Answer:
P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584
0.00885... < 0.01
The test statistic of 46 is significant
There is sufficient evidence to reject H₀ and accept H₁
Air bags are more effective as protection than safety belts
Step-by-step explanation:
821 crashes
46 hospitalisations where car has air bags
7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts
α = 0.01 or 1% ← level of significance
One-tailed test
We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;
The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;
So we are testing if hospitalisations in cars with air bags is less than 0.078;
So, firstly:
Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags
X~B(821, 0.078)
Null hypothesis (H₀): p = 0.078
Alternative hypothesis (H₁): p < 0.078
According to the information, we reject H₀ if:
P(X ≤ 46 | X~B(821, 0.078)) < 0.01
To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;
If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:
[tex]P(X = r) = nCr * p^{r} * (1 - p)^{n - r}[/tex]
You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:
P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584
Now, we need to consider if the condition for rejecting H₀ is met and recognise that:
0.00885... < 0.01
There is sufficient evidence to reject H₀ and accept H₁.
To explain what this means:
The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;
In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.
DIRECTION: Solve each proportion.
1. 6/15 = n/25
2. 3/5 = 21/n
3. n/12 = 15/30
4.3/n = 12/24n
5. 6/12 = n/72
plss help me :(
Answer:
1. n=10
2. n=35
3. n=6
4. n=0 ? not sure for this one. two variables in the proportion
5. n=36
Step-by-step explanation:
set each set of proportion equal to each other and do cross multiplication
hope this helps !
how are you ?
Answer:
10356636Step-by-step explanation:
Please take a look of the attached photo for the solution.
Round 743,214 to nearest ten thousand
I need help this is easy tho!
Answer:
it is true
it's a quadralateral
8. There are 18 trumpets in a music room. These trumpets will be placed in 3 equal rows. Which number sentence can be used to find the number of trumpets in each row?
Answer:
18÷3=6
Step-by-step explanation:
18 trumpets have to be DIVIDED into 3 rows so you would divide 18 by three to get 6 trumpets in each row.
Show work on the graph pls help I’ll brainlest ASAP
Answer:
Slope (known as m) = -3/2; Y-int (known as b) = 3
Step-by-step explanation:
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{{0}-{3}}{{2}-{0}}[/tex]
m = [tex]\frac{-3}{2}[/tex]
b = [tex]3[/tex]
If a rectangle has a base of 6' and a height of 4' its area would be what?
A= bxh
A= 6'x4'
A= 24 sq.ft.
Function 1 is defined by the equation y=-1/4r-5
Function 2
Step-by-step explanation:
as just answered in the other question, the y-intercept is simply the y-value, when x=0.
it is -5 for function 1.
and function 2 clearly crosses the y-axis at y = -7, which is the y-intercept.
as -5 is greater than -7, function 1 had the greater y- intercept.
your paper airplane is launched from 25ft. it descends at a rate of 5ft per second. write an equation that represents the height y of your airplane after x seconds
Answer:
y= -5x + 25
Step-by-step explanation:
y = mx + b
m(slope) = descending 5ft/sec means the height will decrease so the slope must be negative
b(y-int) = starting height of 25 ft added
PLS HELP!!!
simplify 3^2 x 3^4 x 3^6=
3^10
3^12
3^0
3^40
Answer:
3¹² is answer
Step-by-step explanation:
3^(2+4+6)
3^12
1) Order this list from smallest to largest. 0.3 15% 2 1/2
In the year 2001, a person bought a new car for $12000. For each consecutive year after that, the value of the car depreciated by 10%. How much would the car be worth in the year 2004, to the nearest hundred dollars? i need this asap
Answer: $8700.
Step-by-step explanation:
The equation we can use is p x r^years.
p is the original value ($12000).
r is our multiplier, it goes down by 10% so our multiplier is 1-0.1 giving us 0.9.
IT is 2001 to 2004 so 3 years so we do r to the power of 3.
So we use 12000 x 0.9^3.
This is equal to 8748, to the nearest 100 dollars its $8700.
Conner earns 24$ working every 1.5 12 blank
Answer: That makes no sense. Maybe did your copy and paste corrupt? Or mistyped the question? Get back to me and I’ll help!!
Step-by-step explanation:
Help: Whats 8-2x=10?
Answer:
x=-1
Step-by-step explanation:
8-2x=10
(8-2x)-8=10-8
-2x=2
-2x/-2=2/-2
x=-1
The function f is given in three equivalent forms.
Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
f(x) = 1/2(x-5)^2-2
f(x)= 1/2(x -3) (x -7)
f(x) = 1/2x^2-5x+21/2
Write one of the zeros
Answer:
a) best form: (b) f(x)= 1/2(x -3) (x -7)
b) zeros: x=3, x=7
Step-by-step explanation:
The factored form most quickly tells you the zeros of the function. The zeros are the values of x that make the factors zero: the opposite of the binomial's constant.
f(x)= 1/2(x -3)(x -7) reveals the zeros to be x=3 and x=7
Answer:
khan
Step-by-step explanation:
A child has the magnet numbers 1 through 50 on their fridge. What is the probability that the child will choose a number that is not a multiple of 9?
Give your answer in fraction form.
Answer:
9/10
Step-by-step explanation: the magic mushroom said so
13,22,31,...
Find the 31st term.
Find the 31st term.
Answer: 283
Step-by-step explanation:
To do this, it is helpful to get an equation you can use to solve any term.
This equation is:
[tex]13 + 9(n-1)[/tex]
So simply plug in 31 for n to get
[tex]13+9(31-1)[/tex]
[tex]=13+270[/tex]
[tex]=283[/tex]
Answer:
283
Step-by-step explanation:
9x+4=9(31)+4=283
13+9=22
22+9=31
9x
9(1)=9 9+4=13
9x+4
–3 2/6 ÷ 1 1/2=
A. 9/20
B. -3 2/3
C. -2 2/9
D. -5
Answer:
its C
1.convert the mixed number to an improper fraction
([tex]\frac{-20}{6\\}[/tex] x [tex]\frac{2}{3}[/tex] )
2. reduce the numbers with the greatest common factor (2)
[tex]\frac{-20}{3}[/tex] x [tex]\frac{1}{3}[/tex]
3. then multiply and get
[tex]\frac{-20}{9}[/tex]
4. then reduce to get
-2[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
A strand of bacteria has a doubling time of 15 minutes. If the population starts with 10 organisms, how long would it take for the population to grow to 700 organisms?
Answer:
between 1hr 30 and 1hr 45
Step-by-step explanation:
10*2=20 15
20*2=40 30
40*2=80 45
80*2=160 60
160*2=320 1hr 15
320*2=640 1hr 30
In 90 minutes the population to grow to 700 organisms.
Given that,
A strand of bacteria has a doubling time of 15 minutes.
If the population starts with 10 organisms.
We have to determine,
How long would it take for the population to grow to 700 organisms?
According to the question,
A strand of bacteria has a doubling time of 15 minutes.
If the population starts with 10 organisms.
In 15 minutes strand of bacteria has a doubling time the population starts with 10 organisms.
[tex]\rm = 10 \times 2 = 20 \ bacteria[/tex]
In 15 minutes 20 bacteria for the population to grow.
In 30 minutes strand of bacteria has a doubling time the population starts with 20 organisms.
[tex]\rm = 20 \times 2 = 40 \ bacteria[/tex]
In 30 minutes 40 bacteria for the population to grow.
In 45 minutes strand of bacteria has a doubling time the population starts with 40 organisms.
[tex]\rm = 40 \times 2 = 80 \ bacteria[/tex]
In 45 minutes 80 bacteria for the population to grow.
In 60 minutes strand of bacteria has a doubling time the population starts with 80 organisms.
[tex]\rm = 80 \times 2 = 160 \ bacteria[/tex]
In 60 minutes 160 bacteria for the population to grow.
In 75 minutes strand of bacteria has a doubling time the population starts with 160 organisms.
[tex]\rm = 160 \times 2 = 320 \ bacteria[/tex]
In 75 minutes 320 bacteria for the population to grow.
In 90 minutes strand of bacteria has a doubling time the population starts with 320 organisms.
[tex]\rm = 320 \times 2 = 640 \ bacteria[/tex]
In 90 minutes 640 bacteria for the population to grow.
In 120 minutes strand of bacteria has a doubling time the population starts with 640 organisms.
[tex]\rm = 640 \times 2 = 1280 \ bacteria[/tex]
In 120 minutes 1280 bacteria for the population to grow.
Hence, In 90 minutes the population to grow to 700 organisms.
For more details refer to the link given below.
https://brainly.com/question/3188472
Logan walked 2 1/2 miles on Monday and she walked
6 miles. How far did she walk on Tuesday?
Answer:
3 1/2 miles
Step-by-step explanation:
because 6 - 2 1/2 = 3 1/2
The length of a rectangle is times the width. If the perimeter is 32 inches, what is the width of the rectangle
Answer:
11
Step-by-step explanation:
PLEASEEEE HELP!DUE IN 1 HOUR! A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $3000 when sold. A ranch-style house requires $40,000 of capital and provides an $7000 profit. If the contractor has $3.8 million of capital on hand, how many houses of each type should she build for maximum profit?
Answer:
Step-by-step explanation:
A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $2000 when sold. A ranch-style house requires $40,000 of capital and provides an $8000 profit. If the contractor has $3.2 million of capital on hand, how many houses of each type should she build for maximum profit?
? colonials
? ranches
For maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses. The maximum profit achievable is $740,000.
Let x be the number of colonial houses built.
Let y be the number of ranch-style houses built.
Now, we can set up the objective function, which represents the total profit:
Total Profit (P) = 3000x + 7000y
The total cost of the houses built cannot exceed the available capital, which is $3.8 million (or $3,800,000):
30,000x + 40,000y ≤ 3,800,000
The number of building lots used cannot exceed the total number of lots available, which is 100:
x + y ≤ 100
Also, we need to consider that the number of houses (x and y) must be non-negative:
x ≥ 0
y ≥ 0
Now, we have the linear programming model with the objective function and constraints.
We need to find the values of x and y that maximize the total profit (P).
Graph the feasible region determined by the constraints (x + y ≤ 100, x ≥ 0, y ≥ 0, 30,000x + 40,000y ≤ 3,800,000), and then evaluate the objective function (P = 3000x + 7000y) at each corner point of the feasible region to find the maximum profit.
The feasible region is a polygon with vertices at the following points:
(0, 0)
(0, 95) (Intersection of x = 0 and y = 95)
(80, 20) (Intersection of x = 80 and y = 20)
(100, 0) (Intersection of x = 100 and y = 0)
Now, evaluate the objective function (P) at each corner point:
(0, 0): P = 0
(0, 95): P = 665,000
(80, 20): P = 740,000
(100, 0): P = 300,000
The maximum profit of $740,000 occurs when the contractor builds 80 colonial houses and 20 ranch-style houses
Hence, for maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses.
To learn more on Linear programming click here:
https://brainly.com/question/30763902
#SPJ3
4. Solve the equation using square roots.
x2 + 10 = 9
Answer:
+1/-1
Step-by-step explanation:
assuming the original phrase is x^2
x^2 + 10 = 9
x^2 = 1
x = +/- 1
y=x^2 translate 4 units down and 3 units left
Answer: Hello! When a graph is translated 4 units down you are moving all of the y values. This makes it the easiest translation that we do, other than no translation! All you have to do is subtract 4. Your equation is y=x2 - 4. If you wanted to move the graph up it is addition and if you want to move it down it is subtraction. When you translate right to left it is more complicated! Hope this helps. :))
which of the following angle measure combinations will form a triangle?
A. 47° degrees, 63 degrees, and 70 degrees
B. 160 degrees, 50 degrees, and 150 degrees
C. 90 degrees, 1 degrees, and 88 degrees
D. 182 degrees, 1 degrees, and 2 degrees
The position of a scuba diver relative to the water surface was −22 1/3 feet. He saw something interesting beneath him and increased his depth by 12 1/2 feet.
What is the position of the scuba diver now relative to the water surface?
Enter your answer as a mixed number, in simplified form, in the box.
Answer:
-34 5/6
Step-by-step explanation:
Hope this helps
Have a blessed day
Help help help help help
Answer:
100°
Step-by-step explanation:
Answer:
∡5=100°
Step-by-step explanation:
∡5 is perpendicular to the 100° above, therefore your answer is ∡5=100°.
Brainliest would be appreciated! :-)
A graph has a constant of proportionality of 35. Let y represent miles and x represent gallons.
What is the unit rate of the relationship?
Enter your answer in the box 100 POINTS WILL MAKE IT BRAINLIEST
How many 1/4 inch cubes does it take to fill a box with width 1 inches, length 3 3/4 inches and height 1 1/2inches?
Step-by-step explanation:
we need to see how many cubes fit into every dimension.
we can fit 4 cubes along the 1 in width. as 4×1/4 = 1 in.
we can fit 15 cubes along the 3 3/4 in length :
3 3/4 = 12/4 + 3/4 = 15/4
15/4 / 1/4 = 15/4 × 4/1 = 4×15 / 4×1 = 15
we can put 6 cubes on top of each other fit the height of 1 1/2 in
1 1/2 = 2/2 + 1/2 = 3/2 = 6/4
6/4 / 1/4 = ... = 6 (as above - simply 1/4 fits 6 times into 6/4).
so, we have
4 × 15 × 6 = 360
we need 360 cubes to fill the box.
Between which two integers does 7/3 lie?
Answer:
2 and 3
Step-by-step explanation:
7/3=2 1/3
So it lies between 2 and 3
2 1/3 is lesser that 3 but more than 2.
In a chess club there are 10 males and 15 females. What percentage of the club is females?
Answer:
Step-by-step explanation: