Plz urgent <br>inequalities

Write an equation for the nth term of the arithmetic sequence.

tresset_1 [31]

Answer:

Step-by-step explanation:

3, 9, 15, 21, ...

9-3 = 6; 15-9 = 6; 21-15 = 6 ⇒ d = 6

first term: a = 3

difference: d = 6

so the formula:

$a_n=a+d(n-1)\\\\a_n=69+6(n-1)\\\\a_n =3+6n-6\\\\\underline{a_n=6n-3}$

and:

$a_{50}=6\cdot50-3=300-3=297$

5 0

2 years ago

WILL GIVE BRAINLIEST

EastWind [94]

Answer:

Let coordinates of vertex D be (x,y)

In parallelogram diagonals are bisect each other.

∴ Mid-point of AC= Mid-point of BD

⇒ (

2

3+(−6)

,

2

−4+2

)=(

2

−1+x

,

2

−3+y

)

⇒ (

2

−3

,

2

−2

)=(

2

−1+x

,

2

−3+y

)

⇒ (

2

−3

,−1)=(

2

−1+x

,

2

−3+y

)

Now,

⇒

2

−3

=

2

−1+x

⇒ −6=−2+2x

⇒ −4=2x

∴ x=−2

⇒ −1=

2

−3+y

⇒ −2=−3+y

⇒ 1=y

∴ y=1

∴ Coordinates of vertex D is (−2,1)

7 0

3 years ago

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

Luden [163]

Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

6 0

2 years ago

A circle with an area 9pi has a sector with a central angle of 1/9pi what is the area of the sector

ludmilkaskok [199]

Answer:

½pi or 0.5pi units²

Step-by-step explanation:

Area : angle

9pi : 2pi

x : pi/9

9pi/2pi = x/(pi/9)

4.5 × pi/9 = x

x = ½pi or 0.5pi units²

8 0

3 years ago

I can ride my bike 72 miles in 12 hours. What is my

IrinaVladis [17]

Answer: 108 miles

There is 6 miles per hour

Multiply 6x18=108

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Plz urgent inequalities ​

Plz urgent inequalities