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Mnenie [13.5K]
3 years ago
9

What is the equation of a line that passing through points (-2, 5) and (3, 25)

Mathematics
1 answer:
Llana [10]3 years ago
5 0
\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad 
(\stackrel{x_2}{3}~,~\stackrel{y_2}{25})
\\\\\\
% slope  = m
slope =  m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{25-5}{3-(-2)}\implies \cfrac{25-5}{3+2}
\\\\\\
\cfrac{20}{5}\implies 4
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=4[x-(-2)]
\\\\\\
y-5=4(x+2)\implies y-5=4x+8\implies y=4x+13
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An article reports the following data on yield (y), mean temperature over the period between date of coming into hops and date o
skelet666 [1.2K]

Answer:

x1=c(16.7,17.4,18.4,16.8,18.9,17.1,17.3,18.2,21.3,21.2,20.7,18.5)

x2=c(30,42,47,47,43,41,48,44,43,50,56,60)

y=c(210,110,103,103,91,76,73,70,68,53,45,31)

mod=lm(y~x1+x2)

summary(mod)

R output: Call:

lm(formula = y ~ x1 + x2)

Residuals:  

   Min      1Q Median      3Q     Max

-41.730 -12.174   0.791 12.374 40.093

Coefficients:

        Estimate Std. Error t value Pr(>|t|)    

(Intercept) 415.113     82.517   5.031 0.000709 ***  

x1            -6.593      4.859 -1.357 0.207913    

x2            -4.504      1.071 -4.204 0.002292 **  

---  

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  

Residual standard error: 24.45 on 9 degrees of freedom  

Multiple R-squared: 0.768,     Adjusted R-squared: 0.7164  

F-statistic: 14.9 on 2 and 9 DF, p-value: 0.001395

a).  y=415.113 +(-6.593)x1 +(-4.504)x2

b). s=24.45

c).  y =415.113 +(-6.593)*21.3 +(-4.504)*43 =81.0101

residual =68-81.0101 = -13.0101

d). F=14.9

P=0.0014

There is convincing evidence at least one of the explanatory variables is significant predictor of the response.

e).  newdata=data.frame(x1=21.3, x2=43)

# confidence interval

predict(mod, newdata, interval="confidence")

#prediction interval

predict(mod, newdata, interval="predict")

confidence interval

> predict(mod, newdata, interval="confidence",level=.95)

      fit      lwr      upr

1 81.03364 43.52379 118.5435

95% CI = (43.52, 118.54)

f).  #prediction interval

> predict(mod, newdata, interval="predict",level=.95)

      fit      lwr      upr

1 81.03364 14.19586 147.8714

95% PI=(14.20, 147.87)

g).  No, there is not evidence this factor is significant. It should be dropped from the model.

4 0
2 years ago
The value of a semi-trailer when new is $625 000. The value of the semi-trailer depreciates by
Nina [5.8K]

Answer:

$546,875

Step-by-step explanation:

if the trailer brand new costs $625,000 and decreases by 12.5% you want to find 10% which is $62,500. then you want to find 5% which would be $31,250. but you want 2.5% so you need to divide $31,250 by 2 which is $15,625. add $62,500 and $15,625 together which is $78,125. then do $625,000-$78,625 which gets you $546,875.

4 0
3 years ago
Need help solving this problem
Molodets [167]

Answer:

Step-by-step explanation:

q is TFTF

~q use negation, not q so is the opposite of q : FTFT

p↔~q use biconditional ,and will be True only is both statements are T or both are F

p values are TTFF ↔~q values are FTFT : FTTF

(p↔~q )∧~q use conjunction, that is True only if both statements are T

(p↔~q ) values are FTTF ∧~q values are  FTFT : FTFF

(p↔~q )∧~q → p use a conditional statement, where only True False will give a F

(p↔~q )∧~q values are FTFF → p values are TTFF : TTTT

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2 years ago
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Sophie [7]
2 3/5= 13/5
(13/5)/(1/5)=(13/5)5=13
answer: A maximum of 13 tomato plants :)
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3 years ago
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Divide total pain by number of books.

296/8 = 37

He paid $37 per book

4 0
2 years ago
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