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Find the vertex of the equation x2-4x+5=0

amid [387]

Answer:

(2, 1).

Step-by-step explanation:

x^2 - 4x + 5 = 0

(x - 2)^2 - 4 + 5 = 0

(x - 2)^2 + 1 = 0

The vertex is at (2, 1).

4 0

3 years ago

Mike and Alice recycled 147 bottles altogether. Mike recycled 6 times as many bottles as Alice. How many bottles did Alice recyc

ValentinkaMS [17]

Answer:

The number of bottles recycle by Alice is 21.

Step-by-step explanation:

Given:

Mike and Alice recycled 147 bottles altogether. Mike recycled 6 times as many bottles as Alice.

Now, to find the quantity of bottles Alice recycle.

Let the number of bottles recycle by Alice = $x$ .

And the number of bottles recycled by Mike = $6x$ .

So, according to question:

$x+6x=147$

⇒ $7x=147$

<em>Dividing both sides by 7 we get:</em>

⇒ $x=21$ .

Therefore, the number of bottles recycle by Alice is 21.

8 0

3 years ago

A recent health report revealed that a woman with insurance spends an average of 2.3 days in the hospital following a routine ch

cupoosta [38]

Answer:

$t=\frac{2.3-1.9}{\sqrt{\frac{0.6^2}{16}+\frac{0.3^2}{16}}}}=2.385$

$p_v =2*P(t_{30}>2.385)=0.0236$

Comparing the p value with the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis

The confidence interval would be given by:

$(2.3 -1.9) - 2.75*\sqrt{\frac{0.6^2}{16}+\frac{0.3^2}{16}}}=-0.0611$

$(2.3 -1.9) + 2.75* \sqrt{\frac{0.6^2}{16}+\frac{0.3^2}{16}}}=0.861$

Step-by-step explanation:

Data given and notation

$\bar X_{insurance}=2.3$ represent the mean for insurance

$\bar X_{No. ins}=1.9$ represent the mean withour insurance

$s_{Insurance}=0.6$ represent the sample standard deviation for the insurance case

$s_{No. Ins}=0.3$ represent the sample standard deviation for the No insurance case

$n_{Insurance}=16$ sample size for insurance

$n_{No. Iss}=16$ sample size for no insurance

t would represent the statistic (variable of interest)

$\alpha=0.01$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis: $\mu_{Insu}=\mu_{No. Ins}$

Alternative hypothesis: $\mu_{Ins} \neq \mu_{No. Ins}$

Since we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:

$t=\frac{\bar X_{Ins}-\bar X_{No.Ins}}{\sqrt{\frac{s^2_{Ins}}{n_{Ins}}+\frac{s^2_{No. Ins}}{n_{No. Ins}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

$t=\frac{2.3-1.9}{\sqrt{\frac{0.6^2}{16}+\frac{0.3^2}{16}}}}=2.385$

What is the p-value for this hypothesis test?

The degrees of freedom are given by:

$df = n_{ins} +n_{No Ins}-2=16+16-2 =30$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{30}>2.385)=0.0236$

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis

The confidence interval would be given by:

$(2.3 -1.9) - 2.75*\sqrt{\frac{0.6^2}{16}+\frac{0.3^2}{16}}}=-0.0611$

$(2.3 -1.9) + 2.75* \sqrt{\frac{0.6^2}{16}+\frac{0.3^2}{16}}}=0.861$

6 0

3 years ago

A bowl has only red, green, and purple grapes. The probability of picking a red grape out of the bowl, eating it, and then picki

Xelga [282]

The probability of picking a green grape is 1/2.

<h3>What is probability?</h3>

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Since the probability of picking a red grape out of the bowl, eating it, and then picking a green grape out of the bowl is 1/8 and probability of picking just a red grape is 1/4 .

The probability of green grape will be the division. This will be:

= P(R and G) / P(R)

= 1/8 ÷ 1/4

= 1/8 × 4/1

= 1/2

The probability is 1/2.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

8 0

1 year ago

Determine the value of k that partitions a segment into a ratio of 1:4

tiny-mole [99]

1/5 is the value but all you do is take the first number which would be your numerator and add both the first and last number together to get your denominator

3 0

3 years ago