Complete Question
A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4 pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci.
a) In testing the scientist's belief, write the appropriate hypotheses:
[tex]H_o:[/tex] Ha:
b) What decision should be made?
Answer:
a
The null hypothesis is [tex]H_o : \mu \le 4 \ pci[/tex]
The alternative hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]
b
There is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 4 \ pci[/tex]
The sample size [tex]n = 36 \ days[/tex]
The sample mean is [tex]\= x = 4.4 \ pci[/tex]
The standard deviation is [tex]\sigma = 1 \ pci[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 4 \ pci[/tex]
The alternative hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]
=> [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]
=> [tex]t =2.4[/tex]
The p-value is mathematically represented as
[tex]p-value = P(Z > 2.4 )[/tex]
From the z-table
[tex]P(Z > 2.4 ) = 0.008[/tex]
[tex]p-value =0.008[/tex]
So from this obtained value we see that
[tex]p-value < \alpha[/tex] so we reject the null hypothesis
Hence we can conclude that there is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
State the trigonometric substitution you would use to find the indefinite integral. Do not integrate. (25 + x2)−6 dx x(θ) =
Answer:
x(θ) = 5 tan θ
Step-by-step explanation:
Given that:
[tex]\int (25+x^2)^{-6} \ dx[/tex]
we are to state the trigonometric substitution to be used to find the indefinite integral.
Suppose u is the variable and a is the constant
u = x
a = 5
So; (a² + x²)ⁿ
which is a trigonometric substitution for x = a tanθ
Then,
x(θ) = 5 tan θ
In this exercise we have to use the knowledge of trigonometric substitution to calculate the indefinite integral, so we have that this is:
[tex]x(\theta) = 5 tan \theta[/tex]
Knowing that the indefinite integral corresponds to:
[tex]\int\limits {(25+x^2)^{-6}} \, dx[/tex]
we are to state the trigonometric substitution to be used to find the indefinite integral. Suppose u is the variable and a is the constant:
[tex]u = x\\a = 5\\(a^2 + x^2)^n[/tex]
Which is a trigonometric substitution for:
[tex]x = a tan\theta\\x(\theta) = 5 tan \theta[/tex]
See more about trigonometric substitution at brainly.com/question/21368433
Strawberries cost $21.25 for 4 pounds. Find the unit rate. Round to the nearest cent if necessary.
Answer:
$5.31/lb
Step-by-step explanation:
Since 4 pounds cost $21.25, 1 pound of strawberries will cost 21.25 / 4 ≈ 5.31, therefore, the unit rate is $5.31/lb.
Answer:
$5.31 per pound.
Step-by-step explanation:
$21.25 for so
%21.25/4= $5.31
The answer is $5.31 per pound.
.There is a 1/8 chance of a spinner landing on pink. Which statement is true? A. it is certain that the spinner lands on pink. B. it is impossible for the spinner to land on pink. C. it is likely that the spinner lands on pink. D. it is unlikely that the spinner lands on pink.
Answer:
it is unlikely that the spinner lands on pink.
Step-by-step explanation:
[tex]1- \frac{1}{8}\\ = 7/8[/tex]
There is 7/8 chance it is not going to land on pink
Ernie walked 1 1/4 miles from his cabin to a park, then 1 1/2 miles around the park, and then back to his cabin. How many miles did he walk
Answer:
4 miles
Step-by-step explanation:
1 1/4 there + 1 1/2 around + 1 1/4 back= 4 miles
1 x 10^12 = 9 x 10^8 (8/d^2) solve for d
Answer: Go here https://quickmath.com/webMathematica3/quickmath/equations/solve/basic.jsp
Step-by-step explanation:
It will show you how
Select all of the expressions that are not equivalent to ax+bx+ac+bc. A.) x(a+b)+c(a+b) B.) a(x+c)+b(x+c) C.) (b+a)(c+x) D.) ax+bc E.) (a+b)(x+c) F.) ab(x+c)
Answer:
C.) (b+a)(c+x) = True
E.) (a+b)(x+c) = True
Step-by-step explanation:
all others are not equal.
Less than 75% of workers got their job through internet resume sites. A researcher thinks it has increased.
Express the null and alternative hypotheses in symbolic form for this claim. For example, if you have 35%, enter it as 0.35.
H0: p H1: p
Use the following codes to enter the following symbols: ? enter >= ? enter <= ? enter ! =
Answer:
H0 : p = 0.75 against H1: p > 0.75 One tailed test.
Step-by-step explanation:
We state our null and alternative hypotheses as
H0 : p = 0.75 against H1: p > 0.75 One tailed test.
In this case H0 is not defined as p≤ 0.75 because the acceptance and rejection regions cannot be set up. Therefore we take the exact value of H0 : p= 0.75.
The claim is that the probability of the workers getting their job through the internet is greater than 75% or 0.75.
As H0 is supposed to be less than we choose H1 to be greater than equality.
Solve the following equation for D. Be sure to take into account whether a letter is
capitalized or not.
Dm3 + n=r
Answer: capitalized
Step-by-step explanation:
Solve for X.........
Answer:
Hey there!
There is this equation, which states that the angle created by an inscribed angle is half the measure of the arc.
Thus, we can write: 60=5x-5
65=5x
x=13
Let me know if this helps :)
Answer:
x= 13
Step-by-step explanation:
Inscribed Angle =1/2 Intercepted Arc
30= 1/2 (5x-5)
Multiply each side by 2
60 = 5x-5
Add 5 to each side
65 = 5x
Divide by 5
13 =x
Kevin mowed 12 lawns and earned a total of $60.
Which rate represents the amount of money earned per lawn?
Answer:
$5
Step-by-step explanation:
$60 earned for moving 12 lawns
Amount of money per lawn is:
$60/12= $5Answer is amount per lawn is $5
Answer:
$5
or
$5 / 1 lawn
Step-by-step explanation:
The process is quite simple - especially since you already have half of the answer. The question says money per lawn. The creator of the problem gave away a lot of the answer. They already tell us the rate. Now all ou have to do is plug the numbers in:
Money per lawn
Money / lawns (The slash is used to represent per)
What is the money? $60. So plug that in:
$60 / lawns
How many lawns? 12. Plug that in:
$60 / 12 lawns
Now, all you have to do is either simplify the fraction or divide the denominator by the numerator - whichever one you prefer. In that case, the rate can be any of the following:
$5
$5 / 1 lawn
Hope this helps! Tell me if I am wrong!
Use the figure to the right to find the value of PT. T is the midpoint of PQ PT=7x+9 and TQ=9x-5
Answer:
58
Step-by-step explanation:
Since, T is the mid point of PQ,
[tex] \therefore PT = TQ \\
7x + 9 = 9x - 5\\
9 + 5 = 9x - 7x\\
14 = 2x \\
\frac{14}{2} = x\\
7 = x \\
x = 7\\
PT = 7x + 9 = 7\times 7 + 9= 49 + 9 \\
PT= 58
[/tex]
yesterday,it's was negative 7 degrees Fahrenheit outside today, it is 14 degrees Fahrenheit warmer. Click on today's temperature
Answer:
Step-by-step explanation:
-7+14=7
D.7
Write down each of the following statement
using the symbol a and the constant of pro-
portionality, k.
(a) p is directly proportional to q.
(b) y varies directly as the square of x.
(c) y varies directly as the cube of x.
(d) T varies directly as the square root of l.
(e) y is directly proportional to the cube
root of x.
Step-by-step explanation:
Option (e) is the right answer.
Neal opened a savings account 11 years ago with a deposit of $2,335.69. The account has an interest rate of 4.3% compounded daily. How much interest has Neal earned? (3 points)
$1,412.52
$2,436.12
$1,375.75
$3,748.21
Answer: $1,412.52
Step-by-step explanation:
Formula to calculate the accumulated amount if P principal invested for t years at a rate of interest r that compounded daily is given by:-
[tex]A=P(1+\dfrac{r}{365})^{365t}[/tex]
Given: P= $2,335.69
r= 4.3%= 0.043
t= 11 years
Then,
[tex]A=2335.69(1+\dfrac{0.043}{365})^{365\times11}\\\\=2335.69(1+0.000117808219178)^{4015}\\\\=2335.69(1.000117808219178)^{4015}\\\\= 2335.69(1.6047566747)\\\\=3748.09044309\approx3748.21\\\\\Rightarrow\ A=\$3748.21[/tex]
Interest earned = A-P
= $3748.21- 2335.69.
= $1412.52
Hence, Neal earned $1,412.52 as interest.
If x + 4 is one factor of x3 + 64, what is the other factor?
Answer:
[tex]\Huge \boxed{(x^2 - 4x + 16)}[/tex]
Step-by-step explanation:
x³ + 64
64 is a perfect cube. Rewrite 64 as 4³.
x³ + 4³
Apply sum of cubes formula:
a³ + b³ = (a + b)(a² - ab + b²)a = x
b = 4
(x + 4)(x² - (x)(4) + 4²)
(x + 4)(x² - 4x + 16)
(x² - 4x + 16) is the other factor.
the location at which two lines, line segments, or rays intersect
Answer:
vertex
Step-by-step explanation:
took the assignment a bit ago
Solve the system by graphing
- 3x-y=2
solution (-2,0)
solution (0-2)
solution (2,0)
solution (02)
Answer:
(0,-2)
Step-by-step explanation:
Plug in each value for the equation
-3(0) - (-2) = 2
0 - (-2) = 2
2=2
The value 191.5638 rounded to the nearest hundredth is
191.564
191.5600
191.56
200
Answer:
191.56
Step-by-step explanation:
Given
191.5638
Required
Approximate
Approximating to the nearest hundredth implies that, only to digits after the decimal point is needed
This is:
191._ _
The third digit after the decimal point will approximated using the approximation rule;
Since, the third digit after the decimal point (3) is not up to 5, it'll be approximated to 0 and added to the second digit (6)
So, we have:
191.5 _
The next digit is calculated as 6 + 0 = 6
Hence, the full approximated number is 191.56
the temperature was -3° c last night. it is now -4° c. what was the change in temperature
Answer:
The temperature changed by -1 degrees C.
Step-by-step explanation:
-3 + -1 = -4
Answer:
The change was by 1°c
solu.
-3+-1=-4°c.
Combine the like terms to create an equivalent expression. 5x - x
Answer:
the answer is 4x
Step-by-step explanation:
you are subtracting 1x
Help me please!!! Weekly time card help. $11hr
Answer: 8hrs
Step-by-step explanation:
sam is baking cakes at her parents bakery. she gets paid $20 a week in addition to $4 for every cake she bakes. she made $60 this week. write an equation to show how many cakes sam baked this week
Answer:
She made 10 additional cakes
Step-by-step explanation:
x = additional cake
20 = base salary
y = 4x + 20
60 = 4(x) + 20
40 = 4(x)
x = 10
Solve for x x/5= 5 NEED TO KNOW FAST!!!! PLEASE
Answer:
x = 25
Step-by-step explanation:
Multiplying both sides by 5 (to get rid of the denominator) gives us:
x / 5 * 5 = 5 * 5
x = 25
flying against the wind, a jet travels 4600 miles in 5 hours. flying with the wind, the same jet travels 4200 miles in 3 hours. what is the rate of the jet in still air and what is the rate of the wind?
Answer:
The rate of the jet in still wind is 1160 MPH and the rate of the wind is 240 MPH.
Step-by-step explanation:
Distance equals rate times time (d = rt)
Against the wind, the rate is:
4600 = r * 5
r = 4600/5 = 920 MPH
With the wind, the rate is:
4200 = r * 3
r = 4200/3 = 1400 MPH
Let W be the rate of the wind in MPH. We know that:
(rate of the jet against the wind) + (rate of the wind) = (rate of the jet with the wind ) - (rate of the wind), so:
920 + W = 1400 - W
2W = 480
W = 240 MPH
And the speed of the jet in still air would be:
1400 - 240 = 1160 MPH
is -0.23 rational number whole number or integers
Answer:
rational number
Step-by-step explanation:
A whole number does not have a decimal part so it cannot be a whole number
Integers are whole numbers that are positive and negative plus zero
-.23 can be written as the ratio of integers
-23/ 100 so it is a rational number
Answer:
Rational
Step-by-step explanation:
A whole number does not have a decimal part so it cannot be a whole number
Integers are whole numbers that are positive and negative plus zero
-.23 can be written as the ratio of integers
-23/ 100 so it is a rational number
help fast plez 10 points
Answer:
Parallel lines are coplanar lines
Perpendicular lines are two coplanar lines that intersect at a right angle (90º).
Distance around an unmarked circle can NEVER be measured
So:
True
True
Never True
How to find solutions to Discriminat
Answer:
The discriminant is the expression b2 - 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. Based upon the sign of the expression, you can determine how many real number solutions the quadratic equation has. If you get a positive number, the quadratic will have two unique solutions
Step-by-step explanation:
hope it help
Answer:
D = b² - 4ac
Step-by-step explanation:
if,
ax² + bx + c = 0
What is the rule for this pattern? 8, 4, 2, 1 Divide by 2. Multiply by 2. Subtract 4. Add 4.
Answer:
divide by 2
Step-by-step explanation:
because if you subtract 4 -8 =you would get 4then 4-4=0 so eliminate subtract 4 and you can tell the number isnt going higher so you wouldnt add or multiply your welcome
Which inequality is graphed on the coordinate plane shown? image ab8c68c78ad542ac8b6ec0b7c3b7976f A y>2x−6 B y≥2x−6 C y<2x−6 D y≤2x−6
Answer:
D
Step-by-step explanation:
if the length of rectangle changes from 148.5cm to 144 cm. Find the percentage
change in the length.
Answer:
Original height = 144 cm
Increase height = 148.5 cm
Change in height = 148.5 - 144 = 4.5 cm
Percentage change = change/original ×100
= (4.5 / 148.5) × 100
= 3.03%
The height increased by 3.03%.
Step-by-step explanation:
Answer:
3%
Step-by-step explanation:
148.5 - 144 = 4.5
[tex]\frac{Difference}{Initial Amount}[/tex] × 100
[tex]\frac{4.5}{148.5}[/tex] × 100 = 3.03 ≈ 3%
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