Answer:
$55.24
Step-by-step explanation:
Add $32.78 + $27.24 + $5.22
= 65.24
Subtract 10
= $55.24
Answer:
The scale factor of a dilation from ABCD to RSTU is 
Step-by-step explanation:
We know that the rectangle ABCD is similar to rectangle RSTU.
Given that in rectangle ABCD the longest sides are DC and AB and in the rectangle RSTU the longest sides are UT and RS ⇒ The scale factor of a dilation will transform the sides DC and AB into UT and RS
Working with the lengths of the sides :
DC.(Scale factor) = UT
AB.(Scale factor) = RS
Replacing with the values of the lengths (Scale factor : SF) :


Notice that the scale factor is dimensionless.
We can verify this result with the sides AD and BC :


The scale factor (SF) is 
Answer:
The value of y that would make O P parallel to L N = 36
Step-by-step explanation:
This is a question on similar triangles. Find attached the diagram obtained from the given information.
Given:
The length of O L = 14
the length of O M = 28
the length of M P = y
the length of P N = 18
Length MN = MP + PN = y + 18
Length ML = MO + OL = 28+14 = 42
For OP to be parallel to LN,
MO/ML = MP/PN
MO/ML = 28/42
MP/PN= y/(y+18)
28/42 = y/(y+18)
42y = 28(y+18)
42y = 28y + 18(28)
42y-28y = 504
14y = 504
y = 504/14 = 36
The value of y that would make O P parallel to L N = 36
Answer:
Yes, hypertension drugs lowers blood pressure.
Step-by-step explanation:
Claim: The hypertension medicine lowered blood pressure.
The null and alternative hypothesis is
H0:\mu_{d}\geq 0
H1:\mu_{d}< 0
Level of significance = 0.05
Sample size = n = 13
Sample mean of difference = \bar{d} = 10.1
Sample standard deviation of difference = s_{d} = 11.2
Test statistic is
t=\frac{\bar{d}}{s_{d}/\sqrt{n}}
t = ((10.1) / (11.2 /squre root of 13)) = 3.251
Degrees of freedom = n - 1 = 13 - 1 = 12
Critical value =2.179( Using t table)
Test statistic | t | > critical value we reject null hypothesis.
In Conclusion: The hypertension medicine lowered blood pressure
Answer:
a) 0.35
b) 420 drawing pins
Step-by-step explanation:
a) The question relates to the relative frequency of the pins pointing up which is found by the formula as follows;

The total number of pins land 'point up' = 3 + 5 + 6 + 2 + 4 + 7 + 3 + 3 + 4 + 5
The total number of pins land 'point up' = 42 successful trials
Total number of trials = 12 × 10 = 120 trials

Due to the large number of trials, the relative frequency ≈ Probability and the probability that a single pin will land point up = 7/20 = 0.35
b) Given that the number of trials now = 12 × 100 = 1200, we have;
The expected number of drawing pins in total that would land point up = 0.35×1200 = 420 pins.