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3 years ago

What is the y-intercept Of the function Represented by the table of values belowX -2 1 2 4 7 y 15 6 3 -3 -12

Mathematics

2 answers:

Kipish [7]3 years ago

8 0

Given:

The table of values.

To find:

The y-intercept of the given function.

Solution:

The table of values represents a linear function because the rate of change is constant.

Consider any two points from the given table. Let the two points are (-2,15) and (1,6). Then the equation of the linear function is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-15=\dfrac{6-15}{1-(-2)}(x-(-2))$

$y-15=\dfrac{-9}{1+2}(x+2)$

$y-15=\dfrac{-9}{3}(x+2)$

$y-15=-3(x+2)$

Adding 15 on both sides, we get

$y=-3x-6+15$

$y=-3x+9$

Putting x=0, we get

$y=-3(0)+9$

$y=0+9$

$y=9$

The y-intercept is 9. Therefore, the correct option is C.

HACTEHA [7]3 years ago

7 0

Answer: this is correct

Step-by-step explanation:

From turning this assignment in this is correct

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At a local sandwich shop the average customer spends $25 at dinner with a standard deviation of $2.30. In a simple random sample

oee [108]

Answer:

The probability that the mean receipt for dinner is between $24.50 and $25.50 is

P(24.50≤ x ≤ 25.50)= 0.8324

Step-by-step explanation:

Step(i):-

Given mean of Population(μ) = $25

Given standard deviation of the Population (σ) = 2.30

Sample size 'n' = 40

Let 'X' be the random variable in normal distribution

Given X₁ = 24.50

$Z_{1} =\frac{x-mean}{\frac{S.D}{\sqrt{n} } } = \frac{24.50-25}{\frac{2.30}{\sqrt{40} } } = -1.375$

Given X₂ = 25.50

$Z_{2} =\frac{x-mean}{\frac{S.D}{\sqrt{n} } } = \frac{25.50-25}{\frac{2.30}{\sqrt{40} } } = 1.3751$

Step(ii):-

The probability that the mean receipt for dinner is between $24.50 and $25.50

P(x₁≤ x ≤ x₂) = P(Z₁≤ z ≤ Z₂) = A(Z₂) + A(z₁)

P(24.50≤ x ≤ 25.50) = P(-1.375≤ z ≤ 1.375) = A(1.375) + A(1.375)

P(24.50≤ x ≤ 25.50)= 2 A( 1.375)

= 2 × 0.4162 ( from normal table)

= 0.8324

Final answer:-

The probability that the mean receipt for dinner is between $24.50 and $25.50 is 0.8324

4 0

4 years ago

The results of a national survey showed that on average, adults sleep 6.7 hours per night. Suppose that the standard deviation i

Roman55 [17]

Answer:

a) Atleast 75%

b) Atleast 88.9%

c) 95%

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 6.7

Standard Deviation, σ = 1.6

Chebyshev's Theorem:

Atleast $1 - \dfrac{1}{k^2}$ percent of data lies within k standard deviation of mean.

Empirical Rule:

Almost all the data lies within 3 standard deviation for a normal data.
Around 68% of data lies within 1 standard deviation of mean.
Around 95% of data lies within 2 standard deviation of mean.
Around 99.7% of data lies within 3 standard deviations o mean.

a) minimum percentage of individuals who sleep between 3.5 and 9.9 hours

$3.5 = \mu - 2\sigma = 6.7 - 2(1.6)\\9.9 = \mu + 2\sigma = 6.7 + 2(1.6)$

We have to find the percent of data lying within 2 standard deviation of mean.

Putting k = 2

$1 - \dfrac{1}{(2)^2} = 0.75 = 75\%$

Atleast 75% of of individuals who sleep between 3.5 and 9.9 hours.

b) minimum percentage of individuals who sleep between 2.7 and 10.7 hours

$2.7 = \mu - 3\sigma = 6.7 - 3(1.6)\\10.7 = \mu + 3\sigma = 6.7 + 3(1.6)$

We have to find the percent of data lying within 3 standard deviation of mean.

Putting k = 3

$1 - \dfrac{1}{(3)^2} = 0.889 = 88.9\%$

Atleast 88.9% of of individuals who sleep between 2.7 and 10.7 hours.

c) percentage of individuals who sleep between 3.5 and 9.9 hours per day.

Thus, we have to find the percentage of data lying within 2 standard deviation.

By empirical rule, around 95% of data lies within 2 standard deviation.

Thus, 95% of of individuals who sleep between 3.5 and 9.9 hours.

This is higher than the percentage obtained from Chebyshev's rule.

4 0

3 years ago

A girl is on a train that is headed East at 100 miles per hour. The girl is walking at 5 miles per hour

nata0808 [166]

Answer: The speed is 105 miles/ hr and the direction of the train would be East if the girl is the frame of reference.

Step-by-step explanation:

Since we have given that

Speed of train = 100 miles per hour

Speed of girl = 5 miles per hour

Since the girl is moving towards the back of train.

So,it means train and girl are moving in opposite direction.

So, Relative speed would be

$100+5=105\ miles/hr$

Hence, the speed is 105 miles/ hr and the direction of the train would be East if the girl is the frame of reference.

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3 years ago

. The first day of a water polo tournament the total value of tickets sold was $17,610. One-day passes sold for $20 and tourname

Scilla [17]

Answer:

330 day passes, 367 tournament passes

Step-by-step explanation:

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3 years ago

Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t squa

marta [7]

Answer: t = 7.85seconds

Step-by-step explanation:

Given that :

Height of tower = 986 Feets

Function s(t) = 16t^2

To find the time t 8 in Seconds taken for an object to fall to the ground from the top of the building

16t^2 = 986

t^2 = 986/16

t ^2 = 61.625

Take the square root of both sides

t = sqrt(61.625)

t = 7.85seconds

4 0

3 years ago

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What is the y-intercept Of the function Represented by the table of values below￼￼X -2 1 2 4 7 y 15 6 3 -3 -12

What is the y-intercept Of the function Represented by the table of values belowX -2 1 2 4 7 y 15 6 3 -3 -12