Name the property of real numbers illustrated by the equation.

4. If A = 45° and B = 30°, verify the following<br> (a) sin (A - B) = sinA.cosB - COSA, sinB.

noname [10]

Uhh enuhlish okkk hehehehe

7 0

3 years ago

A bus leaves Los Angeles at 8am moving northeast at 60 mph. Three hours later, a truck leaves the same place traveling 1 2/3 tim

love history [14]

Answer:

7.5 hours

Step-by-step explanation:

Using the variable 't' for time, you can set up an equation to find out how long it will take the truck to catch up to the bus. Since the bus is traveling at 60mph and the truck is traveling 1 2/3 times faster, we need to first find the rate of the truck:

1 $\frac{2}{3}=\frac{5}{3}$

$\frac{60}{1}*\frac{5}{3}=\frac{300}{3}=100mph$

Using 't' and the knowledge that they will have traveled the same distance we the truck catches up to the bus and the fact that the truck left 3 hours later:

60t = 100(t - 3) or 60t = 100t - 300

Solve for 't': 60t - 100t = -300 or -40t = -300 so, t = 7.5 hours

5 0

3 years ago

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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

A problem states: "There are 5 more girls than boys at the party. There are 27 children at the party in all. How many boys are t

Shalnov [3]

27-5 = 22

22/11 = 11

there are 11 boys at the party

expression = b+5

6 0

3 years ago

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36A^4+16Y^2<br> Can someone help me

Alenkasestr [34]

Answer:

4(9a^4+4y^2)

Step-by-step explanation:

factor out common term

6 0

3 years ago