Solved on Sep 15, 2023

Seat belt usage affects deaths. For every 1% increase in usage, deaths decrease by 280. Find the slope $b$ and predict deaths if (i) 0%, (ii) 74%, (iii) 100% wear seat belts, given $y$ -intercept is 28,910.
a. The slope is $b = -280$ .

STEP 1

Assumptions1. The initial number of deaths due to not wearing seat belts is9000. . The number of deaths decreases by280 for every1 percentage point increase in seat belt usage.
3. Let $\hat{y}$ be the predicted number of deaths in a year and $x$ be the percentage of people who wear seat belts.
4. The equation for the predicted number of deaths is $\hat{y}=a+b x$ .
5. The $y$ -intercept $a$ is28,910.

STEP 2

First, we need to find the slope $b$ of the equation. The slope represents the change in $\hat{y}$ (the predicted number of deaths) for a1 unit change in $x$ (the percentage of people who wear seat belts). According to the problem, the number of deaths decreases by280 for every1 percentage point increase in seat belt usage. Therefore, the slope $b$ is -280.
$b = -280$

STEP 3

Now, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if no one wears seat belts. This corresponds to $x=0$ . Plugging in the values for $a$ and $x$ gives $\hat{y} = a + b \cdot0$

STEP 4

Calculate the predicted number of deaths when no one wears seat belts.
$\hat{y} =28910 + (-280) \cdot0 =28910$

STEP 5

Next, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if74% of people wear seat belts. This corresponds to $x=74$ . Plugging in the values for $a$ , $b$ , and $x$ gives $\hat{y} = a + b \cdot74$

STEP 6

Calculate the predicted number of deaths when74% of people wear seat belts.
$\hat{y} =28910 + (-280) \cdot74 =28910 -20720 =8190$

STEP 7

Finally, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if100% of people wear seat belts. This corresponds to $x=100$ . Plugging in the values for $a$ , $b$ , and $x$ gives $\hat{y} = a + b \cdot100$

STEP 8

Calculate the predicted number of deaths when100% of people wear seat belts.
$\hat{y} =28910 + (-280) \cdot100 =28910 -28000 =910$ a. The slope is $b=-280$ . b. The predicted number of deaths in a year is i.28,910 if no one wears seat belts. ii.8,190 if74% of people wear seat belts. iii.910 if100% of people wear seat belts.

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Seat belt usage affects deaths. For every 1% increase in usage, deaths decrease by 280. Find the slope $b$ and predict deaths if (i) 0%, (ii) 74%, (iii) 100% wear seat belts, given $y$ -intercept is 28,910.
a. The slope is $b = -280$ .

STEP 1

STEP 2

STEP 3

Now, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if no one wears seat belts. This corresponds to $x=0$ . Plugging in the values for $a$ and $x$ gives $\hat{y} = a + b \cdot0$

STEP 4

Calculate the predicted number of deaths when no one wears seat belts.
$\hat{y} =28910 + (-280) \cdot0 =28910$

STEP 5

Next, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if74% of people wear seat belts. This corresponds to $x=74$ . Plugging in the values for $a$ , $b$ , and $x$ gives $\hat{y} = a + b \cdot74$

STEP 6

Calculate the predicted number of deaths when74% of people wear seat belts.
$\hat{y} =28910 + (-280) \cdot74 =28910 -20720 =8190$

STEP 7

Finally, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if100% of people wear seat belts. This corresponds to $x=100$ . Plugging in the values for $a$ , $b$ , and $x$ gives $\hat{y} = a + b \cdot100$

STEP 8

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Seat belt usage affects deaths. For every 1% increase in usage, deaths decrease by 280. Find the slope bbb and predict deaths if (i) 0%, (ii) 74%, (iii) 100% wear seat belts, given yyy-intercept is 28,910.a. The slope is b=−280b = -280b=−280.

STEP 1

STEP 2

STEP 3

Now, we can use the equation y^=a+bx\hat{y}=a+b xy^​=a+bx to predict the number of deaths in a year if no one wears seat belts. This corresponds to x=0x=0x=0. Plugging in the values for aaa and xxx givesy^=a+b⋅0\hat{y} = a + b \cdot0y^​=a+b⋅0

STEP 4

Calculate the predicted number of deaths when no one wears seat belts.y^=28910+(−280)⋅0=28910\hat{y} =28910 + (-280) \cdot0 =28910y^​=28910+(−280)⋅0=28910

STEP 5

Next, we can use the equation y^=a+bx\hat{y}=a+b xy^​=a+bx to predict the number of deaths in a year if74% of people wear seat belts. This corresponds to x=74x=74x=74. Plugging in the values for aaa, bbb, and xxx givesy^=a+b⋅74\hat{y} = a + b \cdot74y^​=a+b⋅74

STEP 6

Calculate the predicted number of deaths when74% of people wear seat belts.y^=28910+(−280)⋅74=28910−20720=8190\hat{y} =28910 + (-280) \cdot74 =28910 -20720 =8190y^​=28910+(−280)⋅74=28910−20720=8190

STEP 7

Finally, we can use the equation y^=a+bx\hat{y}=a+b xy^​=a+bx to predict the number of deaths in a year if100% of people wear seat belts. This corresponds to x=100x=100x=100. Plugging in the values for aaa, bbb, and xxx givesy^=a+b⋅100\hat{y} = a + b \cdot100y^​=a+b⋅100

STEP 8

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Seat belt usage affects deaths. For every 1% increase in usage, deaths decrease by 280. Find the slope $b$ and predict deaths if (i) 0%, (ii) 74%, (iii) 100% wear seat belts, given $y$ -intercept is 28,910.
a. The slope is $b = -280$ .

Now, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if no one wears seat belts. This corresponds to $x=0$ . Plugging in the values for $a$ and $x$ gives $\hat{y} = a + b \cdot0$

Calculate the predicted number of deaths when no one wears seat belts.
$\hat{y} =28910 + (-280) \cdot0 =28910$

Next, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if74% of people wear seat belts. This corresponds to $x=74$ . Plugging in the values for $a$ , $b$ , and $x$ gives $\hat{y} = a + b \cdot74$

Calculate the predicted number of deaths when74% of people wear seat belts.
$\hat{y} =28910 + (-280) \cdot74 =28910 -20720 =8190$

Finally, we can use the equation $\hat{y}=a+b x$ to predict the number of deaths in a year if100% of people wear seat belts. This corresponds to $x=100$ . Plugging in the values for $a$ , $b$ , and $x$ gives $\hat{y} = a + b \cdot100$