Answers
AB = BA, the first pair of matrices does not satisfy [tex]AB \neq BA[/tex].
Is AB BA correct for all matrices?AB = BA in general, even if A and B are both square. We say that A and B commute if AB = BA. We cannot argue that AB = AC provides B = C for a generic matrix A. (However, since A is invertible, we may multiply both sides of the equation AB = AC to the left by A1 to yield B = C.)
For matrices, A and B, the product AB is not necessarily equal to BA. In fact, matrix multiplication is not commutative in general. Therefore, we need to check each pair of matrices to see if their products are equal in order to determine which pair satisfies [tex]$AB \neq BA$[/tex].
[tex]$$\begin{align*}AB &= \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \left[\begin{array}{cc}7 & 0 \ 3 & 4\end{array}\right] \\\&= \left[\begin{array}{cc}1 \cdot 7 + 0 \cdot 3 & 1 \cdot 0 + 0 \cdot 4 \ 3 \cdot 7 - 2 \cdot 3 & 3 \cdot 0 - 2 \cdot 4\end{array}\right] \\\&= \left[\begin{array}{cc}7 & 0 \ 15 & -8\end{array}\right]\end{align*}[/tex]
[tex]$$\begin{align*}BA &= \left[\begin{array}{cc}7 & 0 \ 3 & 4\end{array}\right] \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \\\&= \left[\begin{array}{cc}7 \cdot 1 + 0 \cdot 3 & 7 \cdot 0 + 0 \cdot (-2) \ 3 \cdot 1 + 4 \cdot 3 & 3 \cdot 0 + 4 \cdot (-2)\end{array}\right] \\\&= \left[\begin{array}{cc}7 & 0 \ 15 & -8\end{array}\right]\end{align*}[/tex]
Since AB = BA, the first pair of matrices does not satisfy [tex]AB \neq BA[/tex]. We can proceed in the same manner to check the other pairs of matrices:
[tex]$$\begin{align*}\\AB &= \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \left[\begin{array}{cc}8 & 0 \ 11 & -3\end{array}\right] \\\&= \left[\begin{array}{cc}1 \cdot 8 + 0 \cdot 11 & 1 \cdot 0 + 0 \cdot (-3) \ 3 \cdot 8 - 2 \cdot 11 & 3 \cdot 0 - 2 \cdot (-3)\end{array}\right] \\\&= \left[\begin{array}{cc}8 & 0 \ 2 & 6\end{array}\right]\end{align*}[/tex]
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Related Questions
Solve each trigonometric function IN THE INTERVAL [0, 2).
sin(x) + 1 = cos(x)
Answers
The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The trigonometric function is given below.
sin(x) + 1 = cos(x)
Simplify the equation, then we have
sin(x) + 1 = cos(x)
(sin(x) + 1)² = cos² (x)
(sin(x) + 1)² = 1 - sin² (x)
sin² (x) + 2sin x + 1 = 1 - sin² (x)
2sin² (x) = 0
sin (x) = sin 0
x = 0
The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.
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RIGHT ANSWER GETS 15 POINTS
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x.
Write and solve an equation to determine the measure of angle x. (5 points)
Your answer:
Answers
Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.
What is the vertical angles theorem?In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;
60° + 70° + y = 180°
130° + y = 180°
y = 180° - 130°
y = 50°
Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.
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suppose none of the four customers gets their meal in less than 77 minutes. is there any evidence to suggest that the manager's claim is false? justify your answer. because the probability that none of the customers gets the meal in less than 7 7 minutes is
Answers
The Probability Distribution of X is P(X = k) = (4 choose k) * (0.75)^k * (0.25)^(4-k) and there is no evidence to suggest that the manager's claim is false.
a. The probability distribution for X can be found using the binomial distribution, since the number of customers who get their meal in less than 7 minutes is a count of the number of successes in a fixed number of independent trials, each with the same probability of success. The probability distribution for X is given by:
P(X = k) = (4 choose k) * (0.75)^k * (0.25)^(4-k)
where k = 0, 1, 2, 3, or 4, and (4 choose k) is the number of combinations of 4 items taken k at a time.
b. The probability of observing exactly 0 customers getting their meal in less than 7 minutes is P(X = 0) = (0.25)^4 = 0.390625. This is a low probability, but it is still possible to observe 0 customers getting their meal in less than 7 minutes, even if the manager's claim is true. Therefore, observing 0 customers getting their meal in less than 7 minutes does not provide any evidence to suggest that the manager's claim is false.
The complete question is:
The Cornbread Cafe in Eugene, Oregon, recently installed a new computer system that allows customers to order their meals electronically from their tables. The manager of the restaurant claims that this new system will decrease the waiting time, and that the probability of getting a meal in less than 7 minutes (with this system in place) is 0.75. Suppose four customers are selected at random. Let the random variable X be the number of customers who get their meal in less than 7 minutes. (a) Find the probability distribution for X. (b) Suppose none of the four customers gets the meal in less than 7 minutes. Is there any evidence to suggest that the manager's claim is false? Justify your answer.
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Write an equivalent expression to 9 1/2k - (7 + 31/4k) without parentheses. Then, combine like terms
Answers
An equivalent expression to 9 1/2k - (7 + 31/4k) is 51k/4 +7
How to find the equivalent fraction?The given expression is 9 1/2k - (7 + 31/4k)
This involves the the simplification of the fraction above following the rule of BOADMAS
⇒19k/2 - 7/1 + 13k/4
Simplifying the right hand side of the fraction with parenthesis,
18k/2 - [(28+13k)/4
This fraction gives
*38k - 28+ 13k)/4
Collecting the like terms
= 25k + 28
Therefore the equivalent expression is 25k/1 + 7
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20. AARP and Medicare (3.5) To find out what pro-
portion of Americans support proposed Medicare
legislation to help pay medical costs, the AARP
conducted a survey of their members (people
over age 50 who pay membership dues). One of
the questions was: "Even if this plan won't affect
you personally either way, do you think it should
be passed so that people with low incomes or peo-
ple with high drug costs can be helped?" Of the
respondents, 75% answered yes.¹
(a)
Describe how undercoverage might lead to bias in
this study. Explain the likely direction of the bias.
(b) Describe how the wording of the question might
lead to bias in this study. Explain the likely direc-
tion of the bias.
Answers
There will be a bias in the data samples in favor of the opinions of a limited subset of the research community.
What are data samples?To find patterns and trends in the broader data set being reviewed, data sampling is a statistical analysis approach that is used to choose, modify, and analyze a representative selection of data points.
a. Under coverage happens when some members of the population are less likely to be selected for the sample or are not eligible for selection. Bias results from under coverage when the "under covered" individuals' differences from the general population have an impact on their responses.
Undercover prejudice may lead to bias in the voluntary response. This suggests you run the risk of obtaining information from a small number of people who are enthusiastic about the research issue. Your data samples will be biased toward the opinions of a tiny subset of your research population as a result.
b. People who don't have a phone number listed in the phone book are probably more worried about privacy issues than the ordinary person. The results would have probably revealed a higher percentage of people who were concerned about privacy if they had been included in the sample.
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A book sold 32,900 copies in its first month of release. Suppose this represents 9.1% of the number of copies sold to date. How many copies have been sold to date?
Answers
The number of copies that have been sold to date approximately is equal to 361,538 copies.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
How many copies have been sold to date?In order to determine the number of copies that have been sold to date, we would develop an expression to multiply the total number of copies (T) by the percentage of the number of copies sold in its first month of release as follows;
9.1/100 × T = 32,900
0.091T = 32,900
Dividing both sides of the equation by 0.091, we have the following:
Total number of copies (T) = 32,900/0.091
Total number of copies (T) = 361,538 copies.
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A man started his Journey at 11.57am and was scheduled to arrive of 12:25 if he arrived 15 minutes late, how long did be journey bake
Answers
The man's journey took 43 minutes.
In physics, what is the average distance?
The distance traveled divided by the motion's duration gives the average speed, or vavg. Time is calculated as distance divided by average speed. Time is calculated as distance divided by average speed. distance = v avg 150 kilometers in time 3.2 h = 47 km/h.
How can I determine my trip's duration?Take the start time and subtract the end time.
The man was supposed to arrive at 12:25, but he was 15 minutes late, thus his actual arrival time was 12:40 (12:25 plus 15).
The man's journey began at 11:57, therefore we can calculate how long it took by deducting the start time from the end time.
End time - Start time = Journey time
12:40 - 11:57 = 43 minutes
So, The man's journey took 43 minutes.
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Find the coordinates of the vertices after a 90 rotation about the origin and about each of the points L, M, and N
Answers
After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-3, -6) and (3, -4). Therefore, option D is the correct answer.
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
Given that, triangle LMN with vertices L(2, -2), M(6, -3) and N(4, 3).
After clockwise rotation 90° we get
Here, L(2, -2) →L'(-2, -2)
M(6, -3) →M'(-3, -6)
N(4, 3) →N'(3, -4)
Therefore, option D is the correct answer.
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A restaurant has a bag of potatoes that weighs 4 kilograms 500 grams. All the potatoes needs to be peeled. Kayla peels 1,841 grams of potatoes. Lacy peels 2,358 grams of potatoes.how many grams of potatoes still need to be peeled?
Answers
The grams of potatoes that still need to be peeled is equal to 301 grams.
How to determine the weight of the unpeeled potatoes?In this exercise, we would determine the total weight of the bag of potatoes in grams:
Note: 1,000 grams is equal to 1 kilogram.
Total weight of the bag of potatoes = 4 kilograms + 500 grams
Total weight of the bag of potatoes = 4,000 grams + 500 grams
Total weight of the bag of potatoes = 4,500 grams.
For the total weight of peeled potatoes, we have the following:
Total weight of peeled potatoes = 1,841 grams + 2,358 grams
Total weight of peeled potatoes = 1,841 + 2,358
Total weight of peeled potatoes = 4,199 grams.
Now, we can determine the weight of the unpeeled potatoes:
Weight of the unpeeled potatoes = 4,500 grams - 4,199 grams.
Weight of the unpeeled potatoes = 301 grams.
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a survey for kindergartners asked about their favorite color. the children were asked to check the box corresponding to blue, red, green, yellow, or orange. what is the scale of measurement for this question? group of answer choices ordinal interval nominal ratio
Answers
Nominal scale- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories.
Measurements on an interval scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.
Ratio scales are interval scales where lengths are expressed in relation to a rational zero.
Ordinal scale: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.
Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.
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identify the number as real, complex, pure imaginary, or nonreal complex. (more than one of these descriptions may apply)
-5
Answers
Answer:
real
Step-by-step explanation:
-5 is real. It is not complex because it is not in the form a+bi. It also has no imaginary part so it is neither of the other two.
Hope that helps, let me know if you have any other questions!
How would you describe the plant's growth over 6 weeks?
Plant Growth
10
9
8
7
6
3
2
1
0
1 2
6
3 4 5
Weeks
can't be determined
decreasing
about the same
O increasing
Answers
The plant's growth over 6 weeks is described as the increasing of plant volume and/or mass with or without formation of new structures such as organs, tissues, cells or cell organelles.
The term volume in math is called as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Here we need to describe the plant's growth over 6 weeks.
As we know that the stages that plants go through are from seed to sprout, then through vegetative, budding, flowering, and ripening stages.
On the other hand the nutritional needs of people and plants change as they grow.
Then the main stages in the life cycle of a plant are seed germination, seedling formation, growth, development and differentiation leading to a mature plant, pollination and fertilizations and the formation of fruit and seeds.
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A rectangle has an area of 174. 8m2
One of the sides is 3. 8m in length.
Work out the perimeter of the rectangle.
Answers
The perimeter of the rectangle with area 174.8m² and side-length 3.8m is equal to 99.6 meters.
Area of the rectangle is equal to 174.8 m².
Length of the rectangle is equal to 3.8 m
let us consider 'w' be the width of the rectangle.
area of the rectangle = length × width
⇒ 174.8 = 3.8 × w
⇒ w = 174.8 / 3.8
⇒ w = 46 m
Perimeter of the rectangle = 2 ( length + width )
⇒ Perimeter of the rectangle = 2 ( 3.8 + 46 )
⇒ Perimeter of the rectangle = 2 ( 49.8 )
⇒Perimeter of the rectangle = 99.6 meter.
Therefore, the perimeter of the rectangle with length 3.8m and width 46m is equal to 99.6m.
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find the probability that a randomly selected bank has an overdraft fee greater than $25. (use decimal notation. give your answer to two decimal places.
Answers
Answer:
Step-by-step explanation:
amy drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 12 hours. when amy drove home, there was no traffic and the trip only took 8 hours. if her average rate was 20 miles per hour faster on the trip home, how far away does amy live from the mountains?
Answers
If her average rate was 20 miles per hour faster on the trip home, Amy live 480 miles far from the mountains
Suppose Amy lives x miles from the mountains.
Fill in x as both distances and the times
going and coming 12 hours and 8 hours.
Distance | speed | time
To mountains | x | 8
Coming home | x | 5
Use: speed =distance/ time
to fill in the two rate boxes:
Distance | Speed | time
To mountains | x | x/12 | 8
Coming home | x | x/8 | 5
The equation comes from this sentence:
Her average rate was 20 miles per hour faster on the trip home
Her speed coming home late = Her speed going to the mountains + 20 miles per hour
x/8 = x/12+20
20 = x/8-x/12
20 = x/24
x = 24×20
x = 480
So Amy lives 480 miles from the mountains.
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help asap. ninas garden is 4 1/5 meters long and 3/10 meters wide what is the area of ninas garden?
Answers
Answer:
1.26 meters
Step-by-step explanation:
how many grams of an 80% solution and how many grams of a 54% solution do we have to mix in order to obtain 25 liters of a 42% solution
Answers
So you need 14.58 liters of 80% solution and 10.42 liters of 54% solution. To convert these to grams, you need to multiply by density of the solution.
Mixing solution to obtain 42% solutionTo obtain 25 liters of a 42% solution, you would need to mix a certain amount of an 80% solution with a certain amount of a 54% solution. To determine the specific amounts, you would need to set up and solve a system of equations.
Let x be the amount of 80% solution in liters and y be the amount of 54% solution in liters. The total volume of the mixture is the sum of the volumes of the two solutions, so we have:x + y = 25
The percentage concentration of the mixture is the sum of the mass fractions of the solute in the two solutions, so we have:(0.8x) + (0.54y) = 0.42(x + y)
Solving this system of equations will give you the amount of each solution you need to use.x = (0.42*25) / (0.8 + 0.54) = 14.58 liters
y = 25 - x = 10.42 liters
So you need 14.58 liters of 80% solution and 10.42 liters of 54% solution. To convert these to grams, you need to multiply by density of the solution.Learn more about Mixing solution to obtain 42% solution here:
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using only the digits $7$, $8$ and $9$, how many positive seven-digit integers can be made that are palindromes?
Answers
Using the digits 7,8 and 9, the positive seven-digit integers can be made that are palindromes are 729.
When constructing a seven-digit palindrome out of the digits 7, 8, and 9, the first three digits must be the same as the last three digits in reverse order.
This means that each of the first three digits can be either a 7, 8, or 9. Therefore, the total number of combinations for the first three digits is 3 x 3 x 3 = 27.
Since the last three digits must match the first three, the total number of possible combinations of integers is 27 x 27 = 729.
Thus, the total number of positive seven-digit palindromes that can be created using the digits 7, 8 and 9 is 729.
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a bicycle chain fits tightly around two gears the smaller gear has a radius of 4 cm and the bigger one has a radius of 8 cm find the distance between the center of the two gear
Answers
The unknown side of a right-angled triangle can be located using Pythagoras' theorem.Answer is 43.19 cm
What is Pythagorean theorem example?The unknown side of a right-angled triangle can be located using Pythagoras' theorem.Using the formula c2 = a2 + b2—where "c" stands for the hypotenuse and "a" and "b" are the two legs—it is possible to determine the third side of a right-angled triangle if the two other sides are provided as 4 and 6 units, respectively.
The sum of the squares on the shorter two sides of a right triangle equals the length of its longest side.
A2 + B2 = C2 is a formula that illustrates this.
Use the phytagorean theorem for this problem:
C= √a²+b²
C = hypotenuse = distance between the centers of the two gears
A = one side of the chain attaching the gears
= 43cm
B = the difference of the radii = (8 - 4) = 4
√43² +(8 - 4) ²
= 43.1856
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Write the equation of the line that passes through the points
(
−
3
,
−
8
)
(−3,−8) and
(
6
,
−
4
)
(6,−4). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line
Answers
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{-4 +8}{6 +3} \implies \cfrac{ 4 }{ 9 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ \cfrac{ 4 }{ 9 }}(x-\stackrel{x_1}{(-3)}) \implies y +8 = \cfrac{ 4 }{ 9 } ( x +3)[/tex]
What is the value of 8.3x10^4
Answers
Answer: 83000
Step-by-step explanation:
The populations of Siberian tigers and narwhals since 199019901990 are represented by the following tables
Answers
It is recommended to model the data in the tables using a ilnear or exponential function.
The exponential function will be the best model for tigers.
The optimal model for narwhals will be a linear function.
Test for vertical lines:
A vertical line test can be used to determine whether an expression is a function or not. In this test, we look for a single image of x and determine whether we receive one or many images.
It won't be a function if we receive more photographs.
For illustration, use y2 = 4ax.
y = ±√4ax
We receive two values of y for a single value of x.
Consequently, it won't be a function.
Due to that,
There are two data sets for the numbers of tigers and narwhals.
first gather tiger info,
Let's see if it satisfies the requirement for a linear function or not.
y = mx + c
x = 0, y = 1204
1204 = m0 + c
c = 1204
y = mx + 12-04
when y = 1050 and x = 3
1050 = 3m + 1205
m = -155/3
If a linear relationship exists,
Therefore, y should be 902 for x = 6.
However, is not the same as 902.
So, for this dataset exponential function will be best.
Similarly, we can check for the second dataset.
And it will satisfy the all the conditions of linear function.
So, for the Narwhals linear function is best model.
Complete question:
The populations of Siberian tigers and narwhals since 1990 are represented by the following tables:
Determine whether the data described in the tables is best modeled by a linear function or an exponential function.
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The triangle below is equilateral. Find the length of side x to the nearest tenth.
x
12
Answers
Answer:
[tex]x = 4\sqrt{3}[/tex]
Step-by-step explanation:
[tex]a^{2}+b^{2} =c^{2}[/tex]
[tex]x^{2} + 12^{2} =c^{2}[/tex]
Equilateral --> c = 2x
[tex]x^{2} +144 = (2x)^{2} \\x^{2} +144 = 4x^{2} \\3x^{2} =144\\x^{2} =48\\x=4\sqrt{3}[/tex]
g(x)=14x2^x
a=_
b=_
identify the initial amount a and the growth fact b in the exponential function
Answers
In the exponential function the initial amount a = 14 and the growth fact b = 2.
What is exponential function?One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function.
The simplest kinds of dynamical systems have solutions in the form of exponential functions.
Growth or decay can both be described by an exponential function.
g(x)=14x2^x
It is an exponential function.
g(x)=axb^x
where, a is initial amount and b is growth/decay factor.
Now we will compare the function with this one.
a = 14
b = 2
Hence, The initial amount a=14 and factor b=2
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Cost of carpeting a floor 2.50 per square feet how much will it cost to carpet a rectangular floor 10 feet by 12 feet
Answers
Explanation: To find the cost of the 10 by 12, you first need to multiply them together and then divide by the cost of carpet per square foot. 10x12 is 120
And 120 divided by 2.50 is 48
A toy factory makes toy bunnies.
Each toy bunny holds a carrot. A bunny's height, h(x)
is three times the length of the carrot, x.
2. Write an equation for the function h(x).
h(x) =
Answers
Answer: h(x) = 3x
Step-by-step explanation:
The height of a toy bunny, h(x), is directly proportional to the length of the carrot, x. The given information is that the height of the bunny is three times the length of the carrot. Therefore, the equation for the function h(x) would be the answer above.
Answer:
h(x) = 3x
I'm so cool w/ my fashionista lipstick! :D
Liam tarted with $12 in hi wallet. He kept track of the amount he gained and pent throughout the day, a hown in The table
Answers
Liam started with $12 amount in his wallet and ended up with $4 after spending $5 on ice cream, $8 on a movie ticket, and $3 on candy.
Total: $16
Liam has $4 amount left in his wallet.
1. Start by adding up the amount that Liam spent:
Ice Cream: $5
Movie Ticket: $8
Candy: $3
Total Spent: $16
2. Subtract the total amount spent from the amount Liam started with:
Initial Amount: $12
Total Spent: $16
Remaining Amount = Initial Amount - Total Spent
Remaining Amount = $12 - $16
Remaining Amount = -$4
Since the result is negative, this means that Liam has spent more than he started with and now has $4 left in his wallet.
Liam started with $12 in his wallet and ended up with $4 after spending $5 on ice cream, $8 on a movie ticket, and $3 on candy.
The complete question is:
Liam started with $12 in his wallet. He kept track of the amount he gained and pent throughout the day, as shown in The table below.
Expense | Amount
Ice Cream | $5
Movie Ticket | $8
Candy | $3
What is the amount of money Liam has left in his wallet?
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43% of all statistics classes require a statistical calculator and 27% require the use of a computer that has statistical software. Of the classes that require a statistical calculator, 17% also require the use of a computer. If a statistics course is selected at random find: (round to 4 decimal places where possible)
Answers
The probabilities of the events are
a. 0.43
b. 0.27
c. 0.1161
d. 0.2444.
According to the question,
Statistics classes require a statistical calculator = 43% = 0.43
Statistics classes require a computer that has statistical software = 27% = 0.27
Of the classes that require a statistical calculator, classes also require the use of a computer = 17% = 0.17
a. P(Statistical Calculator)
= 0.43
b. P(Statistical Software)
= 0.27
c. P(Require a Statistical Calculator and Statistical Software)
⇒ (0.43)(0.27)
= 0.1161
d. P(Require a Statistical Calculator GIVEN Require Statistical Software)
⇒ 0.066/0.27
⇒ 0.2444
Hence we can conclude that the probabilities of the events are
a. 0.43
b. 0.27
c. 0.1161
d. 0.2444
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Sean is conducting an experiment with an isotope of a particular element that has a half-life of 4 hours. He begins with a sample of the isotope with a mass of 92 grams. He then measures the mass of the object every hour. What is the approximate mass of the sample after 20 hours?
Answers
As per the given half life the approximate mass of the sample after 20 hours is 0.03125
The term half life is defined as the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.
Here we have know that Sean is conducting an experiment with an isotope of a particular element that has a half-life of 4 hours.
And here we also know that he begins with a sample of the isotope with a mass of 92 grams and then measures the mass of the object every hour.
Then the approximate mass of the sample after 20 hours is calculated as,
=> 20/4 = 5
Then the value after 5 hours of time is calculated as,
=> 1/2⁵
=> 0.03125
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mr. brown went grocery shopping to buy meat for his annual office picnic. he bought 7 3 4 pounds of hamburger, 17.85 pounds of chicken, and 6 1 2 pounds of steak. how many pounds of meat did mr. brown buy?
Answers
There are 32.1 pounds of meat.
Addition is an operation used in math to add numbers. The result that is obtained after addition is known as the sum of the given numbers. The addition symbol is one of the widely used math symbols. The addition symbol consists of one horizontal line and one vertical line. It is also known as the addition sign or the plus sign (+). The addition formula is the statement that shows an addition fact and is expressed as, addend + addend = sum. This can be understood with the help of the example shown in the figure given below. While adding numbers, if the sum of the addends is greater than 9 in any of the columns, we regroup this sum into tens and ones. Then we carry over the tens digit of the sum to the preceding column and write the ones digit of the sum in that particular column. In other words, we write only the number in 'ones place digit' in that particular column, while taking the 'tens place digit' to the column to the immediate left.
Add up the pounds of meat.
7.75 + 17.85 + 6.5 = 32.1 pounds
Thus, there are 32.1 pounds of meat.
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