Answer:
C. 36 in.
Step-by-step explanation:
The wall is 66 inches high by 72 inches wide.
The tiles are
a) 9 inch square = 3 by 3
b) 16 inch square = 4 by 4
c) 36 inch square = 6 by 6
d) 64 inch square = 8 by 8
Factors of 66 = 2 x 3 x 11
Factors of 72 = 2 x 2 x 2 x 3 x 3
Now, we can see that in both 66 and 72 , we have 2 x 3 common that is 6.
And square of 6 is 36.
So, the answer is option C.
Find the point, P, at which the line intersects the plane. x equals negative 3 minus 8 tx=−3−8t, y equals negative 6 plus 5 ty=−6+5t, z equals negative 6 minus 6 tz=−6−6t; negative 7 x plus 2 y plus 8 z equals negative 4−7x+2y+8z=−4 The point, P, at which the line intersects the plane is left parenthesis nothing comma nothing comma nothing right parenthesis,,. (Simplify your answer. Type an ordered triple.)
Answer:
P = (-18 5/9, 3 13/18, -17 2/3)
Step-by-step explanation:
The given point must satisfy both the equation of the line and that of the plane. We can substitute for x, y, and z in the plane's equation to get ...
-7(-3-8t) +2(-6+5t) +8(-6-6t) = -4
21 +56t -12 +10t -48 -48t = -4
18t -39 = -4 . . . collect terms
18t = 35 . . . . . . add 39
t = 35/18 . . . . . .divide by the coefficient of t
The point is ...
(x, y, z) = (-3-8(35/18), -6+5(35/18), -6-6(35/18))
P = (x, y, z) = (-18 5/9, 3 13/18, -17 2/3)
x + y = 40
x + 10 = 60
What is the value of x? Of y?
Answer:
x = 50
y = -10
Step-by-step explanation:
x + y = 40
x + 10 = 60
60 - 10 =x
60 - 10 = 50
x = 50
50 + y = 40
40 - 50 = y
40 - 50 = -10
y = -10
Hey!
------------------------------------------------
Solve for x:
x + y = 40
x + y - y = 40 - y
x = 40 - y
50 - 10 = 40
50 + (-10) = 40
x = 50
y = -10
------------------------------------------------
Solve for x:
x + 10 = 60
x + 10 - 10 = 60 - 10
x = 50
------------------------------------------------
Hope This Helped! Good Luck!
The following data are direct solar intensity measurements (watts/m2 ) on different days at a location in southern Spain: 562, 869, 708, 775, 775, 704, 809, 856, 655, 806, 878, 909, 918, 558, 768, 870, 918, 940, 946, 661, 820, 898, 935, 952, 957, 693, 835, 905, 939, 955, 960, 498, 653, 730, and 753. Calculate the sample mean and sample standard deviation. Prepare a dot diagram of these data. Indicate where the sample mean falls on this diagram. Give a practical interpretation of the sample mean.
Answer:
Mean: 810.51
Standard deviation: 128.32
Step-by-step explanation:
First, we calculate the sample mean. We have 35 data samples, so we compute it as [tex]\displaystyle \frac{562 + .... + 753}{35}[/tex].
In general, given a set of n samples [tex]\{ X_1,...,X_n\}[/tex], we calculate the sample mean as
[tex]\displaystyle \bar{X} = \sum_{i=1}^n \frac{X_i}{n}[/tex].
For the standard deviation [tex]\sigma[/tex], we first begin by calculating it's square. It can be obtained from the formula
[tex]\displaystyle \sigma ^2 = \sum_{i=1}^{n} \frac{(X_i - \bar{X})^2}{n-1}[/tex]
By taking square root after computing the right hand side, we attain the desired value.
The attached image shows the dot diagram of this sample. The bottom pink vertical line shows the mean, and the two horizontal pink lines have a lenght of [tex]\sigma[/tex].
The standard deviation means "The average expected distance a new sample will be from the mean". That's why usually, data samples which are denser around the mean have smaller standard deviations (as opposed to distributions who have a lot of values far away from the mean, which will make the standard deviation grow bigger).
Determine whether the following possible responses should be classified as interval, nominal or ordinal data.
? Ordinal Nominal Interval 1. Heidi's favorite brand of tennis balls
? Ordinal Nominal Interval 2. Number of cars in a parking lot
? Ordinal Nominal Interval 3. Amount of time you spend per week on your homework
? Ordinal Nominal Interval 4. Whether you are a US citizen
Answer:
1. Nominal data 2. Responses here can't be classified as interval or nominal or ordinal data 3. Responses here can't be classified as interval or nominal or ordinal data 4. nominal
Step-by-step explanation:
1. Heidi's favorite brand of tenis balls is only a "label" in the set of brands that can be regarded. So, because we are dealing with names or "labels" we should classify responses here as nominal data.
2. Possible values for the number of cars in a parking lot are 0, 1, 2, 3, 4,... Besides we can say that 4 cars is twice than 2 cars, and exist a true zero. We can't say that responses here correspond to interval data, in fact, we can say that responses here correspond to the kind of data called ratio data.
3. You can spend zero hours in your homework, so, there exists an absolute zero, besides, to say that you spend 4 hours in your homework is twice that if you spend 2 hours in your homework is meaningful. We can't classify responses here as interval data or ordinal or nominal. We can classify responses here as ratio data.
4. There are only two different responses here, i.e., You are a US citizen or You are not a US citizen. We are dealing with "labels" again, and in general, we can't say there is a better response or stablish an order.
Final answer:
The correct classifications are: Heidi's favorite brand of tennis balls (Nominal), Number of cars in a parking lot (Nominal, with an explanation), Amount of time spent on homework per week (Interval), and Whether you are a US citizen (Nominal).
Explanation:
To determine whether the listed responses should be classified as interval, nominal, or ordinal data, it is essential to understand what each type of data signifies. Nominal data are categories without any order, ordinal data have a meaningful order or ranking but not necessarily consistent differences between rankings, and interval data have a consistent scale and order, but no true zero point.
Nominal: Heidi's favorite brand of tennis balls. This is a category (brand) without a numerical value or order.
Nominal: Number of cars in a parking lot. Although it involves numbers, it is essentially counting the frequency of an item, which falls under ratio data. However, as the question specifically asks among nominal, ordinal, and interval, the correct identification in this context is not provided.
Interval: Amount of time you spend per week on your homework. Time has a consistent scale and can be ordered, but there is no true zero time (you cannot have negative time).
Nominal: Whether you are a US citizen. This is a categorical variable with no inherent order.
Use the row operations tool to solve the following system of equations, obtaining the solutions in fraction form.
12x + 2y + z = 4
3x + 3y - 4z = 5
2x - 2y + 4z = 1
Give the values for x, y, and z with the fractions reduced to lowest terms (for example 4/7 rather than 8/14).
x = ____
y = ____
z = ____
Answer:
[tex]x=\frac{45}{4}, y=-\frac{201}{4}, z=-\frac{61}{2}[/tex]
Step-by-step explanation:
We start by putting our equation in a matricial form:
[tex]\left[\begin{array}{cccc}12&2&1&4\\3&3&-4&5\\2&-2&4&1\end{array}\right][/tex]
Then, we multiply the second row by 4 and substract the first row:
[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\2&-2&4&1\end{array}\right][/tex]
Now, multiply the third row by 6 and substract the first row:
[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\0&-14&23&2\end{array}\right][/tex]
Next, we will add [tex]\frac{7}{5}[/tex] times the second row to the third row:
[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\0&0&\frac{-4}{5}&\frac{122}{5}\end{array}\right][/tex]
Now we can solve [tex]\frac{-4}{5} z=\frac{122}{5}[/tex] to obtain
[tex]z=-\frac{61}{2}[/tex]
Then [tex]10y-17\frac{-61}{2}=16[/tex] wich implies that
[tex]y=\frac{16-\frac{17*61}{2}}{10} =\frac{\frac{32-17*61}{2}}{10}=\frac{-1005}{20}=\frac{-201}{4}[/tex]
Finally
[tex]x=\frac{4-2*\frac{-201}{4}+\frac{61}{2}}{12} =\frac{\frac{8+201+61}{2}}{12}=\frac{270}{24}=\frac{135}{12}=\frac{45}{4}[/tex].
[tex]z=-\frac{61}{2}\\ y=-\frac{201}{4} \\x=\frac{45}{4}[/tex]
To review the solution to a similar problem, consult Interactive Solution 1.43. The magnitude of a force vector is 86.4 newtons (N). The x component of this vector is directed along the +x axis and has a magnitude of 72.3 N. The y component points along the +y axis. (a) Find the angle between and the +x axis. (b) Find the component of along the +y axis.
We have a vector [tex]\vec F[/tex] with a magnitude [tex]F[/tex] of 86.4 N.
a. Let [tex]\theta[/tex] be the angle [tex]\vec F[/tex] makes with the positive [tex]x[/tex]-axis. The [tex]x[/tex]-component of [tex]\vec F[/tex] is
[tex]F_x=(86.4\cos\theta)\,\mathrm N[/tex]
and has a magnitude of 72.3 N, so
[tex]72.3=86.4\cos\theta\implies\cos\theta=0.837\implies\theta=\boxed{33.2^\circ}[/tex]
b. The [tex]y[/tex]-component of [tex]\vec F[/tex] is
[tex]F_y=(86.4\cos33.2^\circ)\,\mathrm N=\boxed{47.3\,\mathrm N}[/tex]
a) The angle between the vector and the +x axis is approximately 33.196°.
b) The component of the force along the +y axis is approximately 47.304 newtons.
Vector analysis of a given force
In this question we should apply the concepts of magnitude and direction of a vector to solve each part. The magnitude ([tex]\|\vec F\|[/tex]), in newtons, is a application of Pythagorean theorem and direction ([tex]\theta[/tex]), in degrees, is an application of trigonometric functions.
a) The angle between the vector and the component along the x axis ([tex]F_{x}[/tex]), in newtons, is found by means of the following expression:
[tex]\theta = \cos^{-1} \frac{F_{x}}{\|\vec F\|}[/tex] (1)
([tex]\|\vec F\| = 86.4\,N[/tex], [tex]F_{x} = 72.3\,N[/tex])
[tex]\theta = \cos^{-1} \left(\frac{72.3\,N}{86.4\,N} \right)[/tex]
[tex]\theta \approx 33.196^{\circ}[/tex]
The angle between the vector and the +x axis is approximately 33.196°. [tex]\blacksquare[/tex]
b) The magnitude of the +y component of the vector force ([tex]F_{y}[/tex]), in newtons, is determined by the following Pythagorean expression:
[tex]F_{y} = \sqrt{(\|\vec F\|)^{2}-F_{x}^{2}}[/tex] (2)
([tex]\|\vec F\| = 86.4\,N[/tex], [tex]F_{x} = 72.3\,N[/tex])
[tex]F_{y} = \sqrt{(86.4\,N)^{2}-(72.3\,N)^{2}}[/tex]
[tex]F_{y} \approx 47.304\,N[/tex]
The component of the force along the +y axis is approximately 47.304 newtons. [tex]\blacksquare[/tex]
To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13188123
A lady buys 20 trinkets at a yard sale.
The cost of each trinket is either $0.30
or $0.65. If she spends $8.80, how
many of each type of trinket does she
buy?
Answer:
Lady purchased 12 trinkets costing $0.30 each and 8 trinkets costing $0.65 each.
Step-by-step explanation:
A lady buys total number of trinkets = 20
Cost of each trinket is either $0.30 or $0.65.
Let the number of trinkets is x she purchased for $0.30 and y for $0.65
Then x + y = 20 --------(1)
Since she spends total amount = $8.80
Then the equation will be
0.30x + 0.65y = 8.80 ---------(2)
We replace x = (20 - y) from equation (1) to equation (2)
0.30(20 - y) + 0.65y = 8.80
6 - 0.30y + 0.65y = 8.80
0.35y + 6 = 8.80
0.35y = 8.80 - 6
0.35y = 2.80
y = [tex]\frac{2.80}{0.35}[/tex]
y = 8
Now we put y = 8 in equation (1)
x + 8 = 20
x = 20 - 8
x = 12
Therefore, lady purchased 12 trinkets costing $0.30 each and 8 trinkets costing $0.65 each.
A small military base housing 1,000 troops, each of whom is susceptible to a certain virus infection. Assuming that during the course of the epidemic the rate of change (with respect to time) of the number of infected troopers is jointly proportional to then number of troopers infected and the number of uninfected troopers. If at the initial outbreak, there was one trooper infected and 2 days later there were 5 troopers infected, express the number of infected troopers as a function of time.
Answer:
[tex]I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}[/tex]
Step-by-step explanation:
The rate of infection is jointly proportional to the number of infected troopers and the number of non-infected ones. It can be expressed as follows:
[tex]\frac{dI}{dt}=a*I*(1000-I)[/tex]
Rearranging and integrating
[tex]\frac{dI}{dt}=a*I*(1000-I)\\\\\frac{dI}{I*(1000-I)}=a*dt\\\\\int\frac{dI}{I*(1000-I)}=\int a*dt\\\\-\frac{ln(1000/I-1)}{1000}+C=a*t[/tex]
At the initial breakout (t=0) there was one trooper infected (I=1)
[tex]-\frac{ln(1000/1-1)}{1000}+C=0\\\\-0,006906755+C=0\\\\C=0,006906755[/tex]
In two days (t=2) there were 5 troopers infected
[tex]-\frac{ln(1000/5-1)}{1000}+0,006906755=a*2\\\\-0,005293305+0,006906755=2*a\\a = 0,00161345 / 2 = 0,000806725[/tex]
Rearranging, we can model the number of infected troops (I) as
[tex]-\frac{ln(1000/I-1)}{1000}+0,006906755=0,000806725*t\\\\-\frac{ln(1000/I-1)}{1000}=0,000806725*t-0,006906755\\-ln(1000/I-1)=0,806725*t-0.6906755\\\\\frac{1000}{I}-1=exp^{0,806725*t-0.6906755} \\\\\frac{1000}{I}=exp^{0,806725*t-0.6906755}+1\\\\I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}[/tex]
Let P={ 1,2,3,5,7,9}, Q= { 1,2,3,4,5}, and R= {2,3,5,7,11}
Find P n R?
Answer:
[tex]P \cap R=\{2,3,5,7\}[/tex]
Step-by-step explanation:
Given : Let P={ 1,2,3,5,7,9}, Q= { 1,2,3,4,5}, and R= {2,3,5,7,11}
To find : The value of [tex]P \cap R[/tex] ?
Solution :
The intersection of two sets is defined as the set of their common elements or the elements appear in both the sets.
The sets are P={ 1,2,3,5,7,9} and R= {2,3,5,7,11}
Common elements in P and R are {2,3,5,7}
So, [tex]P \cap R=\{2,3,5,7\}[/tex]
Therefore, The value of [tex]P \cap R=\{2,3,5,7\}[/tex]
The average number of points you scored in the first 9 basketball games of the season was 23. What do you need in the 10th game to get your average to n? OA. n-23 OB, 10n-207 O C. 9n-23 D. 207-9n
Answer:
B. 10n-207
Step-by-step explanation:
Given,
The average number of points of 9 games = 23,
∵ Sum of observations = their average × number of observations
So, the total points for 9 games = 9 × 23 = 207,
Now, if the average of 10 games is n,
Then the total points for 10 games = 10n,
Hence, the number of points earned in 10th game = the total points for 10 games - the total points for 9 games
= 10n - 207
i.e. OPTION B is correct.
The correct option is (B) 10n-207. To raise the average points per game to 'n' after the 10th basketball game, one would need to score '10n - 207' points in the 10th game, based on the previous average of 23 points in the first 9 games.
To solve the problem, we need to use the formula for calculating an average. The average score after 10 games would be the total points scored divided by 10. If the first 9 games had an average of 23 points, the total points from these games is 9 × 23 = 207.
To get an average of n after the 10th game, the total points should be 10× n. Therefore, the points needed in the 10th game would be the difference between 10 × n and the sum score from the first 9 games (207). That gives us the equation 10n - 207 for the number of points needed in the 10th game.
Prove that for all x and y in Z, x +3y is a multiple of 7 iff 3x +2y is a multiple of 7. Might be helpful to calculate 2(3x +2y)+(x +3y) and/or 4(x +3y)+(3x +2y).
Proof :
First, it is important to have in mind that a number [tex] m \in \mathbb{Z} [/tex] is a multiple of [tex]n\in\mathbb{Z} [/tex] iff there exists [tex]k\in\mathbb{Z}[/tex] such that [tex] m = n \cdot k[/tex].
Also, you have to prove a logical equivalence. To this end, it is possible to prove two logical implications.
Step-by-step explanation:
1.) Let x, y be integers such that x + 3y is a multiple of 7. You have to prove that 3x +2y is a multiple of 7.
In effect, by hypothesis there exists k [tex]\in\mathbb{Z}[/tex] such that x + 3y = 7 k . So, you get
[tex]\begin{equation*} 4(x+3y) + (3x + 2y) = 7x + 14y = 7 (x + 2y) \ \mbox{(direct computations and factoring)}\end{equation*} [/tex].
Therefore, 4(x +3y) + (3x +2y) is a multiple of 7. Then,
[tex](3x + 2y) = 7 (x + 2y) - 4(x + 3y) = 7 (x+2y) - 4 \cdot 7 k = 7 (x + 2y -4k) \ \mbox{(factoring)}[/tex].
Given that x,y,k are integers, then x + 2y - 4k is an integer and hence, 3x + 2y is a multiple of 7.
To finish, it remains to prove its reciprocal statement.
2.) Let x, y be integers such that 3x + 2y is a multiple of 7. You have to prove that x +3y is a multiple of 7. Reasoining as before , there exists q [tex]\in\mathbb{Z}[/tex] such that 3x + 2y = 7 \cdot q. Thus,
[tex]$$ \begin{equation*} 2(3x+2y) + (x + 3y) = 7x + 7y = 7 (x + y) \ \mbox{direct computations and factoring} \\\end{equation*} $$[/tex] Thus, [tex] 2(3x +2y) + (x +3y)[/tex] is a multiple of 7.
On the other hand, using the hypothesis [tex] $$ \begin{equation*} (x + 3y) = 7 (x + y) - 2(3x + 2y) = 7 (x+y) - 2 \cdot 7 q = 7 (x + y -2q) \ \mbox{(factoring)} \end{equation*} $$ [/tex] .
Finally, thanks that [tex]x,y,q [/tex] are integer numbers, then [tex] x + y - 2q[/tex] is a integer number and therefore, [tex] 3x + 2y [/tex] is a multiple of 7.
Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour. What is the probability that in the next hour there will be exactly 9 arrivals?
a. 0.7500
b. 0.1322
c. 0.0000
d. 0.0213
e. none of the above
Answer:
d. 0.0213
Step-by-step explanation:
If a variable follow a poisson distribution, the probability that x events happens in a specific time is given by:
[tex]P(x)=\frac{e^{-a}*a^{x} }{x!}[/tex]
Where a is the mean number of events that happens in a specific time.
So, in this case, x is equal to 9 arrivals and a is equal to 16 customers per hour. Replacing this values, the probability is:
[tex]P(9)=\frac{e^{-16}*16^{9} }{9!}[/tex]
[tex]P(9)=0.0213[/tex]
In preparing a certain ointment, a pharmacist used 28.35 g of zinc oxide instead of the 31.1 g called for. Calculate the percentage of error on the basis of the desired quantity.
Answer: 9.70%
Step-by-step explanation:
The formula to find the percentage error is given by :-
[tex]\%\text{ error}=\dfrac{|\text{Estimate-Actual}|}{\text{Actual}}\times100[/tex]
Given : Actual mass of zinc oxide used by pharmacist = 28.35 g
Estimated mass of zinc oxide used by pharmacist =31.1 g
Now, [tex]\%\text{ error}=\dfrac{|31.1-28.35|}{28.35}\times100[/tex]
i.e. [tex]\%\text{ error}=\dfrac{2.75}{28.35}\times100[/tex]
i.e. [tex]\%\text{ error}=9.70017636684\approx9.70\%[/tex]
Hence, the percentage of error on the basis of the desired quantity.= 9.70%
A tube feeding formula contains 6 grams of protein per each 80 ml of the formula. If the patient needs 120 grams of protein per day, how much tube-feeding formula should he get every day?
Answer:
1600 ml.
Step-by-step explanation:
Let x represent amount of tube-feeding formula.
We have been given that a tube feeding formula contains 6 grams of protein per each 80 ml of the formula.
To solve our given problem, we will use proportions as:
[tex]\frac{x}{\text{120 gram}}=\frac{\text{80 ml}}{\text{ 6 grams}}[/tex]
[tex]\frac{x}{\text{120 gram}}*\text{120 gram}=\frac{\text{80 ml}}{\text{ 6 grams}}*\text{120 gram}[/tex]
[tex]x=\text{80 ml}*20[/tex]
[tex]x=\text{1600 ml}[/tex]
Therefore, the patient should get 1600 ml of tube feeding formula every day.
Let v1, v2, w be three linearly independent vectors in R 3 . That is, they do not all lie on the same plane. For each of the following (infinite) set of vectors, carefully sketch it in R 3 , and determine whether or not it is a vector space (i.e., a subspace of R 3 ). Explain your reasoning.
Answer:
Where are the sets of vectors?
Step-by-step explanation:
Which set of vectors?
The admissions office of a private university released the following data for the preceding academic year: From a pool of 4200 male applicants, 30% were accepted by the university, and 30% of these subsequently enrolled. Additionally, from a pool of 3300 female applicants, 35% were accepted by the university, and 30% of these subsequently enrolled. What is the probability of each of the following?
a) A male applicant will be accepted by and subsequently will enroll in the university?
b) A student who applies for admissions will be accepted by the university?
c) A student who applies for admission will be accepted by the university and subsequently will enroll?
Answer:
(a) 0.09 (b) 0.322 (c) 0.0966
Step-by-step explanation:
Let's define first the following events
M: an applicant is a male
F: an applicant is a female
A: an applicant is accepted
E: an applicant is enrolled
S: the sample space
Now, we have a total of 7500 applicants, and from these applicants 4200 were male and 3300 were female. So,
P(M) = 0.56 and P(F) = 0.44, besides
P(A | M) = 0.3, P(E | A∩M) = 0.3, P(A | F) = 0.35, P(E| A∩F) = 0.3
(a) 0.09 = (0.3)(0.3) = P(A|M)P(E|A∩M)=P(E∩A∩M)/P(M)=P(E∩A | M)
(b) P(A) = P(A∩S) = P(A∩(M∪F))=P(A∩M)+P(A∩F)=P(A|M)P(M)+P(A|F)P(F)=(0.3)(0.56)+(0.35)(0.44)=0.322
(c) P(A∩E)=P(A∩E∩S)=P(A∩E∩(M∪F))=P(A∩E∩M)+P(A∩E∩F)=0.0504+P(E|A∩F)P(A|F)P(F)=0.0504+(0.3)(0.35)(0.44)=0.0966
T F IfA and B are similar matrices, then AT=BT
Answer:
Step-by-step explanation:
We know that for two similar matrices [tex]A[/tex] and [tex]B[/tex] exists an invertible matrix [tex]P[/tex] for which
[tex][tex]B = P^{-1} AP[/tex][/tex]
∴ [tex]B^{T} = (P^{-1})^{T} A^{T} P^{T} \\[/tex]
Also [tex]P^{-1}P = I\\[/tex]
and [tex](P^{-1})^{T} = (P^{T})^{-1}[/tex]
∴[tex](P^{-1})^{T}P^{T} = I[/tex]
so, [tex]B^{T} = (P^{-1})^{T} A^{T} P^{T} = (P^{T})^{-1}A^{T} P^{T}\\B^{T} = A^{T} I\\B^{T} = A^{T}[/tex]
120 cm = _______ inches Round UP to nearest 100th
Answer:
120cm = 46.8 inches
Step-by-step explanation:
This can be solved as a rule of three problem.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Unit conversion problems, like this one, is an example of a direct relationship between measures.
Each cm has 0.39 inches. How many inches are there in 120 cm?
1cm - 0.39inches
120cm - x inches
[tex]x = 120*0.39[/tex]
[tex]x = 46.8[/tex] inches
120cm = 46.8 inches
There are 18,017 AIDS deaths in 2003, or 34.5% of the 1995 AIDS deaths. Determine the number of AIDS deaths in 1995.
Answer: There are 52223.18 AIDS death in 1995.
Step-by-step explanation:
Since we have given that
Number of AIDS deaths in 2003 = 18,017
Percentage of deaths of 1995 AIDS deaths =34.5%
Let the number of AIDS deaths in 1995 be 'x'.
According to question, it becomes ,
[tex]\dfrac{34.5}{100}\times x=18017\\\\x=18017\times \dfrac{100}{34.5}\\\\x=52223.18[/tex]
Hence, there are 52223.18 AIDS death in 1995.
Weinstein, McDermott, and Roediger (2010) conducted an experiment to evaluate the effectiveness of different study strategies. One part of the study asked students to prepare for a test by reading a passage. In one condition, students generated and answered questions after reading the passage. In a second condition, students simply read the passage a second time. All students were then given a test on the passage material and the researchers recorded the number of correct answers. a. Identify the dependent variable for this study. b. Is the dependent variable discrete or continuous? c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?
Answer:
Dependent variable: number of correct answers
Step-by-step explanation:
The dependent variable is the number of correct answers, because it is the variable that the researchers were recording as response in the experiment.
As it is a counting, it can only take finite values (0 correct answers, 1 correct answer, 2 correct answers and so on). Then, it can be classified as a discrete variable. Discrete values always represent exact quantities that can be counted. For example, number of passengers per car, or number of cows per acre.
Discrete variables can be divided into nominal (they haven’t an order or a hierarchy, as in the example of cows/acre), ordinal (they follow a natural order or hierarchy), interval (they can be divided into classes) or ratio (they represent relative quantities).
The number of correct answers is an ordinal variable, because they have a natural hierarchy. 1 correct answer it’ s better than 0, and 2 corrects answers are better than 1 and 0. Then, you can order your results: 0, 1, 2, 3, 4, etc.
A pawnshop with a monthly interest rate of 3.15 percent would have an annual interest rate of percent. (Round your answer to 2 decimal places.) Multiple Choice 3.15 31.50 3780 18.90 6.30
Annual is 1 year.
1 year has 12 months.
Multiply the monthly rate by 12:
3.15 x 12 = 37.80%
a number has seven digits. all the digits are 6 except the hundred-thousands' digit, which is 2, and the thousands' digit, which is 4. what is the number?
Answer:
264,666.
Step-by-step explanation:
We have been given that a number has seven digits.
All digits are 6 except the hundred-thousands' digit.
Hundred thousands: 100,000.
The hundred thousand's digit is 2, so its value would be 200,000.
We have been given that thousands's digit is 4, so its value would be:
4 thousands: 4,000
The number with given hundred thousand's and thousands's digit would be 204,000.
Since all digits are 6 except the hundred-thousands' digit, therefore, our number would be 264,666.
A computer assembling company receives 24% of parts from supplier X, 36% of parts from supplier Y, and the remaining 40% of parts from supplier Z. Five percent of parts supplied by X, ten percent of parts supplied by Y, and six percent of parts supplied by Z are defective. If an assembled computer has a defective part in it, what is the probability that this part was received from supplier Z?
Answer:
There is a 33% probability that this party was received from supplier Z.
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
-In your problem, we have:
P(A) is the probability of a defective part being supplied. For this probability, we have:
[tex]P(A) = P_{1} + P_{2} + P_{3}[/tex]
In which [tex]P_{1}[/tex] is the probability that the defective product was chosen from supplier X(we have to consider the probability of supplier X being chosen). So:
[tex]P_{1} = 0.24*0.05 = 0.012[/tex]
[tex]P_{2}[/tex] is the probability that the defective product was chosen from supplier Y(we have to consider the probability of supplier Y being chosen). So:
[tex]P_{2} = 0.36*0.10 = 0.036[/tex]
[tex]P_{3}[/tex] is the probability that the defective product was chosen from supplier Z(we have to consider the probability of supplier Z being chosen). So:
[tex]P_{2} = 0.40*0.06 = 0.024[/tex]
So
[tex]P(A) = P_{1} + P_{2} + P_{3} = 0.012 + 0.036 + 0.024 = 0.072[/tex]
P(B) is the probability of the supplier chosen being Z, so P(B) = 0.4
P(A/B) is the probability of the part supplied being defective, knowing that the supplier chosen was Z. So P(A/B) = 0.06.
So, the probability that this part was received from supplier Z is:
[tex]P = \frac{0.4*0.06}{0.072} = 0.33[/tex]
There is a 33% probability that this party was received from supplier Z.
Solve the system of linear equations using the Gauss-Jordan elimination method.
2x + 2y + z = 18
x + z = 7
4y − 3z = 20
Answer:
Values for each variable are:
x = 19
y = -4
z = -12
Step-by-step explanation:
As we can remember the Gauss-Jordan elimination method consists of creating a matrix with all the equations of the system. Remember that, if a variable does not appear in one of the equations, we give a value of 0 to its coefficient . Each equation will constitute a line of the matrix. So, the matrix will look like this:
2 2 1 18
1 0 1 7
0 4 -3 20
For the Gauss-Jordan elimination we can multiply lines, add or subtract one line to another or we can rearrange the order at any given time. The goal is to get only 1s in the matrix diagonal, to determine the value of each variable.
Since we already have a line with a 1, we'll take that line as our starting point, and we'll rearrange it as our 1st line. By multiplying the 1st line for 2 and then subtracting the result to the second line:
1 0 1 7
0 2 -1 4
0 4 -3 20
Now, we multiply the second line by 2 and subtract the result to the third line
1 0 1 7
0 2 -1 4
0 0 -1 12
In order to get the value of Z all we have to do is multiply the third line by (-1).
1 0 1 7
0 2 -1 4
0 0 1 -12
Now, we add the third line to the second line.
1 0 1 7
0 2 0 -8
0 0 1 -12
Then, multiply the second line by a fraction 1/2, to get the value for Y
1 0 1 7
0 1 0 -4
0 0 1 -12
Finally, we subtract the third line to the 1st line to get the value for X
1 0 0 19
0 1 0 -4
0 0 1 -12
All we got left is to prove our answer is correct by replacing the variables in the system with the values found:
First equation
2(19) + 2(-4) + (-12) = 18
38 - 8 - 12 = 18
38 - 20 = 18
Second equation
19 + (-12) = 7
19 -12 = 7
Third equation
4(-4) - 3(-12) = 20
-16 + 36 = 20
Find the 100th and the nth term for each of the following sequences.1 , 4 , 7 , 10 , .
Answer: The value of 100 th term is 298 and the value of n th term is 1+3n.
Step-by-step explanation:
Since we have given that
1,4,7,10............
Since it forms an A.P. in which
a = 1
d = [tex]4-1 =3[/tex]
So, the value of 100 th term is given by
[tex]a_{100}=a+(n-1)d\\\\a_{100}=1+(100-1)\times 3\\\\a_{100}=1+99\times 3\\\\a_{100}=1+297\\\\a_{100}=298[/tex]
And the value of n th term is given by
[tex]a_n=1+3n[/tex]
Hence, the value of 100 th term is 298 and the value of n th term is 1+3n.
Assume that the sales of a certain appliance dealer can be approximaed y sraig were $6000 in 1982 and $ 64,000 in 1987. Let x - O represent 1982 Find the equation giving yearly alesSand then use it to predict the yearly sales in 1990.
Answer:
[tex]y=11,600x+6,000[/tex]
Yearly sales in 1990: $98,800.
Step-by-step explanation:
We have been given that the sales of a certain appliance dealer can be approximated by a straight line. Sales were $6000 in 1982 and $ 64,000 in 1987.
If at 1982, [tex]x=0[/tex] then at 1987 x will be 5.
Now, we have two points (0,6000) and (5,64000).
[tex]\text{Slope}=\frac{64,000-6,000}{5-0}[/tex]
[tex]\text{Slope}=\frac{58,000}{5}[/tex]
[tex]\text{Slope}=11,600[/tex]
Now, we will represent this information in slope-intercept form of equation.
[tex]y=mx+b[/tex], where,
m = Slope,
b = Initial value or y-intercept.
We have been given that at [tex]x=0[/tex], the value of y is 6,000, so it will be y-intercept.
Substitute values:
[tex]y=11,600x+6,000[/tex]
Therefore, the equation [tex]S=11,600x+6,000[/tex] represents yearly sales.
Now, we will find difference between 1990 and 1982.
[tex]1990-1982=8[/tex]
To find yearly sales in 1990, we will substitute [tex]x=8[/tex] in the equation.
[tex]S=11,600(8)+6,000[/tex]
[tex]S=92,800+6,000[/tex]
[tex]S=98,800[/tex]
Therefore, the yearly sales in 1990 would be $98,800.
4,275.50= 391/2 of ____
Answer:
The required value for the blank is 21.8696
Step-by-step explanation:
Consider the provided information,
4,275.50= 391/2 of ____
Replace blank with x.
4,275.50 = 391/2 of x
Use sign of multiplication for "of".
[tex]4,275.50 = \frac{391}{2} \times x[/tex]
Solve the above expression for x.
[tex]x=\frac{4,275.50\times 2}{391} [/tex]
[tex]x=21.8696 [/tex]
Thus, the required value for the blank is 21.8696
Is the following relation a function?
Yes
No
Answer: This represents a function
Step-by-step explanation: In this problem, we are given a relation in the form of a mapping diagram and we are asked if it represents a function. The easiest way to do this problem is to first translate the mapping diagram into a list of ordered pairs.
(6,-2) (-2,2) (4,1) (-1,1)
Now to determine if the relation is a function, we can simply look at the x coordinates of each ordered pair. Notice that all of them are different so the relation must be a function. It's important to understand that even though two of the Y coordinates are the same, this relation is still a function because the y coordinates do not have any effect on whether or not the relation is a function.
2. In an experiment with a mass attached to a spring, a student measures the period of the oscillation t as follows: 1.94 s, 1.96 s, 2.01 s, 1.98 s, 2.02 s, 2.00 s, 1.99 s, 2.01 s, 1.98 s, 1.97 s. a) What is the average and b) standard deviation? Use the instructions for excel to find statistics on a set of similar numbers, round to the correct # sig figs. Zeroes to the right do. ALWAYS include units for a number that has units. These statistics have the same units all the way throug
Answer: a) The average of this set of numbers is 1.98 s. b) the standard deviation is 0.02 s.
Step-by-step explanation: The average is calculated by adding all numbers found in the experiment divided by the number of values. [tex]average = \frac{Sumxi}{n}[/tex]
The standard deviation is given by the square root of the squared sum of the difference between each number and the average divided by the total number of values. For instance, std deviation = [tex]\frac{sqrt{(1.94-1.98)^{2}+(1.96-1.98)^2+(2.01-1.98)^2...}}{11}[/tex] and that is done with all 11 terms of data minus the average to find the standard deviation.
In excel, the average of a certain set of numbers (displayed in cells A1 to A5) can be found by the commands =average(A1:A5). The standard deviation can be found by the commands =stdedv.p(A1:A5) in which p is the population. You can decrease decimals by clicking on the icon displayed in the Ribbon.
Calculate:
5,500 milliliters(mL) =__liters (L)
Answer:
5.5 liters
Step-by-step explanation: there are 1000 milliliters in a liter, so divide 5,500/1000
Answer:
5.5 liters
Step-by-step explanation:
because 5500 millilitres is 5.5 liters