Let f(x)=5x^2-4x and g(x)=5x+1. Find f-g

The sum of two consecutive odd integers is 28. What are the integers?

Fantom [35]

The correct option is B): "<span>Let x = 1st integer. Let x + 2 = 2nd integer.</span><span>"
Given that "The sum of two consecutive odd integers is 28."

Now the difference between two odd numbers is 2. So this means that one odd number has to be greater than the other by 2.

Let the smaller number be 'X' therefore the bigger number will be 'x+2' thus x + (x+2) = 28

therefore, x + x + 2 = 28 now we subtract "2" from both the sides
therefore, 2x = 26 now dividing throughout by 2 we get:

x = 13 therefore, x + 2 = 13+2
= 15

therefore, the numbers are 13 AND 15</span>

4 0

4 years ago

Is it true or false that 16.371 rounded to the nearest whole number 16 feet per second

rusak2 [61]

Answer:

true

Step-by-step explanation:

To round off a number to its nearest whole number, look at the first number after the decimal point. If the number is equal or greater than 5, add 1 to the number before the decimal point. If it is less than 5, add zero.

Because the first number after the decimal point is 3, which is less than 5, add zero to 16 . 16 + 0 = 16

If the number were 16.571, rounding off to the nearest whole number would give 17

4 0

3 years ago

Sketch the graph of y = (x + 3)2 – 4 and identify the axis of symmetry.

Sloan [31]

Answer: Thought I’d return the favor and help u with this question! But anyways, the axis of symmetry is at x = -3.

Explanatio: This can be found by looking at the basic form of vertex form:

y = (x - h)^2 + k

In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = -4. This means the vertex is at (-3, -4).

It is a fact that the axis of symmetry is a vertical line of x = (vertex value of x). So we can determine that the axis of symmetry is at x = -3

i hope this helps u

4 0

3 years ago

The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, al

Valentin [98]

Answer:

a) $p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 0$

Alternative hypothesis: $\mu_y -\mu_x$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679$

The next step is calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Now we can calculate the p value, since we have a left tailed test the p value is given by:

$p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

Part b

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

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

Now we have everything in order to replace into formula (1):

$-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469$

$-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069$

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0

3 years ago

PLEASE WHAT IS THE AREA OF THIS HELP ME PLEASE

BARSIC [14]

Answer:

it should be 14,580 m^2

(the ^2 means squared btw)

7 0

3 years ago