The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.
What is the mean?The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.
A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.
If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.
Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.
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With respect to the average cost curves, the marginal cost curve: Intersects average total cost, average fixed cost, and average variable cost at their minimum point b. Intersects both average total cost and average variable cost at their minimum points Intersects average total cost where it is increasing and average variable cost where it is decreasing d. Intersects only average total cost at its minimum point
With respect to the average cost curves, the marginal cost curve: intersects both average total cost and average variable cost at their minimum points that is option B.
The fixed cost per unit of production is the average fixed cost (AFC). AFC will reduce consistently as output grows since total fixed costs stay constant. The variable cost per unit of production is known as the average variable cost (AVC). AVC generally declines until it reaches a minimum and then increases due to the growing and then lowering marginal returns to the variable input. The average total cost curve's (ATC) behaviour is determined by the behaviour of the AFC and AVC.
The marginal cost is the cost added to the overall cost of producing one extra unit of output. MC initially falls until it hits a minimum and then increases. When both AVC and ATC are at their minimal points, MC equals both. Also, when AVC and ATC are dropping, MC is lower; when they are growing, it is higher.Initially, the marginal cost of manufacturing is lower than the average cost of preceding units. When MC falls below AVC, the average falls. The average cost will reduce as long as the marginal cost is smaller than the average cost.When MC surpasses ATC, the marginal cost of manufacturing one more extra unit exceeds the average cost.Learn more about Marginal cost curve:
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Complete question:
With respect to the average cost curves, the marginal cost curve:
A) Intersects average total cost, average fixed cost, and average variable cost at their minimum point
B) Intersects both average total cost and average variable cost at their minimum points
C) Intersects average total cost where it is increasing and average variable cost where it is decreasing
D) Intersects only average total cost at its minimum point
what is -0.33333333333 as a fraction
Answer:
-1/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
a fraction nonconforming control chart is to be established with a center line of 0.01 and two-sigma control limits. (a) how large should the sample size be if the lower control limit is to be nonzero? (b) how large should the sample size be if we wish the probability of detecting a shift to 0.04 to be 0.50?
a) Sample size if the lower control limit is to be nonzero: 50
b) Sample size if the probability of detecting a shift to 0.04 is to be 0.50: 100
a) How large should the sample size be if the lower control limit is to be nonzero?
n = (2σ / d)²We know that:
Center line (CL) = 0.01
Sigma (σ) = LCL = 0.005
d = Centerline - LCL = 0.01 - 0.005 = 0.005
Substituting the values in the formula, we get
n = (2 * 0.005 / 0.01)²= 50 Hence, if the lower control limit is to be nonzero, the sample size should be 50.
b) How large should the sample size be if we wish the probability of detecting a shift to 0.04 to be 0.50?
The probability of detecting a shift to 0.04 is denoted by β and is calculated using the following formula:
β = Φ [(-Zα/2 + Zβ) / √ (p₀q₀/n)], Where, Φ is the standard normal distribution function, Zα/2 is the critical value for the normal distribution at the (α/2)th percentile, Zβ is the critical value for the normal distribution at the βth percentile, p₀ is the assumed proportion of nonconforming items, q₀ is 1 – p₀, and n is the sample size.
In order to determine the sample size, we must first select a value for β. If we select a value for β of 0.50, then β = 0.50. This implies that we have a 50% chance of detecting a shift if one occurs. Since the exact value for p₀ is unknown, we assume that p₀ = 0.01, which is equal to the center line.
n = (Zα/2 + Zβ)² p₀q₀ / β², Substituting the values in the formula, we get,
n = (Zα/2 + Zβ)² p₀q₀ / β²= (1.96 + 0.674)² (0.01) (0.99) / 0.50²= 99.7 ≈ 100
Hence, if we wish the probability of detecting a shift to 0.04 to be 0.50, the sample size should be 100.
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andrew is buying a cell phone that has a regular price of $485. the cell phone is on sale for 35% off the regular price. what will be the sale price?
the sale price of the cell phone after the 35% discount is $315.25.
How to solve and what is sale?
To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:
Sale price = Regular price - Discount amount
Sale price = $485 - (0.35 x $485)
Sale price = $485 - $169.75
Sale price = $315.25
Therefore, the sale price of the cell phone after the 35% discount is $315.25.
A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.
In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.
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the relation r is defined on z as follows: [ is an even number] prove that the relation is an equivalence relation. for full credit you must prove that the relation is reflexive, symmetric, and transitive using the formal definitions of those properties as shown in lectures. you must give your proof line-by-line, with each line a statement with its justification. you must show explicit, formal start and end statements for the overall proof and for the proof case for each property. you can use the canvas math editor or write your math statements in english. for example, the universal statement that is to be proved was written in the canvas math editor. in english it would be: for all integers m and n, m is related to n by the relation r if, and only if, the difference m minus n is an even number.
Let m and n be two arbitrary integers. We want to prove that the relation R is an equivalence relation, i.e. it is reflexive, symmetric, and transitive.
Reflexive: We must show that mRm for all m ∈ Z.
Since the difference of m and m is 0, which is an even number, we have mRm.
Therefore, the relation R is reflexive.
Symmetric: We must show that if mRn, then nRm.
Let mRn, i.e., the difference of m and n is an even number.
Then the difference of n and m is also an even number.
Therefore, nRm, and the relation R is symmetric.
Transitive: We must show that if mRn and nRp, then mRp.
Let mRn and nRp, i.e., the difference of m and n is an even number and the difference of n and p is also an even number.
The sum of the difference of m and n and the difference of n and p is the difference of m and p, which is an even number.
Therefore, mRp, and the relation R is transitive.
Since the relation R is reflexive, symmetric, and transitive, it is an equivalence relation.
Conclusion: The relation R is an equivalence relation.
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Determine whether the following subsets are subspaces of the given vector spaces or not.text Is end text W subscript 2 equals open curly brackets space p equals a subscript 2 t squared plus a subscript 1 t plus a subscript 0 space element of space straight double-struck capital p subscript 2 space left enclose space a subscript 0 equals 2 space end enclose close curly brackets space space text a subspace of the vector space end text space straight double-struck capital p subscript 2 ?(Note: space straight double-struck capital p subscript 2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.)Answer 1text Is end text W subscript 1 equals open curly brackets open square brackets table row a b c row d 0 0 end table close square brackets space element of space M subscript 2 x 3 space end subscript space left enclose space b equals a plus c space end enclose close curly brackets space text a subspace of the vector space end text space space M subscript 2 x 3 space end subscript?(Note: space M subscript 2 x 3 space end subscript is the set of all 2x3 matrices with the standart matrix addition and scalar multiplication with reals.)
Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.
Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.
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The number of bacteria in a culture is growing at a rate of 3,000e^(2t/5) per unit of time t. At t=0, the number of bacteria present was 7,500. Find the number present at t=5.a. 1.200 e^2b. 3,000 e^2c. 7,500 e^2d. 7,500 e^5e. 15.000/7 e^7
The number of bacteria present with the given growth rate at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.
What is exponential growth?An exponential growth pattern is one in which the rate of increase is proportionate to the value of the quantity being measured at any given time. This indicates that the amount by which the quantity increases in each period is a constant proportion of the quantity's present value. Many branches of mathematics and science, such as physics, biology, and finance, utilise exponential growth. Modeling population expansion, the spread of infectious illnesses, the decay of radioactive materials, and the behavior of financial assets are all popular applications.
Given that, the number of bacteria present was 7,500.
The exponential growth is given by the formula:
[tex]N(t) = N(0) * e^{(kt)}[/tex]
Substituting the values N(0) = 7,500 and the growth rate is k = 2/5 we have:
[tex]N(5) = 7,500 * e^{(2/5 * 5)}\\N(5) = 7,500 * e^2[/tex]
Hence, the number of bacteria present at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.
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243➗ _ =81
Multiplying and dividing integers
Given:
81x = 243x
= 243 / 81x
= 3
Answer:x = 3
y=x^2+7x-3
complete the square to re-write the quadratic function in vertex form.
pls help
Answer:
Y=x^2+7x-3
complete the square to re-write the quadratic function in vertex form.
pls help
Step-by-step explanation:
To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.
y = x^2 + 7x - 3
y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)
y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)
y = (x + 7/2)^2 - 49/4 - 3
y = (x + 7/2)^2 - 61/4
So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).
Suppose an angle has a measure of 140 degrees a. If a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is______ times as long as 1/360th of the circumference of the circle. b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long. What is the length of the arc subtended by the angle's rays? _______ cmc. Another circle is centered at the vertex of the angle. The arc subtended by the angle's rays is 70 cm long. - 1/360th of the circumference of the circle is _____ cm long. - Therefore the circumference of the circle is _______ cm
If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle. Also if a circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long then length of the arc subtended by the angle's rays 8.4 cm. Another circle is centered at the vertex of the angle then arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.
a.) To find the fraction of the circle's circumference subtended by the angle's rays, we divide the angle measure by 360 degrees:
fraction of circle's circumference = 140/360
Simplifying this fraction, we get:
fraction of circle's circumference = 7/18
To find the length of the arc subtended by the angle's rays, we multiply the fraction of the circle's circumference by the circumference of the circle. Let's call the circumference of the circle "C":
length of arc = (7/18)*C
We're also told that the length of 1/360th of the circumference is equal to 0.06 cm. So, we can write:
(1/360)*C = 0.06
Multiplying both sides by 360, we get:
C = 360*0.06 = 21.6 cm
Now, we can substitute this value of C into the expression for the length of the arc:
length of arc = (7/18)*C
length of arc = (7/18)*(21.6)
length of arc = 8.4 cm (rounded to one decimal place)
Therefore, the length of the arc subtended by the angle's rays is 8.4 cm.
b.) We're given that 1/360th of the circumference of the circle is 0.06 cm long. To find the length of the arc subtended by the angle's rays, we need to multiply 140/360 by 0.06:
length of arc = (140/360)*0.06
length of arc = 0.0233 cm (rounded to four decimal places)
Therefore, the length of the arc subtended by the angle's rays is approximately 0.0233 cm.
c.) We're told that the length of the arc subtended by the angle's rays is 70 cm. To find the circumference of the circle, we need to find the length of 1/360th of the circumference first. We can do this by dividing 70 by 1/360:
(1/360)*C = 70
Multiplying both sides by 360, we get:
C = 70*360 = 25,200 cm
Therefore, the circumference of the circle is 25,200 cm. We can also verify this by dividing the length of the arc by the fraction of the circumference subtended by the angle's rays:
length of arc = (7/18)*C
C = (18/7)*length of arc
C = (18/7)*70
C = 180 cm (rounded to one decimal place)
This is a different value than we got earlier, so we need to check our calculations. It turns out that the previous calculation was incorrect - we made a mistake when multiplying 7/18 by 21.6. The correct calculation gives us:
length of arc = (7/18)*C
length of arc = (7/18)*(21.6)
length of arc = 8.4 cm (rounded to one decimal place)
Now, we can calculate the circumference of the circle:
length of arc = (7/18)C
C = (18/7) *length of arc
C = (18/7) *70
C = 180 cm (rounded to one decimal place)
Therefore, the circumference of the circle is 180 cm.
Also, If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle.
b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long.The length of the arc subtended by the angle's rays 8.4 cm
c. Another circle is centered at the vertex of the angle.
The arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.
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Convince Me! How does the unit rate describe Sergio's cycling speed? How is the unit rate helpful in determining how much farther Sergio must cycle in a given amount of time each time he increases his target speed?
The unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.
What is the formula for Speed?The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel. This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.
In the given question,
The unit rate describes Sergio's cycling speed by giving the distance he travels in a given amount of time, which is 6 miles per hour. This means that for every hour he cycles, he travels a distance of 6 miles.
By expressing Sergio's cycling speed as a unit rate, we can easily compare it to other speeds and determine how long it will take him to travel a certain distance.
For example, if Sergio increases his target speed to 8 miles per hour, we can use the unit rate to calculate how much farther he must cycle in a given amount of time.
If he wants to cycle for 2 hours, we know that he will travel 6 x 2 = 12 miles at his original speed of 6 miles per hour.
If he wants to cycle for the same 2 hours at a speed of 8 miles per hour, we can use the unit rate to calculate that he will travel 8 x 2 = 16 miles.
This means that he must cycle an additional 4 miles to reach his target distance.
Overall, the unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.
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An object moves in the xy-plane so that its position at any time tis given by the parametric equations X(0 = ? _ 3/2+2andy (t) = Vt? + 16.What is the rate of change of ywith respect t0 when t = 3 1/90 1/15 3/5 5/2'
The given parametric equations are X(t) = -3/2 + 2t and y(t) = vt² + 16, the rate of change of y with respect to "t" when t = 3 is 6v
We have the parametric equations that are X(t) = -3/2 + 2t and y(t) = vt² + 16.
At time t, the rate of change of y with respect to t is given by the derivative of y with respect to t, that is dy/dt.
So, y(t) = vt² + 16
Differentiating with respect to t, we get
⇒ dy/dt = 2vt.
Now, t = 3 gives us,
y(3) = v(3)² + 16 ⇒ 9v + 16.
Therefore, the rate of change of y with respect to t at t = 3 is
dy/dt ⇒ 2vt ⇒ 2v(3) ⇒ 6v.
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At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour. )
The speed (in knots) at which the distance between the ships A and B is changing at 6 PM is given as 36 knots or 36 nautical miles per hour.
Consider that the ship A is in the west direction and the ship B is in the north direction and both the ships are in regular motion of speed which is 16 knots and 15 knots and the distance between them is 50 nautical miles.
Using the Pythagoras theorem, the relation of the distance x which represents the distance between ships at 6PM to the distances that each ship has travelled can be given as follows:
x^2 = (50 + 16t)^2 + (15t)^2
where, t is the number of hours that has passed since noon.
Differentiating both sides of the above equation with respect to time, we get:
2x*(dx/dt) = 2(50 + 16t)*(16) + 2*(15t)*(15)
t = 6, at 6 PM, therefore substituting the value and solving, we get:
2x(dx/dt) = 2[(50 + 16(6)]*(16) + 2*[15(6)]*(15)
2x(dx/dt) = 4194
dx/dt = 2097/x
Now substituting the value of x that corresponds to 6 PM:
x^2 = (50 + 16(6))^2 + (15(6))^2
x^2 = 3385
x = √3385 ≅ 58.19
Putting this value in dx/dt, we get:
dx/dt = 2097/58.19 ≅ 36.00 knots
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on saturday a local hamburger shop sold a combined total of 416 hamburgers and cheeseburgers.the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold?
Answer: Let x be the number of hamburgers sold.
Then, the number of cheeseburgers sold is 3x.
The total number of burgers sold is x + 3x = 4x.
Given that the total number of burgers sold is 416, we have:
4x = 416
x = 416/4
x = 104
Therefore, 104 hamburgers were sold.
Step-by-step explanation:
for class three girls taking classes at a martial art school, there are 4 boys who are taking classes, if there are 236 boys taking classes, predict the number of girls taking classes at the school. what's the answer
There are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.
What is ratio?A ratio is a means to indicate the relative sizes of two or more items for the purpose of comparison. It can be shown with a colon or as a fraction. Mathematicians employ ratios for a variety of purposes, including comparing numbers, scaling up or down, and resolving proportions. Moreover, ratios can be employed in other mathematical processes, simplified, and transformed to percentages or decimals.
Given that for every three girls there are 4 boys in class.
Thus, the proportion can be given as:
4x = 236
x = 59
Now, the proportion of girls are 3x.
3(59) = 177 girls.
Hence, there are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.
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A random sample of size 64 is to be used to test the null hypothesis that for a certian age group
the mean score on an achievement test (the mean of a normal population with sigma square (variance)variancesigma square= 256) is
less than or equal to 40 against the alternative that it is greater than 40. If the null hypothesis
is to be rejected if and only if the mean of the random sample exceeds 43.5, nd
(a) the probabilities of type I errors when\mu=37, 38, 39, and 40;
(b) the probabilities of type II errors when\mu= 41, 42, 43, 44, 45, 46, 47, and 48.
Also plot the power function of this test criterion.
Answer:
A random sample of size 64 is used to test the null hypothesis that for certain age group the mean score on an achievement test is less than or equal to 40 against the alternative that it is greater than 40. The scores are assumed to be normally distributed with variance 0? 256 _ Consider the hypotheses Ha: L <40 versus HA Lt > 40 and suppose the null hypothesis is to be rejected if and only if the sample mean X exceeds 43.5. What is the size of this test? Compute the probability of type Il error at L = 42
Step-by-step explanation:
Lara opened a savings account 1 year ago. The account earns 11% interest, compounded
continuously. If the current balance is $7,000.00, how much did she deposit initially?
Round your answer to the nearest cent.
As a result, Lara made a $6,262.71 initial deposit into her savings account.
How long will it take for your money to double if the interest rate is 12% annually compounded?A credit card user who pays 12% interest (or any other loan type that charges compound interest) will double their debt in six years. The rule can also be applied to determine how long it takes for inflation to cause money's value to decrease by half.
To calculate the initial investment, we can apply the continuous compounding formula:
A = Pe(rt)
Where:
A = the current balance ($7,000.00)
P = the initial deposit (unknown)
r = the annual interest rate (11% or 0.11 as a decimal)
t = the time in years (1 year)
Plugging in these values, we get:
$7,000.00 = Pe(0.11 * 1)
A shorter version of the exponential expression:
$7,000.00 = Pe0.11
$7,000.00 = P * 1.1166 (rounded to 4 decimal places)
Dividing both sides by 1.1166:
P = $6,262.71 (rounded to the nearest cent)
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what type of data is a questionnaire
Answer:
A questionnaire can collect quantitative, qualitive or both types of data.
Step-by-step explanation:
Answer:
Categorical data
Step-by-step explanation:
Data that relates to certain categories e.g males, females or any types of car
WILL GIVE BRAINLIEST 15 POINTS PLEASEE Fill in the blanks pleaseee
Therefore, we have the values of:
a = -g(x) for -10 < x < -8
b = lower limit of the range where g(x) = -6
c = -C for -1 < x < 1
d = upper limit of the range where g(x) = 4
e = we cannot determine the value of e based on the given information.
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.
Here,
We can find the values of a, b, c, d, and e by examining the given information:
For -15 < x < -10: g(x) = -(-10) = 10
For -10 < x < -8: g(x) = -a
For -1 < x < 1: g(x) = -C
For b < x < l: g(x) = -(-6) = 6
For 10 < x < 15: g(x) = -8
For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.
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use a direct proof to show that every odd integer is the difference of two squares. [hint: find the difference of the squares of k 1 and k where k is a positive integer.]
Yes, every odd integer can be written as the difference of two squares.
To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.
To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.
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4x 2 +6x−13=3x 2 to the nearest tenth.
The solutions to the equation are x = -4 and x = 1.
What is quadratic formula?The quadratic formula, which is often employed in the disciplines of mathematics, physics, engineering, and other sciences, is a potent tool for resolving quadratic problems. We must first get the values of a, b, and c from the quadratic equation in order to apply the quadratic formula. To get the answers for x, we then enter these values as substitutes in the formula and simplify.
The given equation is 4x² + 6x - 13 = 3x².
Rearranging the equation we have:
x² + 6x - 13 = 0
The quadratic formula is given as:
x = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a = 1, b = 6, and c = -13.
x = (-6 ± √(6² - 4(1)(-13))) / 2(1)
x = (-6 ± √(100)) / 2
x = (-6 ± 10) / 2
x = -8/2 or x = 2/2
x = -4 or x = 1
Hence, the solutions to the equation are x = -4 and x = 1
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A box with a square base and open top must have a volume of 62500 cm3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A'(x). A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x² .] A'(x) = 0 when x =
The area of the square base = x².
we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...
The dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.
To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.
Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x
Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x² A'(x) = 0 when x = (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
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If x=3, solve for y
y=2*3^(3)
Answer:
54
Step-by-step explanation:
Answer:
y=54
as x=3
so y=2*x^3
y= 2*3^3
y=2*27
y=54
Anyone know the answer?
As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.
what is volume ?The quantity of space occupied by a three-dimensional object is measured by its volume. Units like cubic meters (m3), cubic centimeters (cm3), or cubic inches (in3) are frequently used to quantify it. Depending on the shape of the item, different formulas can be used to determine its volume. For instance, the volume of a cube can be calculated by multiplying its length, breadth, and height, while the volume of a cylinder can be calculated by dividing the base's area (typically a circle) by the cylinder's height.
given
We must apply the calculation for the volume of a cone's frustum in order to determine the volume of the Styrofoam collar:
[tex]V = (1/3)\pi h(R^2 + Rr + r^2)[/tex]
where h is the height of the frustum, r is the small radius, and R is the large radius.
Given the numbers, we can determine:
R = 5 in.
3 centimeters is r.
24 inches tall
With these numbers entered into the formula, we obtain[tex]V = (1/3)\pi (24)(5^2 + 5*3 + 3^2)\\\\ 179.594 cubic inches[/tex]
As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.
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Find the missing side of each triangle round your answers to the nearest 10th
Calculate (3.7 x 10¹⁴) + (9 × 10¹²) Give your answer in standard index form.
Answer:3.79*10^14
Step-by-step explanation:
370000000000000+9000000000000=379000000000000
=3.79 x 10^14
Answer:
(3.79×10^14)
Step-by-step explanation:
sjskakakzks
(8,-4) and (-1-2) to the nearest tenth
The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value proble,dN/dt=N(1-0.0005N), N(0)=1(a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedure over a long period of time.dN/dt = N(1 − 0.0005N), N(0) = 1.(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a).How many supermarkets are expected to adopt the new technology whent = 15?(Round your answer to the nearest integer.)
(a) To predict how many supermarkets are expected to adopt the new procedure over a long period of time, we can analyze the behavior of the differential equation using a phase portrait.
The equation can be rewritten as dN/N = (1-0.0005N)dt. Integrating both sides, we get ln|N| = t - 0.0005N^2/2 + C, where C is the constant of integration. Solving for N, we have:
N(t) = +/- sqrt((2ln|N| - 2C)/0.001)
We can see that the solutions are of the form of a hyperbola, with N approaching the asymptotes y=0 and y=2000. The equilibrium point is N=0, which is unstable, and the critical point is N=2000, which is stable.
Therefore, over a long period of time, we expect the number of supermarkets using the computerized checkout system to approach 2000.
(b) To solve the initial-value problem, we can use the separation of variables:
dN/N = (1-0.0005N)dt
ln|N| = t - 0.00025N^2 + C
N(0) = 1
Substituting N=1 and t=0, we get C=0. Therefore, the solution is:
ln|N| = t - 0.00025N^2
N = e^(t-0.00025N^2)
Using a graphing utility, we can plot the solution curve for N(t):
The graph confirms that the solution curve approaches 2000 as t increases.
When t=15, we can evaluate N(15) using the solution:
N(15) = e^(15-0.00025N^2)
Rounding to the nearest integer, we get N(15) = 1719.
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Simplify to an expression involving a single trigonometric function with no fractions.
cos(−x)+tan(−x)sin(−x)
Sec x is the simplified expression cos(−x)+tan(−x)sin(−x) involving a single trigonometric function with no fractions.
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
The Given expression is
cos(−x)+tan(−x)sin(−x)
Now,
cos(−x) + tan(−x)sin(−x)
= cos x + (- tan x) (- sin x)
= cos x + tan x * sin x
= cos x + (sin x / cos x) * sin x
= (cos²x + sin²x) / cos x ( As sin²x + cos²x = 1)
= 1/ cos x
= sec x (As sec x = 1/cos x)
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MR. Swanson wants to buy some mugs as gifts on his trip to California.There are three gifts shops, and each is offering a different deal. Which gift shop has the best deal for mugs
Answer: The one that has the best deals.
Step-by-step explanation:
