

z2 - z1 = 9+i/3i - (2+i))/3i)

z2-z1 = (9+i-(2+i))/31

z2 - z1 = 9+i -2-i/3i

z2-z1 = 9-2/3i

z2 - z1 = 7/3i

Note that the complex number given was not properly written and the ones used were assumed. Same procedure an be used for other complex numbers that might be given.

Answer:

54.4pounds

Step-by-step explanation:

40/100= 0.4 times 36=14.4 14.4+40=54.4

Answer:

1) El valor de los ocho helados de crema es 76,48 pesos, 2) El valor total de la compra es 85,97 pesos, 3) A Miguel le queda 13,59 pesos después de pagar en el supermercado.

Step-by-step explanation:

Supóngase que los costes son en pesos mexicanos. (MXN)

1) ¿Cuál es el valor de los ocho helados y que operación debe realizar?

Se multiplicar la cantidad de helados comprados por su valor unitario, es decir:

\(x = (8\,helados)\cdot \left(9,56\frac{MXN}{helado} \right)\)

\(x = 76,48\,MXN\)

El valor de los ocho helados de crema es 76,48 pesos.

2) ¿Cuál es el valor total que debe pagar en la tienda?

El valor total es la suma de todos los costes de los elementos comprados:

\(y = 76,48\,MXN + (1\,papa)\cdot \left(3,70\,\frac{MXN}{papa} \right)+(1\,gaseosa)\cdot \left(4,525\frac{MXN}{gaseosa} \right)+(1\,chocolatina)\cdot \left(1,267\,\frac{MXN}{chocolatina} \right)\)

\(y = 85,97\,MXN\)

El valor total de la compra es 85,97 pesos.

3) Si Miguel tiene en su bolsillo $99,56. ¿Cuánto dinero le queda después de pagar en el supermercado?

El remanente se obtiene al sustraer el valor total de la compra del efectivo disponible:

\(z = 99,56\,MXN-85,97\,MXN\)

\(z = 13,59\,MXN\)

A Miguel le queda 13,59 pesos después de pagar en el supermercado.

Answer:

Both angles are 51°

Step-by-step explanation:

By the Vertical Angles Theorem, both angles are congruent.

Step 1: Set up equation

68 - x = 3x

Step 2: Solve for x

68 = 4x

x = 17

Step 3: Find angles

68 - 17 = 51°

Answer:

4x=68

x=17

51°

Step-by-step explanation:

Answer:

not proportional

Step-by-step explanation:

Answer:

The answer is option B

\(859\) \(m^2\) \(,\) \(891\) \(m^2\)

Step-by-step explanation:

Step 1

Find the lateral area

we know that

The formula to calculate the lateral area is equal to

\(LA=Ph\)

where

P is the perimeter of the base of the prism

h is the height of the prism

In this problem we have

\(P=4+8+8.94=20.94\) \(m\)

\(h=41\) \(m\)

substitute in the formula

\(LA=20.94*41=858.54\) \(m^2\)

\(LA=859\) \(m^2\)

Step 2

Find the surface area

we know that

The formula to calculate the surface area is equal to

\(SA=2B+Ph\)

where

B is the area of the base of the prism

P is the perimeter of the base of the prism

h is the height of the prism

In this problem we have

\(B=8*4/4=8\) \(m^2\)

\(P=4+8+8.94=20.94\) \(m\)

\(h=41\) \(m\)

substitute in the formula

\(SA=4(8)+20.94*41=890.54\) \(m^2\)

\(SA=891\) \(m^2\)

\(\rm y\ \le2x+1\) , \(\rm y\le-x+3\)  , Option B represents the the graph given .

An Inequality is a statement that connects two algebraic expression by an inequality operator.

To determine the solution of the inequalities , the common area that comes under the inequality will be found

The graph plotted using

y ≥ 2x +1 and y ≥ - x+3

it doesn't represent the solution as given in the question graph , graph no.1

The graph given in the question is the solution of the  set of inequalities

This can be understood by Graph 2

\(\rm y\ \le2x+1\)

\(\rm y\le-x+3\)

As all the inequalities of all the options were plotted  and the solution to the system of inequality is represented by the graph

Therefore Option B is the correct answer.

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The Economic Order Quantity (EOQ) is calculated to be 547.72 units. The number of orders placed per year is 5.84, and the reorder point (ROP) is 32.01.

The total holding cost of lawnmowers is R1369.30, and the total ordering cost of lawnmowers is R876.00. These calculations provide valuable insights for efficient inventory management.

The Economic Order Quantity (EOQ) can be calculated by using the formula: EOQ = √2DS / H,

where D = Total Demand = 3200 units,

S = Ordering cost per order = R150,

and H = Annual holding cost per unit = R5.

Therefore, EOQ = √ (2 x 3200 x 150) / 5 = 547.72 units.

4.2 Number of orders placed per year: No of orders per year = D / Q,

where D = Total Demand = 3200 units and Q = EOQ = 547.72 units.

Therefore, No of orders per year = D / Q = 3200 / 547.72 = 5.84 orders.

4.4 Total holding cost of lawnmowers:

Total holding cost of lawnmowers = (Average inventory level) x (Annual holding cost per unit),

where (Average inventory level) = EOQ / 2 = 547.72 / 2 = 273.86 units and Annual holding cost per unit = R5.

Thus, the Total holding cost of lawnmowers = 273.86 x R5 = R1369.30.

4.1 Reorder Point (ROP): ROP can be calculated by using the formula:

ROP = dL, where d = Daily demand = D / Number of working days

= 3200 / 300 = 10.67 and L = Lead time = 3 days.

Hence, ROP = dL = 10.67 x 3 = 32.01.

4.5 Total ordering cost of lawnmowers:

Total ordering cost of lawnmowers = (Number of orders placed per year) x (Ordering cost per order),

where (Number of orders placed per year) = 5.84 orders and Ordering cost per order = R150.

Therefore, the Total ordering cost of lawnmowers = 5.84 x R150 = R876.00.

The Economic Order Quantity (EOQ) is calculated to be 547.72 units.

The number of orders placed per year is 5.84, and the reorder point (ROP) is 32.01.

The total holding cost of lawnmowers is R1369.30, and the total ordering cost of lawnmowers is R876.00.

These calculations provide valuable insights for efficient inventory management.

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Answer:

the one with the 6.....?...........

AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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Answer:

138 : 269

Step-by-step explanation:

Last year, the number of bicyclists that showed up was 1345.

This year, there were 690 bicyclists.

The ratio of the number of bicyclists that showed up for the past two years is the ratio of those that showed up this year to those that showed up last year:

690 : 1345

Let us put it in simplest terms:

138 : 269

For every mile the car is driven the cost increases by $ 0.74 or 74 cents.

It is given in the question that the equation y = 0.74x + 64 gives the cost y of renting a car if the car is driven x miles.

It is a linear equation in 2 variable.

We have to find, for every mile the car is driven the cost increases by how much.

As we can observe from the equation, 64 is the fixed cost of renting a car, $ 0.74 is the cost of driving per mile.

Hence, for every mile the car is driven the cost increases by  $ 0.74 or 74 cents.

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It is true that the indexed variables (members) of an array must be integers.

The indexed variables or members of an array must be integers. This is because arrays are data structures that store elements in a contiguous block of memory, and each element is accessed using an index. Indexing allows us to uniquely identify and retrieve specific elements within the array. In most programming languages, including C, C++, Java, and Python, array indices are integers and must be whole numbers (positive or negative) without any fractions or decimals. Attempting to use non-integer values as indices would result in a compilation error or unexpected behavior.

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Answer:

her is a screenshot fot the answer and step by step they all in side the screenshot please check it

The t-statistic for testing H0: μ = 100 against Ha: μ < 100 with an SRS of 9 observations, X-hat = 98, and s = 3 is -2.

To calculate the t-statistic, follow these steps:

1. Determine the null hypothesis (H0) and alternative hypothesis (Ha): H0: μ = 100, Ha: μ < 100
2. Identify the sample size (n), sample mean (X-hat), and sample standard deviation (s): n = 9, X-hat = 98, s = 3
3. Calculate the standard error (SE): SE = s / √n = 3 / √9 = 1
4. Compute the t-statistic: t = (X-hat - μ) / SE = (98 - 100) / 1 = -2

The t-statistic of -2 indicates that the sample mean is 2 standard errors below the hypothesized population mean. This value helps you determine the significance of your test and whether to reject the null hypothesis.

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Answer:

127

Step-by-step explanation:

Answer:

$ 27.92

Step-by-step explanation:

If you discount 60%, then you have 40% of the item as cost. So multiply that number by 0.4 to get 27.92.

Question 5

Vertical angles are congruent. Therefore, \(3y=\boxed{150}\). The sum of two supplementary angles equals \(\boxed{180^{\circ}}\).

Therefore, \(6x+150=\boxed{180}\)

Question 6

\(\angle b-14=90-\angle b\\\\2\angle b=104\\\\\angle b=\boxed{52^{\circ}}\)

Question 7

\(\angle d+32=180-\angle d\\\\2\angle d=146\\\\\angle d=\boxed{73^{\circ}}\)

Question 8

\(7x-80=3x\\\\-80=-4x\\\\x=20\\\\\implies \boxed{m\angle 1=m\angle 3=60^{\circ}}\)

Answer:

149 degrees

Step-by-step explanation:

Since m and n are parallel you need to remember the rules of transversals, this means that <1 and <2 are corresponding. Corresponding angles are always congruent, so we can solve for x by setting them equal to each other.

\(8x-1=7x+3\)

First, move the variables to one side, I will move them both to the right, but remember you can do it on either side. To do this subtract 7x from both sides

\(8x-1-7x=7x+3-7x\), then simplify

\(x-1=3\)

Next, add 1 to both sides to isolate the variable

\(x-1+1=3+1\), then simplify

\(x=4\)

Now that you know what x equals solve for angle 1, to do this plug 4 in for x in the original equation

\(8(4)-1=31\)

Finally, you can solve for <3 because <1 and <3 are supplementary. So to solve add both and set them equal to 180, in this equation let x stand for <3. \(180=31+x\), then subtract 31 from both sides \(180-31=31+x-31\) and simplify, \(149=x\). So angle 3 is equal to 149.

Th 33.134.25³ is not a prime factorization because not all of the factors are prime numbers, option C.

The prime factorization of the number is: $33,134.25=3² × 5² × 13² × 17$. It is important to understand what is a prime number before discussing prime factorization. A prime number is a positive integer that has only two factors, 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are prime numbers.

All other numbers greater than 1 are called composite numbers. For example, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, etc., are composite numbers.A prime factorization is a set of prime numbers that when multiplied together, give the original number.

This can be done using a factor tree or by dividing the original number by its prime factors until only prime factors remain. A number is said to be prime if it cannot be divided by any other number other than 1 and itself.

So, the correct answer is option C.

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Answer:

Linda = z - 15

Step-by-step explanation:

Linda spent $15 less than Juan, it means: Linda + 15 = z

                                                                     Linda + 15 - 15 = z - 15

                                                                     Linda = z - 15

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The line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation , Option A is the correct answer.

When a quantity increases and the other quantity also increases , then those two quantities are said to be in direct variation.

It is asked in the question that which option depicts whether On a coordinate plane, a line goes through points (0, 0) and (1, 3) , represents a direct variation

As it is mentioned in the question that the line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation.

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Answer:

a

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

First, notice that this is a cubic function.

The standard form for a cubic function is:

\(f(x)=a(x-b)^3+c\)

Where a is the vertical stretch, b is the horizontal shift, and c is the vertical shift.

From our graph, we can see that unlike the parent function, x³, this cubic is 3 units to the right and 1 unit up from the standard position.

Therefore, our b is +3 and c is +1. Let's substitute these values. Also, let's assume a is 1. So:

\(f(x)=(x-3)^3+1\)

Therefore, our answer is C.

And we're done!