The percentile rank of 64 in the twelve students exam result is 42%
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
Ordering the data we have:
90 64 99 71 72 93 40 85 45 50 55 66
40 > 45 > 50 > 55 > 64 > 66 > 71 > 72 > 85 > 90 > 93 > 99
The 64 result is the 5th term of all the results, so:
percentile rank = (term / total term) * 100%
percentile rank = 5/12 * 100%
percentile rank = 41.66%
41.66% round to the nearest percentile 42%
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Describe each x-intercept as "crosses" or "touches" the x-axis
Answer:
Third option
touches at x = 1crosses at x = -3crosses at x = -5Step-by-step explanation:
If the polynomial has a factor of the form [tex](x - h)^p,[/tex] the behavior of its graph is determined by the value of p. p .
One zero of the polynomial is x = h
x - h is a zero of multiplicity p
The following is a summary of rules regarding multiplicities and x-intercepts.
For even multiplicities, i.e. p = 2, 4, 6, 8,... the graph will touch the x-axis for the zerosFor odd multiplicities, i.e. p = 1, 3, 5, 7,... the graph will cross the x-axis for the zerosThe given polynomial is:
[tex]\mbox {\large \textsf(x - 1)^2(x+3)(x + 5)^5}}[/tex]
The zeros can be found by setting each of these factors to 0 and solving for x
x - 1 = 0 ==> x = 1
x + 3 = 0 ==> x == -3
x + 5 = 0 ==> x = -5
Hence, the zeros of this polynomial are
x = 1 with a multiplicity of 2x = -3 with a multiplicity of -3x = -5 with a multiplicity of -5Using the rules provided we see that the graph
touches at x = 1crosses at x = -3crosses at x = -5This corresponds to
Third option
help_outline (a) what is the cardinality of p({1, 2, 3, 4, 5, 6})?
Cardinality of the power set of the given set = 64
Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.
Example set:
{1,2,3}
All the possible subsets of this set:
{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}
The power set of the above set is written as:
P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })
Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.
Cardinality of the power set of a given set is expressed by a formula:
where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.
Hence in the given case, we have n = 6.
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the average weight of a honeycrisp apple is 110 grams and the standard deviation is 20 grams. what is the z-value for an apple that weighs 140 grams?
the z-value for an apple that weighs 140 grams is 1.5.
The z-value is used to determine how many standard deviations an observation is from the mean of a normal distribution. To find the z-value for an apple that weighs 140 grams, we need to calculate the difference between the apple's weight and the mean weight, and divide by the standard deviation.
Given that the average weight of a honeycrisp apple is 110 grams and the standard deviation is 20 grams, we can calculate the z-value as follows:
(140 - 110) / 20 = 1.5
This means that the apple that weighs 140 grams is 1.5 standard deviations above the mean weight of 110 grams. This information can be used to calculate the probability of finding an apple with a weight of 140 grams. For example, if we use a standard normal distribution table, we can find that the probability of finding an apple with a weight greater than 140 grams is 0.0668, or 6.68%.
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the admissions office wants to estimate the cost of textbooks for students at our college. let the variable x be the total cost of all textbooks purchased by a student this semester. the plan is to randomly identify 100 students and obtain their total textbook costs. the average cost for the 100 students will be used to estimate the average cost for all students. (a) describe the parameter the admissions office wishes to estimate.
The admissions office wishes to estimate the average cost of textbooks for all students, represented by the parameter μ (the population mean).
The parameter of the admissions officeThere are steps followed to determine the parameter the admissions office wishes to estimate:
Define the population: In this case, the population is all students at the college.Define the variable of interest: The variable of interest is the cost of textbooks for each student, represented by the variable x.Determine the parameter of interest: The parameter of interest is the average cost of textbooks for all students, represented by the population mean μ.Choose a sample: The admissions office plans to randomly select 100 students and obtain their total textbook costs.Use the sample to estimate the population parameter: The average cost for the 100 students will be used to estimate the average cost of textbooks for all students, represented by the population mean μ.Learn more about The parameter of the admissions office here:
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Explain the answer step by step please
The answer is D.
The portion of the statement [tex]{x\to 0}[/tex] says we're looking at the graph as the x-values get closer to 0. So we're looking at x-values like 0.1, 0.01, 0.001, 0.0001, etc and -0.1, -0.01, -0.001, -0.0001, etc.
The [tex]\lim\limits_{x\to 0}f(x)[/tex][tex]\lim\limits_{x\to 0}f(x) = 1[/tex] as a whole is asking "are the y-values on the graph headed towards a specific y-value as x-values get closer to 0?"
As you move towards x = 0 from either side, the y-values get closer to y=1.
So [tex]\lim\limits_{x\to 0}f(x)=1[/tex].
if a man casts a 3 ft shadow at noon, and a 9 ft shadow at 6pm, then what length of shadow does his dog cast at 6pm, if it casts an 2ft shadow at noon?
His dog casts a shadow of 6ft at 6 pm if it casts a 2ft shadow at noon.
A man casts a 3 ft shadow at noon and a 9 ft shadow at 6 pm.
His dog casts a 2 ft shadow at noon.
Therefore we can find the length of shadow casts by his dog at 6 pm as follows:
Length of the shadow of a man at noon/length of the shadow of a man at 6 pm = length of the shadow of his dog at noon/length of the shadow of his dog at 6 pm
⇒3/9 = 2/length of the shadow of his dog at 6 pm
⇒length of the shadow of his dog at 6 pm = (2 × 9)/3
⇒length of the shadow of his dog at 6 pm = 6 ft
Hence, the shadow cast by his dog at 6 pm will be 6 ft.
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3) Mrs. Ramirez is planning a family reunion and deciding where to buy food and drinks. She considers the information below. She expects 96 family members to attend. How much would it cost to buy 96 hotdogs purchased from Value Market? Show your work.
b) How much would 96 hotdogs cost from Sammy's Bulk Store? Show your work. c) Which store offers the better buy for bottled water? Explain your reasoning. PLEASE HELP ME GUYS IM DESPERATE !!
The cost of 96 hotdogs from Value Market would be $94.04.
The cost of 96 hotdogs from Sammy's Bulk Store would be $75.84.
The better buy for bottled water would be from Value Market.
What is a Value Market?Value Market is a store that offers products at low prices, usually with a focus on basic household items, food and drink.
a) The cost of 96 hotdogs from Value Market would be 96 × $0.99 = $94.04.
b) The cost of 96 hotdogs from Sammy's Bulk Store would be 96 × $0.79 = $75.84.
c) The better buy for bottled water would be from Value Market. Value Market offers bottled water for $0.69 per bottle while Sammy's Bulk Store offers bottled water for $0.89 per bottle. Therefore, buying bottled water from Value Market would result in a lower cost for 96 bottles, which would be $0.69 × 96 = $66.24, compared to $0.89 × 96 = $83.84 from Sammy's Bulk Store.
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A veterinarian knows that the supplement glucosamine is beneficial for dogs’ joints. He wants to determine if a supplement with both glucosamine and chondroitin would be more beneficial than glucosamine alone for dogs’ joint health. The veterinarian asks the owners of dogs with known joint issues if they would be willing to have their dog participate in his study, and 32 owners agree to the study. The veterinarian also knows that breed and age may affect the results of the experiment.
Which of the following designs would be most appropriate for this experiment?
A) Completely randomized design: Randomly assign the treatments to the dogs.
B) Matched pairs design: Block the dogs based on breed. Then, within each block, pair the dogs based on age. Randomly assign the treatments to each dog in the pairs.
C) Randomized block design: Block the dogs based on breed. Then, randomly assign half of the dogs in each block to receive glucosamine only and the other half to receive glucosamine with chondroitin.
D) Observational study: The veterinarian should randomly select patient records. Then, use the joint health of dogs that use glucosamine only and those that use glucosamine with chondroitin.
The correct option: A) Completely randomized design: Randomly assign the treatments to the dogs.
How does randomized design work?"Any randomized design is regarded as a form of experiment that is assigned to various treatments by carrying out various experiments on various groups.
The answer to the query is
A veterinarian performs an experiment to see if glucosamine on its own or glucosamine + chondroitin is more useful.By randomly splitting the canines into 2 groups of sixteen each, a veterinarian experimented on 32 dogs. 16 dogs receive glucosamine therapy, and the remaining 16 receive glucosamine and chondroitin therapy.Each dog's health is assessed and compared after six months.Therefore, we get to the conclusion that the treatment given to the dogs at random is the best course of action.
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If No, give a reason.Let if be a function. Is it possible that f(2)=9 and f(3)=9 Multiple choiceA. Yes.B. No. A function assigns each value of x in its domain to exactly one value of fox).C. No. A function assigns each value of Fx) in its range to exactly one value of x.D. No. A function expecting a variable cannot be called with a constant argument.E. No. There is no possible function operations that would yield 9 from 3
(a) Yes,f(x)=9 since every point on this line would have a y-coordinate of 9.
(b) No. A function can have only one value of y corresponding to each value of x.
A function is an equation where each value of x corresponds to exactly one value of y, This means that different x-values can correspond to the same y value but different y-values cannot correspond to the same x value.
(a)
if f(1)=9and f(2)=9 then both x=1 and x=2 corresponds to y=9.
Since different x-values can go to the same y-value for a function, then it is possible that f(1)=9 and f(2)=9
For example, the function could be the horizontal line
f(x)=9 since every point on this line would have a y-coordinate of 9 .
b) If
f(1)=9 and f(1)=3, then y=3 and y=9correspond to x=1. Since functions cannot have different y-values corresponding to the same x-value, then it is not possible for f(1)=9 and f(1)=3
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A cyclit leave home and ride due eat for a ditance of 45 km. She return home on the ame bike path, if the entire trip take 4 hr , what i her diplacement
The displacement made by the cyclist is 0, this is caused by the same path traveled by the cyclist.
DisplacementDisplacement is the change in position of a moving object relative to a frame of reference. That is, locking is a change in the initial position of the object to the final position of the object.
The displacement in this case is calculated by the Pythagorean theorem.
Displacement² = S₁² + S₂²
The displacement will be zero when the start and end points are the same, that's what makes the problem zero. In the question, the distance traveled by the rider is 45 km, but because there is no position lock because the rider is traveling the same path, the closing done by the cyclist is 0.
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in response to recent unusual earthquake activity, a large city has enacted an ordinance requiring the permanent placement of seismographic equipment in the basements of 20 randomly selected commercial buildings throughout the city as part of the creation of an early-warning network. although the owners of the buildings will not be compensated, the cost of the purchase and installation of the equipment is to be borne by a private university that will operate the early-warning network. the owner of one building that has been randomly selected as a site for this equipment has challenged this law as unconstitutional, though the actual impact on him would be negligible. should the court rule in favor of the owner?
The court should not rule in favor of the owner, as the ordinance is likely constitutional. The ordinance is likely to be upheld as an exercise of the city's police power, which grants local governments the authority to pass laws and regulations in the interests of public health, safety, and welfare.
Furthermore, the ordinance does not appear to be an unreasonable exercise of the city's police power, as the installation of seismographic equipment is likely to benefit the public interest by providing early warning in the event of an earthquake. Moreover, the ordinance does not appear to be overly burdensome on the owner, as the cost of the purchase and installation of the equipment is to be borne by a private university, and the owner will not be compensated.
In short, the ordinance does not appear to be an unconstitutional taking of private property, as the owner's burden is minimal and the public benefit is substantial.
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Pleaseee help :) thank you!
Salut/Hello!
Answer: C. SAS~
Step-by-step explanation:
I left a photo for you so you can tell what I'm talking about.
1. The angles are equal because they are opposites.
2. Side AE is congruent with side ED.
3. Side BE is congruent with side EC.
I hope it was helpful! :]
Answer: SAS~
Step-by-step explanation:
Describe the transformations from shape A to B
Answer:
Therefore the transformation is a dilation of Figure a by a scale factor of -2
Step-by-step explanation:
Take any point on figure A and see what its coordinates are
Take the corresponding point on figure B and see what its coordinates are
This will give you an idea of what transformation has taken place
In figure A, take point (1, 3)
The corresponding point in Figure B is (-2, -6)
This is a dilation of the point (1, 3) by a scale factor of -2 since -2 x (1, 2) = (-2, -6)
The other points are similarly dilated
(3, 3) ==> (-6, -6)
(3, 4) ==> (-6, -8)
Therefore the transformation is a dilation of Figure a by a scale factor of -2
14. there are two bags. bag a contains 1 red ball and 9 blue balls. bag b contains 10 blue balls. you choose a ball at random from bag a and place it into bag b. you then choose a ball at random from bag b and place it into bag a. if after this process the red ball is in bag a, what is the probability that it was moved?
The probability the that red ball was moved is 1/100
Given that there are two bags. Bag A contains 1 red ball and 9 blue balls. Bag B contains 10 blue balls. A ball is chosen at random from bag A and placed into bag B. Then a ball is chosen at random from bag B and placed into bag A. After this process, the red ball is in bag A and we are asked to find the probability that it was moved.
Probability of the red ball chosen from bag A = 1/10
Probability of the red ball chosen from bag B = 1/10
After this process, the red ball is in bag A, the probability that it was moved.
1/10 × 1/10 = 1/100
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Use the branch-and-bound method to find the optimal solution to the following IP: max z = 7x1 + 3x2 s.t. 2x1 + x2 ≤ 9 3x1 + 2x2 ≤ 13 x1, x2 ≥ 0; x1, x2 integer
As per the branch and bound method, the optimal solution of IP is (0,6.5).
The term called branch and bound method is defined as an algorithm design paradigm which is generally used for solving combinatorial optimization problems
Here we have know that following equation and they are written as,
=> z = 7x₁ + 3x₂
=> 2x₁ + x₂ ≤ 9
=> 3x₁ + 2x₂ ≤ 13
where the value of x₁, x₂ ≥ 0 and the value of x₁, x₂ integer
In order to solve this one then we have to make the table for each of the constraint given here.
Then we get,
=> 2x₁ + x₂ ≤ 9
When x₁=0 then x₂=?
⇒2(0)+ x₂ =9
⇒x₂=9
Similarly When x₂=0 then x₁=?
⇒2x₁+(0)=9
⇒2x₁=9
⇒x₁= 9/2 = 4.5
Then the table for the constraint is written as
x₁ 0 4.5
x₂ 9 0
Similar way the table for the constraint 3x₁ + 2x₂ ≤ 13 is written as,
x₁ 0 4.33
x₂ 6.5 0
When we plot the graph, then we get the graph like the following.
The value of the objective function at each of these extreme points is as follows:
Extreme Point Lines through Objective
Coordinates Extreme Point function value
(x1,x2) Z=3x1+5x2
O(0,0) 3→x1≥0,4→x2≥0 3(0)+5(0)=0
A(4.33,0) 2→3x1+2x2≤13 4→x2≥0 3(4.33)+5(0)=13
B(0,6.5) 2→3x1+2x2≤13 3→x1≥0 3(0)+5(6.5)=32.5
Here the maximum value of the objective function Z=32.5 occurs at the extreme point (0,6.5).
Hence, the optimal solution to the given LP problem is : x1=0,x2=6.5 and max Z=32.5.
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Which expression is equivalent to 5^6/(5^0)^-4
A. 0
B. 5^8
C. 5^4.
D 5^6
Answer: 5^6
Step-by-step explanation:
5^6/(50)^−4 5*5*5*5*5*5=15625
=15625/(50)^−4
=15625/1^−4
=15625/1
=15625
5^6 = 5*5*5*5*5*5 = 15625
Hope this helps!!!
Am truck weigh 4,725 pound. The truck can carry 7,500 pound. What i the total weight of the truck and full load
The total weight of the truck is 7,500 pounds and the full load weighs 2775.
This is a simple subtraction problem and we can easily find out the required values by subtracting the correct values. It has been mentioned that the Truck can carry 7500 pounds and that the Truck's weight is 4725 pounds.
The weight of the load can be calculated as follows-
= 7500 - 4725 pounds
= 2775 pound
So, the total weight of the truck same as its total capacity with which it can carry, that is, 7500 pounds, and the weight of its full load which can be put in the truck is 2775 pounds.
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A rectangle ha an area of 24 quare meter. The width of the rectangle i 4 meter. What i the length of the rectangle? meter
Expected length = 6 meter.
Using the formula,
A = W × L
where,
Area (A) = 24
Width (W) = 4
Length (L) = ?
so, A/W = 24/4 = 6
Hence, length of the rectangle is 6 meter.
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The table below represents the value of the equation 2x+y=7 for x=0,1,2.....8
1. Find the value of A
2. Find the value of 2b
Answer:
Q10: a = 1 (Choice D)
Q11. 2b = -10 (Choice A)
Step-by-step explanation:
The given equation is
[tex]2x + y = 7[/tex]
We can rewrite this equation with y on the left side and other terms on the right:
Subtract [tex]2x[/tex] from either side:
[tex]2x + y - 2x = 7 - 2x\\\\y = 7 - 2x\;\;\cdots \cdots(1)\\[/tex]
Q10
The value of [tex]y = a[/tex] corresponds to an [tex]x[/tex] vlaue of [tex]6[/tex]
Plug in [tex]x = 3[/tex] into the equation [tex](1)[/tex] :
[tex]a = 7-2(3)\\\\a = 7 - 6\\\\a = 1\\\\[/tex] ANSWER
Q11
We can find b using the same technique as Q10
[tex]b = 7 - 2(6)\\\\b = 7-12\\\\b = -5\\\\[/tex]
Therefore
[tex]2b = 2(-5) = -10[/tex] ANSWER
a fair die is rolled six times. what is the probability that the rolls are 1, 2, 3, 4, 5, and 6, in any order?
The probability that the rolls are 1, 2, 3, 4, 5, and 6, in any order is [tex]\frac{1}{46656}[/tex].
A fair die is rolled six times.
The rolls are 1, 2, 3, 4, 5, and 6.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur. The probability of all the events in a sample space adds up to 1.
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes.Hence there is a [tex]\frac{1}{6}[/tex] chance a 1 will be rolled first, [tex]\frac{1}{6}[/tex] chance a 2 will be rolled second, [tex]\frac{1}{6}[/tex] that a 3 will be rolled third, etc. Therefore the probability of the sequence appearing is [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex].
On each of the six independent rolls there is a probability of 1/6
for rolling the desired number, so by the multiplicative principle, the probability for rolling the required sequence is:
Since each sequence of six rolls is equally likely, the answer is
[tex]\frac{1}{number of possible sequences of six rolls}[/tex]=[tex](\frac{1}{6} )^{6} =\frac{1}{46656}[/tex]
Therefore, the probability is [tex]\frac{1}{46656}[/tex].
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point-slope(urgent please,will give brainliest)
a. Plot the points (-3, 17) and (-1, 1) and draw a line through them.
b. Plot the points (-3, -14/3) and (-1, -2/3) and draw a line through them.
c. Plot the points (3, 2) and (5, 4) and draw a line through them.
What is the stepwise explanation of plotting the points?a. Point slope form equation for a line with slope m that passes through a point (x1, y1) is given by:
y - y1 = m(x - x1)
Using the given point (-2, 5) and slope -6, we have:
y - 5 = -6(x + 2)
Graph: The graph of the line can be drawn by finding two points on the line and plotting them, then drawing a line through the points.
For example, to plot the line when x= -3 and x = -1, we can substitute the respective x-values into the equation to find the corresponding y-values, then plot the points:
when x = -3, y = -3 * -6 + 5 = 17
when x = -1, y = -1 * -6 + 5 = 1
Plot the points (-3, 17) and (-1, 1) and draw a line through them.
b. Using the given point (-2, -8) and slope 5/6, we have:
y + 8 = (5/6)(x + 2)
Graph: Plotting the line using the same steps as above, for example, when x= -3 and x = -1,
when x = -3, y = (5/6)(-3 + 2) - 8 = -14/3
when x = -1, y = (5/6)(-1 + 2) - 8 = -2/3
Plot the points (-3, -14/3) and (-1, -2/3) and draw a line through them.
c. Using the given point (4, 3) and slope -1/2, we have:
y - 3 = -1/2 (x - 4)
Graph: Plotting the line using the same steps as above, for example, when x= 3 and x = 5,
when x = 3, y = -1/2 (3 - 4) + 3 = 2
when x = 5, y = -1/2 (5 - 4) + 3 = 4
Plot the points (3, 2) and (5, 4) and draw a line through them.
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What is the rule of greater than?
Greater than or less than symbols are used when a number is greater or less than another number. A greater than sign (>) is used if the first number is greater than the second number. If the first number is less than the second number, the less than sign (<) is used.
What is the greater than sign?In mathematics, the greater-than sign represents an inequality between two values. A common form of > joining two strokes of equal length at an acute angle on the right is found in documents dating from 1631.
> is the greater than sign. So 9>7 is interpreted as "9 is greater than 7".
less than icon. (greater than or equal to) and two other comparison characters (less than or equal to). Think of the symbol as something like a crocodile's mouth, with numbers representing small fish on either side.
Alligators always prefer to eat more fish. The higher the number, the more the crocodile's mouth opens.
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2/5x10/7 in simplest form
Answer:
4/7
Step-by-step explanation:
On average yasmin drinks 3/4 of an 8 ounce glass of water in 1 1/4 hours how much can she drink per hour
Answer:
She drinks 4.8 ounces of water per hour
Step-by-step explanation:
We know
Yasmin drank 3/4 of an 8-ounce glass of water in 1 1/4 hours
3/4 of 8 ounce = 6 ounces
1 1/4 = 5/4 = 1.25 hours
How much can she drink per hour?
6 divided by 1.25 = 4.8 ounces of water per hour
So, she drinks 4.8 ounces of water per hour.
find the value of for which the area enclosed by the curves =−2 and =2− is equal to 128.
At the value of c = 21 (approx) for which the area enclosed by the curves y = c - x^2 and y = x^2 - c is equal to 128.
The curves are y = c - x^2 and y = x^2 - c
The area enclosed by these curves is 128.
We must determine the x-coordinates of the places of intersection in order to determine the bounds of integration:
c - x^2 = x^2 - c
Subtract c on both side, we get
-x^2 = x^2 - 2c
Subtract x^2 on both side, we get
-2x^2 = -2c
Divide by -2 on both side, we get
x^2 = c
Taking square root on both side, we get
x = ±√c
The between the curve is given by
[tex]\int\limits^{\sqrt{c}}_{-\sqrt{c}}{[(c-x^2)-(x^2-c)]} \, dx[/tex] = 128
Simplify
[tex]\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(c-x^2-x^2+c)} \, dx[/tex] = 128
[tex]\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(2c-2x^2)} \, dx[/tex] = 128
[tex]2\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(c-x^2)} \, dx[/tex] = 128
Now integrating with respect to x
[tex]2\left(cx-\frac{x^3}{3}\right)^{\sqrt{c}}_{-\sqrt{c}}[/tex] = 128
[tex]2\left[\left(c(\sqrt{c})-\frac{(\sqrt{c})^3}{3}\right)-\left(c(-\sqrt{c})-\frac{(-\sqrt{c})^3}{3}\right)\right][/tex] = 128
[tex]2\left[\left(c(\sqrt{c})-\frac{(\sqrt{c})^3}{3}\right)-\left(-c\sqrt{c}+\frac{(\sqrt{c})^3}{3}\right)\right][/tex] = 128
[tex]2\left[c\sqrt{c}-\frac{(\sqrt{c})^3}{3}-c\sqrt{c}-\frac{(\sqrt{c})^3}{3}\right][/tex] = 128
[tex]2\left[-\frac{2(\sqrt{c})^3}{3}\right][/tex] = 128
[tex]-\frac{4}{3}(\sqrt{c})^3[/tex] = 128
[tex]-\frac{4}{3}(c\sqrt{c})[/tex] = 128
Multiply by -3/4 on both side, we get
c(√c) = -96
Square on both side, we get
c^2(c) = 9216
c^3 = 9216
Taking cube root on both side, we get
c = 20.97
c = 21 (approx)
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The complete question is:
Find the value of c for which the area enclosed by the curves y = c - x^2 and y = x^2 - c is equal to 128.
The difference of a number (n) and 8 is no less than 10.
For given expression n-8>=10 to be true, n>=18.
Describe expressions.Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.
e.g. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the expression x/2 + 6. Complex riddles are solved using mathematical expressions.
Now
Given
The difference of a number (n) and 8 is no less than 10.
We can write this as expression n-8>=10,
and for this to be true n>=18.
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Which number is closest to total deaths resulting from ladder misuse each year?
Select the best answer:
a. More than 1,000
b. More than 300
c. Less than 100
d. More than 600
Option C is correct. Less than 100 is closest to total deaths resulting from ladder misuse each year.
According to the Consumer Product Safety Commission (CPSC), on average, approximately 300 people die each year in the United States from falls involving ladders.
However, not all of these deaths are due to ladder misuse. In fact, the number of deaths resulting specifically from ladder misuse is likely to be lower. It is estimated that a significant portion of ladder-related fatalities are caused by factors such as overreaching, misusing the ladder, or failing to follow proper safety guidelines.
To reduce the number of deaths and injuries resulting from ladder misuse, it is important to follow safety guidelines and to choose the right ladder for the job, taking into consideration factors such as height, weight, and stability.
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Launch Problem
The Martinez twins, Carlos and Clarita, are trying to find a way to make money during summer
vacation. When they overhear their aunt complaining about how difficult it is to find someone to
care for her pets while she will be away on a trip, Carlos and Clarita know they have found the
perfect solution. Not only do they have a large, unused storage shed on their property where
they can house animals, they also have a spacious fenced backyard where the pets can play.
Carlos and Clarita need to clean the storage shed where they plan to board the pets. They have
decided to hire a company to clean the windows. After collecting the following information, they
have come to you for help deciding which window cleaning company they should hire.
• Sunshine Express Window Cleaners charges $50 for each service call, plus $10 per window.
• "Pane "less Window Cleaners charges $25 for each service call, plus $15 per window.
1. Which company would you recommend, and why? Prepare an argument to convince Carlos
and Clarita that your recommendation is reasonable. (It is always more convincing if you
can support your claim in multiple ways. How might you support your recommendation
using a table? A graph? Algebra?)
I recommend hiring "Pane "less Window Cleaners since it's less expensive compared to Sunshine Express Window Cleaners.
What is the recommendations about?I recommend hiring "Pane "less Window Cleaners". This is because for a fixed number of windows, "Pane "less Window Cleaners" is less expensive compared to Sunshine Express Window Cleaners. The difference in cost can be calculated by subtracting the cost of "Pane "less Window Cleaners" from that of Sunshine Express Window Cleaners.
For example, for 10 windows, the cost of Sunshine Express Window Cleaners is $50 + 10 * $10 = $150, whereas the cost of "Pane "less Window Cleaners" is $25 + 10 * $15 = $175.
Therefore, the difference in cost is $175 - $150 = -$25, meaning that "Pane "less Window Cleaners" is cheaper. This recommendation is reasonable because it provides the best value for their money.
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In the mesosphere, the atmospheric layer
between 50 km and 80 km in altitude, the average
atmospheric temperature varies linearly with
altitude. If the average temperature at 50 km
altitude is 10°C and the average temperature at
80 km is-80°C, then at what altitude is the average
temperature -50°C?
For the slope of -3, the altitude where the average temperature is -50°C is 70 km.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
At 50 kilometer from earth's surface, the temperature is 10°C.
At 80 kilometer from earth's surface, the temperature is -80°C.
The given temperature for unknown altitude is -50°C.
We are told that the temperature varies linearly with altitude, so if y represents the temperature (in °C) and x represents altitude (in km), these variables are related by the equation y = mx + b, where m (the slope) and b (the y-intercept) are constants.
The two points on this line are (50 km , 10°C) and (80 km , -80°C).
Use these points to find the slope m -
m = (y2 - y1)/(x2 - x1)
m = (-80 - 10)/(80 - 50)
m = -90/30
m = -3
Recall that the slope of a linear relationship is the "unit rate of change". In other words, the slope of -3 means that the temperature declines by 3°C for every 1 km of additional altitude.
Since the altitude at which the temperature is -50°C is needed, the value of x such that (x, -50°C) is on this line is needed. To find x, simply use the slope formula again, using either of the other two points:
Slope formula using (50,10) and (x,-50) -
m = (y2 - y1)/(x2 - x1)
-3 = (-50 - 10)/(x - 50)
-3(x - 50) = -60
-3x + 150 = -60
-3x = -60 - 150
-3x = -210
x = -210/-3
x = 70
Therefore, the altitude will be 70 km.
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how much mewtal is needed to cast a cubical metal box with 12 inch long exterior edges if the thickness of its walls should be exactly 3 inches?
Total metal needed to cast a cubical metal box with exterior edge length 12 inches and thickness 3 inches is equal to 999cubic inches.
Length of the exterior edge of the cubical metal box = 12 inches
Thickness of the wall of cubical metal box = 3 inches
Length of the interior edge of the cubical metal box
= 12 inches - 3 inches
= 9 inches
Volume of the exterior cubical metal box = 12³
= 1728 cubic inches
Volume of the interior cubical metal box = 9³
= 729cubic inches
Total metal required to cast a cubical metal box
= (Volume of the exterior - Volume of the interior )cubical metal box
= (1728 - 729 )cubic inches
= 999 cubic inches
Therefore, the total metal required to cast a cubical metal box is equal to 999 cubic inches.
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