Answer:
15
Step-by-step explanation:
4! +3! /2
4!=4*3*2*1=24
3!=3*2*1=6
24+6/2=30/2=15
"Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L). 1.92.45.75.51.98.23.96.9 (a) Find the mean, median, and mode. (Round your answers to two decimal places.) mean 4.55 median 4.7 mode 1.9 (b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.) s CV % range (c) Based on the data, would you recommend radon mitigation in this house
Answer:
a) Mean = 4.55
Median = 4.7
Mode = 1.9
b) S = 2.3952
CV = 52.64 %
Range = 6.3
c) Yes, since the average and median values are both over "acceptable" ranges.
Step-by-step explanation:
Explanation is provided in the attached document.
P(x)=2x^5+9x^4+9x^3+3x^2+7x-6;x=i,-2
Answer:
The value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.
Step-by-step explanation:
We are given with the following polynomial function below;
[tex]\text{P}(x) = 2x^{5} +9x^{4} +9x^{3} +3x^{2}+7x-6[/tex]
Now, we have to calculate the value of P(x) at x = 1 and x = -2.
For this, we will substitute the value of x in the given polynomial and find it's value.
At x = 1;
[tex]\text{P}(1) = 2(1)^{5} +9(1)^{4} +9(1)^{3} +3(1)^{2}+7(1)-6[/tex]
[tex]\text{P}(1) = (2\times 1) +(9\times 1)+(9 \times 1)+(3\times 1)+(7\times 1)-6[/tex]
[tex]\text{P}(1) = 2 +9+9+3+7-6[/tex]
P(1) = 30 - 6
P(1) = 24
At x = -2;
[tex]\text{P}(-2) = 2(-2)^{5} +9(-2)^{4} +9(-2)^{3} +3(-2)^{2}+7(-2)-6[/tex]
[tex]\text{P}(-2) = (2\times -32) +(9\times 16)+(9 \times -8)+(3\times 4)+(7\times -2)-6[/tex]
[tex]\text{P}(-2) = -64 +144-72+12-14-6[/tex]
P(-2) = 156 - 156
P(-2) = 0
Hence, the value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.
simplify 2.5a–7–6.8a+11.1
Answer:
-4.3a + 4.1
Step-by-step explanation:
Well in the given expression,
2.5a - 7 - 6.8a + 11.1
We need to combine like terms,
2.5a + -6.8a = -4.3a
-7 + 11.1 = 4.1
Ans: -4.3a + 4.1
Thus,
the answer is -4.3a + 4.1
Hope this helps :)
The simplification form of given expression is -4.3a + 4.1
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
The given expression,
⇒ 2.5a - 7 - 6.8a + 11.1
Combine like terms in expression,
⇒ 2.5a - 6.8a + 11.1- 7
Apply the arithmetic operations
⇒ -4.3a + 4.1
Hence, the simplification form of given expression is -4.3a + 4.1
Learn more about Arithmetic operations here:
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The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is as follows:
Houses Sold (x) Probability P(x)
0 0.24
1 0.01
2 0.12
3 0.16
4 0.01
5 0.14
6 0.11
7 0.21
Find the mean of the given probability distribution.
A. μ = 3.35
B. μ = 3.50
C. μ = 3.60
D. μ = 3.40
Answer:
C. μ = 3.60
Step-by-step explanation:
Two tables have been attached to this response.
One of the tables contains the given data and distribution with two columns: Houses Sold and Probability
The other table contains the analysis of the data with additional columns: Frequency and Fx
=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,
When the number of houses sold = 0
F = P(0) x Total number of houses sold
F = 0.24 x 28 = 6.72
When the number of houses sold = 1
F = P(1) x Total number of houses sold
F = 0.01 x 28 = 0.28
=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,
When the number of houses sold = 0
Fx = F * x
F = 6.72 x 0 = 0
Now to get the mean, μ we use the relation;
μ = ∑Fx / ∑F
Where;
∑Fx = summation of the items in the Fx column = 100.8
∑F = summation of the items in the Frequency column = 28
μ = 100.8 / 28
μ = 3.60
Therefore, the mean of the given probability distribution is 3.60
The mean of the discrete probability distribution is given by:
C. μ = 3.60
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:
[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]
Hence option C is correct.
More can be learned about the mean of discrete distributions at https://brainly.com/question/24855677
A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 11% chose chocolate pie, and the margin of error was given as plus or minus5 percentage points. What values do ModifyingAbove p with caret, ModifyingAbove q with caret, n, E, and p represent? If the confidence level is 95%, what is the value of alpha?
Answer:
[tex]\r p = 0.11[/tex]
[tex]\r q = 0.89[/tex]
n = 2000
[tex]E = \pm 5[/tex]
p - population proportion
[tex]\alpha = 5[/tex]%
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 2000[/tex]
The proportion of the population for chocolate pie is [tex]p_c = 0.11[/tex]
The margin of error is [tex]E = \pm 5[/tex]%
Now in the question we are asked to provide the meaning of
[tex]\r p , \r q , n , E , and\ p[/tex]
Now [tex]\r p[/tex] is the sample proportion of the population that those chocolate pie as favorite pie of which is given from the question as 0.11
Now
[tex]\r q[/tex] is the sample proportion of the population that choose other pies apart from chocolate pie as their favorite and it is evaluated as
[tex]\r q = 1 - \r p[/tex]
[tex]\r q = 1 - 0.11[/tex]
[tex]\r q = 0.89[/tex]
n is the sample size which is given as n = 2000
E is the margin of error which given as [tex]E = \pm 5[/tex]%
p is the population proportion
Given that the confidence level is 95 % then the level of significance is mathematically evaluated as
[tex]\alpha =(100 - 95)[/tex]%
[tex]\alpha =[/tex]5%
The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the slips are placed into a hat. If the slips are drawn randomly without replacement, what is the probability that "E" is drawn first and "B" is drawn second?
Answer:
1/30
Step-by-step explanation:
The probability of getting ”E” is 1/6.
There is only 1 “E” out of 6 letters.
There is no replacement.
There are now 5 letters without “E”.
”A”, “B”, “C”, “D”, “F”
The probability of getting ”B” is 1/5.
There is only 1 “B” out of 5 letters.
⇒ 1/6 × 1/5
⇒ 1/30
Which of the following shapes can NOT be created by revolving a two-dimensional figure around an axis? There can be more than 1. A. come B. cube C. Rectangular pyramid D. Rectangular Prism E. Cylinder F. Sphere
PLEASE HELP
Answer:
A. Cone
D. Rectangular Prism
E. Cylinder
F. Sphere
Step-by-step explanation:
Rectangular Prism is a solid three dimensional shape. It has six faces which are sides of a rectangle. It is also known as Cuboid. The rectangular prism cannot be formed with two dimensional shapes. Sphere is a geometrical object which is a three dimensional circle. This shape has a circumference so this shape cannot be formed with two dimensional shapes.
helppppppppp pleaseeeeeeeeeeeeeee
Answer:
Number is yellow box=3
Step-by-step explanation:
We know this because the way we get that number is subtracting the two numbers above it, which is 8 and 5, which give us 3.
if you appreciated this, please consider giving me brainliest, it will help me a lot
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solve for the inequality ᵏ⁄₄ ≥ 6
Answer:
k ≥ 24
Step-by-step explanation:
ᵏ⁄₄ ≥ 6
Multiply each side by 4
ᵏ⁄₄ *4 ≥ 6*4
k ≥ 24
Answer:
k≥24
Step-by-step explanation:
k/4≥6
Use the multiplication property of equality by multiplying both sides by 4 to get
k≥24
If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem
Thank you
A cash register has $10 and $50 dollars bills with total of $1080.there are 28 bills in total how many of each bills.
Hey there! I'm happy to help!
Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.
10x+50y=1080
x+y=28
We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.
x+y=28
Subtract x from both sides.
y=28-x
Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.
10x+50(28-x)=1080
We use distributive property to undo the parentheses.
10x+1400-50x=1080
We combine like terms.
-40x+1400=1080
We subtract 1400 from both sides.
-40x=-320
We divide both sides by -40.
x=8
Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.
Have a wonderful day! :D
1. What are foci? 2. What is the first step to take to write the equation of a hyperbola? 3. How do you represent parts of a hyperbola algebraically?
Answer: see below
Step-by-step explanation:
1) Foci is plural for Focus. Since a hyperbola has two focus points, they are referred to as foci. The foci is where the sum of the distances from any point on the curve to the foci is constant.
2) When determining the equation of a hyperbola you need the following:
a) does the hyperbola open up or to the right?
b) what is the center (h, k) of the hyperbola?
c) What is the slope of the asymptotes of the hyperbola?
3) The equation of a hyperbola is:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]
(h, k) is the center of the hyperbola± b/a is the slope of the line of the asymptotesThe equation starts with the "x" if it opens to the right and "y" if it opens upFind the volume of the figure below. Round to the nearest tenth.
7 cm
7 cm
9 cm
20 cm
11 cm
Answer:
3057.6 cm³
Step-by-step explanation:
You have a cylinder and a rectangular prism. Solve for the area of each separately.
Cylinder
The formula for volume of a cylinder is V = πr²h. The radius is 7, and the height is 7.
V = πr²h
V = π(7)²(7)
V = π(49)(7)
V = 343π
V = 1077.57 cm³
Rectangular Prism
The formula for volume of a rectangular prism is V = lwh. The length is 20, the width is 11, and the height is 9.
V = lwh
V = (20)(11)(9)
V = (220)(9)
V = 1980 cm³
Add the areas of the two shapes.
1077.57 cm³ + 1980 cm³ = 3057.57 cm³
Round to the nearest tenth.
3057.57 cm³ ≈ 3057.6 cm³
WHOEVER ANSWERS FIRST GETS BRAINLIEST:) Which expression represents the surface area of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. S A = pi r l + pi r squared (pi) (6) (10) + (pi) (6 squared) (pi) (8) (10) + (pi) (8 squared) (pi) (12) (10) + (pi) (12 squared) (pi) (10) (12) + (pi) (10 squared)
Answer:
Step-by-step explanation:
The surface area of a cone is:
● Sa = Pi*r^2 +Pi*r*l
r is the radius and l is the slant heigth
The diameter of this cone is 12 inches so the radius is 6 (12/2=6).
●Sa = Pi*36 +Pi*6*10
●Sa = 301.59 in^2
Answer:
pi (6) * 10+ pi ( 6)^2
Step-by-step explanation:
The surface area of a cone is given by
SA = pi rl +pi r^2 where r is the radius and l is the slant height
We know the diameter is 12 so the radius is 12/2 = 6
SA = pi (6) * 10+ pi ( 6)^2
What is the range of y=log2(x-6)
Answer:
6<y<∞
Step-by-step explanation:
Logarithmic curves can never go left to 0 and go on forever to the right.
x=6 would make the function 0, so 6 is the lower limit and infinity would be the upper limit.
In how many ways can 13 people be divided into four groups with 3, 6, 2 and 2 people respectively?
Answer:
6227020800
Step-by-step explanation:
There are 13 ways to choose the first person in the first group, 12 ways to choose the second person in the first group and so on until we get 1 way to choose the second person in the last group so the answer is 13 * 12 * 11 * ... * 3 * 2 * 1 = 13! = 6227020800.
The perimeter of a rectangular field is 344m . If the width of the field is 75m, what is its length?
Answer:
97 m
Step-by-step explanation:
Perimeter = 2 * (length + width); perimeter = 344, width = 75 (solving for length)
344 = 2(length + 75)
172 = length + 75
length = 97
The circumference of C is 72cm. What is the length of AB (the minor arc)
Answer:
Step-by-step explanation:
Can you please include a image?
Thanks!!!
A father's age is 4 times as that of his son's age. in 5 years time, the father will be 3 times as old as his son. what are their present ages?
Answer:
present age of son = 10 present age of father = 40Step-by-step explanation:
Let, present age of son be 'x'
present age of father be 'y'
y = 4x→ equation ( i )
After five years,
Son's age = x + 5
father's age = y + 5
According to Question,
[tex]y + 5 = 3(x + 5)[/tex]
Put the value of y from equation ( i )
[tex]4x + 5 = 3(x + 5)[/tex]
Distribute 3 through the parentheses
[tex]4x + 5 = 3x + 15[/tex]
Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S. and change its sign
[tex]4x - 3x = 15 - 5[/tex]
Collect like terms
[tex]x = 15 - 5[/tex]
Calculate the difference
[tex]x = 10[/tex]
Now, put the value of X in equation ( i ) in order to find the present age of father
[tex]y = 4x[/tex]
plug the value of X
[tex] = 4 \times 10[/tex]
Calculate the product
[tex] = 40[/tex]
Therefore,
Present age of son = 10
present age of father = 40
Hope this helps..
Best regards!!
I need some help, see the picture for the question. Solve for V
Answer:
the answer is A) h=3V/(Pi*r^2)
Step-by-step explanation:
This question is asking to solve for h, the equation is allready solved for V.
to solve for h means to get h by itself on one side of the equation.
1) V=(1/3)*pi*r^2*h. Divide 1/3*pi*r^2 to the other side of the equation
2) V/(1/3)*pi*r^2=h. 1/3 on the bottom denominator means we can multiply the reciprocal to the bottom and the top and get an equivalent answer. In short, move the 3 from the 1/3 onto the top.
3) (3*V)/(pi*r^2)=h. Simplify.
4) 3V/(Pi*r^2)=h.
calculate the value of angle A to one decimal place. Picture Attached
Answer:
[tex] A = 50.7 [/tex] (to nearest tenth)
Step-by-step explanation:
Use the Law of Cosines to find the value of angle A as follows:
[tex] cos(A) = \frac{b^2 + c^2 - a^2}{2*b*c} [/tex]
Where,
a = 7 in
b = 5 in
c = 9 in
Plug in the values into the formula
[tex] cos(A) = \frac{5^2 + 9^2 - 7^2}{2*5*9} [/tex]
[tex] cos(A) = \frac{57}{90} [/tex]
[tex] cos(A) = 0.6333 [/tex]
[tex] A = cos^{-1}(0.6333) [/tex]
[tex] A = 50.7 [/tex] (to nearest tenth)
less than 0 but greater than (−5)
Answer:
-5 < x < 0
Step-by-step explanation:
i have to write equations in standard form using integer coefficients for A,B, and, C Example: y= -8/15x + 1/20
Answer:
c
Step-by-step explanation:
how many solutions does this linear system hacve y=2/3x+2 6x-4y=-10
Answer:
the linear system has two valid solution.
Answer:one solution
Step-by-step explanation:
Find two numbers in a given ratio such that the difference of their squares is to the sum of the numbers in a given ratio.Ratios, respectively, are 3 to 1 and 6 to 1.
According to the given situation, the computation of two number in a given ratio is shown below:-
We assume the numbers is x and y
Given that
[tex]\frac{x}{y} = \frac{3}{1}[/tex]
x = 3y
and
[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]
With the help of above formula we will put the value and be able to find the values of x and y
x - y = 6
3y - y = 6
2y = 6
y = 3
x = 3y = 9
x = 9, y = 3
Therefore the correct answer is x = 9 where as y = 3
An ice sculpture is melting at a constant rate. It's weight changes -1 4/5 pounds every hour. What is the total change in weight of the sculpture after 3 1/2 hours?
Answer:
It will decrease by 6 3/10 lbs in the 3 1/2 hours
Step-by-step explanation:
The rate is -1 4/5 lbs per hour
The time is 3 1/2 hours
Multiply to find the weight change
-1 4/5 * 3 1/2
Change to improper fractions
- ( 5*1 +4) /5 * ( 2* 3+1)/2
- 9/5 * 7/2
-63/10
Changing back to a mixed number
-6 3/10
It will decrease by 6 3/10 lbs in the 3 1/2 hours
Answer:
-6 3/10 pounds
Step-by-step explanation:
The weight of ice sculpture changes -1 4/5 pounds every 1 hour.
In 3 1/2 hours, multiply the time with the weight.
-1 4/5 × 3 1/2
Multiply.
-9/5 × 7/2
-63/10 = -6 3/10
What is the value of the fourth term in a geometric sequence for which a1 =
30 and r= 1/2
Answer:
3¾
Step-by-step explanation:
Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.
Formula for geometric sequence:
[tex] a^n = a ( n-1 ) * r [/tex]
Given:
First term, a1 = 30
ratio, r = ½
Required:
Find the fourth term
Where, the first term, a¹ = 30
Second term: a² = 30 * ½ = 15
Third term: a³ = 15 * ½ = 7.5
Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾
Therfore the fourth term of the geometric sequence is 3¾
What is the range of the function f(x)=3/4|x|-3
Range is [tex]y\in[-3,+\infty)[/tex].
Hope this helps.
A manufacturer claims that its rechargeable batteries are good for an average of more than 1.000 charges. A random sample of 100 batteries has a mean life of 1002 charges and a standard deviation of 14. Is there enough evidence to support this claim at a significance level of 0.01?
a. State the hypotheses.
b. State the test statistie information
c. State either the p-value or the critical information d. State your conclusion and explain your reasoning
It's 1000 charges and not 1.000 charges
Answer:
A)Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = 1.4286
C) p-value = 0.15628
D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges
Step-by-step explanation:
We are given;
x = 1002 charges
s = 14
μ = 1000 charges
n = 100
degree of freedom = n - 1 = 100 - 1 = 99
A) The hypotheses are;
Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = (x - μ)/(s/√n)
(1002 - 1000)/(14/√100) = 1.4286
C) From the t-score calculator results attached, the p-value is approximately 0.15628
D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.
How many solutions does the following equation have? 14(z+3)=14z+21
Answer:
No solutions
Step-by-step explanation:
14(z + 3) = 14z + 21
Expand brackets.
14z + 42 = 14z + 21
Subtract 14z on both sides.
42 = 21
There are no solutions.
Answer:
No solution
Step-by-step explanation:
First, We have to simplify the right side.
Distribute 14, 14z+42.
Now the equation stands as 14z+42=14z+21
Subtract 14z from both sides,
this makes it 42=21.
We know when the solution is #=#, our answer is no solution.
Based on the dot plot, which statements are correct? Check all that apply
Eleven students answered Mr. Chiu's question.
Twelve students answered Mr. Chiu's question.
Three people studied for two hours.
Three people studied for three hours.
Everyone who responded studied for at least one hour.
Four people studied for four or more hours
Answer: options 2,3and 6
Answer:
option
2-Twelve students answered Mr. Chiu’s question.
3-Three people studied for two hours.
6-Four people studied for four or more hours.
Step-by-step explanation:
hope this helps:)