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3 years ago

Find the value of x. Part 1c

Mathematics

2 answers:

aniked [119]3 years ago

6 0

Answer: x = 11

<u>Step-by-step explanation:</u>

a) bottom triangle, bottom right angle: Using Linear Pair Postulate, 180° - 114° = 66°

b) bottom triangle, top angle: Congruent sides implies congruent angles = 66°

c) bottom triangle, bottom left angle: Using the Triangle Sum Theorem, 66° + 66° + y = 180° --> y = 48°

d) top triangle, bottom angle: Using Complimentary Angles Theorem, 90° - 48° = 42°

Congruent sides implies congruent angles:

42° = ∠2

42 = 2x + 20

22 = 2x

11 = x

gtnhenbr [62]3 years ago

4 0

Answer:

x=11

Step-by-step explanation:

Please see attached image.

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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

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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

A first alloy contains x pounds of 55% silver. It is mixed with a second alloy containing 30% silver to make 60 pounds of an all

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Answer:

"24 pounds" is the appropriate answer.

Step-by-step explanation:

According to the question, the equation will be:

⇒ $x+y=60$ ...(equation 1)

or,

⇒ $\frac{55}{100}x+\frac{30}{100}y=\frac{40}{100}\times 60$

$55x+30y=2400$ ...(equation 2)

Now,

By multiplying (equation 1) by 55 and (equation 2) by 1, we get

⇒ $55x+55y=3300$ ...(equation 3)

⇒ $55x+30y=2400$ ...(equation 4)

From equation 3 and 4, we get

⇒ $25y=900$

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By putting the values of "y" in equation 1, we get

⇒ $x=60-36$

$=24$

Thus the value of x be "24 pounds".

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2 years ago

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2 years ago

Find the value of x. Part 1c​

Find the value of x. Part 1c