Answer:
a. The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).
Step-by-step explanation:
The second equation needs to be ...
5x +5y = 50
because the wording "short of $18" means that the actual cost of that purchase would be $18 more than the $32 that Harry had. 18+32 = 50.
The only answer choice that shows this as the second equation is choice A.
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In fact, the solution to the system of equations is (8, 2), as can be seen in the graph below.
Y = x + 1.75...so we sub in x + 1.75 for y in the other equation
4x - 2y = 4
4x - 2(x + 1.75) = 4....distribute thru the parenthesis
4x - 2x - 3.5 = 4....add 3.5 to both sides
4x - 2x = 4 + 3.5...simplify
2x = 7.5....divide both sides by 2
x = 7.5 / 2
x = 3.75
now we sub in 3.75 for x in either of the original equations to find y.
y = x + 1.75
y = 3.75 + 1.75
y = 5.5
so ur solution is : (3.75,5.5) <==
3(j+4)-9=9
3j + 12 -9 =9
3j +3 =9
3j =6
j=2
Answer:
a) 0.145
b) 0.013
c) 0.783
d) 0.586
Step-by-step explanation:
a) there are always 52 cards in total, 13 hearts
Pa = 39/52 × 38/51 × 13/50 = 19266/132600 = 257/1700 =0.145
b) there are always 13 diamonds in a complete card
Pb = 13/52 × 12/51× 11/50 = 11/850 = 0.013
c) there are always 4 aces, and 48 that are not aces
Pc = 48/52 × 47/51 × 46/50 = 4324/5525 = 0.783
d) there are 13 hearts,to get at least one heart we have.
Pd = 1 - p
Where p is the probability of no hearts
p = 39/52 × 38/51 × 37/50 = 703/1700 = 0.414
Pd = 1 - 0.414
Pd = 0.586
Answer:
There is sufficient evidence to support the claim that the new balls have bounce heights with a mean different from 92.8292.82 inches, and it appears that the new baseballs are different
Step-by-step explanation:
Given that in previous tests, baseballs were dropped 24 feet onto a concrete surface, and they bounced an average of 92.82 inches
But new balls showed mean of 92.6 inches with s = 1.72 inches
Sample size = 23
Since sample size is less than 30 and population std deviation is not know we use t test
(Two tailed test at 5% significance level)
Mean difference = 
Std error of sample mean = s/sqrt n = 
Test statistic t = mean diff/std error = -3.402
df = 23-1 =22
p value = 0.002559
since p value <5% we reject H0
There is sufficient evidence to support the claim that the new balls have bounce heights with a mean different from 92.8292.82 inches, and it appears that the new baseballs are different
