Find the sum of the geometric sequence –3, 15, –75, 375, … when there are 7 terms and select the correct answer below.

The greatest common factor (GCF) of x^3, x^7, x^9 is ?<br> Please help

solong [7]

Answer:

$x^3$

Step-by-step explanation:

Let the greatest common factor of $a,b,c$ such that $a,b,c \in\mathbb{Z}$ and they are not all equal to zero, $d$ is the common divisor of $a$ and $b$ . Therefore, $d \mid a$ and $d \mid b$

You can write

$D(a) = \{d \in\mathbb{Z} : d \mid a\}$

$D(b) = \{d \in\mathbb{Z} : d \mid b\}$

The greatest common factor of $a,b$ is given as

$D(a,b) = \{d \in\mathbb{Z} : d \mid a \text{ and } d \mid b\}$

and

$D(a, b) = D(a) \cap D(b)$

This happens because $D(a,b)$ is upper bounded because if $a\neq 0$ then $d \leq |a|$

for all $d\in D(a, b)$ . Therefore, the set $D(a, b)$ has the greatest elements.

Taking $x^3, x^7, x^9$ such that $x>0$

You can note that $x^7 = x^3 \cdot x^4$ and $x^9 = x^3 \cdot x^6 = x^3 \cdot x^3 \cdot x^3$

Therefore, the greatest common factor is $x^3$

Note: $x^3 \cap x^7 \cap x^9 = x^3$

6 0

3 years ago

The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time).

NeX [460]

Answer:

(a) PRIVATE COLLEGES

Sample mean is $42.5 thousand

Sample standard deviation is $6.65 thousand

PUBLIC COLLEGES

Sample mean is $22.3 thousand

Sample standard deviation is $4.34 thousand

(b) Point estimate is $20.2 thousand. The mean annual cost to attend private colleges ($42.5 thousand) is more than the mean annual cost to attend public colleges ($22.3 thousand)

(c) 95% confidence interval of the difference between the mean annual cost of attending private and public colleges is $19.2 thousand to $21.2 thousand

Step-by-step explanation:

(a) PRIVATE COLLEGES

Sample mean = Total cost ÷ number of colleges = (51.8+42.2+45+34.3+44+29.6+46.8+36.8+51.5+43) ÷ 10 = 425 ÷ 10 = $42.5 thousand

Sample standard deviation = sqrt[summation (cost - sample mean)^2 ÷ number of colleges] = sqrt([(51.8-42.5)^2 + (42.2-42.5)^2 + (45-42.5)^2 + (34.3-42.5)^2 + (44-42.5)^2 + (29.6-42.5)^2 + (36.8-42.5)^2 + (51.5-42.5)^2 + (43-42.5)^2] ÷ 10) = sqrt (44.24) = $6.65 thousand

PUBLIC COLLEGES

Sample mean = (20.3+22+28.2+15.6+24.1+28.5+22.8+25.8+18.5+25.6+14.4+21.8) ÷ 12 = 267.6 ÷ 12 = $22.3 thousand

Sample standard deviation = sqrt([(20.3-22.3)^2 + (22-22.3)^2 + (28.2-22.3)^2 + (15.6-22.3)^2 + (24.1-22.3)^2 + (28.5-22.3)^2 + (22.8-22.3)^2 + (25.8-22.3)^2 + (18.5-22.3)^2 + (25.6-22.3)^2 + (14.4-22.3)^2 + (21.8-22.3)^2] ÷ 12) = sqrt (18.83) = $4.34 thousand

(b) Point estimate = mean annual cost of attending private colleges - mean annual cost of attending public colleges = $42.5 thousand - $22.3 thousand = $20.2 thousand.

This implies the the mean annual cost of attending private colleges is greater than the mean annual cost of attending public colleges

(c) Confidence Interval = Mean + or - Margin of error (E)

E = t×sd/√n

Mean = $42.5 - $22.3 = $20.2 thousand

sd = $6.65 - $4.34 = $2.31 thousand

n = 10+12 = 22

degree of freedom = 22-2 = 20

t-value corresponding to 20 degrees of freedom and 95% confidence level is 2.086

E = 2.086×$2.31/√22 = $1.0 thousand

Lower bound = Mean - E = $20.2 thousand - $1.0 thousand = $19.2 thousand

Upper bound = Mean + E = $20.2 thousand + $1.0 thousand = $21.2 thousand

95% confidence interval is $19.2 thousand to $21.2 thousand

6 0

3 years ago

Whoever helps gets brainlyess answer and it's worth 10 points :)

goldenfox [79]

Its 15

hope this helps

3 0

3 years ago

Read 2 more answers

Use completing the aquare to solve for x in the equation (x+7)(x-9)=25

Tema [17]

Answer:

x = 1 + sqrt(89) or x = 1 - sqrt(89)

Step-by-step explanation:

Solve for x:

(x - 9) (x + 7) = 25

Expand out terms of the left hand side:

x^2 - 2 x - 63 = 25

Add 63 to both sides:

x^2 - 2 x = 88

Add 1 to both sides:

x^2 - 2 x + 1 = 89

Write the left hand side as a square:

(x - 1)^2 = 89

Take the square root of both sides:

x - 1 = sqrt(89) or x - 1 = -sqrt(89)

Add 1 to both sides:

x = 1 + sqrt(89) or x - 1 = -sqrt(89)

Add 1 to both sides:

Answer: x = 1 + sqrt(89) or x = 1 - sqrt(89)

7 0

4 years ago

Victor and Carlos went to the store to buy toys for a youth center. They bought games, trucks, and dolls. They bought 4 times as

ella [17]

D) 4x-3 because x represents the trucks and the 4 represents and i he bought 4 times as trucks so its 4x. and i there's 3 fewer so ur subtracting 3 from whatever 4 times x equals.<span />

5 0

3 years ago