A bag of marbles contains 28 red marbles, 30 green marbles, and 24 yellow marbles. What is the ratio of red marbles to yellow ma
2 answers:
You might be interested in
Answer:
The first option is correct. Option A is correct.
LCL = 0.270, and UCL = 0.397
80% Confidence interval = (0.270, 0.397)
Step-by-step explanation:
The data for Y and N for the 90 companies is attached to this solution provided.
Y represents companies with at least 1 bilingual operator and N represents companies with no bilingual operator.
The number of Y in the data = 30
Hence, sample proportion of companies with at least one bilingual operator = (30/90) = 0.3333
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = 0.3333
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 80% confidence level for sample size of 90 is obtained from the z-tables.
Critical value = 1.280
Standard error of the mean = σₓ = √[p(1-p)/n]
p = sample proportion
n = sample size = 90
σₓ = √[0.3333×0.6667)/90] = 0.0496891568 = 0.04969
80% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.3333 ± (1.28 × 0.04969)
CI = 0.3333 ± 0.0636021207
80% CI = (0.2696978793, 0.3969021207)
80% Confidence interval = (0.270, 0.397)
Hope this Helps!!!
Answer:
128 feet
Step-by-step explanation:
So now we will substitute the values of T and π into the equation.
Divide both sides by 6.28
Square both sides.
Multiply both sides by 32
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
<h3>How to estimate a definite integral by numerical methods</h3>In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:
∫ f(x) dx = F(b) - F(a) (1)
The steps of Euler's method are summarized below:
- Define the function seen in the statement by the label f(x₀, y₀).
- Determine the different variables by the following formulas:
xₙ₊₁ = xₙ + (n + 1) · Δx (2)
yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ) (3) - Find the integral.
The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
To learn more on Euler's method: brainly.com/question/16807646
#SPJ1
