Determine if the statement is always ,sometimes, or never true.

Which of the following expressions are meaningful? Which are meaningless? Explain. (a) (a · b) · c (a · b) · c has ---Select---

rodikova [14]

Answer:

(a) (a · b) · c has Meaningless because it is the dot product of two scalars.

(b) (a · b)c has Meaningful because it is a scalar multiple of a scalar and a vector .

(c) |a|(b · c) has Meaningful because it is the product of two scalars .

(d) a · (b + c) has Meaningful because it is the dot product of two vectors .

(e) a · b + c has Meaningless because it is the sum of a scalar and a vector.

(f) |a| · (b + c) has Meaningless because it is the dot product of a scalar and a vector .

4 0

2 years ago

A circular go-kart track has a diameter of 75 meters. Approximately how long is the track? A225 meters B100 meters C750 meters D

worty [1.4K]

Answer:

<h2> 235 meters</h2>

Step-by-step explanation:

This problem is on the mensuration of flat shapes, a circular shape.

the problem also requires that we find the perimeter of the circular track

the expression for the perimeter of a circle is given as

$C= 2\pi r$

Given

diameter of the circular track = 75 meters

radius of circular track = d/2 = 75/2= 37.5 meters

Substituting our data into the expression for perimeter we have

$C= 2*3.142 *37.5\\\\C= 235.65$

<em>Approximately the length is 235 meters.</em>

8 0

3 years ago

Jimmy is selling used books at a yard sale. A customer buys 9 books at a cost of $0.75 each and pays with a $20.00 bill. Jimmy m

never [62]

C= 20-0.75x
c= 20-0.75(9)
c= 20-6.75
c= 13.25

Here c is the amount of change and x is the number of books bought.

The customer's change will be $13.25

3 0

3 years ago

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Suppose a simple random sample of size nequals81 is obtained from a population with mu equals 79 and sigma equals 18. (a) Descr

Daniel [21]

Answer:

(a) The sampling distribution of $\overline{X}$ = Population mean = 79

(b) P ( $\overline{X}$ greater than 81.2 ) = 0.1357

(c) P ( $\overline{X}$ less than or equals 74.4 ) = .0107

(d) P (77.6 less than $\overline{X}$ less than 83.2 ) = .7401

Step-by-step explanation:

Given -

Sample size ( n ) = 81

Population mean $(\nu)$ = 79

Standard deviation $(\sigma )$ = 18

(a) Describe the sampling distribution of $\overline{X}$

For large sample using central limit theorem

the sampling distribution of $\overline{X}$ = Population mean = 79

(b) What is Upper P ( $\overline{X}$ greater than 81.2 ) =

$P(\overline{X}> 81.2)$ = $P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}> \frac{81.2 - 79}{\frac{18}{\sqrt{81}}})$

= $P(Z> 1.1)$

= $1 - P(Z< 1.1)$

= 1 - .8643 =

= 0.1357

(c) What is Upper P ( $\overline{X}$ less than or equals 74.4 ) =

$P(\overline{X}\leq 74.4)$ = $P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}\leq \frac{74.4- 79}{\frac{18}{\sqrt{81}}})$

= $P(Z\leq -2.3)$

= .0107

(d) What is Upper P (77.6 less than $\overline{X}$ less than 83.2 ) =

$P(77.6< \overline{X}< 83.2)$ = $P(\frac{77.6- 79}{\frac{18}{\sqrt{81}}})< P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}\leq \frac{83.2- 79}{\frac{18}{\sqrt{81}}})$

= $P(- 0.7< Z< 2.1)$

= $(Z< 2.1) - (Z< -0.7)$

= 0.9821 - .2420

= 0.7401

3 0

3 years ago

Factor -24a3b3c3 - 84a4b2c.

sammy [17]

Answer:

-12a³b²c ( 2bc² + 7a)

Step-by-step explanation:

To factorize, we must separate the highest common factors between the products that make up the given expression. To get the highest common factor between the two products,

-24a3b3c3 = -2 * 2 *2 * 3 * a³ *b² *b * c² * c

- 84a4b2c = -2 * 2 *3 * 7 * a³ * a *b² * c

The common elements are -2, 2, 3, a³, b², c

The product of the common elements

= -12a³b²c

Hence, factorizing

-24a3b3c3 - 84a4b2c = -12a³b²c ( 2bc² + 7a)

4 0

3 years ago

Read 2 more answers