[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-8}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{(-4)}}} \implies \cfrac{-11}{-6 +4} \implies \cfrac{ -11 }{ -2 } \implies \cfrac{11 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-7}-\underset{x_1}{(-7)}}} \implies \cfrac{2 +1}{-7 +7} \implies \cfrac{ 3 }{ 0 } \implies \stackrel{\textit{vertical line}}{{\Large \begin{array}{llll} unde fined \end{array}}} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{9}}} \implies \cfrac{ 0 }{ -15 } \implies \stackrel{\textit{horizontal line}}{\text{\LARGE 0}}[/tex]
keep in mind that whenever you notice the x-coordinates are the same, it's a vertical line, and whenever the y-coordinates are the same, is a horizontal line.
1^4 x 1^? = 1^12 Find '?'
put numbers in order smallest to largest: 0.5, 0.03, 0.42, 0.3, 0.243
Answer: 0.03, 0.243, 0.3, 0.42, 0.5
Step-by-step explanation:
Hope this helps you!
Answer:
Step-by-step explanation:
0.243, 0.03, 0.3, 0.42, 0.5
(1 point) The expression 4^65536g³y² √√/65536g³y² equals kg³y³
where r, the exponent of g, is:
and s, the exponent of y, is:
and k, the leading coefficient is:
The 4 is the square root
The exponent of g, r, is -65536.
The exponent of y, s, is 1.
The leading coefficient, k, is 4.
Note: The expression 4^65536g³y² √√/65536g³y² is not equal to kg³y³, but instead represents the value of 4 raised to the power of 65536 times g raised to the power of -65536, divided by the square root of 65536 times g raised to the power of -65536 times y squared. The square root symbol is used twice, which is equivalent to taking the square root of the square root, or the fourth root.
OAB is a triangle. OA = 4a + 7b
OB = 5a - b
Write AB in terms of a and b. Fully simplify your answer.
Answer:
AB = a - 8b
Step-by-step explanation:
AB = AO + OB
= - OA + OB
= - (4a + 7b ) + (5a - b )
= - 4a - 7b + 5a - b ← collect like terms
= a - 8b
Solve for x show proofs
The value of x in the triangle is 6√5
How to determine the value of xfrom the question, we have the following parameters that can be used in our computation:
The triangle
Using the above as a guide, we have the following:
x/20 = 9/x
Cross multiply the equation
so, we have the following representation
x^2 = 180
TAke the square root of hoth sides
This gives
x = 6√5
Hence, the solution of x is 6√5
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What is an equation of the line that passes through the points (-1,6) and (4,-4)
The linear equation that passes through the two given points is:
y = -2x + 4
How to write the equation of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, if a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, 6) and (4, -4), then the slope is:
a = (-4 - 6)/(4 + 1) = -2
y = -2x + b
To find the value of b, we can replace the values of any of the points in the equation, if we use (-1, 6) we will get:
6 = -2*-1 + b
6 = 2 + b
6 - 2 = b = 4
The linear equation is y = -2x + 4
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While shopping for clothes, Tracy spent $38 less than 3 times what Daniel spent. Write and solve an equation to find how much Daniel spent. Let x represent how much Daniel spent.
This is 7th grade math lol and i have no idea how to do it
On solving the provided question, we can say that equation for getting amount spent by Daniel is y + 38 / 3 = x
What is equation?A mathematical equatiοn is a formula that joins two statements and uses the equal symbοl (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equatiοn in algebra.
For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.
equatiοn for getting amοunt spent by Daniel -
x = y+38 / 3
Tracy then spent (in dοllars) accοrding to the provided descriptiοn (we don't write symbols like $ when writing equations because it is clear from the cοntext what the quantity stands fοr).
y = 3x - 38
y + 3x8 = 3x
y + 38 / 3 = x
equation for getting amοunt spent by Daniel is
y + 38 / 3 = x
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Kelly is reading a 456- page book. During the past 7 days she has read 168 pages. If she continues reading at the same rate, how many more days will it take her to complete the book?
Answer:
12 Days
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
To find the ratio of the problem (days: pages) we can use this equation:
pages read ÷ days it took = pages read each day
Fitting the numbers into the equation:
168 ÷ 7 = 24
So, everyday Kelly reads 24 pages.
To find out how many more days Kelly needs to read, if she reads at the same rate, we can use this equation:
(456 - 168) ÷ 24 = days left
We can use this to check our work:
168 + (24 ×?) = 456
Solving for the first equation:
(456 - 168) ÷ 24 = days left
288 ÷ 24 = 12
Now, we can check our work.
168 + (24 ×?) = 456
Inserting 12 into the equation:
168 + (24 × 12) = 456
168 + 288 = 456
Therefore, to complete the book it will take Kelly 12 more days.
the number of people living in baltimore is 183,000. the number of new active cases of tb occurring between january 1 and june 30, 2012 was 26. the number of active tb cases according to the city register on june 30, 2012 was 264. the incidence rate of active cases of tb for the 6-month period was:
The incidence rate of active cases of tb for the 6-month period was 0.00014
An incidence rate describes how quickly disease occurs in a population.
Incidence rate is the rate of new occurrence of a particular disease divided by the population of people at risk of the disease.
So for this question
The number of new active cases of tb occurring between January 1 and June 30, 2012 was 26
Population at risk in Baltimore is 183,000
Incidence rate = 26/183,000
The incidence rate of active cases of tb for the 6-month period was 0.00014 or 14 per 100,000 population.
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suppose you believe that stress causes headaches. what is the hypothesis? explain why we would use an experiment study to test this hypothesis. identify the independent and dependent variables. explain the treatments for the experimental and control groups. make sure all parts of your potential experiment are defined and labeled
If the presented hypothesis is confirmed, it can be assumed that individuals in the experimental group suffer from headaches more frequently than those in the control group.
The study examines how stress affects headaches. The theory can be stated as follows: People who encounter stress episodes more than twice per day would feel headaches more frequently than people who do not experience stress. This question concerns a cause and effect analysis, which can be done with reliable results when using an experimental investigation. Therefore, it is advised to use an experimental design for dealing with headaches brought on by stress. Stress events are the only unchanging factor in our study, however they do cause changes in the frequency of headaches. The degree of headaches, which fluctuates when the independent variable is changed, can be thought of as the dependent variable. Here, the technique can be applied as follows: Informed consent is obtained from a sample of 400 persons, all of whom fall within the age range of 25 to 40 (to lessen the impact of any auxiliary variables on the results). The volunteers are divided into two groups at random, one of which is the experimental group and the other the control group (double-blind design to avoid any potential biases). Three times a day, participants in the experimental group are exposed to a show that is heavy on the negative feelings that can lead to stress; in contrast, individuals in the control group are not exposed to any of the shows mentioned above. Then, the presence of headaches is assessed in both groups' members.
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Which list of numbers is ordered from greatest to least?
Responses
52%, 0.45, 3.1×101, 1011
52%, 0.45, 3.1×101, 1011
3.1×101, 52%, 0.45, 1011
3.1×101, 52%, 0.45, 1011
52%, 3.1×101, 1011, 0.45
52%, 3.1×101, 1011, 0.45
3.1×101, 1011, 52%, 0.45
PLEASE HELP!! 100 points!
The set representing the ordered numbers is given as follows:
0.45, 52%, 10/11, 31.
How to order the numbers?The numbers for this problem are given as follows:
52% = 0.52 -> conversion of percentage to decimal.0.45.3.1 x 10¹ = 31 -> scientific notation to decimal.10/11 = 0.909. -> fraction to decimal.For the three numbers with an integer part of zero, we order them according to the decimal part, hence:
0.45, 52%, 10/11.
31 has an integer part of 31 and is greater than the other numbers, hence the ordered data-set is given as follows:
0.45, 52%, 10/11, 31.
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Rewrite x(t)=(1.45)^t/2 in the form y=a(1+r)^t or y=a(1-r)^t to determine whether it represents exponential growth or exponential decay. Round a and r to the nearest hundredth if necessary.
The given function represents exponential growth, the value of a is 1 and the value of r is 0.45.
What is the exponential growth?The quantity increases slowly after which the rate of change and the rate of growth increases over a period of time rapidly. This increase in growth is calculated by using the exponential growth formula.
The exponential growth formula is [tex]Amount = Initial value(1+\frac{r}{100} )^{\frac{t}{n}}[/tex].
The given exponential function is [tex]x(t)=(1.45)^{\frac{t}{2} }[/tex].
Now, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex]
Compare, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex] with [tex]y=a(1+r)^t[/tex], we get
a=1 and r=0.45
Therefore, the value of a is 1 and the value of r is 0.45.
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In the diagram below,
ABCE is a trapezium,
AD is parallel to BC,
DE=4cm
Area of ABCE=60cm^2
Area of ABCD=48cm^2
Work out the values of f and g.
You must show all your working.
The values of f and g based on the given diagram ABCE is 6cm and 8cm respectively.
What is the values of f and g?Area of ABCE = 60cm²
Area of ABCD = 48cm²
Area of ADE = Area of ABCE - Area of ABCD
= 60 cm² - 48 cm²
= 12 cm²
Area of ADE = 1/2 × base × height
12 = 1/2 × 4 × h
12 = 4/2h
12 = 2h
divide both sides by 2
h = 12/2
h = 6 cm
AD = height = BC = 6 cm
Area of ABCD = length × width
48 = l × 6
48 = 6l
l = 48/6
l = 8 cm
In conclusion, f and g are 6cm and 8cm respectively.
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30 minutes twice a day for 184 days how many gallons of water will be used in each hole
30 minutes twice a day for 184 days, total 368 gallons of water will be used in each hole.
Assuming that each hole uses one gallon of water per 30 minutes.
1 hole = 1 gallon of water
The total amount of water used in each hole over 184 days would be 184 gallons.
So, in 184 days = 184 gallons of water
This is because each hole would be watered twice a day for 184 days, which comes out to 368 separate waterings.
= 184 × 2
= 368 gallons
The total amount of water used would be 368 gallons.
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The complete question is:
How many gallons of water will be used in each hole if 30 minutes is spent twice a day for 184 days?
Robin and 2 friends each were able to jump rope for 4/5 minute. How long did they jump rope for altogether?
Answer:
[tex]p(3and7)andq(1and9)[/tex]
what is the measure of the angle of one slice of pizza if the length of the crust (arc) is 4.9 in and the length of one side of the slice is 6.2 in?
The correct answer is 45.28°
In order to get that answer, you must set up the arc length formula.
l = m/360 • 2πr
4.9 = m/360 • 12.4π
We are trying to find the angle measure; therefore, we are going to divide.
4.9 = 0.10821m
Flip the equation
0.10821m = 4.9
0.10821m/0.10821 = 4.9/0.10821
m = 45.28°
We can use the formula angle = (arc length / radius) or an online calculator to find the angle of the slice, which is approximately 47 degrees in this case.
To find the measure of the angle of one slice of pizza, we can use the formula:
angle = (arc length / radius)
However, we are not given the radius of the pizza, so we first need to find it. One way to do this is to use the length of one side of the slice and the central angle of the slice. We know that the central angle of the slice is twice the angle at the center of the pizza that the slice occupies, so we can find this angle by:
angle at center = (angle of slice) / 2
We can then use the law of cosines to find the length of the radius:
radius² = (side length / 2)^2 + (side length / 2)² - 2 * (side length / 2) * (side length / 2) * cos(angle at center)
Once we have the radius, we can use the formula above to find the angle of the slice. However, since this calculation can be quite involved, it may be simpler to use an online pizza slice angle calculator. Using this tool with the given values, we find that the angle of one slice of pizza is approximately 47 degrees.
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The sharks are fed three times a day. During the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning. if the total weight of the fish fed in a day is 1/2 of a ton, how much is fed during the feeding at night?
The shark is fed during the feeding at night is 1/6 tons.
What is a proper fraction?
A proper fraction is one that doesn't contain any whole numbers and has a smaller numerator than a denominator. A fraction that represents a number greater than one and has a larger numerator than the denominator is said to be improper.
Given that during the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning.
The shark fed (2/15 + 1/15) ton during the afternoon.
Assume that the shark fed x tons at night.
Therefore, the total fed is 2/15 + (2/15 + 1/15) + x
The equation is:
2/15 + (2/15 + 1/15) + x = 1/2
Add like terms:
5/15 + x = 1/2
1/3 + x = 1/2
Subtract 1/3 from both sides:
x = 1/2 - 1/3
x = (3-2)/6
x = 1/6
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Yousuff deposits $2,500 into a savings account that has a simple interest rate of 3.8%.
5A) How much interest will Yousuff make in one year? Show your work!
5B) How much interest will Yousuff make after 8 years? Show your work!
5C) After 8 years, how much money will Yousuff have in his account? Remember to include both the original principal money AND the interest she made.
Step-by-step explanation:
Principal = $2,500
Rate = 3.8%
5A). The interest Yousuff make in one year
Therefore Time = 1 year.
Simple interest
[tex] = \frac{pincipal \times time \times rate}{100 \\ } \\ = \frac{2500 \times 1 \times 3.8}{100} \\ = 25 \times 1 \times 3.8 \\ = 95 .[/tex]
Therefore the interest Yousuff make in one year = $95.
5B). Interest Yousuff make in after 8 years
the time = 8 years
the interest
[tex] = \frac{pincipal \times time \times rate}{100} \\ = \frac{2500 \times 8 \times 3.8}{100} \\ = 25 \times 8 \times 3.8 \\ = 200 \times 3.8 \\ = 760 [/tex]
Therefore the interest Yousuff make after 8 years = $760.
5C). Principal - interest that Yousuff made after 8 years.
$2500 - $ 760
= $ 1,740.
Mrs. Jacobson is shopping for school supplies with her children. Isabelle selected 4 one-inch binders and 5 two-inch binders, which cost a total of $24. Bill selected 1 one-inch binder and 2 two-inch binders, which cost a total of $9. How much does each size of binder cost?
ANSWER is one- incher=1 while two inch binder=2.By using simultaneous equation.
39. Tugboat A and Tugboat B are pulling a barge. Each tugboat is connected to the barge via a cable. If the length of the cables are 63 meters and 68 meters and the tugboats are 35 meters apart, find the angle formed between the cables.
The angle formed between the cables is 48.7°.
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
Given: Tugboat A and Tugboat B are pulling a barge. Each tugboat is connected to the barge via a cable. If the length of the cables is 63 meters and 68 meters and the tugboats are 35 meters apart.
a = 68 m
b = 63 m
c = Distance between the tugboats = 35 m
m∠C = Angle between the cables
c² = a² + b² - 2abcosC
m∠C = cos⁻¹(c² - a² - b²)/(-2ab)
m∠C = cos⁻¹(35² - 68² - 63²)/(-2(68)(63))
m∠C = 48.7°
Hence, the angle formed between the cables is 48.7°.
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Boat
Boat A
Boat B
Cost
$2400
$2800
< Previous
Miles Per Gallon
(MPG)
15
18
Estimated Repairs
$600
$250
Stephanie wants to compare the total cost of buying and using these boats on her local lake.
Stephanie estimates she will drive the boat at least 40 miles per month.
The average cost of gasoline per gallon in her city is $3.89.
• Stephanie plans on owning the boat for 3 years.
Which boat will cost Stephanie the least to buy and use? How much will the difference in cost be?
Boat A will cost less for Stephanie. The difference in cost will be $400.
Boat B will cost less for Stephanie. The difference in cost will be $12.24
Boat A will cost less for Stephanie. The difference in cost will be $12.24.
O Boat B will cost less for Stephanie. The difference in cost will be $400.
The boat that will cost Stephanie less to buy and use is boat B, and the difference between the cost is $11.7.
How much will each boat cost?Let's calculate first the cost of each boat:
Boat A
cost + repairs + gasoline for 3 years= total cost
2400 + 600 + gasoline cost
gasoline cost = 40 / 15 = 2.66 gallons per month x 36 = 95.76 X 3.89 = 372.5
2400 + 600 + 372.5 = 3,372.5
Boat B
cost + repairs + gasoline for 3 years= total cost
2800 + 250 + gasoline cost
gasoline cost = 40 / 18 = 2.22 gallons per month x 36 = 79.92 X 3.89 = 310.88
2800 + 250 + 310.88 = 3,360.88
Difference: 3,372.5 - 3, 360.88 = 11.7
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PLEASE HELP !!
----------------------------------
A university has 32,370 students. In a random sample of 180 students, 12 speak three or more languages. Predict the number of students at the university who speak three or more languages.
The expected number of students at the university who speak three or more languages is ___________ .
The institution anticipates having 2158 students who can speak three or more languages.
Describe proportion in simple terms.The two ratios given are equivalent to one another, as demonstrated by the proportional equation. The percentage expresses the equality of something like the two ratios as well as fractions.
How do you teach pupils about proportion?Comparing two integers that each stand for a component of a whole results in a percentage. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.
[tex]\frac{x}{32370}=\frac{12}{180}[/tex]
[tex]{x} = \frac{12}{180}\times32370\\{x}=2158[/tex]
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how many significant figures do each of the following measurements contain? type a number (i.e., 1, 2, 3, etc) for each of your responses, not the written word for the number.
Each of the following measurements contain a) 1, b) 4,c) 3,d) 1,e) 2,f) 4,g) 2 significant figures.
Significant digit -Precision refers to the number of digits to which a value can be assigned. Therefore, numbers that can have a value of digits are called significant digits.
Below are the key figures for each value reported.
(a) 2- 1significant digits
(b) 81.640 - 4 significant digits;
(c) 7.03 - 3 Significant Figures
(d) 0.003 - 1significant digits
(e) 0.0086 to 2 significant digits
(f) 3236 - 4 significant digits
(g) 8700 - 2 significant digits
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The bike has 3 sprockets on the front and 7 sprockets on the cogset at the rear of the bike. How many gears does the bike have
The bike has 21 gears, 3 on the front and 7 on the rear cogset, giving a total of 21 average possible gear combinations.
The bike has 3 sprockets on the front and 7 sprockets on the cogset at the rear of the bike. This combination of 3 sprockets on the front and 7 on the rear creates a total of 21 possible gear combinations. This is calculated by multiplying the number of sprockets on the front by the number of sprockets on the rear. When you change the gear on the bike, you are changing the combination of the front and rear sprockets. By doing this, you can adjust the gearing of the bike to make it easier or harder to pedal depending on the terrain. Having a wide range of gears helps you to climb hills, accelerate and maintain speed on flat roads, as well as descend hills. Having 21 gears gives you a lot of options to make your ride as comfortable and efficient as possible.
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Assume you owe $16,783 to a credit card company and interest is at 19% compounded monthly, at the end of the month, how much do you owe in interest?
This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.
The interest rate in this situation is 19% compounded monthly. This means that each month, the interest rate is applied to the total balance. The formula to calculate the amount of interest owed is:Interest Owed = Balance x (Interest Rate/12) .In this case, the formula would be:Interest Owed = 16,783 x (0.19/12).This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.
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When factoring a tricky trinomial, a > 1, and you have more than one pair of factors for a term, which pair should you always try first?
When factoring a tricky trinomial with a leading coefficient greater than 1, and you have more than one pair of factors for a term, it is usually best to try the pair of factors that multiplies to give the constant term first.
This is because when factoring a trinomial with a leading coefficient greater than 1, the first term will always have fewer factors than the last term, and it can be easier to find the correct pair of factors for the constant term than for the first term.
If the correct pair of factors for the constant term is found first, it can be easier to use that information to deduce the correct pair of factors for the first term.
In addition, once you have found one pair of factors for the trinomial, you can use the factoring by grouping technique to factor the trinomial completely. This involves grouping the terms of the trinomial in pairs, factoring out the greatest common factor of each pair, and then factoring out the greatest common factor of the resulting expressions.
Overall, when factoring a tricky trinomial with a leading coefficient greater than 1, it can be helpful to start by trying the pair of factors that multiplies to give the constant term first, and then using the factoring by grouping technique to factor the trinomial completely.
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multivariate data set contains 25 subjects and 7 variables (5 numerical and 2 categorical). what is the correct size of the distance matrix? question 15 options: 25 x 25 25 x 7 25 x 2 7 x 7
The correct size of the distance matrix for a multivariate data set with 25 subjects and 7 variables is 25 x 25.
Understanding the many objectives and histories of the various types of multivariate analysis, as well as how they connect to one another, is the focus of multivariate statistics.
The distance matrix contains the pairwise distances between all pairs of subjects in the dataset, and therefore has the same number of rows and columns as the number of subjects in the dataset. Since there are 25 subjects in this dataset, the distance matrix will have 25 rows and 25 columns.
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Find Integral 0 to 1 f’(x)dx if f(5) = -7.8.
Answer:
[tex]-22.8[/tex]
Step-by-step explanation:
[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]
A pet store has 80
geckos and anole lizards altogether.
The ratio of geckos to anole lizards is 1:3
.
How many geckos does the pet store have?
Answer:
About 54 geckos
PLEASE HELP A WHOPPING 100 POINTS!!! AND BRAINLY NO LINKS
Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30°-60°-90° Triangle Theorem to find the answer.
Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answer: 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The 30-60-90 triangle rule states that the hypotenuse is twice the length of the shortest leg (which would be 5) and the longer leg is [tex]\sqrt{3}[/tex] times the length of the shorter leg.
Since we are trying to find x we would use the rule for the longer leg
so 5 * [tex]\sqrt{3}[/tex] would just be 5[tex]\sqrt{3}[/tex]
The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.
What is Triangle theorem?The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.
here, we have,
Using this theorem, we can write:
y = hypotenuse
Opposite of 30° angle = 5 = hypotenuse/2
Opposite of 60° angle = x = hypotenuse × (√(3)/2)
Solving for the hypotenuse in terms of y from the first equation, we get:
hypotenuse = 5×2 = 10
Substituting this value into the third equation, we get:
x = 10 × (√(3)/2) = 5 × √(3)
Hence, The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.
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