Answer:
32.64%
Step-by-step explanation:
Let's define the random variable X in the following way:
X: the volume of a soda in a quart soda bottle. We know that X is normally distributed with a mean of 32 ounces and a standard deviation of 1.2 ounces, i.e.,
[tex]\mu[/tex] = 32 ounces
[tex]\sigma[/tex] = 1.2 ounces
The normal density function for a random variable with a mean of 32 and a standard deviation of 1.2 is given by
[tex]f(x)=\frac{1}{\sqrt{2\pi }1.2} \exp[-\frac{(x-32)^{2} }{2(1.2)^2} ][/tex]
and we need to calculate the following probability
[tex]P(X\leq 31.46)[/tex], this probability is given by
[tex]P(X\leq 31.46) =\int\limits^{31.46}_{-\infty} {\frac{1}{\sqrt{2\pi }1.2} \exp[-\frac{(x-32)^{2} }{2(1.2)^2} ]} \, dx[/tex] = 0.3263552
you can use a computer to calculate this probability or a table from a book. You can use the following instruction in the R statistical programming language for example
pnorm(31.46, mean = 32, sd = 1.2) with give us 0.3263552, then,
the percentage we are looking for is (0.3263552)(100)=32.64.
How do I find the value of x?
Hey Is anyone really good at math? I need help with this one.
What is the average of 96, 49 , 68 and 75?
A wise man once said 400 reduced by 3 times my age is 112. what is his age
3 4 6 9 1 3 1 8 2 4 what would be the next number
The brady bunch has three boys who ages are consecutive even integers. The sum of the boy's ages is equal to four times the youngest boy's age. What are the ages Brady boys?
x+x+2+x+4 =4x
3x+6 =4x
x=6
6 +8+10 = 24
ages are 6, 8 & 10
The Brady boys' ages are consecutive even integers, and their respective ages are 6, 8, and 10 years old, as derived from setting up and solving an equation based on the given sum and multiple conditions.
Explanation:We have a mathematical problem involving consecutive even integers and the relationship between their sum and a single integer's multiple. Since the Brady boys' ages are consecutive even integers, we can represent the youngest boy's age as x. The ages of the other two boys would then be x + 2 and x + 4 respectively, because even integers are two units apart.
The information given states that the sum of the boys' ages equals four times the youngest boy's age. This gives us the equation:
x + (x + 2) + (x + 4) = 4x. Simplifying this equation,
3x + 6 = 4x
3x - 4x + 6 = 0
-x + 6 = 0
x = 6.
Therefore, the youngest Brady boy is 6 years old, the middle boy is 8 years old, and the oldest is 10 years old
If the sum of the interior angles in a regular polygon is 1440°, then what kind of polygon is it?
Sound a measures 25 decibels and sound b is 8 times as loud as sound
a. what is the decibel rating of sound b to the nearest integer?
Final answer:
To find the decibel rating of sound b, we calculate the decibel difference between sound a and sound b, which is 9.031 decibels. Adding this to the decibel rating of sound a gives us an approximate decibel rating of 34 for sound b.
Explanation:
To find the decibel rating of sound b, we need to determine how many decibels louder it is compared to sound a. We know that sound b is 8 times as loud as sound a, so we can use the formula for decibel difference:
Decibel difference = 10 * log10(intensity ratio)
Since sound b is 8 times as loud as sound a, the intensity ratio is 8. Plugging this into the formula gives:
Decibel difference = 10 * log10(8) = 10 * 0.9031 = 9.031 decibels
To find the decibel rating of sound b, we add the decibel difference to the decibel rating of sound a:
Decibel rating of sound b = Decibel rating of sound a + Decibel difference = 25 + 9.031 ≈ 34 decibels
PLEASE HELP! ill give you brainliest
Which answers are examples of the Law of Detachment? Select each correct answer.
If two angles are linear pairs, the angles are supplementary. The two angles are linear pairs. Therefore, the angles are supplementary.
If an object is a square, it is a parallelogram. The object is a square. The object is a parallelogram.
If it is snowing, the play will be cancelled. It is snowing. Therefore, the play is cancelled.
If it is snowing, the play will be cancelled. If the play is cancelled, the theater will refund the cost of admission. Therefore, if it is snowing, the theater will refund the cost of admission to the play.
Answers:
A. If two angles are linear pairs, the angles are supplementary. The two angles are linear pairs. Therefore, the angles are supplementary.
B. If an object is a square, it is a parallelogram. The object is a square. The object is a parallelogram.
C. If it is snowing, the play will be cancelled. It is snowing. Therefore, the play is cancelled.
These are right.
Answer:
Law of detachment:
Statement 1: If a, then b
Statement 2: a
Conclusion: b
(A)
1. If two angles are linear pairs, then the angles are supplementary.
2. The two angles are linear pairs.
Let a be the statement " two angles are linear pairs"
let b be the statement "the angles are supplementary"
then, 1 and 2 can be written as;
1. if a , then b
2. a
So, by the law of detachment we can deduce that b is true.
i.e, The angles are supplementary.
(B)
1. If an object is a square, then it is a parallelogram.
2. The object is a square.
Let a be the statement " an object is a square"
let b be the statement "The object is a square"
then, 1 and 2 can be written as;
1. if a , then b
2. a
So, by the law of detachment we can deduce that b is true.
i.e, The object is a parallelogram.
(C)
1. If it is snowing, then the play will be cancelled.
2. It is snowing.
Let a be the statement "it is snowing"
let b be the statement "the play will be cancelled"
then, 1 and 2 can be written as;
1. if a , then b
2. a
So, by the law of detachment we can deduce that b is true.
i.e, The play is cancelled.
Only option A, B and C are examples of the Law of Detachment.
−7x−50≤−1 AND−6x+70>−2
Answer:
[tex]-7\geq x<12[/tex] and [tex][-7,12)[/tex] in interval notation.
Step-by-step explanation:
We have been given a compound inequality [tex]-7x-50\leq -1\text{ and }-6x+70>-2[/tex]. We are supposed to find the solution of our given inequality.
First of all, we will solve both inequalities separately, then we will combine both solution merging overlapping intervals.
[tex]-7x-50\leq -1[/tex]
[tex]-7x-50+50\leq -1+50[/tex]
[tex]-7x\leq 49[/tex]
Dividing by negative number, flip the inequality sign:
[tex]\frac{-7x}{-7}\geq \frac{49}{-7}[/tex]
[tex]x\geq -7[/tex]
[tex]-6x+70>-2[/tex]
[tex]-6x+70-70>-2-70[/tex]
[tex]-6x>-72[/tex]
Dividing by negative number, flip the inequality sign:
[tex]\frac{-6x}{-6}<\frac{-72}{-6}[/tex]
[tex]x<12[/tex]
Upon merging both intervals, we will get:
[tex]-7\geq x<12[/tex]
Therefore, the solution for our given inequality would be [tex]-7\geq x<12[/tex] and [tex][-7,12)[/tex] in interval notation.
David wants to install a fence fence around his garden. The garden is rectangular and has an area of 240 square feet. One side of the garden is along the street and is 12 feet long. For this side of the garden, David will use fencing that costs 18$ per linear foot. For the other three sides of the garden, David will use fencing that costs 15$ per linear foot. What is the total cost of fencing?
The total cost of fencing is $996.
Cost calculationGiven that David wants to install a fence fence around his garden, and the garden is rectangular and has an area of 240 square feet, and one side of the garden is along the street and is 12 feet long, and for this side of the garden , David will use fencing that costs 18$ per linear foot, while for the other three sides of the garden, David will use fencing that costs 15$ per linear foot, to determine what is the total cost of fencing the following calculation must be made :
12X = 240240 / 12 = X20 = X12 x 18 + 12 x 15 + 20 x 15 + 20 x 15 = Cost216 + 180 + 300 + 300 = Cost996 = CostTherefore, the total cost of fencing is $996.
Learn more about calculus in https://brainly.com/question/9384208
PLZ Help fast. It's Pre Calculus. This is the only day i get to spend time with my baby sister. please help fast. WILL MARK BRAINLIEST.
Which of the following is a root of the polynomial shown below? Look at the graph of the function and find the solutions.
f(x)=x^3+2x^2-x-2
a.1
b.0
c.3
d.2
Which of the following represents the set of possible rational roots for the polynomial shown below? This question is a review from Algebra 2. Remember that possible rational roots take the form of p/q. Where p is a factor of the constant and q is a factor of the leading coefficient.
2x^3+5x^2-8x-20=0
Answer:
Step-by-step explanation:
Given is the polynomials as
1) [tex]f(x) = x^3+2x^2-x-2[/tex]
The graph of this function has x intercepts as
-2, -1 and 0
Since f(x) =0 has solutions equivalent to x intercepts we see that the roots are
-2,-1 and 0
2) Given is a polynomial as
[tex]f(x) = 2x^3+5x^2-8x-20 =0[/tex]
Using rational roots theorem we find that
the roots possible are ±1.±2,±4,±5,±10,±20,±1/2,±5/2
Using remainder theorem we see that
f(2) =f(-2)=0
By using division, we find that the other factor is 2x+5
Hence roots are 2,-2, -2.5
PLEASE HELP WITH THIS
PLEASE HELP MEEHH...
Divide. −3/8 ÷ −6/7
In fraction form please.
What is 300 in scientific notation
If 9 is a factor of 63, then what other number must also be a factor of 63? Explain your reasoning.
The area of a square with sides of length s is given by a = s2. find the rate of change of the area with respect to s when s = 4 meters.
Round each mixed number to the nearest whole number 7 2/14 kuanto
MATH HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. intersection is all the numbers both sets have in common
so 3, ,7 , 13
2. union is all the numbers from both sets so 1, 5, 8, 12, 17
Forty-eight divided by (two plus six)
joy is planning to purchase a sweater that costs 30$ dollars at her local department store. The sweaters are on sale for for 20% off.
Which steps are needed to find the sale price of the sweater in words?
1. A log cabin in the shape of a rectangular prism is modeled using a scale of 1 to 0.5 meter. If the model is 14x19x11 centimeters, what is the volume of the actual log cabin?
a) 182.875 m^3
b) 365.75 m^3
c) 548. 625 m^3
d) 1463 m^3
2. A circle graph below represents a family's monthly budget. If the total monthly income is $2000, how much money is spent on food?
(graph) food=35% other=25% housing=40%
a) $700
b) $800
c) $350
d) $400
3. solve the equation. round the result to two decimal places.
4.8x-1.3=1.7
a) 0.83
b) -1.80
c) 0.63
d) 0.08
Thirty-five percent of 160 is ?
Answer:
56.
Step-by-step explanation:
We are asked to find 35% of 160.
To 35% of 160, we will divide 35 by 100 and multiply the result by 160 as:
[tex]35\%\text{ of 160}=\frac{35}{100}\times 160[/tex]
[tex]35\%\text{ of 160}=0.35\times 160[/tex]
[tex]35\%\text{ of 160}=56[/tex]
Therefore, 56 is 35% of 160.
A box contains 10 transistors, 4 of which are defective. If 3 are sold at random, find the probability that exactly 1 are defective.
If 5 rubber stamps cost $9.70 which equation would help determine the cost of 11 rubber stamps
To find the cost of 11 rubber stamps, we calculate the unit price by dividing the given cost of 5 stamps by 5 and then multiply the unit price by 11.
Explanation:To determine the cost of 11 rubber stamps when 5 stamps cost $9.70, first we need to find the cost of one rubber stamp. We divide the total cost by the number of stamps to find the unit price, which is $9.70 ÷ 5 = $1.94 per stamp. Using this unit price, we can then multiply by the desired number of stamps to find the total cost for 11 stamps. The equation to determine the cost of 11 rubber stamps is:
Cost of 11 stamps = 11 × $1.94
By calculating this, we find that 11 stamps will cost $21.34.
Learn more about Unit Price Calculation here:https://brainly.com/question/28965958
#SPJ12
Sawyer has triple the number of Hot Wheels cars as Fisher. If Fisher has x number of cars, how many does Sawyer have?
A) x + 3
B) 3x
C) 3/x
D) 2x
fisher has x cars
sawyer has 3 times as many so he has 3x cars
Answer is B
The function p(x)= -2000x^2 + 16000x - 5000 models the monthly profit P of a smoothie company, where x represents the price per smoothie. Identify the price range that will generate a monthly profit of at least 25,000?
a. between $3 and $5, inclusive
b. less than $3
c. more than $5
Answer: Between $3 and $5, inclusive
Step-by-step explanation:
Write an equation to represent: four-fifths of z added to six equals eight
A) 4 5 z + 6 = 8
B) 4 5 + 6z = 8
C) 4 5 (6)(z) = 8
D) 4 5 (6) + z = 8
write 171 miles in 3 hours as a unit rate
Which equation represents a line that passes through (4, 1/3 ) and has a slope of 3/4?
y – 3/4 = 1/3(x – 4)
y – 1/3 = 3/4(x – 4)
y – 1/3 = 4(x – 3/4 )
y – 4 = 3/4(x – 3/4 )
Answer:
The correct option is 2.
Step-by-step explanation:
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is slope.
The line passes through (4, 1/3 ) and has a slope of 3/4.
The equation of line is
[tex]y-\frac{1}{3}=\frac{3}{4}(x-4)[/tex]
Therefore the correct option is 2.
Please help having a lot of trouble :(
There is 4 inches of water in the swimming pool before the day started. The rainfall is falling at 3 inches per minute.
a. Write an inequality for how much water is in the pool, let x represent the minutes.
b. Graph the Inequality
(could help if you give me the graph points)