The length of his rectangular field is 35 metres.
How to find the length of the field?Farmer Fred has a rectangle field. 2 / 5 of the field is planted with carrots and the rest is for cabbages.
Therefore, the width of the field is 13 metres. The length of the field can be found as follows:
area of the carrot section = 182 m²
let
x = area of the field.
Therefore,
2 / 5 x = 182
cross multiply
2x = 910
x = 910 / 2
x = 455 m²
Therefore,
length of the field = 455 / 13
length of the field = 35 metres.
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PLEASE HELP IT’S TIMED!!!! 50 POINTS!!!
You deposit $4,500 in an account that earns 6% simple interest.
How much will be in your account after 5 years?
Researchers try to gain insight into the characteristics of a ______ population by examining a of the population. Select one:
a. Description
b. Model
c. Replica
d. Sample
Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.
A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.
The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.
By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.
Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.
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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A(n) = 5 + (n - 1) 1/6
Answer:
A(1) = 5
A(4) = 5.5
A(10) = 6.5
Step-by-step explanation:
An nth term formula works, whether for a arithmetic or geometric sequence, can be used to find any term in a sequence;
Simply substitute the number that corresponds with the position of the term you want to find and the formula will give the value of that term;
So:
A(1) = 5 + ⅙((1) - 1) = 5
A(4) = 5 + ⅙((4) - 1) = 5.5
A(10) = 5 + ⅙((10) - 1) = 6.5
A chef uses a warming oven to maintain the temperature of food until all items are ready for plating. Potato croquettes, whose temperature is 200 C, are placed in the warming oven. The relationship between the core temperature of the potato in degrees Celsius, and the cooking time, t in minutes, is modelled by the equation 200 – T=180(0.94)t. If the chef needs to plate the entrée before the potato croquettes have a core temperature of 1400 C, how much time does he have?
Given
\(200-T=180(0.94)^t\)Solution
When T=140
\(\begin{gathered} 200-T=180(0.94)^{t} \\ \\ 200-140=180(0.94)^t \\ 60=180(0.94)^t \\ \\ 60=180\cdot\:0.94^t \\ Divide\text{ both side 180} \\ \frac{180\cdot \:0.94^t}{180}=\frac{60}{180} \\ \\ simplify \\ 0.94^t=\frac{1}{3} \end{gathered}\)Apply exponent rule
\(\begin{gathered} t\ln \left(0.94\right)=\ln \left(\frac{1}{3}\right) \\ \\ t=-\frac{\ln \left(3\right)}{\ln \left(0.94\right)} \\ \\ \\ t=17.7552 \end{gathered}\)The final answer
t =1 7.7552years
Find the volume of this cone.
To start calculating the volume of the cone, we obtain the following data:
r = 4 cmh = 9 cmπ = 3To calculate the volume of a cone, we apply the following formula:
\(\boldsymbol{\sf{V=\dfrac{\pi r^{2}h }{3} }}\), where
V = volumeh = heightr = radiusπ = piWe solve, substituting our data in the formula:
\(\boldsymbol{\sf{V=\dfrac{3*(4 \ cm)^{2}*9 \ cm }{3} }}\)taking the square root
\(\boldsymbol{\sf{V=\dfrac{3 *16 \ cm^{2}*9 \ cm }{3} }}\)Multiplying
\(\boldsymbol{\sf{V=\dfrac{432 \ cm^{3} }{3} }}\)Dividing
\(\boxed{\boldsymbol{\sf{V=144 \ cm^{3} }}}\)Therefore the volume of the cone is 144 cm³.
\(\huge\text{Hey there!}\)
\(\huge\textbf{What is the formula for finding the}\\\\\huge\textbf{the volume of a cone?}\)
\(\large\boxed{\mathsf{\dfrac{\pi \times r^2\times h}{3} = volume}}\)
\(\bullet\large\textsf{ Whereas, \boxed{r} is your \underline{radius}, \boxed{h} is your \underline{height}, \& \boxed{\pi} is your pi.}\)
\(\bullet\large\textsf{The pi }\boxed{(\pi)}\large\textsf{ is approximately equal to 3.14.}\)
\(\huge\textbf{What are the labels in your equation?}\)
\(\star\ \large\boxed{{Radius}}\rightarrow \textsf{\underline{4\ centimeters}}}}}\)
\(\star\ \large\boxed{{Height}}\rightarrow \textsf{\underline{9\ centimeters}}}}}\)
\(\star\ \large\boxed{{\pi}}\rightarrow \textsf{\underline{3}}}}}\)
\(\huge\textbf{What does should the equation look}\\\\\huge\textbf{like?}\)
\(\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}\)
\(\huge\textbf{What are the steps to solve for the}\\\\\huge\textbf{question to get the result?}\)
\(\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}\)
\(\large\boxed{\mathsf{= \dfrac{3\times4\times4\times9}{3}}}\)
\(\large\boxed{= \mathsf{\dfrac{3\times16\times9}{3}}}\)
\(\large\boxed{\mathsf{= \dfrac{48\times9}{9}}}\)
\(\large\boxed{\mathsf{= \dfrac{432}{3}}}\)
\(\large\boxed{\mathsf{= \dfrac{432 \div 3}{3\div3}}}\)
\(\large\boxed{= \mathsf{\dfrac{144}{1}}}\)
\(\large\boxed{\mathsf{= 144\div1}}\)
\(\large\boxed{= \textsf{144}}\)
\(\huge\textbf{What is the result to this question?}\)
\(\huge\boxed{\frak{144\ cm^3}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)Percy thinks that since the data {5, 0, 4, 0, 0} has a mode of 0, the data has no mode.
Using 3-5 sentences, critique Percy's reasoning.
The reasoning of Percy is incorrect because there is one mode for the data set.
What is Mode?Mode of a data set is the value that occur most frequently in a data set.
There may be no mode, one mode or more than one mode for a data depending on the number of times values are repeating.
Given data is {5, 0, 4, 0, 0}.
Here the value 0 is repeating three times.
No other number has repeated three times.
So there is only one mode for the data set and is 0.
This does not mean that there is no mode for the set.
A data set has no mode if and only if all the numbers in the set are repeated same number of times.
Hence the reasoning of Percy is incorrect.
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Write and solve an equation for the situation.
The perimeter of a parallelogram is 56 meters. The width of the parallelogram is 8 meters less than its length. Find the length and the width of the parallelogram.
is it ever appropriate to reach a causal conclusion from data collected in a scientific study that showed a statistically significant effect?
No, its not appropriate to reach a causal conclusion from data collected in a scientific study that showed a statistically significant effect.
No, reaching a causal conclusion solely based on statistical significance is not appropriate. Statistical significance indicates that an observed effect is unlikely to have occurred by chance, but it does not imply causation. There may be other factors or confounding variables that have not been considered or controlled for, which could be responsible for the observed effect.
Establishing causation requires additional evidence beyond statistical significance, such as a well-designed experimental study with proper control groups, randomization, and replication. Additionally, causal conclusions often involve a combination of statistical analysis, scientific theory, and a comprehensive understanding of the underlying mechanisms at play.
Therefore, while statistical significance is an important criterion in scientific studies, it should be considered as part of a broader analysis and interpretation of the results, taking into account other relevant factors before making any causal conclusions.
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helpppppppppppppppppppppppppppppppppp pleaseeeeeeeeeee
Answer:
Y:(0,.4), x: (.3, 0)
Step-by-step explanation:
The y intercept is where the line crosses the y axis which is (0,.4).
The x intercept is where the line crosses the x axis which is (.3,0)
A process in which a number is changed, such as by adding, subtracting, dividing, or multiplying.A. operation.B. smart.C. super cool.
Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.
The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.
The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.
Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.
Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.
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Write the following numbers in scientific notation: a. 20405000 b. 0.0202020 c. 0.3450 d. .000011111 e. 101010 f. 0.090650 2. Write the answers to the correct significant figures: a. 10.0592+5.601+4.210 b. (19.341−7.23)×6.9111/4.321= c. 2.34965×8.231= d. 51.41/5.42= e. (7.59+9.20)/(6.23×1.110) 3. Convert 425 K to
∘
F 4. Convert 30
∘
C to
∘
F 5. Conver 97
∘
F to K 6. 10 grams of Al occupy 4ml. What is the density 7. 30 grams of one item in 1.1 quarts. What is the density in g/ml 8. Convert 10Km to miles by using all the steps
a. 2.0405 x 10^7
b. 2.0202 x 10^-2
c. 3.450 x 10^-1
d. 1.1111 x 10^-5
e. 1.0101 x 10^2
f. 9.0650 x 10^-2
a. To convert 20405000 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 2.0405, and since we moved the decimal point 7 places to the left, we multiply by 10^7. Therefore, 20405000 can be expressed as 2.0405 x 10^7.
b. To convert 0.0202020 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 2.0202, and since we moved the decimal point 2 places to the right, we multiply by 10^-2. Therefore, 0.0202020 can be expressed as 2.0202 x 10^-2.
c. To convert 0.3450 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 3.450, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.3450 can be expressed as 3.450 x 10^-1.
d. To convert 0.000011111 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 1.1111, and since we moved the decimal point 5 places to the right, we multiply by 10^-5. Therefore, 0.000011111 can be expressed as 1.1111 x 10^-5.
e. To convert 101010 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 1.01010, and since we moved the decimal point 2 places to the left, we multiply by 10^2. Therefore, 101010 can be expressed as 1.0101 x 10^2.
f. To convert 0.090650 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 9.0650, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.090650 can be expressed as 9.0650 x 10^-2.
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Math word problems please help
Suzie's Slushes has increasing profits each week during the hot summer months. Suzie finds that each week during the summer her profits increase by 30% over what they were the previous week. In her first week of business, her profits were $300. How much money will she make in all over 4 weeks
The amount of money that Suzie will make over the four weeks is; $1856
How to find amount of profit made?
Suzie will make a profit of:
The first week = $300
The second week = (300 * 30%) + 300 = $390
The third week = 390 * (1430%) = $507
The fourth week: 507 × (1430%) = $659.1
Thus, Sum of profit = $300 + $390 + $507 + $659.1
Sum of Profit = $1856.1 ≈ $1856
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Question 37 1 pts Which of the following is a solution to the differential equation: t². d^2y/dt^2 - 6t dy,dt + 12 = 0
a.y=t² + 1 b.y=t³+2t^4
c.no solution d.y = t-1 Question 38 1 pts Newton's law of cooliing states that the rate of change of the temperature T of an object is proportional to the temperature difference between the temperature S of the surroundings and the temperature T. Write down the differential equation. A cup of tea is prepared from boiling water at 100 degrees and cools to 50 degrees in 3 minutes. The temperature in the room is 20 degrees. What will the tea temperature be after a very long time? a.dT/dt=k(S-T); T≈ 20 degrees after a very long time b.dt/dT =k(ST); T≈ 30 degrees after a very long time c.dt/dT =K(S-T); T≈ 0 degrees after a very long time d.dt/dT = K (S+T); T≈ 30 degrees after a very long time
Question 37: The following is a solution to the differential equation y = t - 1. d.
Question 38: The tea temperature be after a very long time is dT/dt = k(S - T); T ≈ 20 degrees after a very long time. a.
To determine the solution to the given differential equation: t²(d²y/dt²) - 6t(dy/dt) + 12 = 0, we can solve the equation by assuming a solution in the form of y = tⁿ, where n is a constant.
By differentiating y with respect to t, we can substitute the derivatives into the differential equation to determine the value of n.
Let's differentiate y = tⁿ with respect to t:
dy/dt = n × tⁿ⁻¹
d²y/dt² = n(n-1) × tⁿ⁻²
Substituting these derivatives into the differential equation:
t²(n(n-1)tⁿ⁻²) - 6t(ntⁿ⁻¹) + 12 = 0
Simplifying the equation:
n(n-1)tⁿ - 6ntⁿ + 12 = 0
n(n-1)tⁿ - 6ntⁿ = -12
Since this equation must hold for all values of t, the coefficients of the tⁿ terms on both sides of the equation must be equal.
We can equate the coefficients:
n(n-1) = 0
n = 0 or n = 1
The general solution to the differential equation is y = c₁ + c₂ × t, where c₁ and c₂ are constants.
According to Newton's law of cooling, the rate of change of the temperature T of an object is proportional to the temperature difference between the object's temperature T and the surroundings' temperature S.
We can write the differential equation as follows:
dT/dt = k(S - T)
dT/dt represents the rate of change of temperature, k is the proportionality constant, and (S - T) represents the temperature difference between the object and the surroundings.
The cup of tea starts at 100 degrees and cools to 50 degrees in 3 minutes, with the room temperature at 20 degrees.
We can assume that the temperature of the tea will tend toward the room temperature as time goes to infinity.
This option correctly represents that as time goes to infinity, the temperature T of the tea will approach the temperature S of the surroundings, which is approximately 20 degrees.
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Help please I don’t know the answer to this
Answer:
ima just say 10 and 6 my G I'm kinda dumb but u could try it
Answer:
5pt=10cups
24qt=6gal
Step-by-step explanation:
5*2=10
24/4=6
a numerical description of the outcome of an experiment is called ______
Answer: A random variable.
Step-by-step explanation:
a numerical description of the outcome of an experiment is called a random variable.
Last week salazar played 13 more tennis games than perry. if they played a combined total of 53 games. How many games did salazar play?
If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.
Let the total number of games played by Perry be x.
It is given that, Salazar played 13 more tennis games than Perry.
⇒ Total games played by Salazar = x + 13
Also, Salazar and Perry played a combined of 53 games.
Hence, total number of tennis games played by Salazar and Perry = 53
⇒ Games played by Salazar + Games played by Perry = 53
⇒ x + (x + 13) = 53
2x + 13 = 53
2x = 53 - 13
2x = 40
x = 40 / 2
x = 20
Therefore, total number of games played by Salazar = x+13
= 20 + 13
= 33
Thus, Salazar played total 33 games.
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Can u help me solve this plsssss???
Dilating the triangle ABC would create a triangle with a different side length from triangle ABC
How to dilate the figure?From the diagram, we have the coordinates to be:
A = (2,-5)
B = (2,4)
C = (-4,3)
The dilation rule is given as:
(x,y) => (1.5x, 1.5y)
So, we have:
A' = (3,-7.5)
B' = (3,6)
C' = (-6,4.5)
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Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. N=123, p=0. 86
The standard deviation of a binomial distribution is simply the square root of the variance. Therefore, the standard deviation of this distribution would be sqrt(17.5776) = 4.1895 (rounded to four decimal places).
The question asks us to find the mean, variance, and standard deviation of a binomial distribution with n=123 and p=0.86.
The mean of a binomial distribution is simply the product of the number of trials (n) and the probability of success (p). Therefore, the mean of this distribution would be 123 x 0.86 = 105.78.
The variance of a binomial distribution is given by the formula np(1-p). Plugging in the values of n and p given in the question, we get: 123 x 0.86 x (1-0.86) = 17.5776. Therefore, the variance of this distribution is 17.5776.
Finally, the standard deviation of a binomial distribution is simply the square root of the variance. Therefore, the standard deviation of this distribution would be sqrt(17.5776) = 4.1895 (rounded to four decimal places).
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Determine whether the following problem involves a permutation or combination. (It is not necessary to solve the problem.)How many different 2-letter passwords can be formed from the letters H, I, J, K, L, M, and N if no repetition of letters is allowed?
A permutation is an arrangement of outcomes in which the order does matter.
A combination is an arrangement of outcomes in which the order does not matter.
In this case, for example, the password HI is different from the password IH. In both cases, the outcomes (letters H and I) are the same, but the order of them changes the arrangement (the password). Therefore, the problem involves a permutation because the order of letters selected does matter
A. -3
B. 6
C. 5
D. -4
Answer:
B
Step-by-step explanation:
So we want to find the value of x.
Note that the entire segment (JK) is the sum of the segments JI and IK. In other words:
\(JK=JI+IK\)
We know that JK is (2x-1), JI is (2), and IK is (x+3). Substitute:
\(2x-1=(2)+(x+3)\)
On the right, add:
\(2x-1=x+5\)
Add 1 to both sides:
\(2x=x+6\)
Subtract x from both sides. The right cancels:
\(x=6\)
And the value of x is 6.
Our answer is B.
The baker at The Bake Shop makes 24 muffins in 1 hour. How many muffins will the baker make in 5 hours?
97 muffins
100 muffins
101 muffins
120 muffins
120
Step-by-step explanation:
if "1 hour is 24 muffins"
you can either use '+' or '×' to find the ans,
for example,
- 24+24+24+24+24 = 120
[formula 1]
using '+' is the longer way to solve the question
the easier way is by using '×', which will solve the question faster (with this you need to memorise the time table!^^)
- 24 × 5 = 120
[formula 2]
Both gives the same amount of ans, but only has a different way of solving it!
A survey was done to determine the relationship between gender and subject preference. A total of
56 students were surveyed to determine if they liked math, English, social studies, or science as their
favorite subject. The results were then broken down based on whether the respondent was male or
female.
The question is incomplete. The complete question is :
A survey was done to determine the relationship between gender and subject preference. A total of 56 students were surveyed to determine if they liked math, English, social studies, or science as their favorite subject. The results were then broken down based on whether the respondent was male or female.
Which of the following is the closest to the joint relative frequency of being a male who likes social studies ?
Solution :
A two way table used in statistics and mathematics is used to show the frequencies or the relative frequencies for any two categorical variables. One of the category is represented by the rows while the other categories by a column.
Here, in this table it is given that the total surveyed = 56 students
From the table, we know that number of males who likes social studies = 8
Therefore, the closest to the joint relative frequency for being a male who likes the subject social studies is given by :
\($=\frac{8}{56}$\)
\($=\frac{1}{7}$\)
=0.14
EXPLAIN AND I WILL GIVE BRAINLIEST
Answer:
(-3, 2)
Step-by-step explanation:
To find the coordinates of a point being reflected across the x-axis you need to use the rule (x, -y) on the point. Example: If the point was (4, 7) you would make the y value negative since it is positive, which would give you (4, -7) which is the point after being reflected across the x-axis. I know this one is for reflecting on the x-axis but for future problems if you want to reflect across the y-axis you do the same thing but with the x value, so (-x, y)
Mitchell’s neighborhood was having a contest to see who could grow the most peppers. Deer lived close by, and they loved peppers. In one week, the deer ate ସ ହ of the peppers from 7 of the yards. How much of the peppers did they eat in total?
The deer ate ସ ହ x N / 7 of the peppers in total.
What is multiplication?
Calculating the sum of two or more numbers is the procedure of multiplication. It is expressed as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.
Let's assume that the same amount of peppers were planted in each yard. If the deer ate ସ ହ of the peppers from 7 yards, that means they ate ସ ହ/7 of the peppers from each yard.
To find out how much of the peppers they ate in total, we can multiply the amount they ate from each yard by the total number of yards. Let's say there were N yards in the neighborhood. Then the total amount of peppers the deer ate would be:
Total amount of peppers = (ସ ହ/7) x N
We don't know the value of N, but we can simplify the expression by multiplying ସ ହ/7 by N:
Total amount of peppers = (ସ ହ x N) / 7
Therefore, the deer ate ସ ହ x N / 7 of the peppers in total.
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April is considering a 7/23 balloon mortgage with an interest rate of 4.15% to
purchase a house for $197,000. What will be her balloon payment at the end
of 7 years?
OA. $173,819.97
OB. $170,118.49
OC. $225,368.29
OD. $170,245.98
SUBMIT
The balloon payment at the end of 7 years would be $173,819.97, which is option A.
How to find the balloon payment at the end of 7 yearsA 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.
To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:
n = 23 * 12 = 276 (total number of payments)
r = 4.15% / 12 = 0.003458 (monthly interest rate)
P = (r * PV) / (1 - (1 + r)^(-n))
where
PV is the present value of the loan (the loan amount)n is the total number of paymentsr is the monthly interest ratePV = $197,000
P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)
Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.
Using the formula for the remaining balance of a loan after t payments:
B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)
Where
B is the remaining balancePV is the initial loan amount r is the monthly interest rateP is the monthly payment t is the number of payments madet = 84 (number of payments made)
B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)
B = $173,819.97
Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.
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Use the given information to solve for x.
x+3
2x-9
What is x?
Answer:9
Step-by-step explanation:
Currently there are 14 butterflies in my garden. I predict that in 6 months, there will be 24 butterflies in my garden. Determine the doubling time for this population of butterflies
The doubling time for this population of butterflies is approximately 12 months.
To determine the doubling time for this population of butterflies, we can use the rule of 70. The rule of 70 states that to find the approximate doubling time of a population, you divide 70 by the growth rate as a percentage.
In this case, the initial population is 14 and the predicted population in 6 months is 24, so the growth rate can be calculated as follows:
Growth rate = (Predicted population - Initial population) / Initial population x 100%
Growth rate = (24 - 14) / 14 x 100%
Growth rate = 71.43%
Using the rule of 70:
Doubling time = 70 / Growth rate
Doubling time = 70 / 71.43
Doubling time ≈ 0.98 years or approximately 12 months
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A ladybug starts at the center of a 12.0 in .-diameter turntable and crawls in a straight radial line to the edge. While this is happening, the turntable turns through a 45.0 ∘ angle.
Part A
Find the magnitude of the ladybug's displacement vector.
Part B
Find the direction of the ladybug's displacement vector.
The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.
Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.
Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.
Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.
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