The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Now, According to the question:
Optimization using Derivatives:
Suppose the function F(x) has continuous first- and second-order derivatives, F′(x) and F″(x).
At a point x=c in the domain of F(x), the function:
has a relative minimum if F′(c)=0 (critical point) and F″(c)>0 (concave up); and,has a relative maximum if F′(c)=0 (critical point) and F″(c)<0 (concave down).600 [tex]u^2[/tex] of land to be enclosed by fence
Area inside plot should be maximized, amount of fence should be minimized
If we draw a quick sketch, we get something like this:
_____ _____
| | |
| | |
| | |
| | |
The two rectangles could be different sizes but if one rectangle size maximizes area then it would make sense to use that some rectangle for both sides.
Let's put some variables into our picture so we can define our constraints.
y y
| | |
x | x | x |
| | |
| | |
Now we just need an equation to connect our unknowns (how much fence to use) to our constraint (it has to have an exact area of 600 u^2.
A = x × 2y = area = 600
P = 3x + 4y = perimeter = a minimum
First we solve the area equation for y:
y = [tex]\frac{600}{2x}[/tex] = [tex]\frac{300}{x}[/tex]
and then we substitute that result into our perimeter equation:
P = 3x + 4 (300/x)
P = 3x + 1200/x
Our perimeter equation is: P(x) = 3x + 1200/x OR P(x) = 3x +1200[tex]x^-^1[/tex]
We can find what value of x makes our perimeter as small as possible (a minimum) by graphing or by using Calculus.
In Calculus we know that maximums and minimums always occur when the derivative is zero. This is because the slope (rate of change) at these points in a graph are always flat or zero. Our derivative is
P'(x) = 3 - 1200[tex]x^-^2[/tex]
When set equal to zero, we can solve for x:
3 - 1200[tex]x^-^2[/tex]= 0
1 - 400[tex]x^-^2[/tex] = 0
1 = 400/[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 400
x = ± 20
Our fence length can't be a negative number so our answer must be 20u.
If our x length is 20, then our y length must be 300/x to ensure our area is 600 u^2.
The y length is 300/(20) = 15
Let's put all of our numbers into our picture to see if it make sense.
15 15
| | |
20 | 20 | 20 |
| | |
| | |
15 15
Sure enough our area is 600.
Here's what we have right now:
A(20, 15) = 600
P(20, 15) = 120
How about we try something a little bigger like 20.5 for x and 14.63 for y?
A(20.5, 14.63) = 600
P(20.5, 14.63) = 120.02
How about we try something a little smaller like 19.5 for x and 15.38 for y?
A(19.5, 15.38) = 600
P(19.5, 15.38) = 120.02
It looks like if we try to change x, even a little, to make it bigger or smaller the perimeter only gets bigger.
You might have guessed at the beginning that a square is the best shape to use to maximize area, so let's try that as well.
Each rectangle is 300[tex]u^2[/tex]. We want a square so each side would be √(300) = 17.32
17.32 17.32
| | |
17.32 | 17.32 | 17.32 |
| | |
17.32 17.32
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Hence, The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
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An ant crawling along the floor follows a semi-circular path, going halfway around the circumference of a circle of radius R.
The distance traveled and the displacement of the ant are, respectively,
πR and πR
2R and πR
πR and 2R
πR and zero
none of these
The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.
The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.
So, the option c is most suitable option.
Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.
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If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, which of the following probabilities is not correct?
a. P(x ≥ 1) =.1587
b. P(x < 2) =.9772
c. P(x = 0) =.50
d. P(x ≤ 1) =.8413
If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, the probability P(x = 0) =.50 is not correct.
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. The degree to which something is likely to happen is basically what probability means.
The probability of all the events in a sample space adds up to 1.
Thus, If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, the probability P(x = 0) =.50 is not correct.
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a bag of fruits contains 10 peices of fruit chosen randomly from a bin of apples and oranges. what is the probability the bag contains at least 6 oranges
The probability of getting at least 6 oranges in a bag of 10 fruits is the sum of probability of getting 6 oranges, probability of getting 7 oranges, probability of getting 8 oranges, probability of getting 9 oranges and probability of getting 10 oranges.
We can use the binomial probability formula to calculate the probability of getting at least 6 oranges in a bag of 10 fruits, which is:
P(X >= 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
Where X is the number of oranges in the bag, and the probability of getting an orange is p and the probability of getting an apple is (1-p)
Now, since we don't know the proportion of oranges to apples in the bin, we can't find p. However, we can use the cumulative binomial distribution function to find the probability of getting 6 or more oranges in a bag of 10 fruits.
The cumulative binomial distribution function is the probability of getting r or less successes in n trials, where a success is getting an orange and a failure is getting an apple.
So
P(X >= 6) = 1 - P(X <= 5)
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jackie says that the constant of proportionality in the equation is 0.25 is jackie correct
Yes, Jackie is correct as the equation x = 0.25y could be written as x = ky which means x ∝ y. thus, 0.25 is a constant of proportionality.
What is a constant of proportionality?The ratio between two proportional quantities has a constant value, which is known as the constant of proportionality. When either their ratio or their product produces a constant, two varying quantities are said to be in a proportional relationship. The Direct Variation and Inverse Variation types of proportion between the two given quantities determine the proportionality constant's value.
When two variables are directly or indirectly proportional to one another, their relationship can be expressed as y = kx or y = k/x, where k specifies how the two variables are related to one another. The proportionality constant, k, stands for this.
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Full question
Jackie was given a proportion x = 0.25y. Jackie says that the constant of proportionality in the equation is 0.25 is Jackie correct.
Look at the simultaneous equations below. x 6y=10 - 3y² = 4x + 1 a) Show that 3y² - 24y - 41 = 0 b) Use part a) to solve the simultaneous equations. If any of your answers are decimals, give them to 1 d.p.
Answer:
I don't know if it is true
does it make sense that the number of cats falling frm the 5th floor would be greater than those of the 4th
Yes, it makes sense that the number of cats falling from 5th floor would be greater since the terminal velocity of the cat would be greater at higher altitudes.
What is velocity?The pace at which an object's location changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
What is altitude?A distance measurement between a reference datum and a point or object, typically in the vertical or "up" direction, is known as altitude, height, or depth.
The terminal velocity of the cat would be greater at higher altitudes; hence cats have higher risk of falling from heights.
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$73 is what percent of $125
Answer:
58.4%
Step-by-step explanation:
Find the value of X and Y
==========================================================
Explanation:
Let z be adjacent to angle y, and angle z is inside the triangle on the right.
Adding up the inside angles of any triangle always gets us to 180 degrees.
We'll use this fact to find z.
z+30+50 = 180
z+80 = 180
z = 180-80
z = 100
Angle y and angle z are supplementary angles. They form a straight line of 180 degrees.
So,
y+z = 180
y+100 = 180
y = 180-100
y = 80
--------------
We can follow the same steps as in the previous section to determine that angle x is 110 degrees.
A shortcut is to use the Remote Interior Angle Theorem.
This theorem says that adding two interior angles will get us the exterior angle that isn't adjacent to either interior angle mentioned.
Notice for instance that angle x is not adjacent to the bottom-left 30 degree angle nor is it adjacent to angle y.
Furthermore, you could use the Remote Interior Angle Theorem to determine the measure of angle y. Note how y = 30+50 = 80. This time the "30" we focus on here is inside the triangle on the right.
Determine the partial fraction expansion for the rational function below. s ( ) (s – 7)(s? - 49) S (s - 7) (s2 - 49) Determine the partial fraction expansion for the rational function below. -25-56 (5+3) (s+ 16) - 2s - 56 II (s +3)(s? + 16)
The partial fraction expansion for the rational function is:-25/((s+3)(s + 16)) + 56/((s+3)(s2 + 16)) - 2s/((s+3)(s2 + 16))
To determine the partial fraction expansion for the rational function, we first need to factor the denominator into two linear factors. This can be done using the Factoring by Grouping method. We will factor the denominator of the rational function as follows:
(s+3)(s2 + 16)
Now, we can write the partial fraction expansion for the rational function as:
-25/((s+3)(s + 16)) + 56/((s+3)(s2 + 16)) - 2s/((s+3)(s2 + 16))
The partial fraction expansion for the rational function is -25/((s+3)(s + 16)) + 56/((s+3)(s2 + 16)) - 2s/((s+3)(s2 + 16)).
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The twenty-four students who earned A Honor Roll at Harmony School were twelve less than three times the number of students who earned B Honor Roll. How many students earned B Honor Roll?
Answer:
12 students earned B Honor Roll
Step-by-step explanation:
Let A be the number of students who earned A Honor Roll and B the number who earned B.
We are told that A = 24,
and that A = 3B-12 [ . . .were twelve less than three times the number of students who earned B Honor Roll]
Since we know the value of A (24) use the second equation to find B:
A = 3B-12
24 = 3B-12
3B = 36
B = 12
CHECK:
Is 24 12 less than three times B(12)?
24 = 3*12 - 12?
24 = 36 - 12?
24 = 24
YES
a cylindrical water tank with its circular base parallel to the ground is being filled at the rate of 4 cubic feet per minute. the radius of the tank is 2 feet. how fast is the level of the water in the tank rising when the tank is half full?
Answer:
To solve this problem, we need to use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.
Step 1: We know that the radius of the tank is 2 feet and that it is being filled at a rate of 4 cubic feet per minute. We also know that the tank is half full, so we can assume that the height of the water in the tank is half the height of the tank itself.
Step 2: We can use the volume formula to find the volume of the tank when it is half full.
V = πr^2h
V = π(2^2)(h/2)
V = 4πh/2
Step 3: We can divide the rate of fill by the volume of the tank when it is half full to find the rate of change of the height of the water.
dh/dt = 4/(4π/2)
dh/dt = 2/π ft/min
Final Answer: The level of the water in the tank is rising at a rate of 2/π feet per minute when the tank is half full.
The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle?
(A) 32√π32π
(B) 33√π33π
(C) 3√3
(D) 6π6π
(E) 3√∗π
The radius of the circle is s√3π, which is equal to 3√π. Hence, the answer is option (B).
To calculate the radius of the circle, we need to first calculate the perimeter of the equilateral triangle. The perimeter of an equilateral triangle is equal to 3 times the side length of the triangle. Thus, we can say that the perimeter of the equilateral triangle is 3s.
Now, we need to calculate the area of the circumscribed circle. The area of a circle is equal to π times the square of the radius. Thus, the area of the circumscribed circle is equal to πr2.
Therefore, we can say that 3s = πr2. Solving this equation for r, we get r = s√3π. Thus, the radius of the circle is s√3π, which is equal to 3√π. Hence, the answer is option (B).
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how many non-empty subsets of $\{ 1 , 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \}$ consist entirely of prime numbers? (we form a subset of the group of numbers by choosing some number of them, without regard to order. so, $\{1,2,3\}$ is the same as $\{3,1,2\}$.)
The number of non-empty subsets of the given set that consist entirely of prime numbers is [tex]$31-16=7$[/tex]
The total number of non-empty subsets of [tex]$\{1,2,3,4,5,6,7,8,9,10,11\}$[/tex] that consist entirely of prime numbers is 7. The prime numbers in the given set are {2,3,5,7,11}. The formula to calculate the number of non-empty subsets of a set with n elements is [tex]$2^n-1$[/tex]. Thus, the number of non-empty subsets of the given set is [tex]$2^{5}-1=31$[/tex]. To calculate the number of subsets that consist of prime numbers only, we need to subtract the number of subsets that contain at least one non-prime number from 31. There are 16 such subsets, as the non-prime numbers in the given set are[tex]$\{4,6,8,9,10\}$[/tex]. Thus, the number of non-empty subsets of the given set that consist entirely of prime numbers is[tex]$31-16=7$.[/tex]
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2x^2 -19x + 2 = -10x
The solutions of the quadratic equation are given by x = (29 ± √825) / 4 which are two complex numbers.
What is a quadratic equation?
A quadratic equation is a type of polynomial equation that has the form of ax^2 + bx + c = 0, where x is the variable, and a, b, and c are coefficients. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants. The solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b^2-4ac)) / 2a
To solve for x in the equation 2x^2 -19x + 2 = -10x, we need to rearrange it in the standard form of a quadratic equation by isolating the x^2 term and moving the other terms to the other side:
2x^2 -10x -19x +2 = 0
2x^2 -29x +2 = 0
Now we can apply the quadratic formula:
x = (-b ± √(b^2-4ac)) / 2a
x = (-(-29) ± √((-29)^2-422)) / 2*2
x = (29 ± √(841-16)) / 4
x = (29 ± √(825)) / 4
Hence, the solutions of the quadratic equation are given by x = (29 ± √825) / 4 which are two complex numbers.
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Emily is entering a bicycle race for charity. Her mother pledges $0.40 for every 0.75 mile she bikes. If Emily bikes 24 miles, how much will her mother donate?
Applying proportion, the money her mother donated is: $64.
What is Proportion?Proportion is a mathematical concept that describes the relationship between two or more values that are expressed as a ratio. It is used to compare the size of one value to another.
A proportion can be written in the form of an equation, such as a/b = c/d, where a, b, c, and d are values, and a and b are the values being compared to c and d.
We can use the proportion of the pledge to the distance biked to find the amount of money Emily's mother will donate.
The proportion of the pledge to the distance biked is 0.40/$ for every 0.75 mile.
So for 24 miles, the amount of money pledged would be:
0.40/0.75 * 24 = $64
So Emily's mother will donate $64 to charity.
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Greg made pudding every weekend. The more times he made pudding, the more practice he gained. The time he took to make the same amount of pudding every week decreased with practice. The function below shows the number of hours f(x) Greg took to make pudding after he had made it x times: f(x)
The function below shows the number of hours f(x) Greg took to make pudding after he had made it x times is f(x) = 2(0.8)ˣ and the graph of the function is attached below.
The term function in math is defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here we have given that Greg made pudding every weekend.
And here we also know that the more times he made pudding, then the more practice he gained.
According to the time he took to make the same amount of pudding every week decreased with practice.
Here we need to write the function below shows the number of hours f(x) Greg took to make pudding after he had made it x times.
Then the function is written as,
=> f(x) = 2(0.8)ˣ
While we plot the function on the graph then we get the graph like the following.
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Which number gives the same result if it is multiplied by 999/998 or if any number is added to it?
Please give me the answer with an explanation!
Thanks in advance!
Answer:
The number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).
The property of a number being unchanged after being multiplied by a fraction and a constant is called an "Identity element". The identity element for multiplication is 1 and for addition is 0.
When any number is multiplied by 1, it stays the same. So, if we multiply any number by 999/998, which is equivalent to multiplying by 1, it stays the same.
Similarly, when any number is added to zero, it stays the same. So, if we add any number to 0, it stays the same.
Therefore, the only number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).
help me please with this work
Step-by-step explanation:
we know
[tex]y = mx + c[/tex]
Answer:
y-intercept: -3
slope: 4
equation: y=4x-3
Step-by-step explanation:
To find the y-intercept, it shows in the table of value that when x is 0, y is -3 so y-intercept = -3. To find the slope, find the first differences which is 4.
select which shortcut can be used to prove that this pair of triangles are similar. If no method applies, choose none.
answers
A hypotenuse-leg
B angle angle similarity
C side angle side similarity
D side side side similarity
E None
several different types of cheese are produced in the shape of a wheel. because of the differences in consistency of these different types of cheese, there is variation in the amount of cheese in the wheel. cam embert wishes to determine if there is a significant difference, at the 5% level, between gouda cheese and brie cheese. she randomly samples 18 wheels of gouda and finds the mean is 1.3 pounds with a standard deviation of 0.31 pound and 13 wheels of brie and finds a mean of 0.95 pounds and a standard deviation of 0.26 pound. is the difference between the weights of the two cheeses significant at the 0.05 level of significa
There is a statistically significant difference between the weights of the two cheeses at the 5% level of significance.
What is standard deviations?Standard deviation is a measure of how spread out a set of numbers is from the mean. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. In other words, it is a measure of how much the values in a dataset differ from the mean, or average, value. Standard deviation is a useful tool for understanding the distribution of data and can be used to identify outliers and compare data sets.
To answer this question, we must use a two-tailed hypothesis test, where the null hypothesis is that there is no difference between the two cheeses. The alternative hypothesis is that there is a significant difference between the two cheeses.
Using the sample data provided, we are able to calculate the test statistic, which in this case is 2.02. This can be compared to the critical value from the t-distribution table, which is 1.711 for a 5% level of significance and 31 degrees of freedom.
Since the test statistic is larger than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference between the weights of the two cheeses at the 5% level of significance.
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A large cheese pizza at a palanzios pizzeria costs $6.80 plus $0.90 for each topping. the cost of a large cheese pizza at gordos pizza is $7.30 plus $0.65 for each topping. how many toppings need to be added in the order for the pizzas to cost the same.
For Palanzios' Pizzeria and Guido’s Pizza to cost the same, the number of toppings needed is 2.
Let's begin by assigning a letter to represent our unknown:
x = Number of toppings to be added to each pizza
Now,
Based on the Given information :
Expressions for the cost of each pizza with its toppings:
Palanxio's Pizza: 6.80 + 0.90x
Guido's Pizza: 7.30 + 0.65x
Now,
Equating the costs of both pizzas and solve for our unknown (x):
⇒ 6.80 + 0.90x = 7.30 + 0.65x
⇒ 0.90x - 0.65x = 7.30 - 6.80
⇒ 0.25x = 0.50
⇒ x = 0.50/0.25
⇒ x = 2
Therefore, There are 02 toppings to be added to each pizza.
Finally, we can verify our answer by putting the values back into our equation :
6.80 + 0.90x = 7.30 + 0.65x
6.80 + 0.90(2) = 7.30 + 0.65(2)
6.80 + 1.80 = 7.30 + 1.30
= $8.60 [both costs are the same]
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if i had 304,770 in total. 8.3% female viewers, 91.2% male viewers, and 0.5% user-specified viewers how many female viewers would i have in numbers (without percent)
Answer:
25,295.91
Step-by-step explanation:
304,770
1%=3047.7
0.1%=304.77
8%=24,381.6
0.3%=914.31
24,381.6+914.31=25,295.91
female viewers =25,295.91
an education researcher gathers data about freshman students in an economics course. she collects the number of hours that students study and the number of questions they missed (got wrong) on exams. the regression results were:
On solving the provided question we can say that the linear regression results were: = 9.23 X [tex]10^{-3}[/tex]
what is linear regression?When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable. The procedure is known as multiple linear regression if there are numerous. A straight line is used to evaluate the relationship between the independent and dependent variables in a regression model known as simple linear regression. Both factors ought to be quantitative. The effect of the independent variable on the dependent variable is examined using simple linear regression. The second scenario, known as multiple linear regression, examines how various independent factors affect the dependent variable.
an education researcher gathers data about freshman students in an economics course.
he collects the number of hours that students study and the number of questions they missed (got wrong) on exams
the linear regression results were: = 9.23 X [tex]10^{-3}[/tex]
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what is the probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards? round to the nearest thousandth.
The probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards is 0.050
Since, a deck of cards contain 52 cards,
So, we have the value of sample space = n(S)=52
Consider the following values
A=in first draw there is a face card but
B= in the second draw there is a face card
[tex]$$\begin{aligned}& E=\{\boldsymbol{\bullet} J, \bullet J, \boldsymbol{\bullet} J, \boldsymbol{\wedge} J, \bullet Q, \bullet Q, \bullet Q, \wedge Q, \bullet \mathrm{K}, \bullet \mathrm{K}, \boldsymbol{\bullet} \mathrm{K}, \boldsymbol{\wedge} \mathrm{K}\} \\& n(E)=12\end{aligned}$$[/tex]
The probability in the first draw is a face card will be
P(A)=(12/52)
The Probability in the second draw there is also a face card will be
(B/A)=(11/52)
Now, from the formula for P(A and B),
We will get it as:
[tex]$$P(A \cap B)=P(A) \times P\left(\frac{B}{A}\right)$$[/tex]
Therefore,
[tex]P(A \cap B) & =\frac{12}{52} \times \frac{11}{51}[/tex]
=(132/2652) = 0.052
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The lengths of two sides of a triangle are 7 cm and 17 cm. Identify the range of possible lengths for the third side.
The range possible length of the third side of the triangle is greater than 11.
How to find the third side of a triangle?The lengths of two sides of a triangle are 7 cm and 17 cm. The range of the possible length for the third side can be calculated as follows:
The triangle inequality theorem simply states that the sum of any two sides in a triangle must be greater than the length of the third side of the triangle.
Using triangle inequality theorem, if a, b and c are the sides of the triangle. Hence,
a + b > c
a + c > b
b + c > a
Hence,
7 + 17 > c
7 + c > 17
17 + c > 7
Therefore, using 7 + c > 17, c should be greater than 11.
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Need help on this algebraic question!
Thank you
$39.99+238.8+1.75x and $4.99=1.99x+$40 are the algebraic expressions of given data.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given that $39.99 /month, unlimited texting , 120MB data (Overages $1.99 /MB talk is $1.75 /minutes
$39.99+120(1.99)+1.75x
$39.99+238.8+1.75x
$4.99 /month, unlimited texting ,$40 for 80MB data talk is $1.99 /minutes
$4.99+1.99x+$40
Hence, $39.99+238.8+1.75x and $4.99+1.99x+$40 are the algebaic expressions of given data.
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The time to manufacture a pair of headphones on each assembly line is 1/3 hour. if there are 24 assembly lines and they operate 8 hours a day, how many pairs of headphones can be manufactured in a day?
you get brainliest if you answer!!!!!! i need this right now! +15 points
The number of pais of headphones that can be manufactured in a day = 576
Given that the time to manufacture a pair of headphones on each assembly line is 1/3 hour.
By unitary method the number of pairs of headphones can be manufactured in an hour :
1 ÷ (1/3)
= 1/ (1/3)
= 3
So, 3 pairs of headphones can be manufactured in an hour.
We need to determine the number of pairs of headphones that can be manufactured in a day.
Since we can operate assemply line 8 hours a day.
By unitary method the number of pairs of headphones can be manufactured in 8 hours:
3 × 8 = 24
And there are such 24 assembly lines.
So, the number of pais of headphones that can be manufactured in a day:
24 × 24 = 576
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Find the slope, if it exists, of the line containing the pair of points.
(-15,-10) and (-20,- 12)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- The slope is _____. (Type an integer or a simplified fraction.)
- The slope is undefined.
[tex](\stackrel{x_1}{-15}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-20}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-10)}}}{\underset{\textit{\large run}} {\underset{x_2}{-20}-\underset{x_1}{(-15)}}} \implies \cfrac{-12 +10}{-20 +15} \implies \cfrac{ -2 }{ -5 } \implies {\Large \begin{array}{llll} \cfrac{2 }{ 5 } \end{array}}[/tex]
Answer: The slope is -2/5
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenths.
In a trapezium, the sum of the outer angles is always equal to 360 degrees because, in any convex quadrilateral, the sum of the four angles is consistently 360 degrees. As a trapezium is a type of convex quadrilateral, the sum of its four angles is 360 degrees, regardless of its shape or size.
Solve for xWe can simplify this equation by combining like terms on one side and isolating the variable on the other.
First, combine like terms: x + 5 + 3x - 8 + 5x + 10 + x + 10 = 360
(x + x) + (5 + 10 + 10) + (3x + 5x) = 360
10x + 17 = 360
Then, subtract 17 from both sides to isolate the variable on one side:
10x = 343
Finally, divide both sides by 10 to solve for x:
x = 34.3
So the solution to the equation is x = 34.3
a circumfrence of 10. it has an arc of the length 9/2. what is the central angle of the arc,in degrees/
The central angle of the arc in degrees is 162 degrees.
How to find the central angle ?The circumference of the circle is 10 units. The length of the arc is 9 / 2 units. The central angle can be calculated as follows;
We can find the central angle by comparing it to the length of the arc.
Therefore, we know the circle has a circumference of 10. We also know a circle is 360°. The length of the arc is given as 9 / 2 units(4.5 units).
To determine the degrees of the central angle, we have to set up a ratio and set the unknown angle as x.
Hence,
length of the arc / circumference = angle of the arc / angle of the circle
4.5 / 10 = x / 360
cross multiply
360 × 4.5 = 10x
1620 = 10x
divide both sides by 10
x = 1620 / 10
x = 162 degrees
Hence,
central angle = 162 degrees.
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