Given that Allison’s dog is 6 pounds more than 5 times the weight of Gail’s dog, it is important to know the following:
1. The word "more" indicates an Addition.
2. The word "times" indicates Multiplication.
Knowing this, you can write the following expression to represent "5 times the weight of Gail’s dog", where "g" is the weight of Gail’s dog:
Therefore, you can determine that the weight of Allison's dog (in pounds) is the sum of 6 pounds and 5 times the weight of Gail's dog (in pounds). Then, you can represent this with this algebraic expression:
Hence, the answer is:
Answer:
57.93% probability that a trip will take at least 35 minutes.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What is the probability that a trip will take at least 35 minutes
This probability is 1 subtracted by the pvalue of Z when X = 35. So
has a pvalue of 0.4207
1 - 0.4207 = 0.5793
57.93% probability that a trip will take at least 35 minutes.
Subtract 350 from both sides then divide both sides by 25.
(c-350)/25 = h
Answer:
The answer to your question is x = 3; y = 3
Step-by-step explanation:
Data
angle = 45°
Opposite side = x
Adjacent side = y
hypotenuse = 3√2
To solve this problem, use trigonometric functions.
1) To find x, use the trigonometric function sine.
sin Ф = Opposite side / hypotenuse
-Solve for Opposite side (x)
Opposite side = hypotenuse x sin Ф
-Substitution
Opposite side = 3√2 sin 45
-Simplification
Opposite side = 3√2 (1 / √2)
Opposite side = 3(1)
-Result
x = 3
2) To find y use the trigonometric function cosine
cos Ф = Adjacent side / hypotenuse
-Solve for Adjacent side
Adjacent side = hypotenuse x cos Ф
-Substitution
Adjacent side = 3√2 x cos 45
-Simplification
Adjacent side = 3√2 x (1/√2)
Adjacent side = 3(1)
-Result
y = 3
Complete the table for the function y = 0.1^x
The first step: plug values from the left column into the ‘x’ spot in the formula <u>y=0.1^x</u>.
* 0.1^-2 : We can eliminate the negative exponent value by using the rule a^-1 = 1/a. Keep this rule in mind for future problems. (0.1^-2 = 1/0.1 * 0.1 = 100).
* 0.1^-1 = 1/0.1 = 10
* 0.1^0 = 1 : (Remember this rule: a^0 = 1)
* 0.1^1 = 0.1
Our list of values: 100, 10, 1, 0.1
Now, we can plug these values into your table:
![\left[\begin{array}{ccc}x&y\\2&10\\1&10\\0&1\\1&0.1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%26y%5C%5C2%2610%5C%5C1%2610%5C%5C0%261%5C%5C1%260.1%5Cend%7Barray%7D%5Cright%5D)
The points can now be graphed. I will paste a Desmos screenshot; try to see if you can find some of the indicated (x,y) values: [screenshot is attached]
I hope this helped!
