There is a 20% probability that a person inoculated with a particular vaccine will get the disease anyway. a county health office inoculates 83 people. What is the probabythat exactly 10 of them will get the disease at some point their lives?
Answer: 0.021
Step-by-step explanation:
Given : The probability that a person inoculated with a particular vaccine will get the disease anyway. : p= 20%=0.20
The total people inoculates : n= 83
The binomial probability formula :-
[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that exactly 10 of them will get the disease at some point their lives :-
[tex]P(X)=^{83}C_{10}(0.2)^{10}(0.8)^{73}\\\\=\dfrac{83!}{10!(83-10)!}(0.2)^{10}(0.8)^{73}=0.0209841759622\approx0.021[/tex]
Hence, the probability that exactly 10 of them will get the disease at some point their lives =0.021
bernie and chloe hiked the tremont trail 3 1/2 miles to the end and back then they hiked the wildflower trail 2 3/8 miles how far did they hike
Final answer:
Bernie and Chloe hiked a total of 9 3/8 miles after completing the round trip on Tremont Trail and the Wildflower Trail.
Explanation:
Bernie and Chloe hiked the Tremont Trail which was 3 1/2 miles to the end and back, meaning they hiked 7 miles on this trail (since they had to return). After that, they hiked the Wildflower Trail, which was 2 3/8 miles long. To find out the total distance they hiked, you would add these two distances together.
The total distance for the Tremont Trail (to the end and back):
3 1/2 miles to the end + 3 1/2 miles back = 7 miles
The total distance for the Wildflower Trail:
2 3/8 miles
Adding both distances gives us:
7 miles (Tremont Trail) + 2 3/8 miles (Wildflower Trail) = 9 3/8 miles
Therefore, Bernie and Chloe hiked a total of 9 3/8 miles.
What’s the surface area of a rectangle if it’s 5 by 10 in
Franklin saved money to buy art supplies. He used 1/5 of his savings to buy brushes. He used 1/2 of his savings to buy paint. What fraction of his savings does he have remaining?
Answer is down below
↓↓↓↓↓↓↓↓↓↓↓
What would happen to a monthly payment if the interest rate increased
The diameter of small nerf balls manufactured at a factory in china is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. suppose a random sample of 20 balls is selected. find the interval that contains 95.44 percent of the sample means.
Answer:
The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches
Step-by-step explanation:
We need to understand the normal probability distribution and the central limit theorem to solve this question.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 5.2, \sigma = 0.08, n = 20, s = \frac{0.08}{\sqrt{20}} = 0.0179[/tex]
Find the interval that contains 95.44 percent of the sample means.
0.5 - (0.9544/2) = 0.0228
Pvalue of 0.0228 when Z = -2.
0.5 + (0.9544/2) = 0.9772
Pvalue of 0.9772 when Z = 2.
So the interval is from X when Z = -2 to X when Z = 2
Z = 2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2 = \frac{X - 5.2}{0.0179}[/tex]
[tex]X - 5.2 = 2*0.0179[/tex]
[tex]X = 5.2358[/tex]
Z = -2
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2 = \frac{X - 5.2}{0.0179}[/tex]
[tex]X - 5.2 = -2*0.0179[/tex]
[tex]X = 5.1642[/tex]
The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches
What percent decrease occurs when a stock goes from 6.50 per share to 4.25 per share?
Please help!!!!:
Mrs. Greenhaus has a six-sided number cube and a spinner. The number cube has the numbers 1 through 6 on its faces, and the spinner has four equal regions with blue, red, yellow, and green each in a different region. This tree diagram represents the outcomes of rolling the number cube and then spinning the spinner.
What is the probability of rolling an even number and landing on blue?
A.1/2
B.7/8
C.1/4
D.1/8
Last year, a person wrote 134134 checks. let the random variable x represent the number of checks he wrote in one day, and assume that it has a poisson distribution. what is the mean number of checks written per day? what is the standard deviation? what is the variance?
Sarah has read aloud in class 3 more times than Joel. Sarah has read 9 times. Which equation represents this situation?
A j + 3 = 9
B j − 9 = 3
C 3j = 9
D j − 3 = 9
The formula for finding the present value of an item that depreciates yearly is v = c - crt. In this formula, v is the present value, c is the original cost, r is the rate of depreciation per year, and t is the number of years that have passed. After 7 years, what is the value of a car originally costing $27,000 that depreciated at a rate of 0.1 per year
Final answer:
To calculate the present value of a car after 7 years, using the formula v = c - crt with the given values, the present value is $8,100.
Explanation:
The question involves finding the present value of a depreciating asset, in this case, a car. Using the provided formula v = c - crt where v is the present value, c is the original cost, r is the rate of depreciation per year, and t is the number of years, we can calculate the value of a car after a certain time period.
Given that the original cost c is $27,000, the rate of depreciation r is 0.1 (or 10%), and the time t is 7 years, we can substitute these values into the formula to find the present value of the car after 7 years. The calculation is as follows: v = $27,000 - ($27,000 × 0.1 × 7). Simplifying, we get: v = $27,000 - ($27,000 × 0.7) = $27,000 - $18,900 = $8,100.
What’s 3 1/3 times 4 3/4
If $7300 is invested in a savings account for which interest is compounded monthly, and if the $7300 turns into $8600 in 2 years, what is the interest rate of the savings account?
Answer:
8.22%
Step-by-step explanation:
The interest rate of the savings account is 8.22%
What is compound interest formula?[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]
where, A : Amount
P = Principal amount
r = Annual interest rate as a decimal
R = Annual interest rate as a percent
r = R/100
n = number of compounding periods per unit of time
t = time in decimal years
What is the formula to find the interest rate?[tex]r=n[(\frac{A}{P} )^{\frac{1}{nt} }-1][/tex]
For given question,
the principal amount (P) = $7300
the amount (A) = $8600
period (t) = 2
n = 12 (since it's monthly compounding)
To find 'r'
Using the formula of rate of interest,
[tex]\Rightarrow r=n[(\frac{A}{P} )^{\frac{1}{nt} }-1]\\\\\Rightarrow r=12\times [(\frac{8600}{7300} )^{\frac{1}{12\times 2} }-1]\\\\\Rightarrow r=12\times [(1.18)^{\frac{1}{24} }-1]\\\\\Rightarrow \bold{r=0.0822}[/tex]
The rate of interest in percentage form,
[tex]\Rightarrow R=r\times 100\\\\\Rightarrow R=0.0822\times 100\\\\\Rightarrow \bold{R=8.22\%}[/tex]
Therefore, the interest rate of the savings account is 8.22%
Learn more about compound interest here:
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HELP!!!
1. A machine makes bolts that are 12 mm long. The bolts are considered acceptable if they are within 0.2 mm of 12 mm.
a. What is the longest the bolt can be and still be acceptable?
b. What is the shortest the bolt can be and still be acceptable?
PLEASE HELP ME WITH THIS!!! Also make sure I can understand it it is also preferable to post a picture but either one will do thank you. (NEVER MIND I GOT IT IF YOU NEED IT JUST TELL ME)
What is the equation of the line?
y = 0 . . . . is the equation of the line.
_____
The line shows y to have the same value for every value of x. Thus the value of y is a constant, and there is no dependence on x at all. This is true for any horizontal line. Here, the constant value is zero, so the equation is ...
... y = 0
Round 9.098 to the nearest tenth.
Final answer:
To round 9.098 to the nearest tenth, we round up because the hundredths digit is 9, resulting in 9.1.
Explanation:
Rounding 9.098 to the nearest tenth:
Identify the tenths place in 9.098, which is 0.1.The digit immediately after the tenths place is 9, which is 5 or higher, so you need to round up.Therefore, when rounding 9.098 to the nearest tenth, the result is 9.1.Calculate the median of the data set below. {3, 7, 9, 2, 5, 3, 4, 6, 1, 0} A. 3 B. 3.5 C. 4 D. 10
Answer:
The median of the data set is 3.5 ⇒ answer (B)
Step-by-step explanation:
* Lats talk about the median of the data
- The median is the middle value of the arranged data
- You must to arrange the data at first to find the median
- The number of data is very important when you find the median
- If the number of data odd (1 , 3 , 5 , 7 , .....), then the median
will be the middle one of the data
* Ex: if the number of data is 13, then the median will be the 7th on
∵ 13 ÷ 2 = 6.5, then there are 6 numbers before and 6 number after
∴ The median is the 7th one
- If the number of data even (2 , 4 , 6 , 8 , .....), then there is no
middle on, we will find two numbers on the middle.
So we take the average of them
* Ex: if the number of data is 12, then the median will be the
average of the 6th and 7th numbers
* Lets use this conditions in our problem
- The data are 3 , 7 , 9 , 2 , 5 , 3 , 4 , 6 , 1 , 0
- At first arrange the data
* 0 , 1 , 2 , 3 , 3 , 4 , 5 , 6 , 7 , 9
- The number of data is 10
∵ 10 ÷ 2 = 5
∴ The median will be the average of the 5th and 6th numbers
∵ The 5th number is 3 and the 6th number is 4
∴ The median = (3 + 4)/2 = 3.5
* The median of the data set is 3.5
Answer:
c
Step-by-step explanation:
got it right on edge
A coin is loaded so that the probability of heads is 0.55 and the probability of tails is 0.45. suppose the coin is tossed twice and the results of the tosses are independent. what is the probability of obtaining exactly one head?
What is 1/x divided by 1/y equal to ?
Final answer:
To calculate 1/x divided by 1/y, you multiply 1/x by the reciprocal of 1/y, which is y, resulting in y/x.
Explanation:
The question asks us to find the value of 1/x divided by 1/y. This is a division problem involving fractions and can be solved using the rules of division for fractions.
To divide one fraction by another, we multiply the first fraction by the reciprocal of the second. In this case, the reciprocal of 1/y is y/1 which simplifies to y. Therefore, the division 1/x ÷ 1/y becomes 1/x × y.
When we multiply these together, we get:
So, the answer is y/x.
A line of best fit predicts that when x equals 25, y will equal 27.745, but y actually equals 29. What is the residual in this case? A. 1.255 B. -1.255 C. -2.745 D. 2.745
Answer:
The correct option is A.
Step-by-step explanation:
From the given information it is clear that at x=25, the predicted value of y is 27.745 and the actually value is 29.
Predicted value = 27.745
Observed value = 29
The formula for residual is
Residual = Observed value - predicted value
[tex]Residual=y-\hat{y}[/tex]
[tex]Residual=29-27.745[/tex]
[tex]Residual=1.255[/tex]
The residual in this case is 1.255, therefore option A is correct.
The residual is 1.255.
Explanation:The residual is the difference between the actual y-value and the predicted y-value for a given x-value. In this case, the predicted y-value when x equals 25 is 27.745, but the actual y-value is 29. Therefore, the residual is calculated by subtracting the predicted value from the actual value: 29 - 27.745 = 1.255. So, the answer is A. 1.255.
Evaluate the expression 42+6⋅52−33÷32.
The diagram below shows a process in earths crust which of the following statements best describes the process in the diagram
The layer with a plastic nature is the mantle (Layer C). The rocks in the mantle can deform and flow over long periods due to heat and pressure, giving them a plastic-like quality. This deformation is crucial for the movement of tectonic plates and various geological processes on Earth.
The Earth is composed of several layers, each with distinct properties and compositions. Starting from the center and moving outward, the major layers are:
Inner Core (Layer A):
The innermost layer is solid and composed mainly of iron and nickel. It is extremely hot, with temperatures reaching up to 9,000 degrees Fahrenheit (5,000 degrees Celsius). Despite the high temperature, the inner core remains solid due to intense pressure.
Outer Core (Layer B):
Surrounding the inner core is the outer core, which is also composed of molten iron and nickel. However, in the outer core, these materials are in a liquid state. The movement of the molten metal in this layer generates the Earth's magnetic field through the geodynamo process.
Mantle (Layer C):
Above the outer core is the mantle, a thick layer of solid rock that can flow slowly over geological timescales. The mantle is mostly composed of silicate minerals rich in iron and magnesium. The convection currents in the mantle are responsible for the movement of tectonic plates.
Crust (Layer D):
The outermost layer is the Earth's crust, which is relatively thin compared to the other layers. The crust is composed of solid rock and is divided into two types: the continental crust (found beneath continents) and the oceanic crust (found beneath oceans). The crust is where we find the solid ground we walk on.
The layer with a plastic nature is the mantle (Layer C). The rocks in the mantle can deform and flow over long periods due to heat and pressure, giving them a plastic-like quality. This deformation is crucial for the movement of tectonic plates and various geological processes on Earth.
The complete question is:
The diagram below shows four layers of the Earth.
Source:
Which of these layers is composed of materials with a plastic nature?
Layer A
Layer B
Layer C
Layer D
The layer with a plastic nature is the mantle (Layer C). The rocks in the mantle can deform and flow over long periods due to heat and pressure, giving them a plastic-like quality. This deformation is crucial for the movement of tectonic plates and various geological processes on Earth.
The Earth is composed of several layers, each with distinct properties and compositions. Starting from the center and moving outward, the major layers are:
Inner Core (Layer A):
The innermost layer is solid and composed mainly of iron and nickel. It is extremely hot, with temperatures reaching up to 9,000 degrees Fahrenheit (5,000 degrees Celsius). Despite the high temperature, the inner core remains solid due to intense pressure.
Outer Core (Layer B):
Surrounding the inner core is the outer core, which is also composed of molten iron and nickel. However, in the outer core, these materials are in a liquid state. The movement of the molten metal in this layer generates the Earth's magnetic field through the geodynamo process.
Mantle (Layer C):
Above the outer core is the mantle, a thick layer of solid rock that can flow slowly over geological timescales. The mantle is mostly composed of silicate minerals rich in iron and magnesium. The convection currents in the mantle are responsible for the movement of tectonic plates.
Crust (Layer D):
The outermost layer is the Earth's crust, which is relatively thin compared to the other layers. The crust is composed of solid rock and is divided into two types: the continental crust (found beneath continents) and the oceanic crust (found beneath oceans). The crust is where we find the solid ground we walk on.
The layer with a plastic nature is the mantle (Layer C). The rocks in the mantle can deform and flow over long periods due to heat and pressure, giving them a plastic-like quality. This deformation is crucial for the movement of tectonic plates and various geological processes on Earth.
The question probable maybe: The diagram below shows four layers of the Earth.
Which of these layers is composed of materials with a plastic nature?
Layer A
Layer B
Layer C
Layer D
5(2x − 3) = 5
Part A: How many solutions does this equation have?
Part B: What are the solutions to this equation? Show your work.
for Owens lemonade recipe, 6 lemons are required to make 5 cups of lemonade?express your answer in simplest form.
plz help
solve 5x<-10
help plz
Which conversion requires division? Use the metric table to help answer the question.
Answer:
Decigrams to Decagrams/Dekagrams
Step-by-step explanation:
1 decigram is equal to 0.01 Deca/Dekagrams
Decigrams have less value than Decagrams.
Therefore,
You divide 1 decigram by 100 to get 0.01 decagrams.
Suppose heights of 20-year-old men are approximately normally distributed with a mean of 71 in. and a population standard deviation of 5 in. a random sample of twenty 20-year-old men is selected and measured. find the probability that the sample mean x lies between 68 and 74 inches.
true Value Hardware buys 200 snow blowers for $90 each to stock the store for the winter. If True Value sells the 200 snow blowers at $120 each, what is the profit?
What is the value of x?
#2
a. 71
b. 142
c. 152
d. 76
#3
a. 68
b. 62
c. 112
d. 124