For the two lines to be parallel, the value of n must be 3
How are two lines parallel in a coordinate?When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line. If the slopes are the same then the lines are parallel.
The slope of each line is calculated as (y2-y1)/x2-x1
for line AB, the slope = (6n-n)/10-4 = 5n/6
for line CD, the slope= 8n-(-6)/9-(-3)=( 8n+6)/12
for AB and CD to be parallel,
5n/6 = (8n+6)/12
multiply both sides by 12
10n= 8n+6
collect like terms
10n-8n= 6
2n= 6
n= 6/2= 3
therefore for the value of n= 3 line CD and AB are parallel.
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If the equation of f(x) goes through (1, 4) and (4, 6), what points does f-1(x) go through?.
The positions through which the equation of f^-1(x) travels are: (4, 1), (6, 4)
What are equations?A mathematical statement called an equation is comprised of two expressions joined together with the equal sign.
A formula would just be 3x - 5 = 16, for instance.
When this equation is solved, we observe that the value of the variable x is 7.
So, (1, 4) and (4, 6) are points through which the equation of f(x) goes.
If the f (x) equation contains (x, y).
Therefore, the f^-1(x) equation is as follows: (y, x).
Here, the f (x) equation passes through the following points: (1, 4) and (4, 6).
So, (4, 1) and (6, 4) are the points through which the equation of f^-1(x) goes through.
Therefore, the positions through which the equation of f^-1(x) travels are:
(4, 1), (6, 4)
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Correct question:
If the equation of f(x) goes through (1,4) and (4,6), what points does f^-1(x) go through?
Is joni correct? explain. joni is not correct, because $230 is just the interest she will earn; she will have $430 total. joni is not correct; $230 will be her balance after 1 year. after 3 years, she will have $290. joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. she will have $231.53. joni is correct. she correctly applied the i = p · r · t formula, and will have $230.
Joni is mistaken because she applied the compounding rate formula rather than just the simple interest rate equation, which is incorrect. $231.53 will belong to her.
Explain the term compounded annually?The equation A=P(1+r)t can be used to calculate the amount A you would have after t years if you deposit P dollars together in savings account including an annual interest rate of r and also the interest is compounded annually.The $200 was deposited by Joni into an account that earned interest at a 5% annual compound rate.
Joni calculated and she'll have a final balance of $230 after three years.
The steps are as following,
P = 200, r = 5, t = 3I = 200*0.05* 3I = 3030 + 200 = 230Because Joni employed the simple interest rate method instead of the compound interest rates formula, she is mistaken $231.53 will belong to her.
The yearly compound interest rate if 5% is stated above.
As a result, she ought to have used the compound interest calculation when calculating.
A = P(1 + r/n)∧(nt)
Amount then becomes:
A = 200(1 + 0.05)³
A = $231.53.
Thus, final amount will be obtained as $231.53.
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The complete question is-
Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230. Her work is shown below. Step 1: P = 200, r = 5, t = 3 Step 2: I = 200 ∙ 0.05 ∙ 3 Step 3: I = 30 Step 4: 30 + 200 = 230 Is Joni correct? Explain. Joni is not correct, because $230 is just the interest she will earn; she will have $430 total. Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290. Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53. Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.
use the appropriate normal distribution to approximate the resulting binomial distributions. a fair coin is tossed 130 times. what is the probability of obtaining between 70 and 82 tails, inclusive? a) 0.2137 b) 0.1908 c) 0.2154 d) 0.1880 e) 0.2166 f) none of the above.
The probability of obtaining between 70 and 82 tails is 0.2137, that is, option A.
Here, we are given that a fair coin is tossed 130 times.
Thus,
number of trials ⇒ n = 130
p = P(getting tails in a single toss) = 0.5
mean of a binomial distribution = np
= 130*0.5
= 65
variance = np(1-p)
= 65*0.5
= 32.5
standard deviation = sqrt(variance)
= sqrt(32.5)
= 5.7
Now, x = number of tails
X follows a normal distribution with mean 65 and variance 5.7
P(70 < x < 82)
= P( 69.5 < X < 82.5) [applying continuity correction]
= P[(69.5-65)/5.7 < Z < (82.5-65)/5.7)]
= P(0.79 < Z < 3.07)
= P(Z < 3.07) - P(Z < 0.79)
= 0.9989- 0.7852
= 0.2137
Thus, the probability of obtaining between 70 and 82 tails is 0.2137, hence, option A. .
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Given the diagram below, if Z is the incenter of WXY, WYX =86, and WXZ=33. Find each measure.
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The values of each measure:
m∠WYZ = 43
m∠WXY = 33
m∠YWX = 61
m∠ZWX = 30.5
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Z is the incenter of WXY.
m∠WYX = 86
This means,
m∠WYZ = m∠XYZ = x
m∠WYZ + m∠XYZ = m∠WYX
2x = 86
x = 43
m∠WXZ = 33.
m∠WXZ = m∠WXY
Now,
The triangle WXY.
m∠YWX + m∠WXY + m∠WYX = 180
m∠YWX + 33 + 86 = 180
m∠YWX = 180 - 119
m∠YWX = 61
m∠ZWX = 61/2 = 30.5
Thus,
The values of each measure:
m∠WYZ = 43
m∠WXY = 33
m∠YWX = 61
m∠ZWX = 30.5
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Find the value of x in the trapezoid below. Type only the numerical answer.
The value x of the trapezoid is 3 units.
How to find the side of a trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides .
The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides.
The midsegment of a trapezoid is parallel to each base, and its measure is half the sum of the lengths of the bases.
Therefore,
29 = 1 / 2 × (23 + 11x + 2)
29 = 1 / 2 × (25 + 11x)
cross multiply
29 × 2 = 25 + 11x
58 = 25 + 11x
58 - 25 = 11x
33 = 11x
divide both sides by 11
x = 33 / 11
x = 3
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the quotient of a number n and "-3" is no less than 6. What is the value of n?
Answer: n >= -18
Step-by-step explanation:
n/-3 >= 6
(-3) (-3)
n >= -18
Remember
to estimate first
by rounding and multiplying
to find where the first digit
goes in the quotient.
1. 1,593/13
Answer:
Step-by-step explanation:
1593/13
122.538
answer: 122.5
Which mixed number is represented on the number line?
4
5
4
5
nine new employees, two of whom are married to each other, are to be assigned nine desks that are lined up in a row. if the assignment of employees to desks is made randomly, what is the probability that the married couple will have adjacent desks? (round your answer to the nearest tenth of a percent.)
The probability that the married couple will have adjacent desks is 0.22.
Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.
Thus, by Fundamental Principle of Counting, the number of possible arrangements where the married coupe has adjacent desks is 80640.
= 8 x 7! x 2
= 80640
Ans the total number of possible arrangements is 362880.
= 9!
= 362880
Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.
probability = desired outcome / total outcomes
probability = 80640/362880
probability = 0.22
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chegg how many cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected?
26 cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.
We have given that standard deck of 52 cards.
And we have to find the number of cards must be selected from a deck to get at least four hearts, four diamonds and five clubs.
So four hearts + four diamonds + five clubs = 13 cards
The worst case, we may select all the spade i.e 13 cards before any heart, diamond and club.
So the guarantee that at least four hearts, four diamonds and five clubs are selected, 13 + 13 = 26
Therefore 26 cards must be selected from standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.
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Write this number in word form 84,052
Answer:
eighty-four thousand fifty-two
Step-by-step explanation:
the way i think about it is writing it as the sum of the digits together.
80000+4000+50+2
eighty-four thousand fifty-two
question if x, y, and z are integers and xy z is an odd integer, is x an even integer? (1) xy xz is an even integer. (2) y xz is an odd integer.
xy + xz is an even integer & x is even and y + xz is an odd integer & either (x-1) is even or (y-z) is even .
1. xy + xz is an even integer - SUFFICIENT
Given:
xy + z is odd ...(i)
xy + xz is even ...(ii)
subtracting (ii) from (i)
we get xz - z, which should be odd (* since odd - even = odd)
=> z(x-1) is odd
=> both z and (x-1) is odd
=> since (x-1) is odd, x must be even.
2. y + xz is an odd integer -INSUFFICIENT
Given:
xy + z is odd ...(i)
y + xz is odd ...(ii)
subtracting (ii) from (i)
we get xy + z - y - xz
= (x-1)(y-z) , which should be even
=> either (x-1) is even or (y-z) is even ....insufficient to determine
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If x = 6 and y = -4, evaluate the following expression: 20 - 5y + 2x
answer:
20-5y+2x=52
step-by-step explanation:
plug in the values of x & y into the expression and calculate using the order of operations to get the answer. hope that helps!
Answer: 52
Step-by-step explanation:
1. plug in x and y into the expression : 20 - 5(-4) +2(6)
2. multiply the numbers in the parenthesis: 20 + 20 + 12
3. add all the numbers together (simplify): 52
The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is cubic inches when its base area is square inches and its height is inches. What is the volume of a pyramid with a base area of square inches and a height of inches?.
The volume of a pyramid is 60 inches.
Given that,
A pyramid's volume varies in tandem with both its base area and height. When a pyramid's base is square inches and its height is inches, its volume is cubic inches.
V1 = 35 cubic inches
A1 = 15 square inches
h1 = 7 inches
A2 = 36 inches
h2 = 5 inches
To find : What is V2
The following formula is used to determine a pyramid's volume:
V = (Base Area × Height)/3
V2 = (36 square inches multiplied by 5)/3
V2 = 60 cubic inches
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1. Solve for the missing angle measures.
1)
a = 75⁰
d
b
C
2)
a
b
с
d = 104°
Answer: 24 26 37 60
Step-by-step explanation: im sure
PLEEEEEASE HELP ME ASAP
By evaluating the function we will see that the difference is:
f(1) - f(-7) = 3
How to evaluate the piecewise function?Here we have a piecewise function, this is a function that behaves differently on different intervals of its domain.
On the image you can see the different pieces of the function, and on the right the domain of each of the pieces.
The first part works for all the values smaller than -4 and x = -4.
So if we want to evaluate the function in x = -7, we need to use that piece:
f(-7) = |-7 + 5| - 9 = -7
And the second piece works on the interval (-4, 1], so to evaluate in x = 1 we need to use that piece.
f(1) = -1³ - 3*1 = -4
Then the difference is:
f(1) - f(-7) = -4 + 7 = 3
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The table represents some points on the graph of linear function f.
x = -2, 1, 5, 10
f(x) = -224, 64, 448, 928
Which function represents f`? Please show your work.
A. f(x) = 32(3x - 1)
B. f(x) = -32(x - 3)
C. f(x) = -2(32x - 3)
D. f(x) = 16(2x - 1)
The function representing the points relation is f(x) = 32(3x - 1)
What is function?A function is defined as a relation between a set of inputs having one output each.
Given a table, represents some points on the graph of linear function f.
x = -2, 1, 5, 10
f(x) = -224, 64, 448, 928
From option A)
f(x) = 32(3x - 1)
Put x = -2
= 32(-2x3-1)
= 32x(-7) = -224
Hence, The function representing the points relation is f(x) = 32(3x - 1)
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Can I get 10 comments in 10 minutes
Answer: Welp, here it is.
Step-by-step explanation:
I clicked the keyboard :)
hhhhhhhhhhhhhhhhhhhhhhhhh
The relationship between a company’s profit, y, and the number of units sold, x, is represented by the equation 6x − 9y = 12. rewrite the equation to give the profit in terms of the number of units sold.
After solving the equation in terms of y will be y = (2/3)x - 4/3.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
The given equation is,
6x - 9y = 12
Then, the equation in terms of y will be,
9y = 6x - 12
Divide the above equation by 3,
3y = 2x - 4
y = (2/3)x - 4/3
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a person stands on a scale in an elevator. as the elevator starts, the scale has a constant reading of 590 n. as the elevator later stops, the scale reading is 386 n. assume the magnitude of the acceleration is the same during starting and stopping.
Assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.
What is the magnitude?The magnitude or size of a mathematical object determines whether it is larger or smaller than other objects of the same kind in mathematics.
Formally speaking, the magnitude of an object is the visible outcome of an ordering—of the class of objects to which it belongs.
So, the weight of the person will be:
The scale measures the passenger's normal upward force as it is applied by the floor.
When moving upward, the most force is generated (when starting an upward trip or ending a downward trip).
When there is a downhill acceleration, the normal force is at its lowest.
For any such circumstance:
∑F y =ma y becomes for starting +591N−mg=+ma and for stopping +391N−mg=−ma.
Where a stands for the acceleration's magnitude.
To get rid of a and find mg, add these two simultaneous equations:
+591N−mg+391N−mg=0
OR
982N–2mg=0
Fg = mg = 982N/2 = 491N
Therefore, assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.
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Complete question:
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.
MAKING AN ARGUMENT Your friend claims that given f(0) and any other value of a linear function f, you can write an
equation in slope-intercept form that represents the function. Your cousin disagrees, claiming that the two points could lie on a
vertical line. Who is correct? Explain.
O Your friend. You can write an equation in slope-intercept form even if the two points are on a vertical line.
O Your cousin. You may need more than two points to write an equation in slope-intercept form.
O Your friend. If f is a function, then the line is not vertical.
O Your cousin. If the line is vertical, it will not have a slope.
The correct one is Your cousin. If the line is vertical, it will not have a slope.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
So, from the Discussion we came to know about Vertical Line.
But the slope of vertical line is undefined.
Then, the slope intercept form is not possible in vertical line.
Hence, the correct one is Your cousin. If the line is vertical, it will not have a slope.
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a jet flies 5985 miles in 4 3/4 hours. At the same rate, how long will it take the jet to fly 8505 miles?
[tex]\begin{array}{ccll} miles&hours\\ \cline{1-2} 5985&4\frac{3}{4}\\[1em] 8505&h \end{array}\implies \cfrac{5985}{8505}~~ = ~~\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{h}[/tex]
[tex]\cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{\frac{h}{1}}\implies \cfrac{19}{27}=\cfrac{19}{4}\cdot \cfrac{1}{h}\implies \cfrac{19}{27}=\cfrac{19}{4h}\implies 76h=513 \\\\\\ h=\cfrac{513}{76}\implies h=\cfrac{27}{4}\implies {\Large \begin{array}{llll} h=6\frac{3}{4} \end{array}}[/tex]
Solve for bbb.
-11b+7 = 40−11b+7=40minus, 11, b, plus, 7, equals, 40
b =b=b, equals
The value of 'b' will be;
⇒ b = 7 / 11
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 40 - 11b + 7 = 40
Now,
Solve the expression for b as;
The expression is,
⇒ 40 - 11b + 7 = 40
⇒ - 11b + 7 = 0
⇒ 11b = 7
⇒ b = 7 / 11
Thus, The value of 'b' will be;
⇒ b = 7 / 11
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167. for the training adaptation of maximum strength, what is the recommended number of repetitions per set?
Each strength training exercise should be performed for 2 to 6 sets with no more than 6 repetitions. To encourage the greatest outcomes, the training intensity for each set should be 85% or greater.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). %, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
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you have 2,000 feet of fencing to enclose a rectangular pasture. one side of the pasture is up against a river. what is the maximum area you could enclose?
Maximum area to enclose a rectangular pasture with one side up against a river is equal to 500,000 square feet.
As given in the question,
Let 'l' be the length of the rectangular pasture
And 'w' be the width of the rectangular pasture
Condition:
One side of the pasture is up against a river
Perimeter of the rectangular pasture with one side up against river = l + 2w
⇒ 2000 = l + 2w
⇒ l = 2000 - 2w
Area of the rectangular pasture
=( 2000 - 2w )( w )
= - 2 ( w² - 1000w )
= -2( w² - 1000w + 250000 - 250000 )
= -2 ( w - 500 )² + 500, 000
Maximum area is at w = 500
Maximum area is 500,000
Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.
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between 149714971497 and 150015001500, amerigo vespucci embarked on two voyages to the new world. according to vespucci’s letters, the first voyage lasted 434343 days longer than the second voyage, and the two voyages combined lasted a total of 1{,}0031,0031, comma, 003 days. how many days did the second voyage last?
The number of days that the second voyage last's is 480 days.
Given,
The discrepancy in the length of the two excursions, we are asked to determine how many days the second voyage lasted.
We initially assign variables in order to overcome this issue. Let the duration of the first cruise be f days and the duration of the second expedition be s days.
We are aware that the first journey lasted 43 days longer than the second.
In mathematics, f = 43 plus s. (I)
The cumulative duration of the two journeys was 1003 days. Mathematically:
f + s = 1003........(ii) (ii)
We transform I into ii
43 + s + s = 1003
43 +2s = 1003
2s = 1003 - 43
2s = 960
s = 960/2 = 480 days
That is,
The second voyage lasted about 480 days
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NEED HELP. ASAP For the bleacher section, what is the minimum number of games a fan needs to attend to make purchasing a season ticket a less expensive option than single-game tickets?
Seating Area
Single-Game Ticket
Season Ticket
Main box
$50
$3240
Bleachers
$12
$810
Left field reserve
$20
$1377
The best way is to pick the one you think has a higher chance
One day in February, the temperature at 9 A.M. is -6.8°F. At 3 P.M. on the same day, The temperature is 1.72°F.
a) Find the change in temperature.
b) Find the average hourly rate of change in temperature
Answer:
The change in temperature is -6.64
The average hourly rate of change is
6 hours or -3.32
Find the 54th term of the arithmetic sequence -2, -8, -14,
Answer:
-2n+4
-2×54+4
-108+4
-104
you draw a card from a standard deck of 52 cards, replace it, and draw another card. find each probability. (enter your probabilities as fractions.)
The probabilities when choosing a card of the respective color are
1/26, 1/8, 3/169, 1/676
What are probability and examples?The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.
How do I solve probability?Multiply the total number of possible outcomes by the total number of occurrences. Divide the entire number of ways the event can occur by the total number of potential outcomes after determining the probability event and its related consequences.
The probabilities are:-
p= (1/13)*(1/2)=1/26
p=(1/2)*(1/4)=1/8
p=(1/13)*(3/13)=3/169
p=(1/52)*(1/13)=1/676
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