Si un triángulo tiene de lados 4 y 5 metros y el ángulo entre ellos es de 30°, ¿Cuál es el área de la figura?

Answer:

231.59 years

Step-by-step explanation:

To model this situation we are going to use the exponential decay function:

f(t)= a (1-b)^t

where f(t) is the final amount remaining after t years of decay

a is the final amount

b is the decay rate in decimal form

t is the time in years

For Substance A:

Since  we have 300 grams of the substance, a=300. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r = 0.15/100 = 0.0015. Replacing the values in our function:

f(t) = a (1-b)^t

f(t) = 300 (1-0.0015)^t

f(t) = 300 (0.9985)^t equation (1)

For Substance B:

Since we have 500 grams of the substance, a= 500. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r=0.37/100= 0.0037. Replacing the values in our function:

f(t) = a (1-b)^t

f(t)= 500 (1-0.0037)^t

f(t)=500(0.9963)^t equation (2)

Since they are trying to determine how many years it will be before the substances have an equal mass M, we can replace f(t) with M in both equations:

M=300(0.9985)^t equation (1)

M=500(0.9963)^t equation (2)

We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, M, is :

{M=300(0.9985)^t

{M=500(0.9963)^t

The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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Answer:

2, 0

Step-by-step explanation:

The x intercept is always where the line drawn through the graph meets the X Axis on the grid.

Answer:

(2, 0)

Step-by-step explanation:

The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).

The volume of any cylinder can be calculated using the formula,

V = πr²h

(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)

As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:

Volume of oil = (1/5) x Total Volume

Substituting the given values, we have:

Total Volume =  π(80cm)²(200cm) = 4,031,240 cm³

Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³

Converting cm³ to litres, we have:

1 litre = 1000 cm³

Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres

Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.

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Answer:

18 liquid quarts ≈ 17 litres

Answer:

18 us liquid quart =17.034 liters

Step-by-step explanation:

1) 1 us liquid quart = 0.946 liter

2) Multiply 0.946 *18 = 17.034

Answer:

∠ W = 30°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos W = \(\frac{adjacent}{hypotenuse}\) = \(\frac{WY}{WX}\) = \(\frac{2\sqrt{21} }{4\sqrt{7} }\) = \(\frac{1}{2}\) \(\sqrt{\frac{21}{7} }\) = \(\frac{\sqrt{3} }{2}\) , then

∠ W = \(cos^{-1}\) ( \(\frac{\sqrt{3} }{2}\) ) = 30°

Vector is the quantity that has magnitude as well as direction. The component form of the vector that translates P(-3,6) to P'(-4,8)  is -i + 2j.

A vector quantity has both magnitude and direction. It is added using parallelogram law of addition.

The sum of two vector quantities is always a vector quantity.

The sum of two vector quantities can vary from their scalar difference to their scalar addition.

The given points are P(-3,6) to P'(-4,8) .

The vector component form of two points (x₁,y₁) and (x₂,y₂) is given by ,

(x₂-x₁)i + (y₂-y₁)j

Therefore, The vector component form of given points are,

(-4-(-3))i + (8-6)j

-i + 2j.
Hence "The component form of the vector that translates P(-3,6) to P'(-4,8) -i + 2j.

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Answer:

A

Step-by-step explanation:

two numbers that times to make -12 but add to make +4

+6×-2=-12

+6+-2=4

Step-by-step explanation:

The angle is 13.134 degree

I Hope this is right and help for you

good night :)

Answer:

1. 12

2. 0

3. 9

Step-by-step explanation:

Answer:

  3x³ and 6x³, y and 7y

Step-by-step explanation:

Like terms have variables with the same exponents. This fact eliminates choices A, C, D.

The like terms are ...

  3x³ and 6x³, 7y and y . . . . . . choice B

Answer:

y=-x+2

x+y=2

Step-by-step explanation:

hopefully this helps :)

Answer:

y = -x + 2

x + y = 2

Step-by-step explanation:

y = mx + b

y = mx + 2    (0,2) (2,0)

\(\frac{2 - 0}{0 - 2}\) = \(\frac{2}{-2}\) = -1

y = -x + 2

Ax + By = C

y = -1x + 2

x + y = 2

All we need to so substitute and simplify:

18/3(3)

18/9

2

Best of Luck!

Answer:

z = 32

Step-by-step explanation:

Add 3 to both sides.

5 + 3 = z/4 -3 + 3

8 = z/4

Multiply 4 on both sides. 8 times 4 is 32.

32 = z

When dividing the polynomial \(2x^4 - 4x^3 - 7x^2 - 10x + 14\)by the polynomial x + 2, the quotient is 2x^3 - 8x^2 + 6x - 22 and the remainder is 58.

To perform polynomial division, we follow a similar process to long division. We start by dividing the highest degree term of the dividend by the highest degree term of the divisor. In this case, we divide \(2x^4\) by x, resulting in \(2x^3\). We then multiply the divisor (x + 2) by this result \((2x^3)\), giving us \(2x^4 + 4x^3.\) Next, we subtract this product from the dividend \((2x^4 - 4x^3),\)which leaves us with\(-8x^3 - 7x^2 - 10x + 14\).
We repeat the process by dividing the highest degree term of the remaining polynomial (-8x^3) by the highest degree term of the divisor (x). This yields -8x^2. Multiplying the divisor by this result (-8x^2) gives us -\(8x^3 - 16x^2.\)Subtracting this product from the remaining polynomial results  in \(9x^2 - 10x + 14.\)
We continue the process until we have no more terms to divide. After dividing 9x^2 by x, we obtain 9x. Multiplying the divisor by this result (9x) gives us 9x^2 + 18x. Subtracting this from the remaining polynomial \((9x^2 - 10x + 14)\)leaves us with -28x + 14.
Since the degree of the remaining polynomial (-28x + 14) is less than the degree of the divisor (x + 2), we have reached the end of the division process. The quotient is \(2x^3 - 8x^2 + 6x - 22, and the remainder is 58.\)

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Answer:

the length in ft would be 0.52 but im not entirely sure hope this helps!

Step-by-step explanation:

Answer:

\( \angle A \cong \angle D \)

Step-by-step explanation:

The Side-Angle-Side method cana only be used when information given shows that an included angle which is between two sides of a ∆, as well as the two sides of the ∆ are congruent to the included side and two sides of the other ∆.

Thus, since John already knows that \( \overline{AB} \cong \overline{DE} \) and \( \overline{AC} \cong \overline{DF} \), therefore, an additional information showing that the angle between \( \overline{AB} \) and \( \overline{DE} \) in ∆ABC is congruent to the angle between \( \overline{AC} \) and \( \overline{DF} \) in ∆DEF.

For John to prove that ∆ABC is congruent to ∆DEF using the Side-Angle-Side method, the additional information needed would be \( \angle A \cong \angle D \).

See attachment for the diagram that has been drawn with the necessary information needed for John to prove that ∆ABC is congruent to ∆DEF.

The total area of the quadrilateral field with diagonal 120m is 3000m².

It is defined as a two-dimensional shape with four sides, four vertices, and four corners. There are two main types:

concave and convex. There are also various subcategories of convex quadrilaterals such as trapezoids, parallelograms, rectangles, rhombuses and squares. 

Solution according to the given information in the question:

Given, Diagonal (base of triangle)=120m

           Height(H₁) = 20m

           Height(H₂) = 30m

∴Area of both triangles = 1/2 × base × height

                             = 1/2 × 120 × (20+30)

                             = 1/2 × 120 × 50

                             = 60 × 50

                             = 3000m²

Thus, the total area of the quadrilateral field is 3000m².

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Average Auction Price is 0.9925the noncompetitive bidders will receive $750 million at a price of $0.9925 per $1 of par value.

To determine who will receive T-bills, what quantity, and at what price, we need to rank the bidders based on the bid prices and allocate the T-bills in descending order of bid prices until the entire $2.5 billion par value has been allocated. The bid prices listed are quoted as a percentage of par value, so we need to calculate the dollar amount bid for each bidder as follows:

Bid Amount = Bid Price × Par Value

For Bidder A:

Bid Amount = 0.9940 × 500 million

Bid Amount = $497 million

For Bidder B:

Bid Amount = 0.9901 × 750 million

Bid Amount = $742.6 million

For Bidder C:

Bid Amount = 0.9925 × 1.5 billion

Bid Amount = $1.48875 billion

For Bidder D:

Bid Amount = 0.9936 × 1 billion

Bid Amount = $993.6 million

For Bidder E:

Bid Amount = 0.9939 × 600 million

Bid Amount = $596.34 million

Total Bid Amount = $3.31874 billion

Since the total bid amount exceeds the $2.5 billion par value of the T-bills being auctioned, we need to allocate the T-bills to the highest bidders until the entire $2.5 billion has been allocated.

Ranking the bidders in descending order of bid prices, we have:

Bidder B with a bid price of $0.9901

Bidder C with a bid price of $0.9925

Bidder D with a bid price of $0.9936

Bidder E with a bid price of $0.9939

Bidder A with a bid price of $0.9940

Allocating T-bills to the highest bidders until the entire $2.5 billion par value has been allocated, we have:

Bidder B will receive $750 million at a price of $0.9901 per $1 of par value.

Bidder C will receive $750 million at a price of $0.9925 per $1 of par value.

Bidder D will receive $500 million at a price of $0.9936 per $1 of par value.

Bidder E will receive $250 million at a price of $0.9939 per $1 of par value.

The noncompetitive bids of $750 million will be allocated at the average auction price, which is calculated as the simple average of the four highest accepted bid prices:

Average Auction Price = (0.9901 + 0.9925 + 0.9936 + 0.9939) / 4

Average Auction Price = 0.9925

Therefore, the noncompetitive bidders will receive $750 million at a price of $0.9925 per $1 of par value.

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Answer:this is the answer

Step-by-step explanation:

Answer:

Monica = 48.50

Samuel = 24.25

Kara = 17.25

Step-by-step explanation:

First you write equations as you are reading the text:

m = 2s ("Monica earned twice as much as Samuel")

s = k+7 ("Samual earned 7 more than Kara")

m = 48.50

Next, you convert these equations to solve for s and k respectively.

So, if m=2s, then s=m/2:

s = m/2 = 24.25

Likewise, if s=k+7, then k=s-7

k = s-7 = 17.25

The difference between greatest and least is 48.50 - 17.25 = 31.25

Answer:

3000

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

"If the expression has exponents or square roots, they are to be performed after parentheses and other grouping symbols have been simplified and before any multiplication, division, subtraction and addition that are outside the parentheses."

Answer:

27.5253% increase

Step-by-step explanation:

i got this answer right on khan academy

The volume of the cone is 48 cubic units when the height of the cone is 4 units.

The given equation V = 12h represents the volume of cones with a radius of 6 units.
The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the cone, h is the height of the cone and π is the value of pi which is approximately equal to 3.14.
Given that radius, r = 6 units. Therefore, the formula for the volume of the cone can be written as
V = (1/3)π(6)²h= 12h cubic units
As per the problem, this relation is used to find the volume of cones with a radius of 6 units. For instance, if the height of the cone is 4 units, then using the formula above, the volume of the cone can be calculated by substituting h = 4 units.V = 12 × 4= 48 cubic units

Therefore, the volume of the cone is 48 cubic units when the height of the cone is 4 units.

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Answer:

Step-by-step explanation:

Answer; present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

The present value of $12,200 to be received 4 years from today can be calculated using the formula for present value. The formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:
- Future Value is the amount to be received in the future ($12,200 in this case)
- Discount Rate is the interest rate used to discount future cash flows (5 percent in this case)
- n is the number of periods (4 years in this case)

Plugging in the given values into the formula:

Present Value = $12,200 / (1 + 0.05)^4

Calculating the exponent first:

(1 + 0.05)^4 = 1.05^4 = 1.21550625

Dividing the future value by the calculated exponent:

Present Value = $12,200 / 1.21550625

Calculating the present value:

Present Value = $10,027.51

Therefore, the present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

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Answer:

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

did the test

Answer:

6/10

Step-by-step explanation:

divide the numerator and denominator by ten to remake the hundredths as tenths