Answer:
The correct option is;
c. Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.
Step-by-step explanation:
Here we have the values
μ = 275 mL
275.4
276.8
273.9
275
275.8
275.9
276.1
Sum = 1928.9
Mean (Average), = 275.5571429
Standard deviation, s = 0.921696159
We put the null hypothesis as H₀: μ₁ = μ₂
Therefore, the alternative becomes Hₐ: μ₁ ≠ μ₂
The t-test formula is as follows;
Plugging in the values, we have,
Test statistic = 1.599292
at 7 - 1 degrees of freedom and α = 0.05 = ±2.446912
Our p-value from the the test statistic = 0.1608723≈ 0.1609
Therefore since the p-value = 0.1609 > α = 0.05, we fail to reject our null hypothesis, hence the evidence suggests that the mean does not differ from 275 mL.
All congruent rectangles similar because comparable shapes are not always congruent.
Given that,
We have to find are all congruent rectangles similar.
We know that,
Each side's length and the angles that separate them match those of the other shape's corresponding sides and angles. Comparable shapes are not always congruent, whereas congruent shapes are always similar.
So,
Similar figures are not always congruent, whereas congruent figures are always similar. For similar figures, we simply take into account the shapes, however for congruent triangles, we take into account both the shapes and sizes of the figure.
Therefore, All congruent rectangles similar because comparable shapes are not always congruent.
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Answer:
The second one (answer of 3), but the other ones could've worked, they were just calculated wrong.
Step-by-step explanation:
Here's why each one did or didn't work:
First answer- you had the right idea by cancelling out the two in the denominator, however if you're going to divide 2, you have to divide it from everything in the equation. Meaning you would divide 4 by 2 to get 2, and then add the 1 + 2 to get final answer 3.
Second answer- since you added the numerator separately and then did the basic division, this worked.
Third one- similarly to the first one, you would have to also divide the 2 by 2 to get 1, then adding 1 + 2 to get 3.
Equivalent Expressions are expression that have the same value on both side of the equal sign.
Expression 1:
First simplify both sides of the expression. One of them are already fully simplified.
8x-4y=4(-y+2x)
8x- 4y=-4y+8x
This expression IS an equivalent expression.
Expression 2:
Do the same as in expression one (we will be simplifying all of the expressions).
8x+4y=4(2x+y)
8x+4y=8x+4y
This expression IS an equivalent expression.
Expression 3:
4x-8y=4(-x+2y)
4x-8y=-4x+8y
This expression IS NOT an equivalent expression.
Expression 4:
4x+8y=4(x+2y)
4x+8y=4x+8y
This expression IS an equivalent expression.
Expression 5:
4x+8y=4(8xy)
4x+8y=32xy
This expression IS NOT an equivalent expression.
