select the subset(s) that are subspaces. the set of all vectors in of the form where are real numbers all polynomials in that have a non-zero term. the set of all matrices of the form where . the set of all vectors in whose endpoint lies on the line .
Subsets 1 and 3 are subspaces, while subsets 2 and 4 are not.
How to determine which subsets are subspaces?To determine which subsets are subspaces, we need to check if they satisfy the three conditions of being a subspace:
closure under addition, closure under scalar multiplication, and containing the zero vector. Let's evaluate each subset:
The set of all vectors in ℝ³ of the form (a, b, c) where a, b, c are real numbers:This subset is a subspace. It satisfies closure under addition, closure under scalar multiplication, and contains the zero vector (0, 0, 0). Therefore, it is a subspace of ℝ³.
The set of all polynomials in ℝ[x] that have a non-zero term:This subset is not a subspace. While it satisfies closure under addition, it fails to satisfy closure under scalar multiplication. If we multiply a polynomial with a non-zero term by zero, the result will not have a non-zero term. Therefore, it does not contain the zero vector, violating the subspace condition.
The set of all matrices of the form [a, b; c, d] where a, b, c, d are real numbers:This subset is a subspace. It satisfies closure under addition, closure under scalar multiplication, and contains the zero matrix [0, 0; 0, 0]. Hence, it is a subspace of the space of 2x2 matrices.
The set of all vectors in ℝ² whose endpoint lies on the line y = 2x:This subset is not a subspace. It fails to satisfy closure under scalar multiplication.
If we scale a vector whose endpoint lies on the line y = 2x by a non-zero scalar, the endpoint will no longer lie on the line y = 2x.
Thus, it does not contain the zero vector, violating the subspace condition.
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What is the answer to this equation 4(x-3)=20
Step-by-step explanation:
X=8 if that's what you are asking
Answer:
x=8
Step-by-step explanation:
First distribute the 4
4x-12=20
Then add 12 to both sides
4x=32
Then divide both sides by 4
x=8
Find three consecutive numbers whose sum is 84.
You need 3 numbers, divide the total by 3:
84/3 = 28
This is the middle value.
Now you use the one lower and the one higher:
27 + 28 + 29 = 84
The numbers are 27, 28, 29
Answer: 26, 28, 30
Step-by-step explanation:
26, 28, and 30 follow each other in consecutive order without haps of more than two and are arranged smallest to largest.
the graph of part of linear function G is shown on thw grid. which inequality best represents the range of the part shown?
the price p of a pizza is 6.95 plus 95. for each topping t on the pizza
James washes cars to earn money. He charges $7.00 per compact car, $10.00 per mid -sized car, and $15.00 per SUV. On Saturday, he washed 3 compact cars, 4 mid-sized cars, and 2 SUVs. How much money did he earn?
Answer:
$91.00
Step-by-step explanation:
From the above question, we obtained the following information.
James charges:
1 compact car = $7.00
1 mid sized car = $10.00
1 SUV = $15.00
On Saturday, he washed:
a) 3 compact cars
1 compact car = $7.00
3 compact cars = ?
= $7.00 × 3
= $21.00
b) 4 mid-sized cars
1 mid- sized car = $10.00
4 mid-sized cars = ?
= $10.00 × 4
= $40.00
c) 2 SUVs.
1 SUV = $15.00
2 SUVs = ?
= $15.00 × 2
= $30.00
How much money did he earn?
$21.00 + $40.00 + $30.00
= $91.00
Therefore, James earned $91.00
The administrator of a new paralegal program at Seagate Technical College wants to estimate the grade point average in the new program. He thought that high school GPA, the verbal score on the Scholas
The administrator of a new paralegal program at Seagate Technical College wants to estimate the grade point average in the new program. A grade point average (GPA) is a measure of scholastic achievement earned over a defined period, typically one term or semester or an entire academic year.
The administrator of a new paralegal program at Seagate Technical College wants to estimate the grade point average in the new program. He thought that high school GPA, the verbal score on the Scholas (a college admissions test), and the numerical score on the Scholas (a college admissions test) might be good predictors of the grade point average in the new program.
A grade point average (GPA) is a measure of scholastic achievement earned over a defined period, typically one term or semester or an entire academic year. The higher the GPA, the more significant the achievement. It is a calculated average of the grades obtained by the student in all of their classes. Grades received in Honors or Advanced Placement (AP) courses may have a higher point value when calculated to determine a GPA.
The administrator of a new paralegal program at Seagate Technical College wanted to estimate the GPA in the new program. He considered the high school GPA, the Scholas' verbal score, and the Scholas' numerical score as possible predictors of the grade point average in the new program. However, it would be beneficial to have more information about the administrator's hypothesis and the study's design before answering more thoroughly about the question.
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the average college student in the united states spends 145 minutes per day studying, according to a 2014 research study of national student engagement. suppose students at glendale college test the hypothesis that glendale students spend more than 145 minutes per day studying. suppose students distribute a survey to a random sample of 25 students enrolled at the college. suppose the students have the results shown in the plot below:dotplot with a central peak and a left tail that is only slightly longer than the right tailonce they have collected the data, the students get into a disagreement about the next steps for their research analysis.true or false? the students should use a t-test to analyze the significance of the data they collected.
The students should use a t-test to analyze the significance of the data they collected is a true statement.
In this scenario, the population standard deviation is unknown and the sample size is small (n=25). Therefore, a t-test should be used instead of a z-test. The t-test is a statistical hypothesis test that is used to determine if there is a significant difference between the means of two groups when the sample size is small and/or the population standard deviation is unknown.
Using a t-test will allow the students to analyze the significance of their data in a more appropriate and accurate way, taking into account the small sample size and the fact that they do not know the population standard deviation.
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Question 4.
A high school sports team is ordering sports drinks online from a company. The price of sports drinks varies, based on the number of drinks purchased. For orders of 50 or fewer sports drinks, the price is $0.80 per drink, plus $10 shipping and handling. When more than 50 sports drinks are ordered, the price is $0.70 per drink, plus $15 shipping and handling. What is the maximum amount of sports drinks you can purchase for $75?
A. 85
B. 81
C. 92
D. 107
Using the equatiοns, we fοund that the maximum amοunt οf spοrts drinks yοu can purchase fοr $75 is 86.
What is meant by an equatiοn?A mathematical equatiοn is a fοrmula that uses the equals symbοl (=) tο cοnnect twο expressiοns and express their equality. The definitiοn οf an equatiοn in algebra is a mathematical statement that prοves twο mathematical expressiοns are equal. LHS = RHS (left-hand side = right-hand side) appears in all mathematical equatiοns. Yοu can sοlve equatiοns tο determine an unknοwn variable's value, which cοrrespοnds tο an unknοwn quantity. It is nοt an equatiοn if there is nο "equal tο" sign in the statement. That shall be taken intο accοunt as an expressiοn.
Let,
the number οf drinks = x
the tοtal cοst οf the x drinks = y
Then we can write equatiοns using the given infοrmatiοn.
When the οrder cοntains 50 οr fewer spοrts drinks, the equatiοn is:
y = 0.8x + 10
When the οrder cοntains mοre than 50 spοrts drinks, the equatiοn is:
y = 0.7x + 15
Since we have tο find the number οf drinks fοr $75, we can write that:
y = 75
Substituting in the equatiοns,
75 = 0.8x +10
65 = 0.8x
x= 81.25 = 81
75 = 0.7x +15
60 = 0.7x
x = 85.7 = 86
Nοw, 86 > 81
Therefοre using the equatiοns, we fοund that the maximum amοunt οf spοrts drinks yοu can purchase fοr $75 is 86.
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Please open the document to see the picture of the triangle. Find the area of the triangle. Remember: 1/2bh (1/2 x b x h). Also, remember to label your answer.
Answer:
So the answer is 12cm square
Step-by-step explanation:
Base is 6cm and hight is 4 so 6×4 is 24÷2 is 12
At work, Nick lifts packages that weigh 50 pounds each. A package consists of 2 small speakers, 2 large speakers, and a subwoofer. The small speakers and subwoofer together weigh 22 pounds. The large speakers weigh n pounds each, as expressed in this equation. 50 = 2 n + 22 What is the weight of each large speaker?
Weight of the each large speaker from the linear equation 50=2n+22 will be 14 kg.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
As Given linear equation 50=2n+22
where n=weight of large speakers 22=weight of small speakers and subwoofer together and 50=weight of whole package.
Therefore,
2n=28
n=14
Hence,
Weight of the each large speaker from the linear equation 50=2n+22 will be 14 kg.
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Let A be the set of all strings of decimal digits of length 5. For example 00312 and 19483 are two strings in A. You pick a string from A at random. What is the probability that the string has no 4 in it
Answer:
0.59049
Step-by-step explanation:
Set of all digit strings of length 5
Digit range = (0 - 9) = 10
Length of digit = 5
Total possible outcomes = 10^5 = 100000
String without a 4 ;
Digit range = (0,1,2,3,5,6,7,8,9) = 9
Length of digit = 5
Required outcome = 9^5 = 59049
Required outcome / Total possible outcomes
59049 / 100000
= 0.59049
Which function translates each point on the graph of y=mx+b so that the slope of the segment from the original point to the translated point is 43?
Answer:
s(x)=32mx+b
Step-by-step explanation:
It should be this
Simplify.
Rewrite the expression in the form b^n
(b^3)^2
Answer: b⁶
Step-by-step explanation:
The for bⁿ can be optained by multiplying 3 and 2. If there is an exponent on the outside of the parenthesis, you multiply it with the exponent on the inside.
(b³)²=b³ˣ²=b⁶
The height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet. Find the length of the base and the height of the triangle
Answer:
Step-by-step explanation:
The length of the base is 3 feet and the height of the triangle is 6 feet.
What is the area of a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.
Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.
The dimensions of the triangle will be calculated as,
A = (1/2) x b x h
A = (1/2) x b x ( b + 3 )
54 = ( 1 / 2 ) x ( b² + 3b )
108 = ( b² + 3b )
( b² + 3b - 108) = 0
( b² + 12b -3b -108 ) = 0
(b - 3 ) ( b+ 12 ) = 0
b = 3 and b = -12 ignore negative value.
The height will be calculated as,
h = b + 3
h = 3 + 3
h = 6 feet
Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.
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what is the sum of 3/20+ the square root of 10
Answer:
3.31
Step-by-step explanation:
sqr 10 = 3.16
3/20 = .15
3.16+ .15
3.31
Which of the following correctly translates "quotient"?
A. addition
B. division
C. multiplication
D. subtraction
Answer:
B. division
Step-by-step explanation:
quotient is the result of a division
Answer: B. division
Four more than five times a number is -16. What's the number
please help me this assignment is already late
Which expression best estimates 6 and three-fourths divided by 1 and two-thirds?
A) 7 divided by 2
B) 6 divided by 1
C) 8 divided by 3
D) 3 divided by 2
The expression that best estimates 6 3/4 divided by 1 2/3 is 7/2. 6 3/4 (or 6.75) divided by 1 2/3 (or 1.66...) comes out to 4 1/20 (or 4.05). The closest value to this in the options available is 7/2 (or 3.5). This answer is only .55 away from the correct value, while the rest of the options are far less close.
Answer:
7/2 or
7 dived by 2
Step-by-step explanation:
bruh A
10) A submarine starts on the surface, and dives at an angle of depression of 13° from the surface. It goes
diagonally a distance of 890 meters before reaching the bottom. How deep is the water where the submarin
reaches the bottom? (Drawing 1 pt, distance 1.5 pts, units .5 pt)
890
The water where the submarine reaches the bottom is approximately 212.43 meters deep.
To determine the depth of the water where the submarine reaches the bottom, we can use trigonometry.
The angle of depression of 13° tells us that the submarine is diving at an angle below the horizontal line.
The distance traveled diagonally, which is 890 meters, represents the hypotenuse of a right triangle.
Using trigonometric functions, we can find the length of the adjacent side, which represents the depth of the water.
In this case, we can use the tangent function:
tan(13°) = opposite/adjacent
We know the opposite side is the depth we're trying to find, and the adjacent side is the distance traveled diagonally.
Solving for the depth:
\(depth = 890 \times tan(13) \approx 212.43 meters\).
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Kristen baked a pan of brownies for a potluck. The number of squares she cuts the brownies
into will depend on the number of people attending the potluck.
s = the number of squares Kristen cuts the brownies into
p = the number of people attending the potluck
Which of the variables is independent and which is dependent?
A. p is the independent variable and s is the dependent
variable
B. s is the independent variable and p is the dependent
variable
Answer:
A. p is the independent variable, and s is the dependent variable.
Step-by-step explanation:
In this scenario, the number of people attending the potluck is the independent variable because it is the variable that is being controlled or determined before the brownies are cut. The number of squares the brownies are cut into, on the other hand, depends on the number of people attending the potluck. Therefore, the number of squares is the dependent variable in this scenario.
solve the simultaneous equations y=3x+2 and y=x+6
Answer:
x=2
Step-by-step explanation:
y=3x+2
y=x+6
Since you're stating that, they both equal because equation is equated to equation 2 because of the Y.
Therefore, substitute into both equations as shown:
3x+2=x+6
3x-x=6-2 (bring 2 to the other side by subtracting 2 as well as x)
2x=4
2x/2=4/2 (dividing 2 on both sides to get rid off 2 in 2x)
x=2.
The solution of the given system of equations y=3x+2 and y=x+6 using the substitution method will be x = 2 and y = 8.
What is the equation?More than one variable may be present inside a linear equation.
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given system of equations,
y=3x+2 and y=x+6
Compare both values,
3x + 2 = x + 6
3x - x = 6 - 2
x = 4/2 = 2
And, y = 2 + 6 = 8
Hence "The solution of the given system of equations y=3x+2 and y=x+6 using the substitution method will be x = 2 and y = 8".
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What is the probability of rolling a number less than 6 on a 20-sided die?
Tim is choosing between two cell phone plans that offer the same amount of free minutes. Cingular’s plan charges $39.99 per month with additional minutes costing $0.45. Verizon’s plan costs $44.99 with additional minutes at $0.40. How many additional minutes, a, will it take for the two plans to cost the same?
Help me out and show work for this!
Answer: 100 minutes.
Step-by-step explanation:
Make both equations equal each other:
39.99 + 0.45m = 44.99 + 0.40m
Wash out some of the clutter by finding combining like terms:
0.05m = 5
Now, divide by the coefficent of x:
\(\frac{0.05m}{0.05} = \frac{5}{0.05}\)
m = 100
it takes jesse four times as long to edit a chapter in a book as it takes curtis. if it takes curtis t hr to edit the chapter, at what rate does jesse do the job? write your answer as a single fraction in exact simplest form.
The rate at which Jesse did the job is 1/4t chapter/hour
What is rate?A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.
It takes Jesse four times as long as Curtis to edit a chapter
if takes Curtis t hrs, then,
it will take Jesse 4t hours
therefore the rate of Jesse = 1 chapter/4t hours
= 1/4t chapter/hour
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please help me with this question
Answer:
V = 3 * 3 * 7 + 2 * 3 * 5 = 63 + 30 = 93 just adding 2 segments
A line has a slope of -2/3and passes through the point (-3, 8). What is the equation of the line?
O y=-2/3x+6
o y=-2/3x+8
0 y = 6x-2 / 3
O y=8x - 2/3
Answer:
y = -2/3 + 6
Step-by-step explanation:
Slope = -2/3
Point (- 3, 8)
b = 8 - (-2/3)(-3)
= 8 - 2
= 6
how does an individual affect the society
Answer:
When a individual tries and modifies their bodies away from the knowledge of the society, it makes no difference. However, when individual tries to modify the society by habits and behavior, it creates a social impact.
Step-by-step explanation:
Hope it helps :)
help meh pls i give brainiest
numbers:
2, 4, and 5
I am so sorry if i'm wrong!!! :|