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2 years ago

Which equation represents a parabola that opens upward has a minimum at x=3 and has a line of symmetry at x=3

Mathematics

2 answers:

Advocard [28]2 years ago

5 0

Answer:

A. y = x^2 -6x + 13

Step-by-step explanation:

umka2103 [35]2 years ago

4 0

Answer:

$y=x^2-6x+5$

Step-by-step explanation:

Let us consider the equation $y=x^2-6x+5$

For a quadratic equation in a standard form, $y=ax^2+bx+c$ , the axis of symmetry is the vertical line $x = \frac{-b}{2a}$ .

Here in this case we have, $a=1, b=-6 , c =5$

Putting the values we get,

$x = \frac{-(-6)}{2\times 1} = \frac{6}{2} =3$

We can see that the axis of symmetry is x=3 and the graph is giving minimum at x=3.

Therefore, the required equation is $y=x^2-6x+5$ . Refer the image attached.

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If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?

Andrei [34K]

<h3>Answer: 2p + 3q</h3>

Work Shown:

log(200) = log(2^3*5^2)

log(200) = log(2^3) + log(5^2)

log(200) = 3*log(2) + 2*log(5)

log(200) = 3*q + 2*p

log(200) = 2p + 3q

The log rules I used were

log(A*B) = log(A)+log(B)

log(A^B) = B*log(A)

8 0

2 years ago

A group of 54 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic

Ket [755]

Answer:

$t=\frac{5.25-4.73}{\frac{3.98}{\sqrt{54}}}=0.9601$

P-value

First we find the degrees of freedom given by:

$df = n-1= 54-1=53$

Since is a two-sided test the p value would be:

$p_v =2*P(t_{53}>0.9601)=0.3414$

Step-by-step explanation:

Data given and notation

$\bar X=5.25$ represent the sample mean

$s=3.98$ represent the sample standard deviation

$n=54$ sample size

$\mu_o =4.73$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean differs from 4.73, the system of hypothesis would be:

Null hypothesis: $\mu =4.73$

Alternative hypothesis: $\mu \neq 4.73$

Since we know don't the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{5.25-4.73}{\frac{3.98}{\sqrt{54}}}=0.9601$

P-value

First we find the degrees of freedom given by:

$df = n-1= 54-1=53$

Since is a two-sided test the p value would be:

$p_v =2*P(t_{53}>0.9601)=0.3414$

7 0

3 years ago

To find the height of a pole, a surveyor uses a theodolite. The theodolite is 4 ft tall. The surveyor stands 140 feet away from

Ad libitum [116K]

Tan 44° = x/140

x = 140 tan 44°

x approx = 140 * 0.9657 = 135.198

Remember, we need to add another 4 feet, so the answer would be 139.198 feet

6 0

2 years ago

Read 2 more answers

What is the meaning of life? What makes this world so great? Is there something to look forward to in the future?

marysya [2.9K]

Well if your one of those people, this question is actually very easy to answer.the meaning of life too me is simply to live.and anything good is not bad so, anything you can think of that is good is what makes the world good.;)

8 0

3 years ago

Read 2 more answers

An alternating current E(t)=120sin(12t) has been running through a simple circuit for a long time. The circuit has an inductance

Dvinal [7]

Answer:

14.488 amperes

Step-by-step explanation:

The amplitude I of the current is given by

$\large I=\displaystyle\frac{E_m}{Z}$