The equation of a line that passes through (x1,y1) and has a slope of m is
y-y1=m(x-x1)
find slope
slope between (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
given
(-3,2) and (2,1)
slope=(1-2)/(2-(-3))=(-1)/(2+5)=-1/5
pikc a point
if we pick (-3,2)
(x1,y1)
x1=-3
y1=2
y-2=-1/5(x-(-3))
y-2=-1/5(x+3)
that is D
To solve this problem, let us first assign some
variables. Let us say that:
x = pigs
y = chickens
z = ducks
From the problem statement, we can formulate the
following equations:
1. y + z = 30 --->
only chicken and ducks have feathers
2. 4 x + 2 y + 2 z = 120 --->
pig has 4 feet, while chicken and duck has 2 each
3. 2 x + 2 y + 2 z = 90 --->
each animal has 2 eyes only
Rewriting equation 1 in terms of y:
y = 30 – z
Plugging this in equation 2:
4 x + 2 (30 – z) + 2 z = 120
4 x + 60 – 2z + 2z = 120
4 x = 120 – 60
4 x = 60
x = 15
From the given choices, only one choice has 15 pigs. Therefore
the answers are:
She has 15 pigs, 12 chickens, and 18 ducks.
Answer:
8 and 19
Step-by-step explanation:
To some this, let's first list all the factors of 152. They are;
1, 2, 4, 8, 19, 38, 76, 152.
Now, let's arrange them to reflect being multiplied to get 152.
Thus;
1 × 152 = 152
2 × 76 = 152
4 × 38 = 152
8 × 19 = 152
Also, let's do the same for their sum;
1 + 152 = 153
2 + 76 = 78
4 + 38 = 42
8 + 19 = 27
Looking at the figures above, the ones that their product is 152 but have the least sum are 8 and 19
Answer:
And on this case if we see the significance level given 
we see that 
so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.
Step-by-step explanation:
A chi-square goodness of fit test determines if a sample data obtained fit to a specified population.
represent the p value for the test
O= obserbed values
E= expected values
The system of hypothesis for this case are:
Null hypothesis: ![O_i = E_i[/tex[Alternative hypothesis: [tex]O_i \neq E_i](https://tex.z-dn.net/?f=O_i%20%3D%20E_i%5B%2Ftex%5B%3C%2Fp%3E%3Cp%3EAlternative%20hypothesis%3A%20%5Btex%5DO_i%20%5Cneq%20E_i%20)
The statistic to check the hypothesis is given by:
On this case after calculate the statistic they got: 
And in order to calculate the p value we need to find first the degrees of freedom given by:
, where k represent the number of levels (on this cas we have 10 categories)
And in order to calculate the p value we need to calculate the following probability:
And on this case if we see the significance level given we see that so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.
