The number y of duckweed fronds in a pond after t days is y=a(1230.25)t/16, where a is the initial number of fronds. By what percent does the duckweed increase each day? Round your answer to the nearest whole number.
Answers
Answer:
\(56\%\)
Step-by-step explanation:
The function is
\(y=a(1230.25)^{t/16}\)
We need to convert it into the form
\(y=a(1+r)^n\)
where r = Growth rate
n = Time taken
a = Initial quantity
\(y=a(1230.25)^{t/16}\\\Rightarrow y=a((1230.25)^{1/16})^t\\\Rightarrow y=1.56^t\)
1.56 can be written as \(1+0.56\), so
\(y=(1+0.56)^t\)
So, \(r=0.56\)
In percent \(0.56\times 100\%=56\%\)
The duckweed will increase each day by \(56\%\).
Related Questions
The distance between the points (a, b) and (c, d) is _____. So the distance between (4, 3) and (8, 6) is _____.
a. √((c - a)^2 + (d - b)^2); 5
b. √((c + a)^2 + (d + b)^2); 7
c. √((c - a)^2 - (d - b)^2); 9
d. √((c + a)^2 - (d + b)^2); 2
Answers
The distance between two points on a plane is calculated by finding the length of the straight line between them. The formula used to find the distance between two points (a,b) and (c,d) is given below:Distance = √((c - a)^2 + (d - b)^2)Hence,
the distance between the points (4, 3) and (8, 6) is calculated below:Distance = √((8 - 4)^2 + (6 - 3)^2) = √(4^2 + 3^2) = √(16 + 9) = √25 = 5Therefore, the correct answer is option A, i.e. √((c - a)^2 + (d - b)^2); 5.
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All of the following solid figures except____
have two congruent, parallel bases.
cube
cylinder
rectangular pyramid
heptagonal prism
Answers
When a number is raised to a power, is the result always larger than the original number? Support your answer with some examples.
Answers
Answer:
That actually kind of depends. If it is raised to a negative exponent, it will be a fraction of its original value. However, to answer your question, it will be a bigger number because you are basically multiplying the number by another number, x amount of times. For example, 6^3 is equal to the equation 6x6x6. Using GEMDAS, our answer is 216. Essentially, you're following the basic rules of multiplication...
I'm not if this will help. Hopefully, it does though...
Step-by-step explanation:
The result of raising a number to power can be larger or smaller than the original number depending on the value of the power.
Whether a number raised to a power is larger than the original number depends on the power that the number is raised to.
If the power is 1, then the result will be the same as the original number. For example, 5 to the power of 1 is 5.
However, if the power is greater than 1, then the result will be larger than the original number. For example, 5 to the power of 2 (written as 5²) is 25, which is larger than 5.
On the other hand, if the power is between 0 and 1, then the result will be smaller than the original number. For example, 5 to the power of 0.5 (written as √5) is approximately 2.236, which is smaller than 5.
To summarize, the result of raising a number to power can be larger or smaller than the original number depending on the value of the power.
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Write an inequality to model the situation a number exceeds 21
Answers
An inequality to model the situation a number exceeds 21 is x > 21.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let, 'x' be the number of that exceeds 21.
Now, Exceeds means greater than not greater than or equal to.
Therefore, The inequality that represents a number that exceeds 21
is x > 21.
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A woman's age and her son's add up to 45 years. Five years ago, the woman was 6 times as old as her son . How old was the woman when her son was born
Answers
Answer:
39
Step-by-step explanation:
i think
In a 2-sample z-test for two proportions, you find the following: X1 = 24 n1 = 200 X2 = 17 my = 150 You decide
to run a test for which the alternative hypothesis is Hj: p1 > p2- Find the appropriate test statistic for the
test. Enter the test statistic - round to 4 decimal places. Z =
Answers
The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).
To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:
SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]
Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.
In this case, we have the following values:
X1 = 24 (number of successes in sample 1)
n1 = 200 (sample size 1)
X2 = 17 (number of successes in sample 2)
n2 = 150 (sample size 2)
To calculate the sample proportions, we divide the number of successes by the respective sample sizes:
p1 = X1 / n1 = 24 / 200 = 0.12
p2 = X2 / n2 = 17 / 150 = 0.1133
Now, we can plug these values into the formula to calculate the standard error:
SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]
SE ≈ 0.0319
Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:
Z = (p1 - p2) / SE
Z = (0.12 - 0.1133) / 0.0319
Z ≈ 0.2103
Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).
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Six times a larger number is equal to the sum of a smaller number and 18. the difference of twice the larger number and the smaller number is 6. let x represent the smaller number and y represent the larger number. which equations represent the situation? y = 6 x 18. y = 2 x minus 6. y = 6 (x 18). y = 2 (x minus 6). y = one-sixth x 3. y = one-half x 6. y = one-sixth x 3. y = one-half x 3.
Answers
y = x/6 + 3 and y = x/2 + 3 are the equations that represents the situation.
Given,
Smaller number = x
Larger number = y
It is implied that six times a larger number is equal to the product of a smaller number and 18;
6y = x + 18
Divide both sides by 6
y = x/6 + 3
The fact that the greater number is twice as little as the smaller number, which equals 6;
2y = x + 6
Divide both sides by 2
y = x/2 + 3
Solve both equations;
2y = x + 6
x = 2y - 6
Apply the value of x in 6y = x + 18
6y = x + 18
6y = 2y - 6 + 18
6y - 2y = 12
4y = 12
y = 12/4
y = 3
Now,
x = 2y - 6
x = 2 × 3 - 6
x = 6 - 6
x = 0
Therefore,
The equations that represents the situation are;
y = x/6 + 3
y = x/2 + 3
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alfred and bonnie play a game in which they take turns tossing a fair coin. the winner of a game is the first person to obtain a head. alfred and bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. suppose that alfred goes first in the first game, and that the probability that he wins the sixth game is m n , where m and n are relatively prime positive integers. what are the last three digits of m n ? (1993,
Answers
So, the last three digits of m*n is 001.
Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.
Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:
p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2
Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.
Therefore, the last three digits of m*n is 001.
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What is the largest circle contained in a triangle where the center of the circle is the incenter of the triangle?
Answers
Answer:
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter.
Elisa and her friend are dividing a 34-ounce bag of pretzels. Elisa
shares her portion equally with her two sisters. Which fraction
represents the amount of pretzels, in pounds, each person receives?
A. 17/48 lb
B. 2 1/8 lb.
c. 11 1/3 lb.
D. 1/2 lb.
Answers
Amount of pretzel each person receives is 17/16 lb.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Total weight of the bag of pretzels = 34 ounce
Elisa shares this among her two sisters equally.
Share of pretzels each sister gets = 34 / 2 = 17 ounces
We need this amount in pounds.
We know that,
16 ounce = 1 lb.
17 ounces = 17/16 lb.
Hence the amount of pretzels each get is 17/16 lb.
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Hilda adds 5 to a number, then multiplies the sum by -2. The result is 6. Write an equation to find the number x.
Answers
Answer:
x+5·-2=6
Step-by-step explanation:
What is the probability of drawing a king or a queen, given
that you have already drawn two kings and two queens and
have not replaced them?
(A) 12
1
(B) 26
(C) 13
2.
(D) 25
(E) 0.080
Answers
Answer:
D
Step-by-step explanation:
What is a numerical expression for the verbal expression. eight times six divided by two minus nine
Answers
Answer:
15
Step-by-step explanation:
8×6÷2-9
48÷2-9
24-9
15
Kerrville, Kerrville Municipal Airport/Louis Schreiner Field (KERV) During the 24 hour period between 4pm on 12/26/2015 and ending at 4pm∗1 point on 12/27/2015, Dew Point Temperature Did not Change much during the period. Changed Substantially during the period. Between 00:00 (12am) and 6:00 (6am) on 12/27/2020, Dew Point * 1 point Temperature Reamined the Same Decreased Substantially Increased Substantially Based on what we know about dew point, we can safely say that water * 1 point vapor content: Didn't Change Much between 12am and 6 am Decreased Substantially between 12am and 6am Increased Substantially between 12am and 6am During the same 6 hour period, Air Temperature * 1 point Remained the Same Increased Decreased Based on what we know, we can safely say that Water Vapor Capacity: * 1 point Did not change much between 12 am and 6 am Increased between 12 am and 6 am Decreased between 12am and 6am The biggest change in temperature and dew point happened: * 1 point Between 2:55am and 3:15am Between 2:15am and 2:35am Between 3:15 am and 3:35 am In the same period you mentioned above, Relative Humidity * 1 point Increased substantially (a change of over 20% ) Decreased substantially (a change of over 20% ) Didn't really change much (a change less than 20% ) During the 6 hour period from 12am to 6 am, How did Relative Humidity * 1 point Change with Temperature? Relative Humidity Increased slighty when Temperature Decreased Relative Humidity Increased slightly when Temperature Increased Relative Humidity didn't change with Temperature at all However, during that same 6 hour period: * 1 point Relative Humidity Increased even when Dew Point Temperature Decreased Relative Humidity Also Decreased when Dew Point Temperature Decreased Based on the information above, what mainly affected Relative Humidity * 1 point during the entire 24 hour period? (Hint: Even though water vapor content had a huge drop, did Relative Humidity see the same drop?) Water Vapor Content (Dew Point) Had a Substantial Impact Water Vapor Capacity (Temperature) Had a Substantial Impact Both Content and Capacity Had a Substantial Impact on Relative Humidity during this period.
Answers
During the 24-hour period between 4pm on 12/26/2015 and 4pm on 12/27/2015, the dew point temperature changed substantially. The water vapor content and relative humidity were also affected by this change.
Based on the information provided, it is indicated that the dew point temperature changed substantially during the 24-hour period. The dew point temperature is the temperature at which air becomes saturated, causing water vapor to condense into dew or fog. A substantial change in the dew point temperature suggests a significant shift in the moisture content of the air.
As a result, the water vapor content and relative humidity are also affected. Water vapor content refers to the amount of water vapor present in the air, while relative humidity measures the percentage of moisture in the air compared to its maximum capacity at a given temperature. When the dew point temperature changes substantially, it implies that the air's capacity to hold water vapor has also changed, thus influencing the relative humidity.
Therefore, the main conclusion is that the change in the dew point temperature had a substantial impact on both the water vapor content and the relative humidity during the entire 24-hour period.
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Dan selected a random sample of 100 students from the 1,200 at his school to investigate preferences for making up school days lost due to emergency closings. The results are shown in the table. Dan incorrectly performed a large sample test of the difference in two proportions using 58/100 and 42/100 and calculated a p-value of 0.02. Consequently, he concluded that there was a significant difference in preference for the two options. Which of the following best describes his error in the analysis of these data?
A. No statistical test was necessary because 0.58 is clearly larger than 0.42.
B. The results of the test were invalid because less than 10% of the population was sampled.
C. Dan performed a two-tailed test and should have performed a one-tailed test.
D. A one-sample test for a proportion should have been performed because only one sample was used.
E. More options should have been included, and a chi-square test should have been performed.
Answers
The error that Dan made was that D. A one-sample test for a proportion should have been performed because only one sample was used.
Facts about Dan's researchHe used only one sample being the 100 students he selected.He tested the difference in two proportions.Dan should however have only used a one-sample test because the he only used one sample. By using a test that catered for two proportions, he misanalysed the data.
In conclusion, option D is correct.
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Triangle DEF is a scale drawing of triangle ABC
What is the scale factor?
Enter your answer as a fraction in simplest form, like this: 42/53
Answers
Since triangle DEF is a scale drawing of triangle ABC, the scale factor used is equal to 1/3.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either vertically or horizontally enlarge or reduce (compress) a function representing their size.
Mathematically, the scale factor of a geometric object such as a triangle can be calculated by using this formula:
Scale factor = Dimension of image/Dimension of original figure
Substituting the given parameters into the formula, we have the following;
Scale factor = 3/9
Scale factor = 1/3.
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Erica is studying two number patterns. Pattern A starts at 0 and has the rule "add 5." Pattern B starts at 0 and has the rule "add 10." What is the relationship between corresponding terms in the two patterns? The terms in Pattern B are 5 times the corresponding terms in Pattern A. The terms in Pattern B are 2 times the corresponding terms in Pattern A. The terms in Pattern B are one half the corresponding terms in Pattern A. The terms in Pattern B are one fifth the corresponding terms in Pattern A.
Answers
Answer:
The terms in Pattern B are 2 times the corresponding terms in Pattern A
Step-by-step explanation:
Given
Pattern A
\(Start = 0\)
\(Rule: Add\ 5\)
Pattern B
\(Start = 0\)
\(Rule: Add\ 10\)
Required
The relationship between both patterns
First, we calculate the nth term of both pattern.
For A
\(A(n) = Start + Rule\)
\(A(n) = 0 + 5n\)
\(A(n) = 5n\)
For B
\(B(n) = Start + Rule\)
\(B(n) = 0 + 10n\)
\(B(n) = 10n\)
So, we have:
\(A(n) = 5n\)
\(B(n) = 10n\)
B(n) can be expressed as:
\(B(n)=2* 5n\)
Substitute \(A(n) = 5n\)
\(B(n)=2* A(n)\)
This means that the term of B(n) is twice the corresponding term of A(n)
Determine the geometric mean of 11 and 8.
Answers
Answer:
\(\sqrt{88}\)
Step-by-step explanation:
The geometric mean of 11 and 8 is equal to \(\sqrt{88}\).
According to the question it is clear that we have to calculate the geometric mean of two positive numbers 11 and 8.
The geometric mean of two positive numbers a and c is the positive number b in such a way that it satisfies the condition
\(\frac{a}{b}=\frac{b}{c}\)
The geometric mean of a and b is √ab if a and b are both positive numbers and it will be −√ab if a and b are negative numbers.
The geometric mean is the positive square root of the product of two numbers.
For a square the geometric mean of two numbers a and b, is the length of one side of a square whose area is equal to the area of a rectangle with the sides of a and b lengths.
If we talk about the n numbers then the geometric mean is the nth root of the product of n numbers. If n positive values are given then the geometric mean is the nth positive root of the product of that n numbers.
So, the geometric mean is equal to \(\sqrt{a.b}\)
Here, a = 11 and b = 8
The geometric mean of this is equal to = \(\sqrt{11.8}\) = \(\sqrt{88}\)
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PPPLLLLZZZZZZZ help need this done quick and corrrectly
Part A.
Can you map shape I onto shape II by a sequence of rotations, translations, reflections, or dilations? If so, give a sequence that maps shape I onto shape II.
Part B.Can shape I be mapped onto shape III by a sequence of rotations, translations, reflections, or dilations? If so, give a sequence that maps shape I onto shape III.
Part C.Can shape I be mapped onto shape IV by a sequence of rotations, translations, reflections, or dilations? If so, give a sequence that maps shape I onto shape IV. please answer all parts
Answers
Answer:
Part A: rotate 90° counter clockwise
left 2 up 2
Part B: Dilation. 8 units down and 8 units left
Part C: Dilating shape I by a scale factor of 2, then reflecting it across the x-axis, and translating it 1 unit left will map shape I onto shape IV.
Step-by-step explanation:
ANSWER RIGHT OR I WILL REPORT YOU.
FAST
BRAINLIST
Answers
Answer:
28 i tryed an this is wat i got so
Step-by-step explanation:
Use long division to find the quotient below.
(4x3 + 2x2 + 50) / (2x+5)
Answers
The quotient of the equation 4x³ + 2x² + 50 ÷ 2x + 5 using long division method is 2x² - 4x
Long division4x³ + 2x² + 50 ÷ 2x + 5
\( \sqrt[2x + 5]{ {4x}^{3} + {2x}^{2} + 50 } \)
2x² - 4x
_____________
= 2x + 5 | 4x³ + 2x² + 50
4x³ + 10x²
__________
- 8x² + 50
-8x² - 10
__________
40
Therefore,
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Put in order the fractions and decimals from least to greatest 0.85, 3/5, 0.15, 7/10
Answers
Answer:
0.15, 0.85 3/5 7/10
Step-by-step explanation:
Answer: .15, 3/5, 7/10, .85
Step-by-step explanation:
3/5= .60
7/10= .70
a quadrilateral whose diagonals do not always bisect each other is a. an isosceles trapezoid b. a rectangle c. a square d. a rhombus
Answers
A quadrilateral whose diagonals do not always bisect each other is a rectangle.
A rectangle is a quadrilateral with four right angles. The diagonals of a rectangle are perpendicular to each other and bisect each other, but not all quadrilaterals with perpendicular diagonals and diagonals that bisect each other are rectangles. For example, a square is a type of quadrilateral with perpendicular diagonals and diagonals that bisect each other, but it has four congruent sides and four right angles, unlike a rectangle.
The word "rectangle" comes from the Latin words "rectus," meaning "right," and "angulus," meaning "angle." This reflects the fact that a rectangle has four right angles.
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Find the product.
406
×
18
A.
7,308
B.
4,148
C.
7,348
D.
4,248
Answers
406 times 18 equals 7,308
A survey indicates that there are approximately 120 dairy farms in a given area. If there are exactly 400 farms, and exactly 20% of them are dairy farms, what is the percent error? Fill in the table below.
Answers
Answer:
a = 120
b = 80
c = 40
d = 0.5
e = 50%
Step-by-step explanation:
Answer:
he is right
Step-by-step explanation:
A survey indicates that there are approximately 120 dairy farms in a given area. If there are exactly 400 farms, and exactly 20% of them are dairy farms, what is the percent error? Fill in the table below.
a =
✔ 120
b =
✔ 80
c =
✔ 40
d =
✔ 0.5
e =
✔ 50%
Exploring the 45°-45°-90° Triangle Theorem
Answers
AB and AC are equal in length and are represented by x, while BC (the hypotenuse) is √2 times the length of either leg.
We have,
The given triangle is an isosceles triangle.
So,
The angles opposite to the equal sides are equal.
The other angle = 90
Now,
The sum of the triangle = 180
So,
90 + 2x = 180
2x = 180 - 90
2x = 90
x = 45
Now,
In a right triangle with ∠A = 90 degrees, ∠B = 45 degrees, and ∠C = 45 degrees, we have a special case known as a 45-45-90 triangle.
In a 45-45-90 triangle, the sides are in a specific ratio: 1 : 1 : √2.
Let's use this ratio to find the lengths of the sides:
Since AB = AC, let's denote both lengths as x.
AB = AC = x
BC is the hypotenuse, which is √2 times the length of either leg:
BC = √2x
So, the lengths of the sides are:
AB = AC = x
BC = √2 * x
Therefore,
AB and AC are equal in length and are represented by x, while BC (the hypotenuse) is √2 times the length of either leg.
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question if r and s are positive integers, is r over s less than one third ? (1) r is less than 20. (2) s is greater than 65.
Answers
The correct option e. Statements (1) and (2) TOGETHER are NOT sufficient.
(1) r is less than 20: NOT sufficient.(2) s is greater than 65: NOT sufficient.Define the term positive integers?The counting numbers or natural numbers, which are also known as the positive integers, are the numbers 1, 2, 3,... Any figure higher than zero is considered positive.For the stated question-
1. R is less than 20: insufficient since s is unknown.
2. Because there is no date for r, statement 2 is insufficient because S is bigger than 65.
We now have two conditions when combined. s>0 and s>65, r 20 and r>0.
Using the maximum possible value of r as an example and the least possible value of s as an example, the value is greater than 1/3.
Therefore, every values for r would only decrease, while s will rise.
Therefore, simply stating that it won't be below 1/3 will do.
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The complete question is-
If r and s are positive integers, is r/s less than 1/3 ?
(1) r is less than 20.
(2) s is greater than 65.
a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d. EACH statement ALONE is sufficient.
e. Statements (1) and (2) TOGETHER are NOT sufficient.
the gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. a simple random sample of 81 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. construct a 95% confidence interval for the mean gas mileage for this car model.
Answers
The 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.
The confidence interval for a statistical data is written as-
(x+ zr/√n, x- zr/√n)
Here, we are given that-
Mean ⇒ x = 27.5 mi/gallon.
Standard deviation ⇒ r = 4 mi/gallon
Number of samples ⇒ n = 49
and Confidence interval = 95%
z-score at 95% confidence level = 2.17
Substituting the values we have;
= [27.5 - 2.17(4.0) /(√49), 27.5 + 2.17(4.0) /(√49)]
= (27.5 - 8.68 / 7, 27.5 + 8.68 / 7)
= (27.5 - 1.24, 27.5 + 1.24)
= ( 26.26, 28.74)
Therefore, the 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.
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whats -4x+8=9
⬆️
question
Answers
Answer:
-1/4
Step-by-step explanation:
-4x+8=9
-8 -8
-4x=1
/-4 /-4
x= -1/4
Find the measure of the reference angle for each given angle. Part 1
10. θ = 95°
11. θ = -250°
12. θ = 230°
Answers
Answer:
10. 85°
11. 70°
12. 50°
Step-by-step explanation:
Please see attached picture for full solution.
