Answer:
Step-by-step explanation:
Given data and notation
indicates the sample mean
refers to the sample standard deviation
is the sample size
represents the value we are testing.
indicates the significance level for the hypothesis test.
t refers to the statistic of interest.
is the p-value for the test (the variable we are interested in).
Formulate the null and alternative hypotheses.
I will set up the hypotheses to verify if the mean weight falls below 4 ounces, formalizing:
Null hypothesis: 
Alternative hypothesis: 
Since our sample size is < 30 and the population standard deviation is unknown, it’s advisable to utilize a t test to compare the actual mean against the reference value, with the statistic calculated as follows:
(1)
t-test: "This test compares group means and is commonly utilized to determine if the mean is (greater than, less than, or not equal to) a specific value."
Calculate the statistic
We can substitute the provided information into formula (1):
Answer:
a) The first inequality is 100 + 55x > 150 + 51x;
b) The final inequality results in x > 12.5
c) Sal's mother will need to use the second phone for at least 13 months.
Step-by-step explanation:
a) Let x represent the number of months.
1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.
2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.
3. For the second phone to be cheaper, we set up the inequality:
150 + 51x < 100 + 55x
which simplifies to
100 + 55x > 150 + 51x
b) Now solve this:
55x - 51x > 150 - 100
4x > 50
so x > 12.5
c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).
Answer:
qt's length = 16
Step-by-step explanation:
The problem states that qrs is a right triangle,
where qr = 20
sr =?
qs = 25
qt =?
1)
Calculate sr
hypotenuse² = base² + height²
sq² = sr² + rq²
25² - 20² = sr²
sr = √(25² - 20²)
sr = 15
2)
When altitude rt is dropped to hypotenuse qs, it creates
two right triangles: rtq and rts.
Δrtq
height = rt
base= tq = 25 - x
hypotenuse = qt = 20
Δrts
height = rt
base= ts = x
hypotenuse = sr = 15
Both triangles share the same height, which is rt
Using the Pythagorean theorem:
Δ rtq Δ rts
hypotenuse² - base² = height²
20² - (25 - x)² = 15² - x²
400 - (625 + x² - 50x) = 225 - x²
400 - 625 - x² + 50x = 225 - x²
-225 - x² + 50x - 225 + x² = 0
-450 + 50 x = 0
50x = 450
x = 450/50
x = 9
Base of Δ rtq = tq = 25 - x
tq = 25 - 9
tq = 16
<span><span>Response
26 1/2 does not correspond to an integer but can be rounded to 27, which is an integer.
Clarification
An integer comprises whole numbers only. It does not include fractions.
253/2=25+3/2=25+1 1/2=26 1/2
</span><span>26 1/2 does not correspond to an integer but can be rounded to 27, which is an integer.
</span></span>
Hello! C and D aren't correct answers, as they fall downward due to gravity. The object accelerates downward at -10 m/s, resulting in an increasing speed as it descends, going beyond 10 m/s, which indicates that speed isn't steady. Hence, the correct answer is A.
