What inequality sign do you use if c is at most 3

The function y = x2 â€“ 4x + 7 approximates the height, y, of a bird, and its horizontal distance, x, as it flies from one fence

Salsk061 [2.6K]

From the function y=x^2-4x+7
to complete the square we proceed as follows:
The vertex form is given by:
y=(x-h)^2+k
where (h,k) is the vertex:
thus from the function we shall have:
y=x^2-4x+7
c=(b/2a)²
c=(4/2)²=4
thus adding an subtracting 4 in the expression:
y=x^2-4x+4-4+7
y=(x-2)^2+3
thus the vertex will be:
(2,3)

The answer is:
<span>D. Minimum at (2, 3)</span>

7 0

2 years ago

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TIME CRUCIAL!! i will give you thanks please help!!! ASAP! will mark as brainliest!!

ozzi

$\overline{y}$ (prounounced "y bar") is the mean of the y values

Add up the y values to get
5+7+10+15+18 = 55

Then divide by 5 (because there are five y values) to get
55/5 = 11

Therefore,
$\overline{y} = 11$

The answer is choice C

3 0

3 years ago

Need answer quickly. Thanks

ratelena [41]

Answer:

sopa de macaco

Step-by-step explanation:

macacoooooooo

8 0

3 years ago

Iodine-131 is a radioactive material with half-life of eight days. A scientist starts with 100 grams of iodinie- 131. Which func

MrRissso [65]

The correct answer is Choice A.

This is an example of an exponential equation, so we need the formula $y=ab^x$ .

The a value is the starting value of 100. The b value must be a decimal lower than 1 because it is decreases.

If you substitute in 8 for x, you will see that the output is about 50 (half of 100).

6 0

3 years ago

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Below are three different hypothesis tests about population proportions. For each test, use StatKey and the information given to

Ilia_Sergeevich [38]

Answer:

1a) p-hat=0.38

1b) P=0.08

1c) The null hypothesis is not rejected

2a) p-hat=0.64

2b) P=0.0027

2c) The null hypothesis is rejected

3a) p-hat=0.55

3b) P=0.153

3c) The null hypothesis is not rejected

Step-by-step explanation:

(1) H0: p = 0.3 vs Ha: p ≠ 0.3. In their survey, they had a count of 38 using a sample size n=100.

1a) The p-hat is p-hat=38/100=0.38.

1b) The standard deviation is

$\sigma=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.3*0.7}{100}}=0.046$

The sample size is n=100.

The z-value is:

$z=\frac{\hat{p}-p}{\sigma}=\frac{0.38-0.3}{0.046}=\frac{0.08}{0.046}= 1.74$

As it is a two-sided test, the p-value considers both tails of the distribution.

The p-value for this |z|=1.74 is P=0.08.

1c) The null hypothesis is not rejected.

(2) H0: p = 0.7 vs Ha: p ≠ 0.7. In their survey, they had a count of 320 using a sample size n=500.

2a) The p-hat is p-hat=320/500=0.64.

2b) The standard deviation is

$\sigma=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.7*0.3}{500}}=0.02$

The sample size is n=500.

The z-value is:

$z=\frac{\hat{p}-p}{\sigma}=\frac{0.64-0.7}{0.02}=\frac{-0.06}{0.02}=-3$

As it is a two-sided test, the p-value considers both tails of the distribution.

The p-value for this |z|=3 is P=0.0027.

2c) The null hypothesis is rejected.

(3) H0: p = 0.6 vs Ha: p < 0.6. In their survey, they had a count of 110 using a sample size n=200.

2a) The p-hat is p-hat=110/200=0.55.

2b) The standard deviation is

$\sigma=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.6*0.4}{200}}=0.035$

The sample size is n=200.

The z-value is:

$z=\frac{\hat{p}-p}{\sigma}=\frac{0.55-0.6}{0.035}=\frac{-0.05}{0.035}=-1.43$

As it is a two-sided test, the p-value considers both tails of the distribution.

The p-value for this |z|=1.43 is P=0.153.

2c) The null hypothesis is not rejected.

8 0

3 years ago