Divide 420 in the ratio of 2:1

We have been given that company A has a 30% chance of losing $12,000.

Let us calculate the amount that Yun can loose.

[tex]\frac{12000\times 30}{100} \\ \\ =\$3600[/tex]

Now, 45% chance of breaking even. It means neither loss nor profit.

Then, 25% chance of earning Yun $11,000.

Let us calculate the amount of profit

[tex]\frac{11000 \times 25}{100} \\ \\ =\$2750[/tex]

Since, 3,600 > 2,750. It means that Yun will be in loss on investing in the company.

Hence, she will not invest in the company A.

d is the correct option.

d. no, 3,600 > 2,750

Answer: B. [tex]\frac{16}{25}[/tex]

Step-by-step explanation:

We know that if a figure or solid shape is dilated to create a new shape then the new shape is similar to the original shape.

Also, the scale factor of dilation is the ratio of the sides of new shape to the corresponding sides of the original shape .

Let k be the scale factor of dilation, then

Given : Original shape - larger prism

New shape - smaller prism

Surface area of prism with all sides equal (a)=[tex]4a^2[/tex]

Surface area of original prism =[tex]4(10)^2=400[/tex]

Surface area of new prism =[tex]4(8)^2=256[/tex]

[tex]\Rightarrow k=\frac{256}{400}=\frac{16}{25}[/tex]

Hence, the scale factor =  [tex]\frac{16}{25}[/tex]

Final answer:

After 140 hours, which is equivalent to 4 half-lives, the amount of bromine-82 remaining from an 80 mL sample will be 5 mL, as the amount is halved after each half-life period of 35 hours.

Explanation:

The question involves the half-life of a radioactive isotope, which is a concept in Chemistry specifically related to nuclear chemistry and radioactive decay. Since bromine-82 has a half-life of about 35 hours, after 140 hours, which is equivalent to 4 half-lives, the amount of the element remaining in the sample will be reduced by a factor of two after each half-life. To calculate this, we start with the initial 80 mL and reduce it by half 4 times.

After the first half-life (35 hours), 40 mL remains.

After the second half-life (70 hours), 20 mL remains.

After the third half-life (105 hours), 10 mL remains.

After the fourth half-life (140 hours), 5 mL remains.

Therefore, the correct answer is D. 5mL.

Final answer:

After 140 hours, which is four half-lives of Bromine-82, only 5 mL of an initial 80 mL sample will remain, making the correct answer D. 5mL.

Explanation:

The question is asking how much of a radioactive isotope will remain after a certain amount of time, given its half-life. In this example, the half-life of Bromine-82 is about 35 hours, and we want to know how much of an 80 mL sample will remain after 140 hours. To solve this, we will use the concept of half-life, which is the time it takes for half of the radioactive atoms in a sample to decay.

Since 140 hours is equal to 4 half-lives (140 hours ÷ 35 hours/half-life), we can calculate the remaining amount of Bromine-82 in the sample by halving the initial amount repeatedly, four times:

After the first half-life (35 hours), the remaining amount is ⅓ × 80 mL = 40 mL.

After the second half-life (70 hours in total), the remaining amount is ⅓ of 40 mL = 20 mL.

After the third half-life (105 hours in total), the remaining amount is ⅓ of 20 mL = 10 mL.

After the fourth half-life (140 hours in total), the remaining amount is ⅓ of 10 mL = 5 mL.

The correct answer is D. 5mL.

The charge per day and charge per mile for the compact car is $36 and $0.22 respectively

let

x = charge per day

y = charge per mile

6x + 550y = 337 (1)

3x + 350y = 185 (2)

multiply (2) by 2

6x + 700y = 370 (3)

6x + 550y = 337 (1)

subtract (1) from (3)

700y - 550y = 370 - 337

150y = 33

y = 33/150

y = 0.22

substitute y = 0.22 into (2)

3x + 350y = 185

3x + 350(0.22) = 185

3x + 77 = 185

3x = 185 - 77

3x = 108

x = 108/3

x = 36

Therefore, charge per day and charge per mile for the compact car is $36 and $0.22 respectively

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Answer:

-1/3x is the answer

Step-by-step explanation:

Do the problem.

An equation of the direct variation that includes the point (6, –2) is y = -1/3(x).

In Mathematics, a direct variation is also referred to as direct proportion and it can be modeled by using the following mathematical expression or function:

y = kx

Where:

Under direct variation, the value of x represent an independent variable while the value of y represents the dependent variable. Therefore, the constant of proportionality (variation) can be calculated as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = -2/6

Constant of proportionality (k) = -1/3

Therefore, the required equation is given by;

y = kx

y = -1/3(x)

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For independent events A and B, the probability of both happening is the product of their individual probabilities. In this case, the probability of both A and B happening is 1/16.

In the field of probability in mathematics, when dealing with independent events like A and B in your question, the probability of both A and B happening (denoted as P(A AND B)) is calculated by multiplying the probability of A happening (P(A)) by the probability of B happening (P(B)) This is known as the multiplication rule for independent events.

So, if the probability that A will happen (P(A)) is 1/4, and the probability that B will happen (P(B)) is also 1/4, then the probability that both A and B will happen (P(A AND B)) is (1/4) * (1/4) = 1/16.

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The maximum height at the moment is 266.0625 ft.

The equation for a projectile's height versus time is

[tex]&h(t)=-16 t^{2}+V t+h \\[/tex]

h = 2

V = 130

Substitute these values into the function

[tex]$h(t)=-16 t^{2}+130 t+2$[/tex]

Take the first derivative

[tex]$h^{\prime}(t)=-16* 2 t+130[/tex]

[tex]=-32 t+130$[/tex]

Equate the derivative with zero [tex]$h^{\prime}(t)=0$[/tex].

Solve the equation -32 t + 130=0

32 t = -130

t = -130 /(-32)

= 4.0625(s) .

Find the maximum height at the moment

t = 4.0625 (s)

h(4.0625) [tex]= -16(4.0625)^{2}+130 * 4.0625+2[/tex]

= - 264.0625+528.125+2

= 266.0625 ft.

Therefore, the maximum height at the moment is 266.0625 ft.

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96 holes I think is the correct answer

Answer:

d) r=0.90

Step-by-step explanation:

When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables. A correlation nearerto -1 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation.

Correlation coefficient measures the strength of association between two variables.

It may be positive or negative.

If nearer to 1 or - there is strong correlation

Since here is it 0.90 positive and nearer to 1 out of all 4 options

option d is correct

The square's area is relatively simple:

A=b²
A=6²=36 ft²

But now let's observe the triangles, a triangle's area is:

A=(1/2)*b*h

the base is equal to 6 ft

b=6 ft

AC=BC----------> because the angle is 45°

AC=6 ft/2----> 3 ft

so

BC=3 ft

A=(1/2)*6*3----> 9 ft²

Multiply the triangle's area by four to account for all four triangular faces and add the squares area for your answer

Surface area=36 +4*9-----> 72 ft²

the answer is

72 ft²

Answer:

72

Step-by-step explanation:

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