If you use a 0.05 level of significance in a two-tail hypothesis test and the calculated z-statistic is -1.79, you would fail to reject the null hypothesis.
In a hypothesis test, we compare the calculated test statistic (in this case, the z-statistic) to a critical value from a standard normal distribution based on the chosen level of significance (0.05). For a two-tailed test, the critical values are ±1.96. If the calculated z-statistic falls outside this range, we reject the null hypothesis. If it falls inside this range, we fail to reject the null hypothesis. In this case, the calculated z-statistic is -1.79, which falls between the critical values of ±1.96. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the alternative hypothesis at the 0.05 level of significance.
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It's a dark and stormy night. You are lying in bed and a bright flash of lightning lights up your room. You count
from the moment you see the lightning and reach 3 seconds when you hear the thunder. How far away is the
lightning bolt if it takes 5 seconds for sound to travel 1 mile?
O 3 miles
O 15 miles
O 5 miles
O.6 miles
Answer:
Step-by-step explanation:
Answer: 0.6
Any other answer would be too far away
If it takes 5 seconds to travel and you hear it in 3, then 3/5 equals 0.6
Answer:
0.6 miles
Step-by-step explanation:
5 sec is to 1 mile as 3 sec is to x miles
5/1 = 3/x
5x = 3
x = 3/5 = 0.6
Answer: 0.6 miles
suppose you cut the ice cube from exercise 3 in half horizontally into two smaller rectangles prisms find the surface area of one of the two smaller prisms
The surface area of the two rectangular prisms is S = 2 ( 2B + ph )
Given data ,
Surface Area of the prism = 2B + ph
The area of the triangular prism is A = ph + ( 1/2 ) bh
Now , ice cube is cut horizontally into two smaller rectangles prisms
where the length of the prism is l and width is w , and height is h
On simplifying , we get
The surface area of 2 prisms is S = 2 ( 2B + ph )
where B = base area of prism = l x w
And , p = perimeter of prism
h = height of prism
Hence , the surface area is S = 2 ( 2B + ph )
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find n in the picture provided please!
Answer:
n = 16
Step-by-step explanation:
LO is parallel to MN since they both make a right angle with KM.
Therefore, triangles KLO and KMN are similar triangles.
As corresponding sides of similar triangles are always in the same ratio:
KL : KM = LO : MN
From inspection of the given diagram:
KL = 30KM = 30 + 15 = 45LO = nMN = 24Substitute the values into the ratio and solve for n:
[tex]\implies \sf KL : KM = LO : MN[/tex]
[tex]\implies \sf 30: 45= n: 24[/tex]
[tex]\implies \sf \dfrac{30}{45}=\dfrac{n}{24}[/tex]
[tex]\implies \sf n=24 \cdot \dfrac{30}{45}[/tex]
[tex]\implies \sf n=\dfrac{720}{45}[/tex]
[tex]\implies \sf n=16[/tex]
Therefore, the value of n is 16.
Which side must have the same length as BC ?
A.CD
B.QR
C. RS
D. ST
The side which must have the same length as BC is RS.
The correct answer choice is option C.
Which side must have the same length as BC ?Given the figure ABCD with a similar figure QRST
If AD = 12 and QT = 12
AB = 8 and QR = 8
Then,
BC = RS
and
CD = ST
Hence, the side corresponding to BC is RS
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sampling in which the population is first divided into groups, and then random samples are drawn from each group?
The sampling method described in which the population is first divided into groups and then random samples are drawn from each group is called stratified sampling. In this sampling method, the population is divided into homogeneous subgroups called strata, based on some characteristic of interest such as age, gender, income level, or geographic location. Random samples are then drawn from each stratum, and the data collected from each sample are combined to form the final sample.
Stratified sampling is often used when the population is heterogeneous, meaning that it has distinct subgroups with different characteristics that may affect the outcome of the study. By dividing the population into homogeneous subgroups, stratified sampling increases the precision of the estimates and reduces the sampling error, compared to simple random sampling. Stratified sampling also ensures that each subgroup of the population is represented in the sample, which may be important for making inferences about the entire population. However, stratified sampling can be more complex and time-consuming than simple random sampling, especially if the population has many subgroups.
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find the general indefinite integral. (use c for the constant of integration.) sec(t)(3 sec(t) 7 tan(t)) dt
To find the indefinite integral of sec(t)(3sec(t)7tan(t))dt, we can start by using the substitution u = sec(t) + tan(t). Then, du/dt = sec(t)tan(t) + sec^2(t), which simplifies to du/dt = u(tan(t) + 1). We can rearrange this equation to get dt = du/u(tan(t) + 1), which allows us to rewrite the original integral as ∫(3u-21)/u^2du. Simplifying this expression, we get 3ln|u| - 21/u + c.
Substituting back in for u and simplifying, our final answer is 3ln|sec(t) + tan(t)| - 21/(sec(t) + tan(t)) + c.
1. Rewrite the integral: ∫(3 sec^2(t) + 7 sec(t)tan(t)) dt.
2. Integrate each term separately:
a) ∫3 sec^2(t) dt: Since the integral of sec^2(t) is tan(t), we have 3∫sec^2(t) dt = 3tan(t) + C1.
b) ∫7 sec(t)tan(t) dt: We use substitution method. Let u = sec(t), then du = sec(t)tan(t) dt. So, the integral becomes 7∫u du = (7/2)u^2 + C2 = (7/2)sec^2(t) + C2.
3. Combine both results: 3tan(t) + (7/2)sec^2(t) + C, where C = C1 + C2 is the constant of integration.
So, the general indefinite integral of the given function is 3tan(t) + (7/2)sec^2(t) + C.
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in a sample of 16, and x¯ = 74, with a standard deviation of s = 5, the standard error of the sample mean is
The standard error of the sample mean is 1.25.
The formula for the standard error of the sample mean is s/√n, where s is the standard deviation of the sample and n is the sample size. In this case, s=5 and n=16, so the standard error of the sample mean is 5/√16=1.25.
The standard error measures the variability of sample means that could be obtained from the population, and it decreases as the sample size increases. A smaller standard error means that the sample mean is a more precise estimate of the population mean.
In this example, the standard error of 1.25 indicates that the sample mean of 74 is relatively precise, but without additional information, we cannot determine how accurately it estimates the population mean.
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please help me!! thank you :)
The function represented in the table is:
y = 6*cos(x) + 4
Evaluationg this in x = 45 we will get:
y = 3√2 + 4
How to find the value of y when x = 45°?Here we have the table of the function:
y = a*cos(x) + b
We can see that when x = 0, y = 10, then:
10 = a*cos(0) + b
10 = a + b
And when x = 90, y = 4, then:
4 = a*cos(90) + b
4 = b
Replacing that value in the equation above:
10 = a + 4
10 - 4 = a
6 = a
Then the function is:
y = 6*cos(x) + 4
Evaluating this in x = 45 we will get:
y = 6*cos(45) + 4
y = 6*√2/2 + 4
y = 3√2 + 4
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3. Write 2 different equations you could use to solve for side m.
Picture Included
Here are two different equations you can use to solve for side m in right triangle MNI:
Pythagorean Theorem:
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum.
The equation is:
[tex]m^2 = MN^2 + NI^2[/tex]
Trigonometric Function (Sine or Cosine):
If you have information about the angles in the triangle, you can use trigonometric functions to find the length of side m.
In this equation, m represents the length of side m, MN represents the length of side MN, and NI represents the length of side NI.
The two equations:
m = MN / sin(I) (using the sine function)
m = MN / cos(M) (using the cosine function)
Here are two different equations you can use to solve for side m in right triangle MNI:
Pythagorean Theorem:
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, side m is the hypotenuse. The equation is:
[tex]m^2 = MN^2 + NI^2[/tex]
Trigonometric Function (Sine or Cosine):
If you have information about the angles in the triangle, you can use trigonometric functions to find the length of side m. For example, if you know the length of side MN and one of the acute angles in the triangle (angle M or angle N), you can use the sine or cosine function. Here are the two equations:
m = MN / sin(I) (using the sine function)
m = MN / cos(M) (using the cosine function)
In these equations, m represents the length of side m, MN represents the length of side MN, and I and M represent the measures of the respective angles in the triangle.
To solve for side m, you need to have at least two known values among the side lengths and angle measures. Once you have these values, substitute them into the appropriate equation and solve for m using basic algebraic operations. Ensure that your calculator is set to the appropriate angle mode (degrees or radians) when using trigonometric functions.
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In a two population proportions problem, why is the use of the individual proportions for X and Y (i.e, p_x,q_x and p_y,q_y ) used for confidence intervals instead of the "common p" used in hypothesis testing? 1. It's not. Unless the sample sizes are outside the 1/3 to 3/1 ratio, the two methods result in the same boundaries 2. Because it's a Cl on the difference". If you're going in assuming that the proportions are in fact different, it doesn't make sense to support using an average p and q 3. It doesn't make any difference.......this is not the answer, don't pick this 4. It's not, you use the common p in both instances 5. Because it's a Cl on the "difference", so it makes sense to use an averaged value for p.
In a two population proportions problem, the use of individual proportions for X and Y (i.e., p_x, q_x, and p_y, q_y) is used for confidence intervals instead of the "common p" used in hypothesis testing.
The reason for this is that in hypothesis testing, we are assuming that the two population proportions are equal (i.e., p_x = p_y = p), which means that we can estimate p using the combined sample proportion. However, in a confidence interval problem, we are interested in estimating the difference between the two population proportions, and using the combined sample proportion to estimate p would not be appropriate. Instead, we use the individual sample proportions for X and Y to construct separate confidence intervals for each population proportion, which we can then use to estimate the difference between them.
In other words, when constructing a confidence interval for the difference in proportions, we are interested in estimating the variability of each population proportion separately, and not the variability of the combined sample proportion. This is why we use the individual sample proportions for X and Y in constructing confidence intervals, rather than the common sample proportion used in hypothesis testing.
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use the following set of numbers of calculate the standard deviation of hypothetical hours of televisionw atched by high school students per week
To calculate the standard deviation of hypothetical hours of television watched by high school students per week, we need to use the formula for standard deviation with the given set of numbers.
The standard deviation is a measure of the spread of data around the mean. To calculate the standard deviation of the hypothetical hours of television watched by high school students per week, we need to first determine the mean of the data. Let's say the data set is {10, 8, 12, 6, 14, 10, 8, 16}. The mean is found by adding up all the numbers and dividing by the total number of numbers, which in this case is 10. The sum of the numbers is 84, so the mean is 8.4.
Next, we need to calculate the deviation of each number from the mean. This is done by subtracting the mean from each number. For example, the deviation of the first number (10) is 10 - 8.4 = 1.6. The deviation of the second number (8) is 8 - 8.4 = -0.4 (note that negative deviations indicate values below the mean).
Then, we square each deviation and add up all the squared deviations. This gives us the sum of squared deviations, which is 40.8 for this data set.
Finally, we divide the sum of squared deviations by the total number of numbers minus one, and then take the square root of this value. In this case, the calculation would be:
sqrt(40.8 / (10 - 1)) = 2.31
So the standard deviation of the hypothetical hours of television watched by high school students per week is 2.31 hours. This means that the data is relatively tightly clustered around the mean of 8.4 hours, with most values falling within 2.31 hours of the mean.
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What is the smallest integer of 3x+4>=14
The smallest integer value of x that satisfies the inequality 3x+4>=14 is 4.
To find the smallest integer value of x that satisfies the inequality 3x+4>=14, we need to isolate x on one side of the inequality sign.
First, we subtract 4 from both sides of the inequality to get:
3x >= 10
Next, we divide both sides of the inequality by 3 to get:
x >= 10/3
So any value of x that is greater than or equal to 10/3 will satisfy the inequality 3x+4>=14. However, since x is an integer, we need to round up to the smallest integer value that satisfies the inequality.
The smallest integer that is greater than or equal to 10/3 is 4, so the smallest integer value of x that satisfies the inequality is 4.
To check this, we can substitute x=4 back into the original inequality:
3(4) + 4 >= 14
12 + 4 >= 14
16 >= 14
Since 16 is indeed greater than or equal to 14, we have verified that x=4 is a valid solution to the inequality.
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Find the length of the arc of the curve y=lnx over the interval: [1,5]. Round the answer to four decimal places
The length of the arc of the curve y=lnx over the interval [1,5] is approximately 43.85 units long.
To find the length of the arc of the curve y=lnx over the interval [1,5], we need to use the arc length formula:
L = [tex]\int_1^5[/tex] √(1+(dy/dx)²) dx
We can find dy/dx by taking the derivative of y=lnx:
y' = 1/x
Then, we can substitute into the formula:
L = [tex]\int_1^5[/tex] √(1+(1/x)²) dx
Using substitution, let x = eⁿ, so dx = eⁿ dt:
L = [tex]\int_1^{ln5}[/tex] √(1+e²ⁿ) eⁿ dt
We can use u-substitution with u=1+e²ⁿ, so du/dt=2e²ⁿ:
L = (1/2) [tex]\int_1^{26}[/tex] √(u) du
L = (1/2) * (2/3) * ([tex]26^\frac{3}{2}[/tex] - 1)
L = 43.85
Therefore, the length of the arc of the curve y=lnx over the interval [1,5] is approximately 43.85 units long.
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Find the probability that a randomly
selected point within the large square falls
in the red-shaded square.
Answer:
[tex] \frac{ {6}^{2} }{ {15}^{2} } = \frac{36}{225} = .16 = 16\%[/tex]
give functions f(x)=x^2 -1 and function g(x)=3^x, for which values of x does f(x)=g(x)?
which one of the following fractions is less than 1
a)4/1 b)16/11 c)19/23 d)8/7
Answer: 19/23
Step-by-step explanation: 4/1=4 16/11=1 5/11 8/7=1 1/7 leaving 19/23 as the only fraction less than one.
Solve for x.
5x - 2 = 6 + 3x
x = [?]
X
Answer:x=4
Step-by-step explanation: subtract the 3x from its self then do it to the 5x and then you cross out the 3x's because the cancel out and then your left with 2x-2=6, then you add the 2 to itself which means they cancel out then you add it to the 6 and that gives you 8 then you are left with 2x=8 now you divide the 2x by its self then the 2 cancels out and then 8 divide by 2 is 4 and then x=4
N(5*-26 + *3*)^
que 5* meno 26 + 3 no se puede resolver
what does the statement rxy = 0 represent? group of answer choices research hypothesis t statistic null hypothesis mean difference
The statement "rxy = 0" represents the null hypothesis in correlation analysis, indicating no linear relationship between variables x and y.
In correlation analysis, the correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, usually denoted as x and y. When the statement "rxy = 0" is made, it refers to the null hypothesis in correlation testing. The null hypothesis states that there is no significant correlation between the variables.
If the correlation coefficient (r) between x and y is found to be exactly 0, it suggests that there is no linear relationship between the variables. This means that changes in x are not associated with any predictable changes in y.
Researchers use statistical tests, such as hypothesis testing, to evaluate whether the observed correlation coefficient is significantly different from 0. If the calculated correlation coefficient is significantly different from 0, the null hypothesis is rejected, indicating evidence of a linear relationship between x and y. However, if the calculated correlation coefficient is close to 0, it supports the null hypothesis, suggesting no linear relationship between the variables.
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what would happen (other things being equal) to a confidence interval if you calculated a 95onfidence interval rather than a 99onfidence interval?
If you calculated a 95% confidence interval instead of a 99% confidence interval, the width of the interval would typically decrease.
A confidence interval represents a range of values within which we have a certain level of confidence (expressed as a percentage) that the true population parameter lies. The higher the confidence level, the wider the interval because we want to be more confident in capturing the true parameter.
When you calculate a 99% confidence interval, you allow for a larger range of values, which means the interval will be wider. This wider interval provides a higher level of confidence that the true parameter falls within it.
On the other hand, a 95% confidence interval allows for a smaller range of values, resulting in a narrower interval. This narrower interval provides a slightly lower level of confidence compared to the 99% interval.
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find ∫ ∫ r 2 x d a over the region r = { ( x , y ) ∣ 0 ≤ x ≤ 4 , 0 ≤ y ≤ 5 } by indentifying it as the volume of a solid
The volume of the solid is 80 cubic units.
How to find the volume?The given double integral is:
∫ ∫ r 2 x d a
where r = { ( x , y ) ∣ 0 ≤ x ≤ 4 , 0 ≤ y ≤ 5 }
We can identify the integrand 2x as the area of a rectangular strip of thickness dx along the x-axis, with width 2x and height y, located at a distance x from the y-axis. Therefore, the double integral represents the volume of the solid obtained by stacking such rectangular strips over the region r.
To find the volume, we integrate the area of each rectangular strip over the interval 0 ≤ y ≤ 5 and then sum up the volumes of all such strips over the interval 0 ≤ x ≤ 4. Hence, we have:
∫ ∫ r 2 x d a = ∫ 0 4 ∫ 0 5 2x dy d
= ∫ 0 4 [2x(y)|0⁵] dx
= ∫ 0 4 10x dx
= [5x²|0⁴]
= 80
Therefore, the volume of the solid is 80 cubic units.
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The table below shows Alexa's earnings on the job. Time (hours) Time (hours) Earnings (dollars) Earnings (dollars) 8 8 $ 213.60 $213.60 16 16 $ 427.20 $427.20 31 31 $ 827.70 $827.70 How much does she make in 5.5 5.5 hours?
Answer:
approximately $147.60 in 5.5 hours
Step-by-step explanation:
To find how much Alexa makes in 5.5 hours, we can use linear interpolation. Linear interpolation is a method of estimating a value between two known values based on the assumption that the value changes linearly between them.
We can use the first two data points to calculate the hourly rate:
Hourly rate = (Earnings at 16 hours - Earnings at 8 hours) / (16 - 8) = ($427.20 - $213.60) / 8 = $26.40 per hour
Then we can use this hourly rate to estimate the earnings for 5.5 hours:
Earnings at 5.5 hours = Earnings at 8 hours + (5.5 - 8) x Hourly rate
Earnings at 5.5 hours = $213.60 + (-2.5) x $26.40
Earnings at 5.5 hours = $213.60 - $66.00
Earnings at 5.5 hours = $147.60
Therefore, Alexa would make approximately $147.60 in 5.5 hours.
A high school surveyed students to determine if new foreign language classes should be added to the course offerings for the next school year. The two-way frequency table below shows the interest of next year's underclassmen in the new courses.
German Mandarain Neither Total
freshmen: 30 80 230 340
Sophomores: 15 65 200 280
Total: 45 145 430 620
Approximately what percentage of the underclassmen have an interest in taking a Mandarin course next year?
44.83%
33.72%
23.39%
55.17%
Approximately 23.39% of the underclassmen have an interest in taking a Mandarin course next year.
Option C is the correct answer.
We have,
To determine the percentage of underclassmen interested in taking a Mandarin course, we need to calculate the ratio of the number of underclassmen interested in Mandarin to the total number of underclassmen.
Looking at the two-way frequency table, we can see that there are 145 underclassmen interested in Mandarin out of a total of 620 underclassmen.
To find the percentage, we divide the number of underclassmen interested in Mandarin by the total number of underclassmen and multiply by 100:
= (145 / 620) x 100
= 23.39%
Therefore,
Approximately 23.39% of the underclassmen have an interest in taking a Mandarin course next year.
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TRUE OR FALSE. if the means of two groups are the same, then the underlying distributions of the two groups must also be the same.
False. If the means of two groups are the same, it does not necessarily mean that the underlying distributions of the two groups are the same.
The statement is false. While the means of two groups provide information about the central tendency of the data, they do not provide a complete description of the underlying distributions. Two groups can have the same mean but exhibit different distributions in terms of shape, spread, or other characteristics.
For example, consider two groups: Group A and Group B. Group A has a normal distribution centered around the mean, while Group B has a bimodal distribution with two distinct peaks. Despite having the same mean, the distributions of Group A and Group B are fundamentally different.
The mean only represents the average value and does not capture the full picture of the data. Other statistical measures such as variance, skewness, and kurtosis provide information about the shape, spread, and symmetry of the distributions, respectively. To determine if the underlying distributions of two groups are the same, additional analyses such as hypothesis testing or graphical comparisons are necessary. Therefore, having the same means does not guarantee that the underlying distributions of the two groups are the same.
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In the diagram below, the expression in each circle is the result of the sum of the two rectangles connected to it. Complete the diagram,writing the expressions in their simplified form.
In the diagram below, the expression in each circle is the result of the sum of the two rectangles connected to it. The blanks an be filled with 6x + 2y, 3x + y and 5x.
A mathematical equation comprises a formula that uses the equals sign to represent the sameness of two expressions. The meanings of the word equation or its cognates in various languages can vary slightly. For instance, in French, an equation is defined as having any number of variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
The circle by your left:
(4x + 3y) + (2x - y)
Distribute +1
4x + 3y + 2x - y
Add like terms together
6x + 2y
The rectangle by at the bottom right:
(4x + 5y) - (x + 4y)
Distribute -1
4x + 5y - x - 4y
Group like terms
4x - x + 5y - 4y
3x + y
The circle at the bottom middle:
(2x - y) + (3x + y)
Distribute +1
2x - y + 3x + y
Group like terms
2x + 3x - y + y
5x
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which approach is more likely to result in a sample that is representative of the population?
Answer:
the last option
Step-by-step explanation:
The first choice would only target certain customers who come at a very specific time.
the second choice only surveys customers who spend over ten dollars.
The third only surveys muffin eaters!
The last choice has the most unbiased and random sampling to get a sample of all customers.
Which expression is equivalent to 6 × 3,725?
6 × 3,725 is equivalent to the value of 22,350.
We have,
To find the value of 6 × 3,725, we multiply the number 6 by the number 3,725.
This can be done by adding 3,725 to itself 6 times or by adding 6 to itself 3,725 times.
However, it is more efficient to use the multiplication operation, which is a shorthand way of adding a number to itself multiple times.
Using the multiplication operation, we can write 6 × 3,725 as:
6 × 3,725 = 6 × (3,000 + 700 + 20 + 5)
= (6 × 3,000) + (6 × 700) + (6 × 20) + (6 × 5)
= 18,000 + 4,200 + 120 + 30
= 22,350
Therefore,
6 × 3,725 is equivalent to the value of 22,350.
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1 have 4 sides all the same size and I have 4
corners. What am I?
If fis continuous and ∫250f(x)dx=20find ∫50f(5x)dx
Using the substitution method and the given information, we can evaluate ∫50f(5x)dx as 4.
We can use the substitution method to evaluate the integral ∫50f(5x)dx. Let u = 5x, then du/dx = 5 and dx = du/5. Substituting these expressions into the integral, we get:
∫50f(5x)dx = ∫10f(u) du/5
Next, we can apply the constant multiple rule for integrals, which states that ∫a kf(x)dx = k ∫a f(x)dx for any constant k. Using this rule, we can move the constant factor 1/5 outside the integral:
∫50f(5x)dx = (1/5) ∫10f(u) du
Now, we can use the given information that ∫250f(x)dx = 20 to find a relationship between ∫10f(u) du and ∫250f(x)dx. Substituting u = 5x into the bounds of integration, we get:
∫50f(5x)dx = (1/5) ∫250f(u) du, evaluated from u = 50 to u = 250
Using the Fundamental Theorem of Calculus, we can evaluate the definite integral ∫250f(u) du as follows:
∫250f(u) du = F(250) - F(50)
where F(x) is an antiderivative of f(x). Since f(x) is continuous, it has an antiderivative F(x). We are given that ∫250f(x)dx = 20, so we can write:
F(250) - F(50) = ∫250f(x)dx = 20
Simplifying, we get:
F(250) = F(50) + 20
Now we can substitute this relationship back into our expression for ∫50f(5x)dx:
∫50f(5x)dx = (1/5) ∫250f(u) du, evaluated from u = 50 to u = 250
= (1/5) [F(250) - F(50)]
= (1/5) [F(50) + 20 - F(50)]
= 4
Therefore, we have found that:
∫50f(5x)dx = 4
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:
C. m∠5 + m∠6 =180°.
D. m∠2 + m∠3 = m∠6.
E. m∠2 + m∠3 + m∠5 = 180°.
What is the exterior angle property?In Mathematics and Geometry, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:
m∠2 + m∠3 = m∠6.
According to the Linear Pair Postulate which states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair, we have:
m∠5 + m∠6 =180°.
As a general rule in geometry, the sum of all the angles that are formed by a triangle is equal to 180º and this gives:
m∠2 + m∠3 + m∠5 = 180°.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
find the standard form of the equation of the parabola with the given characteristics. vertex: (5, 25) points on the parabola: (0, 0), (10, 0)
We know that the vertex form of a parabola is given. Therefore, there is no parabola that satisfies these conditions.
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and a is a constant that determines the shape of the parabola.
We are given the vertex (5, 25), so we can write:
y = a(x - 5)^2 + 25
We are also given two points on the parabola: (0, 0) and (10, 0). Plugging these into the equation, we get:
0 = a(0 - 5)^2 + 25 => 25 = 25a => a = 1
0 = a(10 - 5)^2 + 25 => 0 = 25a => a = 0
We get two different values for a, which means that the given points do not lie on the same parabola. Therefore, there is no unique solution to this problem.
We can also see this geometrically: the points (0, 0) and (10, 0) lie on the x-axis, which means that the parabola would have to open either upwards or downwards. However, the vertex is above the x-axis, which means that the parabola cannot intersect the x-axis. Therefore, there is no parabola that satisfies these conditions.
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