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.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
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.
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
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
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
↓↓↓↓↓↓↓↓↓↓↓
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
wendy weighs 8lb less than jean if jeans weight is p lb then what is an appropriate expression fir wendys weight
Answer:
p-8
Step-by-step explanation:
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?
Evaluate the expression 42+6⋅52−33÷32.
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
A teacher made a pair of foam dice to use in math games. Each cube measured 10 in. On a side. How many square inches of fabric were needed to cover the two cubes?
Final answer:
A teacher will require 1200 square inches of fabric to cover the surface area of two foam cubes, with each side measuring 10 inches.
Explanation:
The question involves finding the total surface area of two foam cubes to determine how much fabric a teacher needs to cover both cubes. To solve this, we must calculate the surface area of one cube and then multiply by two because there are two identical cubes. Each face of a cube measures 10 inches on a side.
The area of one face is given by:
Area of one face = side × side = 10 in × 10 in = 100 square inches
Since a cube has 6 faces, the total surface area of one cube would be:
Total surface area of one cube = 6 × Area of one face = 6 × 100 square inches = 600 square inches
Therefore, for two cubes, we need:
Total surface area for two cubes = 2 × 600 square inches = 1200 square inches
The teacher will require 1200 square inches of fabric to cover the two cubes.
What would happen to a monthly payment if the interest rate increased
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
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?
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.
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.
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 percent decrease occurs when a stock goes from 6.50 per share to 4.25 per share?
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
the length of rectangular garden is 5 feet longer than the width. If the are of the garden is 50 square feet, find the length and the width of the garden
Final answer:
To solve for the length and width of the garden, we set up a quadratic equation based on the given area and the relation between length and width. Upon solving the quadratic equation, we find the width to be 5 feet and the length to be 10 feet.
Explanation:
The problem states that the length of a rectangular garden is 5 feet longer than its width and that the area of the garden is 50 square feet.
To find the length and width, let's define the width as w feet. Therefore, the length will be w + 5 feet. The area of a rectangle is found by multiplying the length and width, so we have the equation:
w × (w + 5) = 50
Expanding this we get:
w^2 + 5w - 50 = 0
Now we need to solve this quadratic equation for w. Factoring the quadratic, we find that (w + 10)(w - 5) = 0, which gives us two possible solutions for w: -10 and 5.
Since a width can't be negative, we discard -10 and take w = 5 feet. So, the width of the garden is 5 feet and the length is 5 + 5 = 10 feet.
What’s the surface area of a rectangle if it’s 5 by 10 in
What is the value of x?
#2
a. 71
b. 142
c. 152
d. 76
#3
a. 68
b. 62
c. 112
d. 124
solve 5x<-10
help plz
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.
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:
https://brainly.com/question/14295570
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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’s 3 1/3 times 4 3/4
15a^2 + 14a -8 use A.C method
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.