Expand & simplify
(2x + 3)(x + 2)

Answer:

See explanation

Step-by-step explanation:

Solving (a):

[tex]a_n = 6a_{n-1}[/tex] where [tex]a_0 = 2[/tex]

n = 1

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_1 = 6a_{1-1}[/tex]

[tex]a_1 = 6a_{0}[/tex]

Substitute 2 for [tex]a_0[/tex]

[tex]a_1= 6 * 2[/tex]

[tex]a_1= 12[/tex]

n = 2

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_2 = 6a_{2-1}[/tex]

[tex]a_2 = 6a_{1}[/tex]

Substitute 12 for [tex]a_1[/tex]

[tex]a_2= 6 * 12[/tex]

[tex]a_2= 72[/tex]

n = 3

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_3 = 6a_{3-1}[/tex]

[tex]a_3 = 6a_2[/tex]

Substitute 72 for [tex]a_2[/tex]

[tex]a_3= 6 * 72[/tex]

[tex]a_3= 432[/tex]

n = 4

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_4 = 6a_{4-1}[/tex]

[tex]a_4 = 6a_{3}[/tex]

Substitute 432 for [tex]a_3[/tex]

[tex]a_4 = 6 * 432[/tex]

[tex]a_4 = 2592[/tex]

n = 5

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_5 = 6a_{5-1}[/tex]

[tex]a_5 = 6a_4[/tex]

Substitute 2592 for [tex]a_4[/tex]

[tex]a_5 = 6 * 2592[/tex]

[tex]a_5 = 15552[/tex]

n = 6

[tex]a_n = 6a_{n-1}[/tex]

[tex]a_6 = 6a_{6-1}[/tex]

[tex]a_6 = 6a_{5}[/tex]

Substitute 15552 for [tex]a_5[/tex]

[tex]a_6 = 6 * 15552[/tex]

[tex]a_6 = 93312[/tex]

[tex]a_1= 12[/tex]   [tex]a_2= 72[/tex]   [tex]a_3= 432[/tex]   [tex]a_4 = 2592[/tex]   [tex]a_5 = 15552[/tex]   [tex]a_6 = 93312[/tex]

Solving (b):

[tex]a_n = a^2_{n - 1[/tex] where [tex]a_1 = 2[/tex]

We have

[tex]a_1 = 2[/tex] which serves as the first term

n =2

[tex]a_n = a^2_{n - 1[/tex]

[tex]a_2 = a^2_{2-1}[/tex]

[tex]a_2 = a^2_{1}[/tex]

Substitute 2 for [tex]a_1[/tex]

[tex]a_2 = 2^2[/tex]

[tex]a_2 = 4[/tex]

n = 3

[tex]a_3 = a^2_{3-1}[/tex]

[tex]a_3 = a^2_{2}[/tex]

[tex]a_3 = 4^2[/tex]

[tex]a_3 = 16[/tex]

n = 4

[tex]a_4 = a^2_{4-1}[/tex]

[tex]a_4 = a^2_3[/tex]

[tex]a_4 = 16^2[/tex]

[tex]a_4 = 256[/tex]

n =5

[tex]a_5 = a^2_{5-1[/tex]

[tex]a_5 = a^2_4[/tex]

[tex]a_5 = 256^2[/tex]

[tex]a_5 = 65536[/tex]

n = 6

[tex]a_6 = a^2_{6-1[/tex]

[tex]a_6 = a^2_{5[/tex]

[tex]a_6 = 65536^2[/tex]

[tex]a_6 = 4294967296[/tex]

[tex]a_1 = 2[/tex]   [tex]a_2 = 4[/tex]   [tex]a_3 = 16[/tex]   [tex]a_4 = 256[/tex]   [tex]a_5 = 65536[/tex]   [tex]a_6 = 4294967296[/tex]

Solving (c):

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] [tex]a_0=1[/tex]  ; ;  [tex]a_1=2[/tex]

[tex]a_1=2[/tex] ---- First term

n = 2

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_2=a_{2-1}+3a_{2-2}[/tex]

[tex]a_2=a_1+3a_0[/tex]

Substitute values for a1 and a0

[tex]a_2=2+3 * 1[/tex]

[tex]a_2=2+3[/tex]

[tex]a_2=5[/tex]

n = 3

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_3=a_{3-1}+3a_{3-2}[/tex]

[tex]a_3=a_{2}+3a_{1}[/tex]

[tex]a_3=5+3 * 2[/tex]

[tex]a_3=5+6[/tex]

[tex]a_3=11[/tex]

n = 4

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_4=a_{4-1}+3a_{4-2}[/tex]

[tex]a_4=a_{3}+3a_{2}[/tex]

[tex]a_4=11+3 * 5[/tex]

[tex]a_4=11+15[/tex]

[tex]a_4=26[/tex]

n = 5

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_5=a_{5-1}+3a_{5-2};[/tex]

[tex]a_5=a_{4}+3a_3[/tex]

[tex]a_5=26+3 * 11[/tex]

[tex]a_5=26+33[/tex]

[tex]a_5=59[/tex]

n = 6

[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes

[tex]a_6=a_{6-1}+3a_{6-2}[/tex]

[tex]a_6=a_{5}+3a_4[/tex]

[tex]a_6=59+3*26[/tex]

[tex]a_6=59+78[/tex]

[tex]a_6=137[/tex]

[tex]a_1=2[/tex]   [tex]a_2=5[/tex]   [tex]a_3=11[/tex]   [tex]a_4=26[/tex]   [tex]a_5=59[/tex]   [tex]a_6=137[/tex]

Solving (d):

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex];     [tex]a_0=1[/tex]; [tex]a_1=1[/tex]

[tex]a_1=1[/tex] --- First term

n = 2

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_2=2 * a_{2-1}+2^2a_{2-2}[/tex]

[tex]a_2=2 * a_1+4*a_0[/tex]

[tex]a_2=2 * 1+4*1[/tex]

[tex]a_2=2 +4[/tex]

[tex]a_2=6[/tex]

n = 3

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_3=3 * a_{3-1}+3^2 * a_{3-2}[/tex]

[tex]a_3=3 * a_{2}+9 * a_{1}[/tex]

[tex]a_3=3 * 6+9 * 1[/tex]

[tex]a_3=18+9[/tex]

[tex]a_3=27[/tex]

n = 4

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_4=4*a_{4-1}+4^2*a_{4-2}[/tex]

[tex]a_4=4*a_{3}+16*a_{2}[/tex]

[tex]a_4=4*27+16*6[/tex]

[tex]a_4=204[/tex]

n = 5

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_5=5 * a_{5-1}+5^2 * a_{5-2}[/tex]

[tex]a_5=5 * a_{4}+25 * a_{3}[/tex]

[tex]a_5=5 * 204+25 *27[/tex]

[tex]a_5=1695[/tex]

n = 6

[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes

[tex]a_6=6 * a_{6-1}+6^2*a_{6-2}[/tex]

[tex]a_6=6 * a_{5}+36*a_{4}[/tex]

[tex]a_6=6 * 1695+36*204[/tex]

[tex]a_6=17514[/tex]

[tex]a_1=1[/tex]   [tex]a_2=6[/tex]   [tex]a_3=27[/tex]   [tex]a_4=204[/tex]   [tex]a_5=1695[/tex]   [tex]a_6=17514[/tex]

Solving (e):

[tex]a_n= a_{n-1}+a_{n-3};\ a_0=1; a_1=2; a_2=0[/tex]

First term: [tex]a_1=2[/tex]

Second Term: [tex]a_2=0[/tex]

n = 3

[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes

[tex]a_3= a_{3-1}+a_{3-3}[/tex]

[tex]a_3= a_{2}+a_0[/tex]

[tex]a_3= 0+1[/tex]

[tex]a_3= 1[/tex]

n = 4

[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes

[tex]a_4= a_{4-1}+a_{4-3}[/tex]

[tex]a_4= a_{3}+a_{1}[/tex]

[tex]a_4= 1+2[/tex]

[tex]a_4=3[/tex]

n = 5

[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes

[tex]a_5= a_{5-1}+a_{5-3}[/tex]

[tex]a_5= a_{4}+a_{2}[/tex]

[tex]a_5= 3 + 0[/tex]

[tex]a_5= 3[/tex]

n = 6

[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes

[tex]a_6= a_{6-1}+a_{6-3}[/tex]

[tex]a_6= a_{5}+a_{3}[/tex]

[tex]a_6= 3 + 1[/tex]

[tex]a_6= 4[/tex]

[tex]a_1=2[/tex]   [tex]a_2=0[/tex]   [tex]a_3= 1[/tex]   [tex]a_4=3[/tex]   [tex]a_5= 3[/tex]   [tex]a_6= 4[/tex]

Answer:

the number of men be 56

And, the number of women be 74

Step-by-step explanation:

The computation of the number of each genders attended the conference is shown below;

Let us assume the number of men be x

And, the number of women be y

Now the equations would be

x + y = 130 .............. (1)

And,

y = 18 + x ................ (2)

Now put the y value in the equation 1

x + 18 + x = 130

2x = 130 - 18

2x = 112

x = 56

Now the y is

= 18 + 56

= 74

So, the number of men be 56

And, the number of women be 74

Answer:

y=mc

Step-by-step explanation:

Answer:

search that question up on brainly it got the answer bruu

Step-by-step explanation:

Answer:

1. Yes. Two or more angles are equivalent

2. 2700 ft

3. 3000 ft

Step-by-step explanation:

1.

∠EAD = ∠CAB (same angle)

∠AED = ∠ACB (because AC is a straight line and ED and CB are parallel)

2.

1200:3600

1:3

This means that for any given side for triangle AED, the corresponding side for triangle ACB is three times bigger. ED corresponds to CB, so:

900 x 3 = 2700

3.

We know that for any given side for triangle AED, the corresponding side for triangle ACB is three times bigger. AE corresponds to AC, so:

1000 x 3 = 3000

Answer:

it turns out google has the answer

Step-by-step explanation:

can i get brainlyest

Answer:

B. 4 mL

Step-by-step explanation:

Answer:

M = 4/3 - c/3

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

The slope formula is the difference in y over the difference in x, so 4-0/3-0.

Answer:

M=6 OR slope=6

Step-by-step explanation:

Use slope formula

Answer:

Step-by-step explanation:

Slope is defined as the change of y over the change of x or rise over run. This is calculated by subtracting the second set of vales from the first set of values.

For y:

We have 10 and 4 for the y coordinates (y is the second number in a coordinate set). We will subtract 4 from 10, to get a result of 6.

For x:

We have 3 and 0 for the x coordinates (x is the first number in a coordinate set). We will subtract 0 from 3, to get a result of 3.

Slope is 6/3 or 2/1

Answer:

we dont have the info

Step-by-step explanation:

Answer:

0.55199

Step-by-step explanation:

When we have a random number of samples, We solve using z score formula

z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation

n is random number of samples

z = 0.83/77/√147

z = 0.13069

Probabilty value from Z-Table:

P(x<48.83) = 0.55199

The probability that the mean of the sample would differ from the population mean by less than 0.83 months is 0.55199

The result of first step is 6y+3+3y = 5 and values of x and y after solving are 1/4 and 9/2 respectively.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Given that, the two equations x=6y+3 and x+2y=5 being solved by substitution method

So, the equations are,

x=6y+3.......(i)

x+2y=5......(ii)

Substituting eq(i) in eq(ii)

6y+3+2y = 5

8y = 2

y = 1/4

Put y = 1/4 in eq(i)

x = 6x1/4+3

x = 9/2

Hence, The result of first step is 6y+3+3y = 5 and values of x and y after solving are 1/4 and 9/2 respectively.

For more references on substitution method, click;

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#SPJ2

Answer:

Step-by-step explanation:

Given that:

A list of 25 recently sold paintings in an auction house is available, and eight artists were represented in the sales.

The objective is to determine if the correlation coefficient would be an appropriate way to summarize the relationship between the artist (x) and sale price (y).

From the information given;

NO, The correlation coefficient would not be an appropriate way to summarize the relationship between artist (x) and sale price (y).

The reason is being that since variable (x) is the artist and which is regarded as the categorical variable even though it is attributed to numerical values, it cannot and will not be used in quantitative studies like correlation.  

Answer:

88.9%

Step-by-step explanation:

Answer:

Uhm answer what? there is no picture nor question.

Step-by-step explanation:

theres nothing there

Step-by-step explanation:

do u play among us

Answer:

10/9

Step-by-step explanation:

1/3+7/9=10/9

Step-by-step explanation:

= 1 + 7

3 9

= 9+21

27

= 28

27 ans

Answer:

.

Step-by-step explanation:

We want to find the expected value for Jessie on the come out roll.

The expected value is EV = $0.50

We know that for an event with outcomes {x₁, x₂, ..., xₙ}, each with probability {p₁, p₂, ..., pₙ}, the expected value is given by:

EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ

Where the probabilities are written in decimal form.

We have the outcomes:

x₁ = winning $5.

p₁ = 0.29

x₂ = losing $5

p₂ = 0.19

x₃ = not win nor lose

p₃ = 1 - 0.19 - 0.29 = 0.52

Then the expected value is:

EV = $5*0.29 - $5*0.19 + $0*0.52 = $0.50

If you want to learn more, you can read:

https://brainly.com/question/22097128

Answer: d,d,a,,d,c,

Step-by-step explanation:

Answer:

ddadc

Step-by-step explanation:

Answer:

1) future value = present value x [1 + (i x n)] = $300 x [1 + (3.5% x 4)] = $342

2) using the compound interest formula:

future value = $225 x (1 + 4.1%)¹°⁵ = $238.98

Using the simple interest formula doesn't yield the same answer = $225 x [1 + (4.1% x 1.5)] = $238.84. In this case it is close due to a very short period of time and low interest rate.

3) future value = present value x (1 + i)ⁿ = $1,700 x (1 + 6%)⁴ = $2,146.21

since the interest is annual, we must convert 48 months to 4 years

Answer:

5

Step-by-step explanation:

Since Riley has already saved 80 dollars and she needs to save 150 dollars.

150-80=70

She earns 14 dollars per week:

70/14=5

I also wrote a equation:

(150-80)/14=x

Hope this was helpful!

Answer:

46

Step-by-step explanation:

it wouldn't change if it was to be rotated

Answer:

a) Kylie has 8 marbles

b) 7 Cylinders

c) 17 carrots

d) 8 marbles belong to Shauntay

Step-by-step explanation:

5. Identify the type and subtype of each of the fol-

lowing problems.

a. Shawn has 15 marbles, which is 7 more marbles than Kyle has. How many marbles does Kyle have?

Shawn = 15 marbles

S = K + 7

15 = K + 7

K = 15 - 7

K = 8 marbles

Kylie has 8 marbles

b. Tiffany has 12 blocks, 5 of which are cubes and the rest cylinders. How many blocks are cylinders?

T = 12 blocks

Cubes = 5

Cylinders = the rest

12 blocks = Cubes + Cylinders

Cylinders = 12 - Cubes

Cylinders = 12 - 5

Cylinder = 7

c. Peter had some carrots. After he ate 3 of them, he had 14 carrots left. How many carrots did Peter have before?

Number of carrots Peter has before

= Number of carrots he ate + Number of carrots he has now

= 14 + 3

= 17 carrots

d. In a bag of 17 marbles, 9 marbles belong to Kelly and the rest belong to Shauntay. How many marbles belong to Shauntay?

Total number of Marbles = 17

Kelly = 9 marbles

Shauntay = ?

Total = Kelly + Shauntay

Shauntay = Total - Kelly's marbles

= ( 17 - 9) marbles

= 8 marbles

8 marbles belong to Shauntay

Answer:

a) Kylie has 8 marbles

b) 7 Cylinders

c) 17 carrots

d) 8 marbles belong to Shauntay

Step-by-step explanation:

5. Identify the type and subtype of each of the fol-

lowing problems.

a. Shawn has 15 marbles, which is 7 more marbles than Kyle has. How many marbles does Kyle have?

Shawn = 15 marbles

S = K + 7

15 = K + 7

K = 15 - 7

K = 8 marbles

Kylie has 8 marbles

b. Tiffany has 12 blocks, 5 of which are cubes and the rest cylinders. How many blocks are cylinders?

T = 12 blocks

Cubes = 5

Cylinders = the rest

12 blocks = Cubes + Cylinders

Cylinders = 12 - Cubes

Cylinders = 12 - 5

Cylinder = 7

c. Peter had some carrots. After he ate 3 of them, he had 14 carrots left. How many carrots did Peter have before?

Number of carrots Peter has before

= Number of carrots he ate + Number of carrots he has now

= 14 + 3

= 17 carrots

d. In a bag of 17 marbles, 9 marbles belong to Kelly and the rest belong to Shauntay. How many marbles belong to Shauntay?

Total number of Marbles = 17

Kelly = 9 marbles

Shauntay = ?

Total = Kelly + Shauntay

Shauntay = Total - Kelly's marbles

= ( 17 - 9) marbles

= 8 marbles

8 marbles belong to Shauntaya) Kylie has 8 marbles

b) 7 Cylinders

c) 17 carrots

d) 8 marbles belong to Shauntay

Step-by-step explanation:

5. Identify the type and subtype of each of the fol-

lowing problems.

a. Shawn has 15 marbles, which is 7 more marbles than Kyle has. How many marbles does Kyle have?

Shawn = 15 marbles

S = K + 7

15 = K + 7

K = 15 - 7

K = 8 marbles

Kylie has 8 marbles

b. Tiffany has 12 blocks, 5 of which are cubes and the rest cylinders. How many blocks are cylinders?

T = 12 blocks

Cubes = 5

Cylinders = the rest

12 blocks = Cubes + Cylinders

Cylinders = 12 - Cubes

Cylinders = 12 - 5

Cylinder = 7

c. Peter had some carrots. After he ate 3 of them, he had 14 carrots left. How many carrots did Peter have before?

Number of carrots Peter has before

= Number of carrots he ate + Number of carrots he has now

= 14 + 3

= 17 carrots

d. In a bag of 17 marbles, 9 marbles belong to Kelly and the rest belong to Shauntay. How many marbles belong to Shauntay?

Total number of Marbles = 17

Kelly = 9 marbles

Shauntay = ?

Total = Kelly + Shauntay

Shauntay = Total - Kelly's marbles

= ( 17 - 9) marbles

= 8 marbles

8 marbles belong to Shauntay

Step-by-step explanation:

Answer:

a. vfsvcsgefceveggevehe

Answer:31

Step-by-step explanation:

Answer:

b) 31 %

Step-by-step explanation:

Answer:

Negative 1/8 is the answer

Answer:

A

Step-by-step explanation:

We are given the equation:  

[tex]x^2+xy-3y=3[/tex]

And we want to find dy/dx at the point (2, 1).

Find dy/dx. We can take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}[x^2+xy-3y]=\frac{d}{dx}[3][/tex]

Implicitly differentiate:

[tex]\displaystyle 2x+y+x\frac{dy}{dx}-3\frac{dy}{dx}=0[/tex]

Solve for dy/dx:

[tex]\displaystyle \begin{aligned} x \frac{dy}{dx} - 3\frac{dy}{dx} & = -2x - y \\ \\ \frac{dy}{dx}(x - 3) & = -2x - y \\ \\ \frac{dy}{dx} & = \frac{-2x-y}{x-3} \\ \\ & = \frac{2x+y}{3-x} \end{aligned}[/tex]

To find dy/dx at (2, 1), evaluate dy/dx for x = 2 and y = 1. Hence:

[tex]\displaystyle \frac{dy}{dx}\Big|_{(2, 1)}=\frac{2(2)+1}{3 - (2)}=\frac{5}{1}=5[/tex]

Hence, our answer is A.

We want to find the differential dy/dx for the given expression at the given point. We will see that the correct option is A.

We have:

x^2 + xy - 3y = 3

First, we need to isolate the variable y in one side of the equation, so we get:

xy - 3y = 3 - x^2

y*(x - 3) = 3 - x^2

y = (x - x^2)/(x - 3)

Now we can differentiate this, remember that if:

f(x) = g(x)*h(x)

then:

f'(x) = g(x)*h'(x) + g'(x)*h'(x)

Using that rule.

dy/dx = (1 - 2x)/(x - 3) - (x - x^2)/(x - 3)^2

Now we need to evaluate this in x = 2 (the x-value of the point) so we get:

(1 - 2*2)/(2 - 3) - (2 - 2^2)/(2 - 3)^2

= (-3)/(-1) - (-2)/(1) = 5

So the correct option is A.

If you want to learn more about differentiation, you can read:

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Answer:

Option C: 0.28

Step-by-step explanation:

This is a binomial probability distribution problem.

Now, we want to find the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed. This is written as;

P(X ≥ 2) = P(2) + P(3) + P(4) + P(5)

From the histogram;

P(5) = 0.02

P(4) = 0.02

P(3) = 0.05

P(2) = 0.19

Thus;

P(X ≥ 2) = 0.19 + 0.05 + 0.02 + 0.02

P(X ≥ 2) = 0.28

From the histogram, it is found that there is a 0.28 = 28% probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed, option C.

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

The probabilities given by the histogram are:

[tex]P(X = 0) = 0.33[/tex]

[tex]P(X = 1) = 0.39[/tex]

[tex]P(X = 2) = 0.19[/tex]

[tex]P(X = 3) = 0.05[/tex]

[tex]P(X = 4) = 0.02[/tex]

[tex]P(X = 5) = 0.02[/tex]

The probability of at least 2 up is:

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.019 + 0.05 + 0.02 + 0.02 = 0.28[/tex]

0.28 = 28% probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed, option C.

A similar problem is given at https://brainly.com/question/24141790