What is the sum of the first 6 terms of the sequence defined by an = 3n - 2?

Answer:

15

Step-by-step explanation:

Let 2n+1 be the first odd integer.

Therefore, the consecutive odd integers will be 2n+3 and 2n+5

If the sum of the consecutive odd integers is 51 then:

⇒ 2n + 1 + 2n + 3 + 2n + 5 = 51

⇒ 6n + 9 = 51

⇒ 6n = 42

⇒ n = 7

To find the values of the integers, substitute the found value of n into the expressions:

Therefore, the three consecutive odd integers that sum to 51 are 15, 17 and 19.  The smallest of which is 15.

Answer:

-66

Step-by-step explanation:

add the numbers

-26 -37 = -66

[tex] - 26 - 37 = - 63[/tex]

Whenever the sign of the numbers is same , add them but don't forget the negative sign.

Please give brainliest

The probability that can be chosen by Jake will be 33.5%.

The area of the whole dartboard will be:

= πr²

where r will be:

= 3 + (4 × 4)

= 3 + 16

= 19

Area = π(19)² = 361π²

The area of 30, 40, and 50 points will be:

= π × [3 + (2 × 4)]²

= 121π²

The probability will be:

= (361π - 121π) × 100

= 33.5%

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:

(-4,1)

Step-by-step explanation:

Factoring, Guess and check.

Answer:

4x ÷ 7

Step-by-step explanation:

the product of 4 and a number (x)

would be 4x. Then you would divide by 7.

Answer:

see explanation

Step-by-step explanation:

a translation of 3 squares right means add 3 to the x- coordinate

a translation of 3 squares up means add 3 to the y- coordinate

then

(1, 1 ) → (1 + 3, 1 + 3 ) → (4, 4 )

(3, 1 ) → (3 + 3, 1 + 3 ) → (6, 4 )

(1, 4 ) → (1 + 3, 4 + 3 ) → (4, 7 )

Collin's sampling method will better represent the entire population.

Determine which sampling method will better represent the entire population.

From the question, we understand the Collin selected random names from the school directory.

While Karl surveyed only the students sitting close to him.

Karl's method is biased because students sitting far from him do not have a chance of being surveyed.

Hence, Collin's sampling method will better represent the entire population.

Read more about sampling method at:

https://brainly.com/question/16587013

#SPJ1

Answer:

1 / 1024

Step-by-step explanation:

Each flipping has 1/2 chance

In ten flippings:

[tex](\frac{1}{2} )^{10} =\frac{1^{10} }{2^{10} } =\frac{1}{1024}[/tex]

Hope this helps

Answer:

41.34

Step-by-step explanation:

We can use the Pythagorean theorem to solve for the distance. First we will create an imaginary triangle with the leg lengths being the x distance and y distance between the 2 points and the hypotenuse being the distance between the 2 points.

x distance =

[tex]15 - (-20) = 35[/tex]

y distance =

[tex] |-17-5| = | - 22| = 22[/tex]

We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle

xdistance²+ydistance²=distance²

35²+22²=distance²

1709=distance²

[tex] \sqrt{1709} = distance[/tex]

In decimal form the distance would be around 41.34.

That is the answer

- Kan Academy Advance

Answer:

4. x = 9 and y = 18

Step-by-step explanation:

Hello there!

When given such a problem we have to methods to handle this:

On this problem, let's limit ourself to substitution method;

x + y = 27 ..................... eq.1

y = 2x ........................ eq.2

Eq.2 is already manipulated. Substitute it into eq.1

x + y = 27

=> x + 2x = 27

3x = 27

x = 9

Substitute x into eq.2

y = 2 (9)

= 18

In terms of x and y;

(x, y) => (9, 18)

I hope this helps you.

Have a nice time and nice studies.

Answer:

see the attachment photo!

The different ways Johnny can improve his meal is 16

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex]  ways.

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]

This is called permutation of k items chosen out of m items (all distinct).

Given;

Mother tells him he may only make two additions to his meal

First addition; 1C4

Second addition; 1C4

1C4=4

=4x4

=16

Therefore, by combinations and permutations their will be 16ways

Learn more about combinations and permutations here:

https://brainly.com/question/16107928

#SPJ2

Step-by-step explanation:

the median is the value, where half of the other values is smaller (or equal), and the other half bigger (or equal).

with an even number of data points that is not directly possible to find.

in this case the 2 middle values are taken and their mean value is the median.

in our case, the 2 middle values are 12 and 14.

their mean value is

(12+14)/2 = 26/2 = 13

so,

13 is the median (even though if is not a data point itself).

Answer:

10 percent

Step-by-step explanation:

look closl

it's 10 percent ...................... 10%

The area of the triangle DEF is 2 square units

The given parameters are:

D(9,-8), E(8,-3), and F(2,-5),

The area of the triangle is calculated using:

Area = 0.5|x1 * (y2 -y3) + x2 * (y1 -y3) + x3 * (y2 -y1) |

This gives

Area = 0.5|9 * (-3 + 5) + 8 * (-8 + 5) + 2 * (-3 + 8) |

Evaluate

Area = 0.5|4|

Expand

Area = 2

Hence, the area of the triangle DEF is 2 square units

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

(x+8/3)²+y²=1

(x+8/3)²+y²+0²+2×0y=1

(x+8/3)²+(y+0)²=(V1)²

->center: C(8/3,0)

-> radius: V1

2y=x+10

3y=3x+15

2y-10=x

3y=3(2y-10)+15

2y-10=x

3y=6y-30+15

2y-10=x

0=3y+15

2y-10=x

3y=15

x=2y-10

y=5

2y=x+10

2×5=x+10

x=0

x=0, y=5

The formula for calculating the height is h = 3V/πr²

The formula given is the formula for calculating the volume of a cone

V = 1/3πr²h

where

h is the height

r is the radius

Make h the subject of the formula

Cross multiply

3V = πr²h

Divide both sides by πr²

3V/πr² = πr²h/πr²

h = 3V/πr²

Hence the formula for calculating the height is h = 3V/πr²

Learn more on subject of formula here: https://brainly.com/question/657646
#SPJ1

Answer:

2/7  ?

Step-by-step explanation:

Because 1/4 divided by 7/8th is 1/4. Hope this works

Answer:

X=70

Step-by-step explanation:

aw we can for a triangle, where the 2 angles are complementary from the outer ones, so the 2 angles are 50, and 60

so the third one will be 70

Answer:

[tex]2( \frac{2}{5} x + 2) = \frac{4}{5} x + 4[/tex]

Step-by-step explanation:

Use the distributive property.

Problem 1

Triangle ABE is similar to triangle DCE. This is because we have two pairs of congruent corresponding angles.

Refer to the angle angle (AA) similarity theorem for more info.

-------------------

For the other pair of triangles, we don't have enough info to determine if they are similar or not. We have info about one pair of sides, and a pair of angles, but that's about it.

We need to know if JL is proportional to MO, and in the same ratio as KL & NO are, if we wanted to use the side angle side (SAS) similarity theorem.

-------------------

============================================================

Problem 2

Divide the corresponding sides

We see the three ratios are equal to the same value (2) and that proves the triangles LNM and POQ are similar by the SSS (side side side) similarity theorem.

-------------------

Like before, we'll divide the corresponding sides

We don't have a match. Let's try rotating the second rectangle so that the side '8' is horizontal, and the side '3' is vertical

We don't have a match here either. There are other approaches we could take, but basically the two rectangles are not similar.

-------------------

Answer:

Discount amount = 34

Step-by-step explanation:

Discount amount = 202 - 168 = 34

The amount of iced tea left in quartz is  3 quartz

The coach makes 9 quarts of iced tea.

she fills 12 bottles with 2 cups of iced tea each to share with her team.

1 quartz = 4 cups

Therefore, she shared the following amount of tea in cups:

amount shared = 12 × 2 = 24 cups

Then, let's convert to quartz,

4 cups = 1 quartz

24 cups = ?

amount shared in quartz = 24 / 4 = 6 quarts

Therefore,

the amount of ice tea left = 9 - 6 = 3 quartz

learn more on quarts here: https://brainly.com/question/22443564

#SPJ1

To factorize a polynomial you need to find the zeros, and then you can write the polynomial as a product of bynomials.

For a polynomial of the form:

[tex]p(x) = A_n*x^n + A_{n-1}*x^{n-1} + ... + A_1*x + A_0[/tex]

We define the zeros as the values of x such that:

p(x) = 0.

On the above case, the degree of the polynomial is n (the maximum exponent). Then the number of zeros of the polynomial is n (same as the degree).

Once we know the n zeros, we can factorize the polynomial as:

[tex]p(x) = A_n*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]

For example, for the polynomial:

[tex]p(x) = 2x^2 - 8[/tex]

The two zeros are x = 2 and x = -2, then it can be rewriten as:

[tex]p(x) = 2*(x + 2)*(x - 2)[/tex]

If you want to learn more about polynomials:

https://brainly.com/question/4142886

#SPJ1