Answer: x=9
Step-by-step explanation:
7x=2x+45
5x=45
x=9
Answer:
12.6
Step-by-step explanation:
The two left sides have lengths, so this allows you to establish the ratio of the lengths of the sides of the triangles,
left triangle : right triangle
ratio = 25 : 17.5
The bottom sides are also in the same ratio.
ratio = 18 : w
Write a proportion by setting the ratios equal and solve for w.
25/17.5 = 18/w
Cross multiply.
25w = 17.5 * 18
25w = 315
w = 12.6
Answer: 12.6
Answer:
Hypothenus = 22
Step-by-step explanation:
From the question given above, we were told that the triangles are congruent (i.e same size). Thus,
AC = EF
BC = DE
To obtain the length of each Hypothenus, we shall determine the value of y and x. This can be obtained as follow:
For y:
AC = y + 3
EF = 2y + 1
AC = EF
y + 3 = 2y + 1
Collect like terms
3 – 1 = 2y – y
2 = y
y = 2
For x:
BC = 5x + 7
DE = 6x + 2y
y = 2
DE = 6x + 2(2)
DE = 6x + 4
BC = DE
5x + 7 = 6x + 4
Collect like terms
7 – 4 = 6x – 5x
3 = x
x = 3
Finally, we shall determine the length of each Hypothenus. This can be obtained as follow:
Hypothenus = BC
Hypothenus = 5x + 7
x = 3
Hypothenus = 5x + 7
Hypothenus = 5(3) + 7
Hypothenus = 15 + 7
Hypothenus = 22
OR
Hypothenus = DE
DE = 6x + 2y
y = 2
x = 3
Hypothenus = 6(3) + 2(2)
Hypothenus = 18 + 4
Hypothenus = 22
Answer:
9.18% probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What is the probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated?
This is 1 subtracted by the pvalue of Z when X = 16. So
has a pvalue of 0.9082
1 - 0.9082 = 0.0918
9.18% probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated
The mean is calculated by adding up all of the given numbers and dividing by the number of numbers.
Lets, for ease of understanding, say that the first three number were 64...
Mean=(64+64+64)/3=192/3=64
Now, lets solve for the mean where 'x' is the unknown fourth number and 128 is the mean. (since, the answer said that when the fourth number was added the mean, 64, was doubled '64*2=128')
128=(64+64+64+x)/4
128=(192+x)/4
Multiply both sides by 4
512=192+x
subtract 192 from both sides
320=x
The missing number is 320..
Now lets double check our work.
Mean=(64+64+64+320)/4=512/4=128
Answer=320
