Answer: The vertex of the function is (-1, -7).
Step-by-step explanation: We are given to find the vertex of the following function.
We know that the vertex of the function is given by (h, k).
So, for the given function f(x), the vertex will be (-1, -7).
The graph of the function f(x) is shown in the attached figure, where the vertex is at the point (-1, -7).
Thus, the vertex of the function is (-1, -7).
The best and the most correct answer among the choices provided by the question is the third choice. The data that corresponds to the function is in the link: <span>http://media.education2020.com/evresources/2003-08-05-00-00_files/i0180002.jpg. </span>I hope my answer has come to your help. God bless and have a nice day ahead!
The number of units of tiles he will need is 18.96 units
Step-by-step explanation:
The parallelogram ABCD has a right triangle ABD with A as 90°
The length of segment AB is given as 3.16 units and that of the diagonal BD is 7.07 units.
Apply Pythagorean relationship to find length of segment AD=BC
The sum of squares of the sides equals the square of the hypotenuse.
a²+b²=c²
In this case, side a=3.16 units, b=AD and c=hypotenuse=7.07
Applying the formula;
a²+b²=c²
3.16²+b²=7.07²
9.99+b²=49.99
b²=49.99-9.99
b²=40
b=√40=6.3245 =6.32
AD=BC=6.32 units
Find the perimeter of the quadrilateral
=3.16+3.16+6.32+6.32=18.96 units
Learn More
Perimeter of a quadrilateral :brainly.com/question/12708927
Keywords : single line of tiles, pool,quadrilateral,length,hundredth
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Answer:
The p-value of the test is 0.0207.
Step-by-step explanation:
Test of the claim that more than 60% of the people following a particular diet will experience increased energy (H1: p > 0.6).
The null hypothesis is:
![H_0: p = 0.6](https://tex.z-dn.net/?f=H_0%3A%20p%20%3D%200.6)
The alternate hypothesis is:
![H_1: p > 0.6](https://tex.z-dn.net/?f=H_1%3A%20p%20%3E%200.6)
The test statistic is:
![z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.6 is tested at the null hypothesis:
This means that ![\mu = 0.6, \sigma = \sqrt{0.6*0.4}](https://tex.z-dn.net/?f=%5Cmu%20%3D%200.6%2C%20%5Csigma%20%3D%20%5Csqrt%7B0.6%2A0.4%7D)
Of 100 randomly selected subjects who followed the diet, 70 noticed an increase in their energy level.
This means that ![n = 100, X = \frac{70}{100} = 0.7](https://tex.z-dn.net/?f=n%20%3D%20100%2C%20X%20%3D%20%5Cfrac%7B70%7D%7B100%7D%20%3D%200.7)
Test statistic:
![z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![z = \frac{0.7 - 0.6}{\frac{\\sqrt{0.6*0.4}}{\sqrt{100}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B0.7%20-%200.6%7D%7B%5Cfrac%7B%5C%5Csqrt%7B0.6%2A0.4%7D%7D%7B%5Csqrt%7B100%7D%7D%7D)
![z = 2.04](https://tex.z-dn.net/?f=z%20%3D%202.04)
P-value of the test:
The p-value of the test is the probability of finding a sample proportion of at least 0.7, which is 1 subtracted by the p-value of z = 2.04.
Looking at the z-table, z = 2.04 has a p-value of 0.9793
1 - 0.9793 = 0.0207
The p-value of the test is 0.0207.
Answer:
9/14
Step-by-step explanation:
9/7(9-7)
9/7(2)
9/14