Answer:
43
Step-by-step explanation:
172/4= 43
Hehe. Suppose 3 < a < 4 and 4
If 3 < a < 4 and 4 then, 3 < a ≤ 4 is the relationship.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, A number 'a' which is 3 < a < 4 and 4.
This implies that the number 'a' is less than or equal to 4.
∴ 3 < a ≤ 4.
Q. Suppose 3 < a < 4 and a is also equal to 4, write this statement in inequality form.
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An amusement park charges an admission fee of 40 dollars per person. The cost, C (in dollars), of admission for a group of p people is given by the following.
C=40 p
What is the cost of admission for a group of 4 people?
_____dollars
The cost of admission for a group of 4 people is $160
How to determine the cost of admission for a group of 4 people?From the question, we have the following parameters that can be used in our computation:
C = 40 p
Where p is the number of people
For a group of 4 people, we have
p = 4
Substitute p = 4 in the equation C = 40 p
So, we have the following representation
C(4) = 40 * 4
Evaluate the products
C(4) = 160
hence, the cost is $160
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1.
What is the area of this figure?
Answer:
44 unit^2.
Step-by-step explanation:
Divide the figure into 2 trlangles, a rectangle and a trapezium
Area = 2 * 1/2 *4 * 3 + 2 ** + 1/2 * 8 * (1 + 3)
= 12 + 16 + 16
= 44.
An elephant weighed 14,000 pounds. The handlers realized the
elephant was overweight and put it on a special meal plan. The
elephant lost 2,100 pounds. What was the percent of decrease in its
body weight?
14000
The value of the decrease percentage of elephant weight is 15%.
What is percentage?A percentage is a value that indicates 100th part of any quantity. A percentage can be converted into a fraction or a decimal by dividing it by 100.
The original weight of elephant is 14000 pounds.
And, the drop in weight is 2100 pounds.
Now, the percent value of the drop in weight is calculated as follows
Percent drop = Drop in weight / Original weight × 100
⇒ 2100/14000 × 100
⇒ 15%
Hence, the percent of decrease in weight is given as 15%.
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Help me solve it the answer
The required top of the ladder from the ground is 7.14 ft.
What is a right angle triangle?A triangle is said to be right-angled if one of its internal angles is 90 degrees, or if any angle is a right angle.
To find the length in right angle triangle, use Pythagoreans theorem,
(hypotenuse)² = (base)² + (height)²
Given that,
The length of the ladder = 10 ft.
The distance of the house from the bottom of the ladder = 7 ft.
Let the length of the top of the ladder from ground is x ft.
To find the height of the ladder from the ground,
Use Pythagoreans theorem,
(hypotenuse)² = (base)² + (height)²
(10)² = (7)² + (x)²
100 = 49 + x²
x² = 100 - 49
x² = 51
x = 7.1414
or x = 7.14 ft
The top of the ladder from the ground is 7.14 ft.
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Please help me!!!!!!! You guys are my only hope!!! Correct answer gets brainliest
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug’s effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient’s can be given by the function C(t)=-5t^2+10t, where the time, t, is hours after injection.
Part A : What are domain and range of the function C(t) based on the context of the problem?
Part B : Graph the function to determine the greatest concentration of the medication that a patient will have in their body
The domain and range of the function are (-∞,∞) and (-∞,5). The greatest concentration will be 5.
What is the range and domain of a function?The set of all values that a function can accept is known as its range, while the set of all values for which a function is defined is known as its domain.
The dependent variable's range is its domain, which is for the independent variable.
Part (A)
As per the given function C(t) = - 5t² + 10t
C'(t) = 0
-10t + 10 = 0
10t = 10
t = 1
C''(t) = -10 < 0
So, at t = 1 the function will be maximum.
C(1) = -5(1)² + 10 x 1 = 5
Thus, the range will be (-∞,5) and the domain will be (-∞,∞).
The range represents the amount of concentration while the domain is the time.
Part (B)
The graph of the function has been drawn below.
At t = 1 the C(t) is maximum as 5 thus it will be the maximum concentration.
Hence"The function's domain and range are (-∞,∞) and (-∞,5), respectively. Five will have the highest concentration.".
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The length of diameter of the base of the cone will be 112 cm. Hence, option b is correct.
What is the Pythagoras Theorem in Math?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.Pythagoras, a Greek philosopher who was born around 570 BC, is remembered by the theorem's name. The theorem has likely been proved the most times of any mathematical theorem using a variety of techniques. The proofs are many, some of which go back thousands of years, and include both geometric and algebraic proofs.Given data :
As per the given information in the question,
Use the equation of Pythagoras's theorem,
106² = 90² + r²
r² = 106² - 90²
r = √3136
r = 56 cm.
Then, the diameter will be,
D = 2r
D = 2(56)
D = 112 cm.
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CAN SOMEONE PLEAE HELP!!!!
Here’s a picture
Answer: f(x) = 1
Step-by-step explanation:
They tell us what we need to do, we must substitute x for 0 in the original function to find the initial value.
[tex]f(x) = (\frac{1}{4} )^x[/tex]
[tex]f(x) = (\frac{1}{4} )^0[/tex]
[tex]f(x) = 1[/tex]
* Anything raised to the power of 0 is equal to 1.
Write an equation of the line that passes through (-1, 3) and is parallel to the line y = -3x + 2
Answer:
y -3 = -3(x +1)
Step-by-step explanation:
You want an equation for the line parallel to y=-3x+2 through the point (-1, 3).
Slope-intercept formThe given line is written in slope-intercept form:
y = mx +b . . . . . . . where m is the slope and b is the y-intercept
Matching your equation to this form, we see that ...
m = -3b = 2The parallel line will have the same slope: m = -3.
Point-slope formAnother form of the equation for a line is "point-slope form." That is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
Perhaps you can see this would be useful for writing the equation of a line with slope -3 through the point (-1, 3).
y -3 = -3(x +1) . . . . . . . line with slope -3 through point (-1, 3)
To ride the Metro, riders must pay $0.50 per stop plus a $2.00 ticket fee. If a rider rides the Metro for 6 stops, how much would their total ride be?
The required cost for the ride in the Metro is obtained as $5.
How to calculate the total cost?The total cost can be calculated by multiplying the cost for one unit to the number of units.The cost for one unit is also called as unit rate. This method is based on the unitary method which states that the value of n number of quantities is equal to the product of n and the value of one quantity.
The cost of the ticket is given as $2.
And, the cost per stop is $0.50.
Now, in order to find the total cost of riding for 6 stops take the sum of fixed cost of ticket and the total cost for 6 stops as follows,
The cost of ticket + The cost for 6 stops
= 2 + 6 × 0.50 = 5
Hence, the cost for the total ride of the rider is $5.
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I just need help with this one
The spending would reach a figure of 1868 billon in the year 2031.
When would the spending reach 1868 billion dollars?We know that we can be able to use a function to be able to show the relationship between variables and it can also serve as a model. In this case, we are modelling the spending by the use of the equation;
y = 1.48x^2 - 25.23x + 416.91
Let x be the number of years since 1990. Then we have that;
1868 = 1.48x^2 - 25.23x + 416.91
1.48x^2 - 25.23x - 1451.1 = 0
When we solve the quadratic we have;
x = 41
In 41 years after 1990, the government spending would reach 1868 billon and that would be in 2031.
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Jacob is traveling down a level roadway with a speed of 9.5 m/s. He slams on the breaks and encounters a coefficient of friction of 0.847. What distance does his 985 kg truck skid before stopping?
To find the distance that Jacob's truck skids before coming to a stop, we can use the formula for the distance traveled while braking, which is:
distance = initial velocity^2 / (2 * coefficient of friction * acceleration due to gravity)
In this case, the initial velocity is 9.5 m/s, the coefficient of friction is 0.847, and the acceleration due to gravity is 9.8 m/s^2. Plugging these values into the formula, we get:
distance = (9.5 m/s)^2 / (2 * 0.847 * 9.8 m/s^2)
Solving for distance, we get:
distance = 8.76 meters
Therefore, Jacob's truck will skid a distance of 8.76 meters before coming to a stop.
en singers have signed up for a signing competition. The order in which they will compete is selected by random draw. Five of the signers will compete before an intermission and five will compete after the intermission. How many different ways are there for the five singers to be selected to sing before intermission? a. 40 b. 100,000 a. с. 252 d. 30,240
As a result, the singers can finish first, second, third, fourth, or fifth in 524,160 different ways.
Permutation, where order is important:
_nP_{r}=\dfrac{n!}{(n-r)!}
P r = (n−r)!n!
Combination of definitions (order is irrelevant):
_nC_{r}=\dfrac{n!}{r!(n-r)!}n C r equals r!(nr)!n!
with n!=n, cdot (n-1) ..., cdot 2..., cdot 1n!=n(n1)...2,1.
We want to know how many different ways we can choose five people from a group of 16 (ranked first, second, third, fourth, and fifth).
n=16 n=16 r=5 r=5 Because we are interested in the first, second, third, fourth, and fifth places, order is important (changing the first and second places results in different rankings and prizes for the people), so we need to use a "textbf permutation" permutation.
Analyze the permutation definition:
"Begin align*" means "16P_5" and "dfrac" 16! color#8895cetextDefinition combination &=dfrac16!11!&color#8895cetext Evaluate difference &=dfrac16cdot 15cdot 14cdot 13cdot 12cdot 11cdot 10cdot...cdot 111cdot 10...cdot 1
16!= 11!
16! = 11⋅10⋅...⋅1
16⋅15⋅14⋅13⋅12⋅11⋅10⋅...⋅1
=16⋅15⋅14⋅13⋅12
=524,160
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Full Question = There are 16 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers finish first through fifth?
Solve the following inequality using the algebraic approach:
x + 2 > 3x-8
Answer: x<5. Work shown below! :)
In a chi-square test for ________________ of proportions, we test whether different populations have the same proportion of individuals with some characteristic.
In a chi-square test for homogeneity of proportions,we test whether different populations have the same proportion of individuals with some characteristic.
What is chi-square test for proportions?Used to test whether different populations have the same proportion of individuals with a particular trait. Suppose we have three populations with four mutually exclusive characteristics. Randomly sample each population and create a crosstabulation or frequency table of the traits you are measuring. If you want to test whether there is an association between a population and a trait (for example, whether the population has a high frequency of one trait), perform a chi-square test to see if the result is significant must be confirmed.
If the chi-square test is significant, it only tells us that there is some relationship between the population and the trait, not how they are related. Also, not all traits need to be population related. For example, the chi-square test can be considered significant even if features A and B have very different distributions, and C and D have very different distributions, for different populations. If you want to measure whether a particular trait is influenced by the population, use an equal proportions test (I call it the z-test, or prop.test() in R) for exactly that trait. You can do. In other words, if the chi-square test reveals a significant relationship, it is appropriate to use prop.test() to more accurately determine the nature of the relationship between the two sets of categories.
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When constructing a perpendicular bisector of a segment, why should you make arcs with the same radius from each endpoint? Select the true statement.
a. this makes the arcs perpendicular to each other
b. this makes the arcs equidistant from each other
c. this makes the intersections of the arcs equidistant from the endpoints
d. this makes the arcs parallel to the segment
When constructing a perpendicular bisector of a segment, you should make arcs with the same radius from each endpoint as D. this makes the arcs parallel to the segment
What is a perpendicular bisector?A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90-degree angle.
A line segment known as a perpendicular bisector divides a straight line segment into two congruent or equal segments. At the exact midpoint of the line segment, they divide it. The arcs with the same radius from each endpoint is important as this makes the arcs parallel.
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A spinner is divided into five equal sections labeled 1, 2, 3, 4, and 5. Another spinner is divided into two equal sections labeled A and B. Nigel will spin each spinner one time.
How many of the possible outcomes have a number less than 3 or an A?
Hint: first write out the sample space (you should have 10)
Which samples have a number less than 3 or an A?
9/10 is the possible outcome that has a number less than 3 or an A.
What is probability?
The proportion of possible outcomes to outcomes in an exhaustive set of equally likely alternatives that result in a certain event.
Here, we have
A spinner is divided into five equal sections labeled 1, 2, 3, 4, and 5. Another spinner is divided into two equal sections labeled A and B.
We have to find how many of the possible outcomes have a number less than 3 or an A.
Denote A the first event and B the second event:
P(A∪B) = P(A) + P(B)
A = Get a number less than 3
P(A) = 2/5
B = Get section A
P(B) = 1/2
Then,
P(A∪B) = 2/5 + 1/2
P(A∪B) = 9/10
Hence, 9/10 is the possible outcome that has a number less than 3 or an A.
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find the mean, variance, and standard deviation for the number of heads when 17 coins are tossed. round your answers to three decimal places.
Factorials and the binomial theorem are utilized in the binomial distribution, a discrete probability distribution. Checking the sample space is the first step in deciding whether or not to use a binomial distribution with a given data set.
The binomial distribution would apply if there were multiple trials of the same experiment and only two outcomes in the sample space.
S=T,H,THT,H,THH,HTH,HHT,HHH in this case.
∴ n(S)=8.
Thus, the probability of each and every outcome is 18.
When tossing three coins, let X be the number of heads.
There can be 0, 1, 2, or 3 heads.
Therefore, X's possible values are 0, 1, 2, and 3.
P(X=0) = P (no head) = P(T) = 18.
P(X=1) = P (getting a single head) = P(HorTHTorH) = 38.
P (X=P (getting 2 P (THH, HTH, HHT)=38.
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7=y/3
Solve and create new equation
felipe graphs the linear relationship passing through the points 5,11 and -3,-9
slope -20/-8
line y = -5/2x - 3/2
it is NOT proportional because it doesnt pass thru 0,0
The correlation between two scores X and Y is equal to 0.8. If both the X scores and the Y scores are multiplied by 2, the correlation of the transformed scores would be:a) 1.6b) 0.4c) 0.8d) 0.16e) None of these
The correct answer is (C) 0.8. The correlation between two scores X and Y is equal to 0.8. If both the X scores and the Y scores are multiplied by 2, the correlation of the transformed scores would be 0.8.
The correlation between two variables measures the strength and direction of the linear relationship between them. It is calculated as the covariance of the two variables divided by the product of their standard deviations. When both the X scores and the Y scores are multiplied by 2, the covariance and standard deviations of the transformed scores are also multiplied by 2. Therefore, the correlation between the transformed scores is equal to the correlation between the original scores.
In this case, the correlation between the original scores is 0.8, and the correlation between the transformed scores is also 0.8.
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Given that the lines are parallel, which statement is true about angles x and y ?
Answer:
a. Angles x and y are supplementary because they are same side interior angles.
Angles x and y are supplementary because they are same side interior angles.
What is transversal?A line that goes through two lines in the same plane at two different points is called a transversal. When determining whether two or more other lines in the Euclidean plane are parallel, transversals play a role. Different kinds of pairs of angles are created when two lines intersect a transversal: alternate angles, corresponding angles, consecutive exterior angles, and consecutive interior angles. If the two lines are parallel, Euclid's parallel postulate states that consecutive interior angles are supplementary, that corresponding angles are equal, and that alternate angles are equal.
Given lines are parallel and cut by a transversal,
and to find the statement for x and y
in figure x and y are interior side of both lines
statement for x and y is
Interior angles on the same side of a transversal are supplementary if it cuts through two parallel lines. Exterior angles on the same side of a transversal are supplementary if it cuts through two parallel lines.
Hence x and y are supplementary angles.
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The perimeter of a rectangle is 38". If the
length is 3" more than the width, find the
width:
9-A 17 1/2"
9-B 8"
9-C
11"
9-D 14 1/2"
Answer:
Length = 11" and width = 8".
Step-by-step explanation:
let L be the length of the rectangle
and w be its width.
Formula (perimeter P of a rectangle) :
P = 2 × (L + w)
================================
Then
L = w + 3
and
P = 2 × (L + w)
= 2 × (w + 3 + w)
= 2 × (2w + 3)
= 4w + 6
Solving the equation P = 4w + 6 for w :
P = 4w + 6
⇔
38 = 4w + 6
⇔
32 = 4w
⇔
w = 32 ÷ 4
= 8
Determining the length L :
L = w + 3
⇔
L = 8 ÷ 3
= 11
Conclusion:
L = 11 and w = 8
Answer:
Width = 8"
Step-by-step explanation:
2(t+w) = 38 Eq. 1
t = w+3 Eq. 2
t = length
w = width
From Eq. 2:
t+w = 38/2
t+w = 19
t = 19 - w Eq. 3
Replacing Eq. 3 in Eq. 2:
19 - w = w + 3
19 - 3 = w + w
16 = 2w
16/2 = w
w = 8
Frm Eq. 2:
t = w + 3
t = 8 + 3
t = 11
Check:
From Eq. 1
2(t+w) = 38
2(11+8) = 38
2(19) = 38
Graph the function y =2x + 5, using a table.
The values are satisfied by
X -5 -4 -3 -2 -1
Y -5 -3 -1 1 3
How do you graph a function?Defining a function's graph The collection of all points in the plane of the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those numbers into the equation. Your coordinates for a single point are made up of your x-values and your y-values.Given data :
Y= 2X +5
let us put the value for X
X= 0
Y = 5
and, X=1
Y = 2 + 5 = 7
and, X= 2
Y= 4 + 5 = 9
and, X=3
Y = 6 + 5 = 11
and, X= 5
Y = 10 + 5= 15
and, X= -1
Y= -2 + 5 = 3
Hence, these values are satisfied by
x y
-5 -5
-4 -3
-3 -1
-2 1
-1 3
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Dr. Bert Vogelstein and his partners study the causes of cancer. In 2017, they published a study of 32 types of cancer. The study concluded that most cancer cases are caused by DNA replication errors. In fact, 66% of the cancer cases they studied were caused by random DNA replication errors. Environmental factors such as diet, sunburns, and smoking caused 29% of the cancers. The last 5% of cancers in the study were caused by inherited factors. Other researchers study the effects of small changes in the DNA sequence. These small changes trigger changes to genes. Genes that differ by a single nitrogen base are called SNPs (pronounced “snips”). SNPs cause many different disorders. What is true of all genes? A. They use the same kinds of tRNA during protein synthesis. B. They have the same DNA sequence. C. They have the same mRNA sequence. D. They code for proteins with the same amino acid sequence.
A true statement for all genes , given Dr. Bert Vogelstein study on cancer , is D . They code for proteins with the same amino acid sequence .
What do all genes share in common ?Genes need a code in order to be able to produce proteins . The genetic code is the code that converts the data stored in DNA and RNA into organized amino acids and proteins . Additionally, every living thing has the same genetic code .
The reason for this, according to scientists, is that every single living organism , has a common evolutionary history .
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let v be a real vector space. suppose that v1, v2, v3, v4 are vectors in v which are linearly independent. show that the vectors v1, v1 v2, v1 v2 v3, v1 v2 v3 v4 are also linearly independent.
given that v1,v2 ,v3,v4 is linearly independent vector so in order for a set of vectors to be linearly independent it must satisfy the below conditon:
[tex]x_1v1+x_2v2+x_3v3+x_4v4[/tex] =0 --(i)
where [tex]x_1, x_2,x_3 ,x_4[/tex] is some real numbers.
a) so in order to show that v1,v2+v4,v3 is linearly independent we have to
check if equations formed by these vectors can be transformed into some equation of equation (i) form.
so we have :
[tex]x_1v1+x_2(v2+v4) +x_3v3[/tex] ---(ii)
where [tex]x_1, x_2,x_3[/tex] is some real numbers.
after evaluating equation (ii) we have:
[tex]x_1v1+x_2v2+x_3v3+x_2v4[/tex]
so the above equation is now transformed in the form of equation (i) where [tex]x_2 = x_4[/tex]
and hence [tex]x_1v1+x_2v2+x_3v3+x_2v4[/tex] =0 ----(iii)
equation (iii) shows that the set of given vectors are linearly independent.
b) so in order to show that v1 +v2, v3, v4 is linearly independent we have to check if equations formed by these vectors can be transformed into some equation of equation (i) form.
so we have this equation:
[tex]x_1(v1+v2)+ x_2v3 + x_3v4[/tex] where [tex]x_1, x_2,x_3[/tex] is some real numbers.
after evaluating equation (iv) we have:
[tex]x_1v1+x_1v2+x_2v3+x_3v4[/tex]
so the above equation is now transformed in the form of equation (i) where the cofficient of v2 is also [tex]x_1[/tex]
and hence [tex]x_1v1+x_1v2+x_2v3+x_3v4[/tex] =0 ----(v)
equation (v) shows that the set of given vectors are linearly independent.
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Complete question :
let v be a real vector space. suppose that v1, v2, v3, v4 are vectors in v which are linearly independent. show that the vectors a) v1, v2+v4, v3 and b) v1 +v2, v3, v4 are also linearly independent.
The vectors v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent is hence proved.
let v be a real vector space.
The v1, v2, v3, v4 are vectors in v which are linearly independent.
V={v1, v2, v3, v4} then set V is called linearly independent if [tex]\forall \alpha_i \in F \\[/tex].
∝1v1+∝2v2+∝3v3+..........+∝nvn=0
then, [tex]\forall \alpha_i =0 \\[/tex] i=1,2,3......n.
let ∝1,∝2,∝3,∝4 ε F
∝1v1+∝2(v1+v2)+∝3(v1+v2+v3)+∝4(v1+v2+v3+v4)=0
v1(∝1+∝2+∝3+∝4)+v2(∝2+∝3+∝4)+v3(∝3+∝4)+v4.∝4=0
Since v1, v2, v3, v4 are linearly independent vectors.
So ∝1+∝2+∝3+∝4=0......(1)
∝2+∝3+∝4=0....(2)
∝3+∝4=0....(3)
∝4=0...(4)
Solving eq(1), (2), (3), (4)
we get ∝1=∝2=∝3=∝4=0
So according to definition of linearly independent vectors.
A set of vectors is called linearly independent if no vector in the set can be expressed as a linear combination of the other vectors in the set. If any of the vectors can be expressed as a linear combination of the others, then the set is said to be linearly dependent.
So v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent vectors hence proved.
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Amy can swim 6 laps in 9 minutes. Each lap is 50 meters.
"At that rate, how many minutes would it take Amy to swim 800 meters? Enter the answer in the box.
minutes
Answer:
I'm pretty sure the answer is 24.024
Step-by-step explanation:
300meters = 9 minutes
300+300=600
2/3 of 300=24minutes
800÷50=16
800÷33.3=24.024 minutes
Answer:
24 minutes----------------------
Since Amy can swim 6 laps in 9 minutes, then it takes:
9/6 = 1.5 minutes to swim one lap.Number of laps in 800 m:
800/50 = 16 lapsTime to swim 16 laps:
16*1.5 = 24 minGraph g(x) = -3x + 9 and identify its x-intercept.
(0, 3)
(0, 9)
(3, 0)
(9,0)
On a graph of g(x) = -3x + 9 the x - intercept is identified to be
What is x - intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
It is x - intercept where the line crosses the x axis and y intercept where the line crosses the y axis
How to identify the intercept from the graphOn the graph, the point where the line crosses the x axis is noted and written in ordered pair in the for (a, b)
Where a represents values in the x direction and y are values in the y direction
From the graph, a = 3 and b = 0
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Answer:
The answer is C. (3, 0)
Triangle BCD with vertices B(2, -1), C(4, 1), and D(5,-2):
scale factor = 3, centered at the origin
Answer:
To find the coordinates of the vertices of triangle BCD after it is scaled by a factor of 3, centered at the origin, you would first need to find the coordinates of the vertices of the triangle when it is centered at the origin. This can be done by subtracting the coordinates of the original centroid, which is the point (3.33, -0.66) for triangle BCD, from the coordinates of each vertex. So the coordinates of vertex B would be (2 - 3.33, -1 + 0.66) = (-1.33, -0.34), the coordinates of vertex C would be (4 - 3.33, 1 - 0.66) = (0.67, 0.34), and the coordinates of vertex D would be (5 - 3.33, -2 + 0.66) = (1.67, -1.34).
To scale the triangle by a factor of 3, you would multiply the coordinates of each vertex by 3. So the coordinates of the scaled triangle would be (-3.99, -1.02) for vertex B, (2.01, 1.02) for vertex C, and (5.01, -4.02) for vertex D.
Therefore, the coordinates of the vertices of triangle BCD after it is scaled by a factor of 3, centered at the origin, would be (-3.99, -1.02), (2.01, 1.02), and (5.01, -4.02).