The point (1,5) is:
Like it is shown this means that we have to move one unit in the right direction and 5 units up.
Answer:
![15x {y}^{7} z](https://tex.z-dn.net/?f=15x%20%7By%7D%5E%7B7%7D%20z)
Step-by-step explanation:
<h3>Factorize the Expressions</h3>
![15x {y}^{2} z = 3 \times 5 \times x \times y \times y \times y \times y \times y \times y \times y \times z](https://tex.z-dn.net/?f=15x%20%7By%7D%5E%7B2%7D%20z%20%3D%203%20%5Ctimes%205%20%5Ctimes%20x%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20z)
![30 {x}^{2} {y}^{7} z = 2 \times 3 \times 5 \times x \times x \times y \times y \times y \times y \times y \times y \times y \times z](https://tex.z-dn.net/?f=30%20%7Bx%7D%5E%7B2%7D%20%20%7By%7D%5E%7B7%7D%20z%20%3D%202%20%5Ctimes%203%20%5Ctimes%205%20%5Ctimes%20x%20%5Ctimes%20x%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20z)
<h3>Factor out the Common Factors</h3>
![gcf = 3 \times 5 \times x \times y \times y \times y \times y \times y \times y \times y \times z](https://tex.z-dn.net/?f=gcf%20%3D%203%20%5Ctimes%205%20%5Ctimes%20x%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20z)
<h3>Multiply the Common Factors</h3>
![3 \times 5 \times x \times y \times y \times y \times y \times y \times y \times y \times z = 15x {y}^{7} z](https://tex.z-dn.net/?f=3%20%5Ctimes%205%20%5Ctimes%20x%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20y%20%5Ctimes%20z%20%3D%2015x%20%7By%7D%5E%7B7%7D%20z)
The Factored expressions are
![15x {y}^{7} z](https://tex.z-dn.net/?f=15x%20%7By%7D%5E%7B7%7D%20z)
And
![15x {y}^{7} (2x)](https://tex.z-dn.net/?f=15x%20%7By%7D%5E%7B7%7D%20%282x%29)
Answer:
![60cm^{2}](https://tex.z-dn.net/?f=60cm%5E%7B2%7D)
Step-by-step explanation:
so first we need to find the height so by splitting the isosceles triangle into two right-angled triangles and then applying Pythagoras' Theorem to one of them.
![h^{2} =13^{2} -5^{2}](https://tex.z-dn.net/?f=h%5E%7B2%7D%20%3D13%5E%7B2%7D%20-5%5E%7B2%7D)
![h^{2} =169-25](https://tex.z-dn.net/?f=h%5E%7B2%7D%20%3D169-25)
![h^{2} =144](https://tex.z-dn.net/?f=h%5E%7B2%7D%20%3D144)
![h=\sqrt{144}](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B144%7D)
![h=12](https://tex.z-dn.net/?f=h%3D12)
We now know the height of the triangle and can use this to go back and find the area of the isosceles triangle.
area of triangle =
x base x height
area of triangle =
x 10 x 12
area of triangle = 60
Answer:
i belive it was 750.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that 33.4% of people have sleepwalked.
Sample size n =1459
Sample favourable persons = 526
Sample proportion p = ![\frac{526}{1459} \\=0.361](https://tex.z-dn.net/?f=%5Cfrac%7B526%7D%7B1459%7D%20%5C%5C%3D0.361)
Sample proportion p is normal for large samples with mean = 0.334 and
std error = ![\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.334(1-0.334)}{1459} } \\=0.0123](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D%20%5C%5C%3D%5Csqrt%7B%5Cfrac%7B0.334%281-0.334%29%7D%7B1459%7D%20%7D%20%5C%5C%3D0.0123)
a) P(526 or more of the 1459 adults have sleepwalked.)
![=P(p\geq 0.361)\\=P(Z\geq \frac{0.361-0.334}{0.0123} \\=P(Z\geq 2.20)\\=0.5-0.4861\\=0.0139](https://tex.z-dn.net/?f=%3DP%28p%5Cgeq%200.361%29%5C%5C%3DP%28Z%5Cgeq%20%5Cfrac%7B0.361-0.334%7D%7B0.0123%7D%20%5C%5C%3DP%28Z%5Cgeq%202.20%29%5C%5C%3D0.5-0.4861%5C%5C%3D0.0139)
b) Yes, because hardly 1.4% is the probability
c) 33.4 is very less compared to the average. Either sample should be improved representing the population or population mean should be increased accordingly.