less than 85 milligrams per liter.
To find the probability that a water specimen has an alkalinity level of fewer than 85 milligrams per liter, we can use the standard normal distribution and convert the value of 85 milligrams per liter to a standard score (z-score). The z-score can be calculated using the formula:
z = (x - mean) / standard deviation
Where x is the value of interest (85 milligrams per liter), mean is the mean of the distribution (80 milligrams per liter), and the standard deviation is the standard deviation of the distribution (4.2 milligrams per liter).
Plugging in the values, we get:
z = (85 - 80) / 4.2 = 1.19
Next, we can use a standard normal table or calculator to find the probability of getting a value less than the z-score of 1.19. This probability is approximately 0.8707, so there is about an 87.07% chance that a water specimen collected from the river has an alkalinity level of fewer than 85 milligrams per liter.
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What is the definition of data
Answer:
A collection of facts, such as numbers, words, measurements, observations.
Step-by-step explanation:
while attending school, you work part time at a coffee shop. last year, you made $8,700. why might you still file your taxes, even though you made less than the standard deduction?
Even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.
What is a freelancer?Freelancer, freelancer, or freelance worker are phrases frequently used to describe someone who is self-employed and isn't necessarily long-term dedicated to a certain employer.
Others work independently or use websites or professional associations to find work.
Freelancers are occasionally represented by a business or a temporary agency that resells their services to clients.
Independent contractors must always pay taxes on their wages, regardless of how much they make.
The term "freelancing" is most frequently used in the culture and creative industries, and use of this term may indicate participation in these sectors, even though the term "independent contractor" would be used in a different register of English to designate the tax and employment classes of this type of worker.
Therefore, even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.
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J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey, May 2012.
a. Did you purchase or lease the vehicle?
b. What price did you pay?
c. What is the overall attractiveness of your vehicle’s exterior? (Unacceptable, Average, Outstanding, or Truly Exceptional)
d. What is your average miles-per-gallon?
e. What is your overall rating of your new vehicle? (1- to 10-point scale with 1 unacceptable and 10 truly exceptional)
A plurality of magnitude can represent the property of number or amount, which exhibits both discontinuity and continuity and in the given situation, we would pay a quantitative amount to the seller.
What is Quantitative?A property called quantity or amount can take the form of a plurality of magnitude, which shows both discontinuity and continuity.
Comparing quantities can be done by using phrases like "greater," "less," or "equal," as well as by assigning a numerical value that is a multiple of the unit of measurement.
Among the well-known examples of quantitative qualities are mass, time, distance, heat, and angle.
Along with quality, substance, change, and relationship, quantity is one of the fundamental categories of things.
Some quantities serve as states (properties, dimensions, qualities) of things like heavy and light, long and short, broad and narrow, little and large, or much and little, while others are such by their very nature (as numbers).
Therefore, in the given situation, we would pay a quantitative amount to the seller.
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Correct question:
J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey, May 2012.
What Price did you pay?
you are given a system of 4 linear equations in 3 variables x, y, z. explain why it is impossible for the system to have exactly two solutions.
A system of 4 linear equations in 3 variables x, y, z can have at most one solution.
It is because a system with more than three equations and only three variables will not have a unique solution due to the fact that the dimension of the solution space of 3-dimensional equations is three, so adding an extra equation will result in an over-determined system.
In other words, there are not enough variables in the system to meet the requirements of all the equations, which leads to an over-determined system where there is either no solution or a unique solution. If the system has exactly two solutions, it means that the solution space of the system of equations has a dimension greater than 3, which contradicts the fact that the dimension of the solution space of a system of 3-dimensional equations is 3.
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Answer below i really really need help with this
Answer: 1/5
Step-by-step explanation:
One angle of a quadrilateral is 160 degrees. The other angles are all the same size. Work out the size of the other three angles
Answer:
Step-by-step explanation:
can you include a picture please
you have two six-sided dice that you roll at the same time. how would you calculate the probability of rolling a 1 with the first die and a 5 with the second die?
The probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.
The probability of rolling a 1 with the first die and a 5 with the second die can be calculated using the joint probability formula. The joint probability formula is P(A ∩ B) = P(A) x P(B|A). In this case, A is rolling a 1 with the first die and B is rolling a 5 with the second die. P(A) is the probability of rolling a 1 with the first die, which is 1/6. P(B|A) is the probability of rolling a 5 with the second die given that a 1 was rolled with the first die, which is also 1/6. Therefore, the probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.
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the eleventh term of an arithmethic sequence is 69 while the sum of the first three terms is 45. find the third term
The third term of this arithmetic sequence is 21.
eleventh term of an arithmetic sequence is 69.
a₁₁ = a + 10 d = 69
also sum of the first three terms is 45
the first three terms are a, a + d, a + 2d
a + a + d + a + 2d = 45
3a + 3d = 45
a + d = 15
a = 15 - d
so, a + 10 d = 69
15 - d + 10d = 69
9d = 69 - 15
9d = 54
d = 6
a = 15 - 6 = 9
a₃ = a + 2d
= 9 + 2(6)
a₃ = 21
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A 5 kilograms bag of beans cost $18.50. At the same rate, what amount of money would 9 kilograms bag of beans cost?
Answer: $33.3
Step-by-step explanation:
1kg of beans cost $3.70 then $3.70x9= $33.3.
Hope this helps.
(i) Express 2x² +8x-10 in the form a(x+b)² + c
Help
Answer:
2(x+2)² - 18
Step-by-step explanation:
Given
2x² +8x-10
express in the form a(x + b)² + c
Take out common factor 2 from 2x² +8x-10 ==> 2(x² + 4x -5)
x² + 4x - 5 can be converted to the form (x + b)² + c as follows using complete the square technique
(x + b)² = x² +2bx + b²
Comparing x² +2bx + b² and x² + 4x - 5 we can see that b = 2
So the expression becomes
x² + 4x - 5 = (x+2)³ + c
= x² + 4x + 4 + c
Therefore -5 = 4 - c
c = -5 -4 = -9
Therefore
x² + 4x - 5 = (x+2)³ -9
2(x² + 4x -5) = 2[(x+2)³ -9]
=2(x+2)² -18
ANSWER
Verify
2(x+2)² -18 = 2(x² +4x + 4) - 18 = 2x²+8x +8 - 18 = 2x² + 8x - 10
Thus verified
rty families gathered for a fund-raising event. suppose the individual contribution for each family is normally distributed with a mean and a standard deviation of $115 and $35, respectively. the organizers would call this event a success if the total contributions exceed $5,000. what is the probability that this fund-raising event is a success?
The probability that fund-raising event is a success and total contributors exceeds $5,000 is 0.0351 or 3.51%
Number of family members = 40
Mean of individual contributions for each family is normally distributed is $115 (μ) and standard deviation(σ) is $35. It is also given that the organizers would call this event a success if the total contributions exceed $5,000
Mean = [tex]\frac{5000}{40}[/tex]
Mean = 125
P-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
P(mean > 125) = P( 2 > [tex]\frac{(125 - 115)\sqrt{40} }{35}[/tex] )
= P(2 > 1.81)
= 1 - P(2 < 1.81)
1.81 has a pvalue of 0.9649
≅ 0.0351
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100 is no less than 20 times a number t
Answer:
You can put this solution on YOUR website!
100 >= 20t (that's "more than or equal to")
Divide each side by 20
5 >= t [5 is more than or equal to t]
or, conversely, t <= 5 [t is less than or equalequal to 5]
a class has 10 boys and 12 girls. 3 students are chosen at random to clean the classroom each day. how many unique cleaning teams exist?
The number of different unique cleaning teams should be 1540.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, A class has 10 boys and 12 girls and 3 students are chosen at random.
So, the team of 3 can be chosen as 3 boys, 3 girls, 1 boy 2 girls, and 1 girl and 2 boys and the total teams will be the sum of different combinations which is,
= [tex]^{10}C_3 + ^{12}C_3 + ^{10}C_1\times^{12}C_2 + ^{12}C_1\times^{10}C_2[/tex].
= (10×9×8)/6 + (12×11×10)/6 + 10×(12×11)/2 + 12×(10×9)/2.
= 120 + 220 + 660 + 540.
= 1540.
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PLEEEEASSE HELP
Consider the function, where C is the total cost, in dollars, for a sports uniform company to manufacture two different uniform pieces, x and y.
C=3x+2y
The given inequalities represent the constraints for a customer’s order.
x+y≥10
x−y≤10
x−y≥0
x≤20
What is the minimum total cost, C, for the company if all of the order constraints are fulfilled?
The minimum total cost for the company if all of the order constraints are fulfilled is given as follows:
$25.
How to obtain the minimum total cost?The cost function is given as follows:
C = 3x + 2y.
Meaning that:
Each item x costs $3.Each item y costs $2.The relevant restrictions to minimize the costs are given as follows:
x+y≥10: at least 10 items.x−y≥0: x equals or greater than y.Since an item y costs less than an item x, considering the second bullet point above, the cost is minimized with an equal amount of x and y.
From the first restriction, they must have at least 10 amounts, hence the cost is minimized with:
x = 5 and y = 5.
And the cost is of:
C = 3 x 5 + 2 x 5
C = $25.
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Haley's clothing store sold 540 shirts with the ratio o f short sleeve to long sleeve being 3:9. how many short sleeve were sold
The short sleeve shirts sold by haley were 405
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: Haley's clothing store sold 540 shirts with ratio of short sleeve to long as 3:9
let 3x and 9x long and short sleeves were sold respectively
Then we have
3x+9x=540
12x=540
x=540/12
x=45
Thus 3x=135 and 9x=405
Hence, The short sleeve shirts sold by haley were 405
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What are the coordinates of the orthocenter of triangle WXY with vertices W(2,7), X(3, 4), and Y(6, 7)?
Answer:
(3, 6)
Step-by-step explanation:
You want the coordinates of the orthocenter of triangle WXY with vertices W(2,7), X(3, 4), and Y(6, 7).
OrthocenterThe orthocenter is the point where the altitudes of the triangle meet. An altitude is the line through a vertex that is perpendicular to the opposite side.
This is an acute triangle, so the orthocenter is within the boundaries of the triangle.
AltitudesWe note that side WY of the triangle is a horizontal line, so the orthocenter will lie on the vertical line through point X. The x-coordinate of point X is 3, so that vertical line has equation x=3.
Side XY can be seen on the graph to have a slope of 1. Or, you can compute it from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (7 -4)/(6 -3) = 3/3 = 1
Then the point-slope equation of the altitude to that line will have the opposite reciprocal slope, and will go through point W(2, 7):
y -7 = -1(x -2)
Concurrent pointThe y-value of the point of intersection of the altitude through W with the altitude through X will be the solution to ...
x = 3y -7 = -x +2Substituting for x in the second equation, we have ...
y -7 = -3 +2
y = 6 . . . . . . . . . . add 7
The orthocenter is (x, y) = (3, 6).
__
Additional comment
The orthocenter of a right triangle is the vertex where the right angle is located. The orthocenter of an obtuse triangle is outside the triangle.
A cylinder has a height of 19 feet and a radius of 12 feet. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
8595.4
Step-by-step explanation:
The formula for volume of cylinder is: V = [tex]\pi[/tex][tex]r^{2} h[/tex]
[tex]\pi[/tex] = 3.14
radius = 12
height = 19
plug in the numbers which would give us = 3.14(12)^2(19)
which gives us 8595.4
if 12 bagels cost $35 how much would one cost
Answer:$2.97
Step-by-step explanation: 35 divided by 12 = 2.97
A bakery is selling breakfast platters. a platter of 12 bagels costs $10.20. additionally, it costs $4.65 for a gallon of coffee. what is the slope of this situation? a. 10.20 b. 4.65 c. 0.85 d. 0.12
The slope of the situation is 10.20. Answer (a) is correct.
How to determine the slope?The cost of the breakfast platter of 12 bagels is $10.20 and the cost of a gallon of coffee is $4.65.
The slope represents the rate of change between two variables, typically represented as y and x. In this case, it's not clear which variables we should use to calculate the slope. If we use the number of bagels as x and the cost as y, then the slope would represent the rate of change in cost per bagel.
Alternatively, if we use the gallons of coffee as x and the total cost as y, then we can calculate the slope. The total cost would be the sum of the cost of bagels and the cost of coffee, which is $10.20 + $4.65 = $14.85.
Using the formula for slope, which is (change in y) / (change in x), we can calculate the slope as follows:
slope = (change in cost) / (change in gallons of coffee)
= ($14.85 - $4.65) / (1 - 0)
= $10.20 / 1
= 10.20
Therefore, the slope of the situation is 10.20. Answer (a) is correct.
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19.Viktor's skating rink is 1.2 miles from his house. If he has practice at 7:00 am and can
walk at an average speed of 3.0 mph, what is the absolute latest he can leave to
arrive on time?
With his average speed of 3mph, Viktor should leave his house by 6:36 am to arrive at the skaring rink on time.
From the case, we know that:
Average speed = 3.0 mph
Distance = 1.2 miles
Arrival time = 7:00 am
Departure time?
Using the average speed concept, we know that average speed can be calculated by dividing the travel distance with the travel time, or it can be formulated as:
Average speed = distance : travel time
3.0 = 1.2 : travel time
travel time = 0.4 hours
After finding the travel time Viktor spend to go from his house to the skating rink, we need to find the departure time for him to arrieve at the skating rink on time. However, we need to convert the travel time into minutes first.
Travel time = 0.4 hours
Travel time = 0.4 x 60 minutes
Travel time = 24 minutes
Arrival time = Departure time + Travel time
7:00 = Departure time + 24 minutes
Departure time = 6:36 am or 24 minutes before 7:00 am
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Round 2 , 236.8 to the nearest ten
A solid metal cube of side 6 cm is recast into a solid sphere. Find the radius of the sphere.
Answer:
Answer provided in image May it help you !!!
Step-by-step explanation:
a ball of radius 13 has a round hole of radius 7 drilled through its center. find the volume of the resulting solid.
The volume of the resulting solid is 3,280.953 cm3.
The volume of the resulting solid is calculated by subtracting the volume of the inner sphere (the hole) from the volume of the outer sphere (the ball). The volume of a sphere is calculated by the formula V=4/3πr3. Therefore, the volume of the outer sphere is V1=4/3π(13)3=4,714.286 cm3. Similarly, the volume of the inner sphere is V2=4/3π(7)3=1,433.333 cm3. Subtracting V2 from V1 gives the volume of the resulting solid as V3=4,714.286 - 1,433.333=3,280.953 cm3. Therefore, the volume of the resulting solid is 3,280.953 cm3.
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recall that in problem 3 of the reading questions for section 2.1, you found that if , then . use this to find a formula for the tangent line to at .
The tangent line is y=x-1 and differentiation of ln(x) is 1/x
What does differentiation in mathematics mean?
Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables.
The most prevalent example is velocity, which is the rate at which a distance changes in relation to time.
The ratio of the vertical to the horizontal distance between any two points on it is called slope of ray or line or line segment in analytical geometry.
y-y1 = m(x-x1)
If the function passes through (1,0) and the slope equals to 1 is:
y-0 = 1(x-1)
y=x-1
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The complete question is -
Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = ln(x), then f'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2.
Simplify the expression:
[tex]\frac{\frac{a+b}{2a^2} }{\frac{a-b}{4a} }[/tex]
The simplification of the given expression gives the value 2(a + b) / a(a - b).
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is,
[(a + b) / 2a²] ÷ [(a - b) / 4a]
The fractional term in the denominator of the main expression can be written as the multiplication of it's reciprocal.
[tex]\frac{a}{b}[/tex] ÷ [tex]\frac{c}{d}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{d}{c}[/tex]
So the expression becomes,
[tex]\frac{a+b}{2a^2}[/tex] × [tex]\frac{4a}{a-b}[/tex]
= 2(a + b) / a(a - b)
Hence the simplified form of the given expression is 2(a + b) / a(a - b).
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what is the potential energy of the water in a lake of surface area 10 square miles, average depth 40 ft, and elevation above the electrical generator of 600 ft?
The potential energy of the water in a lake is 57 trillion N × m, which is 57 trillion joules (J).
Gravitational potential energy applies in this situation. G P E = m g h is the formula for gravitational potential energy, where: mg stands for weight or mass times gravity (w). The height to which an object can fall before kinetic energy replaces potential energy is denoted by the symbol h. In the example of the lake, we first determine the amount of water using the equation for the volume of a typical cylinder in order to determine the weight of the cylinder: V cy l = π r²L , The weight density of the water per cubic foot, which is about 62 lb, can then be multiplied by this volume: W(water) = (Volume) (Density)
W (water) = (28,000,000 ft² ⋅ 40ft) ( 62 lb ÷ ft³ )
W (water) = 69,440,000,000 lb
To calculate the potential energy, multiply this weight by the height. GPE=mgh
GPE=Wh=(69,440,000,000lb)(600ft)
GPE=41,644,000,000,000ft⋅lb
matching the level of precision by rounding the response to two significant digits. 4.2X10¹³ft⋅lb , or 42 trillion ft-lb.
Because joules are measured in N × m units, multiply the result by fractional equivalencies. 42trillionft × lb × (4.45N ÷ lb) × (m ÷ 3.28ft)
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Write 5 2/11 as a decimal rounded to the nearest tenth.
Answer:
5.18181818182
5.2 (nearest 10th)
Step-by-step explanation:
the unit kilowatt-hour is a measure of the unit kilowatt-hour is a measure of power. the amount of power used per second. an amount of energy. the rate at which energy is transformed.
The unit kilowatt-hour measures the amount of energy used or produced, whereas the rate at which energy is transformed is measured in kilowatts.
The unit kilowatt-hour (kWh) is a measure of energy, not power. Energy is a measure of the amount of work that can be done, and is usually measured in joules. Power, on the other hand, is a measure of the rate at which energy is transformed, and is usually measured in watts.
A kilowatt-hour is the amount of energy used or produced when a power of one kilowatt is used for one hour. For example, if a 100-watt light bulb is left on for 10 hours, it will have used
100 * 10 = 1000 watt-hours or 1 kilowatt-hour of energy.
So to summarize, the unit kilowatt-hour measures the amount of energy used or produced, whereas the rate at which energy is transformed is measured in kilowatts.
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Name the following triangles
Answer:
7-isoceles, 8- equilateral 9-scalene
Step-by-step explanation:
isoceles have 2 identical sides unlike scalene, where all sides have different lengths.
is obtuse and acute I think
HELP ASAP! A biologist measured the length and weight of several bluegills, which is a species of fish. Use linear regression to estimate the weight of a bluegill that has a length of 9.5 inches. Round your answer to the nearest tenth of an ounce.
Answer:
The weight is 95.53 ounces of bluegill which has a length of 9.5 inches using linear regression.
Step-by-step explanation:
good luck to you