The 95% upper confidence bound for the population mean μ, given a sample size of 17 and a sample mean of 85 with a sample standard deviation of 6, is 87.85.
87.85
The 95% confidence interval for the population mean is given by
CI = Sample mean ± (t-score) * (Standard Error)
where t-score can be obtained from the t-table with degrees of freedom as n-1 and confidence level as 95%.
Therefore, for a sample size of 17, the t-score is 1.711 and the standard error is 6/√17 = 1.5.
So, the 95% upper confidence bound for μ is
87.85 = 85 + (1.711)*(1.5)
The 95% upper confidence bound for the population mean μ, given a sample size of 17 and a sample mean of 85 with a sample standard deviation of 6, is 87.85.
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Work out the hortet ditance between planet Q and plant R. Give your anwer in tandard form
The shortest distance between planet Q and planet R is 1.64 × 10⁷ .
What is planet distance?RP = 1.6 * 10⁷
most compact distance
The Pythagoras theorem x₂ = R * P² + Q * P² is then used to determine the shortest distance (x).
This results in x = (3.6 * 10⁶) + (1.6 * 10⁷) = 2.
x² = 12.96 * 10¹² + 2.56 * 10¹⁴ should be evaluated.
Write the equation as: x²= 12.96 * 10¹² + 256 * 10¹²
Sums x² = 268.96*10¹² should be evaluated.
multiply both sides' square roots.
x = 16.4 * 10⁶
Replace with: x = 1.64 * 10⁷
In light of this, the distance between planet Q and planet R is 1.64 * 10⁷ km.
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The complete question is
The distances between some planets are given below.
Planet Q is 3.6 x 10⁷ to the power of 6 km from planet P.
Planet R is 1.6 x 10⁷ to the power of 7 km from planet P.
Work out the shortest distance between planet Q and planet R. Give your answer in standard form.
9. Construct Arguments Katya measured
the growth of a plant seedling. The
seedling grew inch by the end of the
first week and another inch by the end
of the second week. About how much did
6
the seedling grow in the first 2 weeks?
Explain how you made your estimate.
The total growth of the plant in 2 weeks is 7/6 inches.
What are fractions?A fraction is defined as a piece of a whole. The complete could be a single thing or a group of objects. The component reflects the percentage of the cake when we really cut a slice of cake from the whole cake. Latin is where the word "fraction" originates.
Given plant grew in the first week = 1/3 inch
the plant grew in the second week = 5/6 inch
total growth in 2 weeks = 1/3 + 5/6
1/3 is equivalent to 2/6 with same diameter,
total growth in 2 weeks = 2/6 + 5/6
total growth in 2 weeks = 7/6 inches
Hence the total growth is 7/6 inches.
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The correct question is,
Katya measured the growth of a plant seedling. The seedling grew 1/3 inch by the end of the first week and another 5 / 6 inch by the end of the second week. About how much did the seedling grow in the first 2 weeks? Explain how you made your estimate.
For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1. 8x2?
A. F(x) = x2 B. G(x) = 1. 2x2 C. H(x) = 1. 5x2 D. K(x) = 2x2
The average rate of change over for the interval 1 < x < 5 k(x) greater than the average rate of change over of g(x)
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
We have,
g(x) = 1.8 [tex]x^{2}[/tex]
The average rate of change of g(x) over the interval 1 < x < 5:
= [tex]$\frac{g(5)-g(1)}{5-1}[/tex]
= [tex]$\frac{1.8 \times (5)^{2} -1.8 \times(1)^{2} }{5-1}[/tex]
= [tex]$\frac{43.2}{4}[/tex]
= 10.8..............(1)
The average rate of change of f(x) = [tex]x^2[/tex] in the interval 1 < x < 5:
= [tex]$\frac{25-1}{4}[/tex]
= [tex]$\frac{24}{4}[/tex]
= 6..............(2)
The average rate of change of g(x) = 1.2 [tex]x^2[/tex] in the interval 1 < x < 5:
= [tex]$\frac{28.8}{4}[/tex]
= 7.2.................(3)
The average rate of change of h(x) =1.5 [tex]x^2[/tex] in the interval 1 < x < 5:
= [tex]$\frac{36}{4}[/tex]
= 9...........(4)
The average rate of change of k(x) = 2 [tex]x^{2}[/tex] in the interval 1 < x < 5:
= [tex]$\frac{48}{4}[/tex]
= 12.........(5)
From (1), (2), (3), (4), and (5) we see that,
The average rate of change of [tex]$\mathbf{k}(x)=2 x^2$[/tex] is larger than the average rate of change of [tex]$g(x)=1.8 x^2$[/tex].
12 > 10.8
Thus,
Option D is the correct answer.
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Luis jogged 9 3/13 laps the morning and 3 5/26 in the evening how many did he do in all?
Answer: 12 11/26 laps
Step-by-step explanation:
9 3/13= 9 6/26
9 6/26+ 3 5/26=12 11/26.
Use RAM to estimate the area of the region enclosed between the graph of Æ and the x-axis for a ⤠x ⤠b. Æ(x) = 1/x, a = 1, b = 3
The area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 is estimated to be 4/3.
Ram's Rule is a numerical integration method used to estimate the area under a curve by dividing it into trapezoids. The formula for calculating the area under the curve is given by A = (1/2) x (b - a) x (f(a) + f(b)), where A is the area, b and a are the limits of the integration and f(a) and f(b) are the values of the function at the limits a and b respectively.
In this case, the area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 can be estimated using Ram's Rule as follows:
A = (1/2) x (3 - 1) x (1/1 + 1/3)
= (1/2) x (2) x (4/3)
= 4/3.
Therefore, the area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 is estimated to be 4/3.
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Triangle PQR is similar to Triangle XYZ. What is the perimeter of Triangle XYZ?
[tex]\cfrac{PQ}{XY}=\cfrac{QR}{YZ}\implies \cfrac{5}{30}=\cfrac{6}{YZ}\implies 5YZ=180\implies YZ=\cfrac{180}{5}\implies YZ=36 \\\\\\ \cfrac{PQ}{XY}=\cfrac{PR}{XZ}\implies\cfrac{5}{30}=\cfrac{10}{XZ}\implies 5XZ=300\implies XZ=\cfrac{300}{5}\implies XZ=60 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Perimeter of }XYZ}{30~~ + ~~36~~ + ~~60}\implies \text{\LARGE 126}[/tex]
Consider a random sample of size 32 from a distribution with mean 40 and variance 8. find the (approximate) probability that the sample mean is between 39.75 and 41.25.
The probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.
The probability that the sample mean is between 39.75 and 41.25 can be calculated using the Central Limit Theorem. This theorem states that the distribution of the sample means will be normally distributed with a mean equal to the population mean (μ = 40) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ = 8/√32).
Using this information, we can calculate the probability that the sample mean is between 39.75 and 41.25, which will be the area under the normal curve between those two points. This area can be calculated using the z-score formula, which is (x-μ)/σ = (41.25-40)/(8/√32). This gives us a z-score of 0.25. The probability can then be calculated using a z-table, which is approximately 0.5987. Therefore, the probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.
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Which led most directly to the Roman Republic's demise and its transition to an empire?
A) Consuls staying in power too long.
B) War with the Etruscans.
C) The growing divide between the rich and the poor.
D) The failure of direct democracy.
The failure of direct democracy most directly led to the Roman Republic's demise and its transition to an empire. That is option D.
What brought about the Roman Republic's demise?Democracy is defined as the government by the people for the people and based of the will of these people.
In the first part of ancient Rome (509-27 BC), the people were governed by elected officials. This is democracy as we understand it today.
But things began to change, people became less interested in the affairs of government, and the failure of democracy led directly to the rise of one-man empires. The Roman Empire lasted from 27 BC to 476 BC.
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September 20, 2019: Sanford pays a $15,000 balance due to the supplier upon delivery of the helmets to its warehouse. how should the transaction be recorded in sanford’s financial accounting system?
The transaction should be recorded as an Accounts Payable (A/P) liability in Sanford’s financial accounting system.
Accounts Payable is a liability account that records the amount of money a company owes to its suppliers for goods and services that have been received, but not yet paid for. In this case, Sanford is responsible for paying the supplier $15,000 for the helmets that have been delivered to its warehouse.
This payment should be recorded in the Accounts Payable account as a debit of $15,000 and a credit to the Cash account of $15,000. By doing this, Sanford’s Accounts Payable balance will be reduced to reflect that the invoice has been paid, and the Cash account will be increased to reflect the payment made. This will keep the company’s financial records up to date and accurate.
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45°
11√2
11
y
45°
(11√2)/2
022
Find y.
11√2
Answer:
Step-by-step explanation:
it is the pink one
Solve this trigonometry problem
Can someone solve this step by step and with a graph?
Which multiplication equation can be used to explain the solution to 15/ by 1/3 of a fraction?
Answer:
Multiply by the inverse.
Answer: 45
Step-by-step explanation:
(15)/(1/3) is the same thing as multiplying the top (numerator), by the inverse of the bottom (denominator).
So we have the following: [tex]\frac{15/1}{1/3}[/tex]
Taking the inverse means flipping the fraction. The inverse of [tex]\frac{1}{3}[/tex] is [tex]\frac{3}{1}[/tex]. So we can keep the top, and multiply by the inverse.
[tex]\frac{15}{1}[/tex] X [tex]\frac{3}{1}[/tex] = 15 x 3 = 45.
Does this make sense?
How do you write 37% as a decimal?
Answer:
0.37
Step-by-step explanation:
37% = 37/100 = 0.37
‼️‼️PLEASEE HELP‼️‼️
When rotated about it’s center, a regular heptagon has __ rotational symmetries. In addition to rotational symmetry, a regular heptagon has __ lines of reflectional symmetry
When rotated about its center, a regular heptagon has 7 rotational symmetries. In addition to rotational symmetry, a regular heptagon has 1 line of reflectional symmetry.
What do you mean by rotation symmetry?Rotation symmetry, also known as radial symmetry or circular symmetry, is a fundamental concept in geometry that refers to the property of a shape to remain unchanged after rotating it about a fixed point. This point is typically the center of the shape, although it can be any point within the shape.
The amount of rotation required for the shape to become congruent to its original form is called the "angle of rotation." If a shape can be rotated multiple times and still remain unchanged, it is said to have multiple rotational symmetries.
For example, a circle has an infinite order of rotational symmetry, as it can be rotated 360 degrees and still look exactly the same. On the other hand, a square has 4 rotational symmetries, as it can be rotated 90 degrees and still look the same 4 times.
Rotational symmetry is a useful concept in mathematics and science as it provides a way to describe the symmetry of objects and shapes in the real world. It also helps us understand how objects and shapes change when they are rotated, and it provides a way to classify objects based on their symmetrical properties.
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help this is urgent hurry pls
Answer:
Step-by-step explanation:
You're right; it's 97 degrees. The angles of a triangle add up to 180, so to solve for each triangle's unknown angle value, subtract the known angles from 180. For the left triangle, that's 33 and for the right triangle it's 50. Those missing angles plus the one the question is asking for should add up to 180 degrees as well. Hence, 180 - 33 - 50 = 97.
Find the area of the shaded region. Round your answer to the nearest tenth.
The area of the shaded region is 17.4 rounded up to the nearest tenth.
How to evaluate for the area of the shaded regionThe unshaded region forms a circle with a radius of 9/2, so to get the area of the shaded region, we subtract the area of the circle from the area of the square as follows:
area of square = 9 m × 9 m = 81 m²
area of the circle = 22/7 × 9/2 × 9/2
area of the circle = 891/14 m²
area of the shaded region = 81 m² - 891/14 m²
area of the shaded region = (1134 - 891)/14
area of the shaded region = 243/14
area of the shaded region = 17.3571
Therefore, the area of the shaded region is 17.4 rounded up to the nearest tenth.
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Which theorem or postulate proves that △ABC and △DEF are similar? SSS Similarity Theorem AA Similarity Postulate SAS Similarity Theorem Two triangles with the same shape. In the first triangle, the vertices are labeled as A, B, and C. Base is B C and the top vertex is A. Side A B is labeled 3. Side B C is labeled 7. Side A C is labeled 6. In the second triangle, the vertices are labeled as D, E, and F. Base is E F and the top vertex is D. Side D E is labeled 18. Side E F is labeled 42. Side D F is labeled 36
The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.
In this case, the ratio of the corresponding sides of the two triangles are:
AB/DE = 3/18 = 1/6
BC/EF = 7/42 = 1/6
Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.
For what value of a does 9= [1/27]^a+3?
Answer:
The answer is a = -11/3.
A bus company uses a grid to locate bus stops. The bus station is at (3, 4). The point (7, 6) represents the first bus stop. The location of the second bus stop is determined using the same relationships as those between the coordinates of the bus station and the first bus stop. A coordinate plane is titled Use the drop-down menus to describe the relationships between the coordinates of the first and second bus stop. The Choose... increases by 4, and the Choose... increases by 2.
The location of the second bus stop is given as follows:
(10, 8).
The relationship is described as follows:
When x increases by 4, y increases by 2.
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.The change in x is given as follows:
7 - 3 = 4.
The change in y is given as follows:
6 - 4 = 2.
Hence, starting from the first bus stop, the coordinates of the second bus stop are given as follows:
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HELP 20 BRAINLY!!<33
The table should be completed as follows;
Object Radius Circumference
ceiling fan 2.8 ft 17.584 ft.
water bottle cap 13 mm 81.64 mm.
bowl 9.0 cm 56.5 cm.
drum 12.0 in 75.4 in.
How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
C = 2πr
Where:
C represents the circumference of a circle.r represents the radius of a circle.For the ceiling fan, the circumference is given by:
C = 2πr
C = 2 × 3.14 × 2.8
C = 17.584 ft.
For the water bottle cap, the circumference is given by:
C = 2πr
C = 2 × 3.14 × 13
C = 81.64 mm.
For the bowl, the radius is given by:
C = 2πr
56.5 = 2 × 3.14 × r
56.5 = 6.28r.
Radius, r = 56.5/6.28 = 8.9968 ≈ 9.0 cm.
For the drum, the radius is given by:
C = 2πr
75.4 = 2 × 3.14 × r
75.4 = 6.28r.
Radius, r = 75.4/6.28 = 12.0 in.
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determine the equation of each radical function which has been tranformed
The equation of a radical function can be determined by using the transformation rules for x- and y- shifts, stretches/compressions, reflections, and rotations.
The equation of a radical function can be determined by applying various transformation rules. The most common transformations are shifts, stretches/ compressions, reflections, and rotations. For example, a radical function that is shifted left two units would have an equation of y = sqrt(x + 2). This is because the function is shifted two units to the left of the origin, so the equation must include an x + 2 term. Similarly, if the function is reflected in the x-axis, the equation would be y = -sqrt(x). This is because the reflection inverts the sign of the y-coordinate, so the equation must include a negative sign in the radical. For stretches and compressions, the equation must include a coefficient in front of the radical. For example, if the function is stretched horizontally by a factor of 3, then the equation would be y = 3 sqrt(x). This is because the function is stretched by a factor of three, so the equation must include a coefficient of 3 in front of the radical. Finally, for rotations, the equation must include a term for the angle of rotation. For example, if the function is rotated counterclockwise by 45 degrees, then the equation would be y = sqrt(x + y/tan45). This is because the angle of rotation is 45 degrees, so the equation must include a tan45 term.
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(3) pilot altitude 1m angle of depression 3°
d=?
The length d for the angle of depression 3° and altitude 1m is equal to 19 m to the nearest metre using the trigonometric ratio of cosine for the angle 87°
What is an angle of depressionThe angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.
Considering the right triangle formed by the length d and the altitude of 1 m, we shall derive a complementary angle as:
90° - 3° = 87°
such that;
cos 87° = 1/d {adjacent/hypotenuse}
d = 1/cos 87°
d = 19.1073.
Therefore, the length d for the angle of depression 3° and altitude 1m is equal to 19 m to the nearest metre using the trigonometric ratio of cosine for the angle 87°.
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it is known that the average number of pushups a u.s marine does daily is 300 with standard deviation of 50. a random sample of 49 marines is selected. a) the population of interest is [ select ] the parameter of interest is [ select ] the value of the parameter is [ select ] b) if is the sample mean number of pushups a u.s. marine does, since [ select ] , the central limit theorem holds and [ select ] , [ select ] ) c) the probability that the sample mean is less than 292 is [ select ] .
To solve we need to calculate the z-score, but since we are given the sample size then we shall begin as follows:
The z-score is calculated as (320 - 300)/(50/6) = 2.4, which means that the value of 320 is 2.4 standard deviations above the population mean of 300. Using a standard normal table or calculator, we can find the probability that a standard normal random variable is less than 2.4, which is approximately 0.9918.
This means that the probability that the sample mean is greater than 320 is approximately 0.9918. In other words, there is a 99.18% chance that a randomly selected sample of 36 U.S. Marines will have a mean number of pushups greater than 320.
μ=300, σ=50, n=36, x=320
So,
σ/√n
= 50/√36
= 8.33333
z=(320-300)/8.33333
z=2.4
Therefore,
P(x>320)=P(z<2.4)=0.9918.
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You decide to invest in government bonds to save money for your eventual wedding. You have an
initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate
of return.
What will be the value of your investment at maturity?
Round off to nearest whole number
The value of your investment at maturity is $16,800. The interest is $9,800.
What is the meaning of initial investment?
The initial sum of money required to open an account or start a buy-in relationship is known as an initial investment. The two distinct but related industries of banking and long-term investment brokering are the main uses of the term "initial investment."
Given that the initial investment is $7,000. The rate of interest is 10% = 0.10. The number of years of investment is 14 years.
The formula of simple interest is
I = Prt
I = interest, P = principal, r = rate of interest, t = time.
Putting P = 7000, r = 0.10, t = 14 in I = Prt:
I = 7000 × 0.10 × 14
I = 9,800
The amount will be interest + principal = 9800+ 7000 = 16,800.
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If the two spinners below are spun, what is the probability that the numbers will add to more than 4?
Answer: The answer is 1/4.
Step-by-step explanation:
from your descriptive statistics, describe your standard deviations of salary, hryly rate, yrs worked, education, and age. what does this tell you about the variables
It is not possible to describe the standard deviations of salary, hourly rate, years worked, education, and age without having the data.
Standard deviation is a measure of the spread or dispersion of a set of data. It is calculated as the square root of the variance and is used to give an idea of how far the individual values in a data set are from the mean or average.
In order to describe the standard deviations of salary, hourly rate, years worked, education, and age, we would need to have the actual data for those variables. Without the data, it is not possible to calculate the standard deviations and describe what they tell us about the variables.
It is important to note that the standard deviation can give us information about the distribution of the data and the variability of the values. For example, if the standard deviation is small, this means that the majority of the values are close to the mean, while a larger standard deviation indicates that the values are more spread out. This information can be useful in making inferences about the variables and in making predictions about future values.
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rosie sold 19 catendars.Suzy sold 26 jaun sold 4 times as many calenars as rosie and sulzy combined how many calendars did juan sell
First, we can find the total number of calendars sold by Rosie and Suzy combined:
19 (calendars sold by Rosie) + 26 (calendars sold by Suzy) = 45 calendars
Next, we can find the number of calendars sold by Juan:
Juan sold 4 times as many calendars as Rosie and Suzy combined, so Juan sold 4 * 45 = 180 calendars.
standard deviation and varianc'e remember that the standard deviation and variance can only be used when the mean is used as the measure of center. True/False ?
True. The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They cannot be used to calculate the dispersion around the median or mode, or any other center-of-mass metric.
The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They can therefore be used to calculate the difference between the highest and lowest values in a data set. The standard deviation, which is the square root of the variance, is used to calculate how far away from the mean each result is on average. The average of the squared deviations between each data point and the mean is the variance. The variance and standard deviation cannot be used to quantify the dispersion of data around other measures of center, such as the median or mode, because they only measure the dispersion of data around the mean.
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An ellipse has foci (0, – 2) and (0, 2) and a minor axis of length 6. What is the equation in standard form of the ellipse?
Length of major axis using formula of eccentricity is √2,2
How to find the length?Given that foci of the ellipse is at (0,2) & (0,−2)
⇒Major axis of ellipse is along y-axis.
So, equation of ellipse can be taken as: x²/a² +y/b² = 1 where a<b
Length of minor axis, 2a=4 (Given)
⇒a=2 ....(1)
and b=2 ....(2)
e = √(1-a²/b²)
⇒a²=b²-b²e²
b²=8
Therefore b=2√2 .....3
Find equation of ellipse using above result
x²/4 + y²/8 = 1
Checking options, we have ( 2,2) satisfying the equation of ellipse above.
Hence the length of the is √2,2
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