find the 9th and 15th terms of the following geometric sequence 2, -4, 8, -16​

Answer:

A) The sequence is {-23, -15, -7, 1,...}

The common difference of the sequence above, d = 8

The first term, a = -23

The number of terms, n = 15

The recursive formula is, aₙ = aₙ₋₁ + d

Using the recursive method gives;

a₅ = a₍₅₋₁₎ + d

Where;

a₍₅₋₁₎ = 1

Therefore, a₅ = 1 + 8 = 9, a₆ = 9 + 8 = 17, a₇ = 17 + 8 = 25, a₈ = 25 + 8 = 33, a₉ = 33 + 8 = 41, a₁₀ = 41 + 8 = 49, a₁₁ = 49 + 8 = 57, a₁₂ = 57 + 8 = 65 a₁₃ = 65 + 8 = 73, a₁₄ = 73 + 8 = 81, a₁₅ = 81 + 8 = 89

The 15th term of the sequence, {-23, -15, -7, 1,...}, a₁₅ = 89

We check by using explicit formula to get, aₙ = a + (n - 1)·d

Therefore

a₁₅ = -23 + (15 - 1)×8 = 89

B) The given sequence is B) {5 5.25, 5.50, 5.75,...}

The common difference, d = 0.25

The first term, a = 5

The required number of terms, n = 15

Using the recursive method gives;

a₅ = a₍₅₋₁₎ + d

Where;

a₍₅₋₁₎ = a₄ = 5.75

Therefore, a₅ = 5.75 + 0.25 = 6

a₆ = 6 + 0.25 = 6.25, a₇ = 6.25 + 0.25 = 6.5, a₈ = 6.5 + 0.25 = 6.75, a₉ = 6.75 + 0.25 = 7, a₁₀ = 7 + 0.25 = 7.25, a₁₁ = 7.25 + 0.25 = 7.5, a₁₂ = 7.5 + 0.25 = 7.75, a₁₃ = 7.75 + 0.25 = 8, a₁₄ = 8 + 0.25 = 8.25, a₁₅ = 8.25 + 0.25 = 8.5

The 15th term, of the sequence, {5 5.25, 5.50, 5.75,...}, a₁₅ = 8.5

We check by explicit formula to get, aₙ = a + (n - 1)·d

Therefore

a₁₅ = 5 + (15 - 1)×0.25 = 8.5

Step-by-step explanation:

9514 1404 393

Answer:

 5/36

Step-by-step explanation:

5 and 36 have no common factors, so the fraction 5/36 is already in simplest form.

Answer:

Step-by-step explanation:

Answer:

The number of ways is 26,400 ways

Step-by-step explanation:

Given;

total number of men, M = 10

total number of women, W = 12

number of committees to be formed = 6

If there must be equal gender, then it must consist of 3 men and 3 women.

[tex]The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways[/tex]

Therefore, the number of ways is 26,400 ways

Step-by-step explanation:

[tex] {m}^{6} - 25 \\ { {m}^{3} }^{2} - {5}^{2} \\ x = {m}^{3} b = 5 \\ ( {m}^{3} - 5)( {m}^{3} + 5)[/tex]

Answer:

b

Step-by-step explanation:

Given:

The area of rectangular garden is [tex]x^2-4x-21[/tex] square units.

To find:

The length and width of the cucumber field.

Solution:

The area of a rectangle is:

[tex]A=l\times w[/tex]

Where l is length and w is width of the rectangle.

The area of rectangular garden is [tex]x^2-4x-21[/tex] square units.

We need to find the factors of [tex]x^2-4x-21[/tex] to get the length and width.

[tex]A=x^2-4x-21[/tex]

Splitting the middle term, we get

[tex]A=x^2-7x+3x-21[/tex]

[tex]A=x(x-7)+3(x-7)[/tex]

[tex]A=(x-7)(x+3)[/tex]

Area of a rectangle is the product of length and width.

Therefore, the length and width of the rectangle are [tex](x-7)[/tex] units and [tex](x+3)[/tex] units.

Answer:

A, B, D, E

Step-by-step explanation:

[tex]\sqrt{81}[/tex] = ± 9 → D and E

Since 9 × 9 = 81 and - 9 × - 9 = 81

[tex]81^{\frac{1}{2} }[/tex] = [tex]\sqrt{81}[/tex] = 9 → B

- [tex]81^{\frac{1}{2} }[/tex] = - [tex]\sqrt{81}[/tex] = - 9 → A

Step-by-step explanation:

180-68=112

112÷293=3.8620

68÷3.87

18

Answer:

- 1.875

Step-by-step explanation:

tan = sin ÷ cos

tan = 8/17 ÷ - 15/17

tan= - 1.875

Answer:

-8/15

Step-by-step explanation:

see image

Answer:

La norma de los signos es para el producto de números reales, y la norma es la siguiente.

(+)*(+) = (+)

(+)*(-) = (-)

(-)*(+) = (-)

(-)*(-) = (+)

Es decir, el producto de dos números de mismo signo es siempre positivo

El producto de dos números de distinto signo es siempre negativo.

Particularmente, para la suma esta norma no funciona (pues no está definida para la suma)

Pero en casos como:

5 - (-4)  

(esto sería: "la diferencia entre cinco y menos cuatro")

notar que podemos reescribir esto como:

5 + (-1)*(-4)

Ahora podemos aplicar la norma de los signos:

5 + 4 = 9

Donde aplicamos la norma de los signos,  

Podemos concluir que, si bien es una regla que aplica al producto, siempre la tenemos que tener en cuenta en cualquier operación que hagamos.

Por lo podemos concluir que la respuesta correcta es verdadero.

Answer:

{-6, 1, 5, 8}

Step-by-step explanation:

The domain is the set of x-coordinates or inputs.

{-6, 1, 5, 8}

Answer:

Only 10 base units to learn

Step-by-step explanation:

The metric system is a decimal based system developed to be universally acceptable by making use of base units from obtained from nature and the use of prefixes for multiples and submultiples of the base units, decimal ratios, which allows easy representation of quantities, as well as having a coherent structure of base and derived units which are obtained from the base units

During conversion in the metric system, which is decimal based, it is only required to move the decimal point

The prefixes which are used to specify multiples and submultiples are the same through out

The decimal system is based on the powers of ten

The number of base units to learn are 7 including; 1. Meter (m), 2. Kilogram (kg), 3. Second (s), 4. Ampere (A), 5. Kelvin (k), 6. Candela (cd), and 7. mole (mol)

Therefore the metric system has several advantages that include all of the following except; Only 10 base units to learn

Answer:

2nd option

Step-by-step explanation:

f(x) + g(x)

= 4x - 5 + 3x + 7 ← collect like terms

= 7x + 2

domain is all real numbers

Answer:

thank you for the points

Step-by-step explanation:

Answer:

[tex]a^4-16[/tex]

[tex]\left(a^2\right)^2-4^2[/tex]

[tex]\left(a^2+4\right)\left(a^2-4\right)[/tex]

[tex]=\left(a^2+4\right)\left(a+2\right)\left(a-2\right)[/tex]

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

Hope it helps...

Have a great day!!

Step-by-step explanation:

The difference of squares: a² - b² factors to (a - b) (a + b)

Let x⁴ = (x²)²

Let 16 = 4²

Now by difference of squares x⁴ - 16 factors as (x² - 4)(x² + 4)

The front factor, (x² - 4), can factor by difference of squares again as (x - 2)(x + 2)

Step-by-step explanation:

[tex] \tan(x \degree) = \frac{54}{32} \\ = \frac{3}{4} \\ x \degree = { \tan}^{ - 1} ( \frac{3}{2} ) \\ = 56.3 \degree[/tex]

Answer:

x=3

Step-by-step explanation:

Equation: 7x-8=3x+4

4x=12

x=3

Answer:

$1,920

$10,880

Step-by-step explanation:

Amount marlene earns per year = $12,800

Percentage of taxes = 15%

how much money is paid in taxes?

Amount of tax Marlene pays = 15% of $12,800

= 15/100 × $12,800

= 0.15 × $12,800

= $1,920

how much money is left for Marlene to spend?

Amount left for Marlene to spend = Amount marlene earns per year - Amount of tax Marlene pays

= $12,800 - $1,920

= $10,880

Answer:

f(k + 4) = -2k² - 13k - 28

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = -2x² + 3x - 8

Step 2: Evaluate

answer

71-17=54

82-28=54

93-39=54

60-06=54

Step-by-step explanation:

Answer:

Step-by-step explanation:

Thinking of this in terms of words, we are looking to solve the equation:

"The price Andre paid for the car is 65% of the original $7200 price" which in algebra-speak is

p = .65(7200) where p is the price Andre paid (our unknown), the word "is" indicates an equals sign, .65 is 65% as a decimal, the word "of" indicates multiplication, and the original price is...well, the original price.

Solving for p:

p = $4680

Answer:

Exact answer = 10.41666666666666666666666666666pi

Estimated answer = 32.70938

Step-by-step explanation:

Semi circle formula: 1/2 * 4/3 * pi * r^3

r = 2.5

1/2 * 4/3 * pi * 2.5^3

2/3 * pi * 2.5^3

2/3 * pi * 15.625

10.416..... * pi

Exact answer = 10.417pi

We can estimate pi as 3.14

So, 10.417 * 3.14 = 32.70938

Exact answer = 10.41666666666666666666666666666pi

Estimated answer = 32.70938

Answer:

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

cos^2x = cos^2x

Step-by-step explanation:

Simplify the left hand side:

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

Using the Pythagorean Identity, we can see that the two sides are equivalent if you subtract sin^2x from both sides:

sin^2x + cos^2x = 1

cos^2x = 1 - sin^2x

Lastly, write it out:

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

cos^2x = cos^2x

Answer:

a) A score of 65 is in the 79.67th percentile.

b) A score less than 70 is below the 95.25th percentile.

c) 20.33% of the scores are greater than 65.

d) 95.25% of scores are less than 70.

e) 45.25% of the scores are between 50 and 60.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean is 60 and the standard deviation is 6.

This means that [tex]\mu = 60, \sigma = 6[/tex]

a. what is the percentile rank of the score 65?

This is the p-value of Z when X = 65.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{65 - 60}{6}[/tex]

[tex]Z = 0.83[/tex]

[tex]Z = 0.83[/tex] has a p-value of 0.7967.

Thus: A score of 65 is in the 79.67th percentile.

b. what is the percentile of the score less than 70?

Below the p-value of Z when X = 70. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 60}{6}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a p-value of 0.9525.

Thus: A score less than 70 is below the 95.25th percentile.

c. what is percent of the scores is greater than 65?

The proportion is 1 subtracted by the p-value of Z when X = 65.

From item a, when X = 65, Z has a p-value of 0.7967

1 - 0.7967 = 0.2033

0.2033*100% = 20.33%

20.33% of the scores are greater than 65.

d. what percent of scores is less than 70?

The proportion is the p-value of Z when X = 70, which, from item b, is of 0.9525.

0.9525*100% = 95.25%

95.25% of scores are less than 70.

e. what percent of the score is between 50 and 60?

The proportion is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 50.

X = 60

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{60 - 60}{6}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5.

X = 50

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{50 - 60}{6}[/tex]

[tex]Z = -1.67[/tex]

[tex]Z = -1.67[/tex] has a p-value of 0.0475.

0.5 - 0.0475 = 0.4525

0.4525*100% = 45.25%

45.25% of the scores are between 50 and 60.

Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

Answer:

Wasim has enough money.

Step-by-step explanation:

1. find the area of the garden path:

600 cm x 120 cm = 72,000 sq. cm

2. find the area of each stone:

it is a square of 30 cm by 30 cm, so:

30 cm x 30 cm = 900 sq. cm

3. find how many stones can fit in the path:

72,000 / 900 = 80 stones

4. multiply that by the price of each stone:

80 stones x $2.50 = $200

Wasim's budget is $220 and the stones will only cost $200, so it is within the budget