Mary has rehearsed her ballet solo for five and a half hours. A week from now, she wants to have rehearsed at least a total of n
2 answers:
Answer:
2 hours per day
Step-by-step explanation:
Given : Mary has rehearsed her ballet solo for five and a half hours. A week from now, she wants to have rehearsed at least a total of nineteen and a half hours.
To Find : If she rehearses for the same amount of time each day for the next 7 days, at least how many hours must she rehearse per day?
Solution :
Mary has rehearsed her ballet solo =
She wants to have rehearsed at least a total of
So, hours left for rehearsel = 19.5-5.5= 14 hours
If she rehearses for the same amount of time each day for the next 7 days
So, she rehearsed each day = 14/7 = 2 hours
Hence she must rehearse for 2 hours per day
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The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.
<h3>How to determine the approximate area of the regions bounded by the curves</h3>
In this problem we must use definite integrals to determine the area of the region bounded by the curves. Based on all the information given by the graph attached below, the area can be defined in accordance with this formula:
A = A₁ + A₂ (1)
A₁ = ∫ [g(x) - f(x)] dx, for x ∈ [- 0.786, 0] (2)
A₂ = ∫ [f(x) - g(x)] dx, for x ∈ [0, 1.151] (3)
g(x) = x⁴ - x (4)
f(x) = x / √(x² + 1) (5)
Then, we proceed to find the integrals:
∫ g(x) dx = ∫ x⁴ dx - ∫ x dx = (1 / 5) · x⁵ - (1 / 2) · x² (6)
∫ f(x) dx = ∫ [x / √(x² + 1)] dx = (1 / 2) ∫ [2 · x / √(x² + 1)] dx = (1 / 2) ∫ [du / √u] = √u = √(x² + 1) (7)
And the complete expression for the integral is:
A = A₁ + A₂ (1b)
A₁ = (1 / 5) · x⁵ - (1 / 2) · x² - √(x² + 1), for x ∈ [- 0.786, 0] (2b)
A₂ = √(x² + 1) - (1 / 5) · x⁵ + (1 / 2) · x², for x ∈ [0, 1.151] (3b)
A₁ = 0.023
A₂ = 0.783
A = 0.023 + 0.783
A = 0.806
The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.
To learn more on definite integral: brainly.com/question/14279102
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Answer:
82.31% of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter
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:
Approximately what percentage of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter?
This is the pvalue of Z when X = 5.4 subtracted by the pvalue of Z when X = 4.2. So
X = 5.4
has a pvalue of 0.9842
X = 4.2
has a pvalue of 0.1611
0.9842 - 0.1611 = 0.8231
82.31% of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter