Answers
Answer:
Step-by-step explanation:
[tex]\frac{30\sqrt{2^{4n-2} +2^{4n+1} } }{(3^{n} +3^{n+1} )^2} \\=\frac{30\sqrt{2^{4n} *2^{-2} +2^{4n} *2^{1} } }{3^{2n} (1+3^{1}) } \\=\frac{30*2^{2n} \sqrt{\frac{1}{2^{2} }+2 } }{4*3^{2n} } \\=\frac{30*2^{2n}*\frac{3}{2} }{4*3^{2n} } \\=\frac{45(2^{2} )^{n} }{4(3^{2} )^{n} } \\=\frac{45}{4} *(\frac{4}{9} )^{n} \\[/tex]
it is a G.P. with common ratio r=4/9 <1
[tex]s=\frac{a}{1-r} ,a=first~term\\s=\frac{\frac{45}{4} *(\frac{16}{81} )}{1-\frac{4}{9} } [by~n=2]\\s=\frac{20}{9} *\frac{9}{5} \\=4[/tex]
Related Questions
FILL IN THE BLANK. In the context of data-flow diagrams (DFDs), a(n) _____ shows either the source or destination of the data.
a. data-flow line
b. entity symbol
c. process symbol d. data store symbol
Answers
In the context of data-flow diagrams (DFDs), a(n) option a. data-flow line shows either the source or destination of the data.
In data-flow diagrams (DFDs), an entity symbol represents an external agent or entity that interacts with the system being modeled. It could be a person, organization, or system that sends or receives data from the system being modeled. An entity symbol is represented as a rectangle with its name written inside it. It shows either the source or destination of the data in the DFD. An example of an entity symbol in a DFD could be a customer who provides orders to a company, or a supplier who delivers goods to a company. The entity symbol helps to illustrate the flow of data between external entities and the system being modeled.
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rewrite each equation without absolute value for the given conditions
y=|x-3|+|x+2|-|x-5| if 3
Answers
Answer:
Step-by-step explanation:
|x-3|=x-3,if x-3≥0,or x≥3
|x-3|=-(x-3),if x-3<0 ,or x<3
Find all the values of
arcsin −√3/2
Select all that apply:
a.π3
b.5π6
c.11π6
d.5π3
e.2π3
f.7π6
g.4π3
Answers
Answer:
g
Step-by-step explanation:
The given expression is arcsin (-√3/2), which represents the angle whose sine is equal to -√3/2. Recall that the range of the arcsin function is from -π/2 to π/2 radians, so we can narrow down the possible solutions to the second and third quadrants.
Since the sine function is negative in the third quadrant, we can start by considering the angle 4π/3, which is in the third quadrant and has a sine of -√3/2:sin(4π/3) = -√3/2
However, we need to check if there are any other angles in the second or third quadrants that satisfy the equation. Recall that sine is periodic with a period of 2π, so we can add or subtract any multiple of 2π to the angle and still obtain the same sine value.
In the second quadrant, we can use the reference angle π/3 to find the corresponding angle with a negative sine:
sin(π - π/3) = sin(2π/3) = √3/2
This angle does not satisfy the equation, so we can eliminate it as a possible solution.In the third quadrant, we can use the reference angle π/3 to find another possible solution:
sin(π + π/3) = sin(4π/3) = -√3/2
This confirms our initial solution of 4π/3, so the answer is (g) 4π/3.
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Answer:
We know that sin(π/3) = √3/2, so we can write:
arcsin(-√3/2) = -π/3 + 2nπ or π + π/3 + 2nπ
where n is an integer.
Therefore, the values of arcsin(-√3/2) are:
a. π/3 + 2nπ
c. 11π/6 + 2nπ
e. 2π/3 + 2nπ
f. 7π/6 + 2nπ
So, options a, c, e, and f are all correct.
The figure to the right shows the results of a survey in which 1007 adults from Country A, 1005 adults from
Country B, 1016 adults from Country C, 1016 adults from Country D, and 1000 adults from Country E were
asked whether national identity is strongly tied to birthplace.
National Identity and Birthplace
People from different countries who believe national
identity is strongly tied to birthplace
Country A
Country B
Country C
Country D
Country E
34%
22%
29%
50%
14%
Construct a 99% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed.
Answers
99% confidence interval is that the true population proportion of adults who say national identity is strongly tied to birthplace in Country A is between 30.7% and 37.3%.
What is confidence interval?The confidence interval is a set of values that, with a given level of certainty, contains the real population parameter. The likelihood that the genuine population parameter falls inside the interval is represented by the degree of confidence. In this instance, we created 99% confidence intervals for the percentage of individuals in each demographic who claim that national identity is highly correlated with birthplace. This indicates that 99% of the intervals we build would include the genuine population percentage if the survey were to be repeated numerous times.
The confidence interval is given using the formula:
CI = p ± z*(√((p*(1-p))/n))
Using the given values for different intervals the 99% for different countries are:
For Country A we have:
p = 0.34
n = 1007
z = 2.58 (based on a 99% confidence level)
CI = 0.34 ± 2.58*(√((0.34*(1-0.34))/1007)) = 0.307 to 0.373
For Country B we have:
p = 0.22
n = 1005
z = 2.58
CI = 0.22 ± 2.58*(√((0.22*(1-0.22))/1005)) = 0.187 to 0.253
For Country C we have:
p = 0.29
n = 1016
z = 2.58
CI = 0.29 ± 2.58*(√((0.29*(1-0.29))/1016)) = 0.259 to 0.321
For Country D we have:
p = 0.5
n = 1016
z = 2.58
CI = 0.5 ± 2.58*(√((0.5*(1-0.5))/1016)) = 0.469 to 0.531
For Country E we have:
p = 0.14
n = 1000
z = 2.58
CI = 0.14 ± 2.58*(√((0.14*(1-0.14))/1000)) = 0.108 to 0.172.
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alexia lunch at a restaurant costs $34.00, without tax. She leaves the waiter a tip of 12% of the cost of the lunch, without tax. What is the total cost of the lunch, including the tip?
Answers
Answer:
$38.08
Step-by-step explanation:
12% of 34.00 as an equation would be [tex]34*0.12[/tex], [tex]34*0.12=4.08[/tex] so we add 4.08 to the total of the lunch already. [tex]34.00+4.08=38.08[/tex]. So the answer is $38.08. Hope this helps :)
Which of the following is a true statement?The area under the standard normal curve between 0 and 2 is twice the area between 0 and 1.The area under the standard normal curve between 0 and 2 is half the area between -2 and 2.For the standard normal curve, the IQR is approximately 3.For the standard normal curve, the area to the left of 0.1 is the same as the area to the right of 0.9.
Answers
For the standard normal curve, the area to the left of 0.1 is the same as the area to the right of 0.9 is true . So, the correct answer is D.
The standard normal curve is a normal distribution with a mean of 0 and a standard deviation of 1. This curve is often used in statistics to model natural phenomena, and it has many important properties.
Option A is incorrect because the area under the standard normal curve between 0 and 2 is not twice the area between 0 and 1. The area under the curve increases as we move away from the mean, so the area between 0 and 2 will be greater than the area between 0 and 1.
Option B is also incorrect because the area under the standard normal curve between 0 and 2 is not half the area between -2 and 2. The area between -2 and 2 covers more of the curve than the area between 0 and 2, so the area between 0 and 2 will be smaller than half the area between -2 and 2.
Option C is incorrect because the standard normal curve does not have a fixed IQR (interquartile range). The IQR depends on the quartiles of the distribution, which can vary depending on the sample size and the distribution's shape.
Option D is the correct answer because the standard normal curve is symmetric around the mean of 0. This means that the area to the left of any point on the curve is the same as the area to the right of its negative counterpart. Therefore, the area to the left of 0.1 is equal to the area to the right of 0.9.
Therefore, Correct option is D.
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In the given figure, mHJ = 106° and F H G Figure not drawn to scale FH ~JH. Which statement is true? K 106° J OA. The measure of ZG is 21°, and triangle FGH is isosceles. OB. The measure of ZG is 56°, and triangle FGH is isosceles. OC. The measure of ZG is 21°, and triangle FGH is not isosceles The measure of ZG is 56°, and triangle FGH is not isoscelesd D.
Answers
Check the picture below.
[tex]\measuredangle G=\cfrac{\stackrel{far~arc}{148}-\stackrel{near~arc}{106}}{2}\implies \measuredangle G=21^o \\\\\\ \hspace{6em}\measuredangle F=\cfrac{106}{2}\implies \measuredangle F=53^o\hspace{8em}\measuredangle G=106^o \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle FGH\textit{ is not an isosceles}~\hfill[/tex]
CDs are on sale for $5 each. Jennifer has $45 and wants to buy as many as she can. How many CDs can Jennifer buy?
Answers
Answer:
9 CDs
Step-by-step explanation:
r u d0mb? 45 divided by 5 = 5 10 15 20 25 30 35 40 45
count the numbers
BOOM ANSWER
NEXT TIME PAY ATTENTION IN 2ND GRADEAn organization wishing to attract more people decides to base its
membership fees on the age of the member. Also, wanting members to
attend more activities, it gives a reduction on the membership fee for each
activity attended in the previous year.
The following table depicts the corresponding fee and reductions. The
minimum membership fee is $1, even if the member attended a lot of
activities.
Age
6 years or less
7-12 years
13-18 years
Over 18 years
Membership
Fee Reduction per Activity
$0.75
$1.25
$2
$5
$10
$15
$25
$2
Write a program that asks the user to input their age and the number of
activities attended and then displays the corresponding membership fee.
Input Validation: Do not accept a negative value for either the age or the
number of activities
C++
Answers
1. Begin the program by including the header file <iostream> which includes basic input/output library functions as well as the <vector> library which is needed for this program.
2. Declare a vector of integer type named 'ageGroups' which will store the age groups and the corresponding membership fee and reductions.
3. Create a void function named 'calculateFee()' which will take a parameters age and activities attended.
4. In the calculateFee() function, use the switch statement for the age group and store the corresponding membership fee and reduction value in variables.
5. Use an if statement to check that the number of activities attended is non-negative.
6. Calculate the membership fee using the variables and store it in a variable named 'fee'.
7. Use an if statement to check if the fee is less than 1 and if yes, assign the fee to 1.
8. Print the fee to the user.
9. End the program.
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.
Answers
Answer:
[tex]\dfrac{4096\pi}{5}\approx 2573.593\; \sf (3\;d.p.)[/tex]
Step-by-step explanation:
The shell method is a calculus technique used to find the volume of a solid revolution by decomposing the solid into cylindrical shells. The volume of each cylindrical shell is the product of the surface area of the cylinder and the thickness of the cylindrical wall. The total volume of the solid is found by integrating the volumes of all the shells over a certain interval.
The volume of the solid formed by revolving a region, R, around a vertical axis, bounded by x = a and x = b, is given by:
[tex]\displaystyle 2\pi \int^b_ar(x)h(x)\;\text{d}x[/tex]
where:
r(x) is the distance from the axis of rotation to x.h(x) is the height of the solid at x (the height of the shell).[tex]\hrulefill[/tex]
We want to find the volume of the solid formed by rotating the region bounded by y = 0, y = √x, x = 0 and x = 16 about the y-axis.
As the axis of rotation is the y-axis, r(x) = x.
Therefore, in this case:
[tex]r(x)=x[/tex]
[tex]h(x)=\sqrt{x}[/tex]
[tex]a=0[/tex]
[tex]b=16[/tex]
Set up the integral:
[tex]\displaystyle 2\pi \int^{16}_0x\sqrt{x}\;\text{d}x[/tex]
Rewrite the square root of x as x to the power of 1/2:
[tex]\displaystyle 2\pi \int^{16}_0x \cdot x^{\frac{1}{2}}\;\text{d}x[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x[/tex]
Integrate using the power rule (increase the power by 1, then divide by the new power):
[tex]\begin{aligned}\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x&=2\pi \left[\dfrac{2}{5}x^{\frac{5}{2}}\right]^{16}_0\\\\&=2\pi \left[\dfrac{2}{5}(16)^{\frac{5}{2}}-\dfrac{2}{5}(0)^{\frac{5}{2}}\right]\\\\&=2 \pi \cdot \dfrac{2}{5}(16)^{\frac{5}{2}}\\\\&=\dfrac{4\pi}{5}\cdot 1024\\\\&=\dfrac{4096\pi}{5}\\\\&\approx 2573.593\; \sf (3\;d.p.)\end{aligned}[/tex]
Therefore, the volume of the solid is exactly 4096π/5 or approximately 2573.593 (3 d.p.).
[tex]\hrulefill[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Power Rule of Integration}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}(+\;\text{C})$\\\end{minipage}}[/tex]
Find the local maximum and minimum values of f using both the first and second derivative tests f(x) = x2 / (x - 1). Summary: The local maximum and minimum values of f(x) = x2 / (x - 1) using both the first and second derivative tests is at x = 0 and x = 2.
Answers
The value of local maximum and local minimum for the function f(x) = x^2/(x -1 ) is equal to f(0) = 0 at x = 0 and f(2) = 4 at x = 4 respectively.
Local maximum and minimum values of the function
f(x) = x^2 / (x - 1),
Use both the first and second derivative tests.
First, let's find the critical points of the function,
By setting its derivative equal to zero and solving for x,
f'(x) = [2x(x - 1) - x^2] / (x - 1)^2
⇒ [2x(x - 1) - x^2] / (x - 1)^2 = 0
Simplifying this expression, we get,
x(x - 2) = 0
This gives us two critical points,
x = 0 and x = 2.
These critical points correspond to local maxima, local minima, or neither.
Use the second derivative test,
f''(x) = [2(x - 1)^2 - 2x(x - 1) + 2x^2] / (x - 1)^3
At x = 0, we have,
f''(0) = 2 / (-1)^3
= -2
Since the second derivative is negative at x = 0, this critical point corresponds to a local maximum.
f(0) = 0^2/ (0 -1 )
= 0
At x = 2, we have,
f''(2) = 2 / 1^3
= 2
Since the second derivative is positive at x = 2, this critical point corresponds to a local minimum.
f(2) = 2^2/ (2 - 1)
= 4
Therefore, at x = 0, the local maximum value is f(0) = 0, and at x = 2, the local minimum value is f(2) = 4.
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In a school district, 57% favor a charted school for grades K to 5. A random sample of 300 are surveyed and proportion of those who favor charter school is found. Let it be X. What is the probability that less than 50% will favor the charter school? Assume central limit theorem conditions apply.
Answers
To find the probability that less than 50% will favor the charter school, we need to standardize the sample proportion and use the standard normal distribution.
z = (X - µ) / σ
z = (0.50 - 0.57) / 0.035
z = -2.00
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -2.00 is approximately 0.0228.
Therefore, the probability that less than 50% will favor the charter school is approximately 0.0228 or 2.28%.
pls helppppppp explain !!!
Answers
Answer:
x²
Step-by-step explanation:
[tex]{ \tt{ \frac{ {x}^{ - 3} . {x}^{2} }{ {x}^{ - 3} } }} \\ \\ \dashrightarrow{ \tt{x {}^{( - 3 + 2 - ( - 3))} }} \\ \dashrightarrow{ \tt{ {x}^{( - 3 + 2 + 3)} }} \: \: \: \: \\ \dashrightarrow{ \boxed{ \tt{ \: \: \: \: {x}^{2} \: \: \: \: \: \: }}} \: \: \: \: [/tex]
ellas normal rate of pay is $10.40 an hour.
How much is she paid for working 5 hours overtime one Saturday at time-and-a-half?
Answers
Answer:
52
Step-by-step explanation:
10.40 TIMES 3
Could you please solve this one.
Answers
The proof that the lines CD and XY are parallel is shown below in paragraghs
How to prove the lines CD and XY are parallelGiven that
∠CAY ≅ ∠XBD
This means that the angles CAY and XBD are congruent angles
The above means that
The angles ∠AYX & ∠ACD correspond to the angle ∠CAYThe angle ∠BXY & ∠BDC corresponds to the angle ∠XBDBy the corresponding angles, we have
∠BXY = ∠AYX
∠ACD = ∠BDC
By the congruent angles above, the following lines are parallel
Line AC and BX
Line AY and BD
Line CD and XY
Hence, the lines CD and XY are parallel
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which of the following equations represent the profit-maximizing combination of resources for a firm?
Answers
The profit-maximizing combination of resources for a firm is MRPl / Pl = MRPc / Pc = 10/2 = 5/1 . The correct option is D).
The profit-maximizing combination of resources for a firm is determined by the equality of the marginal revenue product (MRP) per unit of input (labor, L, or capital, C) to the price per unit of input.
Therefore, the equation that represents the profit-maximizing combination of resources for a firm is:
MRPl / Pl = MRPc / Pc
where MRPl is the marginal revenue product of labor, Pl is the price of labor, MRPc is the marginal revenue product of capital, and Pc is the price of capital.
Among the given options, only option D satisfies the above equation. Therefore, option D represents the profit-maximizing combination of resources for a firm.
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_____The given question is incomplete, the complete question is given below:
Which of the following equations represent the profit-maximising combination of resources for a firm?
A. MRPl / Pl = MRPc / Pc = 1
B. MRPl / Pl = MRPc / Pc = 5
C. MRPl / Pl = MRPc / Pc = 10/10 = 5/5
D. MRPl / Pl = MRPc / Pc = 10/2 = 5/1
A mountain is 13,318 ft above sea level and the valley is 390 ft below sea level What is the difference in elevation between the mountain and the valley
Answers
Answer: 13,708 ft
Step-by-step explanation:
To find the difference in elevation between the mountain and the valley, we need to subtract the elevation of the valley from the elevation of the mountain:
13,318 ft (mountain) - (-390 ft) (valley) = 13,318 ft + 390 ft = 13,708 ft
Therefore, the difference in elevation between the mountain and the valley is 13,708 ft.
Answer: The difference is 13,708 ft.
Given that a mountain is 13,318 feet above sea level. So the elevation of the mountain is [tex]= +13,318 \ \text{ft}[/tex].
Given that a valley is 390 feet below sea level.
So the elevation of the valley is [tex]= -390 \ \text{ft}[/tex].
So the difference between them is [tex]= 13,318 - (-390) = 13,318 + 390 = 13,708 \ \text{ft}.[/tex]
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If m∠ADB = 110°, what is the relationship between AB and BC? AB < BC AB > BC AB = BC AB + BC < AC
Answers
The relationship between AB and BC is given as follows:
AB > BC.
What are supplementary angles?Two angles are defined as supplementary angles when the sum of their measures is of 180º.
The supplementary angles for this problem are given as follows:
<ADB = 110º. -> given<CDB = 70º. -> sum of 180º.By the law of sines, we have that:
AB/sin(110º) = BC/sin(70º).
As sin(110º) > sin(70º), the inequality for this problem is given as follows:
AB > BC.
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Answer:
AB>BC
Step-by-step explanation:
AI-generated answer
Based on the given information, the relationship between AB and BC depends on the measure of angle ZADB. If mZADB is 110°, we can determine the relationship as follows:
Since triangle ABD and triangle CBD share side AB, the larger the angle ZADB, the longer the side AB will be compared to side BC. Therefore, if mZADB is 110°, we can conclude that AB is greater than BC.
In summary, when mZADB is 110°, the relationship between AB and BC is:
AB > BC.
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b (3.5). x + 2y = 5 The equation of the line is ____(Type an equation Type your answer in slope intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer
Answers
The equation of the line is y = -1/2 + 13/2.
The point is (3, 5).
An equation of line is x + 2y = 5.
To determine the slope intercept form of the equation using the point and line we first determine the slope of the equation from the given line.
Convert the equation of line in slope intercept form.
x + 2y = 5
Subtract x on both side, we get
2y = -x + 5
Divide by 2 on both side, we get
y = -1/2 x + 5
On comparing with y = mx + c, where m is slope, we get
m = -1/2
Now the equation of the line is;
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 3)
Simplify the bracket
y - 5 = -1/2x + 3/2
Add 5 on both side, we get
y = -1/2x + 3/2 + 5
y = -1/2 + 13/2
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The complete question is:
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = mx + b.
(3, 5); x + 2y = 5
The equation of the line is ____ . (Type an equation Type your answer in slope intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer)
what is the second derivative of x^n when n= greater than or equal to 2
Answers
Answer:
The second derivative of x^n when n is greater than or equal to 2 is n(n-1)x^(n-2).What is the measure of angle ABC?
Answers
what is the half life of a substance that decays at a rate of 2.5% p.a?
Answers
Answer:
The half-life of a substance is the amount of time it takes for half of the initial amount of the substance to decay.
We can use the following formula to calculate the half-life (t1/2) of a substance with a decay rate of r:
t1/2 = (ln 2) / r
where ln 2 is the natural logarithm of 2 (approximately 0.693).
In this case, the decay rate is 2.5% per year, or 0.025 per year. Plugging this into the formula, we get:
t1/2 = (ln 2) / 0.025
t1/2 = 27.73 years (rounded to two decimal places)
Therefore, the half-life of the substance is approximately 27.73 years.
HELP ME ASAP ITS DUE TODAY!!!!!! I'LL GIVE YOU ONE HUNDRED POINTS AND BE MARKED BRAINLIEST IF YOU HELP ME!!!
Answers
There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability.
15/75=1/5
of being drawn.
This means one would expect a theoretical frequency of 1250/5=250 i.e. any given letter should get drawn 250 times, which means the answer is O
Two trains A and B left the same station at the same time. The speed of
train A is 105 kmph, while train B's is 87 kmph. If they travel in the same
direction, how far apart will they be in three hours?
Answers
Answer:
Step-by-step explanation:
Since they are traveling in the same direction, the distance between them increases at a rate of the difference of their speeds.
The relative speed of train A with respect to train B is:
105 kmph - 87 kmph = 18 kmph
In three hours, the distance between them will be:
Distance = Speed x Time
Distance = 18 kmph x 3 hours
Distance = 54 km
Therefore, the two trains will be 54 kilometers apart after three hours.
Please help me with number 9 and 10!??? Thank you for help anyone who help me ((:!!!
Answers
Answer:
9. $18
10. 68
Step-by-step explanation:
$8 + $2 + $3 + $5= $18
104 - 36= 68
Question 20 (2 points)
Suppose a survey was given to students at WCC and it asked them if they voted for
the Democrat or Republican in the last election. Results of the survey are shown
below:
Democrat Republican
Male. 50. 75
Female. 125. 50
If a student from the survey is selected at random, what is the probability they voted
for the republican?
75/50
50/75
75/300
125/300
Answers
Answer:
The table given provides the number of male and female students who voted for each party, but it does not give the total number of students in the survey. To find the probability of selecting a student who voted for the Republican party, we need to know the total number of students who participated in the survey.
The total number of students in the survey is:
50 + 75 + 125 + 50 = 300
The number of students who voted for the Republican party is:
75 + 50 = 125
Therefore, the probability of selecting a student who voted for the Republican party is:
125/300 = 0.4167 (rounded to four decimal places)
So, the answer is option D: 125/300
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a fire truck is parked 25 feet away from a high rise. the ladder on the truck reaches 100 feet. how high up the high rise can the ladder reach?
Answers
Answer:
If the fire truck is parked 25 feet away from the high rise and the ladder on the truck reaches 100 feet, we can use the Pythagorean theorem to find out how high up the high rise the ladder can reach.
Let's assume that the height the ladder can reach is "x". Then, we can set up the following equation:
25^2 + x^2 = 100^2
Simplifying this equation, we get:
625 + x^2 = 10000
Subtracting 625 from both sides, we get:
x^2 = 9375
Taking the square root of both sides, we get:
x = sqrt(9375)
x ≈ 96.81
Therefore, the ladder on the fire truck can reach a height of approximately 96.81 feet up the high rise
In each case either show that the statement is true, or give an example showing it is false. a. If a linear system has n variables and m equations, then the augmented matrix has n rows.
Answers
The given statements are true or false are shown below, about linear system has n variables and m equations, then the augmented matrix has n rows.
First, let's write how A and C look like.
A = [C|b], where b is the constant matrix.
(a) False.
Example
[tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\\end{array}\right][/tex]
We can see that z = t and so we have infinitely many solutions but there's no row of zeros.
(b) False.
Example
[tex]\left[\begin{array}{cc}1&0&0\1&1&0&0\\\end{array}\right][/tex]
Here; x1 = 1 and x2 = 1 is a unique solution and we have a row of zeros.
(c) True.
In the row-echelon form, the last row is either a row of zeros or a row that contains a leading 1. If the row has a leading 1, then there is a solution. Since we assume there is no solution, then the row must be a row of zeros.
(d) False.
Example
[tex]\left[\begin{array}{cc}1&3\\0&0\end{array}\right][/tex]
Here; x₁ = 1 − 3t and x2 = t. Thus, the system is consistent.
(e) True.
Suppose we have a typical equation in a system
а1x1 + A2X2 + ··· + anxn = b
Now, if b≠0 and x1 = x2 = ··· = x₂ = 0, then the system is Xn inconsistent. But, if b = 0, then we have a solution.
(f) False.
Example
[tex]\left[\begin{array}{cc}1&2&0&0\end{array}\right][/tex]
If a = 0, then it's consistent(infinitely many solutions) but if a 0, then it's inconsistent.
(g) Ture.
Since the rank would be at most 3 and this will lead to a free variable (4 columns in C and the rank is 3, so there is at leat 1 free variable). Thus, the system has more thatn one solution.
(h) True.
Because the rank is the number of leading 1's lying in different rows and A has 3 rows. Thus, the rank ≤ 3.
(i) False.
Because we could have a row of zeros in C and a leading 1 in A. In other words, a31 = a32 = A33 = A34 = 0 and c3 1. This makes the system inconsistent.
(j) True.
If the rank of C = 3, then there will be a free variable and this means the system is consistent.
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Complete question:
In each case either show that the statement is true, or give an example showing it is false. (a) If a linear system has n variables and m equations, then the augmented matrix has n rows. quations • ( *b) A consistent linear system must have infinitely many solutions. . (c) If a row operation is done to a consistent linear system, the resulting system must be consistent. (d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent.
Suppose parametric equations for the line segment between (8,-2) and (9,-2) have the form:
{x(t)=a+bt
{y(t)=c+dt
If the parametric curve starts at (8,-2) when t=0 and ends at (9,-2) at t=1, then find a,b,c, and d. a= b=
c=
d=
Answers
A parametric equation is one where the x and y coordinates of the curve are both written as functions of another variable called a parameter; this is usually given the letter t or θ . And the value of a= 8, b= 1, c= -2 and d= 0.
Equation of this form is known as a parametric equation; it uses an independent variable known as a parameter (often represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables.
You require 4 independent solutions because there are 4 unknowns. You can put two equations at each end point if you know t at each end point. (one for the x value and one for the y value).
At (8,-2), time is equal to zero as follows: 8 = a + bt = a + b(0) a = 8 -2 = c + dt = c + d(0) c = -2
At (9,-2), t = 1 because 9 = a + bt = 8 + b(1) b = 1 and -2 = c + dt = -2 + d(1) d = 0.
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Can anyone help thanks!!!!
Answers
Answer:
B
Step-by-step explanation:
5^2 is the small square, 4(3x4x1/2) are the 4 triangles
Answer: The answer would be B.
Step-by-step explanation:
Hello.
First, we know that the smaller square is 5, and to find the area of the big square, we need to square 5 to get the area. We also know that C wouldn't be a viable option, so, our only remaining choices are A and B. We know that without the smaller square, there are 4 triangles, and the Area of a Triangle is: 1/2*b*h. So, this also takes A out as an option as well. After this, you will have your answer as B; 5^2 + 4(3 * 4 * 1/2)
(Or, you could have found the Area of the Triangles, and realize that neither A, nor C have those options, making B the answer by default.)
Hope this helps, (and maybe brainliest?)