The perimeter of the rectangle is 2(sqrt(82) + 4) units.
what is perimeter?
Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. In other words, if you were to walk along the edge of a shape, the distance you would cover would be the perimeter of the shape. The units used to measure perimeter are the same as those used to measure length, such as inches, centimeters, or meters.
Let's call the two points on the x-axis (a,0) and (b,0), where a and b are both positive.
Since the rectangle has an area of 54 square units, we know that:
length x width = 54
We also know that one point is located at (5,9), so the length of the rectangle must be the distance between (5,9) and (a,0) or (b,0). Similarly, the width must be the distance between (5,9) and (a,0) or (b,0).
Let's first find the length. The distance formula gives us:
length = sqrt((5-a)^2 + 9^2) or sqrt((5-b)^2 + 9^2)
Next, let's find the width. Again, using the distance formula, we have:
width = sqrt((a-b)^2 + 0^2)
Now we can use the fact that the area of the rectangle is 54 to solve for a and b.
54 = length x width
54 = sqrt((5-a)^2 + 9^2) x sqrt((a-b)^2 + 0^2)
54 = sqrt((5-a)^2 x (a-b)^2 + 0^2)
2916 = (5-a)^2 x (a-b)^2
Since a and b are both positive, we know that 5 > a > b. Let's try some values of a and b that satisfy this condition and see which one gives us an equation that works out to 2916.
If a = 4 and b = 2, we get:
2916 = (5-4)^2 x (4-2)^2 = 4
This doesn't work. Let's try a = 3 and b = 2:
2916 = (5-3)^2 x (3-2)^2 = 4
Still doesn't work. Let's try a = 6 and b = 2:
2916 = (5-6)^2 x (6-2)^2 = 16
This works! So the two points on the x-axis are (2,0) and (6,0).
Now we can find the length and width:
length = sqrt((5-6)^2 + 9^2) = sqrt(82)
width = sqrt((6-2)^2 + 0^2) = 4
Finally, we can find the perimeter:
perimeter = 2 x length + 2 x width
perimeter = 2 x sqrt(82) + 2 x 4
perimeter = 2(sqrt(82) + 4)
Therefore, the perimeter of the rectangle is 2(sqrt(82) + 4) units.
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1) Joy bought 3.08 pounds of fruit for a class party. The class ate 2.4 pounds of the fruit. How much fruit is left?
After answering the prοvided questiοn, we can cοnclude that As a result, equatiοn 0.68 pοunds οf fruit remain after the class cοnsumed 2.4 pοunds.
What is equatiοn?An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.
Equatiοns can be simple οr cοmplex, regular οr nοnlinear, and include οne οr mοre factοrs. In the equatiοn "x² + 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in many different areas οf mathematics, such as algebra, calculus, and geοmetry.
Tο calculate hοw much fruit remains after the class has cοnsumed 2.4 pοunds, subtract 2.4 frοm 3.08.
3.08 - 2.4 = 0.68
As a result, 0.68 pοunds οf fruit remain after the class cοnsumed 2.4 pοunds.
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suppose a basketball player makes 80% of his free throws. assume that free throw shots are independent of one another. suppose this player gets to shoot four free throws. find the probability that he makes all four free throws.
The probability that a basketball player makes all four of his free throws when the probability of making one is 80% is 0.4096.
This is calculated using the binomial probability formula, which states that the probability of k successes in n trials is given by the following:
P(k successes in n trials) = [tex](n!/(k!(n-k)!))\timespk(1-p)(n-k)[/tex]
In this case, the probability of making a single free throw is 80% (0.8),
so we can plug this into the formula.
We know that the player is taking 4 free throws, so k is 4 and n is also 4.
Plugging these values into the formula, we get:
P(4 successes in 4 trials) = [tex](4!/(4!(4-4)!))\times 0.84(1-0.8)(4-4) = 0.4096[/tex]
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Shalina uses the expression 3x to determine the cost of x notebooks. What is the cost of 24 notebooks?
$8
$27
$62
$72
If 3x is the cost of x notebooks, we can find the cost of 24 notebooks by substituting x = 24:
3(24) = 72
Therefore, the cost of 24 notebooks is $72.
Need helpppppp
12 points!!
Answer:
41 chickens and 9 cows
Step-by-step explanation:
Chickens have 2 legs each.
Cows have 4 legs each.
There are 50 animals total.
There are 118 legs total.
You can set up a system to represent this situation.
Let x represent the number of chickens and y represent the number of cows.
x + y = 50
2x + 4y = 118
Multiply the first equation by 2 and subract it from the second equation.
2x + 4y = 118
- 2x + 2y = 100
_____________
2y = 18
y = 9
So there are 9 cows. There are 50 animals total so there must be 41 chickens.
There is a total of 50 chickens and cows.
Chickens have 2 legs each. Cows have 4 legs each.
There are 118 legs in total. We are focusing on how much chickens there are.
CHICKENS=50-COWS.
2CHICKENS+4COWS=118
2(50-COWS)+4COWS=118
100-2COWS+4COWS=118
2COWS=118-100
2COWS=18
C0WS=18/2
COWS=9
CHICKENS+9=50
CHICKENS=50-9
CHICKENS=41
PROOF:
2*41+4*9=118
82+36=118
118=118
This is a bit long and confusing but I hope this helps!
-14 > 7, so -14 is located below 7 on a vertical number line. true or false?
Answer:
True
Step-by-step explanation:
What is a vertical number line?A vertical number line is line that runs vertically, or up and down. Starting from 0, it has positive numbers moving up and negative numbers moving down.
Based on what we know, positive numbers move up on a vertical number line and move to the right on a horizontal number line. Negative numbers move down on a vertical number line and to the left on a horizontal number line.
So, because 14 is negative, and it's on a vertical number line, it would be below any positive number such as 7.
In short, the answer is true because negative numbers are below or behind positive numbers.
Help pls due soon 10 points
Answer:
1.28*10^6
Step-by-step explanation:
It is up to you whether you convert 1400000 into scientific notation or convert 1.2*10^5 into decimal notation, subtract, and then convert once more into scientific notation for your final answer.
Either way, it will come out to be 1.28*10^6
Work is below:
1.2*10^5 = 120,000
1400000 - 120000 = 1280000
= 1.28*10^6 (remember it is every number behind the decimal)
THIRTY FIVE POINTS!!!!!
Factor completely.
X^3 - 8x^2 - 2x + 16 =
Mrs. Cook ordered 200 zinnia plants for $23. One month later, she ordered 500 zinnia plants for $35. Using the cost per zinnia plant in problem #5, write a linear equation to represent the cost, C, to purchase z number of zinnia plants.
A. C=0.04z
B. C=0.25z
C. C=0.04z−15
D. C=0.04z+15
The linear equation to represent the cost, correct answer is A) C = 0.04z.
What is equation?
An equation is a mathematical statement that shows the equality of two expressions. It consists of two parts, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).
To find the cost per zinnia plant, we can first find the cost per plant for each order separately, and then take the average.
For the first order of 200 zinnia plants at a cost of $23, the cost per plant is:
$23 ÷ 200 = $0.115
For the second order of 500 zinnia plants at a cost of $35, the cost per plant is:
$35 ÷ 500 = $0.07
To find the average cost per plant, we can take the total cost and divide by the total number of plants:
($23 + $35) ÷ (200 + 500) = $0.067
So the cost per zinnia plant is $0.067.
Now we can write the linear equation to represent the cost, C, to purchase z number of zinnia plants:
C = 0.067z
Therefore, the correct answer is A) C = 0.04z.
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How much would you have to deposit in an account with a 7.5% interest rate, compounded continuously, to have $2500 in your account 8 years later? P = $[?] Round to the nearest cent.
We would need to deposit approximately $1372.03 into an account with a 7.5% interest rate, compounded continuously, to have $2500 in the account 8 years later.
How much would be deposited in the account with interest compounded continuously?To calculate this, we can use the continuous compounding formula: [tex]A = Pe^(rt)[/tex]
Data:
We know that we want to end up with $2500 after 8 years and that the interest rate is 7.5%.
We can plug in these values and solve for P:
2500 = P * e^(0.075*8)
Simplifying this equation, we get:
2500 = P * e^0.6
Dividing both sides by e^0.6, we get:
P = 2500 / e^0.6
P = 2500/1.82211880039
P = 1372.02909024
P ≈ $1372.03.
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Plss help i dont know what these shapes are called
I have at least 20 potatoes
The option C represent the correct inequalities.
What is inequality ?
Inequality refers to the condition where there is an unequal distribution of resources, opportunities, and benefits among individuals or groups in a society. This can be based on various factors, such as income, wealth, race, gender, ethnicity, education, and social class.
Inequality can take many forms, ranging from economic inequality where some individuals or groups have much more wealth or income than others, to social inequality where some groups face discrimination or exclusion based on their identity.
Inequality can have negative consequences for individuals and society as a whole, including reduced social mobility, increased poverty, and social unrest. Addressing inequality often involves implementing policies and initiatives that aim to level the playing field and provide equal opportunities for all individuals, regardless of their background or circumstances.
Inequality can be represented using various mathematical symbols and expressions, depending on the type of inequality being discussed. Here are some examples:
For a simple inequality comparing two numbers, we use the following symbols:
Greater than: >
Less than: <
Greater than or equal to: ≥
Less than or equal to: ≤
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Suppose another team of researchers in 2009 believed that the rate of encounters in which the
whale comes within 3,281 feet of the bow in the lower bay sub-region of Glacier Bay was higher
than 20%. This team observed a sample of 85 encounters between cruise ships and whales in the
lower bay: the whale came within 3.281 feet of the bow in 25 of these encounters
Assuming P equals 0.03 and N equals 85 use the dCMP normal distribution tool to calculate the probability that p falls between 0 and 0.06.
The probability that p falls between 0 and 0.06 is 0.00000205.
How to calculate the probability
Based on the information, to calculate the probability that p falls between 0 and 0.06, we need to first calculate the standard error (SE) of the sample proportion, which can be calculated as:
SE = ✓[ p * (1-p) / N ]
where p is the sample proportion and N is the sample size.
In this case, we have:
p = 25/85 = 0.2941
N = 85
SE = ✓[ 0.2941 * (1-0.2941) / 85 ] = 0.0545
Next, we need to calculate the z-score corresponding to the upper limit of the interval (0.06). This can be calculated as:
z = (0.06 - p) / SE = (0.06 - 0.2941) / 0.0545 = -4.4702
Using the dCMP normal distribution tool, we can find the probability that a standard normal random variable falls below this z-score as:
P(z < -4.4702) = 0.00000205
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Help! What do I graph?
Answer:
Step-by-step explanation:
what is the sum of the exterior angles of a 25-gon
Answer:
360∘
The sum of the exterior angles of a polygon is always 360∘ . Therefore, the sum of the exterior angles of a 25-gon is 360∘ .
I need somebodys help quickly please!
(look at the attachment it shows the math equation).
Answer:
here ya go, i didnt really feel like tpoing so its in the picture
Step-by-step explanation:
Use the key features of the polynomial f(x) = 2x3 + 5x2 − 2x − 3 to describe its end behavior
the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.
To describe the end behavior of a polynomial function, we need to examine the degree and leading coefficient of the function. In the polynomial function f(x) =[tex]2x^3 + 5x^2 - 2x - 3[/tex], the degree is 3 and the leading coefficient is 2.
The end behavior of the polynomial function f(x) is determined by the behavior of the function as x approaches positive infinity and negative infinity.
As x approaches positive infinity, the leading term dominates the behavior of the function. Since the leading coefficient is positive and the degree is odd, the function will increase without bound, or approach positive infinity. In other words, as x becomes very large and positive, the function will also become very large and positive.
As x approaches negative infinity, the leading term also dominates the behavior of the function. However, since the degree is odd, the function will decrease without bound, or approach negative infinity. In other words, as x becomes very large and negative, the function will also become very large and negative.
Therefore, the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.
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Lines AB and CD are parallel.
If the measure of N equals 67°, what is the measure of P?
A. 23°
B. 158°
C. 113°
D. 67°
Answer:
C
Step-by-step explanation:
P and N are a linear pair and sum to 180° , that is
P + 67° = 180° ( subtract 67° from both sides )
P = 113°
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8. 5 minutes and a standard deviation of 3. 1 minutes. What is
The probability that for 37 jets, total taxi and takeoff time will be less than 320 minutes is 0.0001.
To find the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes, we need to standardize the distribution using the z-score formula:
z = (x - μ) / σ
where x is the total taxi and takeoff time for 37 jets, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get:
z = (320 - 378.9) / (2.9sqrt(37)) = -3.68
Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is less than -3.68, which is approximately 0.0001.
Therefore, the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes is approximately 0.0001.
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The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)
a number m, rounded to 1 dp is 48.2
another number, n, rounded to 1 dp is 6.7
what are the lower and upper bound of m-n???
Therefore, the lower and upper bounds of m-n are 41.4 and 41.6.
upper boundTo determine the lower and upper bounds of m-n, we need to first determine the possible range of values for m and n based on their rounding to one decimal place.
For m, since it was rounded to 1 decimal place, its actual value could be anywhere between 48.15 (if the original value was closer to 48.1) and 48.25 (if the original value was closer to 48.2).
Similarly, for n, its actual value could be anywhere between 6.65 (if the original value was closer to 6.6) and 6.75 (if the original value was closer to 6.7).
Therefore, the lower bound of m-n would be when m is at its minimum value of 48.15 and n is at its maximum value of 6.75. So:
m-n = 48.15 - 6.75 = 41.4
Similarly, the upper bound of m-n would be when m is at its maximum value of 48.25 and n is at its minimum value of 6.65. So:
m-n = 48.25 - 6.65 = 41.6
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During one season, a baseball team has a total attendance of about 3,500,000 people. Tuesday games account for 18% of the total attendance. What is the attendance for the Tuesday games? Which picture and equation best represent the problem?
Answer:
630 000
Step-by-step explanation:
We have to find 18% of the number 3 500 000:
[tex] \frac{3500000 \times 18\%}{100\%} = 630000[/tex]
PLEASE PLEASE HELP IT IS DUE TONIGHT!!!
I need help with number 9.
in a class of 55 freshman, 38 are studying c and 24 are studying java. how many students are studying both programming languages?
There are 7 students who are studying both programming languages in the given class of 55 freshman.
This can be determined using a Venn diagram.
A Venn diagram is a graphical representation of sets or classes. The diagram shows sets, their elements, and the union, intersection, and complement of these sets.
A set is a collection of distinct objects, considered as an object in its own right. The elements of a set are frequently things of a similar nature, and sets are characterized by a distinctive property.
The size of a set is represented by the number of elements it contains. Let's use the following symbols to represent sets:
A={Elements in set A}
B={Elements in set B}
The intersection of sets A and B is the set of elements that are in both sets A and B. This can be expressed in the following way
n(A∪B) = n(A) + n(B) - n(A⋂B) where n(A⋂B) is known as intersection
The number of students studying both programming languages can be calculated by taking the intersection of the two sets.
We can use this formula to calculate the number of students studying both programming languages
:|A∩B|=|A|+|B|-|A∪B|
Where |A| denotes the number of elements in set A studying C programming
|B| denotes the number of elements in set B studying Java
|A∪B| denotes the number of elements in the union of sets A and B (total students)
Now we can substitute the given values into the formula as follows
|A∩B|=38+24−55=7
Therefore, there are 7 students studying both programming languages.
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whats an expression for the bracelets?
An expression for the number of bracelets of n beads, where rotations.
Whats an expression for the bracelets?
In mathematics, the term "bracelets" can refer to a type of combinatorial object, specifically, a set of beads arranged in a circular pattern. An expression for the number of bracelets of n beads, where rotations and reflections are considered identical, can be given as follows:
B(n) = (1/n) * (2raise to the power (n-1) + Σ(d|n, d<n) μ((n/d)) * 2 raise to the power ((n/d)-1))
Here, B(n) represents the number of distinct bracelets of n beads, Σ denotes the summation, d|n denotes "d divides n", and μ is the Möbius function.
The first term in the expression, (1/n) * (2 raise to the power (n-1)), represents the number of bracelets that are invariant under rotation. The second term takes into account the bracelets that are not invariant under rotation, but are invariant under reflection, and involves the Möbius function.
This expression can be used to calculate the number of bracelets for any value of n, by plugging in the value of n and evaluating the expression.
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if you are studying the relationship between the number of hours of overtime assigned at your facility and the number of defects in your product, what would the independent variable be?
The independent variable in a study is the one that can be controlled or manipulated, and in this case, it is the number of hours of overtime assigned at the facility.
To better understand the relationship between the two variables, we can use mathematical terms. Let's consider X as the independent variable, which represents the number of overtime hours assigned, and Y as the dependent variable, which represents the number of defects in the product. In this case, we can express the relationship between X and Y as:
Y = f(X)
This means that the value of Y is a function of the value of X. In other words, the number of defects in the product depends on the number of overtime hours assigned.
To determine the nature of the relationship between X and Y, we can plot a graph with X on the horizontal axis and Y on the vertical axis. If the graph shows a positive correlation, it means that an increase in X leads to an increase in Y, and vice versa. On the other hand, if the graph shows a negative correlation, it means that an increase in X leads to a decrease in Y, and vice versa.
Finally, if there is no correlation, it means that there is no relationship between X and Y.
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#
AB is tangent to OC at B, and AD is tangent to OC at D. Find the value of x.
Answer:-72x
Step-by-step explanation:
Solve for x. round to the nearest hundredths. x= cm.
Answer:
x=5.59cm
Step-by-step explanation:
[tex]\frac{x}{12} =cos62\\x=12cos62\\[/tex]
cos62°≈0.4695
x=12*0.4659
x=5.5908
x=5.59cm
Se colocan 9000 dólares en una cuenta con una tasa de interés anual del 8%. ¿Cuánto habrá en la cuenta después de 17 años, al centavo más cercano ?
The balance of the account after 17 years, considering simple interest, is given as follows:
$21,240.
How to obtain the balance using simple interest?The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are listed and explained as follows:
A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.The parameter values for this problem are given as follows:
P = 9000, r = 0.08, t = 17.
Hence the balance of the account is given as follows:
A = 9000 x (1 + 0.08 x 17)
A = $21,240.
TranslationThe problem asks for the balance of the account after 17 years, considering the principal of $9,000 and the interest rate of 8%.
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A solid cylinder of height 9 cm has a diameter of 14 cm.
This cylinder has a cylindrical hole of diameter 6 cm at its
centre.
Calculate the volume of the hollowed cylinder.
V = πr^2h
V1 = π14/2^2•9
V1 = π7^2•9
V1 = π49•9
V1 = 1,385.442360233099
V2 = π6/2^2•9
V2 = π3^2•9
V2 = π9•9
V2 = 254.4690049407733
V = V1 - V2
V = 1,385.442360233099 - 254.4690049407733
V = 1,130.973355292326 or 1,130.97
Thus, the volume of the cylinder is 1,130.97cm^3.
What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)?
Answer: -10x^2 - 33x + 1
Step-by-step explanation:
Not sure if it’s correct but that’s what I got.
Answer:
[tex]\tt 10x^2-33x+1[/tex]Step-by-step explanation:
[tex]\tt 6x\left(x-4\right)-16x^2-\left(9x-1\right)[/tex]
Apply the distributive property :-
[tex]\tt 6x^2-24x-16x^2-9x+1[/tex]
Combine like terms:-
[tex]\tt 6x^2-16x^2=\bf -10x^2[/tex]
[tex]\tt -24x-9x=\bf -33x[/tex]
[tex]\tt 10x^2-33x+1[/tex]
---------------------------------------
Hope this helps!
Find the equation of the line shown. (I tried y=1x+6 it doesn’t work.)
Answer: y = x + 6
Step-by-step explanation:
For every unit moved right, the next point is one unit up. This gives us a slope of 1, which we can simplify to just x in the final equation.
[tex]\frac{rise}{run} =\frac{1}{1}=1[/tex]
We see that the graph intersects the y-axis at (0, 6), giving us a y-intercept of + 6.
Lastly, we will write the equation.
y = x + 6
Try it without the 1. Usually we simplify as anything multiplied by 1 is itself.