No, Yes, No, Yes
using the laws of exponents
(1)
()³ =
4³ × 4³ =
≠
→ No
(2)
()^4 =
×
=
→ Yes
(3)
= (6 × 3 )^8 =
×
≠
×
→ No
(4)
= (4 × 5 )³ = 4³ × 5³ → Yes
Maggie buys a dress and a pair of shoes at The Home Store. Before adding the sales tax, she pays $48 for a dress that normally s
1 answer:
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Refer to the graph shown below. It confirms that points A, B and P are
collinear.
Calculate the length of AP (as a).
a = √[(6 - 2)² + (11 - 3)²]
= 8.9443
Calculate the length of BP (as b).
b = √[(8 - 6)² + (15 - 11)²]
= 4.4721
Calculate ratio a/b.
a/b = 8.9443/4.4721 = 2
Therefore P partitions AB in a 2:1 ratio so that AP = 2*BP.
Answer: 2:1 ratio.
collinear.
Calculate the length of AP (as a).
a = √[(6 - 2)² + (11 - 3)²]
= 8.9443
Calculate the length of BP (as b).
b = √[(8 - 6)² + (15 - 11)²]
= 4.4721
Calculate ratio a/b.
a/b = 8.9443/4.4721 = 2
Therefore P partitions AB in a 2:1 ratio so that AP = 2*BP.
Answer: 2:1 ratio.
Answer:
Step-by-step explanation:
Write the terms of numerator and denominator using a common denominator.
Answer:
We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.
Step-by-step explanation:
We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.
A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0
<u><em>Let </em></u><u><em> = mean contents of cola bottles.</em></u>
SO, Null Hypothesis, :
300 ml {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}
Alternate Hypothesis, :
< 300 ml {means that the mean contents of cola bottles is less than the advertised 300 ml}
The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean contents of cola bottle =
= 299.03 ml
= population standard deviation = 3 ml
n = sample of bottles = 6
So, <em><u>test statistics</u></em> =
= -0.792
<em>Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>
Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.