What is (-2.1) to the third power

Which of the following is equivalent to 0 equals 3 x squared minus 12 x minus 15 when completing the square?

skad [1K]

Answer:

x = 5, -1

Step-by-step explanation:

0 = 3x^2 - 12x - 15 or

3x^2 - 12x - 15 = 0

By solving for x, use the Quadratic Formula.

… x = 5 and/or -1

8 0

3 years ago

The perimeter of a rectangle is 14x - 8 feet. If the width of the rectangle is 5x, what is the rectangle's length?

wariber [46]

Length = 2x+4

Step-by-step explanation:

P=2W+2L

14x+8 =2(5x)+2L

14x+8=10x+2L

14x+8-10x=2L

4x+8=2L

(4x+8)/2=L

2x+4=L

4 0

3 years ago

5 times a number increased by 18 is the same as 36 more than times 4 times the number. Find the number

Tju [1.3M]

Answer:

Step-by-step explanation:

Let's assume that that question is meant to read:

________________________________________________

" 5 times a number increased by 18 is the same as 36 more than 4 times the number. Find the number ".

_______________________________________________

Let the variable "x" (i.e. the lower-case letter ex]—represent the unknown number—for which we are asked to solve.

If the question/problem is meant to read:

_________________________________

" 5 times a number increased by 18 is the same as 36 more than 4 times the number. Find the number ".

_________________________________

Then, treat the problem as:

_________________________________

" 5 times [a number increased by 18] " ; {is the same as}: " 36 more than [4 times the number]". Find the number ".

_________________________________

Note that: " {is the same as:}" ; means: "equals:} ;

So: "...[a number; that is, an unknown number; that is, "x" ; increased by "18" ]" ; would be represented by: "[x + 18]" .

5 times that value would be represented as:

→ 5* (x + 18) ; or: " 5(x + 18) " .

Then we add the: " = " ["equals"] sign:

_________________________________

Then, we consider: "... 36 more than [4 times the number]" .

4 times the [unknown number]: would be written as:

→ " 4 * x " ; or simply: " 4x " .

→ "36 more than this [the above value; i.e. "4x" ; would be represented by adding "36" to said value; as follows:

→ " 4x + 36 " ;

_________________________________________

Now we can:

1) Write our expression as an equation; and then:

2) Solve for the value for "x" ; our unknown number.

___________________________________________

Here is the expression, as an equation:

________________________________________

→ 5(x + 18) = 4x + 36 ;

Now, solve for "x" ;

_________________________________________

Start with the "left-hand side" of the equation:

→ 5(x + 18) ;

Let us expand this expression.

___________________________________

Note the "distributive property" of multiplication:

→ a(b+c) = ab + ac .

___________________________________

As such: " 5(x + 18) = (5 * x) + (5 * 18) " = 5x +120 .

Now, rewrite the equation:

→ 5x + 120 = 4x + 36 ;

Let us subtract "36" from each side of the equation; & subtract "4x" from each side of the equation:

→ 5x + 120 = 4x + 36 ;

- 4x - 36 = - 4x - 36

________________________

to get: 1x + 54 = 10 ;

________________________________________

Rewrite as: " x + 54 = 10 " ;

→ {Since: "1x = x " ;

→ {since: (" 1 * [any numerical value] = that same numerical value"};

Note that this refers to the "identity property of multiplication."

___________________________________________

→

_________________________________________

→ We have: " x + 54 = 10 " ; Solve for "x" ;

Subtract "54" from Each Side of the equation;

to isolate "x" on one side of the equation; & to solve for "x" ;

→ " x + 54 - 54 = 10 - 54 " ;

to get: " x = -44 " .

_______________________________

Answer: The number is " - 44 " .

_______________________________

Let us substitute this value into our equation; to check our work:

→ 5(x + 18) = 4x + 36 ;

→ 5(-44 + 18) ≟ 4(-44) + 35 ?? ;

→ 5(-26) ≟ -176 + 35 ?? ;

→ -130 ≟ -176 + 35

3 0

3 years ago

The Institute of Management Accountants (IMA) conducted a survey of senior finance professionals to gauge members’ thoughts on g

DochEvi [55]

Answer:

(1) The probability that the sample percentage indicating global warming is having a significant impact on the environment will be between 64% and 69% is 0.3674.

(2) The two population percentages that will contain the sample percentage with probability 90% are 0.57 and 0.73.

(3) The two population percentages that will contain the sample percentage with probability 95% are 0.55 and 0.75.

Step-by-step explanation:

Let X = number of senior professionals who thought that global warming is having a significant impact on the environment.

The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.65.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of p if the following conditions are satisfied:

np ≥ 10
n(1 - p) ≥ 10

Check the conditions as follows:

$np= 100\times 0.65=65>10\\n(1-p)=100\times (1-0.65)=35>10$

Thus, a Normal approximation to binomial can be applied.

So, $\hat p\sim N(p, \frac{p(1-p)}{n})=N(0.65, 0.002275)$ .

(1)

Compute the value of $P(0.64$ as follows:

$P(0.64$

$=P(-0.20$

Thus, the probability that the sample percentage indicating global warming is having a significant impact on the environment will be between 64% and 69% is 0.3674.

(2)

Let $p_{1}$ and $p_{2}$ be the two population percentages that will contain the sample percentage with probability 90%.

That is,

$P(p_{1}$

Then,

$P(p_{1}$

$P(\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$P(-z$

The value of z for P (Z < z) = 0.95 is

z = 1.65.

Compute the value of $p_{1}$ and $p_{2}$ as follows:

$-z=\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}\\-1.65=\frac{p_{1}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{1}=0.65-(1.65\times 0.05)\\p_{1}=0.5675\\p_{1}\approx0.57$ $z=\frac{p_{2}-p}{\sqrt{\frac{p(1-p)}{n}}}\\1.65=\frac{p_{2}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{2}=0.65+(1.65\times 0.05)\\p_{1}=0.7325\\p_{1}\approx0.73$

Thus, the two population percentages that will contain the sample percentage with probability 90% are 0.57 and 0.73.

(3)

Let $p_{1}$ and $p_{2}$ be the two population percentages that will contain the sample percentage with probability 95%.

That is,

$P(p_{1}$

Then,

$P(p_{1}$

$P(\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$P(-z$

The value of z for P (Z < z) = 0.975 is

z = 1.96.

Compute the value of $p_{1}$ and $p_{2}$ as follows:

$-z=\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}\\-1.96=\frac{p_{1}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{1}=0.65-(1.96\times 0.05)\\p_{1}=0.552\\p_{1}\approx0.55$ $z=\frac{p_{2}-p}{\sqrt{\frac{p(1-p)}{n}}}\\1.96=\frac{p_{2}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{2}=0.65+(1.96\times 0.05)\\p_{1}=0.748\\p_{1}\approx0.75$

Thus, the two population percentages that will contain the sample percentage with probability 95% are 0.55 and 0.75.

7 0

4 years ago

Select Yes or No to indicate whether a zero must be written in the dividend to find the quotient.

lina2011 [118]

Answer:

no

Step-by-step explanation:

because I know that and u donot

3 0

3 years ago