a and b are in direct proportion. the equation of proportionality is a=8b. work out the value of a when b=4.

34,000 liters of oil = 34 kiloliters.

Based on the concept of conversion in measurement, and the content of the question, the 34000 liters is 34kl

Conversion in measurement is a term that is used to describe the same property as a different unit of measurement.

Generally, the term conversion can be used for instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

To convert liters to kiloliters you need to divide the given volume in liters by 1000.

So to find how much 34000 liters is in kiloliters you would perform the following calculation:

34000 liters ÷ 1000 = 34 kiloliters

Therefore, in this case, it is concluded that 34000 liters is equivalent to 34 kiloliters.

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The time it will take for your account balance to reach $10,000 is given as follows:

t = 10.8 years.

The balance of an account after t years, using continuous compounding, is given as follows:

A(t) = A(0)e^(kt).

In which:

The parameters for this problem are given as follows:

A(0) = 6500, k = 0.04.

Hence the time needed for a balance of $10,000 is obtained as follows:

10000 = 6500e^(0.04t)

e^(0.04t) = 10000/6500

0.04t = ln(10000/6500) -> ln is the inverse operation of the exponential

t = ln(10000/6500)/0.04

t = 10.8 years.

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Answer:

we need a picture of the problem

Step-by-step explanation:

Answer:

Lines are perpendicular

Step-by-step explanation:

slope of y=6 is 0

slope of x=6 inf

Answer:

The answer is A

Step-by-step explanation:

Subtract from right to left

85, 678

-28, 989

=56, 689

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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If you read the decimal version of 4.8 out loud, it should be "four and eight-tenths."  This will always give you a good place to start when changing a decimal into an equivalent fraction.

Now, this is a mixed number: 4 and 8/10. To further simplify it as a mixed number, we can leave the 4 alone and reduce the fraction (8/10).  Both the numerator and denominator are divisible by 2, so we can conclude (8/10) = (4/5).  A correct answer in mixed number form is 4 and (4/5).

However, to change 4 and (4/5) to a single (improper) fraction, you first multiply the denominator (5) by the large number out front on the left (4) and ADD this product to the numerator (4).  This number is your new numerator and it will still have the same denominator as before.

Here, 4 and (4/5) = [(5)*(4) + 4]/5 = (20+4)/5 = 24/5.

24 and 5 have no common factors, so this fraction is already in reduced form.

4.8 = 4 8/10 = 4 4/5

9514 1404 393

Answer:

  158,000

Step-by-step explanation:

Using the given square feet for x in the equation, we have ...

  y = 0.071×1483 +52.48 = 157.773

We presume this is supposed to represent the estimated value of the house in thousands.

The fair price is estimated to be 158,000.

The calculated value of the length x of the square is 11.3 feet

Since the square is inscribed in the circle, its diagonal will be equal to the diameter of the circle, which is 16 feet.

Let's use the Pythagorean theorem to find the length of a side of the square:

x² + x² = 16²

2x² = 256

x² = 128

x ≈ 11.3 feet (rounded to the nearest tenth of a foot)

Therefore, the approximate side length of the square is 11.3 feet.

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it is false but 4 is not y-4x=0

The expected value of x is (m+1)/2, and m must be a positive integer.

The expected value of x is the average value of x that we would expect to get if we selected an integer from the set {1, 2, ..., m} many times. To find the expected value of x, we multiply each possible value of x by its probability of being selected and then sum these products. In this case, each integer in the set {1, 2, ..., m} has an equal probability of being selected, so the expected value is (1 + 2 + ... + m) / m = (m(m+1)) / 2m = (m+1) / 2. So the expected value of x is (m+1)/2, and m must be a positive integer.

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Answer: 485 is the answer.

Step-by-step explanation:

The distance PQ cannot be expressed as k√5, where k is a rational number given that PQ = √18

To find dy/dx, we can use implicit differentiation:

4xy = 2(x² + 4y²) - 9x

Differentiating both sides with respect to x, we get:

4y + 4xy' = 4x + 8yy' - 9

Simplifying and solving for y', we get:

y' = (4x - 4y - 9)/(4x - 16y)

Hence, dy/dx = (4x - 4y - 9)/(4x - 16y).

At point P, the tangent to the curve is parallel to the y-axis.

This means that dx/dy = 0 at P.

We can find the coordinates of P by solving the following equations simultaneously

4xy = 2(x² + 4y²) - 9x

dx/dy = 0

From 4xy = 2(x² + 4y²) - 9x, we have:

4xy + 9x = 2(x² + 4y²)

Dividing both sides by x², we get:

4y/x + 9/x = 2 + 4y²/x²

Since dx/dy = 0, we have:

dy/dx = 0

Using the formula for dy/dx that we derived in part (a), we get:

(4x - 4y - 9)/(4x - 16y) = 0

Solving for y, we get:

y = (4x - 9)/4

Substituting this into 4xy = 2(x² + 4y²) - 9x, we get:

4x * (4x - 9)/4 = 2(x² + 4[(4x - 9)/4]²) - 9x

Simplifying and solving for x, we get:

x = 9/2 and 3/2

Substituting these values of x into y = (4x - 9)/4, we get the coordinates of P:

y = 9/4 and y = -3/4

This means that

P(9/2, 9/4) and P(3/2, -3/4)

At point Q, the tangent to the curve is parallel to the x-axis.

This means that dy/dx = 0 at Q.

Using the formula for dy/dx that we derived in part (a), we get:

(4x - 4y - 9)/(4x - 16y) = 0

Solving for x, we get:

x = (4y + 9)/4

Substituting this into 4xy = 2(x² + 4y²) - 9x, we get:

4 * [(4y + 9)/4] * y = 2([(4y + 9)/4]² + 4y²) - 9 * (4y + 9)/4

Simplifying and solving for y, we get:

y = -3/4, 9/4

Substituting these values of y into x = (4y + 9)/4, we get the coordinates of Q:

x = 3/2 and x = 9/2

This means that

Q(3/2, -3/4) and Q(9/2, 9/4)

Using the distance formula, we can find the distance PQ:

PQ = √[(9/2 - 3/2)² + (9/4 + 3/4)²] or √[(3/2 - 9/2)² + (-3/4 - 9/4)²]

Simplifying, we

PQ = √18 or √18

So, we have

PQ = √18

This gives

k√5 = √18

So, we have

k = √18/√5

Evaluate

k = √3.6

√3.6 is not a rational number

Hence, the distance PQ cannot be expressed as k√5

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Answer:

ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ  = 14√5 units

Step-by-step explanation:

1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units

2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX =  √18 units = 3√2.

3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.

4. YZ is visualized to have a length of 4 units.

5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ  = 14√5 units

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

Medbay

Step-by-step explanation:

Some things you can do to help you decide on a bank include:

When trying to locate a bank that offers competitive returns on savings and favorable borrowing costs, consider comparing interest rates.

To gather additional information about certain banks, why not solicit feedback from acquaintances? People who have personal experience with a particular bank can provide valuable insights into their satisfaction levels with regards to customer service, for example.

Finally, taking the time to visit branch offices can offer valuable clues regarding convenience level and overall atmosphere.

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Answer: B. 6x + 4y ≤ 50 x + y ≥ 10

Step-by-step explanation: To represent this situation with a system of inequalities, we need to consider two constraints: the budget and the number of guests.

The budget constraint is that the total cost of the party favors should not exceed $50. Since each stuffed animal costs $6 and each toy truck costs $4, the total cost can be expressed as 6x + 4y, where x is the number of stuffed animals and y is the number of toy trucks. To satisfy the budget constraint, we need 6x + 4y to be less than or equal to 50. This gives us the first inequality: 6x + 4y ≤ 50.

The number of guests constraint is that Laura wants to provide at least one party favor per person to at least 10 guests. This means that the total number of party favors should be greater than or equal to 10. Since each party favor is either a stuffed animal or a toy truck, the total number of party favors can be expressed as x + y, where x and y are the same as before. To satisfy the number of guests constraint, we need x + y to be greater than or equal to 10. This gives us the second inequality: x + y ≥ 10.

Therefore, the system of inequalities that represents this situation is:

6x + 4y ≤ 50 x + y ≥ 10

Hope this helps, and have a great day! =)

Answer:

y=4, x=-8

Step-by-step explanation:

y=1/2x+8                  (1)

4x+12y=16                (2)

multiply (1) by 2 we get

2y=x+16

or 2y-x=16

or -x+2y=16                 (3)

add (2) and (3)

4x+12y=16

(-x+2y=16 )                      x 4

we will get 20y=80   by adding both equations

                 y=4

put the value of y in (1) or (2)

4x+12y=16⇒4x=16-48

x=-8

\(\huge{ \mathfrak{  \underline{ Answer }\:  \:  ✓ }}\)

The given triangle is a right angled triangle,

therefore, by using trigonometry :

\( \boxed{ \cos(45) = \frac{6}{x} }\)

_____________________________

\(\mathrm{ ☠ \: TeeNForeveR \:☠ }\)

Answer:

The percent increase in the the puppy's weight  is 84%

Step-by-step explanation:

Answer:

1.894

3.169

2.064

3.690

Step-by-step explanation: 90% ; sample size = 8

Degree of freedom, df = n - 1

t(1 - α/2, 7) = t0.05, 7 = 1.894

Answer:

x^3 + 2x - 1.

Step-by-step explanation:

To simplify the expression 2x + x^3 - 1, we can first rearrange the terms in decreasing order of the exponents:

x^3 + 2x - 1

So the simplified expression, rearranged in descending order, is x^3 + 2x - 1.

The vertices of the ΔDEF are given by (-4, 2)D',  (-1,  1)E' ,  (1,  5)F' through mapping.

what is mapping?

Any set, including all whole integers, all the points on a line, or all the objects inside a circle, can be mapped. A mapping of the set of all whole numbers onto the set of even numbers is defined by the expression "multiply by two," for instance. A rotation is an internal map of a plane or of all of space.

The vertices of ΔDEF are given by D(2,-4) - D E(1,-1) - E F(5, 1).

According to the rule defining a reflection across the line, y=x should be stated when reflecting a point across the line. Then, the x and y coordinates are switched as follows:

y(x, y) → (y, x)

Let's now use the aforementioned rule to finish mapping the vertices of DEF. Change the x and y coordinate locations as follows:

The vertices of the ΔDEF are given by (-4, 2)D',  (-1,  1)E' ,  (1,  5)F' through mapping.

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g(x) is the translation 5 units right of f(x)= – 7(x–5)²+3.

A function called f(x) accepts an input of "x" and outputs "y". You can write it out as y = f. (x).‘x’ is a variable that represents an input to a function.

To translate a function, we need to replace x with (x-a) in the function f(x) where ‘a’ is the amount of translation.

To translate a function 5 units right, we need to replace x with (x-5) in the function f(x).

So, g(x) = f(x-5) = -7(x-5-5)²+ 3 = -7(x-10)²+ 3.

Therefore, g(x) is the translation 5 units right of f(x)= – 7(x–5)²+3.

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Answer:

50

Step-by-step explanation:

0.25 * 200 = 50

25% of 200 is 50

Answer:

50

Step-by-step explanation:

25% of 100 is 25 so add another 100 so u have to add 25

Answer:

4 mm

Step-by-step explanation:

\(\sqrt{16}\) = 4

So, the answer is 4 mm.

Answer:

4mm

Step-by-step explanation: