Kaliska is jumping rope. The vertical height of the center of her rope off the ground R(t)R(t)R, left parenthesis, t, right pare
nthesis (in \text{cm}cmstart text, c, m, end text) as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\cos(b\cdot t)+da⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. At t=0t=0t, equals, 0, when she starts jumping, her rope is 0\text{ cm}0 cm0, start text, space, c, m, end text off the ground, which is the minimum. After \dfrac{\pi}{12} 12 π start fraction, pi, divided by, 12, end fraction seconds, it reaches a height of 60\text{ cm}60 cm60, start text, space, c, m, end text from the ground, which is half of its maximum height
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Answer:
We accept the null hypothesis and the population mean is $120.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 100
Sample mean, = $120
Alpha, α = 0.01
Sample standard deviation, s = $25
First, we design the null and the alternate hypothesis
We use two-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
p-value one tail= 0.024
p-value two tail= 0.048
Conclusion:
Since the p-value for two tailed test is greater than the significance level, we fail to reject the null hypothesis and accept it.
Thus, the population mean is $120.
Answer:
1.4in
Step-by-step explanation:
Length of Photo = 4in
Width of Photo = 3in
Unknown:
Value of X = ?
Solution:
Follow these steps:
Area of a rectangle = l x w
Since the photo is a rectangle; area of photo:
Area of photo = 4in x 3in = 12in²
For the area of the ad;
Length of ad = 4 + x
Width of ad = 3 + x
Given that,
the area of the photo = area of ad
12in² = area of ad
Area of ad = 24in²
Area of the ad;
(4 + x) (3 + x) = 24
12 + 4x + 3x + x² = 24
12 + 7x + x² = 24
x² + 7x = 24 - 12
x² + 7x = 12
x² + 7x - 12 = 0
Using the almighty formula where
a = 1, b = 7 and c = -12
x =
x = or
x = 1.4 or -8.4
therefore the answer is 1.4in
x is 1.4in