What number is next in this sequence 1,6,11,16

denis-greek [22]

$-3=2-5\implies -3\mod5=2\mod5$

When taking a polynomial modulo $n$ , you reduce its terms' coefficients modulo $n$ , so that, in conjunction with the result above,

$x^2-3x-3\equiv x^2-3x+2\mod5$

For completeness, the linear term's coefficient should also get reduced in the same way as the constant term, so that

$x^2-3x-3\equiv x^2+2x+2\mod5$

6 0

3 years ago

A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken

mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

$X=1$ number of citrus trees that are infected with the citrus red mite.

$n=5$ random sample taken

$\hat p=\frac{1}{5}=0.2$ estimated proportion of citrus trees that are infected with the citrus red mite.

$p$ true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical values would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.2(1-0.2)}{(\frac{0.01}{1.96})^2}=6146.56$

And rounded up we have that n=6147

5 0

4 years ago

A construction worker needs to determine the volume of a sandpille in a construction yard as shown

postnew [5]

Answer:
6580cm
Step-by-step explanation:
The answer is 6580cm because....
Step one First let's figure out what the smaller shape's volume is. To do so we need to multiply ( LxWxH ) so 6x5x? it does not list what the height is so we know it has the same height as the larger shape and it's height is 14cm so we will use 14cm. 6x5x14=420cm
Step two Now lets find the Volume of the larger shape. So lets do LxWxH so Lx?x14 it does not give us the length so we need to add up all of the numbers along the line. We got 7cm then 5 from the bottom of the smaller shape and 10cm. all ads up to 22cm so 20x22x14=6160
Finally we add up the following shapes Volume which are 6160+420=6580cm

3 0

3 years ago

The sum of three integers is 280. The sum of the first and second integers exceeds the third by 34. The third integer is 30 less

omeli [17]

Answer:

The sum of three integers is 280.

a + b + c = 280

;

The sum of the first and second integers exceeds the third by 70.

a + b = c + 70

:

the third integer is 21 less than the first.

c = a - 21

:

Rearrange the 2nd equation and use elimination with the 1st equation

a + b + c = 280

a + b - c = 70

------------------subtraction eliminates a & b, find c

0 + 0 + 2c = 210

c = 210/2

c = 105

then

105 = a - 21

a = 105 + 21

a = 126

Find b using the 1st equation

126 + b + 105 = 280

b = 280 - 231

b = 49

:

See if that checks out

126 + 49 + 105 = 280

:

the three integers. 126, 49, 105

6 0

3 years ago

The lowest elevation in Vermont is 95 feet above sea level. The lowest elevation in Louisiana is 8 feet below sea level. What in

malfutka [58]

Answer:-95

Idk if it’s correct

4 0

3 years ago