Estimate the average rate of change from x=2 to x=5

If Rachel were to paint her living room alone, it would take 2 hours. Her sister Fran could do the job in 5 hours. How many hour

snow_tiger [21]

Rachel and her sister Fran together can paint the living room in $\frac{10}{7}$ hours

Given that

Rachel can paint half of the living room in 1 hour

Fran can paint $\frac{1}{5}$ th part of the living room in 1 hour

Let's assume together they paint the living room in x hours

⇒ together they can paint $\frac{1}{x}$ th part of the living room in 1 hour

By proportions,

⇒ $\frac{1}{2}$ + $\frac{1}{5}$ = $\frac{1}{x}$ {using operation proportions and addition}

⇒ $\frac{7}{10}$ = $\frac{1}{x}$

⇒x= $\frac{10}{7}$

⇒ together they can paint $\frac{7}{10}$ th part of the living room in 1 hour

It means, Rachel and her sister Fran together can paint the living room in $\frac{10}{7}$ hours

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6 0

2 years ago

5. A survey of student pizza preferences showed that 43 students preferred cheese, 56 preferred sausage, 39 preferred pepperoni,

cestrela7 [59]

Answer:

P (Cheese) = 0.199, P (Sausage) = 0.259, P (Pepperoni) = 0.181,

P (Supreme) = 0.130, P (Another Kind) = 0.144

and P (Does not like any kind) = 0.088

Step-by-step explanation:

Given:

Number of students who prefer cheese = 43

Number of students who prefer sausage = 56

Number of students who prefer pepperoni = 39

Number of students who prefer supreme = 28

Number of students who prefer another kind = 31

Number of students who did not like any kind = 19

∴ The total number of students surveyed = $43+56+39+28+31+19=216$ The number of students who prefer pizza = $43+56+39+28+31=197$

The probability that a students likes pizza is,

$P(Student\ likes\ pizza)=\frac{No.\ of\ students\ who\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}$

$=\frac{197}{216} \\=0.912$

The probability that a students does not likes pizza is,

$P(Student\ does\ not\ likes\ pizza)=\frac{No.\ of\ students\ who\ does\ not\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}$

$=\frac{19}{216} \\=0.088$

The probability distribution of students who prefer different kinds of pizza is:

The probability that a student likes cheese:

$P(A\ Student\ prefers\ cheese)=\frac{No.\ of\ students\ who\ prefer\ cheese}{Total\ no.\ of\ students\ surveyed}$

$=\frac{43}{216}\\=0.199$

The probability that a student likes sausage:

$P(A\ Student\ prefers\ sausage)=\frac{No.\ of\ students\ who\ prefer\ sausage}{Total\ no.\ of\ students\ surveyed}$

$=\frac{56}{216}\\=0.259$

The probability that a student likes pepperoni:

$P(A\ Student\ prefers\ pepperoni)=\frac{No.\ of\ students\ who\ prefer\ pepperoni}{Total\ no.\ of\ students\ surveyed}$

$=\frac{39}{216}\\=0.181$

The probability that a student likes supreme:

$P(A\ Student\ prefers\ supreme)=\frac{No.\ of\ students\ who\ prefer\ supreme}{Total\ no.\ of\ students\ surveyed}$

$=\frac{28}{216}\\=0.130$

The probability that a student likes another kind:

$P(A\ Student\ prefers\ another\ kind)=\frac{No.\ of\ students\ who\ prefer\ another\ kind}{Total\ no.\ of\ students\ surveyed}$

$=\frac{31}{216}\\=0.144$

Thus, the probability distribution table is displayed below:

6 0

3 years ago

Find the length of a side of a square if its area is m^2 square units

zimovet [89]

Answer:

m

Step-by-step explanation:

Square area: m²

The formula for finding the square area: m×m=m²

m²=√(m²)=m

one side of the square is equal to m

4 0

3 years ago

Marian went shopping and bought clothes for $66.17 and books for $44.98. She then had a meal at the mall for $20.15. Which is th

scZoUnD [109]

Answer:

Either 130 or 131 would be acceptable.

Step-by-step explanation:

When we estimate, we do not use exact values.

66.17 is close to 66

44.98 is close to 45

20.15 is close to 20

Add the estimates together: 66+ 45+ 20 = 131

We could also estimate 66.17 to 65 which would give us an estimate of 130

6 0

3 years ago

Read 2 more answers

HELP HELP PLEASE the height of the triangle is 16 cm, and fe=10 cm. What is the area of the triangle? A. 50 CM^2 B. 80 CM^2 C.16

enyata [817]

Answer:

B. 80 cm^2

Step-by-step explanation:

A = bh/2

A = (FE)(16 cm)/2

A = (10 cm)(16 cm)/2

A = 80 cm^2

4 0

3 years ago