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4 years ago

11

When Mr. Smith kicks a football, it has a vertical speed of 20 m/s, and its height, h in meters after t seconds can be modeled b

y the equation h=20t−5t^2 .
Part A.
How long is the football in the air before it lands on the ground?

seconds

Part B
In how many seconds will the football reach its maximum height?

seconds

Part C
What is the maximum height that the football will reach?

meters

1 answer:

adelina 88 [10]4 years ago

6 0

Answer:

look up desmos and do it on there it helps alot

Step-by-step explanation:

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BIG IDEAS MATH <br> help me out please hurry

arsen [322]

I will but the picture is blurry

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3 years ago

An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 m

SVETLANKA909090 [29]

Answer:

a) $y=-6.254 x +75.064$

b) r =-0.932

The % of variation is given by the determination coefficient given by $r^2$ and on this case $-0.932^2 =0.8687$ , so then the % of variation explained by the linear model is 86.87%.

Step-by-step explanation:

Assuming the following dataset:

Monthly Sales (Y) Interest Rate (X)

22 9.2

20 7.6

10 10.4

45 5.3

Part a

And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=278.65-\frac{32.5^2}{4}=14.5875$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=696.9-\frac{32.5*97}{4}=-91.225$

And the slope would be:

$m=\frac{-91.225}{14.5875}=-6.254$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{32.5}{4}=8.125$

$\bar y= \frac{\sum y_i}{n}=\frac{97}{4}=24.25$

And we can find the intercept using this:

$b=\bar y -m \bar x=24.25-(-6.254*8.125)=75.064$

So the line would be given by:

$y=-6.254 x +75.064$

Part b

For this case we need to calculate the correlation coefficient given by:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{4(696.9)-(32.5)(97)}{\sqrt{[4(278.65) -(32.5)^2][4(3009) -(97)^2]}}=-0.937$

So then the correlation coefficient would be r =-0.932

The % of variation is given by the determination coefficient given by $r^2$ and on this case $-0.932^2 =0.8687$ , so then the % of variation explained by the linear model is 86.87%.

6 0

3 years ago

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come f

AlladinOne [14]

Answer:

$z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43$

Now we can calculate the p value with the following probability:

$p_v =P(z>2.43)=0.0075 \approx 0.008$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5

Step-by-step explanation:

Data given and notation

n=75 represent the random sample taken

$\hat p=0.64$ estimated proportion of interest

$p_o=0.5$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to verify if the true proportion is higher than 0.5:

Null hypothesis: $p =0.5$

Alternative hypothesis: $p > 0.5$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43$

Now we can calculate the p value with the following probability:

$p_v =P(z>2.43)=0.0075 \approx 0.008$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5

7 0

4 years ago

Joel wants to buy a new tablet computer from a store having a 20% off sale on all tablets. The tablet he wants has an original c

earnstyle [38]

Answer:

<u>Joel will have to pay $ 159.60 for the tablet.</u>

Step-by-step explanation:

1. Information given to us to answer the question correctly:

Discount percentage of the tablets = 20%

Original cost of the tablet = $ 190

Sales tax = 5%

2. How much will Joel pay for the tablet? Show your work in your notebook. Remember to use $.

Let's find the discounted price and the sales tax for that price, this way:

Discounted price = Original price - Discount

Discounted price = 190 - (190 * 0.2)

Discounted price = 190 - 38 = 152

Sales tax of the discounted price = 152 * 0.05

Sales tax = 7.60

Joel will have to pay = Discounted price + Sales tax

Joel will have to pay = 152 + 7.60

<u>Joel will have to pay = $ 159.60</u>

5 0

4 years ago

Plz answer this i need help its done today

olga55 [171]

Answer:

1) 1/10

2) 1/2

3) 1/5

Step-by-step explanation:

1)

1 favorable outcome and 10 total outcomes.

$P(3) = \frac{1}{10}$

2)

5 favorable outcomes and 10 total outcomes

$P(even) = \frac{5}{10} = \frac{1}{2}$

3)

2 favorable outcomes and 10 total outcomes

$P(multiples\ of\ 5) = \frac{2}{10} = \frac{1}{5}$

3 0

3 years ago