Convert 5 gram in quintal​

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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The required 45-45-90 degree triangle is shown, where each of the two acute angles is 45 degrees and the length of the hypotenuse is equal to the length of each leg multiplied by the square root of 2.

A right-angled triangle, also known as a right triangle, is a triangle in which one of its interior angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

Here,
o construct a 45-45-90 degree triangle with leg AB, we can follow these steps:

The resulting triangle will have sides AB, BC, and AC, where AB and BC are equal in length and AC is the hypotenuse.

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Answer:

it should take the workers 18 days to finish

Step-by-step explanation:

The growth rate for the population of the rabbits each year is 20%

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

Exponential exponential is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

Given the expression \(4(1.20)^t\) represents the population of rabbits each year. If x% represents the growth rate, hence:

b = 1.20

growth rate = 1.20 - 1 = 0.20

growth rate = 20%

The growth rate is 20%

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To calculate the number of four-card hands chosen from a standard 52-card deck that contain two cards of one suit and two cards of another suit, we need to consider the following:

1. Selecting the suits: There are 4 suits in a deck (hearts, diamonds, clubs, and spades). We need to choose two suits out of these four.

2. Selecting the two cards of one suit: Once we have chosen the two suits, we need to select two cards from one of the chosen suits. There are 13 cards in each suit, so we can choose 2 cards from the 13 available.

3. Selecting the two cards of another suit: After selecting the first suit, we need to choose two cards from the remaining suit. Again, there are 13 cards to choose from.

To calculate the total number of four-card hands satisfying these conditions, we multiply the number of choices at each step. Therefore, the total number of such hands is:

4C2 * 13C2 * 13C2 = (4! / (2! * 2!)) * (13! / (2! * 11!)) * (13! / (2! * 11!))

= 6 * (13 * 12 / (2 * 1)) * (13 * 12 / (2 * 1))

= 6 * 78 * 78

= 36,432.

Therefore, there are 36,432 four-card hands chosen from a standard 52-card deck that contain two cards of one suit and two cards of another suit.

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The derivative of the function is

A) dw/dz=z^5 (7z-18)

B) dh/dx=192x^11+36x^5-6x^2+19

C) dy/dx=24x^2-38x-15

In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.

A) w = z^7 – 3z^6 + 14

dw/dz=7z^6-18z^5

dw/dz=z^5 (7z-18)

B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7

dh/dx=192x^11+36x^5-6x^2+19

C) y = (8x + 5)(x^2 – 3x)

dy/dx=  d/dx  [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]

dy/dx=(8*  d/dx  [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])

dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)

dy/dx=8(x^2-3x)+(2x-3)(8x+5)

dy/dx=24x^2-38x-15

Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).

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Answer: 12 weeks

Step-by-step explanation:

Let the week that both of them will have thesame amount of money be represented by x.

Since Mary already has $30 and is able to save $5.50 every week, this will be denoted as: 30 + 5.50x

Since Bill already has $45 and is able to save $4.25 every week, this will be debited by 45 + 4.25x. Then we'll equate both equations and this will be:

30 + 5.50x = 45 + 4.25x

5.50x - 4.25x = 45 - 30

1.25x = 15

x = 15/1.25

x = 12

They'll have thesame amount of money in 12 weeks.

The volume of the cone is approximately 37.7 cubic units

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.

Plugging in the given values, we get:

V = (1/3) * 3.14 * 3² * 4 ≈ 37.7

Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).

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Answer:

C(x)=3x³+4x²-11x-8

Step-by-step explanation:

The water usage is modeled by the equation W(x) = 4x³ + 6x² − 11x + 7

The amount of decrease in water used is modeled by D(x) = x³ + 2x² + 15

C(x)= W(x)-D(x)

C(x)=4x³ + 6x² − 11x + 7-(x³ + 2x² + 15)

C(x)=4x³ + 6x² − 11x + 7-x³-2x²-15

c(x)=3x³+4x²-11x-8

Answer:

the second option

Step-by-step explanation:

Probability of chosen the acre of land as per given conditions are as follow:

a. Probability of chosen the acre of land not forested is 0.62.

b. Probability of chosen the acre of land either forest or agriculture is 0.45.

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

As given in the question,

Given probability are:

Probability of chosen the acre of land is forest is equal to 0.38.

Probability of chosen the acre of land is agriculture is equal to 0.07.

Probability of chosen the acre of land as per given conditions are as follow:

a. Let P(A) represents the probability of chosen the acre of land is forest.

Then P(A') is the probability of not forested.

P(A) + P(A') = 1

⇒0.38 + P(A') = 1

⇒ P(A') = 1 - 0.38

⇒ P(A') = 0.62

b. Let P(G) is the probability of chosen acre of land agricultural.

No common land given for forest or agriculture, they are independent events.

P(A∩G) = 0

Probability of chosen the acre of land either forest or agriculture

= P( A or G)

= P(A) + P(G) - P(A∩G)

= 0.38 + 0.07 -0

= 0.45

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

Therefore, probability of chosen the acre of land as per given conditions are as follow:

a. Probability of chosen the acre of land not forested is 0.62.

b. Probability of chosen the acre of land either forest or agriculture is 0.45.

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

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Answer:

i believe it's decaying

Step-by-step explanation:

based on what i've observed from similar questions, the whole numbers were growing and the fractions were dacaying.

good luck :)

i'm not entirely sure but i hope this helps

**please let me know if this is incorrect/not what you're looking for or both**

have a nice day!

By definition of exponential function, The function y = (1/5)ˣ is an exponential decay.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ y = (1/5)ˣ

Now, We have;

The general form of the exponential function is,

⇒ y = a bˣ

If b < 1 , function is an exponential decay.

If b > 1, function is an exponential growth.

Here, The function is,

⇒ y = (1/5)ˣ

And, b = 1/5 < 1

Hence, By definition of exponential function, The function y = (1/5)ˣ is an exponential decay.

Therefore, By definition of exponential function, The function y = (1/5)ˣ is an ''exponential decay.''

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Answer: it is 5 years old

Step-by-step explanation: because 12 inches is 1 foot long and5feetis5yearsfootlongfoot

There is a 9.85% probability of obtaining a sample with a mean time to relief of 3.3 minutes or less.

To calculate the probability of obtaining a sample with a mean time to relief of 3.3 minutes or less, we need to use the standard error formula:

Standard error = population standard deviation / square root of sample size

In this case, the standard error would be:

Standard error = 1.1 / square root of 50
Standard error = 0.155

Next, we need to calculate the z-score using the following formula:

z-score = (sample mean - population mean) / standard error

Since the population mean is not given, we can use the sample mean as an estimate of the population mean. Therefore, the z-score would be:

z-score = (3.3 - 3.5) / 0.155
z-score = -1.29

Using a z-table or calculator, we can find the probability of obtaining a z-score of -1.29 or less. The probability is approximately 0.0985, or 9.85%.

Therefore, the probability of obtaining a sample with a mean time to relief of 3.3 minutes or less is 9.85%. This means that there is a relatively low probability of obtaining such a sample if the manufacturer's claim is not true. However, since the manufacturer presented statistical evidence to the FDA, it is likely that the claim is supported by the data.
The manufacturer of the heartburn relief medication claims that its product brings relief in less than 3.5 minutes, on average. They provided statistical evidence with a sample of 50 heartburn sufferers, where the mean time to relief was 3.3 minutes and the population standard deviation was 1.1 minutes. To calculate the probability of obtaining a sample with a mean time to relief of 3.3 minutes or less, we can use the z-score formula:

z = (sample mean - population mean) / (population standard deviation / √sample size)

z = (3.3 - 3.5) / (1.1 / √50)
z = -0.2 / (1.1 / 7.071)
z = -0.2 / 0.1556
z ≈ -1.29

Using a standard normal distribution table, the probability of obtaining a z-score of -1.29 or lower is approximately 0.0985, or 9.85%. Therefore, there is a 9.85% probability of obtaining a sample with a mean time to relief of 3.3 minutes or less.

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The probability that the student will answer all 7 problems correctly is approximately 0.03498 or 3.498%.

To calculate the probability that the student will answer all 7 problems correctly, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:

Since the next quiz consists of a random selection of 7 problems out of a set of 14, the total number of possible outcomes can be calculated using the combination formula:

Total possible outcomes = C(14, 7) = 14! / (7! * (14-7)!) = 3432

Number of favorable outcomes:

Since the student has figured out how to do 10 of the problems, we can select all 7 problems from those 10 that the student knows how to solve:

Number of favorable outcomes = C(10, 7) = 10! / (7! * (10-7)!) = 120

Now, we can calculate the probability of answering all 7 problems correctly by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability of answering all 7 problems correctly = Number of favorable outcomes / Total possible outcomes

= 120 / 3432

≈ 0.03498

Therefore, the probability that the student will answer all 7 problems correctly is approximately 0.03498 or 3.498%.

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The two column proof procedure below has shown that  ΔABE ≅ ΔACD by SAS Congruency Postulate

To prove that ΔABE ≅ ΔACD, we will use a two column proof procedure for congruency.

Statement 1; AD ≅ AE

Reason 1; Given

Statement 2; ∠ABC ≅ ∠ACB

Reason 2; Given

Statement 3; AC ≅ AB

Reason 3; Definition of Isosceles Triangles

Statement 4; ΔABE ≅ ΔACD

Reason 4; SAS Congruency Postulate

Both triangles share the included angle A.

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According to trigonometry, the value of sin y cos x.

The term called trigonometry is defined as the type of mathematics that deals with the relationship between the sides and angles of triangles.

Here we know that the function is written as

=> sin x coy y

where r [0, 1/2] [0, 1/2]

Here by Using Fubini’s theorem we can write this as an iterated integral to get,

=> \(\int\limits^{1/2}_0\int\limits^{1/2}_0 {sinxcosy} \, da\)

Here the Fubini's theorem states that  the double integral over a region is equal to an iterated integral, which is computed in a similar manner with definite integrals of functions of single variable.

When we integrate the expression, then we get

=> \(\int\limits^{1/2}_0 {cos(1+y)sin(1+x)} \, da\)

Again we have to integrate this one, then we get the value as,

=> sin y cos x.

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Answer:

4th choice: I and IV only

Step-by-step explanation:

Change the form of the given equation to standard form.

y = -2/3 x + 2

3y = -2x + 6

2x + 3y = 6

Now compare this equation with the 4 choices.

Any equation that has the same x- and y-terms but a different constant term is parallel.

I. is parallel.

II. and III. are not parallel.

Look at IV.:

4x + 6y = 3

Divide both sides by 2:

2x + 3y = 3/2

IV. is also parallel.

Answer: 4th choice: I and IV only

Answer:

I and IV only

Step-by-step explanation:

In order for graphs to be parallel, they must have the same slope

In this case, we are looking for a slope of -2/3

We can find the other slopes by solving for y (y=mx+b)

I. 2x+3y=10

Subtract 2x from both sides

3y=-2x+10

Divide by 3

y=-2/3+10/3 This works since the slope is identical

II. 2x-3y=9

Follow a similar progression as the previous (subtract the x's and divide the y's)

-3y=-2x+9

y=2/3=3 This doesn't work since it is positive

III. 4x-6y=30

-6y=-4x+30

y=2/3 x-5 (4/6 simplified to 2/3) Also doesn't work since it is positive

IV. 4x+6y=3

6y=-4x+3

y=-2/3x+3 (-4/6 simplified to -2/3) This one works, it is identical

Answer:

Yes, it's a rational number

Step-by-step explanation:

-3/7. It is a rational because. It can be written as p/q form. Where p/q are non zero number. And in decimal it would be -0.42

Answer:

-3/7 is a rational because as it can be written as p/q form where p/q are integers and q≠0.

-3/7 = -0.4285

To the nearest hundredth,

=> -0.43

we have that

the total numbers in the spinner are 8 numbers

numbers greater than 5 -----> 6,7 and 8------> 3 numbers

the probability is

3/8

Multiply by 150 times

150(3/8)=56.25

therefore

Answer:

no

Step-by-step explanation:

No, it is not since 2 points have the same x-coordinate and different y-coordinates.

Answer:

See below ~

Step-by-step explanation:

Sin A : opposing side of ∠A / hypotenuse

Sin C : opposing side of ∠C / hypotenuse

Cos A : adjacent side of ∠A / hypotenuse

Cos C : adjacent side of ∠C / hypotenuse

Answer:

its log 5 7/8

Step-by-step explanation:

\((-a+3)(a+4)=-a^2-a+12\).

Hope this helps.

Answer:

-a²-a+12

Step-by-step explanation:

-a²+3a-4a+12

-a²-a+12

Answer: The tip amount is 20% of $26.00, which is:

0.20 x $26.00 = $5.20

So, the total cost including the tip is:

$26.00 + $5.20 = $31.20

Therefore, Isaac paid $31.20 for the haircut, including the tip.

Step-by-step explanation:

Answer:

This would be A.

Step-by-step explanation:

Because

12\(b^{2}\) - 6\(b^{2}\) = 6\(b^{2}\)

-3b - 3b = -6b

0 + ( -2 ) = -2

6\(b^{2}\) - 6b - 2

Hope this helps!

Answer:

$0.40

Step-by-step explanation:

5.60/14 = .40

Answer:

The storage capacity of the USB is far greater than Kilobytes, but less than a Terabyte.

Step-by-step explanation:

Kilograms and pounds are two different units of measurements used to measure mass or weight. 25 pounds is equal to 11.34 kilograms. This is because 1 kilogram is equal to 2.2 pounds. To convert pounds to kilograms, you divide the value by 2.2. In this case, 25 divided by 2.2 is equal to 11.34 kilograms.

The Kilogram is a metric unit of mass, while the Pound is a unit of mass used in the imperial system of measurement. The difference between the two can be easily seen when comparing different objects. For example, a pound of apples will weigh much more than a kilogram of apples.

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Answer:

A = 24 cm²

Step-by-step explanation:

The area (A) of Δ ABC is calculated as

A = \(\frac{1}{2}\) × AB × AC

Calculate AC using Pythagoras' identity

AC² + AB² = BC²

AC² + 6² = 10²

AC² + 36 = 100 ( subtract 36 from both sides )

AC² = 64 ( take the square root of both sides )

AC = \(\sqrt{64}\) = 8

Then

A = 0.5 × 6 × 8 = 24 cm²