5 beads are used for every 3 inches, that makes 5/3 beads per inch.
Thus that can be modeled by the graph y=x*5/3 where x is the number of inches and y is the number of beads.
Answer:
There is sufficient statistical evidence to state that the average hours of productive work, after announcing the stimulus, has increased significantly
Step-by-step explanation:
To solve this problem, we run a hypothesis test about the difference between population means with dependent samples. Consider the differences in average hours of productive work after the stimulus minus average hours of productive work before the stimulus.
Difference in the null hypothesis (Do) = 0
Sample size (n) = 10
Mean of the sample differences (DM) = 0.19
Standard deviation of the sample differences (SM) = 0.1729
Significance level = 0.01
H0: Do = 0
Ha: Do> = 0
Test statistic =
Right critical T value (for 0.01) = 2.8214
Calculated statistic =
p-value = 0.00350
Since, the value of the test statistic is greater than the value of the calculated statistic, the null hypothesis is rejected. There is sufficient statistical evidence to state that the average hours of productive work, after announcing the stimulus, has increased significantly. The p - value is 0.00350.
If B is the midpoint of ZA, then ZB = <span>BA
</span>3x-5 = <span>x+3
3x - x = 3 + 5
2x = 8
x = 8/2
x = 4
</span>ZA = ZB + BA
= 3x-5 + x+3
= 3*4 - 5 + 4 + 3
= 12 - 5 + 7
= 14
Answer: <span>D. 14</span>
Hi there! I can help you with this! First, let's combine like terms and do everything for the right side of the problem. When you do the distributive property, you get 32x - 40. Combine like terms and you'll get 32x - 60. Now, the inequality is 20x = 32x - 60. First, let's subtract 32x from both sides to get the integer by itself. When you do that, you get -12x = -60. Now, divide each side by -12 to isolate the "x". -60/-12 is 5. Let's plug it in. 20 * 5 is 100. 32 * 5 is 160. 160 - 60 is 100. 100 = 100. There. x = 5.
The angular resolution of telescope is roughly given by formula:
Where:
λ = wevelength of light
D = diameter of a telescope
First step in solving this question is to convert diameter given in inches into meters:
Telescope A:
6 * 0.0254 = 0.1524m
Telescope B:
10 * 0.0254 = 0.254m
Wavelength of visible light varies from 390nm to 700nm. We will take 500nm as a number for our calculation.
Telescope A:
Telescope B:
The results are given in radians. We need to transform this into degrees.
Telescope A:
Telescope B:
To find out which telescope can distinguish two stars we must convert given angle.
0.7'' is 0.7 arc seconds or 0.7 / 60 / 60 =0.0001944444444444 degrees
Telescope that has angles smaller than this can distinguish. In our case both telescopes have smaller angle and both can distinguish.