Answer:
16 =2^4
Step-by-step explanation:
16
16 = 4*4
but 4 is not prime
4 = 2*2
16 = 2*2*2*2
Rewriting with exponents
16 =2^4
Answer:
→ Prime factorization of 16 :
Answer:
when a number is divisible by 9, then the number is divisible by 3.
Step-by-step explanation:
They tell us "When a number is divisible by 9, the number is divisible by 3" we could change it by:
when a number is divisible by 9, then the number is divisible by 3.
Which makes sense because the number 9 is a multiple of the number 3, which means that the 9 can be divided by 3, therefore, if the number can be divided by 9, in the same way it can be divided by 3 .
The statement "When a number is divisible by 9, the number is divisible by 3" can be rewritten in if-then form as: If a number is divisible by 9, then the number is divisible by 3.
In this case, the conclusion is that the number is divisible by 3.
Here is a table that summarizes the if-then form of the statement:
| Hypothesis | Conclusion |
|---|---|---|
| A number is divisible by 9 | The number is divisible by 3 |
In other words, if the hypothesis is true (i.e., the number is divisible by 9), then the conclusion must also be true (i.e., the number is divisible by 3).
Here is an example:
Hypothesis: The number 18 is divisible by 9.
Conclusion: The number 18 is divisible by 3.
Both the hypothesis and the conclusion are true, so the if-then statement is true.
For such more question on divisible
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Plz help me
Answer:
its most likey 4 the answer is 4
Answer:
the y intercept is -4 and the slope is 1
Step-by-step explanation:
-x + 4y = 13
solve by elimination
Answer:
i think x=-1 and y=3. ....
Answer:
x = -1 , y = 3
Step-by-step explanation:
2x+5y = 13
-x+4y = 13
Decide whether to add or subtract the two equations by using Different Add Same Subtract (DASS) or in case below as its SUBTRACT
i apply (SDSS).
We subtract 5y as this is easier equation either positive prioritises or if both positive then easier number becomes priory.
Results to SDSS before substituting Y if 5y etc was subtracted
2x+5y = 13 Subtract -5
2x+5y -5y = 13 -5y
2x= 13 - 5y then Divide by 2
2x / 2 = 13/2 - 5y/2 Show then
x = 13 - 5y / 2 + 4y = 13 Simplify
simplify 13 - 13y / 2 as y = 3
as 13/2 = 6.5 and 2.5 +4 = 6.5
y = 3
Substitute y = 3
13-5y )3) / 2
13-5 (3) / 2
BODMAS Brackets first Multiplying only for y substitute 5y = 5 x 3
-5 (3) = 15
13-15 = -2
-2/2 = -1
x = -1
a. If the sample variance is s^2=32 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha=.05
b. If the sample variance is s^2=72 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha=.05 ?
c. Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?
A hypothesis test was conducted to evaluate the treatment's effect. For both variances, we failed to reject the null hypothesis, so we can't conclude that the treatment had a significant effect. The variability of scores plays a crucial role, as more variability makes it harder to identify a significant effect.
To determine if the treatment has a significant effect, we perform a hypothesis test using the sample mean (M), sample variance (s^2), and population mean (μ). The null hypothesis is that there's no effect from the treatment (μ=M), while the alternative hypothesis is that there is an effect (μ≠M).
a. For sample variance s^2=32, we can use the formula for the t score: t = (M - μ)/(s/√n) = (35 - 40)/(√32/√8) = -2.24. Based on a two-tailed t-distribution table, the critical t values for α=.05 and 7 degrees of freedom (n-1) are approximately -2.365 and 2.365. Our t value (-2.24) lies within this range, so we fail to reject the null hypothesis. We cannot conclude that the treatment has a significant effect.
b. Repeat the same process with sample variance s^2=72. The t value is now (35 - 40)/(√72/√8) = -1.48, again falling within the range of the critical t values. We can't conclude that the treatment has a significant effect.
c. As the variability (s^2) of the sample scores increases, it becomes more difficult to find a significant effect. Higher variability introduces more uncertainty, which can mask actual changes caused by the treatment.
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To evaluate the effect of a treatment using a two-tailed test with alpha = 0.05, we compare the calculated t-value to the critical t-value. The sample variance influences the outcome of the hypothesis test, with a larger variance leading to a wider critical region.
a. To test if the treatment has a significant effect, we will conduct a two-tailed hypothesis test using the t-distribution. The null hypothesis states that the treatment has no effect (μ = 40), while the alternative hypothesis states that the treatment has an effect (μ ≠ 40). With a sample size of 8, degrees of freedom (df) will be n-1 = 7. We will use the t-test formula to calculate the t-value, and compare it to the critical t-value from the t-table with α = 0.05/2 = 0.025. If the calculated t-value falls outside the critical region, we reject the null hypothesis and conclude that the treatment has a significant effect.
b. Similar to part a, we will conduct a two-tailed t-test using the same null and alternative hypotheses. With a sample size of 8, df = n-1 = 7. We will calculate the t-value using the sample mean, population mean, and sample variance. Comparing the calculated t-value to the critical t-value with α = 0.05/2 = 0.025, if the calculated t-value falls outside the critical region, we reject the null hypothesis and conclude that the treatment has a significant effect.
c. The variability of the scores in the sample, as indicated by the sample variance, influences the outcome of the hypothesis test. In both parts a and b, the sample variance is given. A larger sample variance (s^2 = 72 in part b) indicates more variability in the data, meaning the scores in the sample are more spread out. This leads to a larger t-value and a wider critical region. Therefore, it becomes easier to reject the null hypothesis and conclude that the treatment has a significant effect.
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Answer:
SU = 32 and <SVT = 32
Step-by-step explanation:
math, i am pretty sure about the angle and positive on the diagonal