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3 years ago

The graph of the quadratic function y=-x^2-2x+3 is shown below

Mathematics

2 answers:

Karolina [17]3 years ago

6 0

Answer:

The axis of symmetry is at $x=-1$

The graph has an x-intercept at $(1,0)$

The graph has a vertex at $(-1,4)$

Step-by-step explanation:

we have

$y=-x^{2}-2x+3$

Statements

case 1) The graph has root at $3$ and $1$

The statement is False

Because, the roots of the quadratic equation are the values of x when the value of y is equal to zero (x-intercepts)

Observing the graph, the roots are at $-3$ and $1$

case 2) The axis of symmetry is at $x=-1$

The statement is True

Observing the graph, the vertex is the point $(-1,4)$

The axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

the equation of the axis of symmetry is $x=-1$

case 3) The graph has an x-intercept at $(1,0)$

The statement is True

see procedure case 1)

case 4) The graph has an y-intercept at $(-3,0)$

The statement is False

Because, the y-intercept is the value of y when the value of x is equal to zero

Observing the graph, the y-intercept is the point $(0,3)$

case 5) The graph has a relative minimum at $(-1,4)$

The statement is False

Because, is a vertical parabola open downward, therefore the vertex is a maximum

The point $(-1,4)$ represent the vertex of the parabola, so is a maximum

case 6) The graph has a vertex at $(-1,4)$

The statement is True

see the procedure case 5)

see the attached figure to better understand the problem

I am Lyosha [343]3 years ago

6 0

Answer:

B, C, F

The axis of symmetry is x= -1

The graph has an x-intercept at (1,0)

The graph has a vertex at (-1,4)

Step-by-step explanation:

just did that quiz and those were the correct ones :)

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A publisher wants to estimate the mean length of time (in minutes) all adults spend reading newspapers. To determine this estima

liq [111]

Answer:

a) $\bar X=9.07$

b) The 95% confidence interval is given by (8.197;9.943)

c) $m=2.14 \frac{1.580}{\sqrt{15}}=0.873$

d) 3 possible ways

1) Increasing the sample size n.

2) Reducing the variability. If we have more data probably we will have less variation.

3) Lower the confidence level. Because if we have lower confidence then the quantile from the t distribution would belower and tthe margin of error too.

Step-by-step explanation:

Notation and definitions

n=15 represent the sample size

$\bar X= 9.07$ represent the sample mean

$s=1.580$ represent the sample standard deviation

m represent the margin of error

Confidence =95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a: Find the point estimate of the population mean.

The point of estimate for the population mean $\mu$ is given by:

$\bar X =\frac{\sum_{i=1}^{n} x_i}{n}$

The mean obteained after add all the data and divide by 15 is $\bar X=9.07$

Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . The degrees of freedom are given by:

$df=n-1=15-1=14$

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,14)" for $t_{\alpha/2}=-2.14$

"=T.INV(1-0.025,14)" for $t_{1-\alpha/2}=2.14$

The critical value $tc=\pm 2.14$

Part c: Calculate the margin of error (m)

First we need to calculate the standard deviation given by this formula:

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$

s=1.580

The margin of error for the sample mean is given by this formula:

$m=t_c \frac{s}{\sqrt{n}}$

$m=2.14 \frac{1.580}{\sqrt{15}}=0.873$

Part b: Calculate the confidence interval

The interval for the mean is given by this formula:

$\bar X \pm t_{c} \frac{s}{\sqrt{n}}$

And calculating the limits we got:

$9.07 - 2.14 \frac{1.580}{\sqrt{15}}=8.197$

$9.07 + 2.14 \frac{1.580}{\sqrt{15}}=9.943$

The 95% confidence interval is given by (8.197;9.943)

Part d: How can we reduce the margin of error?

We can reduce the margin of error on the following ways:

1) Increasing the sample size n.

2) Reducing the variability. If we have more data probably we will have less variation.

3) Lower the confidence level. Because if we have lower confidence then the quantile from the t distribution would belower and tthe margin of error too.

3 0

3 years ago

I’ll give brainliest answer if correct

STatiana [176]

Answer:

x = 1.7272727272

Step-by-step explanation:

8 0

3 years ago

Lawrence performs a survey to determine the number of minutes of exercise seventh-grade athletes get in one week. He gets a list

Delicious77 [7]

<span>He can choose his sample from every third person on each list rather than 10 people.</span>