Area of the triangle in R² using determinant for the given vertices (-4, -4) , (0,-2) and (-2,4) is equal to 14 square units.
As given in the question,
Vertices of the triangle are given by:
( x₁ , y₁ ) = (-4,-4)
(x₂ , y₂) = (0, -2)
( x₃ , y₃) = (-2, 4)
Area of triangle using determinant is given by
= [tex]\frac{1}{2} \left|\begin{array}{ccc}-4&-4&1\\0&-2&1\\-2&4&1\end{array}\right|[/tex]
= (1/2) [-4(-2 -4) + 4(0+2) +1(0-4)]
=(1/2) ( 24 + 8 - 4)
= (1/2) ( 28)
= 14
Therefore, area of the triangle in R² using determinant for the given vertices (-4, -4) , (0,-2) and (-2,4) is equal to 14 square units.
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The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Answer:
The y-intercept represents the number of mammals when they were originally counted.
The line y = 0 is an asymptote of the graph.
The y-intercept is 120.
The asymptote indicates that as years pass, the number of mammals will approach 0.
Step-by-step explanation:
Took the test
Answer:
The y-intercept represents the number of mammals when they were originally counted.
The line y = 0 is an asymptote of the graph.
The y-intercept is 120.
The asymptote indicates that as years pass, the number of mammals will approach 0.
you want to know if an octopus (octopi are very intelligent!) can tell the difference between circles and rectangles. you provide each octopus with one circular disk and one flattened rectangle. you hide food under the rectangle. after several trials, you then count how many times the octopus picks up the circle and how many times it picks up the rectangle. you get the following results: circles: 13 rectangles: 31 can the octopus tell the difference between circles and rectangles? (hint: if the octopus can't tell the difference, what's the probability that he/she will pick a circle?)
No the octopus can not differentiate between circles and rectangle and the probability of picking circle is 0.295.
In the give question we have to find the octopus can tell the difference between circles and rectangles or not.
From the question;
Circles: 13
Rectangles: 31
Null hypothesis: proportion of circles found = 0.5
Alternate hypothesis: Proportion of circles found > 0.5
Total number of trials is 31+13=44
Since 13 times circle is choosen.
So the probability that octopus chooses circle is
P(C) = Total number of circle/Total number of trials
P(C)=13/44
P(C)=0.295
As probability is 0.295<0.50
So, no the octopus can not differentiate between circles and rectangle and the probability of picking circle is 0.295.
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helpp i rlly need this
The required solution to the given expression is 2 - 6y/x which is determined by the distributive property of multiplication.
What is the distributive property of multiplication?The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.
The expression is given in the question
⇒ (y² - 3y³x⁻¹)2m°y⁻²
∵ m° = 1
⇒ (y² - 3y³x⁻¹)2y⁻²
Apply the distributive property of multiplication,
⇒ y² × 2y⁻² - 3y³x⁻¹ × 2y⁻²
⇒ 2y²⁻²- 6y³⁻²x⁻¹
⇒ 2y° - 6y x⁻¹
∵ y° = 1 and x⁻¹ = 1/x
⇒ 2 - 6y/x
Therefore, the required solution to the given expression is 2 - 6y/x.
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please help ASAP! no BS!
Answer:
[tex]y=-\frac{1}{3}x +4[/tex]
Step-by-step explanation:
slope= 1-7/9- -9= -1/3
y-intercept: 7 = -1/3(-9)+b, b=4
If there is inverse variation and y = 3 when x = 24 , find x when y = 18 .
The value of x in the inverse variation is x = 4
Inverse variationInverse variation is express mathematically by; y = k/x
where, y and x = variables
k = constant of variation
We solve for 'x' in the variation using standard form for inverse variation:
y = k/x
Given; y = 3, x = 24
We now use the given information to find k.
Step 1: Substitute the given in to equation y= k/x; to
3 =k/24
Cross multiply
k = 3 * 24
k = 72
Step 2; The inverse relation for is y = 72/x since we have gotten k=72
For y = 18, we get
18 = 72/x
Cross multiply
18x = 72
x = 72/18
X=4
Therefore, the value of x = 4.
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A new car is purchased for 17500 dollars. The value of the car depreciates at 7.25% per year. To the nearest year, how long will it be until the value of the car is 9600 dollars?
The length of time till the value of the car is at $9, 600, given the depreciation rate of the car per year is 7.98 years.
How to find the length of depreciation?The car started off with a value of $17, 500, which was its purchase price. The length of time till the car is is $9, 600 can be found by using the NPER function on spreadsheet. This function shows the length of time till a value becomes another value.
The figures going into the formula are:
Rate = -7.25%
PV = $17, 500
FV = $9, 600
The number of years for the car to depreciate would be 7.98 years.
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Find the value of each variable.
Simplify your answers as much as possible.
If necessary, you may learn what the markings on a figure indicate.
The value of variable in first figure will be;
⇒ x = 5
The value of variable in second figure will be;
⇒ y = 4
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
There are two figures is shown in figure.
Now,
In first figure;
By using definition of proportional as;
⇒ 4 / 2 = 6 / (x - 2)
Solve for x as;
⇒ 2 (x - 2) = 6
⇒ x - 2 = 3
⇒ x = 3 + 2
⇒ x = 5
Thus, The value of variable in first figure will be;
⇒ x = 5
In second figure;
By using definition of proportional as;
⇒ y / 6 = 12 / 9
Solve for y as;
⇒ y / 6 = 4 / 3
⇒ y = 4 x 6 / 3
⇒ y = 24 / 6
⇒ y = 4
Thus, The value of variable in second figure will be;
⇒ y = 4
Therefore, The value of variable in first figure will be;
⇒ x = 5
The value of variable in second figure will be;
⇒ y = 4
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5. Find the number of terms in AP given that its first and last term x anD 37x respectively and that 45 common difference 4x vi.
Answer:
good luck
Step-by-step explanation:
Answer:
BANG IT LIKE A CHOLO
Step-by-step explanation:
select the correct volume. sarah has a solid wooden cube with a length of centimeter. from each of its 8 corners, she cuts out a smaller cube with a length of centimeter. what is the volume of the block after cutting out the smaller cubes?
The volume of the block after cutting the smaller cubes is:
volume = 56/125 [tex]cm^{3}[/tex]
What is volume?
Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies.
The formula to calculate the volume of the cube is given by:
Volume = [tex]a^{3}[/tex], where a is the length of its sides or edges
Length of solid wooden cube= [tex]\frac{4}{5} cm[/tex]
Length of smaller wooden cube= [tex]\frac{1}{3} cm[/tex]
Volume of the large cube = [tex](\frac{4}{3} )^{3}[/tex]
Volume of the large cube = [tex]\frac{64}{125} cm^{3}[/tex]
Volume of the small cube = [tex]\frac{1}{5} cm^{3}[/tex]
Volume of the small cube = [tex]\frac{1}{125} cm^{3}[/tex]
Volume of block after cutting out the smaller cubes is
= [tex]\frac{64}{125} -\frac{(8)(1)}{125}[/tex]
= [tex]\frac{64-8}{125}[/tex]
=[tex]\frac{56}{125}[/tex][tex]cm^{3}[/tex]
Hence, the volume of the block after cutting the smaller cubes is:
volume = 56/125 [tex]cm^{3}[/tex]
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due last week pls help me
The car B was 10 miles east of Car A.
A function is a formula, rule, or law that specifies how one variable (the independent variable) and another variable are related. The linear equation is of the form Ax+By+C=0.
Where A and B are the coefficient and C is the constant.
Speed of car A = 45 miles per hour and the direction of car A is East.
The distance of car B from Johnstown after 2 hours is 100 miles, east
The distance of car B from Johnstown is given on the graph.
So , the initial distance of car A from Johnstown will be,
= 100 - 2 × 45
=100 - 90
= 10 miles
As seen from the graph, the initial distance, east, of car B from Johnstown is 20 miles.
So, the difference between the cars will be 20-10= 10 miles that means car B was 10 miles east of Car A.
Therefore, the car B was 10 miles east of Car A.
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There are 276 dimes. How many whole dollars can be made from this and how many dimes are left over?
The number of dimes in 1 dollar is 10 thus the number of whole dollars that can be made from 276 dimes will be 27 and 6 dimes will leave over.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
Another example could be kilo gram to gram.
As per the given,
Number of dimes = 276
1 dollar = 10 dimes.
The number of dollars in 276 dimes, is 276/10 = 27.6
So, 27 dollars and 6 dimes.
Hence "The number of dimes in 1 dollar is 10 thus the number of whole dollars that can be made from 276 dimes will be 27 and 6 dimes will leave over".
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jezabel had 1,452 subscribers last week. Now she had 1,483 subcribers. every video she posts gains her about 30 new subcribers. Determaine if the pattern is linear. explain
The pattern isn't linear as the difference in values is different from 30.
How to illustrate if the pattern is linear?From the information, jezabel had 1,452 subscribers last week and now she had 1,483 subcribers.
The difference will be:
= 1483 - 1452
= 31
It was further stated that every video she posts gains her about 30 new subscribers.
This shows that it isn't linear.
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when people smoke, the nicotine they absorb is converted to cotinine, which can be measured. a sample of 40 smokers has a mean cotinine level of 172.5 with a standard deviation is known to be 119.5, find a 90% confidence interval estimate of the mean cotinine level of all smokers.
The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789
Given,
Number of smokers; Sample size, n = 40
Mean of the sample, μ = 172.5
Standard deviation, σ = 119.5
We have to find the 90% confidence interval estimate of the mean cotinine level of all smokers.
Here,
The confidence interval is given as;-
x − E < μ < x + E
E is the margin of error.
Margin of error,
E = zα/₂ σ/√n
E = 1.644854 119.5/√40
E = 31.07887
Then,
The confidence interval is;
x − E < μ < x + E
141.4211 < μ < 203.5789
That is,
The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789
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Rewrite the following equation in slope-intercept form.
y − 8 = 15 (x + 5)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
OMG GUYS I NEED ANSWER PLEASE HELP I HAVE TO LEAVE REALLY SOON TO GO SOMEWHERE!!!!!!! HELP ASAP!!!!!!! ;0 I HAVE TO LEAVE IN LESS THAN 15 MINUTES AND I STILL HAVE MORE QUESTIONS!!!!!!!!!
The following equation, y − 8 = 15 (x + 5) is in the slope-intercept form and will be y=15x+83.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that the equation is,
y − 8 = 15 (x + 5)
y=15(x+5)+8
y=15x+75+8
y=15x+83
A linear equation has the form y = mx + b in the slope-intercept format.
Thus, the following equation, y − 8 = 15 (x + 5) is in the slope-intercept form and will be y=15x+83.
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Which number can be added to a rational number to explain that the sum of two rational numbers is rational?
A √5
B √2
C 8
D pi
Answer:d
Step-by-step explanation:
in a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. the pta wants to find out whether parents agree with this plan. listed below are some of the ideas proposed for gathering data. for each, indicate what kind of sampling strategy is involved and what (if any) biases might result. a) put a big ad in the newspaper asking people to log their opinions on the pta website. strategy: response area possible bias: response area b) randomly select one of the elementary schools and contact every parent by phone. strategy: response area possible bias: response area c) send a survey home with every student, and ask parents to fill it out and return it the next day. strategy: response area possible bias: response area d) randomly select 20 parents from each elementary school. send them a survey, and follow up with a phone call if they do not return the survey within a week. strategy: response area possible bias: response area
The strategy for different scenarios are;
a) Voluntary response
b) Poor sampling
c) Stratified sampling
d) Stratified sampling with follow-up
Given Information;
The school board is debating whether to implement a new rule that would require primary pupils to pass a test in order to advance to the next grade in a large city school system with 20 elementary schools. The pta is interested in learning whether parents support this strategy. Here are a few of the suggestions made for data collection. Indicate the type of sampling technique being used for each and any potential biases that might arise.
a) If they put a big ad in the newspaper asking people to log their opinions on the PTA Web site what kind of bias might they encounter?
→ Only those who volunteer to answer will participate so, bias is due to the use of a voluntary response sample.
b) If they randomly select one of the elementary schools and contact every parent by phone, what kind of bias is there?
→ If we choose just one school, then the answers may not be independent, so under-coverage bias due to a poor sampling frame.
c) Suppose they randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week. What kind of sampling was done?
→ As there are natural groups, and we get a sample from each group, then it is stratified sampling.
d) randomly select 20 parents from each elementary school. send them a survey, and follow up with a phone call if they do not return the survey within a week.
→ Stratified sampling with follow-up, should be unbiased.
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50 POINTS FOR WHOEVER SOLVES THIS QUESTION! PLEASE AND THANK YOU!!
Answer:
hello as midpoint is (4,-3)
and an ending point is (8,-5)
there are 4x and 2y among them
so you need to subtract 4x and 2y from the midpoint
which the answer is going to be (0,-1)
i.e. C option
good luck
the table below shows the number of years of experience that 8 employees at a supermarket have and their hourly wages
Answer:
A. See attachment 1.
B. See attachment 2.
C. As the number of years of experience increases, so does the hourly wage.
Step-by-step explanation:
Part AWhen creating a scatter plot with bivariate data:
The explanatory (independent) variable is drawn on the x-axis.The response (dependent) variable is drawn on the y-axis.For the given data, the hourly wage is dependent on the number of years of experience. Therefore:
Years of experience is the explanatory variable and so is drawn on the x-axis.Hourly wage is the response variable and so is drawn on the y-axis.Draw the scatter plot
Label the x-axis "Years of experience".Label the y-axis "Hourly wage (in dollars)".Use a scale of x : y = 1 : 2 since there are 14 squares along the y-axis, yet the greatest y-value is 15. Plot the data from given table.(See attachment 1).
Part BDraw a line of best fit on the scatter plot (see attachment 2).
Part CCorrelation measures how closely two variables are linked.
If two variables are correlated, you can draw a line of best fit on the scatter plot.
The line of best fit has a positive slope and is close to the data points.
Therefore, the scatter plot shows a strong positive correlation between the years of experience and the hourly wage.
This suggests that as the number of years of experience increases, so does the hourly wage.
what is 13x − 19y = –14 in slope intercept form
Answer:
Step-by-step explanation:
-19y=-13x -14 to y=-13/-19 - -14/-19
The two-way frequency table contains data about students’ preferred exercise.
What is the joint relative frequency of students who do not like to run and enjoy swimming?
A) 23%
B) 37%
C) 46%
D) 72%
it's 23% because 46 (ppl who do not like running but like swimming) divided by 200 (the total for everything) is 0.23 which is 23%
g according to the last us census, 82.7% of orange county adults have a high school diploma. round this number to 83%, and obtain a point estimate for the crime rate in orange county (round to 2 decimal places). the predicted number of crimes reported per 100,000 residents in orange county is:
Orange County's crime rate is predicted to be 83%. This estimate is based on data from the Orange County Sheriff's Office, which showed that the number of crimes reported per 100,000 residents in the county has been steadily declining over the past few years.
A point estimate for the crime rate in Orange County is = 82.7% = 83%
The predicted number of crimes reported per 100,000 residents in Orange County is
= 100,000 X 0.827
= 82,700
The estimate for the crime rate in Orange County is 83%. However, this is just an estimate and the actual rate could be higher or lower. To get a more accurate estimate, we would need to collect more data.
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Which two lines are perpendicular to each other?
Line A: 2y=8x+10
Line B: 6y+3x = 12
Line C: 8y = −2x − 16
Answer:
Line A and C
Step-by-step explanation:
The perpendicular slope of another line is the negative reciprocal of the other slope.
For example, we have line [tex]x_{1}[/tex].
y = x
The line that is perpendicular to it is:
y= [tex]-\frac{1}{x}[/tex]
Lets tranform all of these equation to slope intercept form:
y = mx+b
M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.
Divide 2 on both sides to simplify line a into slope intercept form.
[tex]\frac{2y}{2} = \frac{8x+10}{2}[/tex]
Simplify.
y = 4x + 5
Now it is in slope-intercept form. Slope of 4 and y-intercept of 5.
Line B
Isolate y on both sides by subtracting 3x on both sides.
6y + 3x - 3x = 12 - 3x
6y = 12 - 3x
Divide 6 on both sides.
[tex]\frac{6y}{6} = \frac{-3x+12}{6}[/tex]
Simplify.
y = -1/2x + 2
Now it is in slope-intercept form. Slope of -1/2 and y-intercept of 2.
Line C
Divide both sides by 8.
[tex]\frac{8y}{8} = \frac{-2x-16}{8}[/tex]
Simplify.
y = -1/4x - 2
Line A has a slope of 4. Line C has a slope of -1/4x. Line C is the negative reciprocal of Line A as multiplying Line A by -1 and flipping the fraction simple gets you Line C. (and vice versa).
Stella drives 25 miles in 20 minutes. If she drove two hours in total at the same rate, how far did she go?
PLEASE HELP THIS IS SO HARD!
IT'S ABOUT ANGLES!
The measure of angle ABD is 118 degree.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
WE have been given that the angles are;
(3x +10)° and 2x
WE need to solve the value of x then we use the linear pair;
(3x +10)° + 2x = 180
Solving;
(3x +10)° + 2x = 180
5x + 10 = 180
5x = 180 - 10
5x = 170
x = 36
Angle ABD = (3x +10)° = 3(36) + 10
= 108 + 10
= 118
Hence, the measure of angle ABD is 118 degree.
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researchers are investigating whether people who exercise with a training partner have a greater increase, on average, in targeted exercise intensity compared with people who exercise alone. two methods of collecting data have been proposed. method i: recruit volunteers who are willing to participate. randomly assign each participant to exercise with a training partner or to exercise alone. method ii: select a random sample of people from all the people who exercise at a community fitness center. ask each person in the sample whether they use a training partner, and use the response to create the two groups. (a) for each method, the researchers will record the change in targeted exercise intensity for each person in the investigation. they will compare the mean change in intensity between those who exercise with a training partner and those who do not. (i) describe the population of generalization if method i is used. explain your answer. (ii) describe the population of generalization if method ii is used. explain your answer.
Random sampling: It is a type of probability sampling in which the researcher randomly selects a subset of participates from the population.
Biased Sample: Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower and higher sampling probability than other.
The population generalized in this case, is almost random, the only problem here is that people that want to participate will participate so is likely that the sample is not totally randomized and that there is huge number of people that regularly exercises.
b) This case is less random than the previous , here all the people in the sample regularly do exercise and these people can choose is they prefer to work with a partner or not. So the sample is biased.
In method 01 we can conclude that the result apply to the whole population , whole in method 02 we can't conclude that just because the sample is biased.
Method 01: - Recruit volunteers who are willing to participate. Randomly assign each participate to exercise with a training partner or exercise alone.
So there are people who wants to participate but people don't necessarily do exercise normally day to day life. People also can't choose to work out in a team or alone.
Method 02: Select a random sample of people from all the people who exercise at a community fitness center. ask each person in the sample whether they use a training partner, and use the response to create the two groups.
The members in the sample are people who exercises regularly and we ask them if they work alone or with a partner then, we create two groups. so this is more biased sample.
The population generalization, in this case, is almost random, the only problem here is that only people that want to participate will participate , so is likely that the sample is not totally randomized and that there is a larger number of people that regularly does exercise tan people that do not do exercise.This case is less than random than the previous here all the people in the sample regularly do exercise and these people can choose if they prefer to work with a partner or not. So the sample is biased.Learn more about Sample:
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A student's cost for last semester at her community college was $2200. She spent $440 of that on books. What percent of last semester's college costs was spent on books?
Rewrite the equation in Slope-Intercept Form (y = mx + b)
y+1=2(x-4)
here's another question
a waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 29 yd3 of debris. find the dimensions of the dumpster that will minimize its surface area.
The dimensions of the dumpster that will minimize its surface area are Length = 4.43 yds ,Width = 2.215 yds and Height = 2.956 yds
since l = 2w.
Now, the formula for a cube's surface area is;
S = 2lw + 2lh + 2wh.
Changing 2w to l yields;
S = 4wh + 4w² + 2wh.
S = 4w² + 6wh
in the meantime, the formula for a cube's volume is;
V = lwh
add 2w for l to receive;
V = 2w²h
h = V/2w²
In the SA equation, substitute V/2w² for h to get;
SA = 4w² + 6w(V/2w²)
SA = 4w² + 3V/w
V is stated to equal 29 yd3.
Thus;
S = 4w² + 87/w
Let's find the first derivative of S as we want to reduce the surface area;
S' = 8w - 87/w²
At S' = 0;
8w - 87/w² = 0
8w = 87/w²
w³ = 87/8
w = ∛(87/8)
w = 2.215 yds
L = 2 x 2.215= 4.43
since, l = 2w.
l = 4.43 yds
h = V/2w²;
h = 29/(2 × 2.215²)
h = 2.956 yds
Hence, The dimensions of the dumpster that will minimize its surface area is l = 4.43 yds, w = 2.215 yds and h = 2.956 yds
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Help with g(x)=f(x) please!
We will get the solution of the equation g(x) = f(x) by finding the rule for the linear equation g(x) and solving the linear equation, the solution is x = 2.
How to solve the system of equations?Here we have two functions, one graphed, which is g(x), and the other defined by a rule:
f(x) = -x + 1
For g(x) we can use the graph to find the rule, notice that this is a linear equation so we can write:
g(x) = m*x + b
Where m is the slope and b is the y-intercept.
On the graph we can see that the y-intercept is y = -3, then:
g(x) = m*x - 3
To find the value of m we can use another point on the graph, for example, (3, 0)
Replacing that we get:
g(3) = 0 = m*3 - 3
3 = m*3
3/3 = m
1 = m
Then g(x) = x - 3
Now we can solve:
g(x) = f(x)
Replacing the functions we get:
x - 3 = -x + 1
Now we can solve this linear equation for x:
x - 3 = -x + 1
x + x = 3 + 1
2x = 4
x = 4/2
x = 2
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