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1 year ago

The square of a certain number plus ten is equal to 81

Mathematics

1 answer:

Scorpion4ik [409]1 year ago

3 0

Answer:

x = ±8.43 (to 3sf)

Step-by-step explanation:

Let this number be x.

x² + 10 = 81

x² = 81 - 10

= 71

x = ±√71

= ±8.43 (to 3sf)

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More Information From the Online Dating Survey A survey conducted in July 2015 asked a random sample of American adults whether

svet-max [94.6K]

Answer:

90% confidence interval for the proportion of all US adults ages 55 to 64 to use online dating is [0.095 , 0.148].

Step-by-step explanation:

We are given that a survey conducted in July 2015 asked a random sample of American adults whether they had ever used online dating.

The survey included 411 adults between the ages of 55 and 64, and 50 of them said that they had used online dating.

Firstly, the pivotal quantity for 90% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who said that they had used online dating = $\frac{50}{411}$ = 0.122

n = sample of adults between the ages of 55 and 64 = 411

p = population proportion of all US adults ages 55 to 64 to use online dating

Here for constructing 90% confidence interval we have used One-sample z proportion statistics.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

P( $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

90% confidence interval for p = [ $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.122-1.645 \times {\sqrt{\frac{0.122(1-0.122)}{411} } }$ , $0.122+1.645 \times {\sqrt{\frac{0.122(1-0.122)}{411} } }$ ]

= [0.095 , 0.148]

Therefore, 90% confidence interval for the proportion of all US adults ages 55 to 64 to use online dating is [0.095 , 0.148].

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2 years ago

Brian and Christina started keeping track of their workouts. Brian did 85 sit-ups the first week and 90 sit-ups each week after

IrinaK [193]

Brian-90×5+85=535

Christina-90×5+65=515

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2 years ago

Two lines intersect in a point true or false

Levart [38]

True. Two lines intersect in a single point.

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3 years ago

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There are 36 people in a fitness studio. What fraction represents the number of people running? • 3 8 of the people lifted weigh

klio [65]

Answer:

7/24

Step-by-step explanation:

3/8 is changed to 9/24 people lifting weights

1/3 is changed to 8/24 people cross training

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3 years ago

a movie sells tickets for for the cost of 4$ and 6$.there is a total of 75 tickets for a total of 400$,how many tickets were sol

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hope this helped :)

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2 years ago

The square of a certain number plus ten is equal to 81​

The square of a certain number plus ten is equal to 81