The value of the expression 14.5 * 35 is 507.5
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
14.5 * 35
The given expression is a simple expression that can be solved using a calculator
Using a calculator, we have the following solution
14.5 * 35 = 507.5
Hence, the solution is 507.5
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Hue is arranging chairs. She can form 2 rows of a given length with 3 chairs left over, or 8 rows of that same length if she gets 15 more chairs. Complete the equation and solve it to find how many chairs are in that row length.
Answer: If Hue can form 2 rows of a given length with 3 chairs left over, we can represent this as:
2x + 3 = chairs in that row length
Also, if she can form 8 rows of that same length if she gets 15 more chairs, we can represent this as:
8x + 15 = chairs in that row length
Since the number of chairs in that row length is the same in both equations, we can set them equal to each other:
2x + 3 = 8x + 15
To solve for x, we can subtract 3 from both sides:
2x = 8x + 12
Then we can subtract 2x from both sides:
6x = 12
Finally, we can divide both sides by 6:
x = 2
So the number of chairs in that row length is 2x + 3 = 2(2) + 3 = 7.
Step-by-step explanation:
Explain whether rounding or compatible numbers gives a closer estimate for the product below. 48 x 123 = 5,904
Comparing rounding and compatible number, rounding gives a closer estimate than compatible number.
What are compatible or rounded numbers?While compatible numbers are those that are simple to multiply mentally, rounding entails reducing one or both of the numbers to a close "friendly" number.
Estimating the result of 48 x 123 can be done using compatible integers and rounding.
Which numbers can be used to estimate the product?Compatible numbers make it simpler to find an estimate calculation because they are close in value to the real number. A multiplication issue is presented here. By rounding the values to the closest hundreds place, you can obtain an approximation of the product. 400 and 100 are equivalent to 395 and 103.
1) Using compatible numbers :
48 = 50
123 = 100
50 × 100 = 5000
2) By rounding numbers :
48 = 50
123 = 120
50 × 120 = 6000
6000 is closer to the actual value of the product than 5000 ;
Therefore, rounding gives a closer estimate than compatible number.
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8x-3y=11
Solving for Y
Answer:x=13
Step-by-step explanation:
Consider the triangles shown below. Which of the following would also need to be true in order to prove that ΔABD≅ΔABC
To prove that triangles ABD and ΔABC are congruent by SSS, what needs to be true is: A. BC ≅ BD.
What is the SSS Congruence Theorem?For two triangles to be congruent to each other by the SSS Congruence Theorem, the triangles must have three pairs of corresponding sides that are congruent to each other.
In the image given, we can deduce that the two triangles have the following properties:
AB ≅ AB (reflexive property)
AC ≅ AD (given)
This means that have two pairs of corresponding congruent sides. Therefore, in order to prove that ΔABD ≅ ΔABC by SSS, what needs to be true is: A. BC ≅ BD.
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Which of the following are like terms?
The like terms are listed as follows:
-y, 7y and y/2.
What are like terms?Like terms are terms that share these two features:
Same letters. (algebraic variables).Same exponents.If two terms are like terms, then they can be either added or subtracted.
Hence the first option is the only option in which all the three terms are like terms, as:
The letter of each expression is of y.The exponent of each term with the letter y is of 1.The remaining options have terms with different letters(second and third), or different exponents (fourth), hence they are not like terms.
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Jeremiah has slept one hour this week. He will sleep 2 hrs per night. How many days will he have slept in 49 hrs?
Answer:
24.5 days i believe
sauv drove 296 miles in 8 hours.If he continued at the same rate,how far would he travel in 10 hours.
If he continued at the same rate, he would travel 370 miles in 10 hours.
What is proportion?A proportion is described as an equation having two ratios that are set equal to each other.
It is the mathematical comparison of numbers or variables.
In mathematics, the different types of fractions are;
Direct ProportionInverse ProportionCompound ProportionContinued ProportionFrom the information given, we have that;
sauv drove 296 miles in 8 hours
Then,
If 296 miles = 8 hours
x miles = 10 hours
cross multiply
8x = 2960
Make 'x' the subject of formula
x = 370 miles
Hence, the value is 370 miles
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On average a dog lives 10 years. Your company has created a new dog food full of nutrients and vitamins to extend a dog's life You studied so dogs and tracked how long they lived. At a 5 significance level determine if your new dog food extends the life doglivese 10,15,17,13,14,9,8.7.5,8,15,1724,10,12,15,10,98.7.5,15,14,15,10,5,6,98,18,10,8 7,9,10,15,12,13,149,8.7.5.6,15,17,14,10,12,15) State the Alternative Hypothesis for this test. O Hau 10 years Ha: > 10 years O Haru 10 years O Haru >
The alternative hypothesis for this test would be that the new dog food extends the average lifespan of dogs beyond 10 years.
Mathematically, the alternative hypothesis can be stated as:
Ha: μ > 10, where μ is the population mean of the lifespan of dogs on the new dog food.
In this scenario, the null hypothesis is that the average lifespan of dogs on the new dog food is equal to 10 years, which is the commonly accepted average lifespan of dogs. However, the purpose of the study is to determine if the new dog food can extend the lifespan of dogs beyond this average.
Thus, the alternative hypothesis is that the average lifespan of dogs on the new dog food is greater than 10 years. This is represented mathematically as Ha: μ > 10, where μ is the population mean of the lifespan of dogs on the new dog food.
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How can m2n2-25 be factored?
Answer:
(mn+5)(mn-5)
Step-by-step explanation:
This is a difference of squares as m^2n^2 = (mn)^2. So it cna be turned into the form a^2-b^2 = (a+b)(a-b) or in our case (mn+5)(mn-5).
Derek tried to solve an equation step by step. 8d=72 8d/8 = 72/8 d=8 Find Derek's mistake
The mistake Derek did was d = 8.
The correct step is d = 9.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 55 is an equation.
We have,
8d = 72
Step 1:
Divide both sides with 8.
8d/8 = 72/8
[ 8 x 9 = 72 ]
So,
d = (8 x 9)/ 8
d = 9
Thus,
Derek's mistake is d = 8.
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A family spends of its monthly budget on groceries and eating out. If the family's monthly budget is $6012, how much is spent on groceries and eating out?
Estimate the amount the family spent on groceries and eating out per month: $
The family spent $ per month on groceries and eating out.
How much will the family spend on groceries and eating out in 5 months? S
The family spent $2004 per month on groceries and eating out.
The amount spent in five months is given as follows: $10,020.
How to obtain the amounts?The amounts are obtained applying the proportions in the context of this problem.
The monthly budget is given as follows:
$6012.
1/3 of that is spent in groceries and eating out, hence the amount is of:
1/3 x 6012 = $2004.
Hence in five months the amount spent is going to be of:
5 x 2004 = $10,020.
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Josh invested in shares of four different companies at the beginning of the year. At the end of the year the share values had increased or decreased as follows:
SunBlush Technologies Stiller Co. PhotoFinish Co. Cola Company
7.62%
-4.17%
-0.83%
3.70%
For full marks your answers should be given as percents accurate to at least two decimal places.
a) What is the total rate of return if Josh invests the same amount in each company?
Return = 0.00 %
b) What is the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies?
Return 0.00 %
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Answer: a) To calculate the total rate of return if Josh invests the same amount in each company, we need to add up the individual rates of return from each company and divide by the number of companies.
The total rate of return for the four companies is: (7.62% + -4.17% + -0.83% + 3.70%) / 4 = 2.52%
So the total rate of return if Josh invests the same amount in each company is 2.52%.
b) To calculate the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies, we need to multiply the rate of return for Stiller Co. by 3 and add it to the rates of return for the other companies.
The total rate of return for the four companies is: (-4.17% x 3) + 7.62% + -0.83% + 3.70% = -7.32%
So the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies is -7.32%.
It's important to note that the answer may change if the investment amount on each company is different.
Step-by-step explanation:
Let T be an linear transformation from Rr to Rs. Let A be the matrix associated to T.
Fill in the correct answer for each of the following situations.
1. Every row in the row-echelon form of A has a pivot.
2. Two rows in the row-echelon form of A do not have pivots.
3. The row-echelon form of A has a pivot in every column.
4. The row-echelon form of A has a row of zeros.
A. T is onto
B. T is not onto
C. There is not enough information to tell.
Note: The row echelon form of a matrix is a way of putting it in a specific form, in which all the leading entry of a non-zero row is to the right of the leading entry of the row above it, and all the entries below a leading entry are zero. A pivot is the leading entry of a non-zero row. In a matrix in row echelon form, the number of pivots is equal to the rank of the matrix, which is the number of linearly independent rows or columns. A matrix with a pivot in every column is said to be in reduced row echelon form, and it is unique for a given matrix.
Linear Transformation Matrix PropertiesA linear transformation is a function that maps a vector from one vector space to another vector space. The matrix associated with this transformation is a way of representing the linear transformation using a matrix. The row echelon form of the matrix is a specific way of arranging the matrix, where all the leading entry of a non-zero row is to the right of the leading entry of the row above it, and all the entries below a leading entry are zero. The properties of the transformation can be determined by analyzing the row echelon form of the matrix.
For example, if the row echelon form of the matrix has a pivot in every column, it means that the transformation is one-to-one (meaning that the function assigns a unique output for each input). On the other hand, if the row echelon form of the matrix has a pivot in every row, it means that the transformation is onto(meaning that the function's range is equal to the output vector space). If there are zero rows in the row echelon form of the matrix, it means that the transformation is not one-to-one.
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1. Henry and his sister Miranda are walking in the Jimmy Fund Walk-a-Thon to
money for cancer research. They are each collecting sponsors, who
pledge to donate a certain amount of money per mile they walk. Henry
has collected enough sponsors so that he'll earn $5.50 per mile for her
walks. If they both plan to walk all 20 miles of the Walk-A-Thon, and they
hope to raise a total $200, what does Miranda's per-mile sponsorship rate
need to be?
8.8x109
————-
2.2 x10-3
The division of the value 8.8x10^9 and 2.2 x10^-3 in standard form is 4*10^12.
How can the division be made?The concept that will be used here is division. One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.
To simplify the values 8.8x10^9/2.2 x10^-3, the we can write as
8.8/2.2 *10^9*10^3
=4*10^12
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complete question:
simplify 8.8x109/2.2 x10-3
example of a function $f$ with domain $\mathbb{r}$ that is continuous nowhere, but where $|f|$ is continuous on all of $\mathbb{r}$.
An example of such a function can be f(x) { 1 x∈Q
-1 x∈ R\Q}
A function in mathematics is like a machine that takes input and gives output. There is always a limit for output also called the range or image of the function.
A function has two values output and input. The limit within which input is defined is called the domain or pre-image of the function.
A function is represented as f(x) i.e., f of x or function of x. The input and output have a relation defined for them
A function must follow two rules they are:
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A furniture store in Livingston purchased an arcade
machine at a cost of $993 and marked it up 200%. Later
on, Nicholas bought the arcade machine. If the sales tax
in Livingston is 14%, how much did he pay in all?
They marked it up to 2979 since 993*3(aka 200%). You then multiply 2979 by 1.14 to get the total of $3396.06
Answer:
$3396.06
Step-by-step explanation:
Markup is what a store adds to the price they paid in order to come up with a selling price.
store selling price = cost to store + markup
Store purchase price: $993
Store markup of 200%: 200% of $993 = 2 × $993 = $1986
Store selling price: $993 + $1986 = $2979
14% tax: 14% of $2979 = 0.14 × $2979 = $417.06
Total selling price including markup & sales tax: $2979 + $417.06 = $3396.06
Answer: $3396.06
The following pie chart shows how a worker spent his December 1990 salary. Rent charges were GH80.00. How much did the workersave? ary www.a 5) What fraction of on food? How much did he spend on food? a) Find b) Find durin c) Wha 10.) The
According to the pie chart given -
a) The worker saved GH¢ 20.00.
b) 2/5 fraction of worker's salary was spent on food.
c) The worker spent GH¢ 120.00 on food.
What is a pie chart?
One sort of graph that illustrates the information in the circular graph is a pie chart. It is a sort of graphical representation of data where the slices of pie depict the relative sizes of the data. A list of numerical and categorical variables is necessary for a pie chart. Pie in this context refers to the entire thing, and slices to its component portions.
The rent charges is = GH¢ 80.00
The savings can be obtained by ratio method -
Savings is depicted by 24° and rent by 96° in the pie chart.
So, the ratio will be 24/96.
Then the savings value will be -
(24/96) × 80
(1/4) × 80
20
Therefore, the savings value is GH¢ 20.00.
The total angle of pie chart is 360°.
Savings is depicted by 24°, rent by 96°, entertainment by 48° and clothing by 48° in the pie chart.
The angle for food will be -
360° - (24° + 96° + 48° + 48°)
360° - 216°
144°
Now the fraction that is for food -
144/360
2/5
Therefore, food covers 2/5 part of pie chart.
The amount spent on food can be obtained by formula of angle sector -
(144/96) × 80
1.5 × 80
120
Therefore, money for food was GH¢ 120.00.
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How many pieces 1 4/5 in. long can be cut from 22 metal rods each 21 in. long? Disregard the waste.
The required number of pieces cut from 22 metal rods each 21 in are 242 pieces.
What is mixed fraction?A mixed fraction is one that is represented by both its quotient and remainder. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
According to question:We have,
1(4/5) = 9/5 ,
So,
21/9/5
105/9
11(6/9)
Now,the waste is 6/9
Number of pieces are 11(22)
= 242 pieces
Thus, required number of pieces are 242.
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Simplify the expression (12x-13)-2(3x+5)
Answer: The simplified expression is 6x - 23
Step-by-step explanation: To simplify the expression (12x-13)-2(3x+5) we will follow the order of operations:
First, we simplify the inner parentheses: 2(3x+5) = 6x + 10
Next, we substitute this simplified version back into the original expression: (12x-13)-(6x+10)
Now we can simplify the expression by combining like terms: 12x-13-6x-10 = 6x - 23
So the simplified expression is 6x - 23
Answer:6x-23 this your answer to simplify the expression I hope this helps have a good day
Step-by-step explanation:
(12x-13)-2(3x+5)
Remove unnecessary parentheses
12x-13-2(3x+5)
then do this
distribute -2 through the parentheses
12x-13-6x-10
Collect like terms which something like this
6x-13-10
then last thing you do is
Calculate the difference which is like this
6x=23
describe using words, and no equations, what the function f does to vectors. you may find it helpful to probe the behavior of f(v) for concrete fixed vectors c and draw some pictures. your answers to parts (c) and (d) should also prove useful.
A transformation is applied to the input vector v by the function f. This transformation might include extending, rotating, or reflecting the vector in a certain way, depending on the precise shape of the function.
We may enter certain fixed vectors into the function, c, and watch as f transforms them to better understand its behavior (c). It may also be helpful to see the modified vectors as images or diagrams to have a better understanding of how the function behaves.
The term "vector" is used informally to describe constituents of particular vector spaces or some values that cannot be described by a single integer.
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___ planning is the process of identifying long-term organizational goals, strategies, and resources.
a. Opportunity b. Preliminaryc. Strategicd. Vertical
Strategic planning is an essential process for any organization that wants to succeed and achieve long-term success. It involves identifying long-term organizational goals, strategies, and resources that will help the organization reach its objectives.
Option C. Strategic planning is the process of identifying long-term organizational goals, strategies, and resources.Strategic Planning: Achieving Long-Term Organizational GoalsThis process requires a comprehensive assessment of the organization's current and future needs, including its strengths and weaknesses, opportunities and threats, and the external environment. Once identified, the organization must develop and implement a plan to achieve its goals and objectives. This involves setting objectives, developing and implementing strategies and tactics, and allocating resources in a way that will maximize the organization's chances of success.
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Can you guys pls helpp
The numeric value of the expression for this problem is given as follows:
[tex]\sqrt{2} + 1[/tex]
How to simplify the expression?The expression for this problem is defined as follows:
[tex]\frac{4 - 3\sqrt{2}}{(\sqrt[4]{2} - \sqrt[4]{8})^2}[/tex]
Applying the square of the subtraction in the denominator, we have that:
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = \sqrt[4]{4} - 2\sqrt[4]{2}\sqrt[4]{8} + \sqrt[4]{64}[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = 4^{\frac{1}{4}} - 2\sqrt[4]{16} + \sqrt[4]{4^3}[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = (2^2)^{\frac{1}{4}} - 2 \times 2 + 3[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = \sqrt{2} - 1[/tex]
Hence the simplified expression is given as follows:
[tex]\frac{4 - 3\sqrt{2}}{\sqrt{2} - 1}[/tex]
Rationalizing the denominator, we have that:
[tex]\frac{4 - 3\sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}[/tex]
Applying the subtraction of perfect square, the denominator simplifies to one, hence the value of the expression is given by the numerator as follows:
[tex](4 - 3\sqrt{2})(\sqrt{2} + 1) = 4\sqrt{2} + 4 - 3 \times 2 - 3\sqrt{2}[/tex]
[tex][tex](4 - 3\sqrt{2})(\sqrt{2} + 1) = \sqrt{2} + 1[/tex]
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Reciprocity and Reciprocal Theorems: Prove these two theorems (which are written in Lecture Notes 2). Hint: write the condition of F(x, y, z) 0 into explicit forms x-x(y,x) or z-z(x,y), you can then calculate their differentials, manipulate the terms, to get those theorems.
The partials ∂y/∂x = 1 and ∂z/∂x = -1, so we get the Reciprocal Theorem.
Reciprocity Theorem: Let F(x, y, z) be a continuous function of x, y, and z, then we have
∂F/∂x = (∂F/∂y)x - (∂F/∂z)y
This is proven by writing the condition of F(x, y, z) = 0 into explicit forms x-x(y,z) or z-z(x,y). Then from the chain rule, we have
∂F/∂x = (∂F/∂y)(∂y/∂x) + (∂F/∂z)(∂z/∂x)
And since x = x(y,z) and z = z(x,y), the partials ∂y/∂x = -1 and ∂z/∂x = 1, so we get the Reciprocity Theorem.
Reciprocal Theorem: Let F(x, y, z) be a continuous function of x, y, and z, then we have
(∂F/∂y)x + (∂F/∂z)y = F(x, y, z)
This is proven by writing the condition of F(x, y, z) = 0 into explicit forms x-x(y,x) or z-z(x,y). Then from the chain rule, we have
∂F/∂x = (∂F/∂y)(∂y/∂x) + (∂F/∂z)(∂z/∂x)
And since x = x(y,x) and z = z(x,y), the partials ∂y/∂x = 1 and ∂z/∂x = -1, so we get the Reciprocal Theorem.
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Hi, can someone help me find the circumference of these circles, and explain if you can.
Problem 22
The smaller inner circle has a radius of r = 5. That will be plugged into the circumference formula below.
C = 2pi*r
C = 2pi*5
C = 10pi
This is the exact distance around the circle in terms of pi. Think of it like the amount of fencing you need to enclose the circle.
If you want an approximate perimeter, then use something like pi = 3.14
So 10pi = 10*3.14 = 31.4 cm is the approximate perimeter aka circumference of the smaller circle.
-------------
The larger circle is the same idea. The radius is r = 5+5 = 10 cm
C = 2pi*r
C = 2pi*10
C = 20pi .... exact circumference
C = 20*3.14
C = 62.8 ... approximate circumference
Use more decimal digits of pi to get a more accurate value.
===================================================
Problem 23
The smaller circle has a diameter of 9 ft, which means the radius is r = 9/2 = 4.5 ft
C = 2pi*r
C = 2pi*4.5
C = 9pi .... exact circumference
C = 9*3.14
C = 28.26 .... approximate circumference
The units of the circumference are in feet
-------------
The larger circle has radius r = 4.5+2.5 = 7 ft
C = 2pi*r
C = 2pi*7
C = 14pi .... exact circumference
C = 14*3.14
C = 43.96 .... approximate circumference
===================================================
Problem 24
The larger circle has radius 22. This radius is the diameter of the smaller circle.
So the smaller circle has radius 22/2 = 11
C = 2pi*r
C = 2pi*11
C = 11pi .... exact circumference
C = 11*3.14
C = 34.54 .... approximate circumference
The circumference units are "meters".
-------------
Now onto the larger circle
C = 2pi*r
C = 2pi*22
C = 44pi .... exact circumference
C = 44*3.14
C = 138.16 .... approximate circumference
What is 1+1 This question has to be the hardest question I ever done in Math. Please help me.
Answer:
2
Step-by-step explanation:
the vector is a linear combination of the vectors and if and only if the matrix equation has a solution , where and .
The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.
We first thought of a matrix as a rectangular array of numbers. When the number of rows is m and columns is n, we say that the dimensions of the matrix are m×n.
A vector is most simply thought of as a matrix with a single column. There are two operations we can perform with vectors: scalar multiplication and vector addition. Both of these operations have geometric meaning.
Given a set of vectors and a set of scalars we call weights, we can create a linear combination using scalar multiplication and vector addition.
The product of two matrices can be seen as the result of taking linear combinations of their rows and columns. This way of interpreting matrix multiplication often helps to understand important results in matrix algebra.
The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.
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is there a theoretical limit to the order of the spectrum you would be able to observe with your diffraction grating? justify you answer mathematically
In general, the maximum order of the spectrum that can be observed with a diffraction grating is limited by the grating equation.
This equation states that mλ = d(sinθi - sinθr), where m is the order of the diffraction, λ is the wavelength of light, d is the spacing between the grating lines, θi is the angle of incidence, and θr is the angle of diffraction. Since d is fixed and θi is typically kept constant, the maximum order of the spectrum that can be observed is limited by the angle of diffraction (θr). This angle can be calculated using the equation θr = sin-1[(mλ/d)+sinθi]. Thus, the maximum order of the spectrum is limited by the value of θr, which is determined by the wavelength of light and the spacing between the grating lines.
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You wish to test the claim that μ>20 at a level of significance of
α=0.05 and are given sample statistics n=50 and x=20.3.
Assume the population standard deviation is 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal places.
A. 2.31
B. 3.11
C. 0.98
D. 1.77
The value of the standardized test statistic is D. 1.77.
A standardized test statistic is a measure of the difference between a sample statistic and the population parameter it estimates, expressed in units of the standard deviation.
The value of the standardized test statistic can be calculated using the formula:
(x - μ) / (s / √n)
where x is the sample mean, μ is the population mean, s is the population standard deviation, and n is the sample size.
Given the information provided in the question, the standardized test statistic is:
(20.3 - 20) / (1.2 / √50) = 1.7678
Rounding to two decimal places, the answer is D. 1.77.
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shown below is a clock face with no hands. what is the degree measure of the smaller angle formed by the hands of a clock at $10$ o'clock?
The degree measure of the smaller angle formed by the hands of a clock at 10 O'clock is 60°.
The degree measure of a full circle is 360 degrees. The clock face is divided into 12 equal parts, or 30-degree increments, for the hours. At 10 o'clock, the hour hand would point to the 10 on the clock face, and the minute hand would point to the 12.
This makes them 1/6th of a circle apart, and (1/6) * 360° = 60°.
The angle between the two hands would be formed by the distance between the 10 and the 12, which is 60 degrees.
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