How many gallons is the gas tank 2010 toyota corolla hold?

Find an equation for the line tangent to the circle x^2 +y^2=25 at the point (3, -4)

Lostsunrise [7]

Hello :
the center of this cercle is : O( 0, 0)
calculate the slope m of the line : OA .. A (3,-4)
m= (yA - yO) / (xA- xO)
m = (-4-0)/(3-0)
m= -4/3
if : k the slope of the tangent : k×m = -1 (the tangent perpendiclar of : OA)
k× (-4/3) = -1
k = 3/4
an equation of this tangent is : y - (-4) = (3/4)(x-3)

7 0

3 years ago

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the

EastWind [94]

Answer:

a) $\hat p=\frac{471}{1024}=0.460$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

b) The 99% confidence interval would be given by (0.429;0.491)

Step-by-step explanation:

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Data given and notation

n=1024 represent the random sample taken

X=471 represent the people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

$\hat p=\frac{471}{1024}=0.460$ estimated proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

p= population proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

Part a

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

Part b

If we replace the values obtained we got:

$0.460-1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.429$

$0.460+1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.491$

The 99% confidence interval would be given by (0.429;0.491)

8 0

3 years ago

Solve pls for brainliest

Luden [163]

Answer:

19. 6561

20. 196

22. $\frac{256}{25}$

23. $\frac{1}{16}$

24. $\frac{2}{9}$

5 0

3 years ago

A regular polygon has an interior angle of approximately 158.8°.

Step2247 [10]

Answer:

17 sides

Step-by-step explanation:

<u>Property of regular polygons:</u>

Sum of Interior Angles = (n−2) × 180°, where n is number of sides

158.8×n = (n - 2)×180
180n - 158.8n = 360
21.2n = 360
n = 360/21.2
n = 17

5 0

3 years ago

Help if you can do this please

olga nikolaevna [1]

Answer:

Step-by-step explanation:

a. Since the parabola is compressed by a factor of 1/3 we can state:

a parabola is written this way : y=(x-h)²+k
h stands for the translation to the left ⇒ 2*3=6
k for the units down ⇒4*3=12

So the equation is : y=(x-6)²+12

b.Here the parabola is stretched by a factor of 2 so we must multiply by 1/2

We khow that a parabola is written this way : y=(x-h)²+k
(h,k) are the coordinates of the vertex
the maximum value is 7*0.5=3.5
we khow tha the derivative of a quadratic function is null in the maximum value
so let's derivate (x-h)²+k= x²+h²-2xh+k
f'(x)= 2x-2h h is 1 since the axe of simmetry is x=1
f'(x)=2x-2 ⇒2x-2=0⇒ x= 1
Now we khow that 1 is the point where the derivative is null
f(1)=3.5
3.5=(x-1)²+k
3.5= (1-1)²+k⇒ k=3.5

So the equation is : y=(x-1)²+3.5

7.

the maximum height is where the derivative equals 0

h= -5.25(t-4)²+86
h= -5.25(t²-8t+16)+86
h=-5.25t²+42t-84+86
h=-5.25t²+42t+2

Let's derivate it :

f(x)= -10.5t+42
-10.5t+42=0
42=10.5t
t= 42/10.5=4

When the height was at max t=4s

h(max)= -5.25(4-4)²+86 = 86 m

h was 86m

8 0

3 years ago