1. Evaluate the following.

What percentage of 3 is 4?

Artyom0805 [142]

Answer:

13.333% of 3 is 4.

Step-by-step explanation:

Take missing value = x

x% of 3 = 4

x/100 × 3 = 4

3x/100 = 4

3x = 400

x = 400/3

x = 13.333

Hope it helps ⚜

5 0

2 years ago

Read 2 more answers

F(x)=x^4-5x^2-6x-10 is divided by x-3

LiRa [457]

Answer:

Step-by-step explanation:

STEP

1

:

10

Simplify ——

x

Equation at the end of step

1

:

10

((((x4)-(5•(x2)))-6x)-——)-3

x

STEP

2

:

Equation at the end of step

2

:

10

((((x4) - 5x2) - 6x) - ——) - 3

x

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x as the denominator :

x4 - 5x2 - 6x (x4 - 5x2 - 6x) • x

x4 - 5x2 - 6x = ————————————— = ———————————————————

1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

x4 - 5x2 - 6x = x • (x3 - 5x - 6)

Polynomial Roots Calculator :

4.2 Find roots (zeroes) of : F(x) = x3 - 5x - 6

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is -6.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,3 ,6

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -2.00

-2 1 -2.00 -4.00

-3 1 -3.00 -18.00

-6 1 -6.00 -192.00

1 1 1.00 -10.00

2 1 2.00 -8.00

3 1 3.00 6.00

6 1 6.00 180.00

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

4.3 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (x3-5x-6) • x - (10) x5 - 5x3 - 6x2 - 10

———————————————————————— = ———————————————————

x x

Equation at the end of step

4

:

(x5 - 5x3 - 6x2 - 10)

————————————————————— - 3

x

STEP

5

:

Rewriting the whole as an Equivalent Fraction

5.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using x as the denominator :

3 3 • x

3 = — = —————

1 x

Checking for a perfect cube :

5.2 x5 - 5x3 - 6x2 - 10 is not a perfect cube

Trying to factor by pulling out :

5.3 Factoring: x5 - 5x3 - 6x2 - 10

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -6x2 - 10

Group 2: x5 - 5x3

Pull out from each group separately :

Group 1: (3x2 + 5) • (-2)

Group 2: (x2 - 5) • (x3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

5.4 Find roots (zeroes) of : F(x) = x5 - 5x3 - 6x2 - 10

See theory in step 4.2

In this case, the Leading Coefficient is 1 and the Trailing Constant is -10.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,5 ,10

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -12.00

-2 1 -2.00 -26.00

-5 1 -5.00 -2660.00

-10 1 -10.00 -95610.00

1 1 1.00 -20.00

2 1 2.00 -42.00

5 1 5.00 2340.00

10 1 10.00 94390.00

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

5.5 Adding up the two equivalent fractions

(x5-5x3-6x2-10) - (3 • x) x5 - 5x3 - 6x2 - 3x - 10

————————————————————————— = ————————————————————————

x x

Polynomial Roots Calculator :

5.6 Find roots (zeroes) of : F(x) = x5 - 5x3 - 6x2 - 3x - 10

See theory in step 4.2

In this case, the Leading Coefficient is 1 and the Trailing Constant is -10.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,5 ,10

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -9.00

-2 1 -2.00 -20.00

-5 1 -5.00 -2645.00

-10 1 -10.00 -95580.00

1 1 1.00 -23.00

2 1 2.00 -48.00

5 1 5.00 2325.00

10 1 10.00 94360.00

Polynomial Roots Calculator found no rational roots

Final result :

x5 - 5x3 - 6x2 - 3x - 10

————————————————————————

x

3 0

3 years ago

In June 2012, Twitter was reporting 400 million tweets per day. Each tweet can consist of up to 140 characters (letter, numbers,

gulaghasi [49]

Each tweet would cost between 1 and 140 pennies you can write that as an inequality [1 ≤ x ≤ 140] Since you can't tweet 0 characters or above 140.

if you want to change it to pounds divide by 100.

A) 1 ≤ x ≤ 140

B) Each character costs a penny, you can't tweet less than 1 character or above 140.

3 0

2 years ago

When consumers apply for credit, their credit is rated using FICO (Fair, Isaac, and Company) scores. Credit ratings are given be

Flura [38]

Answer:

a) The 99% confidence interval would be given by (589.588;731.038)

b) If we see the confidence interval the 620 is included on the interval we don't have enough evidence to reject the rating is 620. But since we need a score that at least 620 and our lower limit is 589.588 we cant conclude that all the clients would have a score that at least of 620.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The data is:

661 595 548 730 791 678 672 491 492 583 762 624 769 729 734 706

Part a

Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$

=AVERAGE(661, 595, 548, 730, 791, 678, 672, 491 ,492, 583, 762 ,624 ,769, 729, 734, 706)

On this case the average is $\bar X= 660.313$

=STDEV.S(661, 595, 548, 730, 791, 678, 672, 491 ,492, 583, 762 ,624 ,769, 729, 734, 706)

The sample standard deviation obtained was s=95.898

Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =16<30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . The degrees of freedom are given by:

$df=n-1=16-1=15$

We can find the critical values in excel using the following formulas:

"=T.INV(0.005,15)" for $t_{\alpha/2}=-2.95$

"=T.INV(1-0.005,15)" for $t_{1-\alpha/2}=2.95$

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$

And if we find the limits we got:

$660.313- 2.95\frac{95.898}{\sqrt{16}}=589.588$

[tex]660.313+ 2.95\frac{95.898}{\sqrt{16}}=731.038/tex]

So the 99% confidence interval would be given by (589.588;731.038)

Part b

If we see the confidence interval the 620 is included on the interval we don't have enough evidence to reject the rating is 620. But since we need a score that at least 620 and our lower limit is 589.588 we cant conclude that all the clients would have a score that at least of 620.

4 0

2 years ago

ASAP! 70 points! Yan has already finished 3/4 of the 45 math problems he was assigned today. Each math problem took him 1 and 4/

siniylev [52]

I would help but Can u add a pic or something for more understanding

7 0

2 years ago