Type of angle: Angle measures:

Given the arithmetic sequence: u(1)= 124, u(2)= 117, u(3)= 110, u(4)=103,...

omeli [17]

We are given

arithmetic sequence: u(1)= 124, u(2)= 117, u(3)= 110, u(4)=103

so, first term is 124

u(1)= 124

now, we can find common difference

$d=u(2)-u(1)$

$d=117-124$

$d=-7$

now, we can find kth term

$u(k)=u(1)+(k-1)d$

now, we can plug values

and we get

$u(k)=124+(k-1)*-7$

$u(k)=124-7k+7$

$u(k)=131-7k$

u(k) must be negative

so,

$u(k)=131-7k$

$131-7k$

now, we can solve for k

$7k>131$

$k>18.714$

so, it's closest integer value is

$k=19$ ..............Answer

3 0

2 years ago

Find k so that the distance from (–1, 1) to (2, k) is 5 units. k= k= *there are two solutions for 2*

dalvyx [7]

Answer:

k = -3

k =5

Step-by-step explanation:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\$

$5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\$

$\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3$

7 0

2 years ago

Read 2 more answers

A 47-foot-long piece of pipe is to be cut into three pieces. The second piece is three times as long as the first piece, and the

DanielleElmas [232]

A = first piece, b = second piece, c = third piece

a + b + c = 47
b = 3a
c = 5a + 2

a + (3a) + (5a + 2) = 47.....combine like terms
9a + 2 = 47
9a = 47 - 2
9a = 45
a = 45/9
a = 5 ft

b = 3a.....b = 3(5)....b = 15 ft
c = 5a + 2....c = 5(5) + 2.....c = 25 + 2....c = 27 ft

longest piece (c) = 27 ft

7 0

2 years ago

A study found that a 95% confidence interval for the mean μ of a particular population was computed from a random sample of 1200

kotykmax [81]

Answer:

95% confidence interval for the mean μ is (6,14)

The Population mean μ lies between ( 6, 14 )

Step-by-step explanation:

Explanation:-

Given random sample 'n' = 1200

95% confidence interval for the mean μ is determined by

$(x^{-} -Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} +Z_{\alpha } \frac{S.D}{\sqrt{n} } )$

Level of significance = 95% 0r 0.05

Z₀.₀₅ = 1.96

$(x^{-} -Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} +Z_{\alpha } \frac{S.D}{\sqrt{n} } )$ = 10 ± 4

Mean of the small sample = 10

95% of confidence intervals are

( 10 ±4 )

( 10 -4 , 10+4)

( 6 , 14 )

95% confidence interval for the mean μ lies between ( 6, 14 )

8 0

2 years ago

Which lines best approximate the directrices of the ellipse? Round to the nearest tenth.

Mrrafil [7]

C aka y = -4.6 and y = 4.6

Step-by-step explanation:

i just took the unit review test on edg. :)

6 0

1 year ago

Type of angle:Angle measures: