Answer:
Step-by-step explanation:
Two lines are perpendicular if the first line has a slope of 
and the second line has a slope of 
.
With this information, we first need to figure out what the slope of the line is that we're given, and then we can determine what the slope of the line we're trying to find is:
We now know that 
for the first line, which means that the slope of the second line is 
. With this, we have the following equation for our new line:
where 
is the Y-intercept that we now need to determine with the coordinates given in the problem statement, 
:
Finally, we can create our line:
80% of 90 may be found by multiply 90 by 0.8. Once you have that number, you can use it to set up a proportion with 2/5 (the simplified form of 40/100). Thus, you will write out 72/x = 2/5, since x is the number that you're solving for. Multiply numerators and denominators of opposite fractions to get the equation 72(5) = 2x. Finally, simplify 360 = 2x by dividing both sides by 2 to isolate the variable. You should have your answer by now.
Answer:
<em>H₀</em>: <em>μ</em>₁ = <em>μ</em>₂ vs, <em>Hₐ</em>: <em>μ</em>₁ > <em>μ</em>₂.
Step-by-step explanation:
A two-sample <em>z</em>-test can be performed to determine whether the claim made by the owner of pier 1 is correct or not.
It is provided that the weights of fish caught from pier 1 and pier 2 are normally distributed with equal population standard deviations.
The hypothesis to test whether the average weights of the fish in pier 1 is more than pier 2 is as follows:
<em>H₀</em>: The weights of fish in pier 1 is same as the weights of fish in pier 2, i.e. <em>μ</em>₁ = <em>μ</em>₂.
<em>Hₐ</em>: The weights of fish in pier 1 is greater than the weights of fish in pier 2, i.e. <em>μ</em>₁ > <em>μ</em>₂.
The significance level of the test is:
<em>α</em> = 0.05.
The test is defined as:
The decision rule for the test is:
If the <em>p</em>-value of the test is less than the significance level of 0.05 then the null hypothesis will be rejected and vice-versa.
Answer:
Step-by-step explanation:
We want to know "probability that first is vowel AND second is vowel"
In probability theory, "AND" means Multiplication.
<em>Essentially we want to figure out probability of first drawn to be vowel and multiply that with probability second drawn is vowel as well.</em>
<em />
There are 5 vowels and total 12 letters, so
P (vowel) = 5/12
<u>For the second draw, there are STILL 12 letters and 5 vowels (since the first drawn is REPLACED)</u>. Hence, probability of 2nd vowel is the same. So:
P (vowel for 2nd draw) = 5/12
<em>Now we multiply them to get: 
</em>
Answer:
Step-by-step explanation:
The equation is (10 x y)+(5 x n)=1.45
The answer is: 5 nickels and 12 dimes
