Find the fifth term of the arithmetic sequence in which t1 = 3 and tn = tn-1 + 4.

A) 5
B) 7
C) 19
D) 23

Answers

Answer 1

Answer: We have given $t_(1)=3$ and $t_(n) = t_(n-1) + 4$ . Fifth term is $t_(5)= t_(4)+4$ . It means we need to find $t_(4)$ and in order to find the latter, we have to find $t_(4)= t_(3)+4$ , $t_(3)= t_(2)+4$ and $t_(2)= t_(1)+4$ . Since we know the value of $t_(1)$ , beginning from the last equation we can find the value of $t_(5)$ . We can write that $t_(2)= t_(1)+4=3+4=7$ , $t_(3)= t_(2)+4=7+4=11$ and $t_(4)= t_(3)+4=11+4=15$ . Since $t_(5)= t_(4)+4$ , then $t_(5)= 15+4=19$

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Calculate sin a=0.34

Answers

$sina=0.34$ has already been calculated for us, but to calculate the angle, which is what I'm assuming you want to know, we must take the inverse trigonometric function of sin.

From: $sina=0.34$ , we can derive that:

$a=sin ^(-1) 0.34$

Using a scientific calculator to solve this, we can see that the degrees that a is equal to (rounded to the nearest degree) is:

$a=20$ °

Wish you luck! :)

Use elimination to solve this system of equations. 2r + 3s= 9 and 3r + 2s= 12

Answers

2r + 3s= 9 <=> -6r -9s = -27;
3r + 2s= 12 <=> 6r + 4s = 24;
=> 0*r -5*s = -3 => s = 3/5;

2*r + 3*(3/5) = 9<=> 10*r + 9 = 45 <=> 10*r = 36 => r = 18/5;

Answer:

(18/5,3/5)

Step-by-step explanation:

A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 10 cars needs to have oil added. If this is true (and assuming cars arriving independently), find the probability of each of the following:A. One out of the next four cars needs oil.B. Two out of the next eight cars needs oil.C. 5 out of the next 20 cars needs oil.

Answers

This question is about the concept of binomial probability distribution.

A) P(1) = 0.2916

B) P(2) = 0.1488

C) P(5) = 0.03192

Formula for binomial probability distribution is;

P(x) = nCx • p^(x) • q^(n - x)

Where; q = 1 - p

From the question, we are told that the claim is that 1 out of 10 cars need to have their oil checked.

Thus; p = 1/10 = 0.1

q = 1 - 0.1

q = 0.9

A) P(one out of the next four cars need oil) is;

P(1) = 4C1 × 0.1^(1) × 0.9^(4 - 1)

P(1) = 4 × 0.1 × 0.9³

P(1) = 0.2916

B) P(2 out of the next 8 cars needs oil) is;

P(2) = 8C2 × 0.1² × 0.9^(8 - 2)

P(2) = 28 × 0.01 × 0.531441

P(2) = 0.1488

C) P(five out of the next twenty cars needs oil) ;

P(5) = 20C5 × 0.1^(5) × 0.9^(20 - 5)

P(5) = 15504 × 0.00001 × 0.20589113209

P(5) = 0.03192

Read more at; brainly.com/question/24239758

Answer:

0.2916, 0.1488, 0.0319

Step-by-step explanation:

Given that a sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 10 cars needs to have oil added.

Since each trial is independent there is a constant probability for any random car to need oil is 0.10

Let X be the number of cars that need oil

A) Here X is BIN(4,0.1)

$P(X=1) = 4C1(0.1)(0.9)^3 \n= 0.2916$

B) Here X is Bin (8, 0.1)

$P(x=2) = 8C2 (0.1)^2 (0.9)^6\n\n=0.1488$

C) Here X is Bin (20,5)

$P(x=5) = 20C5 (0.1)^5 (0.9)^(15) \n=0.0319$

Please help If triangle ABC is dialted by a scale factor of 2 and the origin as it's center, what would be the coordinates of A'?

A.(4,2)
B.(9,9)
C.(6,6)

Answers

It would be C since a scale factor of 2 makes the original A coordinate of (3,3) times 2 therefore the new coordinates being (6,6)

If you can please help me with this question~ the question is the image :)

Answers

Answer:

Step-by-step explanation:

Start by using the distance formula to find the raidus

The two points are (-2,1) and (-4,1)

√((-4+2)²+(1-1)²)= 2

The radius is two and we have our center which means we can write

(x+2)²+(y-1)²=4

now it's just a matter of expanding everyhting

x²+4x+4+y²-2y-3=0

x²+y²+4x-2y+1=0

This is equal to B

You can find the __________ parts of two congruent triangles by aligning them perfectly on top of each other.A. complementary
B. similar
C. corresponding
D. supplementary

Answers

Answer:

You can find the CORRESPONDING parts of two congruent triangles by aligning them perfectly on top of each other.

Step-by-step explanation:

We know that when two congruent triangles are placed over each other then the congruent sides corresponding to both the triangles also align on each other.

Since, when two triangles are congruent then all corresponding angles and sides of the two triangles are also congruent.

Hence, the answer is:

Option: C

C. corresponding

You can find the C. corresponding parts of two congruent triangles by aligning them perfectly on top of each other.

How is this true for triangles ?

Corresponding parts of two congruenttriangles are the parts that have the same relative position. For example, the corresponding parts of triangle ABC and triangle DEF are AB and DE , ∠A and ∠D, and ∠B and ∠E.

If two triangles are congruent, then their corresponding parts are congruent. This means that if we align two congruent triangles perfectly on top of each other, then the corresponding parts will coincide.

In conclusion, option C is correct.

Find out more on corresponding parts at brainly.com/question/29592419

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