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3 years ago

Sharla is 8 year older than her sister, patricia . The sum of their ages is 102.Find their ages.

Mathematics

2 answers:

Alisiya [41]3 years ago

6 0

Answer:

Patricia is 47 years old

Sharla is 55 years old

Step-by-step explanation:

Rewrite the first sentence as an equation: (S= Sharla) (P= Patricia)

S=P+8

Rewrite the second sentence as an equation:

S+P=102

1) Substitute P+8 as Sharla in the second equation:

P+8+P=102

2) Combine alike terms:

2P+8=102

3) Subtract 8 from both sides:

2P=94

4) Divide both sides by 2:

P=47

5) Substitute 47 as P in the <u>First</u> equation:

S=47+8

6) Solve:

S=55

Y_Kistochka [10]3 years ago

5 0

Answer:

Sharla's age: 55

Patricia's age: 47

Step-by-step explanation:

Let p represent patricia age.

p+(p+8)=102

If we combine like terms, it will end up like this:

2p+8=102

We have to subtract 8 from both sides.

2p=94

We have to divide 2 from both sides.

p=47

Since Patrica's age is 47, and we already know that Sharla is 8 years older than Patrica, Sharla's age is 47+8, which is 55.

Now, we can check our work. Does 47+55=100? Yes.

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JulsSmile [24]

Answer:

a) $\frac{32}{21}$

b) -14

c) -3

d) -96

Step-by-step explanation:

a) The parenthesis indicate multiplication.

b) Minus and plus gives subtraction, and the sign you put behind the number is the sign of the largest number you have (in this case it's 21 since we ignore the -)

c) They already have common denominators, all that's left is to do $\frac{-7 -2}{3} = \frac{-9}{3} = -3$

d) The parenthesis indicate multiplication.

Good luck!

6 0

2 years ago

In the past decades there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one study

DIA [1.3K]

Answer:

$z=\frac{0.384-0.362}{\sqrt{0.374(1-0.374)(\frac{1}{4276}+\frac{1}{3908})}}=2.055$

The p value can be calculated from the alternative hypothesis with this probability:

$p_v =2*P(Z>2.055)=0.0399$

And the best option for this case would be:

C. between 0.01 and 0.05.

Step-by-step explanation:

Information provided

$X_{1}=1642$ represent the number of smokers from the sample in 1995

$X_{2}=1415$ represent the number of smokers from the sample in 2010

$n_{1}=4276$ sample from 1995

$n_{2}=3908$ sample from 2010

$p_{1}=\frac{1642}{4276}=0.384$ represent the proportion of smokers from the sample in 1995

$p_{2}=\frac{1415}{3908}=0.362$ represent the proportion of smokers from the sample in 2010

$\hat p$ represent the pooled estimate of p

z would represent the statistic

$p_v$ represent the value for the pvalue

System of hypothesis

We want to test the equality of the proportion of smokers and the system of hypothesis are:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

The statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{1642+1415}{4276+3908}=0.374$

Replacing the info given we got:

$z=\frac{0.384-0.362}{\sqrt{0.374(1-0.374)(\frac{1}{4276}+\frac{1}{3908})}}=2.055$

The p value can be calculated from the alternative hypothesis with this probability:

$p_v =2*P(Z>2.055)=0.0399$

And the best option for this case would be:

C. between 0.01 and 0.05.

7 0

3 years ago

Index notation simplify 4^9 x 4^3

LenKa [72]

Answer:

$4^{12}$

Step-by-step explanation:

Using the rule of exponents

$a^{m}$ × $a^{n}$ = $a^{(m+n)}$ , then

$4^{9}$ × $4^{3}$ = $4^{(9+3)}$ = $4^{12}$

7 0

2 years ago

For every 15 minutes of a show, there are two minutes to commercial. At this rate, if leila has seen 45 minutes of a show, how m

Ainat [17]

Answer:

51 minutes.

Step-by-step explanation:

We have been given that for every 15 minutes of a show, there are two minutes to commercial. At this rate, Leila has seen 45 minutes of a show. We are asked to find the time for which Leila has been watching TV.

We will use proportions to solve our given problem.

$\frac{\text{Minutes of TV show + Advertisement}}{\text{Minutes of TV show}}=\frac{15+2}{15}$

$\frac{\text{Minutes of TV show + Advertisement}}{\text{Minutes of TV show}}=\frac{17}{15}$

Upon substituting our given values, we will get:

$\frac{\text{Minutes of TV show + Advertisement}}{45}=\frac{17}{15}$

$\frac{\text{Minutes of TV show + Advertisement}}{45}\times 45=\frac{17}{15}\times 45$

$\text{Minutes of TV show + Advertisement}=\frac{17}{1}\times 3$

$\text{Minutes of TV show + Advertisement}=51$

Therefore, Leila has been watching TV together for 51 minutes.

8 0

3 years ago

Darren drank 2 liters of water.How much millilliters of water did he drank

Elodia [21]

1 liter = 1,000 ML
2 X 1,000 = 2,000 ML
2,000 milliliter is your answer

4 0

3 years ago

Sharla is 8 year older than her sister, patricia . The sum of their ages is 102.Find their ages.​

Sharla is 8 year older than her sister, patricia . The sum of their ages is 102.Find their ages.