The probability of finding an average in excess of 4. 3 ounces of this ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline is approximately 0.7972.
We may use the normal distribution and the Z-score to determine the likelihood that 100 randomly selected 1-gallon samples of standard unleaded gasoline will have an average of more than 4.3 ounces of the component. A value's Z-score indicates how many standard deviations away from the mean it is.
We must first get the average of 100 randomly chosen samples' mean and standard deviation. The average's mean will be 4 ounces, which is also the mean of the individual samples. The sample size is divided by the square root of the standard deviation to get the average standard deviation, which is 1.2/100 = 0.12 ounces.
Next, we calculate the Z-score for the value of 4.3 ounces:
Z = (4.3 - 4) / 0.12 = 0.83
Finally, we use a Z-score table or a normal distribution calculator to find the probability of finding an average in excess of 4.3 ounces. The result will be the area under the standard normal distribution curve to the right of 0.83.
There is a 79.72% chance of finding an average in excess of 4.3 ounces of the ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline.
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The peak value of a sine wave is 80 VAC. What is the peak to peak value of this waveform?
The peak to peak value of a sine wave is twice the peak value. Therefore, total number of the peak to peak value of this waveform is 2 x 80 VAC = 160 VAC.
The peak to peak value of a sine wave is an important measure of the waveform's amplitude. It is calculated by multiplying the peak value of the waveform by two. The peak value of this particular waveform is 80 VAC, so the peak to peak value of the waveform is 2 x 80 VAC = 160 VAC. This peak to peak value is a measure of the total number voltage swing of the waveform, from its lowest point to its highest point. The peak to peak value of this waveform is a useful parameter for understanding the waveform's strength and potential for causing electrical damage. As such, it is important to measure and understand the peak to peak value of any sine wave in order to successfully manage its power and potential for causing harm.
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Geometry
You roll a six-sided die. (Write your answer as a fraction, decimal, and percent)
a. What is the probability of rolling an odd number or rolling a 2?
b. What is the probability of rolling an even number or a 4?
the probability of rolling an odd number or rolling a 2 is 2/3
The probability of rolling an even number or a 4 is 2/3
How to find the probability of rolling an odd number or rolling a 2?Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain to occur. The probability of an event can also be expressed as a percentage or as a fraction.
If you roll a six-sided die. The probability of rolling 1, 2, 3, 4, 5 and 6 are as follows:
P (1) = 1/6
P (2) = 1/6
P (3) = 1/6
P (4) = 1/6
P (5) = 1/6
P (6) = 1/6
a. Since there are three odd numbers, P(odd) = 3/6 = 1/2
Thus, the probability of rolling an odd number or rolling a 2 will be:
P(odd or 2) = P(odd) + P(2)
= 1/2 + 1/6 = 2/3
b. Since there are three even numbers, P(even) = 3/6 = 1/2
Thus, the probability of rolling an even number or a 4 will be:
P(even or 4) = P(even) + P(4)
= 1/2 + 1/6 = 2/3
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if x has a geometric distribution what does (1-p)n-1 represent
The probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.
The formula (1-p)n-1 represents the probability of having n-1 failures (or successes, depending on which outcome the probability p is associated with) in a Geometric distribution. For example, if p=0.3, then the formula (1-p)n-1 would represent the probability of having two failures before the first success. This would be equal to (1-0.3)2-1, or 0.49. This means that there is a 49% chance of having two failures before the first success in this example. In general, this formula can be used to calculate the probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.
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Complete question:
What does (1-p)n-1 represent in a geometric distribution?
can a triangle be formed with angles having measures of 30,70, and 110? explain using the model above.
use elimination to solve the system of equations
Elimination.... my biggest enemy
Welp let's dive in.
Elimination is sort of like subtraction BUT it's subtraction of equations.
In Elimination we want to make sure that we are looking for a common/ opposite coefficient.
If we see 5x and 5x stacked on each other, GREAT! or maybe -5x and 5x stacked on each other.
Why am I happy? Welll that just made the whole process easier. You see, if you see those stacked on top of each other, that means free elimation. You can just cancel them out because it becomes zero.
then we solve the problem same old same old.
P.S: If it's opposites coefficients we add the equations if it's the same we subract.
In your elimination, we have the same coefficients.
(yay)
so we can minus ad and ad
6c with 5c and 111 with 103
c=8
so we pick an equation and sustitute every c with 8
6*8+ad=111
48+ad=111
ad=63
questiojns? feel free to ask
solve the initial value problem. ′=−2,(0)=−4 (express numbers in exact form. use symbolic notation and fractions where needed.)
According to the concept of fraction the value of the quantity at any time t is -4.
A fraction is a mathematical representation of division of two numbers. In this case, we will be using fractions to solve an initial value problem.
The initial value problem is ′=−2,(0)=−4.
This means that the rate of change of the quantity is -2 and its starting value at time 0 is -4.
To solve this problem, we need to find the value of the quantity at some other time.
Here the first step is to find the general solution to the differential equation ′=−2.
This can be done by integrating both sides, which gives us
=> −2.
Integrating, we get
=> −2 + C, where C is an arbitrary constant.
Next, we use the initial value to find the value of C.
We know that when t=0, the value of the quantity is -4, so we can substitute these values into the general solution to get
=> -4 = -2 + C.
Solving for C, we get C = -2.
Finally, we substitute C into the general solution to get
=> -2 -2 = -4.
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The given graph represents the polynomial p(x). Find the number of zeros of the polynomial p(x).
The number of zeros of the polynomial p(x) is 3.
What does a polynomial mean?A polynomial is a mathematical expression that solely uses the addition, subtraction, and multiplication operations to combine variables (commonly called coefficients) and variables (often called x). The variables are raised to non-zero, and the coefficients can be any real value.
The number of x-intercepts, or the places where the graph crosses the x-axis, is equal to the number of polynomial roots, also known as zeros.
We can see from the above graph that the polynomial p(x) has three x-intercepts, which indicates that it has three roots or zeros. Consequently, the polynomial p(x) has three zeros.
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Complete question -
Write the equation of the line in fully simplified slope-intercept form.
Answer
Y=-2x+1
-2 is the slope, and 1 is the y intercept
The volume of a gas was measured as
its temperature was increased from 10 K
to 15 K at intervals of 1 K. The volumes
were 1. 5, 2. 2, 3. 38, 5. 1, and 7. 6 cm.
Would a linear or exponential function
better approximate the data described?
Explain why.
An exponential function would better approximate the data described about the volume of a gas.
The relationship between the volume of a gas and its temperature is described by the Ideal Gas Law, which states that the volume of a gas is proportional to its temperature raised to the power of the ratio of specific heat to the universal gas constant. Therefore, as the temperature of a gas increases, its volume will increase exponentially.
The data given in the problem, with the volume increasing as the temperature increases, supports the use of an exponential function to model the relationship between temperature and volume. On the other hand, a linear function, which models a constant rate of change, would not accurately capture the exponential increase in volume as the temperature increases.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
0.625
0.750
0.875
Answer:
Below
Step-by-step explanation:
5 out of 8 are NOT blue 5/8=.625
Sandra, Davion, Taylor, and James each purchased a medium soda from the concession
stand at a soccer game. At the end of the game, Sandra drank of her soda, Davion drank
82% of his, Taylor drank 0.85 of hers, and James drank of his. Who drank the most soda
from their cup?
James and Sandra drank the most soda from their cup.
Why are they the persons that drank most?The information that was given gave specific amount that each person drank from their soda, but James and Sandra were not given a specific amount, so one can only assume they drank the most since their own percentage of drink is not disclose.
Percentage is a way to express a number as a fraction of 100. It's often denoted using the symbol "%". For example, 50% means 50 per 100, or one half
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Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a spade and then selecting a heart.
A. 0.0625
B. 0.0637
C. 0.0588
D. 0.0250
The probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
Given that the cards are selected with replacement.
The probability of selecting a spade card is:
P(S) =13/52
Now, a heart card is selected.
Since, the previous card is replaced in the deck the total number of cards is 52.
The probability of selecting a heart card is:
P(H) = 13/ 52
The probability of selecting a spade and then selecting a heart is:
P = 13 / 52 × 13/52
P = 0.0625
Hence, the probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.
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Simplify the following expressions.
1. 11(5) - 11(4) =
2. 8(-3 + 2) =
3. 6(9) - 4(6) =
4. 7(4) - 2(0) =
5. 15(3) - 2(12) =
6. 9(5 + 3) =
7. 12(2) - 7(2) =
8. 8(3) =
9. (6)(6) =
10. 11(9) =
11. 8(5) - 2(7) =
12. 5(n) =
13. 5y(2) =
14. 13(x + 2) =
15. 16(5x - 8) =
16. 23y( 2 + 4) =
The simplification are as follows:
11(5) - 11(4) = 55 - 44 = 118(-3 + 2) = 8(-1) = -86(9) - 4(6) = 54 - 24 = 307(4) - 2(0) = 28 - 0 = 2815(3) - 2(12) = 45 - 24 = 219(5 + 3) = 9(8) = 7212(2) - 7(2) = 24 - 14 = 108(3) = 24(6)(6) = 3611(9) = 998(5) - 2(7) = 40 - 14 = 265(n) = 5n (Note: n is a variable)5y(2) = 10y13(x + 2) = 13x + 2616(5x - 8) = 80x - 12823y(2 + 4) = 23y(6) = 138y.What is simplification in mathematics?Simplification in mathematics refers to the process of making an expression, equation, or mathematical problem easier to understand, solve, or manipulate by reducing its complexity. This can be achieved by combining like terms, cancelling out common factors, reducing fractions, or using the properties of arithmetic operations.
The goal of simplification is to transform a complex expression into a simpler form that can be more easily understood or used in further mathematical analysis.
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Jane has $14000 in a savings account that earns 2.5% annually. How much interest will she have earned after 9 months?
Answer:
Below
Step-by-step explanation:
Interest for a WHOLE 12 months would be 14 000 * .025 = 350
but Jane had the account for 9 out of 12 months
9/12 * 350 = 262.50 dollars
1). What is the simplified form of 3a^4b^-2c^3?
2). What is -a^-2 if a = -5?
3). What is the simplified form of -(14x)^0y^-7z?
4). What is (-m)^-3n if m = 2 and n = -24
5). Which of the following simplifies to a negative number?
a). -4^-4
b). (-4)^-4
c). 4^-4
d). 1/4^-4
Answer:
1). 3a^4c^3 or D
2). -1/25 or C
3). -z/y^7 or D
4). 3 or A
5). -4^-4 or A
Step-by-step explanation:
I took the quick check already so enjoy your 100% :)
Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?
The ratios are opposites (negative five thirteenths and five thirteenths).
The ratios are both identical (five thirteenths and five thirteenths).
The ratios are reciprocals (five thirteenths and thirteen fifths).
The ratios are both negative (negative thirteen fifths and negative thirteen fifths).
The relationship the ratios of sin x° and cos y° share is The ratios are both identical (five thirteenths and five thirteenths). Option B
What are trigonometric identities?Trigonometric Identities are defined as the qualities involving trigonometry functions and also holds true for all the values of the variables given in the equation.
The different types of trigonometric identities are given as;
secantsinecosinetangentcotangentcosecantFrom the information given, we have that
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
But;
Hypotenuse= 13
Opposite = 5
Adjacent = 12
Substitute the value
sin x = 5/13
cos y = 5/13
Hence, the values are identical
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Answer:
B!
Step-by-step explanation:
took the testt
Round answer to the nearest hundredth
Using the cosine ratio, the measure of angle A, to the nearest hundredth is: 75.52°.
What is the Cosine Ratio?The cosine ratio, also known simply as the cosine, is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right triangle.
It is defined as cos(θ) = adjacent side/hypotenuse, where θ is the angle between the adjacent side and the hypotenuse.
Reference angle (∅) = A
Length of adjacent side = 2
Length of hypotenuse = 8
Therefore:
cos A = adj./hyp. = 2/8
cos A = 1/4
A = cos^(-1)(1/4)
A = 75.52°
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A 6-ft observer casts a 4-ft shadow at the same time a nearby chimney casts a 238-foot shadow. How tall is the chimney?
The height of the chimney is 357 feet according to mentioned dimensions of the chimney and observer.
The ratio of base and height according to angled of elevation will be -
tan theta = perpendicular ÷ base. The same will be for chimney. Hence, equating the ratio of both to find the height of chimney.
The formula will be -
Perpendicular ÷ base of observer = perpendicular ÷ base of chimney
6/4 = height/238
Rewriting the equation according to height of chimney
Height = (6 × 238)/4
Performing multiplication on Right Hand Side of the equation
Height = 1428/4
Performing division on Right Hand Side of the equation
Height = 357
Thus, chimney is 357 feet tall.
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Can someone PLEASE help? I will give brainliest if possible and lots of points
Part A: Find the value of x
Part B: Find ABK
Part C: Show your work to support your answer to Part A and Part B
Answer:
1. x = 20
2. m<ABK = 137
Step-by-step explanation:
1.
(3x - 5) + (4x + 2) + (2x + 3) = 180
9x = 180
x = 20
2.
3x - 5 + 4x + 2
7x - 3
7(20) - 3
140 - 3
m<ABK = 137
A total cot of attending a tate univerity i 19,700 for thi year
a tudent grandparent will pay of thi half
an athletic cholarhip will pay another 5,000
Which amount i cloet to the minimum that the tudent will need to ave every month in order to pay off the remaining cot at the end of 12 month
The student will need to save approximately 488.33 dollars per month in order to pay off the remaining cost at the end of 12 months.
First, let's calculate the amount that the student's grandparent will pay: 19,700 / 2 = 9,850
Next, let's subtract the amount of the athletic scholarship: 19,700 - 9,850 - 5,000 = 5,850
Finally, to find the minimum amount that the student will need to save every month, we can divide the remaining cost by the number of months (12): 5,850 / 12 = 488.33
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Select the shapes that have 8 or more edges.
Right circular cylinder
Right pyramid
Right triangular prism
Sphere
A and B
A and C
B and C
B and D
B and C
Right pyramid has 8, Right triangular prism has 9
write each of these ratios in its simplest form 7:21:35
Answer:
1:3:5
Step-by-step explanation:
[tex]\frac{7}{7}=1\\\\\frac{21}{7}=3\\ \\\frac{35}{7}=5[/tex]
1:3:5
Point P i on line egment O Q. Given O Q = 11 OQ=11 and O P = 9 , OP=9, determine the length P Q ‾. PQ
The numerical length of PQ is 20
Determine the length P Q ‾. PQ ?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that the line segments are: -
OQ=11 O P = 9
The numerical value of PQ will be calculated as below.
OP+OQ=PQ
11+9=PQ=11+9=PQ
Therefore PQ=20=PQ
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what is the time complexity of this pseudocode? for int i = 1; i<=n; i )
The size of the input is doubled, the time taken to execute the loop will also double.
The time complexity of this pseudocode is O(n). This can be determined by analyzing the number of times the loop is executed. The loop is entered once and is then executed n times, where n is the number of times the loop is executed. This can be expressed mathematically as T(n) = 1 + n. Since the loop is executed a constant number of times, regardless of the size of the input, the time complexity of the pseudocode is O(n). This means that the execution time of the loop grows linearly with the size of the input. Thus, if the size of the input is doubled, the time taken to execute the loop will also double.
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what’s the answer to this question i’ve been trying my hardest and i still haven’t go it can somebody please help
a) Dilation 1 has a scale factor of 3 units.
b) Dilation 2 has a scale factor of 4 units.
c) Dilation 3 has a scale factor of 0 units.
What is a scale factor?
A scale factor is a number used to multiply the dimensions of a shape to enlarge or reduce its size. In geometry, the scale factor is used to create similar figures by preserving their shape while changing their size. If a figure is scaled up by a scale factor of 'k', its dimensions are increased by a factor of 'k'. If a figure is scaled down, its dimensions are reduced by a factor of 'k'.
For the triangle, the scale factor would be 3 units.
For the square, the scale factor would be 4 units.
For the line, the scale factor would be 0 units.
Hence,
a) Dilation 1 has a scale factor of 3 units.
b) Dilation 2 has a scale factor of 4 units.
c) Dilation 3 has a scale factor of 0 units.
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Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars. Represent the number of cupcakes that the customer can buy as an inequality.
Write the solution to the inequality in interval notation below.
The number of cupcakes that the customer can buy as inequality will be 3.5C + 2 < 44.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars.
The inequality can be written as:-
3.5C + 2 < 44.
Where C is the number of cupcakes and $2 is the charge for the box. Which should be lesser than the total amount.
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The inequality equation is x ≤ 8 , where x is the number of cupcakes
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of cupcakes be represented as A
Now , the equation will be
The cost of each cupcake = $ 3.50
The cost per box of cupcake = $ 2.00
So , the total cost of x cupcakes = x ( 3.50 + 2.00 )
The total cost of x cupcakes = 5.50x
Now , The amount of money with Rebecca = $ 44
So , the maximum number of cupcakes she can buy is
total cost of x cupcakes < amount of money with Rebecca
Substituting the values in the equation , we get
5.50 x ≤ 44
Divide by 5.50 on both sides of the equation , we get
x ≤ 44/5.50
x ≤ 8 cupcakes
Hence , the inequality equation is x ≤ 8
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Under her cell phone plan, Aubree pays a flat cost of $50. 50 per month and $4 per gigabyte. She wants to keep her bill at $56. 10 per month. Choose the equation which could be used to determine g, the number of gigabytes of data Aubree can use while staying within her budget
54.10Answer:
Step-by-step explanation:
Which equation represents a tangent function with a domain of all real numbers such that x is not equal to pi over 2 plus pi times n comma where n is an integer?.
y = tan(x) - (π/2 + πn)
This equation represents a tangent function with a domain of all real numbers, except for multiples of pi/2 plus pi.
The equation y = tan(x) - (π/2 + πn) represents a tangent function with a domain of all real numbers except for multiples of pi/2 plus pi. This equation is useful for finding the tangent value of any given x-value, as long as it is not equal to a multiple of pi/2 plus pi. The equation works by subtracting the multiple of pi/2 plus pi from the x-value, and then finding the tangent of the new value. This allows the tangent of the x-value to be found, regardless of whether or not it is equal to a multiple of pi/2 plus pi.
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At the top of the mountain, you and your friend tart decending at the ame time. There i an angle of 18o between the two of you. You are travelling fater and therefore cover 250 m, while your friend only cover 195 m. How far apart are you at that point in time?
You and your friend are approximately 181.23 meters apart at that point in time.
Distance Between Friends On MountainTo find the distance between you and your friend, we can use the Pythagorean theorem. Let's call the distance between you two "d".
d² = 250² + 195² - 2 X 250 X 195 X cos(18)
d = √(250² + 195² - 2 X 250 × 195 X cos(18))
d ≈ 181.23 m
So you and your friend are approximately 181.23 meters apart.
The answer was determined using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two smaller sides equals the square of the length of the largest side (the hypotenuse).
In this case, the two smaller sides represent the distances covered by you and your friend, and the hypotenuse represents the distance between you both.
We can use the theorem to calculate the distance "d" between you and your friend by rearranging the equation to isolate "d". We know the lengths of the two smaller sides (250 m and 195 m), and we also know the angle between them (18 degrees).
We can use the cosine formula to find the cosine of 18 degrees, and plug in all the values into the equation to find "d".
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Which choice is equivalent to the product below?
√8 •√5
A. 4√10
OB. 10/2
OC. 2√10
OD. √13
The choice that is equivalent to the product given is 2√10
What are surds ?
Surds in mathematics are the square root values that can't be further condensed into whole numbers or integers. Numbers with surds are illogical.
Surds are the square roots of numbers ( √) that are not able to be divided into whole or rational numbers. It cannot be precisely described by a fraction. A surd, then, is a root of a whole number with an irrational value.
√8 •√5
= √(8*5) = √40
= √(10*4)
= √4 * √10
= 2√10
The choice that is equivalent to the product given is 2√10
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