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earnstyle [38]
3 years ago
5

If Lylah completes the square for f(x) = x 2 + 24x -18 in order to find the minimum, she must write f(x) in the general form f(x

) = (x − a)^2+ b. What is the value of b for f(x)?
Explain (tell me word for word how you arrived at the answer above, include screenshots if necessary) how you found the solutions in detail.
Mathematics
1 answer:
olga nikolaevna [1]3 years ago
3 0

Answer:

Step-by-step explanation:

F(x)=  (x − a)2 + b

Rewrite the equation as (X-a)2 + b= f(X) (X-a)2 + b= f(X)  subtract (x-a)^2 from both sides of the equation b=f(x)- (x-a)^2

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The manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour. (a-1) At α = .05 i
fenix001 [56]

Answer:

Null hypothesis:\mu \geq 250        

Alternative hypothesis:\mu < 250  

p_v =P(t_{15}    

If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not significantly lower than 530 at 5% of significance.      

Step-by-step explanation:

1) Data given and notation        

\bar X=510 represent the mean for the sample    

s=50 represent the standard deviation for the sample  

n=16 sample size        

\mu_o =530 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.      

t would represent the statistic (variable of interest)        

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

2) State the null and alternative hypotheses.        

We need to conduct a hypothesis in order to determine if the claim thet the handle on average is 530 bags per hour:      

Null hypothesis:\mu \geq 530        

Alternative hypothesis:\mu < 530        

We don't know the population deviation and the sample size is lees than 30, so for this case 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{\sigma}{\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".    

3) Calculate the statistic        

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

t=\frac{510-530}{\frac{50}{\sqrt{16}}}=-1.60        

4) Calculate the critical value

We need to begin calculating the degrees of freedom

df=n-1=16-1=15

The critical value for this case would be :

P(t_{15}

The value of a that satisfy this on the normal standard distribution is a=-1.75 and would be the critical value on this case zc=-1.75

5) Calculate the P-value        

Since is a one-side upper test the p value would be:        

p_v =P(t_{15}    

6) Conclusion        

If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not significantly lower than 530 at 5% of significance.      

8 0
2 years ago
BEST ANSWER GETS BRAINLIEST!!!!
Vika [28.1K]
A: 
An independent variable could be how long she works. (Well it's not really independent I guess... Sorta depends.)
A dependent variable could be how much money she makes, depending on how long she works.

B:
Umm, like:
(1, 7)
If 1 was how many hours she worked and $7 is how much money she made, and therefore x would be how many hours she worked and y would be how much total money she made.
(2, 14)
(3, 21)

C: An equation would be 7x = y.
6 0
3 years ago
Triangle ABC has side lengths: V6, V2, and 2/2 units.
Morgarella [4.7K]

Answer:

90°, 60°, and 30°

60°.

Step-by-step explanation:

The triangle ABC has side lengths √6, √2, and 2√2 units.

It is clear that the triangle ABC is right triangle because (2√2)² = (√6)² + (√2)² that means the side lengths satisfy the Pythagoras Theorem.

Now, if the angle between hypotenuse (2√2 units) and base (√2 units) is \theta, then

\cos \theta = \frac{\sqrt{2} }{2\sqrt{2} }  = \frac{1}{2}

Hence, \theta = 60°

Therefore, the three angles of the triangle are 90°, 60°, and 30°.

Now, if the base of the triangle is 16 units, then other two side lengths will also change proportionally to remain the triangle a right triangle.

And in that case the base angle will remain 60°. (Answer)

6 0
3 years ago
How many minutes are there in a 40 hours week?
Pavel [41]
60 minutes times 40 hours equals 2400 minutes
4 0
3 years ago
The rate at which energy is used is called <br> work, voltage, power, or amperage.
SSSSS [86.1K]

Answer:

The rate at which energy is used is called power.

Step-by-step explanation:

5 0
3 years ago
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