Find the 7th term of the geometric sequence
7, 24.5, 85.75, ...

17 cubic units.

The volume (V) of a parallelepiped with one vertex at the origin is given by the absolute value of the scalar vector product of the vectors at the adjacent vertices.

V = |(a x b) · c|

In this case,

a = (1,4,0) = i + 4k + 0j

b = (-2,-5,2) = -2i -5j + 2k

c = (-2,2,1) = -2i + 2j + k

First, let's calculate the cross product of vectors a and b. i.e a x b as follows:

(i) Arrange the vectors in a matrix form

a x b = | i        j         k |

          | 1       4        0 |

          | -2    -5        2 |

(ii) Calculate the determinant of the matrix

a x b = i(8 - 0) -j(2-0) + k(-5+8)

a x b = i(8) -j(2) + k(3)

a x b = 8i - 2j + 3k

Secondly, calculate the scalar product of the cross product found above and the vector c as follows;

(a x b) . c = (8i - 2j + 3k) · (-2i + 2j + k)

Multiply like terms

(a x b) . c = (8 * -2)(i.i) + (-2 * 2)(j.j) + (3 * 1)(k.k)             [i.i = j.j = k.k = 1]

(a x b) . c = (-16) + (-4) + (3)

(a x b) . c = -16 - 4 + 3

(a x b) . c = -17

Thirdly, find the absolute value of the result found above. i.e

|(a x b) . c| = |-17|

|(a x b) . c| = 17

Therefore, the volume of the parallelepiped is 17 cubic units.

Answer:

C. It the correct answer

Answer:

The length of the three sides [tex]5, \sqrt{58} , \sqrt{65}[/tex]

The triangle is not a right triangle

Step-by-step explanation:

A = (3, 2) , B = ( 6, 9) , C = (10, 6)

Find the lengths using distance formula.

[tex]distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]AB = \sqrt{(6-3)^2 + (9-2)^2} = \sqrt{9 + 49 } = \sqrt{58}[/tex]

[tex]BC = \sqrt{(10-6)^2 + (6-9)^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]

[tex]AC = \sqrt{(3-10)^2+(2-6)^2} = \sqrt{49 + 16} = \sqrt{65}[/tex]

Using Pythagoras theorem :

[tex](Longer \ side)^2 = sum \ of \ square \ of \ two \ other \ sides[/tex]

Longest side is AC . So we will check if it satisfies Pythagoras theorem :

[tex]\sqrt{65} = \sqrt{58} + 5^2\\65 = 58 + 25\\[/tex]

65 ≠ 58 + 25

So the sides does not satisfy Pythagoras theorem. Hence the triangle is not a right triangle.

Answer:6

Step-by-step explanation:

Answer:

The profit for any purchased of bananas is R2.

Step-by-step explanation:

Cost of 1 kg banana = R 3

Banana purchased = 4 kg

So, the cost of 4 kg bananas = 4 x 3 = R 12

Amount paid = R 14

Profit = R 14 - R 12 = R 2

So, the profit on any purchased of bananas is R 2.

Answer:

60 square meters

Step-by-step explanation:

Answer:all three of them achieve the sales target together in 120 days.

Step-by-step explanation:

Given: Adam and Paul an achieve the sales target of the company in 30 days, Paul and Charles In 40 days while Charles and Adam In 60 days.

Then,  the number of days taken by all of them to achieve the sales target together = [tex]\dfrac1{30}+\dfrac{1}{40}+\dfrac{1}{60}[/tex]

[tex]=\dfrac{1}{120}[/tex]     [LCM(30,40,60)=120]

Thus, all three of them achieve the sales target together in 120 days.

Step-by-step explanation:

Formula:

[tex]\frac{\alpha y}{\alpha x} =\frac{dy}{dx }[/tex]

Answer:

Step-by-step explanation:

Does the answer help for you?

Answer:

$200 each.

Step-by-step explanation:

You are sharing the $600 bonus with 2 of your kids, meaning that the money will be evenly divided between 3 people. Divide the total amount of money with the total amount of people:

$600/3 persons = $200/person

Each person obtains $200.

~

The temperature rose so you add the amount it rose to the starting temperature

68.7 + 9 = 77.7 degrees

It then dropped so mow you subtract t the amount it dropped:

77.7 - 12.3 = 65.4 degrees

The answer is 65.4 degrees

Answer:

18.75 is the answer

Step-by-step explanation:

since the internet usage is more than 4 hrs, the second equation will be used. that is

cost = (10 + 2.50 (x - 4)) where x is the usage hours.

thus

[tex]cost = 10 + (2.5 \times (7.5 - 4)) \\ = 10 + (2.5 \times 3.5) \\ = 10 + 8.75 \\ = 18.75[/tex]

Answer:

The 95% confidence interval for the true population mean textbook weight is between 66.24 and 71.76 ounces.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{8.2}{\sqrt{34}} = 2.76[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 69 - 2.76 = 66.24 ounces

The upper end of the interval is the sample mean added to M. So it is 69 + 2.76 = 71.76 ounces.

The 95% confidence interval for the true population mean textbook weight is between 66.24 and 71.76 ounces.

Answer:

The answer is C!!!!!!!!

Answer:

Neither

Step-by-step explanation:

Answer:

jane is correct

Step-by-step explanation:

10⁻⁴ can be written as [tex]\frac{1}{10000}[/tex] and as 0.0001

Answer:

Step-by-step explanation:

hope this video link be helpfull to you

Answer:

y=5

y int

x=0

y=2(0)^2-8(0)+5

y=5

note everything multiplied by 0 is 0

A) Coefficient is the correct answer.

Step-by-step explanation:

The 3 is a coefficient. The x is the variable.

Answer:

600 nickels

Step-by-step explanation:

Answer:

g + 200 - 2*600 = 1400

g = 2400 pounds

Step-by-step explanation:

g + 200 - 2*600 = 1400

g + 200 - 1200 = 1400

g - 1000 = 1400

g = 2400

[tex]{\huge{\underbrace{\bf{\pink{Answer}}}}}[/tex]

Length of missing leg = 12 km

Using Pythagoras theorem

a² = 15² - 9²

a = √ 225 - 49

a = √144

a = 12 km

HOPE IT HELPS..

(Hypotenuse)² = (Base)²+ (Perpendicular)²

Taking, Hypotenuse As H

Base As B

Perpendicular As P

_________________________

H²= B²+ P²

[tex]15 {}^{2} = 9 {}^{2} + p {}^{2} \\ \\ p {}^{2} = 15 {}^{2} + 9 {}^{2} \\ \\ p {}^{2} = 225 - 81 \\ \\p {}^{2} = 144 \\ \\ p = \sqrt{144} \\ \\ p = 12[/tex]

Answer:

x = 50 + 95 = 145

.........

Answer:

x = 145°

Step-by-step explanation:

Given,

Measure of the first angle = 50°

Measure of the second angle = 95°

We know,

Sum of 3 angles of a triangle is equals to 180°

∴ The third angle = 180° - (50+95)°

                             = 180° - 145°

                             = 35°

Again,

Straight angle = 180°

∴ x = 180° - 35°

      = 145°

∴x = 145°

Answer:

Step-by-step explanation:

( - ∞ , - 3 ) ∪ [ - 1 , ∞ )

Answer:

12

Step-by-step explanation:

1) 5+19−6(5+1−4)

2)5+19−6(6−4)

3)5+19−(6)(2)

4)5+19−12

5) 5+7

6) 12

Answer: 8 is the value for y.

since x=16 as answered in the previous question, then 10x-3+(3y-1)=180 being in a straight line.