Answer:
The probability that the vaccine is not effective in more than 1 of the 20 individuals is equal to:
P = 1 - P(1) - P(0)
Where:
P(1) = probability that the vaccine is not effective in one individual
P(0) = probability that the vaccine is not effective in 0 individuals.
The probability that the vaccine is effective is 0.95
Then the probability that the vaccine is not effective is 0.05.
Then to calculate P(1), suppose that the vaccine is not effective in the first case and then is effective 19 times, this is:
p(1) = (0.05^1)*(0.95^19)
But this only for one case, we have 20 possible permutations (the vaccine is not effective in the first case, the second case, third case, etc)
Then the actual probability is:
P(1) = 20*((0.05^1)*(0.95^19)) = 0.377
And P(0) is easy to compute:
P(0) = (0.05^0)*(0.95^20) = 0.358
And here we have only one possible permutation, so we do not worry about that.
Then P = 1 - P(1) - P(0) = 1 - 0.377 - 0.358 = 0.265
This means that the probability that the vaccine is not effective in more than one individual is of 0.265 (or 26.5% in percentage form)
An automatic teller machine gives you $150 in five and ten-dollar bills. There are two more than twice as many five-dollar bills as there are ten-dollar bills. How many of each denomination are there?
Answer:
There are 7 ten-dollar bills and 16 five-dollar bills.
Step-by-step explanation:
Let's call:
T: Number of ten-dollar bills
F: Number of five-dollar bills
The amount of money withdrawn from the ATM is $150:
10T+5F=150
Dividing by 5:
[tex]2T+F=30\qquad\qquad [1][/tex]
We also know there are two more than twice as many five-dollar bills as there are ten-dollar bills:
[tex]F=2+2T\qquad\qquad [2][/tex]
Substituting [2] into [1]:
2T+2T+2=30
Rearranging:
2T+2T=30-2
Simplifying:
4T=28
Solving:
T=28/4=7
From [2]:
F=2+2*7=2+14=16
There are 7 ten-dollar bills and 16 five-dollar bills.
What is the equation in slope-intercept form of the line that passes through the points (−12, −4) and (4, 8)?
A. y = −43 − 20
A. , y = −43 − 20
B. y = 43 − 12
B. , y = 43 − 12
C. y = −0.75 − 13
C. , y = −0.75 − 13
D. y = 0.75x +5
D. , y = 0.75x +5
Answer:
Choice D. [tex]y = 0.75\, x + 5[/tex].
Step-by-step explanation:
The general equation for the slope-intercept form of a line in a cartesian plane is [tex]y = m\, x + b[/tex], where:
[tex]m[/tex] is the slope of the line, and[tex]b[/tex] is the [tex]y[/tex]-intercept of the line. (The [tex]y\![/tex]-intercept of a line in a cartesian plane is the [tex]y\!\![/tex]-coordinate of the point where the line intersects the [tex]\! y \![/tex]-axis.)Start by finding the value of [tex]m[/tex]. The slope of a line is equal to its rise-over-run. For the two points in this question:
The "rise" is the [tex]y[/tex]-coordinate of the first point minus that of the second: [tex]\text{rise} = (-4) - 8 = -12[/tex].The "run" is the [tex]x[/tex]-coordinate of the first point minus that of the second. The order of these two points should stay the same: [tex]\text{run} = (-12) - 4 = -16[/tex].Calculate the slope of this line:
[tex]\displaystyle m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{-12}{-16} = 0.75[/tex].
The equation of the line becomes:
[tex]y = \underbrace{0.75}_{m}\, x + b[/tex].
Substitute the coordinates of either of the two points to find [tex]b[/tex]. For example, for the first point [tex](12, -4)[/tex], substitute in the following:
[tex]x = -12[/tex], and[tex]y = -4[/tex].The equation becomes:
[tex]-4 = 0.75 \times (-12) + b[/tex].
Solve for the value of [tex]b[/tex]:
[tex]b = 5[/tex].
Hence, the slope-intercept form of this line shall be:
[tex]y = 0.75\, x + 5[/tex].
CHECK PHOTO Intercepts of the graph BE SURE TO BE CORRECT PLEASE no work needed
Answer:
y= (0, .7)
x= (-1.2, 0)
Step-by-step explanation:
r u taking a test?
PLEASE HELP ASAP
can you help me please
An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a:
Answer:
the speed value that the radar equipment outputs.
Step-by-step explanation:
A random variable in an experiment is also (and most times the case) called a dependent variable. In this scenario, the random variable would be the speed value that the radar equipment outputs. This is because this value depends on the actual velocity of the cars that pass by the equipment. The faster the car is moving when it passes the radar the higher value will be displayed on the equipment. Therefore, depending completely on the vehicles.
Select all the expressions that are rational numbers.
a. 3.14159…
b. –9.1234567123…
c. –9.293847210103938…
d. 227
e. –26
Answer:
d,e
Step-by-step explanation:
rational numbers are positive and negative whole numbers.
Answer:
d,e
Step-by-step explanation:
8.032×10^-4 in standard form
Answer:
0.0008032
Step-by-step explanation:
Hope this helps!
Answer:
80,320
Step-by-step explanation:
At 7:00 one Summer morning Harry and Hermione hopped into their speedy more motorboat and left Hogwarts dock. They arrived at Dumbledore Wharf 35 minutes later. During the busy summer months a car ferry departs from Dumbledore wharf every five minutes. Tourists crowd onto the ferry for the 55 minute ride to Hogswarts dock. If Harry and Hermione followed the route that the car ferries take, how many car ferries did they see on their trip?
9514 1404 393
Answer:
19
Step-by-step explanation:
If we assume that the car ferries start at or before 6:05, and each 5 minutes thereafter, and if we count the ferries at the dock on either end, the total number seen is the number of ferries encountered in ...
55 +35 = 90 . . . minutes
That is, it is the number already in transit when they leave, plus the number that start while they are traveling.
That's 90/5 +1* = 19 ferries.
_____
The attached diagram can give an idea. Each up-sloping line represents a ferry in-transit. The left side is Dumbledore Wharf; the right side is Hogwarts dock. Each horizontal unit represents the distance traveled by a ferry in 5 minutes. Each vertical unit represents a 5-minute interval.
The down-sloping line represents the motorboat travel. The dots at either end of the latter line represent car ferries that are at the dock, just arriving or just-departing. Altogether, there are 17 places where the lines cross, in addition to the boats at the docks.
__
* the +1 is because the number of points defining intervals is 1 more than the number of intervals.
What is the equation for calculating portion size?
Answer:
How to Easily Calculate the Serving Size in Recipes
Weigh the Food. Before you can accurately divide your recipe into servings, you need to know how much it weighs in total. ...
Divide the Recipe into Servings. ...
Calculate Calories. ...
Save the Information.
Step-by-step explanation:
How is 5 represented in 6.75
Answer:
5 is in the hundreths place :))
Step-by-step explanation:
Answer:
0.05
Step-by-step explanation:
since the place value of the five is beyond the decimal point, and it is the second number beyond the decimal point, so it is in the hundredths place.
A pharmaceutical sales representative gets paid $50,000 annually plus
3.5% commission on total sales. This year he sold $420,000 in
pharmaceuticals. What are his annual total earnings?
100% = $420,000
3.5% = 3.5/100 × 420,000
= $ 14,700
Commission he earned = $14,700
Annual total earnings= $50,000 + $14,700
= $ 64,700
Answer:
14,500
Step-by-step explanation:
An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower
Answer:
415 ft/s
Step-by-step explanation:
I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.
From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.
The constant elevation remains 4090 ft while the value of x and s varies with time.
Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.
Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s
Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.
This means that we want to find ds/dt when x = 3010 ft
From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;
s = √(4090² + 3010²)
s = √25788200
s ≈ 5078.21 ft
Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;
x² + 4090² = s²
Differentiating x and s with respect to t, we have;
2x(dx/dt) = 2s(ds/dt)
2 will cancel out to give;
x(dx/dt) = s(ds/dt)
ds/dt = (x/s)(dx/dt)
Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;
ds/dt = (3010/5078.21) × 700
ds/dt ≈ 415 ft/s
10
-25 please answer
Answer:
(-15)
Step-by-step explanation:
10-25 = (-15)
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The length of a rectangle is 10 meters more than the width. If 3 meters is added to both the length and the width, the new area will be 299 square meters. Find the length and width of the original rectangle.
HELP HELP HELP HELP
Answer:
L = 20
W = 10
Step-by-step explanation:
L = (w + 10)
NL = (w + 13)
Divide 299 by 13:
299 ÷ 13 = 23
So, 23 x 13 = 299
L = 23
W = 13
Subtract 3 from both to get the original length and width
O SYSTEMS OF EQUATIONS AND MATRICES
Solving a word problem using a 3x3 system of linear equations....
Over the last 3 evenings, Latoya received a total of 96 phone calls at the call center. The second evening, she received 2 times as many calls as the third
evening. The third evening, she received 8 fewer calls than the first evening. How many phone calls did she receive each evening?
Answer:
Find the midpoint of the line segment joining the points R(,) and S(,).
Step-by-step explanation:
mental math again 60x40x2
Answer:
the answer is 4800
Answer:
What is mental math?
Mental math is definitely what it sounds like—doing math in your head. But it’s also more nuanced than that. Being good at mental math tricks doesn’t mean that you’re able to solve 8974387 x 396 in your head instantly; while cool, that wouldn’t be very practical for daily life. So what does mental math mean?
It really just means being able to calculate in your head. It doesn’t mean you can solve every type of problem every time, nor is it a skill that you either “have” or “don’t have”; it’s a skill that you can learn, practice, and improve so that you can solve a bigger range of problems. And mental math certainly doesn’t have to be entirely in your head, either. Jotting down the numbers you need to remember to give you a head start (no pun intended), or writing down your solutions at each “step,” does not negate the “mental”-ness of the math.
Is mental math useful?
Ask this question again next time you’re trying to figure out a tip or doing any kind of construction or home improvement project! And, in addition to handy practical uses, knowing how to do mental math can also just keep your brain sharp and curb your reliance on calculators. Because, come on, doesn’t it feel good to reach for a calculator only to realize, “Wait, I don’t need it!” and figure out the answer in your head? (Spoiler: It does!) Not to mention knowing how to mentally solve small, simple math problems can save you some steps and help you out if you do need to solve a more complicated, difficult problem. There are always going to be some math problems that it would be silly to not solve with a calculator, but, yes, mental math is useful. And if you’re wondering if math itself is useful, math lessons you’ll actually use in real life.
Step-by-step explanation:
Leon was asked to repaint the sign for his mother's ice cream shop, so he needs to figure out how much paint he will need. Determine the area of the ice cream cone on the sign. Round to the nearest tenth. 6 in 12 in.
Answer:
50.1
The area of the composite figure is 50.1
Trust me
By the end of Tina’s bike ride, she traveled a distance of 40 kilometers. How many miles did Tina ride? (1 mile ≈ 1.6 kilometers)
help plz brainless you help me
Answer:
24.85 or rounded to 24.9
Step-by-step explanation:
Conversion
K H D____D C M
The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.
Calculation of the number of miles:Since
By the end of Tina’s bike ride, she traveled a distance of 40 kilometers.
And we know that
1 mile ≈ 1.6 kilometers
So,
[tex]= 40 \div 1.6[/tex]
= 25 miles
hence, The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.
Learn more about miles here: https://brainly.com/question/13208356
4 Rosie has 150 caramel
apples to sell. Each caramel apple is covered with one topping.
of the caramel apples are covered with peanuts.
are covered with chocolate chips.
• The rest are covered with sprinkles.
How many caramel apples are covered with sprinkles?
F
50
G 80
H 70
J 30
7.3B
Answer:
I'd say 50
Step-by-step explanation:
I just divided 150 by 3 since I only saw 3 toppings.
If paper clips are 7/8 of an inch long and cost $0.02 to make, how much would it cost to produce enough paper clips to make a line, end to end, that stretches 56 inches?
Answer:
$1.12
Step-by-step explanation:
When you multiply 8/7 of 56, you get 64.
This shows that you will need 64 paperclips to make 56 inches worth of paper clips. If each paper clip costs two cents, you need to multiply 56 paperclips by 2 cents. 56x0.02=1.12 so it will cost you 1 dollar and twelve cents
Which is the best description for the graph?
Answer:
decreasing, then increasing. the parabola decreases as it approaches the vertex, then increases afterward
* Pending
This map shows the organization that was
association of nearly 30 countrior
600 students are studying in a private
school, the average monthly fee of a
student is Rs. 1200. How much amount for
tax does the school pay to the government
as education service tax at the rate of 1% in
a year? *
Answer:
600 ×1200=720,000
720,000×12=8,640,000
8,640,000×1%=8,640,000÷100%=86,400
86,400 per year
Which shows another way to write 9.54?
O 0.5 + 0.04
O 9+ 0.4 + 0.05
O (9 * 1) + (5 x 0.1) + (4 x 0.01)
O (9 x 0.1) + (5 x 0.01) + (4 x 0.001)
Answer:
It would be C
Step-by-step explanation:
The average cost of a compact car at a certain dealership over the last 10 years has ranged from $15,000 to $24,500. Suppose you were going to plot these points on a coordinate grid. (a) What is a good scale [range] would be good to use for the y-axis to make a nicely sized graph? Explain your reasoning. (b) What is a good interval [step size] would be good to use for the y-axis to make a nicely sized graph? Explain your reasoning. (c) What is a good scale [range] would be good to use for the x-axis to make a nicely sized graph? Explain your reasoning. (d) What is a good interval [step size] would be good to use for the x-axis to make a nicely sized graph? Explain your reasoning. Note: The step size the distance between the marks on the graph, and the range is the maximum and minimum values (ex: -10 to 10).
Answer:
this is what i did i apologize if i’m late and u no longer need the answer or if i’m wrong
Step-by-step explanation:
Compare: -7 -4
PLEASE HELP ME!
Pure acid is to be added to a 10% acid solution to obtain 99L of a 20% acid solution. which amounts of each should be used ?
Answer:
x = amount of 100% acid solution (pure acid, no water)
y = amount of 10% acid solution (acid + water)
both amounts are in liters
Step-by-step explanation:
you just purchased new tennis shoes for basketball for $99 the cost for washing will be $2.00. you will wear them 110 times between basketball practice and games. what is the cost per wearing?
Answer:
Step-by-step explanation:
espera y termino y te ayudo vale que me falta poco vale
Find the Unit Rate.
216 diving students to 12 instructors
Answer: 216 diving students to 12 instructors = 18 students per instructor.
Step-by-step explanation:
20x+x-2=4 rational equation
Answer:
x = 2/7
Step-by-step explanation:
Step 1: Write equation
20x + x - 2 = 4
Step 2: Solve for x
Combine like terms: 21x - 2 = 4Add 2 to both sides: 21x = 6Divide both sides by 21: x = 6/21Simplify: x = 2/7Step 3: Check
Plug in x to verify it's a solution.
20(2/7) + 2/7 - 2 = 4
40/7 + 2/7 - 2 = 4
42/7 - 2 = 4
6 - 2 = 4
4 = 4
Answer:
x = 2/7
Step-by-step explanation:
Collect like terms:
20x + x = 21x ----> 21x - 2= 4
Move the constant to the right hand side and change the sign of the constant:
21x = 4 + 2
Calculate:
21x = 4 + 2 ---> 21x = 6
Divide both sides by 21:
21/21 and 6/21 = 2/7
Solution:
x = 2/7 or x= 0.285714