Using the given vectors v and w, we found v•w = 66 and v•v = 73.
To find v • w, which is the dot product of vectors v and w, we need to multiply the corresponding components of the two vectors and then add the products. In other words,
v • w = (-8i)(-9i) + (-3j)(-7j)
= 72 + 21
= 93
So, v • w = 93.
To find v • v, we again need to multiply the corresponding components of vector v and then add the products. In other words,
v • v = (-8i)(-8i) + (-3j)(-3j)
= 64 + 9
= 73
So, v • v = 73.
Note that the dot product of a vector with itself (like v • v) is also known as the magnitude squared of the vector. In this case, ||v||² = v • v = 73.
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ASAP PLEASE
The histogram shows data collected about the number of passengers using city bus transportation at a specific time of day.
A histogram titled City Bus Transportation. The x-axis is labeled Number Of Passengers and has intervals of 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 9. There is a shaded bar for 1 to 10 that stops at 2, for 11 to 20 that stops at 4, for 21 to 30 that stops at 5, for 31 to 40 that stops at 6, and for 42 to 50 that stops at 3.
Which of the following data sets best represents what is displayed in the histogram?
1 (4, 5, 7, 8, 10, 12, 13, 15, 18, 21, 23, 28, 32, 34, 36, 40, 41, 41, 42, 42)
2 (4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)
3 (4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42)
4 (4, 6, 11, 12, 16, 18, 21, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 41, 41, 42)
Answer:
Step-by-step explanation:
After organizing the data, the researcher must present them so they can be understood by those who will benefit from reading the study. The most useful method of presenting the data is by constructing statistical charts and graphs. There are many different types of charts and graphs, and each one has a specific purpose.
This chapter explains how to organize data by constructing frequency distributions
and how to present the data by constructing charts and graphs. The charts and graphs
illustrated here are histograms, frequency polygons, ogives, pie graphs, Pareto charts,
and time series graphs. A graph that combines the characteristics of a frequency distribution and a histogram, called a stem and leaf plot, is also explained.
Section 2–2 Organizing Data 35
2–3
Objective
Organize data using
frequency
distributions.
1
2–2 Organizing Data
Suppose a researcher wished to do a study on the number of miles that the
employees of a large department store traveled to work each day. The researcher
first would have to collect the data by asking each employee the approximate distance the
store is from his or her home. When data are collected in original form, they are called
raw data. In this case, the data are
1 2 6 7 12 13 2 6 9 5
18 7 3 15 15 4 17 1 14 5
4 16 4 5 8 6 5 18 5 2
9 11 12 1 9 2 10 11 4 10
9 18 8 8 4 14 7 3 2 6
Since little information can be obtained from looking at raw data, the research
Answer:
c
Step-by-step explanation:
its ez
The entire graph of the function g is shown in the figure below.
Write the domain and range of g as intervals or unions of intervals.
domain=
range =
For the given function 'g':
domain = (-4, -2) ∪ (1, 3]
range = (-5, 4]
If the function is defined as f(x) = y, then the values of x for which the value of function exists, the set of that values is said to be the domain of the function f.
If the function is defined as f(x) = y, then the set of all possible values of the function that is the set of all possible values of y is said to be the range of the function f.
Here given the graph of 'g'.
From the graph we can see that for -4 < x < -2 and 1 < x [tex]\le[/tex] 3 the function has graph.
So the domain = (-4, -2) ∪ (1, 3]
And it is clear that the value of y lies between -5 < y [tex]\le[/tex] 4.
So the range = (-5, 4].
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Solve the equation.
3/4x+3-2x = -1/4+1/2x+5
If necessary:
Combine Terms
Apply Properties:
Add Subtract
Multiply Divide
The solution of the equation is x = -1.
Given is an equation we need to solve it,
3x/4 + 3 - 2x = -1/4 + x/2 +5
Multiplying the equation by 4 both the sides,
3x + 12 - 8x = -1 + 2x + 20
Combining the like terms,
3x - 8x - 2x = 20 - 1 - 12
3x - 10x = 7
-7x = 7
x = -1
Hence the solution of the equation is x = -1.
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Find the slope of the tangent to f(x) = x^2 at the point (-2,4).
Answer:
f'(x) = 2x, so f'(-2) = 2(-2) = -4.
3^-1/2 x^1/2
express with radical signs instead of fractional exponents. rationalize the denominator.
please help
Answer:
[tex]\sqrt{x/3}[/tex]----------------------
Use the following identities:
[tex]a^{-b}=1/a^b[/tex][tex]a^{1/2}=\sqrt{a}[/tex][tex]a^bc^b=(ac)^b[/tex]Apply the identities to the given expression:
[tex]3^{-1/2}x^{1/2}=(3^{-1}x)^{1/2}=(x/3)^{1/2}=\sqrt{x/3}[/tex]3⋅f(−4)−3⋅g(−2) = ?
Ayuda por favor
The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40
Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;
f( - 4 ) = 15
g( - 2 ) = 5
Substitute the given parameters into the expression to have:
3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5
= 45 - 5
= 40
Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40
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which of the following is equivalent to x-5/3?
The following expression is equivalent to [tex]x^{-5/3}[/tex] as option B that is 1/∛x⁵.
What is fraction?A fraction is a numerical representation of a part or a portion of a whole. It is expressed as one integer (numerator) divided by another integer (denominator), separated by a horizontal line.
Here,
We can rewrite [tex]x^{-5/3}[/tex]as [tex](1/ x^{^(5/3)})[/tex].
The negative exponent in the numerator tells us that we need to move the term to the denominator of a fraction and change the sign of the exponent to make it positive. Similarly, the fractional exponent in the denominator indicates that we need to take the reciprocal of the term and change the sign of the exponent to make it positive.
Therefore, we can rewrite [tex]x^{-5/3}[/tex] as:
[tex](1/ x^{^(5/3)})[/tex]
or
[tex]x^{-5/3}[/tex] = [tex](1/ x^{^(5/3)})[/tex]
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Complete question:
Which of the following is equivalent to [tex]x^{-5/3}[/tex]?
Find the distance from G to S.
Answer:
i think its b sorry if it's wrong
Step-by-step explanation:
prove that:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below
How to prove the given identityGiven the following equation
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
We start by simplifying the left-hand side of the equation:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]
Next, we have the following steps to simplify the expression
= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]
= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]
= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]
= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]
= -4(2p² + 1)/(p²-4) (p² - 1)
Hence, the given identity is proven.
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what's equivalent to x^2-4x-l2
Answer:
Assuming you meant to write "x^2 - 4x - 12", there are a few equivalent forms that you could use to represent this expression. One common form is:
(x - 6)(x + 2)
Step-by-step explanation:
This is the factored form of the expression, which shows that it can be written as a product of two linear factors. To see why this is true, you can use the distributive property to expand the product:
(x - 6)(x + 2) = x(x + 2) - 6(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12
i need answer please
The surface area of the rectangular prism is 210 in²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
The surface area of a rectangular prism is the sum of each area for the surface.
Hence:
Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²
The surface area of the prism is 210 in²
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Which of the following is the graph of the quadratic function y = x² - 4x+4?
A. Graph C
B. Graph B
C. Graph D
D. Graph A
Answer:
The correct answer is C, Graph D.
x^2 - 4x + 4 = (x - 2)^2.
Given that f (x) = StartFraction 120 Over x squared EndFraction , What is the domain of the function f ? a. only positive integers c. only negative integers b. All non zero real numbers. d. All real numbers including zero
For the function "f (x) = 120/x²", the domain of the function "f" is (b) All non zero real numbers.
The "Domain" of a function is the set of all possible "input-values" for which the function is defined. In this case, the function is defined as:
f (x) = 120/x²
The only restriction on the input values is that the denominator cannot be equal to zero, because division by zero is undefined.
So, the domain of the function f is all non-zero real numbers.
Therefore, the correct option is (b): All non-zero real numbers.
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The given question is incomplete, the complete question is
Given that f (x) = 120/x², What is the domain of the function f ?
(a) only positive integers,
(b) All non zero real numbers,
(c) only negative integers,
(d) All real numbers including zero.
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet. In how many ways can this be done?
There are 1100 many ways can be done that is when catering service offers 5 appetizers, 11 main courses, and 4 desserts.
Given that,
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet.
We have to find how many ways can this be done.
We know that,
Number of appetizers offered = 5
Number of appetizers customer is to select = 4
Number of main courses offered = 11
Number of main courses customer is to select = 9
Number of desserts offered = 4
Number of desserts the customer is to select = 3
So,
To determine the number of ways this can be selected,
By using the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]^nC_r = ^5C_4\times ^{11}C_9\times^4C_3[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!(5-4)!} \times \frac{11!}{9!(11-9)!}\times \frac{4!}{3!(4-3)!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!1!} \times \frac{11!}{9!2!}\times \frac{4!}{3!1!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!} \times \frac{11!}{9!(2)}\times \frac{4!}{3!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 5 × 11 × 5 × 4
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 1100
Therefore, There are 1100 many ways this can be done.
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for each pair of lines determine whether they are parallel, perpendicular, or neither
Answer:
All lines are parallel.
Step-by-step explanation:
Get each equation in Slope-Intercept form:
1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]
2. No change
3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]
Notice:
a. All slopes are -4/3
b. All y-intercepts are different
can some one help me
Caleb is selecting cards from a set of 12 cards numbered 1-2-4-4-5-5-5-5-6-9-10-13.
What is the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection?
The probability of Caleb selecting a 5 on the first selection and then selecting a 5 on the second selection after returning the card to the deck and shuffling is 1/9.
There are a total of 12 cards, out of which 4 are 5s. Since Caleb returns the card to the deck and shuffles it, the selection of the first card does not affect the probability of selecting a 5 on the second selection.
Therefore, the probability of selecting a 5 on the first selection is 4/12 = 1/3, and the probability of selecting a 5 on the second selection is also 4/12 = 1/3.
Since the events are independent, we can multiply the probabilities to find the probability of both events occurring:
P(selecting a 5 on first selection and selecting a 5 on second selection) = P(selecting a 5 on first selection) x P(selecting a 5 on second selection)
= (1/3) x (1/3)
= 1/9
Therefore, the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/9.
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A sample of a radioactive substance has an initial mass of 45.1 mg. This substance follows a continuous exponential decay model and has a half-life of 19
minutes.
(a)let t be the time (in minutes) since the start of the experiment, and
let y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ()e^()t
(b) How much will be present in 9 minutes?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.
How to Write a formula relating y to t.(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.
To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.
Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:
19 = 0.693 / k
k = 0.693 / 19
So the formula relating y to t is:
y = 45.1 * e^(-0.693/19 * t)
(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):
y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg
So, there will be approximately 30.1 mg of the substance present after 9 minutes.
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Raman is watching the movie 4 times and he fislokw s the value wirh
Answer:learn how to spell :)
Step-by-step explanation:
For any positive values x and y, f(xy) = f(x) + f(y). f(1/2021) = 1.
Find f(2021).
I will give BRAINLIEST to correct answer.
a2=25 i cant find the ancer to thiss
The value of the variable a in the equation is 5 from the calculation here.
How to determine the value?We need to square of a number is described as a number that when multiplied by itself give the original number.
Also, index forms are described as those mathematical forms that are used to represent numbers that are too large or small.
From the information given, we have the equation;[tex]a^2[/tex]=25
find the square root of value of 25,
We have;25 = [tex]5^2[/tex]
Substitute the value, we get;[tex]a^2[/tex] = [tex]5^2[/tex]
Take out the similar factor, this is their exponents.
We then have;
a = 5
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Complete question;
Find the value of a in the equation;a² = 25
The sales of a certain product after an initial release can be found by the equation s=12 sqrt (4t) + 10 , where s represents the total sales (in thousands) and t represents the time in weeks after release. Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release.
about $586,000
about $586
about $93
about $93,000
The sales 12 weeks after release is $586,000 . Option A is the correct answer.
To create a table of values, we can plug in different values of t and find the corresponding values of s:
t s
0 10
1 19.882
2 26.248
3 31.177
4 35.064
5 38.185
6 40.731
7 42.837
8 44.6
9 46.095
10 47.384
11 48.508
12 49.498
To graph the function, we can plot the values from the table on a coordinate plane. The horizontal axis represents time in weeks, and the vertical axis represents sales in thousands of units. The resulting graph is a curve that starts at (0,10) and increases as t increases.
To estimate the sales 12 weeks after release, we can look at the graph and see that the corresponding value of s is around 49.5 thousand units. Therefore, the answer is about $586,000 (49.5 x 1000 x 12). Option A is the correct answer.
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Drag-and-Drop Technology-Enhanced
An expression is shown.
14a +7+ 5b+ 2a + 10b
Move words into the columns to describe the parts of the expression. Not all words will be used, and each column should
have at least one word to describe it.
14a
sum
term
factor
7
5
product
quotient
coefficient
2a + 10b
The value of expression 14a +7+ 5b+ 2a + 10b will be 16a + 15b + 7
Since Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given the expression as;
14a +7+ 5b+ 2a + 10b
Combine like terms;
14a + 2a + 10b +7+ 5b
16a + 15b + 7
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Which linear equation is represented in the graph?
A. y = x – 1
B.y = 2x – 1
C. y = x + 1
D. y = 3x – 1
A worker completes a job in a certain number of hours. The standard time allowed for the job is 10 hours, and the hourly rate of wages is Re. 1. The worker earns at the 50% rate a bonus of Rs. 2 under Halsey Plan. Ascertain his total wages under the Rowan Premium Plan.
I need help to get the residual plot from this data 13.8 1.42 16.7 3.21 0.7 1.11 18 4 16.7 3.21 20 4 18 3.8 19.5 3.78 21.9 3.69 0.7 1.11
Answer:
To create a residual plot, you need to first fit a model to the data. Without any information about the problem you are trying to solve or the model you are fitting, I will assume that you are trying to fit a linear regression model to these data points.
First, you would need to find the equation of the line that best fits the data using a regression analysis software or by hand. Let's assume that the equation of the line is:
y = 0.2x + 2.5
where y is the response variable (dependent variable) and x is the predictor variable (independent variable).
Next, you would calculate the predicted values of y (i.e., the values that the model predicts) for each value of x in your dataset, using the equation of the line. For example, for the first data point (13.8, 1.42), the predicted value of y would be:
y_predicted = 0.2 * 13.8 + 2.5 = 5.06
The residual for this data point would be the difference between the actual value of y and the predicted value of y:
residual = 1.42 - 5.06 = -3.64
You would repeat this process for each data point in your dataset, to get a list of residuals.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x=38.6
Step-by-step explanation:
x=b/cos(alpha)
x=30/cos(39⁰)
x=38.602
How many different ways are there to arrange the letters in the word MISSISSIPPI?
Answer: 34,650 permutations
The vertices of AABC are A (-3, -6), B (-3,5), and C (5,5).
What is the area of AABC?
Answer:
44 units²-----------------------------
AB is vertical with same x-coordinates, and BC is horizontal with same y-coordinates.
Hence this is a right triangle.
Its area is:
A = 1/2 × AB × BCA = 1/2(5 - (-6))(5 - (-3)) = 1/2(11)(8) = 44 units²College Level Trigonometry Question!
The angle measures for this problem are given as follows:
θ = 150º and θ = 330º.
How to obtain the angle measure?The trigonometric expression for this problem is given as follows:
[tex]\theta = \arctan{\left(-\frac{\sqrt{3}}{3}\right)}[/tex]
The solution to the arctangent function is the angle which has the given tangent value.
The angle on the first quadrant with a tangent value of sqrt(3)/3 is given as follows:
θ = 30º.
The quadrants in which the tangent is negative are given as follows:
2nd and 4th.
Hence the equivalent angles are given as follows:
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A business manufactures and sell laptops.Each laptop is sold for R14000.the fixed monthly cost is R32000 and it cost R9000 to manufacture each laptop.let L be number of laptops manufactured and sold per monthly
The total cost equation can be written as:
Total Cost = 32000 + 9000L
What is total cost?
Total cost refers to the complete amount of money or resources that are required to produce or obtain a particular good or service. It includes all of the expenses associated with production, such as labor costs, materials costs, overhead costs, and any other costs necessary to manufacture or acquire the product.
The total cost equation can be expressed as:
Total Cost = Fixed Cost + Variable Cost
where Fixed Cost is the cost that does not vary with the number of laptops manufactured and sold, and Variable Cost is the cost that depends on the number of laptops manufactured and sold.
In this case, the fixed monthly cost is $32,000 and it does not depend on the number of laptops manufactured and sold. The variable cost is the cost of manufacturing each laptop, which is $9,000 per laptop.
If L is the number of laptops manufactured and sold per month, then the variable cost can be expressed as 9000L. Therefore, the total cost equation can be written as:
Total Cost = 32000 + 9000L
This equation represents the total cost of manufacturing and selling L laptops per month. The fixed cost of $32,000 is added to the variable cost of $9,000 per laptop multiplied by the number of laptops sold, L, to obtain the total cost.
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Complete question: A business manufactures and sell laptops. Each laptop is sold for 14000.the fixed monthly cost is 32000 and it cost 9000 to manufacture each laptop. let L be number of laptops manufactured and sold per monthly. What is the total cost equation?
