A scout troop 32 markers along a hiking trail. Each Microway is 9 ounces. On the scale to begin the hike, they put the markers in the backpack. If the empty backpack weighed 3 pounds, how much did the backpack weigh with all the markers in it?

uppose a small cannonball weighing 16 pounds is shot vertically upward, with an initial velocity v0 = 290 ft/s. The answer to the question "How high does the cannonball go?" depends on whether we take air resistance into account. If air resistance is ignored and the positive direction is upward, then a model for the state of the cannonball is given by d2s/dt2 = −g (equation (12) of Section 1.3). Since ds/dt = v(t) the last differential equation is the same as dv/dt = −g, where we take g = 32 ft/s2. If air resistance is incorporated into the model, it stands to reason that the maximum height attained by the cannonball must be less than if air resistance is ignored. (a) Assume air resistance is proportional to instantaneous velocity. If the positive direction is upward, a model for the state of the cannonball is given by m dv dt = −mg − kv, where m is the mass of the cannonball and k > 0 is a constant of proportionality. Suppose k = 0.0025 and find the velocity v(t) of the cannonball at time t.

I need help with this math problem please (3x+2)(5x-7)

Find the critical points, domain endpoints, and local extreme values for the functiony=x^2/5(x+3)

a. What is/are the critical point(s) and domain endpoint(s) where f' is undefined?
b. What is/are the critical point(s) and domain endpoint(s) where f' is 0?
c. From the critical point(s) and domain endpoint(s), what is/are the points corresponding to local maxima?
d. From the critical point(s) and domain endpoint(s), what is/are the points corresponding to local minima?

PLEASE HELP ME WITH THIS ALGEBRA QUESTION!! THANK YOU!!

Four less than a number is at least negative six.A
x−4≤−6


B
x−4≥−6


C
6x−4>−6


D

x−4<−6
HELPPPPPPP



100!!!! POINTS

Right or leftMost people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13–70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​




The symbol π represents the long-run proportion of all the couples that lean their heads
leftright

while kissing.



Which of the following best describes the null hypothesis and the alternative hypothesis using π?



null: π ≠ 0.5, alternative: π > 0.5
null: π = 0.5, alternative: π < 0.5
null: π = 0.5, alternative: π > 0.5
null: π ≠ 0.5, alternative: π < 0.5



Of the 124 kissing couples, 80 were observed to lean their heads right. What is the observed proportion of kissing couples who leaned their heads to the right? What symbol should you use to represent this value? (Round answer to 3 decimal places, e.g. 5.275)
p^=

the absolute tolerance is +/-0.001




Determine the standardized statistic from the data. ​(Hint: You will need to get the standard deviation of the simulated statistics from the null distribution.) (Round answer to 2 decimal places, e.g. 52.75)
z =

the absolute tolerance is +/-0.02




Interpret the meaning of the standardized statistic.



The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50.
The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations away from the null hypothesized value of 0.50.
The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations below the null hypothesized value of 0.50.



Select the best conclusion that you would draw about the null and alternate hypotheses.



We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is less than 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is near to 50%.