Find the sum of the even numbers between 199 to 1999​

Answers

Answer 1

[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]

Answer 2

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.

Learn more about this concept here:

https://brainly.com/question/18837188

#SPJ2


Related Questions

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

Answers

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]

Which expression is equal to 7 times the sum of a number and 4

Answers

Answer:

7(n + 4)

Step-by-step explanation:

Represent the number by n.  Then the verbal expression becomes

7(n + 4).

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

Answers

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

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?​

Answers

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.

For more references on area, click;

https://brainly.com/question/27683633

#SPJ2

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

Answers

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

Answers

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

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​

Answers

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

6. Classify the traianle as scalene, isosceles or equilateral. Explain. Leave answers in square root form.
TAL

Answers

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.

limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)​

Answers

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.

Please help, thanks!!!!!

Answers

Answer:

[ 2+0+8. 0+0+12]

[-4+10+2. 0+25+3]

[10. 12]

[8. 28]

Option 3 is the solution

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 ​

Answers

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.

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.)

Answers

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

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

Answers

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

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.

Answers

Answer:

x + y ≤ 20,000y ≤ 5,000x ≥ 2y

Step-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

7.619 by 10^-3



7.254 by 10^2​

Answers

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 ;) ❤❤❤

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

Answers

Answer:

A. 804

Step-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

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.

Answers

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.

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

Answers

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

Help! Solve equation: xe^2x=0

Answers

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.

Write 41/12 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats. Write as a decimal.

Answers

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


What is an equation of the line that passes through the points (-5, 8) and (5,0)?

Answers

Answer:

y= -0.8x + 4

Midpoint is 0,4

what should be added to 66.778 get 78.2​

Answers

Answer:

11.422

Step-by-step explanation:

[tex]78.2 - 66.778 \\ = 11.422[/tex]

plz help i'm having a really hard time with this

Answers

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

Please Help quick!!! What is the value of a missing angle?​

Answers

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

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?

Answers

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

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

Answers

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]

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

Answers

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

I help! solve 12x^2+54x=-42

Answers

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!

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?

Answers

The answer would be $3000

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?

Answers

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

Other Questions
Delta Insurance Company has a surplus-share treaty with Eversafe Reinsurance. Delta has a retention limit of $200,000, and nine lines of insurance are ceded to Eversafe. How much will Eversafe pay if a $1,600,000 building insured by Delta suffers an 40 precent loss? 1. A) $600,000 2. B) $700,000 3. C) $720,000 4. D) $800,000 I am a fruit. If you change my first letter to a d, Im a window covering. If you take away my first two letters, I am an animal. If you take away my first and my last letters, I am a form of music. What am I? Find the coefficient of third term of (2x1)^6. PLEASE HELPRead the passage from Sugar Changed the World. Cutting cane was hard work, but it was nothing like what came next: Piles of freshly cut cane had to be fed into the ever-turning mill wheels, until they were completely crushed. The owners insisted that during the work hours the grinding never stop, no matter what. The mills were most often tended by women who were doing dangerous work while getting almost no rest. That was a very bad combination. An ax was often propped up near the rollers so if a slave closed her eyes for a second while pushing the cane, her arm could be hacked off before she was pulled through the merciless grinders. Guests at sugar plantations often remarked on how many one-armed people they saw. Day after day, week after week, month after month, the cane was cut, hauled to the mill, and fed through the rollers. The mills kept going as long as there was cane to grindthe season varied between four and ten months, depending on the local growing conditions. A visitor who came to Brazil in 1630 described the scene: "People the color of the very night, working briskly and moaning at the same time without a moment of peace or rest, whoever sees all the confused and noisy machinery . . . will say that this indeed is the image of Hell. Which text evidence best supports the authors' claim that a frantic pace made working conditions even worse? "The owners insisted that during the work hours the grinding never stop, no matter what." "The mills were most often tended by women who were doing dangerous work while getting almost no rest." "Guests at sugar plantations often remarked on how many one-armed people they saw." this indeed is the image of Hell Please help helppp :(((( 3x + 4y = 14 x = 2y - 12 Which point satisfies both equations? A) (-2,-2) B) (-2,5) C) (-4,4) D) (2,2) If 2/3 inch on a map corresponds to an actual distance of 9 miles, what distance on the map will represent 21 miles? the author suggest that the desire to belong is a very powerful-if not most powerful-human emotio do you agree or disagree The cost to manufacture one unit of Rinker Audio Products' bestselling hearing aid, the Magnifier, is $87.50. The CFO of the company, Neha Patel, has determined that if the company expands the output of its biggest U.S. plant by 20 percent, the unit cost would be only $82.50. The concept that as plant output expands, unit costs decrease, is known as Group of answer choices 1. Name one practice that is prohibited under Section 8 of RESPA. 2. List at least three categories under ECOA on which creditors may not base credit decisions. 3. Define rescission as it relates to a mortgage loan transaction. 4. List at least two practices that are not prohibited with regard to appraisers. Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 \text{ cm}35 cm35, start text, space, c, m, end text. What is the distance the hula hoop rolls in 444 full rotations? The following statements are from Enlightenment philosophers: Constant experience shows us that every man invested with power is apt to abuse it. By pursuing his own interest, he frequently promotes that of the society more effectually than when he really intends to promote it. You are free at all times, in all places, as soon as you do what you wish to do. The liberty of man in society is to be under no other legislative power but that established by consent in the commonwealth. Which statement reflects the idea of social contract? 1 2 3 4 Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 8 sin(xy), (0, 9) rewrite each of the sentences, adding an adverb to modify the verb. they walked through the woods. y=2/5x-12 is it liear or nolinear or both A 70 kg human body typically contains 140 g of potassium. Potassium has a chemical atomic mass of 39.1 u and has three naturally occurring isotopes. One of those isotopes, 40K,is radioactive with a half-life of 1.3 billion years and a natural abundance of 0.012%. Each 40K decay deposits, on average, 1.0 MeV of energy into the body. What yearly dose in Gy does the typical person receive from the decay of 40K in the body? Which is a primary function of a vacuole in a cell?O A. enzyme productionO B. protein synthesisO C. storageD. reproduction The cost for an upcoming field trip is $30 per student. The cost of the field trip C. in dollars, is a function of the number of students x.Select all the possible outputs for the function defined by C(x)=30a. 20b. 30c. 50d. 90e. 100 the slope of a line parallel to the given line 8x-2y=5 #1: Simplify the expression below. Type your answer as an integer.7 + 1 - 18 : 6