In triangle abc, a is a right angle, and ab = 16√3, and the measure of b=30 degrees. What is the length of ac.
1 answer:
Answer:
the length of ac is 16.
Step-by-step explanation:
Given;
A is right angle, = 90⁰
B is 30⁰
ab = 16√3
C
↓
↑
A → ← B
If this right angle triangle is considered, length bc is the hypotenuse and length ac is the opposite side of angle B.
The length of ac is calculated as follows;
Therefore, the length of ac is 16.
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Answer:
Step-by-step explanation:
Hello!
To study if the average dollars spend per shopper is different than the expected population average of $84.5 there was a sample of 120 shoppers taken and their spending habit registered.
Then the study variable is:
X: Amount of money spent by a shopper ($)
This population standard deviation is σ= $16
Using the data information I've run a normality test, with p-value: 0.3056 against the test significance level α: 0.05, the decision is to not reject the null hypothesis so there is enough statistical evidence to conclude that the study variable has a normal distribution.
X~N(μ;σ²)
I've also calculated the sample mean and standard deviation:
X[bar]= $81.01
S= $19.62
a.
If the objective is to test that the true mean spending for the population is significantly different than the expected average of 84.5, the parameter of interest is the population mean μ and the hypothesis test will be two-tailed.
H₀: μ = 84.5
H₁: μ ≠ 84.5
α:0.05
The statistic is a standard normal for one sample:
p-value two tailed 0.016894
b.
The decision rule using the p-value method is:
If p-value ≤ α ⇒ Reject the null hypothesis.
If p-value > α ⇒ Do not reject the null hypothesis.
Since the p-value is less than the significance level, the decision is to reject the null hypothesis.
c.
Using a level of significance of 5% the null hypothesis was rejected. So there is enough statistical evidence to support the researcher's claim that the true mean spending for the population is significantly different than the expected average of $84.5.
I hope it helps!
Answer:
To purchase 700 business cards, Jamie needs to pay $43.
Step-by-step explanation:
We are given that Jamie ordered 200 business cards and paid $23 in total.
We are also given that Jamie ordered 500 business cards and paid $35.
We can use the rate of change formula to find the average change.
This can also be represented with:
Therefore, we need to identify our variables.
In every relationship, there is a <u>dependent variable</u> and an <u>independent variable</u>.
- The independent variable is the variable that an experimenter adjusts in order to receive an altered effect from an output.
- The dependent variable is the variable that adjusts based on the changes made to the independent variable.
We change the amount of business cards that are purchased, which in turn, changes the price.
The y-variable is assigned to the dependent variable and the x-variable is assigned to the dependent variable.
Therefore, if we use the coordinate system:
- (200, 23)
- (500, 35)
Now, we can name our coordinates. We use this system:
- (x₁, y₁)
- (x₂, y₂)
This means that we can name our points:
- x₁ = 200
- y₁ = 23
- x₂ = 500
- y₂ = 35
Revisiting the rate of change formula, we can insert these values.
Next, we need to find the y-intercept of our line. We can do this by using one coordinate pair from above and our slope.
The slope-intercept equation is:
We already know m:
We also know x and y (we take them from of the coordinate pairs):
Now, we can substitute these values into the equation and solve for b.
Now, we can set up our linear equation.
Therefore, in order to find the price of 700 business cards, we make x in the equation equal 700 and then solve.
Therefore, the price of 700 business cards is equal to $43.