What is the solution of the system?

Use the substitution method.

{y−2x=8
{16+4x=2y

The only solution is (24, 0)

The only solution is (1, 10)

There is no solution.

There are an infinite number of solutions.

A 25-year-old male would pay $491 less for a $50,000 policy of 20-year life insurance at $5.84 per $1,000, than for a straight life policy at $15.66 per $1,000. This is calculated by first determining the total cost of each policy and then finding the difference between the two.

To calculate the cost difference between the 20-year life policy and the straight life policy, we first need to calculate the cost of each policy. The cost of the policies is given per $1,000, and the policies provided are worth a total of $50,000.

To find out how much less a 25-year-old male would pay for the 20-year policy than the straight life policy, we subtract the cost of the 20-year policy from the cost of the straight life policy: $783 - $292 = $491.

So, a 25-year-old male would pay $491 less for a $50,000 20-year policy than a straight life policy.

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Answer: x^2 + x + 4

Step-by-step explanation:

You factor the expression to x + x^2 +4

Then you simplify to x^2 + x +4

To determine the number of adult and child tickets sold, we can set up a system of equations based on the given information. By solving the system of equations, we find that the number of adult tickets sold is 300, and the number of children's tickets sold is 900.

Let's assume that the number of adult tickets sold is represented by 'x'.

Since the number of children's tickets sold is three times the number of adult tickets, the number of children's tickets sold can be represented as '3x'.

The total revenue from ticket sales is $15,000, so we can create the following equation:

20x + 10(3x) = 15,000

Simplifying this equation, we get:

20x + 30x = 15,000

Combining like terms, we have:

50x = 15,000

Dividing both sides by 50, we find:

x = 300

So, the number of adult tickets sold is 300, and the number of children's tickets sold is 3 times that, which is 900.

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Answer:  (a) an agreement between all parties involved in the contract.

Step-by-step explanation: While forming a contract, we generally use the phrase "meeting of the minds" , which implies that both the parties which are involved in the contract agree to the terms and conditions mentioned in the contract and are aware of the commitments made by each of the parties. Out of the four given options, only option (a) is acceptable, because the other three do not match with our requirement.

Thus, the correct option is (a).

An agreement between all parties involved in the contract. The correct option is A.

  While forming a contract, we generally use the phrase "meeting of the minds", which implies that both the parties which are involved in the contract agree to the terms and conditions mentioned in the contract and are aware of the commitments made by each of the parties. Out of the four given options, only option (a) is acceptable, because the other three do not match with our requirements.

Therefore, an agreement between all parties involved in the contract. The correct option is A.

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Answer: option c.) 5

Step-by-step explanation: you must always follow PEMDAS

so first step would be parentheses but there are none so you move on to exponents. 4^0=1. so now you have 1+2x3-2.

Next step is multiplication. 2x3 is 6 so now you have 1+6-2.

Now we only have addition and subtraction so you move from left to right. 1+6=7

7-2=5

giving you option c. 5

Answer:

the answer is the second option; because 4+(-7) is an equivalent expression the answer Is -3

Opposite sides of parallelogram LMNO must be equal. By setting the equations for opposite sides equal and solving, we find x = 11 and y = 5.

To determine the values of x and y for which LMNO is a parallelogram, we can use the properties of a parallelogram which state that opposite sides are equal in length. Since ON and LM are opposite sides, as well as OL and MN, we set their equations equal to each other:

Solving the first equation gives us x = 11. Substituting x = 11 in the second equation gives 2y - 6 = 4, which simplifies to y = 5. Therefore, the values are x = 11 and y = 5 for LMNO to be a parallelogram.

The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.

Given that

A 4 cm bean plant grows at a rate of 1/2cm per week.

A 5.5 cm flower grows at a rate of 1/4cm per week.

If h is the height of the plant in centimeters and t is the number of weeks, then the system of equations is:

h = 1/2t + 4

h = 1/4t + 5.5

According to the question

The solution of the system of equation is;

h = 1/2t + 4

h = 1/4t + 5.5

Substitute the value of h from equation 1 in equation 2

[tex]\rm h = \dfrac{1}{4}+5.5\\\\\dfrac{1}{2}t +4 = \dfrac{1}{4}t +5.5\\\\\dfrac{1}{2}t-\dfrac{1}{4}t = 5.5-4\\\\\dfrac{2t-t}{4} = 1.5\\\\\dfrac{t}{4} = 1.5\\\\t = 4\times 1.5\\\\t = 6[/tex]

Substitute the value of t in equation 1

[tex]\rm h = \dfrac{1}{2}\times 6+4\\\\h = 3+4\\\\h = 7[/tex]

Hence, The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.

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After the first year, with an initial investment of $5,000 and an annual interest rate of 6%, the total amount in the savings account is $5,300. After the second year, the total amount in the account increases to $5,618.

You are investing $5,000 in a savings account with an annual interest rate of 6%. The amount of interest you earn each year is calculated using the formula: principal amount *(interest rate/100).

A. After the first year, you would have:
Interest = $5,000 * (6/100) = $300
Therefore, the total amount in the savings account after one year is $5,000 + $300 = $5,300.

B. For the second year, we apply the same formula to the updated  balance from the first year:
Interest = $5,300 * (6/100) = $318
Therefore, the total amount in the savings account after two years is $5,300 + $318 = $5,618.

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Answer:

Just took the test and got an 100% so the answers are in fact,

in one study it was found that the correlation coefficient between two variables is -0.32. which statement is true?

B. There is a weak negative association between the variable  

A study of several cities shows a positive correlation between the percent of people biking to work and the percent of people spending their vacation time at home.  

Which statement is most likely true?

A. Bike riding makes people want to vacation at home  

Have a wonderful day if you need any other questions from this test let me know!!!!!!!

Final answer:

The correct answer for the correlation coefficient of -0.32 is B. There is a weak negative association.

For the correlation between biking and vacationing at home, the likely third variable is cost of gas, choice D: The correlation is due to a third variable: cost of gas

Explanation:

The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient is -0.32, which indicates a weak negative association between the variables. A negative correlation means that as one variable increases, the other variable tends to decrease. So, option B - There is a weak negative association between the variables - is true.

For the second question, based on the information given, it is most likely that option D - The correlation is due to a third variable: cost of gas - is true. This means that the positive correlation between the percent of people biking to work and the percent of people spending their vacation time at home is likely influenced by the cost of gas as a third variable.

Answer: Yes

Step-by-step explanation:

Hi, to answer this question we have to substitute x =-3 on the function given, and solve for the variable y.

y = 15 • 3x

Replacing the value of the variable x by -3:

y = 15 • 3(-3)

Multiplying

y = 15 .-9

y = -135

It is correct, the answer is y= -135  

Feel free to ask for more if needed or if you did not understand something.

Answer:

the answer is d. Cr= 2 pi

Step-by-step explanation:

The correct answer that is not equivalent to the formula for the circumference of a circle  is:  Cr = 2pi. (Option D).

To prove the options, it is important to test the formulas given:

In option A,  C over r equals 2 times pi:

C/r = 2 * pi

This equation is equivalent to the formula for the circumference of a circle, C = 2 * pi * r, as you can simply multiply both sides by 'r' to get the standard formula.

In Option B, C over pi equals 2 times r:

C/pi = 2 * r

This equation is equivalent to the formula for the circumference of a circle as pi can be multiplied on both sides

In Option C, C over the quantity of r times pi equals 2:

C / (r * pi) = 2

This equation is equivalent to the formula for the circumference of a circle since you can multiply both sides by (r * pi) to get C = 2 * (r * pi).

In option D, This equation is not equivalent to the formula for the circumference of a circle. It is missing the division by 'r' on the right side of the equation.

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Answer:

sin θ [tex]=\frac{3}{5}[/tex]

It is given that , Angle θ lies in the second quadrant.

In the right triangle, Perpendicular =3 units, and Hypotenuse = 5 Units

As, sinθ  is positive in second Quadrant also.That is , sin(π-θ )=sin θ

Also, [tex]sin(\frac{\pi}{2}-\Theta)=cos\Theta[/tex]

[tex]sin (\Theta) = 3/5\\\\  (\Theta) =sin^{-1} \frac{3}{5} {\text{or}} (\Theta) =\pi -sin^{-1} \frac{3}{5}\\\\cos(\frac{\pi}{2}-\Theta)= \frac{3}{5}\\\\ \frac{\pi}{2}-\Theta=cos^{-1}[\frac{3}{5}]\\\\ \Theta= \frac{\pi}{2}-cos^{-1}[\frac{3}{5}][/tex]

So, [tex]\pi-\Theta= \frac{\pi}{2}+cos^{-1}\frac{3}{5}, {\text{or}}\pi -sin^{-1} \frac{3}{5}[/tex]

are values of theta which lies in second quadrant.

Answer:

The length of the blanket should be less than or equal to 60 inches.

The width should be greater than or equal to 30 inches.

Step-by-step explanation:

Let the length of the blanket be = l

Let the width of the blanket be = w

Charlene wants the width, w, to be at least half its length, l. This can be shown as :

[tex]w\geq 0.5l[/tex]

She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches.

This can be shown as :

[tex]2l+2w\leq 180[/tex]

[tex]2l+2(0.5l) \leq 180[/tex]

[tex]2l+1l \leq 180[/tex]

[tex]3l \leq 180[/tex]

[tex]l\leq 30[/tex]

So, we get length of the blanket should be less than or equal to 60 inches.

And the width should be greater than or equal to 30 inches.

The probability model for the number of good batteries when selecting 2 out of 10 with 3 dead is calculated as combinations of selecting good and dead batteries for each scenario. The probabilities are always divided by the total ways of drawing 2 from 10.

This question is a typical problem related to probability. Firstly, we need to identify the number of ways we can draw 2 batteries randomly from this given set. We know there are 10 batteries in total with 3 dead ones. That leaves us with 7 good batteries.

Assuming 'X' is the number of good batteries we could select when drawing two batteries at random, 'X' could be 0, 1, or 2. Here are the three possible cases:

To find out the probability of each scenario, we would have to divide by the total number of ways of drawing 2 batteries from 10, which equals to C(10, 2).

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Answer: 8x+y

Step-by-step explanation:

you always combine your like terms, a trick is to put a line infront of your equation signs making it look like 3x/+2y/+5x/-y. This makes it easier to see if your terms are positive or negative. Now you have 5x+3x and 2y-y giving you 8x+y because its still positive.

The measure of angle ∠XYZ is 66°.

Given:

∠W + ∠X = ∠XYZ (Sum of opposite interior angles is equal to the exterior angle)

Let's solve for x:

2x + 12 + 2x + 14 = 5x + 16

4x + 26 = 5x + 16

26 - 16 = 5x - 4x

10 = x

Now substitute the value of x into the equation for ∠XYZ:

∠XYZ = 5x + 16

∠XYZ = 5 * 10 + 16

∠XYZ = 50 + 16

∠XYZ = 66°

Therefore, the measure of ∠XYZ is 66°.

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Answer:

Length of BO is three times the length of DO.

Step-by-step explanation:

In trapezoid ABCD, [tex]CD\ ||\ AB[/tex]

In ΔCDO and ΔABO,

So, [tex]\Delta CDO\sim \Delta ABO[/tex] according to Angle-Angle similarity.

Therefore, the ratio of corresponding sides will be same.

[tex]\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{OA}[/tex]

[tex]\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{3\cdot OC}[/tex]

[tex]\Rightarrow \dfrac{OD}{OB}=\dfrac{1}{3}[/tex]

[tex]\Rightarrow OB=3\cdot OD[/tex]

The correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).

To express log₃ 6 as a logarithm of base 2, we can use the change of base formula. The change of base formula states that logb x = (logc x) / (logc b), where c is any positive value other than 1.

Applying the change of base formula to log3 6:

log₃ 6 = (log₂ 6) / (log₂ 3)

Therefore, the correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).

To calculate it properly, we need to find the decimal approximation of this expression:

Using the appropriate logarithmic functions, we have:

(log₂ 3) / (log₂ 6) ≈ 1.58496 / 2.58496 ≈ 0.6124

Thus, log₃ 6 as a logarithm of base 2 is approximately 0.6124.

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