The sample mean is less than 26.92 hours per week .
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. In general, it reveals how far away from the mean each value is.
A low standard deviation denotes that values are grouped closely to the mean, while a high standard deviation denotes that values are typically spread widely from the mean.
Let X~ Normal (26, 4/√16) distribution ie Normal (26, 1) distribution
We want,
P(X<a) = 0.82
Using standard normal approximation,
P(z< (a-26)/1) = 0.82
Using standard normal distribution tables, we get
(a-26)/1 = 0.915
(Since P(z<0.915) = 0.82)
So, a= 26+0.915= 26.915
So the required value is 26.92 (rounded to two decimals)
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How do you find how many times greater something is in scientific notation
Answer: The number it is a power too
To determine how many times greater something is in scientific notation, you need to compare the exponents of the numbers and calculate the ratio between them.
In scientific notation, a number is expressed as the product of a coefficient (a decimal number between 1 and 10) and a power of 10. The exponent represents the number of places the decimal point has been moved.
To find how many times greater one number is than another, you compare the exponents of the powers of 10. If the exponent of the first number is n and the exponent of the second number is ᵃ, you can calculate the ratio by dividing 10ⁿ by 10ᵃ.
The result of this division will give you the factor by which the first number is greater than the second number. For example, if the result is 100, it means the first number is 100 times greater than the second number.
In summary, to determine how many times greater something is in scientific notation, compare the exponents of the powers of 10 and calculate the ratio between them.
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the sample midrange for the data. (ii) explain why the sample midrange might be preferred to the sample mean as an estimator of the population mean.
Answer:
The sample midrange for the data is 559
What is Sample midrange?
Although the sample midrange only uses a small fraction of the data, outliers can have a significant impact on it. It offers details on the distribution's skewness and heavy tails, which are identical to those of the random variable's distribution. Although the structure of this distribution is not obvious, with large sample sizes, the central limit will cause it to resemble a normal distribution.
According to question:
Minimum value: 34
Maximum values: 1084
The sample midrange can be computed as:
(Minimum value + Maximum value) / 2
⇒ (34+1084)/2
⇒ (1118)/2
⇒ 559
Hence, the sample midrange is 559
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The Complete Question is
a rectangle has a perimeter of 60 inches. What dimensions would maximize the area.
Answer: 15x15
Step-by-step explanation:
I'm assuming this is an optimization problem in a Calculus class, if not just disregard all of this and be happy with the answer.
We can write two equations for the value of x and y lengths of this rectangle.
2y+2x=60
xy=A
Solve our perimeter equation for y, y=30-x.
This gives us x(30-x)=A, and 30x-x²=A.
Find the derivative of the area function: A'=30-2x
To maximize we set A' to 0: 0=30-2x, x=15
Plug back into our perimeter formula: 2y+2(15)=60, y=15
So both sides will be 15 inches.
for 86 points, Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day.
Draw a graph to represent this situation.
Answer:
it will take him 9 days to complete 36 assignments
Step-by-step explanation:
Help please! Two angles are complementary. One is three times the measure of the other. What are the measures if each angle?
Answer: 22.5 and 67.5
Step-by-step explanation:
A complementary angle means that two angles add up to 90°
If one angle is 3 times the other,
let x be the value of the other angle.
The bigger angle would be 3x.
Therefore,
3x+x=90°
4x=90°
x=22.5
22.5 is the measure of the smaller angle
and 22.5x3=67.5 would be the other (larger) angle.
Answer:
22.5 degrees and 67.5 degrees
Step-by-step explanation:
3x + x = 90
4x=90
x=90/4
x=22.5
other angle is 3x which is 67.5
Suppose a triangle has two sides of length 7 and 8 and the included angle has a measure of theta degrees. What is the maximum area of the triangle?
28sinθ is the maximum area of the triangle
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
The two sides of triangle are of length 7 and 8.
Triangle has an included angle has a measure of θ degrees.
We need to find the maximum area
A=1/2×7×8×sinθ
A equal to one by two time of seven times of eight times sin theta.
A=7×4×sinθ
A=28sinθ
Hence, 28sinθ is the maximum area of the triangle
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a recent study of minimum wage earners found that 55% of them are 16 to 24 years old. suppose a random sample of 12 minimum wage earners is selected. what is the probability that exactly 7 of them are 16 to 24 years old.
The probability that exactly 7 of them are 16 to 24 years old is 0.222
In this question we have been given a recent study of minimum wage earners found that 55% of them are 16 to 24 years old.
A random sample of 12 minimum wage earners is selected. we need to find the probability that exactly 7 of them are 16 to 24 years old.
Here, n = 12
p = 0.55
1 - p = 0.45
x = 7
Using binomial distrubution the required probability would be,
P = 12C7 * (0.55)^7 * (0.45)^(12 - 7)
P = 792 * 0.01522 * (0.45)^5
P = 792 * 0.01522 * 0.01845
P = 0.2224
Therefore, the required probability is 0.222
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Without graphing, determine whether the function represents exponential growth or exponential decay.
y = 129(1.63)x
The exponential growth of three sections is given below.
What is exponential growth?Exponential growth means whose growth more rapid in proportion.
An exponential function is of the form , where b is a positive number not equal to 1.
The value of b determines whether tha function is an exponential growth or an exponential decay.
An exponential function is an exponential growth if b > 1 and an exponential decay if b <1.
Given the function= y 4(5/6)^x
B= 5/6 < 1
Therefore, the function is an exponential decay.
Given the function
Therefore, the function is an exponential growth.
Therefore, the function is an exponential growth is y= 129(1.63)^x is an exponential growth.
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The value of x is the equation X + 5 = 12 is
Answer:
x+5=12
or,x=12-5
or,x=7
Question 9 Which of the following distributions has a mean that varies? I. The population distribution II. The distribution of sample data III. The sampling distribution of the sample mean
O ll only
O IIl only
O I only
O all three distributions
O II and III
II and III only distributions has a mean that varies
The mean of a distribution is a measure of the central tendency of the data, and it can vary depending on the sample being analyzed.
For the population distribution, the mean is a fixed value that is calculated using all of the data in the population. The mean of the population distribution does not vary.
For the distribution of sample data, the mean is calculated using the data in the sample. If you take different samples from the same population, the mean of each sample will be different, so the mean of the distribution of sample data varies.
For the sampling distribution of the sample mean, the mean is calculated using the means of multiple samples. The mean of the sampling distribution is known as the population mean. As with the distribution of sample data, the mean of the sampling distribution varies depending on the samples that are used to calculate it.
Therefore, the mean of the distribution of sample data and the sampling distribution of the sample mean both vary, while the mean of the population distribution does not vary.
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Look at lines PR and ST shown. Suppose a dilation with a scale factor of 2 and a center of dilation at point P is performed on line QR and ST.
Which statements are true about the resulting images Q'R' and S'T'? Select ALL that apply.
1. True (The center of dilation lies on the segment)
2. False (The center of dilation does not line on the segment)
3. False (The center of dilation lies on the segment)
4. True (Since the segments are not collinear as a result of the dilation, they are parallel)
5. True (Scale factor is 2)
6. False (Scale factor is 2)
7. True (by definition)
8. True (by definition)
Vladmir sketches the graph of the function f(x)=12(x+6)2−3
as shown below
He then translates this function 11 units to the right and 4 units down to obtain the new function g(x)=12(x−h)2+k
. Which function correctly shows integer values for h and k?
The function that correctly shows the value of k and h is g(x) = 12(x - 5)² - 7
How to determine the function correctly?From the question, we have the following parameters that can be used in our computation:
f(x) = 12(x + 6)² - 3
The transformation is given as
11 units to the right and 4 units down
This is represented as
(x - 11, y - 4)
So, we have the following representation
g(x) = 12(x + 6 - 11)² - 3 - 4
Evaluate
g(x) = 12(x - 5)² - 7
Hence, the function is g(x) = 12(x - 5)² - 7
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ix different books will be displayed from left to right in the library window. how many different arrangements are there?
The total number of different arrangements possible for the books in the library window are 362880.
The total number of books that has to be arranged is 9.
The books has to be arranged in a pattern of left to right in the library window.
So here by we have a total possible 9 positions for 9 book because we have to create different arrangements every time.
Now, the total possible arrangement of the books can be given as,
= 9x8x7x6x5x4x3x2x1
= 362880
So the total number of possible different arrangements are 362880.
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Which of the following system of equations has no solution?
O 3x - y = 2,9x - 3y = 6
O 4x - 7y + 28 = 0,5y - 7x + 9 = 0
O 3x - 5y - 11 = 0,6x - 10y - 7 = 0
O None of these
4x - 7y + 28 = 0,5y - 7x + 9 = 0 is the system of equation that has no solution.
What is meant by system of equation?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
Name three types of system of equation.Dependent, Independent and inconsistent are the three types of system of equation.
If we solve this system of equation we will get complex roots that means it has no solution.
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The variables x and y vary directly. Use the values to find the constant of proportionality, k. Then write an equation that relates x and y. Write any fractions in simplest form.
y=20; x=12
Step-by-step explanation:
x =ky
x=12,y=20
12 =20k
divide both sides by 20
k=12/20
= 6/5
X=6/5y
If m<1=55, then find the value of m<3
The measure of angle 3 is given as follows:
m < 3 = 55º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles in this problem are listed as follows:
1 and 3.2 and 4.The measure of angle 1 is given as follows:
m < 1 = 55º.
Angle 1 and angle 3 are vertical angles, hence the measure of angle 3 is obtained as follows:
m < 3 = 55º.
As angle 3 is congruent to angle 1.
Angles 2 and 4 are also supplementary to angles 1 and 3, meaning that the sum of their measures is of 180º, hence m<2 = m<4 = 125º.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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When archeologists excavate a site, they mark it off with a coordinate grid so that they can easily
identify where artefacts are found and keep a record of the site forever. At the West Kennet Long
Barrow in England, a grave site back to 3600 BCE was found. There are three chambers at the
coordinates (7,9), (17, 33) and (-36,41). It has been said that they form an isosceles triangle with
height twice the length of its base.
Determine whether the statement is true. Justify your answer. Hint: An isosceles triangle has at
least two sides of equal side lengths.
1. In a party for 30 young children, 12 were served Coca-Cola drink, while 14 were served pepsi-cola. If 9 children were served Coca- Cola but not with pepsi-cola, find a. the number of children served both drink. b. the number of children served at least one type of drink. C.the number of children not served any of the drinks.
solve with showing equations
The number of children served both Coca-Cola and Pepsi-Cola is 3, the number of children served at least one type of drink is 9, and the number of children not served any of the drinks is 9.
To solve this problem, we can use the following equations:
a. The number of children served both drinks = 9 (served Coca-Cola but not Pepsi-Cola) + X (served both Coca-Cola and Pepsi-Cola)
b. The number of children served at least one type of drink = 12 (served Coca-Cola) + 14 (served Pepsi-Cola) - X (served both Coca-Cola and Pepsi-Cola)
c. The number of children not served any of the drinks = 30 (total number of children) - (number of children served at least one type of drink)
Substituting the values given in the problem into the equations above, we get:
a. The number of children served both drinks = 9 + X
b. The number of children served at least one type of drink = 12 + 14 - X
c. The number of children not served any of the drinks = 30 - (12 + 14 - X)
Solving for X in each equation, we get:
a. X = 3 (children served both Coca-Cola and Pepsi-Cola)
b. X = 9 (children served at least one type of drink)
c. X = 9 (children not served any of the drinks)
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How can I solve this ? What is the angle whose tangent is 456/321?
The angle whose tangent is 456/321 is 54.85°
The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.
The Tangent Formula is given as:
Tan A = Opposite Side/Adjacent side
In terms of sine and cosine, tangent may be represented as:
Tan A = Sin A / Cos A
We know that the sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side whereas the cosine of the angle is the ratio of the length of the adjacent side to the ratio of the hypotenuse side.
That is, Sin A = Opposite Side/ Hypotenuse Side
Cos A = Adjacent Side/ Hypotenuse Side
Therefore, tan A = Opposite Side/ Adjacent Side
[tex]tan^{-1} (1.42056)[/tex] =54.85°
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Rewrite the following equation in slope-intercept form.
13x − 3y = 18
Answer: y=(13/3)*x-6
Step-by-step explanation: -3y=18-13x -y=6-13/3 x
y= (13/3)x-6
How do you find 1/10th of a number?
One tenth of a number, something multiply it by 1/10 and then simplify or this is one tenth of that is just divide by 10.
We probably know that the number above the fraction bar is called the numerator and the number below it is called the denominator. To calculate the fraction of a number, we must first convert the whole number to a fraction as well, then multiply by 1/10. Alternatively, finding 1/10 of a number is the same as dividing it by 10.
Let's go through some examples to understand the concept.
a) What is 1/10 of 20?
20 can be put over 1 , since anything divided by
1 is itself. So do that and multiply:
1/10 × 20/ 1 → 20/10 → 2
b) What is 1/10th of 34 ?
=> 34 can be put over 1 and then multiply by 1/10
=> 34×1/10 = 34/10 = 3.4
So as we can see, all we have to do is divide the number by 10 and we've found one tenth of it.
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What is 16/64 simplified?
Answer:
1/2
Step-by-step explanation:
16/64 (divide the numerator and denominator by 4)
-> 4/8 (divide the numerator and denominator by 4)
-> 1/2
If f(7) = 22, then f^-1(22) = [?]
The required value of the given inverse function f⁻¹(22) will be 7.
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
Given that f(7) = 22
To determine the value of the given inverse function f⁻¹(22)
An inverse function's main objective is to show the value that occurs in a specific function value. Which means :
If we have f(x) and f⁻¹(x), then
if f(a) = b then f⁻¹(b) = a
As per the given question, we have
⇒ f(7) = 22 then f⁻¹(22) = 7
Therefore, the required value of the given inverse function f⁻¹(22) will be 7.
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Translate the phrase into an algebraic expression.
The sum 9 of C and.
WHAT IS THE ANSWER.
if you use a different experimental photo-missive material, what would be the same on the graph? (5 points) the y-intercept the intercept the slope
The slope would be the same on the graph.
What is a slope?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b.
M represents the line's slope. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the equation y = 3x - 7.
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Question
Find the range of the function represented by the list of ordered pairs below.
((-9, 4). (-0,3). (-8,0). (-2, -4))
Answer: {4,3,0,-4}
Step-by-step explanation:
The range is the set of all the values of y
Range {4,3,0,-4}
Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
The angle of x in the triangle is 30 degrees.
How to find angles of a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
In other words, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.
Therefore, the value of x can be found using the exterior angle theorem as follows:
x + 45 = 2x + 15
x - 2x = 15 - 45
- x = - 30
divide both sides by - 1
Therefore,
x = 30
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Is y=4+x a proportional relationship??
Hence, [tex]y=4+x[/tex] is a proportional relationship.
What is the proportional?
Proportional or proportion meaning in math means equality between two ratios. In the mathematical equation [tex]\frac{a}{b}=\frac{c}{d}[/tex], where [tex]a[/tex] and [tex]b[/tex] are in a similar proportion as [tex]c[/tex] and [tex]d[/tex].
A proportion is essentially established for solving a word problem in which one of its four quantities is unknown.
Here given that,
We have to check [tex]y=4+x[/tex] is a proportional relationship or not.
So, the given equation is
[tex]y=4+x[/tex]
Here, [tex]4[/tex] is constant.
So, [tex]y=4+x[/tex] is a proportional relationship.
Hence, [tex]y=4+x[/tex] is a proportional relationship.
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Which of the following is not a piece of required information in order to determine sample size? a. estimated population standard deviation b. estimated population median c. acceptable level of sampling error d. desired level of confidence e. All are necessarv to determine sample size.
E. All are necessary to determine sample size is not a piece of required information in order to determine sample size.
Determining an appropriate sample size is an important step in the research process as it helps to ensure that the results from the sample will be representative of the population as a whole. In order to accurately determine the appropriate sample size, you need to have an estimated population standard deviation, an estimated population median, an acceptable level of sampling error, and a desired level of confidence. The population standard deviation and median will help you determine the central tendency and variability of the population, while the acceptable level of sampling error and desired level of confidence will help you determine the margin of error you are willing to accept in your results. All four of these pieces of information must be taken into consideration in order to accurately determine the appropriate sample size.
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Graph the image of the given triangle after the transformation with the rule (x, y)→(−x, y).
Select the "Polygon" button from the tool bar to plot your triangle. You may use the "Move" button to move the triangle after it is created.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
Polygon with coordinates: (3, 4), (4, 7), (8, 2), (3, 4).
The given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).
What is reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image).
We can picture what would happen if you turned the form across the line to graph a reflection.
So, we have a triangle with coordinates:
(8, 2), (3, 4), (2, 7)
Now, we will reflect it according to the rule:
(x, y)→(−x, y)
Then, the coordinates will be:
(-8, 2), (-3, 4), (-2, 7)
(Refer to the graph attached below)
Therefore, the given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).
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