[tex]S_n=\dfrac{n(a_1+a_n)}{2}\\a_1=200\\a_n=1998\\n=?\\\\a_n=a_1+(n-1)d\\d=2\\1998=200+(n-1)\cdot2\\2n-2=1798\\2n=1800\\n=900\\\\S_{900}=\dfrac{900\cdot(200+1998)}{2}=450\cdot 2198=989100[/tex]
The Sum is 989100.
what is sum of Even numbers?The sum of even numbers formula is determined by using the formula to find the arithmetic progression. The sum of even numbers goes on until infinity. The sum of even numbers formula can also be evaluated using the sum of natural numbers formula. We need to obtain the formula for 2 + 4+ 6+ 8+ 10 +...... 2n.
The sum of even numbers = 2(1 + 2+ 3+ .....n). This implies 2(sum of n natural numbers) = 2[n(n+1)]/2 = n(n+1)
Given:
a1 = 200
an= 1998
So, using formula
S= n(a1 + an)/2
now,
d=2
an= a1+(n-1)d
1998= 200 + (n-1) 2
1998-200= (n-1)2
1798/2=n-1
n= 900
S900= 900( 200 + 1998)/2
=450*2198
= 989100
Hence, the sum is 989100.
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Please Help quick!!! What is the value of a missing angle?
Answer:
69
Step-by-step explanation:
90-21=69
Answer:
69 degrees
Step-by-step explanation:
The full angle = 90 degrees.
One part of the full angle = 21 degrees
The other part of the full angle = x
Other angle = 90 - 21
=> the other angle = 69 degrees
Please help, thanks!!!!!
Answer:
[ 2+0+8. 0+0+12][-4+10+2. 0+25+3]
[10. 12]
[8. 28]
Option 3 is the solution
During two years in college, a student earned $9,500. The second year she earned $500 more than twice the amount she earned the first year. How much did she earn the first year?
There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.
a. 804
b. 844
c. 884
d. 0.36
Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804
How many ways are there to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants
Answer:
There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.
Step-by-step explanation:
Given:
There are 5 types of croissants:
plain croissants
cherry croissants
chocolate croissants
almond croissant
apple croissants
broccoli croissants
To find:
to choose 22 croissants with:
at least one plain croissant
at least two cherry croissants
at least three chocolate croissants
at least one almond croissant
at least two apple croissants
no more than three broccoli croissants
Solution:
First we select
At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants
So
1 + 2 + 3 + 1 + 2 = 9
Total croissants = 22
So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.
n = 5
r = 13
C(n + r - 1, r)
= C(5 + 13 - 1, 13)
= C(17,13)
[tex]=\frac{17! }{13!(17-13)!}[/tex]
= 355687428096000 / 6227020800 ( 24 )
= 355687428096000 / 149448499200
= 2380
C(17,13) = 2380
C(n + r - 1, r)
= C(5 + 12 - 1, 12)
= C(16,12)
[tex]=\frac{16! }{12!(16-12)!}[/tex]
= 20922789888000 / 479001600 ( 24 )
= 20922789888000 / 11496038400
= 1820
C(16,12) = 1820
C(n + r - 1, r)
= C(5 + 11 - 1, 11)
= C(15,11)
[tex]=\frac{15! }{11!(15-11)!}[/tex]
= 1307674368000 / 39916800 (24)
= 1307674368000 / 958003200
= 1307674368000 / 958003200
= 1365
C(15,11) = 1365
C(n + r - 1, r)
= C(5 + 10 - 1, 10)
= C(14,10)
[tex]=\frac{14! }{10!(14-10)!}[/tex]
= 87178291200 / 3628800 ( 24 )
= 87178291200 / 87091200
= 1001
C(14,10) = 1001
Adding them:
2380 + 1820 + 1365 + 1001 = 6566 ways
Write 41/12 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats. Write as a decimal.
Answer:
3.416, bar above 6
Step-by-step explanation:
41/12 = 3.4166666666666
41/12 = 3 & 5/12
Answer:
66
Step-by-step explanation:
41/12 = 3.4166
A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?
since there are 3 slots and each slot has 30 positions:
dial 1 can have a max of 30 possible outcomes, and so can dial 2 and 3
hence all the dial have 30 possible outcomes
total combinations = total outcomes of slot 1 X total outcomes of slot 2 X total outcomes of slot 3/ 3!
total combinations = 30 * 30 * 30 / 3 X 2 X 1
total combinations = 9000/3 X 2
total combinations = 1500
hence, there is a total of 1500 different combinations of the 3 slots
the combination required is 1 from the 1500
hence the odds are 1/1500
Answer:
1/27000
Step-by-step explanation:
30*30*30 =27000
each dial has to be in correct position so 1/27000 is correct
limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)
Step-by-step explanation:
I(S) = aS / (S + c)
As S approaches infinity, S becomes much larger than c. So S + c is approximately equal to just S.
lim(S→∞) I(S)
= lim(S→∞) aS / (S + c)
= lim(S→∞) aS / S
= lim(S→∞) a
= a
As S approaches infinity, I(S) approaches a.
Which expression is equal to 7 times the sum of a number and 4
Answer:
7(n + 4)
Step-by-step explanation:
Represent the number by n. Then the verbal expression becomes
7(n + 4).
A school newspaper reporter decides to randomly survey 15 students to see if they will attend Tet festivities this year. Based on past years, she knows that 24% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
Find the probability that at most 4 students will attend. (Round your answer to four decimal places.)
Answer:
0.70319018
Step-by-step explanation:
Given the following:
Number of students surveyed (n) = 15
Probability of attending tet festival (p) = 24% =0.24
Therefore,
Probability of not attending (1 - p) = (1 - 0.24) = 0.76.
The probability that at most 4 students will attend can be obtained using the binomial probability relation:
p(x) = nCx * p^x * (1 - p)^(n-x)
At most 4 students means:
p(x=0) + p(x=1) + p(x=2) + p(x=3) + p(x=4)
p(x=0) = 15C0 * 0.24^0 * 0.76^(15 - 0)
p(x=0) = 1 * 1 * 0.0004701 = 0.00047018
p(x=1) = 15C1 * 0.24^1 * 0.76^(14)
p(x=1) = 15 * 0.24 * 0.021448 = 0.07721
p(x=2) = 15C2 * 0.24^2 * 0.76^(13) =
p(x=2) = 105 * 0.0576 * 0.02822 = 0.17068
p(x=3) = 15C3 * 0.24^3 * 0.76^(12)
p(x=3) = 455 * 0.013824 * 0.037133 = 0.23356
p(x=4) = 15C4 * 0.24^4 * 0.76^(11) =
p(x=4) = 1365 * 0.0033177 * 0.048859 = 0.22127
0.00047018 + 0.07721 + 0.17068 + 0.23356 + 0.22127 = 0.70319018
The minute hand of a watch has a length of 1.4 cm. Find the; (a) distance moved by the tip of the minute hand from 8.13 am to 8.49 am. (b) angle swept by the minute hand if the tip moves 8.8 mm (c)time it will bee when the minute hand sweeps the angle calculated in (b), if the minute hand started moving at 8.39 am
Answer:
A). The distance covered= 5.2752 cm
B). Angle swept = 36°
C). The time = 8:45 am
Step-by-step explanation:
The watch is assumed to be a circle while the minute hand is assumed to be the radius
Radius = 1.4cm
A). From 8:13 to 8:49= 36 minutes
Recall, there is 60 minutes in a round watch.
The distance covered= 2πr*36/60
The distance covered= 2*3.14*1.4*0.6
The distance covered= 5.2752 cm
B). If distance covered is 8.8 mm
8.8 mm = 0.88cm
0.88= 2*3.14*1.4*(x/360)
0.88/(8.792)=x/360
0.1= x/360
0.1= x/360
36°= x
Angle swept = 36°
C). The time it will be if the watch started from 8:39 am and moved 36°
36/360= y/60
0.1= y/60
0.1*60= y
6 minutes= y
The time with be 8:39+6 minutes
The time = 8:45 am
Hakim is making a mosaic
from square tiles. The area he
needs to fill measures 150 mm
by 180 mm. The tiles have side
lengths of 4, 6 or 8 mm and are
too small to cut. Which tiles
should Hakim use?
Answer:
6×6 tile
Step-by-step explanation:
First let's calculate the total area Hakim should fill.
Let A be that area.
The area is a rectangle so its area is the product of the length and the width.
● A = 180*150
● A = 27000 mm^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
The tiles Hakim has are all squares with different sides(4,6,8).
Let calculate the area of each tile.
Let A' , A" and A"' be the areas respectively of the 4,6 and 8 squares.
Since all tiles are squares, the area is the side times itself.
■■■■■■■■■■■■■■■■■■■■■■■■■■
● A' = 4^2 = 16 mm^2
● A" = 6^2 = 36 mm^2
● A"' = 8^2 = 64 mm^2
Divide the total area by each area and see wich one will give you a whole number.
●A÷A' = 27000÷16 = 1687.5
This isn't a whole number
● A÷A" = 27000÷36 = 750
This is a whole number, so it is the right tile.
● A+A"' = 27000÷64 = 421.875
This isn't the right tile.
Hakil should use the 6×6 tile
Hakim should use a tile of 6×6 side.
What is area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
Given that, Hakim is making a mosaic from square tiles. The area he needs to fill measures 150 mm by 180 mm. The tiles have side lengths of 4, 6 or 8 mm and are too small to cut.
To know that which tile fits best, we will divide the area of mosaic to the area of the tile, and see if we get a whole number if not a whole number then it should be cut, but we are restricted to do so, therefore we will look for the whole number,
Area of the mosaic = 150×180 = 27000 mm²
Area of the tile with side 4 mm = 4² = 16 mm²
Number of tile = 27000/16 = 1687.5 tiles. (not a whole number)
Area of the tile with side 6 mm = 6² = 36 mm
Number of tile = 27000/36 = 750 tile. (a whole number)
Hence, Hakim should use a tile of 6×6 side.
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NEED IT ASAP
Tony is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 10% sales tax plus a state-mandated $45 fee for disposing of his old tires. If Tony has determined that he will spend less than $559.80 total, then what is the price range he can spend on the tire set?
Select one:
a. Less than $468
b. At least 472
c. $468 or more
d. Less than 473
Answer:
A
Step-by-step explanation:
Let:
Total price be T
And price of tire set be x
T<559.80 ---(1)
T=x +(10% of x)+ 45. ——(2)
T=x+(1/10)x+45
T=(11/10)x+45
Substitute T into equ. 1
T<559.80
(11/10)x +45<559.80
(11/10)x < 514.80
11x < 5148
x < 468
A projectile is fired vertically upward from a height of 300
300
feet above the ground, with an initial velocity of 900
900
ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0
h
(
t
)
=
−
16
t
2
+
v
0
t
+
y
0
. Write a quadratic equation to model the projectile's height h(t)
h
(
t
)
in feet above the ground after t seconds.
Step-by-step explanation:
It is given that, a projectile is fired vertically upward from a height of 300 feet above the ground, with an initial velocity of 900 ft/s.
The general equation with which a projectile are modled by the function is given by :
[tex]h(t)=-16t^2+v_ot+y_o[/tex]
y₀ is the initial height above the ground
v₀ = initial velocity
So,
[tex]h(t)=-16t^2+900t+300[/tex]
This is the quadratic equation that models the projectile height in feet above the ground after t seconds.
6. Classify the traianle as scalene, isosceles or equilateral. Explain. Leave answers in square root form.
TAL
Answer:
isosceles
Step-by-step explanation:
The point B is located on the perpendicular bisector of AC. No calculation is necessary. AC has a slope of 1, so it is easy to count grid squares to see where the perpendicular bisector goes.
When the altitude of the triangle bisects the side opposite the vertex, it is an isosceles triangle.
_____
Apparently, you're to use the distance formula to determine the lengths of the sides of the triangle. Doing that, you would find ...
AB² = (6-4)² +(1 -6)² = 4 + 25
CB² = (6-1)² +(1-3)² = 25 + 4
At this point, it doesn't require much thought to realize these sides are the same length: √29.
plz help i'm having a really hard time with this
Answer:
Domain all reals
Range all reals
Step-by-step explanation:
The domain is the values that x can take, or the values of the input
x can be any real number
The range is the values that y can take, or the values of the output
y can be any real number
Answer:
C)
Step-by-step explanation:
it's fully continous, linear function thus all values are possible for both, x and y
1. Approximate the given quantity using a Taylor polynomial with n3.
2. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Fourth underroot(94)
a. p3(94)
b. absolute error
Answer:
See the explanation for the answer.
Step-by-step explanation:
Given function:
[tex]f(x) = x^{1/4}[/tex]
The n-th order Taylor polynomial for function f with its center at a is:
[tex]p_{n}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(n)}a}{n!} (x-a)^{n}[/tex]
As n = 3 So,
[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{3!} (x-a)^{3}[/tex]
[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{6} (x-a)^{3}[/tex]
[tex]p_{3}(x) = a^{1/4} + \frac{1}{4a^{ 3/4} } (x-a)+ (\frac{1}{2})(-\frac{3}{16a^{7/4} } ) (x-a)^{2} + (\frac{1}{6})(\frac{21}{64a^{11/4} } ) (x-a)^{3}[/tex]
[tex]p_{3}(x) = 81^{1/4} + \frac{1}{4(81)^{ 3/4} } (x-81)+ (\frac{1}{2})(-\frac{3}{16(81)^{7/4} } ) (x-81)^{2} + (\frac{1}{6})(\frac{21}{64(81)^{11/4} } ) (x-81)^{3}[/tex]
[tex]p_{3} (x)[/tex] = 3 + 0.0092592593 (x - 81) + 1/2 ( - 0.000085733882) (x - 81)² + 1/6
(0.0000018522752) (x-81)³
[tex]p_{3} (x)[/tex] = 0.0092592593 x - 0.000042866941 (x - 81)² + 0.00000030871254
(x-81)³ + 2.25
Hence approximation at given quantity i.e.
x = 94
Putting x = 94
[tex]p_{3} (94)[/tex] = 0.0092592593 (94) - 0.000042866941 (94 - 81)² +
0.00000030871254 (94-81)³ + 2.25
= 0.87037 03742 - 0.000042866941 (13)² + 0.00000030871254(13)³ +
2.25
= 0.87037 03742 - 0.000042866941 (169) +
0.00000030871254(2197) + 2.25
= 0.87037 03742 - 0.007244513029 + 0.0006782414503 + 2.25
[tex]p_{3} (94)[/tex] = 3.113804102621
Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Compute [tex]\sqrt[4]{94}[/tex] as [tex]94^{1/4}[/tex] using calculator
Exact value:
[tex]E_{a}[/tex](94) = 3.113737258478
Compute absolute error:
Err = | 3.113804102621 - 3.113737258478 |
Err (94) = 0.000066844143
If you round off the values then you get error as:
|3.11380 - 3.113737| = 0.000063
Err (94) = 0.000063
If you round off the values up to 4 decimal places then you get error as:
|3.1138 - 3.1137| = 0.0001
Err (94) = 0.0001
Robert has $20,000, part or all of which he wants to invest into a combination of government bonds and municipal bonds. He wants to invest no more than $5,000 into municipal bonds, and at least twice as much into government bonds than into municipal bonds.
Answer:
x + y ≤ 20,000y ≤ 5,000x ≥ 2yStep-by-step explanation:
Given:
Total amount = $20,000
Assume
Government bonds = x
Municipal bonds = y
Computation:
1. Invest total money
x + y ≤ 20,000
2. invest no more than $5,000 into municipal bonds
y ≤ 5,000
3. at least twice as much into government bonds.
x ≥ 2y
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5 . If there were 4545 no votes, what was the total number of votes?
Answer:
The total number of votes= 9999
Step-by-step explanation:
The ratio of vote specifically the ratio of yes to no vote in a city vote is 6 to 5.
There is a total of 4545 no votes.
Yes/no = 6/5
Yes= no(6/5)
Yes= 4545(6/5)
Yes= 5454
The total number of yes votes are 5454.
The total number of votes= yes votes+ no votes
The total number of votes= 5454+4545
The total number of votes= 9999
PLEASE HELP!!!!!! TIMED QUESTION!!!! FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?
1)
1/5 of the students earned a C
2)
3% more students earned an A then B
3)
20% of the students earned a D
4)
1/4 of the class earned a B
Answer:
3) 20% of the students earned a D
Step-by-step explanation:
9 students got a D.
5 students got a C.
14 students got a B.
17 students got an A.
Total number of students:
9 + 5 + 14 + 17 = 45
1) 1/5 of the students earned a C
1/5 of 45 = 9
5 students got a C
False
2) 3% more students earned an A then B
3 more students got an A than a B, but not 3%.
False
3) 20% of the students earned a D
20% of 45 = 9
9 students got a D.
True
4) 1/4 of the class earned a B
1/4 of 45 = 11.25
There were 14 B's.
False
Answer: 3) 20% of the students earned a D
In one city, 35% of all aluminum cans distributed will be recycled each year. A juice company distributes 110,000 cans. The number still in use after time t, in years, is given by
Answer: [tex]n(t) = 110000(0.35)^t[/tex]
Step-by-step explanation:
Given: Rate of of all aluminum cans distributed will be recycled each year. = 35%
= 0.35
Total cans distributed = 110,000
Now , the number of cans recycled in 1 year = 110,000 ×0.35
The number of cans recycled in 2 years = 110,000 ×0.35 ×0.35 = 110,000 ×(0.35)²
..so on
The number of cans recycled in t years = [tex]110000(0.35)^t[/tex]
Let n(t) be the number still in use after time t, in years:
Then, [tex]n(t) = 110000(0.35)^t[/tex]
Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answers down to the nearest whole number.)
(a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0
Answer:
a
[tex]df = 24.32[/tex]
b
[tex]df = 30.10[/tex]
c
[tex]df = 30.7[/tex]
d
[tex]df = 25.5[/tex]
Step-by-step explanation:
Generally degree of freedom is mathematically represented as
[tex]df = \frac{ [\frac{ s^2_i }{m} + \frac{ s^2_j }{n} ]^2 }{ \frac{ [ \frac{s^2_i}{m} ]^2 }{m-1 } +\frac{ [ \frac{s^2_j}{n} ]^2 }{n-1 } }[/tex]
Considering a
a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{15} ]^2 }{ \frac{ [ \frac{4^2}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{15} ]^2 }{15-1 } }[/tex]
[tex]df = 24.32[/tex]
Considering b
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{4^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]
[tex]df = 30.10[/tex]
Considering c
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 3^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{3^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]
[tex]df = 30.7[/tex]
Considering c
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{10} + \frac{ 6^2 }{24} ]^2 }{ \frac{ [ \frac{4^2}{10} ]^2 }{10-1 } +\frac{ [ \frac{6^2}{24} ]^2 }{24-1 } }[/tex]
[tex]df = 25.5[/tex]
Rewrite the expression in part A by breaking up each of the place values. In this case, the place values are tens, ones, and tenths. 72.3 degrees f
Answer:
72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees
Step-by-step explanation:
The number, 72.3 degrees, can be rewritten by breaking up the place value of each digit in the expression as folliws,:
70 degrees + 2 degrees + 0.3 degrees
The place value of 7 is tens
The place value of 2 is ones
The place value of 3 is tenths
[tex] 72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees [/tex]
Answer:
72.3 + (-39.1) = 70 + 2 + 0.3 + (-30) + (-9) + (-0.1)
Step-by-step explanation:
got the off the assignment
If you rent a car for one day and drive it for 100 miles the cost is 40 dollars if you drive it 220 miles the cost is 46 dollars what is the linear equation for this
Answer:
[tex] y = \dfrac{1}{20}x + 35 [/tex]
Step-by-step explanation:
Let y = cost.
Let x = number of miles.
We have two (x, y) points: (100, 40) and (220, 46).
Now we find the equation of the line that passes through those two points using the two-point form of the equation of a line.
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
[tex] y - 40 = \dfrac{46 - 40}{220 - 100}(x - 100) [/tex]
[tex] y - 40 = \dfrac{6}{120}(x - 100) [/tex]
[tex] y - 40 = \dfrac{1}{20}(x - 100) [/tex]
[tex] y - 40 = \dfrac{1}{20}x - 5 [/tex]
[tex] y = \dfrac{1}{20}x + 35 [/tex]
At the dog show, there are 4 times as many boxers as spaniels. If there are a total of 30 dogs,how many dogs are spaniels? Plz help me
Answer:
6 spaniels
Step-by-step explanation:
Create 2 equations to represent this, where b is the number of boxers and s is the number of spaniels:
4s = b
s + b = 30
We can plug in 4s as b into the second equation, s + b = 30:
s + b = 30
s + 4s = 30
5s = 30
s = 6
So, there are 6 spaniels.
What is an equation of the line that passes through the points (-5, 8) and (5,0)?
Answer:
y= -0.8x + 4
Midpoint is 0,4
7.619 by 10^-3
7.254 by 10^2
Answer:
0.007619
0.07254
Step-by-step explanation:
1)7.619*10^-3
0.007619
2)7.254*10^2
0.07254
Explanation:
7.619*10^-3
The number here is 7.619 and the number written in scientific notation has minus 3 as its exponent.
.007.619
So the distance between the first decimal point and the second decimal is only three numbers.
Since it is exponent is minus three.
Another way to get the answer.
[tex]7.619 \times 10 {}^{ - 3} = \frac{7619}{1000} \times \frac{1}{1000} = \frac{7619}{1000000} = 0.007619 [/tex]
This applies to the second one too.
Hope this helps ;) ❤❤❤
I help! solve 12x^2+54x=-42
Answer: Hi!
Let's solve your equation step-by-step.
12x^2 + 54x = −42
Step 1: Subtract -42 from both sides.
12x^2 + 54x − (−42) = − 42 − (−42)
12x^2 + 54x + 42 = 0
Step 2: Factor left side of equation.
6(2x + 7)(x + 1) = 0
Step 3: Set factors equal to 0.
2x + 7 = 0 or x + 1 = 0
You have two answers.
x = −7/2 or x = −1
Hope this helps!
Help! Solve equation: xe^2x=0
Answer: x=0
Step-by-step explanation:
For this problem, there are no calculations needed. You just have to know your algebraic properties. Since we are looking for x, we know that x must be 0. The answer is 0. Figuring out e²ˣ can be tricky, but since there is an x multiplying it in front, we know that x must be 0 to make the equation equal to 0.
what should be added to 66.778 get 78.2
Answer:
11.422
Step-by-step explanation:
[tex]78.2 - 66.778 \\ = 11.422[/tex]
