Answer: The total surface area of the cylinder is 850π m².
Step-by-step explanation:
The cylinder has a curved surface area of 408π m², which is the area of the lateral surface of the cylinder. The lateral surface of a cylinder is the curved surface that connects the top and bottom bases of the cylinder.
The formula for the lateral surface area of a cylinder is given by: Lateral Surface Area = 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder.
We are given that the length of the cylinder is 17 m. Since the length of a cylinder is the same as its height, we can substitute h = 17 m into the formula for the lateral surface area to get:
408π m² = 2πr(17 m)
Simplifying this equation, we get:
r = 12 m
Now that we know the radius of the cylinder, we can find the total surface area of the cylinder. The formula for the total surface area of a cylinder is given by:
Total Surface Area = 2πr(r + h)
Substituting r = 12 m and h = 17 m into this formula, we get:
Total Surface Area = 2π(12 m)(12 m + 17 m) = 850π m²
Therefore, the total surface area of the cylinder is 850π m².
Square root of
3a^2/10b^6
Answer:
Step-by-step explanation:
Rewrite
3
a
2
10
b
6
as
(
a
b
3
)
2
3
10
.
√
(
a
b
3
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2
3
10
Pull terms out from under the radical.
a
b
3
√
3
10
Rewrite
√
3
10
as
√
3
√
10
.
a
b
3
⋅
√
3
√
10
Combine.
a
√
3
b
3
√
10
Multiply
a
√
3
b
3
√
10
by
√
10
√
10
.
a
√
3
b
3
√
10
⋅
√
10
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10
Combine and simplify the denominator.
√
3
√
10
b
3
⋅
10
Simplify the numerator.
Tap for more steps...
a
√
30
b
3
⋅
10
Move
10
to the left of
b
3
.
a
√
30
10
b
3
Step-by-step explanation:
[tex]{ \tt{ \sqrt{ \frac{3 {a}^{2} }{10 {b}^{6} } } }} = { \tt{ \frac{ {(3a {}^{2}) }^{ \frac{1}{2} } }{ {(10b {}^{6} )}^{ \frac{1}{2} } } }} \\ \\ = { \tt{ \frac{a \sqrt{3} }{ {b}^{3} \sqrt{10} } }} \\ \\ = { \tt{ \frac{a \sqrt{3} }{ {b}^{3} \sqrt{10} } }}[/tex]
Given the triangle, find the length of X. Give your answer in simpliest radical form.
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the cosine ratio in the lower right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 4[tex]\sqrt{2}[/tex]
Which of the following steps were applied to ABC obtain AA'B'C'?
A. Shifted 4 units left and 4 units up
B. Shifted 4 units left and 2 units up
C. Shifted 2 units left and 4 units up
D. Shifted 2 units left and 2 units up
Correct Option is Shifted 2 units left and 4 units up
Define triangleA triangle is a geometric shape that is formed by three straight line segments that connect three non-collinear points. The three points where the segments intersect are called the vertices of the triangle, while the segments themselves are called the sides. The area enclosed by the sides of the triangle is called its interior, while the space outside the triangle is called its exterior.
Given are two trianglesThe vertices of ABC are (4, 6), (7, 6), and (5,9)
The transformed image A'B'C' has vertices as
(2,10) (5,10) (3,13)
We see a pattern when we compare the matching vertices.
The y coordinate is raised by 4, while the x coordinate is shrunk by 2.
This implies the transformation is
Shifted 2 units left and 4 units up
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Answer:
Shifted 2 units left and 4 units up
Step-by-step explanation:
hope this helps
2x - 3 = 6 + x
2(2x-3)=6+x
Answer:
x = 9x = 4Step-by-step explanation:
2x - 3 = 6 + x
2x - 3 = 6 + x
2x - x = 6 + 3
x = 9
2. 2(2x-3)=6+x
2(2x - 3) = 6 + x
4x - 6 = 6 + x
4x - x = 6 + 6
3x = 12
x = 12 : 3
x = 4
a particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. twenty fish are placed in a tank containing this concentration of chemical in water. a find the probability that exactly 14 survive. b find the probability that at least 10 survive.
A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore
a. The probability that exactly 14 fish survive is 0.263b. The probability that at least 10 fish survive is 0.983How do we calculate the probability?a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263
b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.
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alex makes a fruit puree by mixing blackcurrants and raspberries in the ratio 2:5 he then makes a milkshake by mixing milk and the fruit puree in the ratio 3:1. what fraction of his drink is made from blackcurrants?
For the given ratio of ingredients 3/14 of Alex's drink is made from blackcurrants.
What are ratios?Comparing two numbers or values using ratios, which are often stated as fractions or colons. In mathematics, ratios are used to represent connections between various objects or numbers, such as the ratio of a rectangle's length to breadth or the proportion of boys to girls in a class. Ratios can be sped up or stated in a variety of ways, such decimals or percentages.
The given ratio for blackcurrants to raspberries is 2:5.
The total ratio is:
2 + 5 = 7
Hence, the fraction of the puree made from blackcurrants is = 2/7.
Now, ratio of fruit puree to milk is 3:1 = 3 + 1 = 4.
Hence, the fraction of the milkshake made from fruit puree is = 3/4.
For blackcurrants we have:
(2/7) * (3/4) = 6/28 = 3/14
Hence, for the given ratio of ingredients 3/14 of Alex's drink is made from blackcurrants.
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3x+4y=34 . In the equation, what is the y-value when x=10? x= 10 , y= ?
Answer:
y = 1
Step-by-step explanation:
3x + 4y = 34 x = 10
3(10) + 4y = 34
30 + 4y = 34
4y = 4
y = 1
So, the y-value is 1 when x = 10
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3x + 4y = 34}[/tex]
[tex]\mathsf{3(10) + 4y = 34}[/tex]
[tex]\mathsf{30 + 4y = 34}[/tex]
[tex]\mathsf{4y + 30 = 34}[/tex]
[tex]\large\text{SUBTRACT 30 to BOTH SIDES}[/tex]
[tex]\mathsf{4y + 30 - 30 = 34 - 30}[/tex]
[tex]\large\text{SIMPLIFY IT!}[/tex]
[tex]\mathsf{4y = 34 - 30}[/tex]
[tex]\mathsf{4y = 4 }[/tex]
[tex]\large\text{DIVIDE 4 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{4y}{4} = \dfrac{4}{4}}[/tex]
[tex]\large\text{SIMPLIFY IT!}[/tex]
[tex]\mathsf{y = \dfrac{4}{4}}[/tex]
[tex]\mathsf{y = 1}[/tex]
[tex]\huge\text{Therefore your answer should most likely be:}[/tex]
[tex]\huge\boxed{\mathsf{y = 1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Draw a shape with fractional side lengths. Describe how you will find its area.
Therefore, the area of the rectangle is 6 7/8 square inches.
What is area?Area is a measurement of the amount of space inside a 2-dimensional shape, such as a rectangle, triangle, circle, or any other polygon. It is usually measured in square units, such as square inches, square feet, square meters, etc. The formula for finding the area of a shape depends on the type of shape. For example, the area of a rectangle is calculated by multiplying its length by its width, while the area of a circle is calculated by multiplying the square of its radius by pi (3.14).
Here,
Here's how to draw a shape with fractional side lengths and find its area:
Draw a rectangle with side lengths of 2 1/2 inches and 3 3/4 inches.
Divide the rectangle into smaller squares or rectangles to make it easier to calculate the area.
For example, you can divide the rectangle into two smaller rectangles with side lengths of 2 1/2 inches and 1 3/4 inches, and 2 1/2 inches and 2 inches respectively.
Calculate the area of each smaller rectangle by multiplying the length by the width.
The total area of the rectangle is the sum of the areas of the smaller rectangles.
So the area of the rectangle would be:
Area = (2 1/2 inches x 1 3/4 inches) + (2 1/2 inches x 2 inches)
Area = (5/2 inches x 7/4 inches) + (5/2 inches x 2 inches)
Area = (35/8 square inches) + (10/4 square inches)
Area = (35/8 square inches) + (20/8 square inches)
Area = (55/8 square inches)
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Expand and simplify (3x - 1)(9x² + 3x + 1)
in a system of two equations, the graph of one line has a positive slope and the graph of the other line has a negative slope. complete the following statement with what you can conclude about the system.
In a system of two equations, the graph of one line has a positive slope and the graph of the other line has a negative slope. This statement is indicative of a system of linear equations which will have no solution.
A system of linear equations is a collection of two or more linear equations with the same variables. A system of linear equations is a collection of two or more linear equations with the same variables. A solution of a system of linear equations is a set of values that make all of the equations true.
Let's look at the general form of two linear equations that are given:
y = mx + by = nx + c
where m and n are the slopes of each line. If m and n have different signs, one is positive and one is negative, then they will never meet and therefore will have no solution. We can thus conclude that the system of two equations has no solution.
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Given the following key, what polynomial is modeled by the diagram below?
The polynomial function modeled by the given diagram is given as follows:
p(x) = 3x² - 7x - 6.
How to obtain the polynomial function?The polynomial function modeled by the given diagram is obtained considering the keys of the problem, which are the terms represented by each figure.
The polynomial is constructed as follows:
3 large non-shaded squares: 3x².Two non-shaded rectangles: 2x.Nine shaded rectangles: -9x.Six shaded small squares: -6.Then the expression used to construct the polynomial is given as follows:
p(x) = 3x² + 2x - 9x - 6.
Combining the like terms, the polynomial function is defined as follows:
p(x) = 3x² - 7x - 6.
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what is the significance of a pedigree symbol consisting of a square with a diagonal slash mark through it?
The significance of a pedigree symbol consisting of a square with a diagonal slash mark through it is that it represents the male members of the family
It is a standard symbol in a pedigree chart. This symbol represents the sex of a person, in this case, it represents the male sex. In other words, a square with a diagonal slash mark through it is used to represent the male gender in pedigree charts.
A pedigree chart is a diagram that shows the genetic relationships between individuals in a family. It is used to track genetic diseases or traits through generations. A pedigree chart can provide information about a family's medical history and can help doctors to understand how genetic disorders are inherited from one generation to the next. Each symbol used in the pedigree chart has a specific meaning.
The squares represent males while the circles represent females. The horizontal line between two symbols represents marriage, and the vertical line from a symbol represents a child of that union.
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Kayla earns $9 an hour regular pay as a hostess. For every hour over 40 hours she works each week, she earns 1.5 times her regular pay. If Kayla worked 47 hours last week. how much
money did she earn?
Liz flips a coin 70 times. The coin lands heads up 42 times and tails up 28 times. Complete each statement
All the experimental probabilities of the coin lands heads up 42 times and tails up 28 times as discuss below 5 points.
Define the term experimental probabilities?Experimental probability is the ratio of the number of times an event occurs to the total number of trials or experiments conducted. It is calculated by performing an experiment or observation and recording the outcomes, and then finding the ratio of the number of times the desired outcome occurred to the total number of trials.
The experimental probability of the coin landing heads up is 42/70, or 0.6.The experimental probability of the coin landing tails up is 28/70, or 0.4The theoretical probability of the coin landing heads up is 1/2, or 0.5.The theoretical probability of the coin landing tails up is 1/2, or 0.5.Liz is more likely to flip heads than tails, based on the experimental probability.To know more about probability, visit:
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As discussed in the next five paragraphs, the coin lands heads up 42 times and tails up 28 times in all experimental probability.
Define the term experimental probabilities?The ratio of the frequency of an occurrence to the total number of trials or experiments is known as the experimental probability. It is determined by carrying out an experiment or making an observation, noting the results, and then calculating the ratio of the number of times the desired result appeared to the total number of trials.
42/70, or 0.6, is the experimental likelihood that the coin will land facing up.
The experimental likelihood that the coin will fall tails up is 28/70, or 0.4.
Theoretically, there is a 0.5 percent chance that the coin will land with its head up.
Theoretically, there is a 0.5 percent chance that the coin will fall tails up.
According to the experimental probability, Liz is more likely to flip heads than tails.
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Simplify 4m^2n-7mn^2
Answer:
mn(4m - 7n)
Step-by-step explanation:
➠ 4m^2n-7mn^2
➠ 2^2 x m^2n - 7mn^2
➠ mn([tex](\frac{2^2*m^2n}{mn} -\frac{7mn^2}{mn} )[/tex]
➠ mn([tex]2^2*m^{2-1}-(7n^{2-1}))[/tex]
➠ mn(4m - 7n)
In tests of significance about an unknown parameter of some population, which of the following is considered strong evidence against the null hypothesis?
A. The value of an estimate of the unknown parameter based on a simple random sample from the population is not equal to zero.
B. The value of an estimate of the unknown parameter lies within 2 units of the sample value.
C. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very consistent with the null hypothesis
D. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true.
In tests of significance about an unknown parameter of some population, "We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true" is considered strong evidence against the null hypothesis. The correct answer is Option (D).
We apply the principle of hypothesis testing to test a population's claims in inferential statistics. The null hypothesis (H₀) is always a statement about the population parameter that we believe to be true. However, we use the sample data to decide whether the null hypothesis is true or not. When we perform the hypothesis testing, we must consider the level of significance, the sample size, and the nature of the test.
The value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true is considered strong evidence against the null hypothesis. In other words, if the value of the test statistic is greater than the critical value, we can reject the null hypothesis. Consequently, we will have sufficient evidence to support the alternative hypothesis.
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23 people attend a party. each person shakes hands with at most 22 other people. what is the maximum possible number of handshakes, assuming that any two people can shake hands at most once?
The maximum possible number of handshakes that can happen at the party with 23 people with at most 22 other people is 253. This is calculated by combination.
What is the maximum possible number of handshakes?Twenty-three people attend a party. each person shakes hands with at most 22 other people.
To find the maximum possible number of handshakes, assuming that any two people can shake hands at most once, we need to use Combination by finding the number of unique pairs of people in the party.
nCr (combination) to find the number of unique pairs of people.
Therefore,[tex]^nC_r = \frac{n!}{(n-r)! r!}[/tex]
where n is the total number of people and r is the number of people in a handshake at a time.
Therefore, the number of unique pairs of people that can shake hands at most once is:
[tex]^{23}C_2 = \frac{23!}{(23-2)! (2!)}[/tex] [tex]=\frac{23 X22}{2} = 253[/tex]
Hence, the maximum possible number of handshakes that can happen at the party is 253.
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the expression when y=-6 y^2+8y-9
Answer:
-21
Step-by-step explanation:
y^2 + 8y - 9 y = -6
(-6)² + 8(-6) - 9
36 - 48 - 9
-21
So, the answer is -21
Answer:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}
Step-by-step explanation:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}
Can y’all explain how to do this really don’t get it please thank you
Write the expression in complete factored
form.
3a(a + 1) + x(a + 1)
Answer:(a + 1) (3a + x)
Step-by-step explanation:
Factor a+1 out of 3a ( a + 1 ) + x (a + 1 )
Hope this helps
Using the inverse transform method for discrete distribution, define a process for generating random variates from a binomial distribution with N 6 and p 0.4. (sixth decimal place.)
The another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.
The process of generating random variates from a binomial distribution using the inverse transform method for discrete distribution is done as follows:Step 1: Determine the probability mass function (pmf) of the binomial distribution with parameters n and p. For example, for a binomial distribution with n = 6 and p = 0.4, the pmf is given by:P(X=k) = (6 choose k)(0.4)^k(1-0.4)^(6-k), where k=0,1,2,3,4,5,6Step 2: Calculate the cumulative distribution function (CDF) of the binomial distribution by summing the pmf up to each value of k. The CDF is given by:F(k) = P(X ≤ k) = ΣP(X=i) for i=0 to k, where k=0,1,2,3,4,5,6Step 3: Generate a uniform random variate, U, between 0 and 1. For example, U=0.23456.Step 4: Find the smallest value of k such that F(k) ≥ U. This value of k is the random variate X. For example, if U=0.23456, then F(0)=0.10737, F(1)=0.38223, and F(2)=0.74304. Since F(1) is the smallest value of F(k) that is greater than or equal to U, X=1. Therefore, a random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=1.To find another random variate from the same distribution, repeat steps 3 and 4. For example, U=0.987654, F(0)=0.10737, F(1)=0.38223, F(2)=0.74304, F(3)=0.91892, F(4)=0.98544, and F(5)=0.99856. Since F(3) is the smallest value of F(k) that is greater than or equal to U, X=3. Therefore, another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.
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What is the value of x in this triangle?
Enter your answer in the box.
X =
xº
44°
5
53°
6 7
(O
Answer:
83°
Step-by-step explanation:
the total angle of a triangle is 180° degree so 180°-(44°+53°)=83°
How much was one movie ticket in 2008
Answer: 7 dollars 18 cents.
Step-by-step explanation:
You want to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units. You will sample the GPAs of 40 SJSU students. Select the correct model from the list. - One sample, Chi-square test of variance - Unequal variance t-test - Matched pairst-test - One sample. Z test of proportion - F-test comparing variances - One sample, t test for mean - Pooled variance t-test
The Chi-square test of variance is appropriate to use.
The correct model from the list to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units by sampling the GPAs of 40 SJSU students is the "One sample, Chi-square test of variance. "The Chi-square test of variance is used to determine whether the variance of a population is equal to a specific value. In the Chi-square test of variance, the null hypothesis is that the variance of the population is equal to the specific value or the variance is not greater than the specific value. The Chi-square test of variance is used when the sample is random, the sample is normally distributed, and the variable is measured on a continuous scale. In the given problem, the researcher wants to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units.
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Good day.....Please urgent assistance needed
the initial speed with which the particle was projected is approximately 29.7 m/s.
How to solve?
We can solve this problem using the equations of motion for a particle moving under constant acceleration due to gravity.
Let v be the initial velocity with which the particle was projected, and let θ be the angle of projection with respect to the horizontal. Since the particle is launched from a height of 15m, its initial vertical velocity is v sin(θ), and its initial horizontal velocity is v cos(θ).
The time taken for the particle to hit the ground can be found by using the equation:
y = y0 + v0t + 1/2at²
where y is the vertical displacement, y0 is the initial vertical position, v0 is the initial vertical velocity, a is the acceleration due to gravity (-9.8 m/s²), and t is the time taken.
Since the particle starts and ends at the same vertical position (15m), we have:
y - y0 = 0
Substituting the values, we get:
0 = 15 + v sin(θ)t - 1/2(9.8)t²
Simplifying and rearranging, we get:
4.9t² - vt - 30 = 0
Using the quadratic formula, we get:
t = (v ±√(v² + 4(4.9)(30))) / (2(4.9))
Since we want the time taken for the particle to hit the ground, we take the positive root:
t = (v + √(v² + 588)) / 9.8
Now, we can use the horizontal displacement to find the initial speed v. Since the particle travels a horizontal distance of 30m in time t, we have:
x = v cos(θ) t
Substituting the values, we get:
30 = v cos(θ) [(v +√(v² + 588)) / 9.8]
Simplifying and rearranging, we get:
v² - 882 = 0
Using the quadratic formula again, we get:
v = ±√(882)
Since the initial velocity must be positive, we take the positive root:
v ≈ 29.7 m/s
Therefore, the initial speed with which the particle was projected is approximately 29.7 m/s.
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1. If f = {(0,2), (-3,2), (2,5)} and g = {(3,4), (1,5), (-1,2)}, Find: f+g
Answer:
Step-by-step explanation:
F = (-1,9)
G = (-3,11)
He scatter plot shows the number of flowers that have bloomed in the garden during the month of March:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Flowers and the x axis is labeled Days in March
Part A: Using computer software, a correlation coefficient of r = 0. 98 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of flowers and the day in March, write a scenario that would be a causal relationship for flowers in a garden. (5 points)
A) Based on the scatter plot, an r value of 0.98 seems to be a reasonable estimate of the correlation between the number of flowers and the days in March. The scatter plot shows an upward trend with points that are moderately spread out from a line of best fit.
B) A scenario that would be a causal relationship for flowers in a garden could be the amount of sunlight the garden receives.
A) Based on the scatter plot, an r value of 0.98 seems to be a reasonable estimate of the correlation between the number of flowers and the days in March. The scatter plot shows an upward trend with points that are moderately spread out from a line of best fit. This indicates that there is a strong positive relationship between the number of flowers and the days in March, which is reflected in the high correlation coefficient. Therefore, it is likely that the r value of 0.98 is an accurate value for this data.
B) A scenario that would be a causal relationship for flowers in a garden could be the amount of sunlight the garden receives. For example, if the garden receives more sunlight, it could cause the flowers to grow more quickly and bloom earlier in the month. On the other hand, if the garden receives less sunlight, the flowers may take longer to grow and bloom, and there may be fewer flowers overall. In this scenario, sunlight would be the independent variable, and the number of flowers bloomed would be the dependent variable.
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The given question is incomplete, the complete question is:
He scatter plot shows the number of flowers that have bloomed in the garden during the month of March:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Flowers and the x axis is labeled Days in March
Part A: Using computer software, a correlation coefficient of r = 0. 98 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of flowers and the day in March, write a scenario that would be a causal relationship for flowers in a garden. (5 points)
A circle has a circumference of 20π meters. If a sector has a central angle of 45°, what is the arc length of the sector? Use pi = 3.14
The arc length of the sector is 7.85 meters whose circumference is 20π meters.
What is sector?In geometry, a sector is a part of a circle enclosed by two radii and an arc. The arc of a sector is a portion of the circumference of the circle. Sectors are often used in geometry and trigonometry to calculate areas, angles, and other measurements.
According to question:The equation for a circle's circumference is:
C = 2πr
Since we know the circumference of the circle, we can solve for the radius:
20π = 2πr
Dividing both sides by 2π, we get:
r = 10
Arc length = (central angle / 360°) x 2πr
where r is the radius and the central angle is in degrees.
Plugging in the given values, we get:
Arc length = (45° / 360°) x 2 x 3.14 x 10
Arc length = (1/8) x 62.8
Arc length = 7.85 meters
Therefore, the arc length of the sector is 7.85 meters.
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Scientific research study tracks the growth of an insect in millimeters. The growth data for each insect in the study during week 1 are 1. 1, 1. 25, 1. 3, 1. 67, 1. 9, 2. 35, 2. 1, 2. 3, 1. 5, 1. 7, 2. 25, 2. 1, 2. 45, 1. 37, 1. 83. The scientist is preparing a histogram to show the distribution of growth across the population. How should the scientist break down his data into categories?
The scientist should group the data into categories or bins of 0.5 millimeters, such as 1.0-1.5, 1.5-2.0, and 2.0-2.5,
To create a histogram to show the distribution of growth across the population, the scientist needs to group the data into categories or bins. The size of the bins will determine the shape of the histogram and how well it represents the data.
One way to determine the bin size is to calculate the range of the data and divide it by the number of bins desired. Another approach is to use a standard bin size, such as 0.5 or 1.0.
For this particular data set, a reasonable bin size could be 0.5 millimeters. The data can then be grouped into the following bins:
1.0 - 1.5
1.5 - 2.0
2.0 - 2.5
This will result in three bins that cover the entire range of the data. The scientist can then count the number of insects that fall into each bin and create a histogram to show the distribution of growth across the population.
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mass weighing 16 pounds is attached to a spring whose spring constant is 25 lb/ft. Find the equation of motion. (Use g = 32 ft/s2 for the acceleration due to gravity. Assume t is measured in seconds) *(t) = -16 cos(251) What is the period of simple harmonic motion (in seconds)?
The equation of motion of the system is, `x(t) = Acos(ωt + ϕ)` where `ω = √(k/m)` is the angular frequency of the system, `A` is the amplitude of motion, `ϕ` is the phase angle, `k` is the spring constant, and `m` is the mass attached to the spring. The period of simple harmonic motion (in seconds) is 0.628` seconds (approx).
The mass weighing 16 pounds is attached to a spring whose spring constant is 25 lb/ft.
So, the mass of the system `m = 16/32 = 0.5` slugs (1 slug = 32 lb.s^2/ft).
Thus, the angular frequency of the system is, `ω = √(k/m) = √(25/0.5) = 10` rad/s.
So, the equation of motion of the system is,x(t) = Acos(10t + ϕ)
Given that, x(0) = 16/25, x(t) = Acos(10t + ϕ) ...(1)
At t = 0, x(0) = Acosϕ = 16/25
So, `A = (16/25)/cosϕ`.
Therefore, by substituting `A` in equation (1), we get
x(t) = (16/25)/cosϕ × cos(10t + ϕ) = 0.64 cos(10t + ϕ)/cosϕ
Comparing this equation with the given equation, x(t) = -16 cos(251), we get`10t + ϕ = 251`, `cosϕ = -16/25`
Therefore, `ϕ = cos^{-1}(-16/25) = 123.7°`.The period of simple harmonic motion (in seconds) is given by,
`T = 2π/ω = 2π/10 = 0.628` seconds (approx).
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Q.4. A shopkeeper bought 18 sets of kurthas at the rate of Rs.1000 each. If 3 sets of kurthas were damaged and the remaining sets of kurthas were sold at the rate of Rs. 1250. Find the profit or loss of the shopkeeper.
Answer:
Rs 750
Step-by-step explanation:
Given, No. of kurtas: 18, Each with CP = Rs 1000.
So, SP of 18 kurtas: 18*1000 = Rs. 18000
Also, 3 sets of kurtas were damaged.
Therefore, Remaining kurtas: 18-3 = 15. SP of each: Rs 1250.
SP of 15 kurtas: 15*1250 = Rs. 18750
So, Clearly SP>CP, Profit.
We know Profit= SP-CP
= 18750-18000 = Rs 750