Point b lies on the segment ac . find the length of the segment ac, if ab=7.8 cm, bc=25mm. how many different solutions can this problem have? what if we said that point b lies on the line defined by points a and c?

The segment AC can have ONE solution in both cases. The solution can either be 103mmn or 10.3cm for (a) and 5.3cm in (b)

If point B lies on the segment AC, then:

AB + BC = AC

Given the following segments

AB = 7.8cm  = 78mm

BC = 25mm

AC = 78mm + 25mm

AC = 103mm

Converting to cm

10mm = 1cm

103mm = AC

10AC = 103

AC = 103/10

AC = 10.3cm

This shows that AC can have just ONE solution but different units

b) If B is not on the line BC, tyhe  the measure of AC will be expressed as:

AC = AB - BC

AC = 7.8cm - 2.5cm (Note that 25mm = 2.5cm)

AC = 5.3cm

This shows that AC can have just ONE solution but different units in both cases

Learn more here: link

a) If B is between A and C, there can only be one solution:

... AC = AB + BC = 7.8 cm + 2.5 cm

... AC = 10.3 cm

b) If B is not on the segment AC, there can only be one solution: C must lie on AB. Then ...

... AC = 7.8 cm - 2.5 cm

... AC = 5.3 cm

This, together with the solution of Part (a) means there are two solutions.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

doubled

step-by-step explanation: