The equivalent expressiοn in the given οptiοns is -13/14t - 17/12.
What are expressiοns?In mathematics, an expressiοn that incοrpοrates variables, cοnstants, and algebraic οperatiοns is knοwn as an algebraic expressiοn (additiοn, subtractiοn, etc.). Terms cοmprise expressiοns.
The cοncept οf algebraic expressiοns is the use οf letters οr alphabets tο represent numbers withοut prοviding their precise values. We learned hοw tο express an unknοwn value using letters like x, y, and z in the fundamentals οf algebra. Here, we refer tο these letters as variables. Variables and cοnstants can bοth be used in an algebraic expressiοn. A cοefficient is any value that is added befοre a variable and then multiplied by it.
frοm the questiοn:
We can simplify the given expressiοn as fοllοws:
-8/7t + 4/12 - (-3/14t + 7/4)
= -8/7t + 1/3 - (-3/14t + 7/4) (4/12 = 1/3)
= -8/7t + 1/3 + 3/14t - 7/4 (dοuble negative becοmes pοsitive)
= (-16/14)t + (2/6) + (3/14)t - (49/14)
= (-24/14)t - (47/14) (cοmbining like terms)
= (-12/7)t - (47/14) (simplifying)
The equivalent expressiοn in the given οptiοns is -13/14t - 17/12.
Thus, the apprοpriate chοice is:
negative 13 οver 14 times t minus 17 οver 12
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100 points please help!!
We locate the [tex](5x+4)(x+7)[/tex] in order to solve this trinomial problem.
How do you formulate a trinomial's equation?The quadratic trinomial formula inside one variable has the general form ax2 + bx + c, where a, b, and c are constant terms and none of them are zero. If b2 - 4ac > 0, we're able to factor a quadratic trinomial for any value of a, b, and c. It denotes that, where h and k are real values,
How can you tell if a given equation has a trinomial?A single-term expression is referred to as a monomial, a two-term expression as a factorial, and a three-term expression as a trinomial. a phrase that contains more than three terms is identified only by the quantity of its terms.
Given, [tex]5 x^{2} + 4 x + 35 x + 28[/tex]
Regroup terms into two proportional parts [tex](5 x^{2} + 4 x) + (35 x + 28)[/tex]
Factor Greatest Common Factors out [tex]x (5 x + 4) + 7 (5 x + 4)[/tex]
Factor Greatest Common Factors out [tex](5 x + 4) (x + 7)[/tex]
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I need help with this question please and thank you
Answer:
b = 6
Step-by-step explanation:
step one: Simplify 10^2 to 100
Step two: Simplify 8^2 to 64
Step three: Subtract 64 from both sides
Step four: Simplify 100 - 64 to 36
Step Five: Take the square root of both sides
Step Six: Since 6*6=36, the square root of 36 is 6
Step Seven: Switch sides b = positive 6
I hoped this helped
Find the exact value, in terms of a, of each of the following. (HINT: Don't let the variable a scare you! The same strategy you used in Problem 2 still works - draw a point on a circle, assign it coordinates, and find the appropriate trig function’s value.)
a. sin (tan^-1(2/a))
b. cot (cos^-1(a))
Answer:
a. i dk how to do this qn
b. cot (cos^-1(a))
let cos^-1(a) = θ
implies, cosθ = a
from the figure, cotθ = [tex]\frac{x}{\sqrt{1 -x^{2} } }[/tex]
pls mrk me brainliest
finnd the equation of straight line passing through the point (3a,0) and (0,3b) also shwo that the line passese throught the poinits (a , 2b)
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3a, 0 ) and (x₂, y₂ ) = (0, 3b )
m = [tex]\frac{3b-0}{0-3a}[/tex] = [tex]\frac{3b}{-3a}[/tex] = - [tex]\frac{b}{a}[/tex]
the line crosses the y- axis at (0, 3b ) ⇒ c = 3b
y = - [tex]\frac{b}{a}[/tex] x + 3b ← equation of line
to show that (a, 2b ) lies on the line , substitute x = a into the equation and if y = 2b then the point lies on the line
y = - [tex]\frac{b}{a}[/tex] (a) + 3b = - b + 3b = 2b
then the line passes through the point (a, 2b )
I need help with this one
Using Pythagorean theorem, the volume of the cylinder is 201.1 cubic units
What is the volume of the cylinderTo determine the volume of the cylinder, we have to find the height of the cylinder.
using Pythagoras theorem, we can find the height of the cylinder.
13² = 5² + x²
x² = 13² - 5²
x² = 144
x = √144
x = 12 units
The volume of a cylinder is given as
V = 1/3 πr²h
h = height of cylinderr = radius of cylinderv = 1/3 * 3.14 * 4² * 12
v = 64π cubic units
v = 201.1 cubic units
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ECOLOGY: DDT is an insecticide that has been used by farmers. It decays slowly and it is sometimes absorbed by plants that animals and humans eat. DDT absorbed in the mud at the bottom of a lake is degraded into harmless products by bacterial action. Experimental data shows that 10% of the initial amount is eliminated in 5 years(so what would remain?)
a) Find the value of k in the decay formula: y = ae-kt (Pert with different letters)
b) How much of the original amount of DDT is left after 10 years?
c) The U.S. Environmental Protection Agency banned almost all use of DDT in the U.S. in 1972. If none has been used near the lake since then, in what year will the concentration of DDT fall below 25%?
Therefοre , the sοlutiοn οf the given prοblem οf percentage cοmes οut tο be a)k ≈ 0.0279,b)y = 0.593a and c)t ≈ 78.5 .
Describe percentages.In statistics, a percentage is a figure οr an integer that is expressed as a fractiοn οf 100. Additiοnally, the wοrds "pct.," "pct," but alsο "pc" are rarely used. The "%" symbοl, hοwever, is cοmmοnly used tο denοte it. There are nο dimensiοns; the percentage tοtal is flat.
Percentages are really just numbers because the numeratοr is 100. Tο indicate that a number is a percentage, either the percent character (%) οr the text "percent" must appear befοre it.
Here,
a) We can apply the exponential decline equation:
=> [tex]y = ae^{(-kt)} (-kt)[/tex]
[tex]0.9a = ae^{(-5k)} (-5k)[/tex]
Using a to divide both sides:
[tex]0.9 = e^{(-5k)} (-5k)[/tex]
Using both sides' natural logarithms:
ln(0.9) = -5k
calculating k:
[tex]k = -ln(0.9)/5[/tex]
k ≈ 0.0279
Consequently, the decline formula's value of k is roughly 0.0279.
b)
[tex]y = ae^{(-kt)} (-kt)[/tex]
[tex]y = an e^{(-0.0279*10)[/tex]
[tex]y = 0.593a[/tex]
As a result, after 10 years, only about 59.3% of the initial DDT is still present.
c)
[tex]0.25a = ae^{(-0.0279t) (-0.0279t)[/tex]
Using a to divide both sides:
[tex]0.25 = e^{(-0.0279t) (-0.0279t)[/tex]
Using both sides' natural logarithms:
ln(0.25) = -0.0279t
calculating t:
t = -ln(0.25)/0.0279
t ≈ 78.5
Therefore, roughly 78.5 years after the ban in 1972, or in the year 2050, the concentration of DDT will drop below 25%.
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-8(6y-2x-5) Use the distributive property to remove the parentheses.
Answer: -48y+6x+40
Step-by-step explanation: when you multiply two minuses that is +.
Pla help algebra1 pls
Answer:
A. 2(4a^3 - 49a)
In this case, you would simply multiply the numbers and leave the a value and exponents alone.
B. 2a(4a^2 - 49)
First, you would distribute(multiply) 2 with the numbers inside the parentheses just like you did for answer A. Then, you would distribute a with the other a values inside the parentheses, you would add this values instead of multiplying it.
F. 2a(2a - 7)(2a + 7)
You would distribute 2a inside the FIRST set of parentheses just like you did before. Then multiply that set of parentheses with the other set of parentheses.
Step-by-step explanation:
can anyone help me with this because its due tomorrow!
what tips can you share with the group? check all that apply. select the survey population carefully limit the number of questions explain why the survey is necessary select the survey population randomly ask as many questions as possible
It is important to carefully select the survey population and explain why the survey is necessary. It is also important to limit the number of questions and ask them in a clear and concise manner.
Select the survey population carefully: This means selecting a group of people who are representative of the target population and have the relevant knowledge or experience to answer the survey questions. For example, if the survey is about customer satisfaction with a product, the survey population should be customers who have used the product.
Limit the number of questions: It's important to keep the survey short and focused to reduce the risk of respondent fatigue and increase the response rate. A shorter survey also makes it easier to analyze the data.
Explain why the survey is necessary: This helps to increase the response rate by providing a clear explanation of why the survey is being conducted, what the data will be used for, and how it will benefit the target population.
Select the survey population randomly: Random selection helps to ensure that the survey results are representative of the target population and minimize the risk of bias in the sample.
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what tips can you share with the group? check all that apply.
Select the survey population carefullyLimit the number of questionsExplain why the survey is necessarySelect the survey population randomlySelect all that apply. Which two rays form BCE? BC CD CE CB
Hi,
The correct answer should be "CE" and "CB" I just had the same question so my answer should be correct.
I hope that this helped you. :)
Quick Check 13.13-3.11 Find the difference. list (3y^(2)+11y-5)/(y^(2)-2y-24)-(2y^(2)+4y-17)/(y^(2)-2y-24)
Answer: pic please so i know some more info thanks
Step-by-step explanation: pic please so i know some more info thanks
Find the zeros of \( f(x) \), and state the multiplicity of each zero. (Order your answers from smallest to largest \( x \) first by real \[ f(x)=x^{4}+12 x^{2}-64 \] \[ x= \] with multiplicity \[ \be
To determine the zeros of f(x) and state the multiplicity of each zero, the following steps should be followed:
Step 1: Determine the roots of the polynomial
To solve for the roots of f(x), use the quadratic formula. f(x) = x⁴ + 12x² - 64
a = 1, b = 12, c = -64
Using the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / 2a
x = (-12 ± √(12² - 4(1)(-64))) / 2(1)
x = (-12 ± √400) / 2
x = (-12 ± 20) / 2
x₁ = -16
x₂ = 4
x₃ = x₄ = 0
Step 2: State the multiplicity of each zero
After determining the roots of f(x), determine the multiplicity of each root by using the concept of multiplicity. A root has a multiplicity of p if and only if f(x) has a factor of (x - r)ᵖ.
From the quadratic equation above, we have:
x₁ = -16 (multiplicity 1)
x₂ = 4 (multiplicity 1)
x₃ = x₄ = 0 (multiplicity 2)
Therefore, the zeros of f(x) and their multiplicities are: x = -16 (multiplicity 1), x = 4 (multiplicity 1), and x = 0 (multiplicity 2).
The final answer is as follows:
x = -16 with multiplicity 1
x = 0 with multiplicity 2
x = 4 with multiplicity 1.
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Thabelo buys R350 worth of electricity .he gets 152,84 units (kwh) , what is the price per unit ?
The price per unit is equal to R2.29 per unit.
How to determine the unit price?Generally speaking, a unit price is sometimes referred to as price per unit or unit rate and it can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In this scenario, we would determine the unit price for number of unit of electricity by using the following mathematical expression;
Unit price = Cost of electricity/Number of units
Substituting the given parameters into the unit price formula, we have the following;
Unit price = R350/152.84
Unit price = R2.29 per unit.
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A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (if an answer does not exist, enter dne. ) f(t) = t3 − 8t2 + 25t
f(t) = t3 − 8t2 + 25t + 10. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.
This equation represents a law of motion, where t is measured in seconds and s in feet. This equation can be broken down into 3 parts; t3, -8t2 and 25t + 10. The t3 part of the equation represents a cubic function, which is usually associated with acceleration. The -8t2 part is a quadratic function, which is typically associated with velocity. Finally, the 25t + 10 is a linear function, which is usually associated with displacement. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.
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Anna’s new baby sister weighs 2076 grams. How many kilograms does the baby weigh
Find the value of x for which PQ and RS are parallel
The value of x for which PQ and RS are parallel, is 83°.
The two parallel lines PQ and RS are stretched from Q to M and S to N, respectively, in the accompanying figure.
In addition, a line from T to O is drawn parallel to PQ and RS.
Now, in the illustration,
∠MPT = 180° - 135°
∠MPT = 45°
The parallel lines MQ and OT are divided by the transversal line PT.
∠MPT = ∠PTO = 45°
∠TRN = 180° - 142°
∠TRN = 38°
A transversal line TR splits the parallel lines NS and OT.
Then, ∠TRN = ∠OTR = 38°
∠PTO + ∠OTR = x
x = 45° + 38°
x = 83°
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If the gyration of the outer perimiter of other galaxies are in a spiral elipse what would the probility of the tangent of collisions
The probability of a collision between two galaxies depends on a variety of factors, such as the size, mass, and relative velocities of the galaxies.
The probability of a collision between two galaxies depends on a variety of factors, such as the size, mass, and relative velocities of the galaxies. If the galaxies are in a spiral elipse, then the tangential velocity of the galaxies may be different, and this could affect the probability of a collision. However, without knowing more information about the galaxies, it is impossible to accurately calculate the probability of a collision.
If the galaxies are in a spiral elipse, then it is important to consider the tangential velocity of the galaxies, as this could affect the probability of a collision. Additionally, the relative angular momentum of the galaxies, their proximity to one another, and their respective trajectories also play a role. Without knowing more information about the galaxies, such as their exact positions, velocities, and masses, it is impossible to accurately calculate the probability of a collision.
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Question one, please help
An equation that represents the relationship is y = 0.01x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios. Also, it passes through the origin (0, 0) and it can be modeled by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 1/90
Constant of proportionality, k = 0.01.
Therefore, the required equation is given by:
y = kx
y = 0.01x
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Radio, diameters, and chords of O are shown. State the measure of angle 1.
Therefore , the solution of the given problem of circle comes out to be 110°
is the angle 1.
Circle – what is it?Each area of a plane with a specific distance from this additional spot forms a circle (center). Thus, it comprises of curved spots that are separated from one another and separated by the surface. Additionally, it rotates evenly around the centre from all sides. Every set of endpoints in a circular, constrained double sphere is uniformly spaced apart from the "centre."
Here,
Given :
To find: the angle of 1
So,
From the diagram , we can see it is showing 110 degree
So ,
Angle 1 comes out to be 110°
So, rest of circle angle is = 360° - 110° = 250°
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help whats the missing side lengths!
Answer:
x = y = 2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
the triangle is a 90- 45- 45 isosceles triangle with congruent legs, that is
x = y
using Pythagoras' identity in the right triangle
x² + y² = (2[tex]\sqrt{6}[/tex] )² , that is
x² + x² = 24
2x² = 24 ( divide both sides by 2 )
x² = 12 ( take square root of both sides )
x = [tex]\sqrt{12}[/tex] = [tex]\sqrt{4(3)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex]
then
x = y = 2[tex]\sqrt{3}[/tex]
For the complex number z = 12 + i, what is Modifying above z with bar?
The conjugate of the complex number z = 12 + i is [tex]\hat{z}=12-i[/tex]
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Complex number are in the form a + bi, where a is the real part and b is the imaginary part. Both a and b are real numbers
The conjugate of a complex number z = a + bi is [tex]\hat{z}=a-ib[/tex]
Given that z = 12 + i
The conjugate of z is [tex]\hat{z}=12-i[/tex]
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•
Read the following and answer the adjoining questions.
John's family is planning a road trip to Florida.
John is using the following information to help plan the trip:
- total distance (one way): 1,023 miles
- average driving speed: 60 miles per hour
- driving time on first day: 10 hours.
The question is, write an equation John can use to represent the relationship between distance traveled, in miles, d, and driving time, in hours, t
The relationship between distance traveled, in miles, d, and driving time, in hours, t. The Equation is 60 miles × 10 hours = 1023 miles
Distance:
Distance is a numerical or sometimes qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria. Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also often used metaphorically to refer to a measure of the amount of difference between two similar objects or some degree of separation.
Most of these concepts of distance, whether physical or metaphorical, are formalized in mathematics using the concept of metric spaces.
According to the Question:
total distance (one way): 1,023 miles
average driving speed: 60 miles per hour
driving time on first day: 10 hours.
Now,
Average driving speed = 60 miles per hour
Driving time on first day = 10 hours.
Total distance on first day = 60 miles × 10 hours
= 600 miles/ Hour.
and,
The relationship obtained from the Given equation is:
60 miles + 10 hours = 1023 miles
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NOTE: Answers using z-scores rounded to 3 (or more) decimal places will work for this problem. The population of weights for men attending a local health club is normally distributed with a mean of 174 lbs and a standard deviation of 29-lbs. An elevator in the health club is limited to 35 occupants, but it will be overloaded if the total weight is in excess of 6475 -lbs. Assume that there are 35 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded?
the average weight beyond which the elevator would be considered overloaded is approximately 7616.56 lbs.
What is probability?
Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities are usually expressed as fractions, decimals, or percentages.
The total weight of 35 men in the elevator can be modeled by the sum of 35 independent and identically distributed normal random variables with mean 174 lbs and standard deviation 29 lbs. Let X be the weight of one man, then the total weight of 35 men is W = 35X.
The mean of W is:
μW = E(W) = E(35X) = 35 E(X) = 35 * 174 = 6090 lbs
The variance of W is:
Var(W) = Var(35X) = 35^2 Var(X) = 35^2 * 29^2 = 899150
The standard deviation of W is:
σW = sqrt(Var(W)) = sqrt(899150) = 947.85
To find the average weight beyond which the elevator would be considered overloaded, we need to find the weight that corresponds to the 95th percentile of the distribution of W, since the elevator is overloaded if the total weight is in excess of 6475 lbs.
Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 95th percentile: z = 1.645 (rounded to 3 decimal places).
We can then find the weight w that corresponds to this z-score:
w = μW + z * σW
w = 6090 + 1.645 * 947.85
w ≈ 7616.56
Therefore, the average weight beyond which the elevator would be considered overloaded is approximately 7616.56 lbs.
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A Ferris wheel has a diameter of 150 ft. Passengers ride in a carriage around the Ferris wheel. Use your approximation in Question 15 to write an equation relating the total distance traveled to the number of rotations of the wheel. Be sure to define your variables. Show or explain your thinking
To get distance we use formula derived in Question 15, which gives an approximation of the circumference of the wheel based on its diameter which is 471.24nft
[tex]C = \pi d[/tex]
where d: diameter and C: circumference.
With the diameter of 150 feet provided, we can calculate the wheel's circumference as follows:
[tex]C = π(150) = 471.24 ft[/tex]
For our issue, let's define some variables:
n: the number of times the Ferris wheel has rotated
d: the Ferris wheel's circumference
C: the Ferris wheel's circumference
S: the total distance a passenger travels
Given that a passenger travels one circumference every spin, the overall distance after n rotations is roughly equal to:
S ≈ nC
In place of our values, we obtain:
[tex]S = n(471.24) = 471.24n ft[/tex]
So, assuming the Ferris wheel has a 150-foot diameter, we may use the equation S 471.24n to roughly calculate the total distance a passenger would have travelled in ferris wheel spins. However keep in mind that this is just a rough estimate, and it might not be completely correct depending on things like the size of the carriage and the height of the passenger above the ground.
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The expression (6x+5)/(x+7) written in the form quotient +( remainder )/( divisor ) is
6x + 5 + ( -2 )/( x + 7 ), The expression can be written as the quotient of 6x + 5 divided by x + 7, plus the remainder of -2, all divided by the divisor of x + 7.
To calculate (6x+5)/(x+7), first we must add x to both the numerator and the denominator to get (6x+x+5)/(x+7+x), which simplifies to (7x+5)/(2x+7). Then, divide the numerator by the denominator to get (7x+5)/(2x+7) = 3.5x + 2.5. To find the remainder, subtract 3.5x and 2.5 from both the numerator and denominator, which gives us (7x+5)-(3.5x+2.5) = 3.5x + 2.5 - (3.5x + 2.5) = 3.5x - 2.5. Lastly, divide the remainder by the divisor (2x+7) to get (3.5x-2.5)/(2x+7). Therefore, the answer is 3.5x + 2.5 + (3.5x - 2.5)/(2x+7).
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In a factory, three machines, J, K and L, are used to make biscuits. Machine J makes 25% of the biscuits. Machine K makes 45% of the biscuits. The rest of the biscuits are made by machine L. It is known that 2% of the biscuits made by machine J are broken, 3% of the biscuits made by machine K are broken and 5% of the biscuits made by machine L are broken. A biscuit is selected at random. Calculate the probability that the biscuit is made by machine J and is not broken.
B. Probability that the biscuit is made by machine and is not broken is:
1-(25% × 2%)
= 50%
c. The probability of breakage: 2% + 3% + 5% = 10%
d. Probability that biscuit is not made by machine = 1-5% = 95%
What do you mean by probability?Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. About an event's outcome, we might be certain or uncertain.
When this occurs, we state that there is a possibility that the event will occur. In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence.
Now from the question,
The probability that the biscuit is made by machine and not broken:
1 - 25% × 2%
= 50%
Now not broken probability = 1- 25% × 2%
Now next, the probability of breakage: 2% + 3% + 5% = 10%
Finally, the probability that biscuit is not made by machine = 1-5% = 95%
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The weight of the eggs produced by a certain breed of hen are normally distributed with a mean of 65 grams and standard deviation of 5 grams. What is the probability that a sample of 12 eggs will have a mean weight of more than 68 grams?
There is a 0.0838 or 8.38% chance that a sampling of 12 eggs has a weighted mean greater than 68 grammes.
The Central Limit Theorem, which asserts that group means of a large sample size from every population, irrespective of its distribution, will be roughly distributed normally with an average equal to the inhabitants imply and a variance equal to the standard deviation of the population multiplied by the square root of the random sample, must be used to solve this problem.
As a result, there is a 0.0838 or 8.38% chance that a sampling of 12 eggs has a weighted mean greater than 68 grammes. When n is the sample size, x is the sample mean, is the population mean, and seems to be the population standard deviation.
In this instance, n = 12 eggs, x = 68 grammes, = 65 grammes, = 5 grammes. When these values are added to the formula, you obtain:[tex]z = (68 - 65) / (5 / √12) = 1.385[/tex]
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A manufacturer buys a new machine that costs $50,000. The estimated useful life for the machine is ten years. The
achine can produce 1,000 units per month. If the machine ran at its capacity for ten years, what would be the fixed cost per unit based on
e cost of the machine per part manufactured? (Round to the nearest penny)
oooo
a) $. 42 / unit
b) $1. 00/unit
c) $4,167 / unit
d) $5,000/unit
The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
What is multiplication ?
Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.
To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.
The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:
10 years x 12 months/year x 1,000 units/month = 120,000 units
The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:
$50,000 ÷ 120,000 units = $0.4167 per unit
Rounding this to the nearest penny gives us the final answer of:
$0.42 per unit (option a)
Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
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Todd and Eric went to the book store. Eric spent $15 less than three times the
amount that Todd spent. If the shoppers spent a total of $197 in books, How much
did Eric spend?
$34
$53
$65
$71
$29
$59
$48
Using an equation, the amount Eric spent at the bookstore was $45.50.
What is an equation?An equation is a mathematical statement of the equality or equivalence of two or more algebraic expressions.
Equations are depicted using the equal symbol (=).
Let the amount that Todd spent in the bookstore = 3x
Let the amount that Eric spent in the bookstore = x - 15
The total amount spent by the two shoppers = $197
Equation:197 = 3x + x - 15
182 = 4x
45.5 = x
Check:
Amount spent by Eric = $45.50
The amount spent by Todd = 45.50(3) + 15 = $151.50
The total amount spent by the two shoppers = $197 ($45.50 + $151.50)
Thus, the equation shows that Eric spent $45.50 which is $15 less than three times the amount that Todd spent or $151.50.
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