A shipping container will be used to transport several 80-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 26500
kilograms. Other shipments weighing 6300 kilograms have already been loaded into
the container. Write and solve an inequality which can be used to determine x, the
number of 80-kilogram crates that can be loaded into the shipping container.
Answers
Answers:
The inequality to solve is \(80x+6300 \le 26500\)The solution to the inequality is \(x \le 252.5\)Interpretation: The most crates we can load is 252 since we can only load a positive whole number of crates, and because 253 is too many.==============================================================
Explanation:
x = number of 80-kilogram crates
x is some positive whole number
1 crate weighs 80 kilograms, so x of them will weigh 80x kilograms.
This is added on top of the 6300 kg from the other cargo already on board.
We have a total weight of 80x+6300. Let's call this T.
So T = 80x+6300
We want T to be 26500 or smaller. Otherwise, we've gone over capacity.
This must mean we want \(T \le 26500\) which is the same as saying \(80x+6300 \le 26500\) after replacing T with 80x+6300.
---------------------------
Let's follow PEMDAS in reverse to isolate x
\(80x+6300 \le 26500\\\\80x+6300-6300 \le 26500-6300 \ \text{ ... subtract 6300 from both sides}\\\\80x \le 20200\\\\\frac{80x}{80} \le \frac{20200}{80} \ \text{ ... divide both sides by 80}\\\\x \le 252.5\\\\\)
The inequality sign stays the same the entire time. It would only flip if we divided both sides by a negative number.
In the last step, we get a decimal value. However, as stated earlier, x is a positive whole number.
We cannot round to 253 because that's too high. We can check x = 253 is too high by noticing that...
80x+6300 = 80*253+6300 = 26,540
which is over the 26,500 mark by 40 kg
So we must round down to the nearest whole number and find that x = 252 is the largest x value possible. Let's check to see if we're under the weight limit
80x+6300 = 80*252+6300 = 26,460
We're under the 26,500 weight limit (with 40 kg to spare)
In short, the most crates that we can load is 252 crates in addition to the other cargo that collectively weighs 6300 kg (which may or may not consist of those 80-kilogram crates).
Related Questions
An equation is modeled 5x+6= What value of x makes the equation true
A (1)
B (7)
C (-5)
D (-1)
Answers
Explanation: Im Just Answered it
96 020 meters converted into kilometers?
Answers
1 km = 1000 m
1 m = 0,001 km
96 020 m = 96 020 * 0,001 km = 96,02 km
Answer:
96.02 km
Step-by-step explanation:
write an equation for a degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and has a y-int at 5..
Answers
The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:
y = -5/12(x - 3)(x - 2)²(x + 1)³.
How to define the polynomial?The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.
The zeros of the function, along with their multiplicities, are given as follows:
Zero at x = 3 with a multiplicity of 1.Zero at x = 2 with a multiplicity of 2.Zero at x = -1 with a multiplicity of 3.Then the linear factors of the function are given as follows:
(x - 3).(x - 2)².(x + 1)³.The function is then defined as:
y = a(x - 3)(x - 2)²(x + 1)³.
In which a is the leading coefficient.
When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:
5 = -12a
a = -5/12
Hence the polynomial is:
y = -5/12(x - 3)(x - 2)²(x + 1)³.
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what is the length (magnitude) of the vector (5 -2)
a. √29
b. 5√5
c. 5
d.√2
Answers
Answer:
a. √29
Step-by-step explanation:
The formula for the magnitude of a vector is magnitude = sqrt(x^2 + y^2).
For vector (5, -2):
magnitude = sqrt(5^2 + -2^2)
magnitude = sqrt(25 + 4)
magnitude = sqrt(29)
Therefore, the answer is √29.
Hope this helped :D
A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7.50, and tickets for children cost $3.50. How many of each type of ticket were purchased?
Answers
There are 23 tickets which are purchased for children and 9 tickets are purchased for adults which cost total $148.
It is given in the question that 32 tickets are purchased by group which cost total $148.
Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x
Now cost of one ticket for adult = $7.50
Total amount spent on adult tickets = 7.50 × (32-x)
Similarly, cost of one ticket for child= $3.50
Total amount spent on children tickets = 3.50 × x =3.5x
Total amount spent by group on tickets = $148
⇒ 7.5 × (32-x) + 3.5x = 148
⇒ 240 - 7.5x + 3.5x = 148
⇒ 7.5x - 3.5x = 240 - 148
⇒ 4x = 92
⇒ x = 23
Children = 23
Adults = 32-x = 32-23 = 9
Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.
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Find the number which is exactly half way between 16/7 and 2 11/28
Answers
Answer: 2 and 19/56
Step-by-step explanation:
x = (16/7 + 2 11/28)/2
x = (64/28 + 67/28)/2
x = (131/28)/2
x = 131/56 or 2 19/56
If M=1,000,P=2.25, and Y=2,000, what is velocity? a. 2.25 b. 4.5 c. 2 d. None of the above is true
Answers
Answer:d
Step-by-step explanation:
The answer is d. None of the above is true.
To calculate velocity, we need to use the equation:
Velocity = M * P / Y
Given:
M = 1,000
P = 2.25
Y = 2,000
Plugging in the values:
Velocity = 1,000 * 2.25 / 2,000
Simplifying:
Velocity = 2.25 / 2
The result is:
Velocity = 1.125
Therefore, the correct answer is: d. None of the above is true.
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bivariate data is the type of data that a scatterplot is used to analyze?
True
or
False
Answers
What is the inverse function of d(x) = -2x - 6?
a.) d-^1(x) = 2x + 6
b.)d-^1(x) = 2x + 6
c.)d-^1(x) --2x-3
d.)d-^1(x) = -2x-3
Answers
Answer:
d(x)= -x/2 - 3
Step-by-step explanation:
Determine the vertex of a parabola represented by the equation f (x ) = x2 - 2x - 8, with two symmetric points on the parabola (2, -8) and (0, -8).
Answers
The two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The vertex of a parabola in standard form, f(x) = a(x - h)² + k, is at the point (h, k).
We can rewrite the given equation, f(x) = x² - 2x - 8, in standard form by completing the square:
f(x) = x² - 2x - 8
= (x² - 2x + 1) - 1 - 8
= (x - 1)² - 9
So the vertex of the parabola is at the point (1, -9), where h = 1 is the x-coordinate of the vertex, and k = -9 is the y-coordinate of the vertex.
To verify that points (2, -8) and (0, -8) are symmetric about the vertex, we can calculate the axis of symmetry, which is x = h, or x = 1 in this case.
The distance between the vertex (1, -9) and the point (2, -8) is the same as the distance between the vertex and the point (0, -8), since these points have the same y-coordinate:
d((1, -9), (2, -8)) = d((1, -9), (0, -8))
Using the distance formula, we can calculate the left-hand side:
d((1, -9), (2, -8)) = √((2 - 1)² + (-8 - (-9))²)
= √(1 + 1)
= √(2)
Using the distance formula again, we can calculate the right-hand side:
d((1, -9), (0, -8)) = √((0 - 1)² + (-8 - (-9))²)
= √(1 + 1)
= √(2)
Hence, the two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).
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You can compare two marginal distributions to see if the corresponding two variables are related.T or F
Answers
You cannot compare two marginal distributions to see if the corresponding two are related . So, the statement is false .
The answer to the stated question is false . No , you cannot compare two marginal distributions to see if the corresponding two variables are related.
The given question is related to probability and statistics.
Coming to probability distribution , it is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.
The marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.
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A confidence interval is constructed to estimate the value of O a statistic or parameter O a statistic. O a parameter
Answers
A confidence interval is constructed to estimate the value of a parameter.
In statistics, a parameter refers to a numerical characteristic of a population, such as the population mean or population proportion. When we want to estimate the value of a parameter, we construct a confidence interval.
A confidence interval provides a range of values within which we believe the true parameter value is likely to fall, based on our sample data. It is constructed using sample statistics and takes into account the variability and uncertainty in the estimation process.
A confidence interval is constructed to estimate the value of a parameter, not a statistic.
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PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS PLS HELP ASAP ILL GIVE BRAINLKEST PLS
Answers
Answer:
first one is 42/7 = 6
11*6 = 66
second one
1/2 inch = 3/2 feet
17/2 inches = 17*3 = 51/2 = 25.5
Answer:
Question 4
You have actual length of the stage is 42 feet and the scale drawing is 11cm: 7ft. Divide the 42 by 7 and the answer is 6. You would need 6 of the 7 ft increments to equal the total of the 42 ft stage. If you multiply one side of a ratio, then you have to multiply both sides. 11 x 6= 66!
Step-by-step explanation:
42/7 = 6
11cm x 6: 7ft x 6
66cm: 42ft
Question 5
You have an actual length of the garage is 8 1/2 inches, or 8.5 inches on the blueprint. It take 2 of the 1/2 inch segments to get 1 inch. You need 8 1/2 or 8.5 total inches. You have to multiply 8.5 by 2 to get the total number of 1/2 inch increments that you need. 8.5 x 2 = 17. This tells you that you would need 17 of the 1/2 increments to get your total blueprint length. If you multiply one side of a ratio, then you have to multiply the other side. 17 x 1 1/2 or 1.5 = 25.5
Step-by-step explanation:
1/2 inch or 0.5 inch x 2 = 1 inch
8 1/2 inches or 8.5 inches x 2 increments = 17 increments
1 1/2 ft or 1.5 ft x 17 = 25.5 ft
I need help please. I’m struggling badly with number 1
Answers
Answer:
hope it helps
Step-by-step explanation:
what is the correlation
Answers
Answer: moderate, C, B
Step-by-step explanation:
A) A shows a moderate negative correlation. It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation. It is also negative because it has a negative slope
B) C shows the strongest correlation because the points around the line are tight and close.
C) B should not have been drawn. The correlation is very weak. You do know where the line should be because the points are all over the place.
if 26 children were to be born in a hospital on a given day, how many combinations of 6 boys and 20 girls would exist? 230,230 4 x 10^26 500,000 15 Z
Answers
The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.
]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.
In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.
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a local cable company claims that the proportion of people who have internet access is less than 63%. to test this claim, a random sample of 800 people is taken and its determined that 478 people have internet access. the following is the setup for this hypothesis test: h0:p
Answers
The p-value for this hypothesis test for a proportion p is 0.039.
What is a random sample?
In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals is chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.
For the null hypothesis,
H0 : p = 0.63
For the alternative hypothesis,
Ha : p < 0.63
This is a left-tailed test
Considering the population proportion, probability of success, p = 0.63
q = probability of failure = 1 - p
q = 1 - 0.63 = 0.37
Considering the sample,
Sample proportion, P = x/n
Where,
x = number of success = 478
n = number of samples = 800
P = 478/800 = 0.6
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76
From the normal distribution table, the area below the test z score in the left tail is 0.039
Thus,
p = 0.039
Hence, the p-value for this hypothesis test for a proportion p is 0.039.
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Which choice lists the numbers in increasing order?
Answers
Answer:
D
Step-by-step explanation:
Because negative is smaller than fractions. and ABC, is all off.
Answer: I think the answer is D/ the last answer
Step-by-step explanation:
find the marked angle of
Answers
Answer:
∠ C = 100°
Step-by-step explanation:
since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.
consider the angle inside the triangle to the left of 140°
this angle and 140° are a linear pair and sum to 180°
angle + 140° = 180° ( subtract 140° from both sides )
angle = 40°
then the angle on the left of the triangle = 40° ( base angles congruent )
the sum of the angles in a triangle = 180° , so
∠ C + 40° + 40° = 180°
∠ C + 80° = 180° ( subtract 80° from both sides )
∠ C = 100°
If your cell phone bill was 67.82 and there is a 1/20 late fee how much will your bill be with the late fee included?
Answers
Answer:
Assuming 1/20 is a 5% late fee:
$21.211
Step-by-step explanation:
67.82 x 1/20 = 3.391
67.82 + 3.391 = 71.211
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x + 2y = 14
Answers
Answer:
Hope this helps :-) Answer in black and green (the typed one came out a little small)
Step-by-step explanation:
At Ashland Middle School, 70% of sixth graders wore athletic shoes to school on the first day of school. The number of sixth graders wearing athletic shoes that day was 35. Shade the grid to show the percent of sixth graders who wore athletic shoes
Answers
Answer:
Can I see the grid?
Step-by-step explanation:
Which table does not show a direct variation?
(btw I know C is the wrong answer so I highlighted it.)
Answers
Answer:
B… I think…
Step-by-step explanation:
I think it's B because all the other ones increase at a constant rate, whereas B just squares x to get y.
True or False: the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.
Answers
It is false that the probability of the union of two events can be more than the probability of the intersection of the two events occurring.
This is because when two events intersect, the intersection of the two events refers to the occurrence of both events at the same time, while the union of the two events refers to the occurrence of either event or both events at the same time. therefore, the union of two events can have a higher probability of occurring than the intersection of two events since the union includes the possibility of both events occurring, while the intersection does not.
For example, let us consider two events, A and B. Event A has a probability of 0.3, and event B has a probability of 0.4. The probability of the intersection of these two events is 0.12(0.3 X 0.4) while the probability of the union of these two events is 0.7(0.3+0.4-0.12). As seen in this example, the probability of the union of two events (0.7) is greater than the probability of the interaction of two events(0.12)
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A student was given to solve 25 ×36 . Instead ,he solved 25×63. By how much did his answer differ?
Answers
Answer:
His answer differ by 675
Step-by-step explanation:
25*36=900
25*63=1575
1575-900=675
Answer:
He will answer as 25*63=1575
what is the probability that a salesperson selected at random will have an excellent potential for advancement given they have above average sales ability?
Answers
The probability that a salesperson selected at random will have an excellent potential for advancement given they have above average sales ability is 0.3.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. Information about the possibility that something will happen is provided by probability. For instance, meteorologists utilize weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.
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Have a good day! No question
Answers
Answer:
Thanks and have a good day.
In one week, 390 people answered a telephone survey.
The histogram shows their ages.
Ages of People Who Answered a Telephone Survey
200
150
Number of People
100
50
26-30 31-35 36-40 41-45 46-50
Age (years)
How many people who answered the survey were
35 years old or younger?
А
150
B
60
C
90
Answers
Answer:
150 people
Step-by-step explanation:
First, look over the chart and find the rows that have listed as 26 - 30 and 31 - 35.
Find out how high the row goes by looking at the number on the side of the gram.
26 - 30 goes to 60
31 - 35 goes to 90
Then add the 2 numbers together and you will find your total
60 + 90 = 150 people
a girl chooses an item at random from 12 skirts and 16 tops. what is the probability that the girl does not chose a skirt
Answers
Answer:
16/28
Step-by-step explanation:
Total number = 12+16
= 28
If she doesn't choose a skirt then she will choose a top = 16
Probability = number of items
sum of items
= 16/28
The probability of not choosing a skirt is 4/7.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of skirts = 12
Number of tops = 16
The total number of clothes.
= 12 + 16
= 28
The probability of not choosing a skirt.
= 1 - the probability of choosing a skirt
= 1 - 12/28
= 1 - 3/7
= 4/7
or
The probability of not choosing a skirt.
= probability of choosing a top
= 16/28
= 4/7
Thus,
The probability of not choosing a skirt is 4/7.
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Ayuden por favor, no entiendo este problema
Answers
We will get that the angle theta is:
θ = β/2
How to find the value of theta?Remember that the sum of the interior angles of any triangle must be equal to 180°.
Now, looking at the triangle in the left, we can see that the top angle is equal to:
180 - 2α
The right angle is equal to:
180 - 2β
And the left angle is α
Then we can write:
α + (180 - 2α) + (180 - 2β) = 180
-α - 2β = -180
α = 180 - 2β
Now we can go to the other triangle, where theta is, and write:
α + β + 2θ = 180
Replacing what we found above, we get:
180 - 2β + β + 2θ = 180
-β + 2θ = 0
θ = β/2
That is the best simplification we can get with the given diagram.
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