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Dimas [21]
3 years ago
8

Marta can vacuum the house in 30 min. It takes her daughter 45 min to vacuum the house. How long would it take them if they

Mathematics
1 answer:
Mamont248 [21]3 years ago
8 0

Answer:

<h2>18mins</h2>

Step-by-step explanation:

This problem is on combined work rate

given that

Marta can vacuum the house in 30 min

then her rate= 1/30

Also, her daughter will take 45 min to vacuum the house

her  daughter's rate will be = 1/45

then the combined work rate is

1/30+1/45=1/T

30+45/30*45=1/T

75/1350= 1/T

1/18=1/T

This means that they will both take 18 minutes working together to vacum a house

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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
3 years ago
For each system of equations, drag the true statement about its solution set to the box under the system?
natta225 [31]

Answer:

y = 4x + 2

y = 2(2x - 1)

Zero solutions.

4x + 2 can never be equal to 4x - 2

y = 3x - 4

y = 2x + 2

One solution

3x - 4 = 2x + 2 has one solution

Step-by-step explanation:

* Lets explain how to solve the problem

- The system of equation has zero number of solution if the coefficients

 of x and y are the same and the numerical terms are different

- The system of equation has infinity many solutions if the

   coefficients of x and y are the same and the numerical terms

   are the same

- The system of equation has one solution if at least one of the

  coefficient of x and y are different

* Lets solve the problem

∵ y = 4x + 2 ⇒ (1)

∵ y = 2(2x - 1) ⇒ (2)

- Lets simplify equation (2) by multiplying the bracket by 2

∴ y = 4x - 2

- The two equations have same coefficient of y and x and different

  numerical terms

∴ They have zero equation

y = 4x + 2

y = 2(2x - 1)

Zero solutions.

4x + 2 can never be equal to 4x - 2

∵ y = 3x - 4 ⇒ (1)

∵ y = 2x + 2 ⇒ (2)

- The coefficients of x and y are different, then there is one solution

- Equate equations (1) and (2)

∴ 3x - 4 = 2x + 2

- Subtract 2x from both sides

∴ x - 4 = 2

- Add 4 to both sides

∴ x = 6

- Substitute the value of x in equation (1) or (2) to find y

∴ y = 2(6) + 2

∴ y = 12 + 2 = 14

∴ y = 14

∴ The solution is (6 , 14)

y = 3x - 4

y = 2x + 2

One solution

3x - 4 = 2x + 2 has one solution

3 0
3 years ago
I need help ASAP people
nirvana33 [79]

Answer:

point D: (2, -4)

Step-by-step explanation:

5 0
3 years ago
Harry fills up his Jeep with gasoline and notes that the odometer reading is miles. The next time he fills up his Jeep, he pays
lukranit [14]

Complete question :

Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,568.7 miles. The next time he fills up his Jeep, he pays for 12.6 gallons of gasoline. He notes his odometer reading is 23,706.3 miles. How many miles per gallon did he get?

Answer:

10.9 miles per gallon

Step-by-step explanation:

Given that :

Odometer reading when filled up with gasoline = 23,568.7 miles

Odometer reading with 12.6 gallons of gasoline = 23,706.3 miles

Miles per gallon gotten :

(Current Odometer reading - reading when filled up) / gallon of gasoline

(23706.3 - 23568.7) / 12.6

= 10.920634

= 10.9 miles per gallon

6 0
2 years ago
A building is 2 ft from a 12 ft fence that surrounds the property. A worker wants to wash a window in the building 17 ft from th
Marta_Voda [28]
17^2+10^2=x^2
x=19.7
2+8=10

3 0
3 years ago
Read 2 more answers
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