Answer:
9cm
Step-by-step explanation:
- Since PQST is a rectangle, ∠QST=∠QSR=∠90º. So triangle QSR is a right triangle.
- By the Pythagorean Theorem and that SR=6 and QR=10, we can say that 6^2+b^2=10^2. So, 36+b^2=100. And b^2=64 and b=8. So QS=8.
- Now we know that QS=PT=8.
- By the Pythagorean Theorem and that PR=17 and PT=8, we can say a^2+8^2=17^2. So, a^2+64=289. And a^2=225 and a=15.
- We know that TR=15 and SR=6 and TR-SR=TS, so 15-6=9.
Answer:
μ = 5.068 oz
Step-by-step explanation:
Normal distribution formula to use the table attached
Z = (x - μ)/σ
where μ is mean, σ is standard deviation, Z is on x-axis and x is a desired point.
98% of 6-oz. cups will not overflow means that the area below the curve is equal to 0.49; note that the curve is symmetrical respect zero, so, 98% of the cases relied between the interval (μ - some value) and (μ + some value)].
From table attached, area = 0.49 when Z = 2.33. From data, σ = 0.4 oz and x = 6 oz (maximum capacity of the cup). Isolating x from the formula gives
Z = (x - μ)/σ
2.33 = (6 - μ)/0.4
μ = 6 - 2.33*0.4
μ = 5.068
This means that with a mean of 5 oz and a standard deviation of 0.4 oz, the machine will discharge a maximum of 6 oz in the 98% of the cases.
6,2,8,4,and 0 are the only possible value of the ones digit, because
6*1=6, last digit is 6
6*2=12, last digit is 2
6*3=18, last digit is 8
6*4=24, last digit is 4
6*5=30, last digit is 0
6*6=36, last digit is 6
and the whole cycle goes over again.
Answer:
x=-3, y=-19
Step-by-step explanation:
we can solve by substitution.
y = 2x-1 we can derive from the second equation.
plugging it into the first equation, 2x -3(2x-1) = 15.
simplying, 2x-6x+3 = 15 --> -4x+3 = 15, -4x = 12, x = -3.
now we know x, so we can solve for y by plugging it into one of the equations. --> -3*-6+y = -1
simplify, 18+y = -1 --> y = -19.
