Answer:
The probability is [tex]P(\= X > 103.7 ) = 0.9862 [/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 106 \ gallons[/tex]
The population standard deviation is [tex]\sigma = 6 \ gallons[/tex]
The sample size is [tex]n = 33[/tex]
Generally the standard deviation of sample mean is mathematically represented as
[tex]\sigma_{x} = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{6}{\sqrt{33} }[/tex]
=> [tex]\sigma_{x} = 1.044[/tex]
Generally the probability that the sample mean would be greater than 103.7 gallons is mathematically represented as
[tex]P(\= X > 103.7 ) = P(\frac{X - \mu }{\sigma_{x}} > \frac{103.7 - 106}{1.044 } )[/tex]
Generally [tex]\frac{X - \mu }{\sigma_{x}} = Z (The \ standardized \ value \ of \= X )[/tex]
So
[tex]P(\= X > 103.7 ) = P(Z > -2.203 )[/tex]
From the z table the probability of (Z > -2.203 ) is
[tex]P(Z > -2.203 ) = 0.9862[/tex]
So
[tex]P(\= X > 103.7 ) = 0.9862 [/tex]
At a bargain store, Spongebob bought 3 items that each cost the same amount. Patrick bought 5 items that each cost the same amount, but each was $1.50 less than the items that Spongebob bought. Both Spongebob and Patrick paid the same amount of money. What was the individual cost of each person's items?
Write an equation. Let x represent the cost of one of Spongebob's items.
Solve the equation. Show your work.
Check your solution. Show your work.
State the solution in complete sentences.
Answer:
Cost of each item bought by Spongebob [tex]=x=\$3.75[/tex]
Cost of items bought by Spongebob = [tex]3x=3(3.75)=\$11.25[/tex]
Cost of each item bought by Patrick [tex]=x-1.50=3.75-1.50=\$2.25[/tex]
Cost of items bought by Patrick = [tex]5(x-1.50)=5(3.75-1.50)=\$11.25[/tex]
Step-by-step explanation:
Let [tex]x[/tex] denotes cost of each item bought by Spongebob.
Number of items bought by Spongebob = 3
So,
Cost of items bought by Spongebob = [tex]3x[/tex]
Cost of each item bought by Patrick = [tex]x-1.50[/tex]
Number of items bought by Patrick = 5
Cost of items bought by Patrick = [tex]5(x-1.50)[/tex]
Both Spongebob and Patrick paid the same amount of money.
So,
[tex]3x=5(x-1.50)\\3x=5x-7.5\\5x-3x=7.5\\2x=7.5\\x=\frac{7.5}{2} \\x=3.75[/tex]
So,
Cost of each item bought by Spongebob [tex]=x=\$3.75[/tex]
Cost of items bought by Spongebob = [tex]3x=3(3.75)=\$11.25[/tex]
Cost of each item bought by Patrick [tex]=x-1.50=3.75-1.50=\$2.25[/tex]
Cost of items bought by Patrick = [tex]5(x-1.50)=5(3.75-1.50)=\$11.25[/tex]
If 5% more than a is b, and b is 15% less than, what is the ratio of a to c? Please answer quickly.
Is 40 cm equal to 4 m?
Answer:
There are 100 centimetres in one metre. Therefore, 4 metres is equal to 4 x 100 = 400 centimetres. This is longer than 40 centimetres.
Need help like ASAP
Select the correct answer.
Each side of a square is
(st
5) units. Which expression can be used to represent the area of the square?
22 - 50 - 10
I2 – 50 + 10
2 – 100 - 25
22 - 10x + 25
Answer:
D.) x²-10x+25 sq. units
Step-by-step explanation:
The question is not properly written. The question should have been:
If each side of a square is (x-5) units, which expression can be used to represent the area of the square.
Area of a square = L² where:
L is the length of the square
Given
L = x-5
Required
Area of the square
Substitute the given function into the formula to get the required as shown:
Area of the square = (x-5)²
Expand
A(x) = (x-5)(x-5)
A(x) = x(x)-5x-5x-5(-5)
A(x) = x²-10x-25
Hence the area of the square is (x²-10x+25)sq. units. Option D is correct.
PLEASE HELP
Select the correct answer from each drop-down menu. Options are (equal to, not equal to)
Answer:
Not equal to.
Step-by-step explanation:
1. Amy Lynn's Kitchen offers a breakfast
special. Customers have a choice of fried,
poached, scrambled, or soft-boiled eggs;
bacon or sausage; hash browns or grits; and
cornbread or biscuits. How many breakfast
combinations does Amy Lynn serve?
F. 8
G. 10
H. 16
J. 32
Answer: F
Step-by-step explanation: Amy lynn's kitchen offers a variety of breakfast specials, there are four choices for customers to choose from, but each choice has a combination. Which makes it 8 combinations Amy Lynn' serves
Pieces of Mail. The number of pieces of mail
handled by the U.S. Postal Service decreased from
212 billion in 2007 to 168 billion in 2011. What is the
percent decrease?
Answer:
20.8%
Step-by-step explanation:
The number of the pieces of mail handled by the U.S postal service decreased from 212,000,000,000 to 168,000,000
Therefore the percentage decrease can be calculated as follows
= 212,000,000,000-168,000,000,000
= 44,000,000,000/212,000,000,000 × 100
= 0.2075 × 100
= 20.8 %
Hence the percentage decrease is 20.8%
how do you solve for x
-3x-6y=0
Answer:
x = 2y
Step-by-step explanation:
Simplifying
3x + -6y = 0
Solving
3x + -6y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6y' to each side of the equation.
3x + -6y + 6y = 0 + 6y
Combine like terms: -6y + 6y = 0
3x + 0 = 0 + 6y
3x = 0 + 6y
Remove the zero:
3x = 6y
Divide each side by '3'.
x = 2y
Simplifying
x = 2y
One way of solving systems of linear equations is by adding a multiple of one equation to the other. The multiplier for the first equation is chosen so that one of the two variables will cancel out in the sum. What should you multiply the equation y=0 y=0 by so that when added to x+y=40 x+y=40 the variable y yy will cancel out?
Answer:
Multiply y = 0 by -1
Step-by-step explanation:
Given
y = 0 (1)
x + y = 40 (2)
What should you multiply the equation y=0 by so that when added to x + y = 40, the variable y will cancel out ?
Multiply (1) by -1
y = 0 × -1
-y = 0 (1b)
Add (1b) and (2)
-y = 0
x + y = 40
(0 + x) + (-y + y) = 0 + 40
x + (0) = 40
x = 40
You should multiply the equation y = 0 by -1 so that when added to x + y = 40 the variable y will cancel out
1. In 1995, the average level of mercury uptake in wading birds in the Everglades was 15 parts per million. If we assume that the distribution of mercury uptake has a standard deviation of 1 part per million, and a current sample of 25 wading birds has an average of 14.6 parts per million. Which null and alternative hypotheses would be used to test that the level of mercury uptake in the Everglades has decreased since 1995?
Answer:
We reject H₀, we find that the current level of mercury uptake in the Everglades has decrease
Step-by-step explanation:
We need to test the current wading bird average 14,6 vs the 1995 average. As sample mean is 14,6 and population mean is 15 we are going to check test is of one tail (left tail test)
Test Hypothesis:
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ < μ₀
Sample size 25 then n < 30 we will use t-student table
Population mean : μ₀ = 15 ppm
sample mean : μ = 14,6 ppm
sample standard deviation: s = 1 ppm
Sample size n : 25
degrees of freedom df = n - 1 df = 24
We will develop the test for CI 90% then α = 10% α = 0,1 α/2 = 0,05
For that values in t student table we find:
t(c) = 1,711 by symmetry t(c) = - 1,711
To compute ts
t(s) = ( μ - μ₀ ) / s/√n
t(s) = 14,6 - 15 / 1 /√25
t(s) = - 0,4*5 / 1
t(s) = - 2
Comparing t(c)and t(s)
|t(s)| > |t(c) | and t(s) < t(c) -2 < -1,711
Therefore t(s) in in the rejection region, we reject H₀
Which expression is equivalent to 100+20? 5(20+3)5(20+3) 4(25+6)4(25+6) 10(10+2)10(10+2) 5(20+20)5(20+20)
Answer:
Step-by-step explanation:
10 (10+2)
An SEO account manager is concerned website developers are using too many keywords per web page. The SEO account manager would like to carry out a hypothesis test and test the claim that a web page has, on average, more than 10 keywords. Why is this hypothesis test right-tailed
Answer:
The hypothesis test is right tailed because of claim made by SEO account manager that a web page on average has more than 10 keywords.
Step-by-step explanation:
The given hypothesis test is right tailed due to the claim made by SEO account manager. The tail of hypothesis test decided by looking at alternative hypothesis. The claim stated as " a web on average has more than 10 keywords" and this leads to alternative hypothesis as
Ha:μ>10.
The alternative hypothesis shows the greater than area or also known as right tailed area. Thus, given hypothesis test is right tailed.
Suppose the manager of your local McDonalds tracks the
monthly sales of their new McBurger, Mini McBurger, and
Choco-Latte Shake. The data is listed below.
For January through December, the sales are as follows.
McBurger: 46, 63, 58, 77, 81, 102, 183, 197, 125, 111, 83, 218.
Mini McBurger: 23, 41, 35, 44, 62, 88, 95, 99, 108, 111, 98, 63.
Choco-Latte Shake: 88, 46, 39, 52, 67, 99, 189, 238, 188, 97,
51, 12
Create a matrix to display the data.
Answer:
Step-by-step explanation:
The question says "Create a matrix to display the data".
The are 3 products:
- McBurger - Mini McBurger - ChocoLatte Shake
The figures represent monthly sales for each product, in a given year. This means 12 figures for each product - represent the 12 months of the year.
These figures will appear on the matrix, with the horizontal arrangement representing each month of the year and the vertical arrangement representing each product's sales.
In that light, you'll have a 12 by 3 matrix.
[tex]\left[\begin{array}{ccc}46&23&88\\63&41&46\\58&35&39\\77&44&52\\81&62&67\\102&88&99\\183&95&189\\197&99&238\\125&108&188\\111&111&97\\83&98&51\\218&63&12\end{array}\right] 12 by 3 matrix[/tex]The first row represents sales in January, the second row represents sales in February, the third row represents sales in March, the fourth row represents sales in April, etcetera.
The first column represents sale of McBurger, the second column represents sale of Mini McBurger, the third column represents sale of Choco-Latte Shake.
7th grade math help me plzzz
Answer:
11.a) is 15+5.50+3 maybe
11.b) is $3.50 because 15-12=3 3+5.50=8.50 8.50+3=11.50 11.50-8=3.50
PLEASE HELP!!! 30 POINTS
Solve the inequality for x. Show each step of the solution.
12 + 7 > 9(2 − 3)− 8
Answer:
True
12+7>9(2-3)-8
19> (-9)-8
19>-17
Step-by-step explanation:
Answer:
12+7=19 and 9(2-3)-8=-17
Step-by-step explanation:
For a school project, the school bought 36 hamsters for $5.90 each and 40 cages for $30.25 each.
How much did the school spend in all?
You own 16 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
Answer:
[tex]\frac{1}{524160} or 1.910^{-6}[/tex]
Step-by-step explanation:
In order to solve this, you would need to multiply the probability of you choosing the one that goes first, so 1 in 16 discs, then the next one so 1 in 15, and so on untill the fifth disc.
So you would have to do this:
[tex](\frac{1}{16})(\frac{1}{15})(\frac{1}{14})(\frac{1}{13})(\frac{1}{12})\\\frac{1}{524160}[/tex]
That is the probability that the rack ends up in alphabetical order, if you pull discs randomly, 1 in 524160 chances.
Probabilities are used to determine the chances of an event.
The probability that the rack ends up in alphabetical order is [tex]\mathbf{ \frac{1}{524160}}[/tex]
The given parameters are:
[tex]\mathbf{CD = 16}[/tex]
[tex]\mathbf{r = 5}[/tex] -- CDs to arrange
So, the total number of arrangements of 5 CDs from the 16, is:
[tex]\mathbf{Total = ^{16}P_5}[/tex]
Apply permutation formula
[tex]\mathbf{Total = \frac{16!}{(16 - 5)!}}[/tex]
This gives
[tex]\mathbf{Total = \frac{16!}{11!}}[/tex]
Expand
[tex]\mathbf{Total = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11!}{11!}}[/tex]
[tex]\mathbf{Total = 16 \times 15 \times 14 \times 13 \times 12 }[/tex]
[tex]\mathbf{Total = 524160}[/tex]
There is only one possibility of the CDs being in alphabetical order.
So, the probability is:
[tex]\mathbf{Pr = \frac{1}{524160}}[/tex]
Hence, the probability that the rack ends up in alphabetical order is [tex]\mathbf{ \frac{1}{524160}}[/tex]
Read more about probabilities at:
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2〖sen〗^2 x+3 senx+1=0
2cotxsecx+ 2secx+cotx+1=0
senx〖cos〗^2 x=senx
2〖cos〗^2 x+2senx-12=0
2〖csc〗^2 x+〖cot〗^2 x-3=0
2 sin²(x) + 3 sin(x) + 1 = 0
(2 sin(x) + 1) (sin(x) + 1) = 0
2 sin(x) + 1 = 0 OR sin(x) + 1 = 0
sin(x) = -1/2 OR sin(x) = -1
The first equation gives two solution sets,
x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ
x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ
(where n is any integer), while the second equation gives
x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ
2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0
2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0
(2 sec(x) + 1) (cot(x) + 1) = 0
2 sec(x) + 1 = 0 OR cot(x) + 1 = 0
sec(x) = -1/2 OR cot(x) = -1
cos(x) = -2 OR tan(x) = -1
The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives
x = tan⁻¹(-1) + nπ = -π/4 + nπ
sin(x) cos²(x) = sin(x)
sin(x) cos²(x) - sin(x) = 0
sin(x) (cos²(x) - 1) = 0
sin(x) (-sin²(x)) = 0
sin³(x) = 0
sin(x) = 0
x = sin⁻¹(0) + 2nπ = 2nπ
2 cos²(x) + 2 sin(x) - 12 = 0
2 (1 - sin²(x)) + 2 sin(x) - 12 = 0
-2 sin²(x) + 2 sin(x) - 10 = 0
sin²(x) - sin(x) + 5 = 0
Using the quadratic formula, we get
sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2
but the square root contains a negative number, which means there is no real solution.
2 csc²(x) + cot²(x) - 3 = 0
2 (cot²(x) + 1) + cot²(x) - 3 = 0
3 cot²(x) - 1 = 0
cot²(x) = 1/3
tan²(x) = 3
tan(x) = ± √3
x = tan⁻¹(√3) + nπ OR x = tan⁻¹(-√3) + nπ
x = π/3 + nπ OR x = -π/3 + nπ
Explain answer??????????????????
Answer:
the answer is a
Step-by-step explanation:
RADIO A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original
price to the nearest nickel?
Answer:
10% of $50.00 is $5.00 SO ORGINAL PRICE IS $55.00
Step-by-step explanation:
50÷10=5
5 00+50.00= $55.00
he:
os and Proportions
This table shows the relationship between the
number of cups of popcorn, p, a popcorn
machine pops and the time in minutes, 1, the
popcorn machine operates.
Answer:
can you give a chart or something?
In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?
Answer:
Callie has 4 months to pay off the bill. The rational number is +4. The sign is positive because it represents a quantity of something, in this case, months.
Step-by-step explanation:
this is correct...
trust me :)
The sign is positive because it represents a quantity of something, in this case, months.
Callie has 4 months to pay off the bill.
The rational number is +4.
What is the rational number?
A number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
The sign is positive because it represents a quantity of something, in this case, months.
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7. Sociologists can get three possible answers to a typical survey question such as "Do you believe in the tooth fairy?" - namely, yes, no and no opinion. With this in mind, the Sociomagnetic Computer Company has decided to build a computer to process survey data. This computer has a trinary memory - that is, each byte (tryte?)consists of 8 trits, with a trit holding a 0, 1, or 2. How many trits are needed to hold a 6-bit number? Give an expression for the number of trits needed to hold n bits.
Answer:
1. n ≥ 4
2. N ≥ nlog(2)÷log3
Step-by-step explanation:
1
1 byte = 8 bits
each byte = 8 trits
a 6 bit number = [tex]2^{6} = 64[/tex]
3n ≥ 64
divide through by3
n ≥ 64/3
we take the logarithm
n ≥ [tex]\frac{log64}{log3}[/tex]
n ≥ 1.8062 ÷ 0.4771
n≥3.785
when approximated, n ≥ 4. So the number of trits needed in the storage of 6 bit is atleast 4
2.
to hold n bits, we can do something similar.
3N ≥ 2n
we take log of both sides
such that;
N ≥ [tex]\frac{nlog(2)}{log(3)}[/tex]
PLS HELP!! What is the value of X
Which type of graph is typically not used for quantitative data?
Answer:
bar graph
pie chart
histogram
Step-by-step explanation:
A chemist is performing an experiment by observing the effects when she combines two solutions. She monitors the temperature of the combined solution over the course of eight hours and records it in this table below.
The chemist can model the temperature with a polynomial function. During these eight hours, over what interval is the temperature decreasing?
A. From hour 0 to hour 8
B. From hour 5 to hour 8
C. From hour 0 to hour 5
D. From hour 2 to hour 6
Answer:
A. From hour 0 to hour 5
Step-by-step explanation:
For all Plato users
Interval of the temperature decreasing is from hour 0 to hour 5.
What is interval?
an interval is defined as a group of numbers which includes all numbers between the beginning and the end.
According to given data is showing that the temperature decreasing zero hour to 1 hour , then 1 to 2 hour, then 2 to 3 hour, then 3 to 4 hour, then 4 to 5 hour.
So the interval of the temperature decreasing is from hour 0 to hour 5.
Learn more about interval
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Solve the inequality. Graph the solution. -4s<6s +1
Answer:
Step-by-step explanation:
First solve the inequality by writing it.
-4s < 6s + 1
Now subtract -1 on both sides.
-4s - 1 < 6s
Now add 4s on both sides to combine like terms.
-1 < 10s
Now divide 10 on both sides.
-0.1 < s
Now flip it over properly.
s > -0.1
Hope this helped! <3
on the map above.
In the United States, large quantities of oil and natural gas can be found in region
A. 1
B. 2
C. 3
D. 4
Please select the best answer from the choices provided
A
B
С
D
Answer: C
Step-by-step explanation:The top producing states are Texas, Oklahoma, New Mexico, Wyoming, and Louisiana, which produce more than 50 percent of U.S. natural gas.
Answer:
Your answer is C
Each costume needs 46 centimeters of red ribbon and 3 times as much yellow ribbon. What is the total length of the ribbon needed for 64 costumes? Express your answer in meters.
Answer:
I think its 117.76 meters
Step-by-step explanation:
you multiply the 46 x 3 then you get 138 yellow ribbon then 138 + 46 then its 184 then 184 x 6 = 11776
Answer:
117.76 meters
Step-by-step explanation:
46x64=2,944 (red ribbon)
46x3=138x64=8,832 (yellow ribbon)
8,832+2,944=11,776 (all ribbon)
11,776 centimeters converted into meters is 117.76 meters
