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2 years ago

Find the 66th term of the arithmetic sequence -28,-45, -62,-

Mathematics

2 answers:

navik [9.2K]2 years ago

7 0

Answer:

-1133

Step-by-step explanation:

-17(66-1)+(-28)

-17(65)+(-28)

type in calculator or desmos

-1133

Alexeev081 [22]2 years ago

6 0

Answer:

-1133

Step-by-step explanation:

Formula for nth term

aₙ = a + (n - 1)d

Finding d

d = -45 - (-28)
d = -45 + 28
d = -17

Solving for a₆₆

a₆₆ = -28 + 65(-17)
a₆₆ = -28 - 1105
a₆₆ = -1133

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3 years ago

Listed below are amounts (in millions of dollars) collected from parking meters by a security company in a certain city. A lar

Alona [7]

Answer: B

Step-by-step explanation: To obtain the mean for a general set of data, the formula used is;

= (sum of all the data set)/ (number of data set)

The number of data set for the two samples is 10

For the mean for the security company;

= (1.6+1.8+1.6+1.8+1.7+1.2+1.1+1.2+1.2+1.5)/10 = 14.7/10

= $ 1.47million

For the mean for the other companies;

= (1.5+2.1+1.9+2.2+1.9+1.7+2.1+2.2+2.2+1.8)/10 =19.6/10

= $ 1.96 million

The data from the samples have to be rearranged before the median can be obtained;

For the Security Company;

1.1 1.2 1.2 1.2 1.5 1.6 1.6 1.7 1.8 1.8

There are two data sets in the middle, therefore the median will be obtained by finding the average of the data sets;

= (1.5+1.6)/2 =$ 1.55 million

For the other companies;

1.5 1.7 1.8 1.9 1.9 2.1 2.1 2.2 2.2 2.2

There are two data sets in the middle, therefore the median will be obtained by finding the average of the data sets;

= (1.9+2.1)/2 = $ 2.00 million

Therefore, the answer is B

4 0

3 years ago

Find the measures of each angle in the inscribed quadrilateral.

Marat540 [252]

Answer:

m∠P = 55° , m∠R = 125° , m∠Q = 110° , m∠S = 70°

Step-by-step explanation:

* Lets study the figure

- A circle and inscribed quadrilateral PQRS

- The four vertices of the quadrilateral lie on the circumference

of the circle

∴ PQRS is a cyclic quadrilateral

* Lets revise the properties of the cyclic quadrilateral

- Each two opposite angles are supplementary, that means

the sum of each two opposite angles = 180°

- The measure of the exterior angle = the measure of the

opposite interior angle

* Lets solve the problem

∵ PQRS is a cyclic quadrilateral

∴ m∠P + m∠R = 180° ⇒ opposite angles

∵ m∠P = 5y + 30

∵ m∠R = 15y + 50

∴ 5y + 30 + 15y + 50 = 180 ⇒ add the like terms

∴ 20y + 80 = 180 ⇒ subtract 80 from both sides

∴ 20y = 100 ⇒ divide both sides by 20

∴ y = 5

* Now lets substitute the value of y in each angle to find

their measures

∵ m∠P = 5y + 30

∴ m∠P = 5(5) + 30 = 25 + 30 = 55°

∵ m∠R = 15y + 50

∴ m∠R = 15(5) + 50 = 75 + 50 = 125°

∵ m∠Q = y² + 85

∴ m∠Q = 5² + 85 = 25 + 85 = 110°

∵ ∠S is opposite to ∠Q

∴ m∠S + m∠Q = 180° ⇒ opposite angles in the cyclic quadrilateral

∴ m∠S + 110 = 180 ⇒ subtract 110 from the both sides

∴ m∠S = 70°

* The measures of the angles are

m∠P = 55° , m∠R = 125° , m∠Q = 110° , m∠S = 70°

8 0

3 years ago

Sumeet is building two types of birdhouses. The more traditional type takes 4 pieces of wood and 2 hours to build. The more lavi

mina [271]

Answer:

The no. of traditional type birdhouses are 4 and the no. of lavish type birdhouses are 3.

Step-by-step explanation:

Let x be the no. of traditional type birdhouses

The more traditional type takes 4 pieces of wood and 2 hours to build.

One house requires wood = 4

x houses requires wood = 4x

One house requires time = 2 hours

x houses requires time = 2x

Let y be the no. of lavish type birdhouses

The more lavish type takes 10 pieces of wood and 7 hours to build.

One house requires wood = 10

y houses requires wood = 10y

One house requires time = 7 hours

y houses requires time = 7y

Now we are given that he has a total of 46 pieces of wood and 29 hours to work,

So, equations becomes : $4x+10y = 46\\2x+7y=29$

Plot these equations on graph

$4x+10y = 46$ ---Blue line

$2x+7y=29$ ---Green line

Refer the attached figure

The intersection point provides the solution

Intersection point : (4,3)

So, x = 4 and y = 3

Hence the no. of traditional type birdhouses are 4 and the no. of lavish type birdhouses are 3.

8 0

3 years ago

How to find percentile rank

GuDViN [60]

See this formula in more detail in the Examples section. Formula: To find the percentile rank of a score, x, out of a set of n scores, where x is not included:Example: If Jason graduated 25th out of a class of 150 students, then 125 students were ranked below Jason.

Percentiles - Regents Exam Prep Center is were i for my information for you

6 0

3 years ago