A stem-and-leaf diagram separates each value of a data set into two parts: the stem and the leaf.
The stem is the first part of the number, typically the largest place value, and it is used to group similar values together. The leaves are the last part of the number, typically the smallest place value, and they provide the specific values within each group.
For example, consider a data set with the values 15, 19, 10, 11, 15. In a stem-and-leaf diagram, the stem for these values would be 1 and the leaves would be 5, 9, 0, 1, and 5, respectively.
The stem-and-leaf diagram would then look something like this:
1 | 0 1 5 5 9This format allows for a quick visualization of the distribution of the data and can be useful for identifying patterns and relationships within the data set.
Learn more about stem-and-leaf diagram at: brainly.com/question/17886846
#SPJ4
Select 3 solutions to inequality graphed below.
Equations and inequalities are both mathematical constructions made by joining two expressions.
What is meant by inequality?A connection in mathematics that compares two numbers variables or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. Less than or equal to, larger than, less than, and more than or equal to are the four fundamental inequalities.
Here,
Given :
-1 to 2 in the graph ,
To find the solution for the inequality ,
We get option -1 as the inequality
=> -1 ,0 ,1,2
=> -1 is the solution for this
These symbols for inequality are not equal (≠), less than (<), greater than (>), less than or equal (≤), and more than or equal (≥). Comparing numbers and identifying the range or ranges of values that satisfy the requirements of a given variable are both done using inequalities.
Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >, <, ≤ or ≥ indicate that the two expressions in an inequality are not always equal.
Therefore, the correct answer is option b.
To learn more about inequality refer to;
brainly.com/question/25275758
#SPJ1
what expresion is equivilant to 63+35
Answer: 98
Step-by-step explanation:
63 + 35
= 63 + 30 + 5
= 93 + 5
= 98
Answer:
63+35=98
Step-by-step explanation:
b) A rectangular room contains 600 m³ of air and its height is 5 m. (i) Find the area of its floor. (ii) Find the cost of carpeting its floor at Rs 60 per sq.m.
(i) Area of the floor = 120m²
(ii) Cost of carpeting the floor = Rs 7200
Given:
Amount of the air of a rectangular room (Cuboidal shaped) =Volume of rectangular room= 600m³
Height of the rectangular room = 5m
(i) According to question we have to find area of the rectangular floor.
We know Area of Rectangle = length × breadth
here, length and breadth is not known to us let's find.
We Know, Volume of Cuboid = length × breadth × height
600m³ = length × breadth × 5m
600 ÷ 5 = length × breadth
120 = length × breadth
length × breadth = 120
Area of the rectangular floor = length × breadth
= 120m²
(ii) Now we have to calculate the cost of carpeting rectangular room floor at Rs 60 per sq m.
Area of the rectangular floor = 120m²
Given:
Cost of carpeting the floor at Rs 60
Cost of carpeting the floor= cost × Area of floor
= 60 × 120
Cost of carpeting the floor = Rs 7200
To learn more about Volume of cuboid:
https://brainly.com/question/27090332
let d be an arbitrary set, and let p and q be arbitrary predicates on d. define p = ∀x (p(x)) → ∀x (q(x)) q = ∀x ( p(x) → q(x) ). check all statements that must be true.
Group of answer choices
A) p → q
B) None of the other choices.
C) q → p
A) p → q is true because it states that if all elements in d satisfy the predicate p, then all elements in d also satisfy the predicate q.
p states that for all elements in d, if they satisfy the predicate p, then they must also satisfy the predicate q. q states that for all elements in d, if they satisfy the predicate p, then they must also satisfy the predicate q. Therefore, p → q is true, because it states that if all elements in d satisfy the predicate p, then all elements in d must also satisfy the predicate q. However, q → p is not necessarily true, because it states that if all elements in d satisfy the predicate q, then they must also satisfy the predicate p. This is not necessarily true, because some elements in d may satisfy the predicate q, but not satisfy the predicate p.
Learn more about elements here
https://brainly.com/question/16439717
#SPJ4
Jose just purchased a house for $625,000. His annual homeowner's insurance premium is $0.52 per $100 of value. If his annual premium is divided into equal monthly payments, what will Jose have to pay on a monthly basis to keep his home insured?
Jose has to pay $270.83 on a monthly basis to keep his home insured.
What are percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Given that the annual homeowner’s insurance premium is $0.52 per $100 of value.
The annual home owner insurance premium is 0.52% of the house value and can be evaluated as follows;
0.52% of $625,000 = $3,250.
Therefore, his annual premium is set at $3,250.
However, we are required to determine what will Guillermo have to pay on a monthly basis.
Therefore, we have; $3,250 spread equally over 12 months.
Therefore, we have; $3,250/12 = $270.83
Hence, Jose has to pay $270.83 on a monthly basis to keep his home insured.
Learn more about percentage here:
https://brainly.com/question/14801224
#SPJ1
Janet wants to order a pizza for delivery to her home. Fast Delivery charges $15 per large pizza plus $2 for delivery. Order for Home charges $12 per large pizza plus $8 for delivery.
For how many pizzas is the cost the same?
Which equation represents the problem, where p is the number of large pizzas?
A. 15p+2 = 12p + 8
B. 15p+8 = 12p + 2
C. 15+2p= 12 + 8p
D. 15+ 8p = 12 + 2p
Answer:
A. 15p+2 = 12p + 8 represents the problem, where p is the number of large pizzas.
To find the number of pizzas for which the cost is the same, you need to set the two expressions equal to each other and solve for p.
15p + 2 = 12p + 8
3p = 6
p = 2
So, the cost is the same when two large pizzas are ordered
The equation that represents the problem is D. 15+ 8p = 12 + 2p.
You can solve the equation to find out at which point the cost is the same by isolating the variable (p) on one side of the equation.
You can do that by subtracting 12 from both sides, and then subtracting 8p from both sides.
It will give you : 3 = 2p which means p = 1.5.
So, for 1.5 large pizzas the cost of ordering from Fast Delivery and Order for Home will be the same.
which of the following expressions is correct l-37l = 37 -l37l = 37 l-37l =-37 -l37l =37
Answer:
l-37l = 37
Step-by-step explanation:
The absolute value of a negative number is the positive of the number
A conumer might repond to a negative incentive by
purchaing more of the product. Buying the good at a cheap price. Receiving a dicount. Decreaing ue of the product to ave money
A consumer might respond to a negative incentive by: Decreasing the use of the product to have money.
What is incentive?Positive incentives: monetary benefits for making particular decisions or carrying out particular behaviours. Purchasing particular goods from the shop, dining at particular establishments, or picking particular businesses are a few examples. Negative incentives are financial penalties imposed for choosing particular options or doing certain behaviours. Financial and non-financial incentives are the two different categories of incentives. Financial incentives are payments or awards provided in return for hitting certain targets or goals. Non-monetary incentives include recognition, prizes, and other non-cash benefits.
correct option is: Decreasing the use of the product to have money.
To know more about negative incentive refer to:
https://brainly.com/question/30161826
#SPJ1
consider the aloha example. suppose it is known that x1 = x2. find the probability that there were 0, 1 or 2 collisions during those two epochs analytically and confirm via r simulation.
X1+X2 have distribution Bi(n1+n2, p) then the probability is P(X1+X2 = 1 | X2 = 0) = np(1-p)ⁿ¹⁻¹ ,P(X1+X2 = 1| X2 = 1) = (1-p)ⁿ¹and P(X1 + X2 = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
Since both variables are independent but they have the same probability parameter, you can interpret that like if the experiment that models each try in both variables is the same. When you sum both random variables toguether, what you obtain as a result is the total amount of success in n1+n2 tries of the same experiment, thus X1+X2 have distribution Bi(n1+n2, p).
Note that, if X2 = k, then X1+X2 = 1 is equivalent to X1 = 1-k. Since X1 and X2 are independent, then P(X1+X2 = 1| X2 = K) = P(X1=1-k|X2=k) = P(X1 = 1-k).
If k = 0, then this probability is equal to P(X1 = 1) = np(1-p)ⁿ¹⁻¹
If k = 1, then it is equal to P(X1 = 0) = (1-p)ⁿ¹
Thus,
P(X1+X2 = 1) = P(X1+X2 = 1| X2 = 1) * P(X2=1) + P(X1+X2 = 1| X2 = 0) * P(X2 = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
learn more about of probability here
https://brainly.com/question/14690794
#SPJ4
What type of function is this Linear or Exponential?
The function y = 3x + 7 is a linear function and the second function that is represented in table is an exponential function.
What is a linear and exponential function?The way the y-values change when the x-values increase by a constant amount differs between linear and exponential relationships: The y-values in a linear relationship differ by the same amount. The y-values in an exponential relationship have equal ratios.Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x and y are independent and dependent variables. An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero. The transcendental number e is the most commonly used exponential function base.Here the function y = 3x + 7 is a linear function and the second function is an exponential function because powers of 2.
To learn more about functions refer to :
https://brainly.com/question/725335
#SPJ1
hi, can anyone help me, thanks.
Answer:
187/2
Step-by-step explanation:
Explain why both of the following forms of the SVD are equivalent: A=ULVT AV = US
Both of the following forms of the SVD are equivalent because both are related spectroscopic data.
Singular value decomposition (SVD)
Singular value decomposition (SVD) is a technique commonly used in the analysis of spectroscopic data that both acts as a noise filter and reduces the dimensionality of subsequent least-squares fits.
The singular value decomposition (SVD) of a matrix A is the process of factorizing A into the product of three matrices A = U DV^{T} where the columns of U and V are orthonormal and the matrix D is diagonal with positive real entries. Data matrix A is useful to find a low rank matrix which is a good approximation to the data matrix.
spectroscopic data
spectrographs collect data that tell scientists how much light comes out at each wavelength. These data reveal important details about the makeup of atmospheres on exoplanets, the compositions of stars and nebulas, the motion of galaxies and more.
Learn more about Singular value decomposition here :_
https://brainly.com/question/30007171
#SPJ4
using five bits to represent each number, write the representations of 7 and ‒7 in 1’s complement, signed magnitude, and 2’s complement integers.
The range of decimal values that can be represented is -16 to +15 by using five bits and 2’s complement integers.
5 bit 2's complement representation will be of the form b1b2b3b4b5 where each bit is either 0 or 1.
The largest positive number that can be represented using this scheme is 01111
Translating this to decimal this is [tex]2^{3} +2^{2} +2^{1} +2^{0}[/tex]
= 8 + 4 + 2 + 1
= 15
The smallest negative number that can be represented using this scheme is 10000
Translating this to decimal = -1 * 2^4
= -1 * 2*2*2*2
= -1 * 16
= -16
Therefore,
The range of decimal values that can be represented is -16 to +15 by using five bits and 2’s complement integers.
To learn more about Complement integers visit :
brainly.com/question/13195243
#SPJ4
In a direct variation, y= 1 /7 when x= 8/7 Write a direct variation equation that shows the relationship between x and y.
The equation for direct variation showing the relationship between x and y is y = 8x
What is a direct variation?
A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately. Similar to the last example, if one quantity declines, the other amount also declines. The link between direct variation and the graph will be linear, resulting in a straight line.
Given when x = 8/7, y = 1/7
The general equation for direct variation is
y = mx
m = x/y = ( 8/7 ) / ( 1/7) = 8
Therefore the equation for direct variation for the given question is
y = 8x
To learn more about direct variation, follow the link.
https://brainly.com/question/10617012
#SPJ1
Plot a scatter plot showing the relationship between father and offspring telomere length.a. Do the data require any transformation before analysis? How can you tell?
b. Fit a linear regression that predicts the offspring telomere length from its father's. Is there evidence that the father's telomere length predicts his offspring's value?
The linear regression that predicts the offspring is The regression equation is y = 0.2134x + 0.513 and the box plot of the data is illustrated below.
The term called box plot is defined as a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.
Here we have know that a scatter plot showing the relationship between father and offspring telomere length.
Then the box plot of the data is plotted as follows.
=> 0.281, 0.301, 0.282, 0.425, 0.463, 0.514, 0.506, 0.535, 0.556, 0.59, 0.49, 0.435, 0.482, 0.504, 0.524, 0.487, 0.554, 0.588, 0.631, 0.664, 0.698, 0.513
Then the linear regression is written as
=> y = 0.2134x + 0.513
To know more about box plot here.
https://brainly.com/question/1523909
#SPJ4
what is the finest grain in statistics
The finest-grain property simply means that all possible distinguishable outcomes are identified separately in probability statistics.
The requirement that outcomes be mutually exclusive says that if one outcome occurs, then no other outcome also occurs.
An outcome is often called a finest grain result of the model in the sense that an outcome ω contains no subsets other than the empty set ϕ and the singleton subset {ω}. A sample space is a set of all the possible outcomes or sample points, denoted as Ω. An outcome ω is often called a finest grain result when even {ω} contains no proper subsets. The outcomes in the sample space are mutually exclusive and collectively constitute the entire sample space.
Learn more about the statistics and probability here :
https://brainly.com/question/27342429
#SPJ4
The complete question is :
what is the finest grain property in statistics?
It takes 1 work day to repair 300m of road. At this rate how many days will it take to repair 30km of road?
Answer:
100 days
Step-by-step explanation:
We know
1km = 1000m
30km = 30000m
It takes 1 work day to repair 300m of the road.
30000 divided by 300 = 100 days
So, it takes 100 days to repair 30km of road.
I NEED HELP ON THIS ASAP!!
How many boxes would Alan have to sell to earn less than $2050?
Alan has to sell 540 boxes to earn less than $2050
What is linear model?A linear model is an equation that describes a relationship between two quantities that show a constant rate of change.
Given is graph that represent the relation between the total sales and number of boxes sold,
The linear model for same is given by =
f(b) = 3.75b + 25
We need to find, how many boxes would Alan have to sell to earn less than $2050,
Here, we have, f(b) = $2050
Therefore,
$2050 = 3.75b + 25
3.75b = 2025
b = 540
Hence, Alan has to sell 540 boxes to earn less than $2050,
Learn more about linear model, click;
https://brainly.com/question/29757372
#SPJ1
dr. maldari would like to study the relationship between room lighting and college students' test performance. he randomly assigns students to two groups. the first group takes an exam in a dimly lit room and the second group takes the same exam in a regularly lit room. which is the control group?
In this study, the group of students who take the exam in a regularly lit room can be considered the control group.
The control group provides a baseline or comparison for the experimental group (the group of students who take the exam in a dimly lit room). The control group helps to establish a cause-and-effect relationship between the independent variable (room lighting) and the dependent variable (test performance), as any observed differences in test performance between the two groups can be attributed to the difference in lighting conditions.
By having a control group, the researcher can ensure that any observed effects are due to the independent variable and not due to extraneous variables.
To know more about control group refer to:
brainly.com/question/25801453
#SPJ4
17 students said they enjoy summer the most.
4 of the girls said they enjoy winter.
The ratio between boys and girls is 8 : 11.
The probability of picking a student at random who enjoys Summer is 17/38
Twice as many of the girls chose summer over spring.
7 boys chose summer.
Autumn was chosen by 3 more boys than girls.
The probability of picking a boy at random who chose spring is 18.75%
The total number of boys is 19, out of them 1 spring, 7 summers, 10 autumn leaves 1 to pick winter.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given that there are 17 total summer lovers and 7 boys/summer, we know 10 girls like summer.
girls' summer then, so 10/2 is 5 girls' choice.
Since there are 17 total summer lovers and 7 boys/summer, we know 10 girls like summer and Two girls picked summer over spring,
so, 10/2 is 5 girls picking spring.
The last clue says that if you pick a spring lover, there is an 18.75% chance of it being a boy, so x/(x+5)=0.1875 x=1.
38% of interviewed students preferred summer, so: 17/x = 0.38 Total students= 45
We know that for every 8 guys, there are 11 girls.
So if we fiddle around with scaling that ratio to find the combination that adds up to 45, we get a scale of 2.35.
2.35*8=19 and 2.35*11=26
So the total number of girls is 26, meaning the number of girls/in autumn is 26-5-4-10=7
Three more boys chose autumn than the girls, so 10 boys/autumn.
Therefore, The total number of boys is 19, out of them 1 spring, 7 summers, 10 autumn leaves 1 to pick winter.
Learn more about ratios here:
https://brainly.com/question/13419413
#SPJ1
premise 1: you don’t know how to drive. premise 2: you don’t like the smell of pizza. The conclusion is?
The conclusion is that it is not necessary to learn how to drive in order to enjoy the smell of pizza.
In order to draw a conclusion from two given premises, you must identify the relationship between them. In this case, the two premises are unrelated. The first premise states that you don't know how to drive and the second states that you don't like the smell of pizza. Since there is no relationship between these two premises, there is no conclusion that can be drawn from them. However, you can draw a conclusion based on the absence of a relationship. In this case, the conclusion is that it is not necessary to learn how to drive in order to enjoy the smell of pizza. This is because the two premises have no bearing on each other and, therefore, learning how to drive does not necessarily lead to enjoying the smell of pizza.
Learn more about conclusion here
https://brainly.com/question/14897697
#SPJ4
One of the tables shows a proportional relationship.
Graph the line representing the proportional relationship from this table.
ASAP PLEASE, FIRST CORRECT ANSWER GETS BRAINIEST
The third table shows a proportional relationship. Its graph is shown below.
How to Determine a Table that Represents a Proportional Relationship?A table of a proportional relationship is a set of pairs of values of the two variables involved in the relationship, where one variable is proportional to the other.
If the relationship between the variables on a table is proportional, the values in the table will form a straight line when plotted on a graph.
The constant of proportionality (k) for the third table = y/x = 2. Therefore it represents a proportional relationship.
The graph of the table is shown below.
Learn more about the proportional relationship on:
https://brainly.com/question/28777033
#SPJ1
[tex](2x3)²- 7[/tex]
Answer:
4x⁶ - 7
Step-by-step explanation:
[tex] \sf{( {2x}^{3} )}^{2} - 7[/tex]
[tex] \sf( {2}^{2} \times {x}^{3 \times 2} ) - 7[/tex]
[tex] \sf {4x}^{6} - 7[/tex]
Thank you so much for the answers
The graphs for g(x) = 2x + 7 is produced from graphs equation f(x) = 2x by such a vertically adjustment pushed upwards towards 7 units.
What purposes do graphs serve?Graphs and tables are useful visual aids because they make information accessible and easy to understand. Therefore, it is not unexpected that both print and digital media frequently employ graphs.
An graphs with g(x) = 2x + 7 is produced by vertically translating the graphs of f(x) = 2x upwards through 7 units. A graph's vertical translation simply shifts it up or down the y-axis without altering its form. To create that graphs of g(x) = 2x + 7, the graphs from f(x) = 2x is in this case pushed upward 7 units. To visualize this, imagine starting with the graph of f(x) = 2x, and then moving all the points on the graph upward 7 units along the y-axis. The resulting graph is the graph of g(x) = 2x + 7.
To know more about Graph visit :
https://brainly.com/question/9182097
#SPJ1
Write the equation of the ellipse with center (3,1), vertex (7,1) and focus (3+2sqrt3,1)
Check the picture below, so the ellipse looks more or less like so, with a major axis of 4, namely a = 4, and a "c" distance of 2√3, so
[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=3\\ k=1\\ a=4 \end{cases}\implies \cfrac{(x- 3)^2}{ 4^2}+\cfrac{(y- 1)^2}{ b^2}=1[/tex]
[tex]\stackrel{\textit{we know that}}{2\sqrt{3}=\sqrt{4^2 - b^2}}\implies \sqrt{12}=\sqrt{4^2 - b^2}\implies 12=16-b^2\implies 12+b^2=16 \\\\\\ b^2=4\hspace{5em}\cfrac{(x- 3)^2}{ 4^2}+\cfrac{(y- 1)^2}{ 4}=1\implies \boxed{\cfrac{(x- 3)^2}{ 16}+\cfrac{(y- 1)^2}{ 4}=1}[/tex]
The equation of the ellipse with center (3,1), vertex (7,1), and focus (3+2√3,1) is (x - 3)² / 16 + (y - 1)² / 4 = 1.
To write the equation of the ellipse with the given center (3,1), vertex (7,1), and focus (3+2√3,1), to determine some key properties of the ellipse.
Center (h, k) = (3, 1)
The center of the ellipse is (h, k) = (3, 1).
Major axis length = 2 × distance between center and vertex
The distance between the center and vertex is given by |3 - 7| = 4 units.
So, the major axis length is 2 × 4 = 8 units.
Distance between center and focus = c = |3 + 2√3 - 3| = 2√3 units
Now, we have all the information needed to write the equation of the ellipse in standard form:
(x - h)² / a² + (y - k)² / b² = 1
where (h, k) is the center of the ellipse, and a and b are the semi-major and semi-minor axes lengths, respectively.
Since the center is (3, 1), (h, k) = (3, 1). We already know that the major axis length is 8 units, so a = 4.
To find b, we use the relationship between a, b, and c in an ellipse:
c² = a² - b²
(2√3)² = 4² - b²
4 × 3 = 16 - b²
12 = 16 - b²
b² = 16 - 12
b² = 4
b = 2
Now we have the values of a and b, so the equation of the ellipse is:
(x - 3)² / 4²+ (y - 1)² / 2² = 1
Simplifying further:
(x - 3)² / 16 + (y - 1)² / 4 = 1
To know more about equation here
https://brainly.com/question/29657983
#SPJ2
At a basketball game, a team made 55 successful shots. They were a combination of 1- and 2-point shots. The team scored 91 points in all. Write and solve a system of equations to find the number of each type of shot.
Answer:
We can use a system of equations to solve this problem. Let x be the number of 1-point shots and y be the number of 2-point shots.
The first equation represents the total number of shots taken:
x + y = 55 (1)
The second equation represents the total number of points scored:
x + 2y = 91 (2)
To solve for x and y, we can use the first equation to substitute for one of the variables in the second equation. Using (1) to substitute for x in (2):
y = 55 - x
Then substitute this value of y in equation (1)
x + (55 - x) = 55
Solving for x, we get:
x = 20
So the team made 20 1-point shots and 35 2-point shots.
Answer:
There are:
19 1-point shots
36 2-point shots
Step-by-step explanation:
Solve for the system of equations. The first equation will give you the value based on the total amount of points, while the other equation will be based on the amount of shots in total:
It is given that the team scores 91 points in all, and that they are all 1- and 2- point shots (no 3 pointers). Set the equation. Let x = 1-point shots, and y = 2-point shots:
x + y = 55
1x + 2y = 91
First, isolate the variable, y, in the first equation. Subtract x from both sides of the equation:
y + x = 55
y + x (-x) = 55 (-x)
y = 55 - x
Next, plug in 55 - x for y in the second equation:
x + 2y = 91
x + 2(55 - x) = 91
Then, simplify. First, distribute 2 to all terms within the parenthesis:
2(55 - x)
= (2 * 55) - (2 * x)
= 110 - 2x
x + 110 - 2x = 91
First, combine like terms. Like terms are terms that share the same amount of the same variable:
(x - 2x) + 110 = 91
-x + 110 = 91
Then, isolate the variable, x. First, subtract 110 from both sides of the equation:
-x + 110 (-110) = 91 (-110)
-x = 91 - 110
-x = -19
Isolate the variable, x, completely, by dividing -1 from both sides of the equation:
(-x)/-1 = (-19)/-1
x = -19/(-1)
x = 19
~
Plug in 19 for x in one of the given equations in the system of equations:
x + y = 55
19 + y = 55
Isolate the variable, y, by subtracting 19 from both sides of the equation:
y + 19 = 55
y + 19 (-19) = 55 (-19)
y = 55 - 19
y = 36
~
There are 19 1-point shots & 36 2-point shots
Learn more about solving for system of equations, here:
https://brainly.com/question/13997560
Find the cofactors of A, place them in the matrix C, then use ACT to find the determinant of A, where: [1 1 47 A= 1 2 2 1 2 5]
The cofactor of A is C = [-3 0; 0 -46], and the determinant of A is -3.
The cofactor of each element in a 2x2 matrix is found by switching the signs of the elements in the determinant when the sum is taken (i.e. changing the sign of one element in the determinant if it is in an odd-numbered row or column).
For a 2x2 matrix A = [a b; c d], the determinant is given by det(A) = ad - bc.
For the given matrix A = [1 1 47; 1 2 2; 2 5 1], the cofactor matrix C is found by finding the determinant of each 2x2 sub-matrix obtained by excluding one row and one column of A.
C = [(-1)(2-5) (1)(2-2); (1)(1-1) (-1)(1-47)].
C = [-3 0; 0 -46].
To find the determinant of A using the cofactor matrix C, we take the sum of the products of the elements in each row of A and the corresponding elements in each column of C.
det(A) = 1*-3 + 10 + 470 + 10 + 20 + 2*-46 = -3.
So the determinant of A is -3.
To learn more about cofactor here:
https://brainly.com/question/28207649
#SPJ4
Determine which set of side measurements could be used to form a triangle.
The set of side measurement that will form a triangle is 8, 9 and 15.
How to find the side of a triangle?A triangle is a polygon with 3 sides. The sum of angles in a triangle is 180 degrees.
Therefore, the triangle inequality theorem can be used to know the length of sides that can form a triangle.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
If the length are a, b and c. Therefore,
a + b > c
a + c > b
b + c > a
Therefore, applying this principle the measurement that will form a triangle is 8, 9 and 15.
learn more on triangle here: https://brainly.com/question/29362574
#SPJ1
Determine the value of y if x -4 y=x^(2)-8
The numerical value of y in the equation y = x² - 8 when x = -4 is 8.
What is the numerical value of y when x = -4?Given the equation in the question;
y = x² - 8
x = -4y = ?To determine the numerical value of y, replace all the occurrence of x with -4 in the equation and simplify.
y = x² - 8
Plug in x = -4
y = ( -4 )² - 8
First take the square of -4
y = 16 - 8
Subtract 8 from 16
y = 8.
Therefore, the value of y is 8.
Learn to solve more equation here: https://brainly.com/question/9236233
#SPJ1
a. For what value of c is the quantity Sum(x_1- c)^2 minimized? [Take the derivative with respect to c, set equal to 0, and solve.]
b.Using the result of part (a), which or the two quantities Sum(x, - x)^2 and Sum(x_i - mu)^2 will be smaller than the other (assuming that x yu,)?
Minimizing the Sum of Squared Deviations
In statistics, the objective of many analyses is to identify the values of parameters that minimize the sum of squared deviations between observed and expected values. A common example of this is finding the mean (average) of a set of values. In this context, the deviations are calculated as the difference between each observed value and the mean.
In the problem stated above, we have a sum of squared deviations given by the expression (x_1 - c)^2. The goal is to find the value of c that minimizes this expression. To do this, we will take the derivative of the expression with respect to c, set it equal to 0, and solve for c.
Taking the derivative with respect to c:
The derivative of (x_1 - c)^2 with respect to c is 2 * (x_1 - c) * (-1) = 2 * (c - x_1). Setting this equal to 0 and solving for c:
2 * (c - x_1) = 0
c = x_1
So, the value of c that minimizes the expression (x_1 - c)^2 is equal to x_1.
Comparing Sum(x_i - mu)^2 and Sum(x_i - x_1)^2:
Now, let's consider the two quantities Sum(x_i - mu)^2 and Sum(x_i - x_1)^2. Assuming that mu is the population mean and x_1 is a sample mean, we can say that Sum(x_i - mu)^2 will always be equal to or larger than Sum(x_i - x_1)^2. This is because the sample mean is an unbiased estimator of the population mean and has a smaller variance than the population mean. In other words, the sample mean will be closer to the observed values, on average, than the population mean, leading to smaller deviations and a smaller sum of squared deviations.
Here you can learn more about Deviations
https://brainly.com/question/29750046#
#SPJ11
