The probability of exactly 1 seed not growing is 31.36%. we can use the binomial probability formula, which is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k). P(X=k) is the probability of getting k successes in n trials n is the number of trials
k is the number of successes p is the probability of success in each trial.
To calculate the probability of exactly 1 failure, we can use the binomial probability formula, which is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
P(X=k) is the probability of getting k successes in n trials
n is the number of trials
k is the number of successes
p is the probability of success in each trial
(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items
In this case, n=6, k=1, p=0.65, and (n choose k) = 6. Plugging these values into the formula, we get:
P(X=1) = (6 choose 1) * 0.65^1 * (1-0.65)^(6-1) = 6 * 0.65 * 0.35^5 = 0.3136
Therefore, the probability of exactly 1 seed not growing is 31.36%.
In this case, the probability of getting exactly 1 failure in 6 trials, where the probability of success is 0.65. We use the binomial coefficient to count the number of ways to choose 1 item (the failure) from a set of 6 items (the seeds). We then multiply this by the probability of getting 1 failure and 5 successes, which is given by the formula p^k * (1-p)^(n-k), where p is the probability of success and k and n-k represent the number of successes and failures, respectively. Finally, we calculate the probability of exactly 1 failure by multiplying the binomial coefficient and the probability of getting 1 failure and 5 successes.
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find the taylor polynomial t3(x) for the function f centered at the number a. f(x) = arcsin(5x), a = 0
The third-degree Taylor polynomial for f(x) = arcsin(5x) centered at a = 0 is t3(x) = 5x - (125/2)x³.
To find the Taylor polynomial t3(x) for the function f(x) = arcsin(5x) centered at a = 0, we will need to compute the function's derivatives at a = 0 up to the third order.
First, let's compute the first few derivatives of f(x):
f(x) = arcsin(5x)
f'(x) = 5 / sqrt(1 - 25x^2)
f''(x) = 125x / (1 - 25x^2)^(3/2)
f'''(x) = (9375x^2 - 375) / (1 - 25x^2)^(5/2)
Now, let's evaluate these derivatives at a = 0:
f(0) = 0
f'(0) = 5 / sqrt(1) = 5
f''(0) = 0
f'''(0) = -375 / (1)^(5/2) = -375
Using these values, we can write the third-degree Taylor polynomial t3(x) as follows:
t3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3
t3(x) = 0 + 5x + 0 + (-375/6)x^3
t3(x) = 5x - (125/2)x^3
Therefore, the third-degree Taylor polynomial for f(x) = arcsin(5x) centered at a = 0 is t3(x) = 5x - (125/2)x^3.
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For a test concerning a mean, a sample of sizen = 90is obtained. In testingHo: μ = μο-versusH1: μ + μο-, the test statistic is. Find the-value (round off to third decimal place).
The p-value for a test concerning a mean is 0.064.
What is p-value?
A p-value, also known as a probability value, is a numerical representation of the likelihood that your data would have occurred under the null hypothesis of your statistical test.
As per question given,
This is two tail list then z = 1.85.
p (z > 1.85) = 1 - p (z < 1.85)
= 1 - 0.9678
= 0.0322
Thus, the p-value is
p-value = 2 × 0.0322
= 0.064
Hence, the p-value for a test concerning a mean is 0.064.
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9) π 22/7 are two real number. il Indentify the rational and irrational number between them two ii) Compare these 2 real number
i. π is an irrational number while 22/7 is a rational number.
ii) 22/7 is a rational number since it can be written in the form p/q and π is an irrational number because its values are continuous after the decimal point.
What are the types of number?In Mathematics and Geometry, there are six (6) common types of numbers and these include the following:
Irrational numbersIntegersReal numbersRational numbersNatural (counting) numbersWhole numbersPart i.
In Mathematics and Geometry, a rational number is a type of number which comprises fractions, integers, terminating or repeating decimals such as the 22/7, 0.12345678901234567890.
Additionally, an irrational number is a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11 or √11.
Part ii.
22/7 should be classified as a rational number because it can be written in the form p/q and π is an irrational number because its values are non-terminating or non-repeating, after the decimal point.
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determine the appropriate hypothesis test. a sample of 77 women who smoked during pregnancy and a sample of 161 who did not smoke during pregnancy was taken to see if maternal cigarette smoking has any effect on bone mineral content of healthy newborns.
Based on the given information , the appropriate hypothesis test for this scenario would be an independent samples t-test.
The independent samples t-test is used to compare the means of two independent groups.
To determine if there is a significant difference between them.
In this case, the two groups are women who smoked during pregnancy and women who did not smoke during pregnancy.
The variable of interest is the bone mineral content of healthy newborns.
The null hypothesis (H₀) would state that ,
There is no significant difference in the mean bone mineral content between,
newborns of women who smoked during pregnancy and newborns of women who did not smoke during pregnancy.
The alternative hypothesis (Hₐ) would state that there is a significant difference in the mean bone mineral content between the two groups.
To conduct the independent samples t-test,
We would calculate the t-statistic using the sample means, sample sizes, and standard deviations of the two groups.
The t-statistic is then compared to a critical value from the t-distribution with appropriate degrees of freedom.
To determine if the difference in means is statistically significant.
Assumption of normality and equal variances between the groups, should be checked before conducting the t-test.
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The comparison distribution in a t test for dependent means is a distribution of
The comparison distribution in a t test for dependent means is a distribution of the differences between the pairs of scores on the dependent variable.
This distribution is used to determine whether the observed differences between the means of two related groups are statistically significant or could have occurred by chance. The t statistic is calculated by dividing the mean difference between the pairs of scores by the standard error of the mean difference, which is based on the variance of the differences in the sample. The t statistic is then compared to a t distribution with degrees of freedom equal to the number of pairs of scores minus one to determine the probability of obtaining the observed difference by chance.
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A farmer has 200 feet of fencing available to construct a garden with the shape shown below, with a and y measured in feet. The expression x + 2y + piX/2 represents the number of feet of fencing needed.
The farmer has correctly determined that the area of the garden is greatest when y = x/2. What length x, in feet, should the farmer choose to maximize the area of the
garden? Use a graphing calculator and round the answer to the nearest tenth.
The required farmer should choose a length of 56 feet for the garden to maximize its area.
we need to maximize A with respect to x, subject to the constraint that the perimeter of the garden (the amount of fencing needed) is 200 feet. The perimeter is given by:
P = x + 2y + π*x/2
Substituting y = x/2, we get:
P = x + 2(x/2) + π*x/2
200 = (2 + π/2)*x
x = 56
Therefore, the farmer should choose a length of 56 feet for the garden to maximize its area.
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find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. 2y^2-9x^2; 3x y=27x
To find the extremum of the function f(x,y) = 2y^2-9x^2 subject to the constraint 3xy = 27x, we can use the method of Lagrange multipliers.
Let g(x,y) = 3xy - 27x be the constraint function. We want to find the critical points of the function f(x,y) subject to the constraint g(x,y) = 0, so we set up the following system of equations:
∇f(x,y) = λ∇g(x,y)
g(x,y) = 0
where λ is the Lagrange multiplier.
Taking the partial derivatives of f(x,y) with respect to x and y, we get:
∂f/∂x = -18x
∂f/∂y = 4y
Taking the partial derivatives of g(x,y) with respect to x and y, we get:
∂g/∂x = 3y - 27
∂g/∂y = 3x
Setting ∇f(x,y) = λ∇g(x,y), we get the following system of equations:
-18x = λ(3y - 27)
4y = λ(3x)
Multiplying the first equation by 4 and the second equation by -6, we get:
-72x = λ(12y - 108)
-24y = λ(-18x)
Simplifying these equations, we get:
4x = λ(y - 9)
y = 3λx/2
Substituting y = 3λx/2 into the first equation, we get:
4x = λ(3λx/2 - 9)
8x = λ^2x - 18λ
x(λ^2 - 8) = 18λ
If x = 0, then y = 0, which is not a critical point since f(0,0) = 0. Therefore, we can divide both sides by x to get:
λ^2 - 8 = 18/ x
If λ^2 - 8 < 0, then there are no critical points since the equation above has no real solutions. Therefore, we assume λ^2 - 8 ≥ 0, which gives:
λ = ±√(8 + 18/x)
Substituting λ into y = 3λx/2, we get:
y = ±√(2x(8 + 18/x))/2
We want to find the extremum of f(x,y) = 2y^2-9x^2, so we evaluate this function at the critical points:
f(x,y) = 2y^2-9x^2 = 2(2x(8 + 18/x))/4 - 9x^2 = (4x^2 + 36) / x - 9x^2
Taking the derivative of f(x,y) with respect to x, we get:
f'(x,y) = (8x - 36)/x^2 - 18
Setting f'(x,y) = 0, we get:
8x - 36 = 18x^2
18x^2 - 8x + 36 = 0
Solving for x, we get:
x = (2 ± √13)/9
Substituting x into y = ±√(2x(8 + 18/x))/2, we get:
y = ±(4 ± √13)√2/3
Therefore, the critical points are (x,y) = x = (2 ± √13)/9, y = ±(4 ± √13)√2/3
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3. A 10-inch tall candle is lit. The
graph below shows its height after
each hour.
Height of Candle
10
2
8
9
2
4
6 8 10 12
Hours
a) Write an equation for the line of
best fit.
b) Estimate the height of the canc
after 15 hours.
3) The height is 5.1 inches after 15 hours.
4) The weight is 166 lbs. after 24 weeks.
What is the line's equation?Depending on the details, there are various ways to express a line's equation. The slope-intercept form and point-slope form are the two most typical forms.
3) It is obvious;
The graph's slope is;
m = 6 - 10/12 - 0
= -4/12 = -0.33
The line's equation is then;
y = -0.33x + 10
If we have 15 hours today, then;
y = -0.33(15) + 10
= 5.1 inch
4) Once more, the slope is;
m = 235 - 238/2 -1
m = -3
y = -3x + 238
24 weeks later, we have that;
y = -3(24) + 238
= 166 ibs
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I need this question
When two sides of a triangle measure 18 meters and 13 meters, the measures that could represent the perimeter of the triangle is B. 37 meters
How to explain the perimeterThe perimeter of a triangle is the sum of the lengths of its three sides. So, if two sides of a triangle measure 18 meters and 13 meters, the third side must be less than 18 meters + 13 meters = 31 meters.
Therefore, the perimeter of the triangle must be less than 31 meters + 31 meters = 62 meters. Only 37 meters is less than 62 meters, so the answer is (b).
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There were 17 students running in a race. How many different arrangements of first, second, and third place are possible?
There are 4,080 different arrangements of first, second, and third place possible for the 17 students running in the race.
To determine the number of different arrangements of first, second, and third place, we need to use the permutation formula.
The number of permutations of n objects taken r at a time is given by:
P(n,r) = n!/(n-r)!
In this problem, we have 17 students running, and we want to determine the number of different arrangements of first, second, and third place, which means we need to find the number of permutations of 17 objects taken 3 at a time.
Using the permutation formula, we get:
P(17,3) = 17!/(17-3)!
= 17!/14!
= 171615
= 4,080
Therefore, there are 4,080 different arrangements of first, second, and third place possible for the 17 students running in the race.
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Jack buys 50 pens for 65p each. He sells 80% of the pens making 20% profit on each. to sell the remainder of the pens he is forced to reduce his price making a loss of 9p on each. Assuming he sells all of his pens calculate his total profit.
Jack's total profit from selling all of his pens is 430p.
To calculate Jack's total profit, we need to consider the profit made from selling 80% of the pens at a 20% profit and the loss incurred from selling the remaining 20% at a reduced price.
Let's break down the calculations :
Cost of purchasing 50 pens
The cost of each pen is 65p, so the total cost of purchasing 50 pens is [tex]50 \times 65p = 3250p.[/tex]
Profit from selling 80% of the pens
Jack sells 80% of the pens, which is[tex]0.8 \times 50 = 40[/tex] pens.
He makes a 20% profit on each pen, which is 20% of 65p = 13p profit per pen.
So, the total profit from selling these 40 pens is [tex]40 \times 13p = 520p.[/tex]
Loss from selling the remaining 20% of the pens
The remaining 20% of the pens is[tex]0.2 \times 50 = 10[/tex] pens.
Jack incurs a loss of 9p on each of these pens.
So, the total loss from selling these 10 pens is [tex]10 \times 9p = 90p.[/tex]
Total profit
To calculate the total profit, we subtract the loss from the profit:
Total profit = Profit - Loss = 520p - 90p = 430p.
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Based on the grouped bar chart below, in which year did the largest number of women exist in the U.S.
workforce?
A) 2010
B)1970
C)1980
D)2000
Answer: A) 2010
Step-by-step explanation:
Triangle XYZ is similar to triangle JKL.
Triangle XYZ with side XY labeled 8.7, side YZ labeled 7.8, and side ZX labeled 8.2 and triangle JKL with side JK labeled 13.92.
Determine the length of side LJ.
4.59
5.13
12.48
13.12
Given that triangle XYZ and triangle JKL are similar, the length of LJ is 13.12
Similar triangles: Calculating the length of side LJFrom the question, we are to determine the length of side LJ given that triangle XYZ and triangle JKL are similar.
From the triangle similarity theorem, we know that
If triangle ABC and triangle DEF are similar,
Then,
AB/DE = BC/EF
Thus,
Since triangle XYZ and triangle JKL are similar, we can write that
XY/JK = ZX/LJ
From the given information,
XY = 8.7
JK = 13.92
ZX = 8.2
Thus,
8.7 / 13.92 = 8.2 / LJ
LJ = (8.2 × 13.92) / 8.7
LJ = 114.144 / 8.7
LJ = 13.12
Hence,
The length of LJ is 13.12
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a pool is being built in a new student rec center at falcon community college. the pool is designed to be a by rectangle, and the deck around the pool is going to be lined with slate tiles that are squares. how many tiles are needed? (this is not quite as easy as it seems at first...)
The area of each tile is 1 sq ft, No of tiles required is 176 sq ft /1 sq ft = 176
What is the area of the rectangle?
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.
Here, we have
Given: The pool is designed to be a 60 ft by 26 ft rectangle, and the deck around the pool is going to be lined with slate tiles that are 1 ft squares.
We have to find out how many tiles are needed.
The internal Length of the rectangle is 60ft
Internal Breadth of the rectangle is 26 ft
External Length of the rectangle is 60+ 2*1 = 62ft
External Breadth of the rectangle is 26+ 2*1 = 28ft
Area of the deck to be tiled = Outer Area - Inner area
= (62×28 ) - (60×26)
= 1736 - 1560
= 176 Sq ft
Hence, the area of each tile is 1 sq ft, No of tiles required is 176 sq ft /1 sq ft = 176
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what is -6 rounded to the nearest tenth?
Answer:
it would be -7 because 6 and up round up once now 5 and down go down
Step-by-step explanation:
A right triangle has acute angles C and D. If cot C= 8/15 and cos D= 15/17, what are tan D and sin C?
The value of Tan D is corect. Sin C is incorrect. From Cot C find cosec C which is equal to 17/15. Therefore sin C = 15/17
Wrong Solution First, we know that cot C is equal to the ratio of the adjacent side to the opposite side in a right triangle. So, cot C = 8/15 implies that the adjacent side is 8 and the opposite side is 15.
Next, we are given that cos D is equal to the ratio of the adjacent side to the hypotenuse in a right triangle. So, cos D = 15/17 implies that the adjacent side is 15 and the hypotenuse is 17.
Now, to find tan D, we can use the relationship between the tangent and sine functions: tan D = sin D / cos D. Since we know cos D = 15/17, we need to find sin D. Using the Pythagorean theorem, we can find the opposite side:
sin D = √(1 - cos^2 D)
= √(1 - (15/17)^2)
= √(1 - 225/289)
= √(289/289 - 225/289)
= √(64/289) = 8/17.
Therefore, tan D = sin D / cos D = (8/17) / (15/17) = 8/15.
Finally, to find sin C, we can use the Pythagorean theorem:
sin^2 C = 1 - cos^2 C = 1 - (15/17)^2 = 1 - 225/289 = 64/289.
Taking the square root of both sides, we get
sin C = √(64/289) = 8/17.
In summary, tan D = 8/15 and sin C = 8/17.
The values of tan D and sin C are tan D = 8/15 and sin C = 8/17
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a baseball collides with a baseball glove. which equation is used to calculate the force the glove exerts on the ball during the collision?(1 point)
Therefore, the force the glove exerts on the ball during the collision can be calculated by measuring the change in momentum of the ball and dividing it by the time of the collision.
The equation used to calculate the force the glove exerts on the ball during the collision is the impulse-momentum equation. This equation states that the force applied to an object is equal to the change in momentum of the object over time. Therefore, the force the glove exerts on the ball during the collision can be calculated by measuring the change in momentum of the ball and dividing it by the time of the collision.
To calculate the force the glove exerts on the ball during the collision, you can use Newton's second law of motion, which states:
Force (F) = Mass (m) × Acceleration (a)
In this scenario, the mass (m) refers to the mass of the baseball, and the acceleration (a) is the change in the baseball's velocity divided by the time it takes for the collision to occur. Keep in mind that the acceleration will have a negative value, as the ball is decelerating during the collision.
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There was a sample of 750 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 4.5% each year. Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between t and y.
The relationship between b (the number of years since the start of the study) and y (the mass of the sample in milligrams) using the exponential function:
y = 750(0.955)ᵇ
The rate of decay is given as 4.5% per year, which means that after one year, the sample will have decayed to 95.5% of its original mass.
After two years, it will have decayed to 95.5% of that amount, and so on. We can express this relationship between b (the number of years since the start of the study) and y (the mass of the sample in milligrams) using the exponential function:
y = 750(0.955)ᵇ
Here, the initial mass of the sample is 750 milligrams, and the factor of 0.955 represents the proportion of the original mass that remains after one year.
Taking this factor to the power of b gives us the proportion of the original mass that remains after t years, which we can multiply by the initial mass to get the current mass of the sample in milligrams.
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I NEED HELP FAST
find the product (k-1) (6k+5)
A.6k²-5
B.6K²-11K-5
C.6k²-k-5
D.6K²+11K-5
Answer:
C
Step-by-step explanation:
(k - 1)(6k + 5)
each term in the second factor is multiplied by each term in the first factor , that is
k(6k + 5) - 1(6k + 5) ← distribute parenthesis
= 6k² + 5k - 6k - 5 ← collect like terms
= 6k² - k - 5
what is the diffrrence between an equation with a variable and an inequality with a variable?
Step-by-step explanation:
An equation with a variable is a mathematical statement that asserts that two expressions are equal. The variable in the equation represents an unknown quantity that needs to be determined. For example, the equation "2x + 3 = 7" asserts that the expression "2x + 3" is equal to the expression "7", and the variable "x" represents the value that makes this equation true.
An inequality with a variable is a mathematical statement that asserts that one expression is greater than, less than, or equal to another expression. The variable in the inequality represents an unknown quantity that needs to be determined. For example, the inequality "2x + 3 < 7" asserts that the expression "2x + 3" is less than the expression "7", and the variable "x" represents the values that satisfy this inequality.
In summary, the main difference between an equation and an inequality is that an equation asserts that two expressions are equal, while an inequality asserts that one expression is greater than, less than, or equal to another expression.
an analysis of variance comparing three treatment conditions produces dftotal = 32. if the groups are all the same size, how many individuals are in each group?
If the total degrees of freedom (dftotal) in an analysis of variance comparing three treatment conditions is 32, the group size for each condition needs to be determined.
To determine the number of individuals in each group, we need to divide the total number of individuals (dftotal) by the number of treatment conditions (groups).
Given that dftotal = 32 and there are three treatment conditions (groups), we can divide dftotal by the number of treatment conditions to find the number of individuals in each group.
Number of individuals in each group = dftotal / number of treatment conditions
Number of individuals in each group = 32 / 3
Number of individuals in each group ≈ 10.67
Since the groups must have the same size, we need to round the result to the nearest whole number. Therefore, there are approximately 11 individuals in each group.
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HELP ANSWER QUICKLY PLEASE!!
y-7=-5(x+2) is the equation of line in point slope form passing through point (-2,7)
The given equation of the line p is 5x-25y=19
We have to find the equation of a line perpendicular to line p that passes through (-2, 7)
Convert equation to slope intercept form 5x-25y=19
-25y=19-5x
25y=5x-19
Divide both sides by 25
y=1/5x - 19/25
So slope is 1/5
Now the slope of perpendicular line is -5
equation of line in point slope form passing through point (-2, 7)
y-7 = -5(x-(-2))
y-7=-5(x+2)
Hence, y-7=-5(x+2) is the equation of line in point slope form passing through point (-2,7)
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they are 8,756 students that attend middle schools in the city of Johnson. Of the students, 3,252 are picked up by car, 2,549 ride the bus home, and 2,955 students walk home. How many students leave school by bus or car?
The number of students that leave by bus or car is given as follows:
5801 students.
How to obtain the union and intersection set of the two sets?The union and intersection sets of multiple sets are defined as follows:
The union set is composed by the elements that belong to at least one of the sets.The intersection set is composed by the elements that belong to at all the sets.The or operation is equivalent to the union operation, meaning that we add the number of students that leave by bus to the number of students that leave by car.
Hence the number of students that leave by bus or car is given as follows:
3232 + 2549 = 5801 students.
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Zoe and Hannah share tips in the ratio 3:7
Last week,Zoe received £24
how much did Hannah receive last week
An appropriate domain of the function is x ≥ 0, where the x-values are
A. real numbers
B. whole numbers
C. Rational numbers
Answer: i think the awnser to your question is A real number
Step-by-step explanation:
Taking the absolute value of a number, whether it's negative or positive, always returns either a positive value or zero.
Let's say we have a number line with the point A on it. Think of the absolute value of A as the distance between point A and zero. Since the distance cannot be negative, the absolute value will always return a positive value.
A positive number is always greater than zero, and zero is equal to zero. Therefore, the answer is True.
Michelle filled 20 flower pots each with 3 cups of soil. Some of the pots, p, each lost 2 cups of soil when the wind knocked them over. Now, there are only 36 cups of soil left in the pots. Which equation represents this situation?
The equation representing the situation is 20(3 cups) - p(2 cups) = 36 cups, where p represents the number of pots knocked over.
The initial amount of soil in the pots is given by 20 pots multiplied by 3 cups per pot, which gives 20(3 cups). The number of pots knocked over is represented by p, and each knocked-over pot loses 2 cups of soil.
Therefore, the total soil lost due to knocked-over pots is p(2 cups). Subtracting this from the initial amount of soil, we get 20(3 cups) - p(2 cups). The result should be equal to the remaining soil, which is 36 cups. Hence, the equation representing this situation is 20(3 cups) - p(2 cups) = 36 cups. This equation relates the number of pots knocked over (p) to the remaining soil (36 cups).
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There are currently 600 bacteria in a Petri dish. If the population of the bacteria in the dish doubles every 2 hours.
After 6 hours, the population of bacteria in the Petri dish would be 4800.
If the population of bacteria in a Petri dish doubles every 2 hours, we can calculate the population at any given time using the formula
P = P₀[tex]\times 2^{(t/d),[/tex]
where P is the final population, P₀ is the initial population, t is the time elapsed, and d is the doubling time.
In this case, the initial population (P₀) is 600 bacteria, and the doubling time (d) is 2 hours. Let's calculate the population after a certain time, say 6 hours:
[tex]P = 600 \times 2^{(6/2)}\\P = 600 \times 2^3\\P = 600 \times 8\\P = 4800[/tex]
Therefore, after 6 hours, the population of bacteria in the Petri dish would be 4800.
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Daniel and Ismaela are kicking soccer balls at a goal. Daniel makes 12 of his 15 shots in the goal. Ismaela takes 20 shots at the goal and makes the same percent of shots as
Daniel. How many of Ismaela's shots make it in the goal?
old mcdonald evenly divided his goats between his two children, lilly and hawk. careless lilly lost 35 goats and reckless hawk lost 40 of his goats. both lilly and hawk sold their herds, lilly sold each goat for $80 while hawk sold each of his goats for $60. if lilly got $1100 more than hawk for her herd, how many goats did mcdonald have?
Let the total number of goats that McDonald had be x. After evenly dividing them between Lilly and Hawk, each of them would have received x/2 goats. However, Lilly lost 35 goats, so she was left with (x/2 - 35) goats. Similarly, Hawk lost 40 goats and was left with (x/2 - 40) goats.
When Lilly sold each goat for $80, she earned (x/2 - 35) * $80 = 80x/2 - 35*80 = 40x - 2800 dollars. When Hawk sold each goat for $60, he earned (x/2 - 40) * $60 = 60x/2 - 40*60 = 30x - 2400 dollars.
Given that Lilly earned $1100 more than Hawk, we can set up the equation:
40x - 2800 = 30x - 2400 + 1100
Solving for x, we get x = 400. Therefore, McDonald had a total of 400 goats.
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If a projectile is launched at an angle θ with the horizontal, its parametric equations are as follows. 70 cos(θ) )t and 70 sin(θ) )t-16t2 x = y = Use a graphing utility to find the angle that maximizes the range of the projectile What angle maximizes the arc length of the trajectory? (Round your answer to one decimal place.)
To find the angle that maximizes the range of a projectile, you can follow these steps:
1. Determine the range formula: The range (R) of a projectile can be found using the formula R = (v² * sin(2θ)) / g, where v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (approximately 9.81 m/s²).
2. In this case, the initial velocity (v) is 70 m/s, so the formula becomes R = (70² * sin(2θ)) / 9.81.
3. To maximize the range, you need to find the angle (θ) that results in the highest value of R. To do this, you can use a graphing utility to graph the function R(θ) = (4900 * sin(2θ)) / 9.81 and find its maximum value.
4. Using a graphing utility, you will find that the maximum range occurs when θ ≈ 45°.
5. Round your answer to one decimal place: The angle that maximizes the arc length of the trajectory is approximately 45.0°.
So, to maximize the range of a projectile launched at 70 m/s, the optimal angle is 45.0° with the horizontal.
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