Fill in the blank with a number to make the expression a perfect square.x²+18x+

So the linear model that describes the growth of the organism over the 5 hour period is: y = 6x + 16, where x is the number of hours and y is the weight of the organism in mg.

A linear model is a mathematical equation that describes a linear relationship between two or more variables. In other words, it is a model that assumes that the relationship between the variables can be represented by a straight line. Linear models are commonly used in various fields, including economics, finance, engineering, and science, to analyze and predict the relationship between variables. They are particularly useful when analyzing data that shows a linear trend, or when making predictions based on historical data. Linear models can be simple or multiple, depending on the number of independent variables involved. They can also be adjusted to fit nonlinear data by transforming the variables or using a different model altogether.

Here,

To find a linear model that describes the growth of the organism over time, we need to determine the rate of growth (change in weight per unit time) and the initial weight.

The rate of growth can be found by taking the difference between the final weight and the initial weight and dividing by the time period:

Rate of growth = (final weight - initial weight) / time period

= (46 mg - 16 mg) / 5 hours

= 6 mg/hour

So the organism is growing at a rate of 6 mg per hour.

The initial weight of the organism is given as 16 mg.

Now we can write the equation of the line as:

y = mx + b

where y is the weight of the organism in mg, x is the time in hours, m is the rate of growth in mg/hour, and b is the initial weight in mg.

Substituting the values we found, we get:

y = 6x + 16

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Answer:

it is too blury to read

Step-by-step explanation:

Answer:

you can make 12 cans of them

Answer:

18.09

Step-by-step explanation:2.4x2.4, then x3.14  

Answer:

answers below

Step-by-step explanation:

If you are trying to find the area the answers are:

Earth= 289.52918

Saturn=6,532.5021

The formula for area for a sphere is:

4 x pie x r2

If you are trying to find the volume the answers are:

Earth=57.90584

Saturn=46,647.01596

The formula for volume for a sphere is:

4/3 x pie x r3

Also the radius (r) is half of the diameter, so you divide the diameter by 2.

Answer:

6

Step-by-step explanation:

Answer: 29000

Step-by-step explanation:

12000 + 2500 = 14500

14500 * 2 = 29000

we have the expressions

3.2^2-1=10.24-1=9.24

10-0.33*2=10-0.66=9.34

therefore

should be joined by a not equal sign to form an inequality

so

9.24 < 9.34

9.24 is less than 9.34

I’ve completed the question.

Would you like me to elaborate on any point?

Answer:

2/15

Step-by-step explanation:

1/3 x 2/5

= ( 1 x 2 ) / ( 3 x 5 )

= 2/15

Answer:

2/15

Step-by-step explanation:

1/3*2/5

(1*2)/(3*5)

2/15

Answer:

$1,620

Step-by-step explanation:

If you are looking for a way to make some money, you might be tempted by the offer of a purchase that has a positive expectation. But before you jump into it, you should know what expectation really means and how to calculate it. Expectation is not the same as the actual outcome of a purchase. It is just an average of what you can expect to get in the long run, based on the probabilities of different outcomes. Sometimes you might get more than the expectation, sometimes less, and sometimes nothing at all. For example, suppose you have a chance to buy a lottery ticket that costs $7,200 and has a 50% chance of winning $9,000, a 10% chance of winning nothing, and a 40% chance of losing your money. How do you know if this is a good deal or not? You can use the formula for expectation to find out:

Expectation = (50% x $9,000) + (10% x $0) + (40% x -$7,200)

Expectation = (0.5 x 9,000) + (0.1 x 0) + (0.4 x -7,200)

Expectation = 4,500 + 0 - 2,880

Expectation = 1,620

The expectation of this purchase is $1,620. This means that on average, you can expect to make $1,620 from this purchase in the long run. But this does not mean that you will always make $1,620 every time you buy the ticket. Sometimes you might win $9,000 and be very happy. Sometimes you might lose $7,200 and be very sad. And sometimes you might win nothing and be very bored. The expectation is just an average of all these possible outcomes.

So what does this mean for your decision? Well, it depends on how much you value risk and reward. If you are a risk-taker who likes to gamble and doesn't mind losing money sometimes, then you might go for the purchase with a positive expectation. After all, you have a chance to make more money than you spend in the long run. But if you are a risk-averse person who prefers to play it safe and avoid losses, then you might stay away from the purchase with a positive expectation. After all, you have a chance to lose money or break even in the short term.

The choice is yours. But remember: expectation is not reality. It is just a mathematical tool to help you evaluate your options. Don't let it fool you into thinking that you know what will happen in the future. The only thing that is certain is uncertainty, and luckily this is just Mathematics!

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer: B. All real numbers

Step-by-step explanation:

See attached image.

Answer:

27.43 (rounded to the nearest hundredths)

Step-by-Step Explanation:

192÷7=27.428571...

The requried, 20 youths use both iPhone and Samsung, and 200 youths use neither iPhone nor Samsung.

Let A be the set of youths using only iPhones, B be the set of youths using only Samsung, and C be the set of youths using both. Then, we have:

|A| = 150

|B| = 770

|A ∪ B| = 900

We want to find |C| and |A ∩ B| (which is the number of youths using both).

Using the inclusion-exclusion principle, we have:

|A ∪ B| = |A| + |B| - |A ∩ B|

900 = 150 + 770 - |A ∩ B|

|A ∩ B| = 20

So, 20 youths use both iPhone and Samsung.

To find the number of youths who use neither, we can use the fact that:

|A ∪ B ∪ C| = 1100

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Plugging in the values we know, we get:

1100 = 150 + 770 + |C| - 20 - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

|C| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 200

Since the number of youths using both is 20, we have:

|A ∩ C| = |B ∩ C| = |A ∩ B ∩ C| = 0

So, we can simplify the equation to:

|C| = 200

Therefore, 200 youths use neither iPhone nor Samsung.

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The requried, probability that both the first digit in the last digit of the three-digit number is even numbers is 20%.

To count the number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9, we can use the permutation formula:

P(n, r) = n! / (n-r)!

In this case, we have n = 6 (since we have 6 digits to choose from) and r = 3 (since we want to form three-digit numbers). Using the formula, we get:

P(6, 3) = 120

We can choose the first digit in two ways (2 or 8), and we can choose the last digit in three ways (2, 8, or 6). For the middle digit, we have four digits left to choose from (1, 3, 5, or 9), since we cannot repeat digits. Therefore, the number of three-digit numbers with distinct digits that have an even first and last digit is:

2 x 4 x 3 = 24

The total number of three-digit numbers with distinct digits is 120, so the probability that a randomly chosen three-digit number with distinct digits has an even first and last digit is:

24/120 = 0.2 or 20%

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The hourly pay that was charged for the repairs to Victor's car was $ 57.14

To find the hourly wage, find the total labor wages that were charged as a cost to Victor's repairs. This cost would be:

= 272 - 6 - 28. 50 - 20 .00 - 15. 00 - 2. 50

= $ 200

The total hourly wage charged was $ 200 for 3 . 5 hours of work.

This means that the hourly pay charged was :

= Total labor wages / Number of hours

= 200 / 3 . 5

= $ 57.14

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Answer:

the semiannual interest payment is $153.77 and the total interest earned over the life of the bond is $9,226.20.

Step-by-step explanation:

To find the semiannual simple interest payment, we need to divide the annual interest rate by 2, since there are 2 semiannual periods in a year:

Semiannual interest rate = Annual interest rate / 2

= 6.268% / 2

= 3.134%

To find the semiannual interest payment, we multiply the face value of the bond by the semiannual interest rate:

Semiannual interest payment = Face value x Semiannual interest rate

= $4900 x 3.134%

= $153.77 (rounded to two decimal places)

To find the total interest earned over the life of the bond, we need to multiply the semiannual interest payment by the number of semiannual periods in the bond's life. Since the bond has a 30-year term and 2 semiannual periods in a year, the bond has a total of 60 semiannual periods:

Total interest earned = Semiannual interest payment x Number of semiannual periods

= $153.77 x 60

= $9,226.20 (rounded to two decimal places)

Therefore, the semiannual interest payment is $153.77 and the total interest earned over the life of the bond is $9,226.20.

Answer:

If M is mid point then XM = MY

2x +5 = 3x -1

2x - 3x = -1 - 5

-x = -6....so

x = 6

MY = 3(6) -1

MY = 18 -1

MY = 17

Answer:

Step-by-step explanation:

\((x-2)(x+2)((x+1)^2\\ \\ (x^2-4)(x+1)^2\\ \\ (x^2-4)(x^2+2x+1)\\ \\ x^4+2x^3+x^2-4x^2-8x-4\\ \\ x^4+2x^3-3x^2-8x-4\)

The point that is marked X on the graph is the standard free energy of the reaction.

Let us note that when we talk about the standard free energy of the reaction what we mean here is the energy of the reaction that is free to be able to do work. In the case of the standard change in the free energy, we are looking at the change of the free energy of the standard states of the substance.

The graph as we have it is trying to show the reaction profile and the reaction profile would give the difference between the free energy of the products and the reactants and this is the standard change in free energy.

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Using a numerical solver or iterative method, we can find that n is approximately 217.92 months. Rounded to two decimal places, this is 217.92 months.

How funds are calculated ?

The calculation of funds depends on various factors, such as the amount of money available, the interest rate, the length of time the money is invested, and any additional contributions or withdrawals made during the investment period.

We can start by using the future value formula to find the value of the trust fund in 30 years when your client turns 65. Let F be the future value of the trust fund, P be the present value of the trust fund, r be the interest rate, and n be the number of years:

F = P * (1 + r)^n

In this case, P is $1.19 million, r is 4.0% per year, and n is 30 years. Plugging these values into the formula gives:

F = $1,190,000 * (1 + 0.04)^30

F = $1,190,000 * 2.2084

F = $2,628,996

So the value of the trust fund when your client turns 65 will be $2,628,996.

Now we can use the present value formula to find how long the trust fund will last once your client starts to withdraw $20,500 per month. Let P be the present value of the trust fund, PMT be the monthly withdrawal amount, r be the monthly interest rate (which is 4.0% divided by 12), and n be the number of months:

P = PMT * ((1 - (1 + r)^-n) / r)

We want to find the value of n that makes P equal to $2,628,996 (the value of the trust fund when your client turns 65). Plugging in the values we know gives:

$1,190,000 = $20,500 * ((1 - (1 + 0.04/12)^-n) / (0.04/12))

Simplifying this equation requires some algebraic manipulation. We can start by multiplying both sides by (0.04/12):

$1,190,000 * (0.04/12) = $20,500 * ((1 - (1 + 0.04/12)^-n) / (0.04/12))

Simplifying further, we can multiply both sides by (1 + 0.04/12)^n:

$1,190,000 * (0.04/12) * (1 + 0.04/12)^n = $20,500 * (1 - (1 + 0.04/12)^-n)

Dividing both sides by $20,500:

($1,190,000 * (0.04/12) * (1 + 0.04/12)^n) / $20,500 = 1 - (1 + 0.04/12)^-n

Subtracting 1 from both sides:

1 - ($1,190,000 * (0.04/12) * (1 + 0.04/12)^n) / $20,500 = (1 + 0.04/12)^-n

Taking the natural logarithm of both sides:

ln(1 - ($1,190,000 * (0.04/12) * (1 + 0.04/12)^n) / $20,500) = -n * ln(1 + 0.04/12)

Now we can solve for n:

n = (ln(1 - ($1,190,000 * (0.04/12) * (1 + 0.04/12)^n) / $20,500)) / (-ln(1 + 0.04/12))

Using a numerical solver or iterative method, we can find that n is approximately 217.92 months. Rounded to two decimal places, this is 217.92 months.

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6/11 is the probability that I cat an English muffin for breakfast.

Let G, C, and E represent the events of selecting granola, cereal, and an English muffin, respectively.

Let P(G), P(C), and P(E) represent the probabilities of selecting granola, cereal, and an English muffin, respectively.

We are given that:

P(E) = 2P(G) (the English muffin is selected twice as often as the granola)

P(E) = 3P(C) (the English muffin is selected three times as often as the cereal)

We can use these relationships to solve for P(G), P(C), and P(E):

P(G) = P(E)/2

P(C) = P(E)/3

P(G) + P(C) + P(E) = 1

Substituting the first two equations into the third equation and solving for P(E), we get:

P(E)/2 + P(E)/3 + P(E) = 1

11P(E)/6 = 1

P(E) = 6/11

Therefore, the probability that an English muffin is selected for breakfast is 6/11.

Hence, option (B) is the correct choice.

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The given product is:

This can be simplified as shown below

Applying the additive rule of exponent, we have:

Answer:

Step-by-step explanation:

Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods

1/PV (FV) = (PV(1 + r^n)1/PV divide by PV

ln(FV/PV) = ln(1 + r^n) convert to natural log function

ln(FV/PV) = n[ln(1 + r)] by simplifying

n = ln(FV/PV) / ln(1 + r) solve for n

n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually

n = 9

n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly

n = 104 months or 8.69 years

n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily

n = 3163 days or 8.67 years

Alternatively

A = P e ^(rt)

Given that r = 8%

= 8/100

= 0.08

2 = e^(0.08t)

ln(2)/0.08 = t

0.6931/0.08 = t

t= 8.664yrs

t = 8.67yrs

Which ever approach you choose to use,you will still arrive at the same answer.

The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.

What is a good example of a line's slope?

The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.

A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.

B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.

C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.

D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.

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Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

The best statement that describes the strategy for estimating the perimeter of the figure (please see the attached diagram) is the option;

Ad the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall

An estimate is an approximation of a true value, which is a value that is close to the actual value of the measured quantity.

Please find attached a diagram of the possible figure created with MS Word

The length of the side of the sides of the possible figure in the figure, obtained from a similar question on the internet are;

Base length = 5 units

Height = 4 units

The figure has a diagonal side which is 4 units wide and 2 units tall.

The length of the slant side, found using Pythagorean theorem can be obtained as follows; Length = √(4² + 2²) = 2·√5 ≈ 5

The correct option is therefore to add the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall

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Answer:

4. Between 11:30 and 12:00, they did nothing. The graph didn't go up or down, it just stayed the same meaning they did nothing.

5. 5 miles an hour

Step-by-step explanation:

Answer:

Welll by the looks of it do the last one then > then do the other big number. Hopefully i helped :)))))))))))))))))))))))))))))))))))))))))))))))))))))))

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

(a) List all the possible outcomes

A dice has 6 sides, ranging from numbers 1 to 6.

As such, the possible outcome for 1 dice is 1, 2, 3, 4, 5 and 6.

Since 2 dice are used, the possible outcome increases, ranging from 2 to 12.

Working:

1 + 1 = 2 (MIN)

6 + 6 = 12 (MAX)

Therefore, the possible outcomes is from 2 to 12.

(b) Find the probability of getting an even number as a score

Total number of score = 11

Total number of even score = 6

P (even number) = 6 / 11

I believe this should be the correct answer... seems logical to me. HAHA. Anyway, do let me know if I am correct or have any queries :)