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3 years ago

A coin bank for donations for the protection of the reef contained Php 1,570. There were twice as many Php 5-coins as

Mathematics

1 answer:

kvasek [131]3 years ago

6 0

Answer:

There are 144 Php 5-coins, 72 Php 10-coins and 130 Php-1 coins

Step-by-step explanation:

The amount of the coins in the coin bank = Php 1,570

The number of Php 5-coins = 2 × The number of Php 10-coins

The number of Php 5 coins = The number of Php 1-coins + 14

Let 'x' represent the number of Php-5 coins, let 'y' represent the number of Php 10-coins, and let 'z' represent the number of Php 1-coins, we get;

x = 2 × y...(1)

x = z + 14...(2)

5·x + 10·y + z = 1,570...(3)

From equation (1) equation (2), and equation three, we have;

y = x/2

z = x - 14

5·x + 10·x/2 + x - 14 = 1,570

11·x - 14 = 1,570

x = (1,570 + 14)/11 = 144

The number of Php 5-coins, x = 144

y = x/2

∴ y = 144/2 = 72

The number of Php 10-coins, y = 72

z = x - 14

∴ z = 144 - 14 = 130

The number of Php 1-coins, z = 130

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I don’t understand :(

viktelen [127]

Answer:

The quotient when $x^3-4x^2-8x+8$ is divided by $x+2$ is $x^2-6x+4$ with no remainder, so x+2 is a factor of p(x).

Step-by-step explanation:

As the question suggests, there are two ways to solve this problem: long division (which can always be used to divide polynomials), and synthetic division (which can only be used when you are dividing by something of the form $(x-a)$ . In this case, we may use synthetic division, since $x+2$ is equal to $x-(-2)$ . I will use synthetic division here as it is slightly faster than long division.

The -2 on the left represents that we are dividing by x-(-2), and the rest of the numbers in the top row are the coefficients of p(x): 1, -4, -8, and 8.

The first step in synthetic division is to being down the leading coefficient of the polynomial: in this case, the 1 (as indicated in red). Now, we multiply the 1 by -2. We get -2, which we place directly below the -4.

Next, we add directly down the column, (-4 + (-2) is equal to -6), and this answer is placed in the box below. We can continue this process, getting the coefficients 1, -6, 4, and 0 in the bottom row.

This is the answer: the quotient is $x^2-6x+4$ , and the remainder is zero (which indicates that x+2 is a factor of p(x)).

Edit: long division

We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since $x \times x^2$ is equal to $x^3$ , the first term in the quotient will be $x^2$ . Since $x^2 \times (x+2)$ is equal to $x^3+2x^2$ , we must now subtract that from $x^3-4x^2-8x+8$ .

We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.

I know this might be difficult to follow, so please comment if you have any questions.

4 0

3 years ago

the terminal side of theta passes through the point (-5,-6). what is the exact value of cos theta in simplified form?

harina [27]

ANSWER

$\cos( \theta) = - \frac{5\sqrt{61}}{ 61 }$

EXPLANATION

The given point is (-5,-6).

This implies that ,

$\tan( \theta) = \frac{6}{5}$

Hence opposite=6 units and adjacent=5 units.

The hypotenuse is,

$= \sqrt{ {5}^{2} + {6}^{2} } = \sqrt{61}$

Since the terminal side is in the third quadrant, the cosine ratio is negative.

$\cos( \theta) = - \frac{adjacent}{hypotenuse}$

$\cos( \theta) = - \frac{5}{ \sqrt{61} }$

Rationalize the denominator,

$\cos( \theta) = - \frac{5\sqrt{61}}{ 61 }$

The correct choice is C.

7 0

3 years ago

A company receives shipments of a component used in the manufacture of a component for a high-end acoustic speaker system. When

Tanya [424]

Answer:

$ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434$

Step-by-step explanation:

For this case we have a sample size of n = 250 units and in this sample they found that 24 units failed one or more of the tests.

We are interested in the proportion of units that fail to meet the company's specifications, and we can estimate this with:

$\hat p = \frac{24}{250}= 0.096$

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 confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 98% confidence interval the value of $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , with that value we can find the quantile required for the interval in the normal standard distribution.