Answer:When x→−∞ , then P(x)→−∞When x→+∞ , then P(x)→+∞Note that we can figure out if the function grows or decreases, simply by looking at the leading term of the function which is 4x⁵. This term shows that the function increases without bound as x → ± ∞.The given function is P(x)=4x⁵−8x³−7x²+9x+7We can now find the horizontal asymptotes of the given function, by computing the limits at infinity as follows;When x→−∞ , then P(x)→-∞When x→+∞ , then P(x)→+∞Therefore, the horizontal asymptotes are: y= - ∞ and y= + ∞
The total length of a road trip was 13. 8 hours. If highway signs are posted every 0. 6 hours, including one at the end of the road trip, how many highway signs will there be on the road trip?
There will be 23 highway signs on the road trip, including one at the end of the road trip.
The total length of the road trip is 13.8 hours. To solve for the number of highway signs on the road trip, we need to use the formula for finding out how many times a certain number can fit into another number. This formula is N = A/B, where N is the number of times B can fit into A. In this case, B is the time between highway signs (0.6 hours) and A is the total length of the road trip (13.8 hours). Plugging these values into the formula, we get N = 13.8/0.6 = 23. So, there will be 23 highway signs on the road trip, including one at the end of the road trip.
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A basketball has a radius of 4.7 inches. What is the approximate volume of the basketball?
The approximate volume of the basketball is 0.00486 cubic meters.
We have,
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume and r is the radius of the sphere.
Converting the radius of the basketball from inches to meters
4.7 inches = 0.11938 meters
Now we can substitute this value for r in the volume formula:
V = (4/3)π(0.11938)³
Using a value of π = 3.14159 and evaluating the expression in the parentheses, we get:
V ≈ 0.00486 cubic meters
Therefore,
The approximate volume of the basketball is 0.00486 cubic meters.
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Stefan has 4 1/2
cups of oats. He uses 3 1/4
cups to make granola bars for a camping trip. He saves the rest of the oats to feed to his parrot, Coco. If Coco needs 1/4
of a cup of oats each day, how many days can Stefan feed Coco with the oats he has left?
Answer:
5 days .......
Step-by-step explanation:
Stefan has 4½ cups of oat
He uses 3¼ to make granola
What he has left 4½-3¼ = 1¼
If he feeds ¼of a cup to parrots a day, then he has 5 days feed from 1¼
Calculation 1¼ ÷ ¼
Change to improper fraction
5/4 ÷ 1/4 = 5/4 x 4/1
Ans 20/4 = 5days
Do you agree that many math concepts “teach themselves”? Why or why not?
Answer:
Yes, they do
Step-by-step explanation:
The more you focus on a concept, the more you get an understanding of it without being taught by another person.
Hard math concepts are hard cause you haven't found an easier way to get an understanding of it.
A cylinder has a diameter of 10 inches and a height of 18 inches what is the volume of the cylinder
if it has a diameter of 10, that means its radius is half that or 5.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=18 \end{cases}\implies V=\pi (5)^2(18)\implies V\approx 1413.72~in^3[/tex]
Find the measure of the arc angle or angle indicated
Answer:
Below
Step-by-step explanation:
For angles whose vertex is inside the circle , the angle measure is the sum of the two arcs subtended divided by 2
? = E
E = (55 + 155)/2 = 105° = ?
Larry owns a shoe store. his starting balance was 17,300 his ending balance was 14,700 what is Larry's burn rate.
Larry's burn rate, which represents the amount of money he spent per unit of time, is $2,600 per month based on the starting balance of $17,300 and the ending balance of $14,700.
Larry's burn rate can be calculated as the amount of money he spent per unit of time, which is usually expressed as a monthly or annual rate. To calculate his burn rate based on the given information, we need to know the time period for which the difference between the starting and ending balances represents.
Assuming that the starting balance of $17,300 represents the beginning of a month or some other specific time period, and that the ending balance of $14,700 represents the end of the same time period, we can calculate Larry's burn rate as follows:
Burn rate = (Starting balance - Ending balance) / Time period
If we assume that the time period is one month, then:
Burn rate = ($17,300 - $14,700) / 1 month = $2,600 per month
Therefore, Larry's burn rate is $2,600 per month. This means that he spent an average of $2,600 per month to run his shoe store during the time period in question.
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5
The diagram shows a sector of a circle of racus 24 cm
Not drawn
accurately
24 cm
Work out the are length AB
(Worked out wrong )
The value of the variable x given the perimeter is 44°.
What is the sector?A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.
Given: radius = 24cm
perimeter (total) of sector = 68cm
Total perimeter of sector=68cm
Radius = 24 cm
24 + x = 68 cm
x =68 - 24
x = 44°
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A diagram shows a sector of a circle of radius 24 cm and perimeter of 68cm. Find the value of x.
A) Given: Regular pyramid KO ⊥ (ABCD) KO = 10. 2, m∠AKO = 38º Find: V
The standard pyramid KO has a volume of roughly 64.88 cubic units.
To find the volume of the given regular pyramid KO, we need to know the area of the base and the height of the pyramid. Since the pyramid is regular, the base is a square. Let the side of the square base be x.
Now, we can use trigonometry to find the height of the pyramid. Draw a line from vertex K to the center O of the base. This line is perpendicular to the base, so it splits the base into two equal parts. Let M be the midpoint of side AB. Then, we have right triangle KMO with hypotenuse KO, and angle MKO equal to half of angle AKO (19 degrees).
We can use the trigonometric function tangent to find the height h of the pyramid:
tan 19 = h/5 (where 5 is half of x, the side length of the base)
h = 5 tan 19 ≈ 1.98
Now, we can use the formula for the volume of a pyramid:
V = (1/3) * area of base * height
Since the base is a square, its area is x². Substituting the known values, we get:
V = (1/3) * x² * h
V = (1/3) * x² * 1.98
V = (0.66) x²
We are given that KO = 10.2, which is the slant height of the pyramid. Using the Pythagorean theorem, we can find x:
x² + (5/2)² = 10.2²
x² = 104.04 - 6.25
x² = 97.79
x ≈ 9.89
Substituting this value for x into the equation for the volume, we get:
V = (0.66) * 9.89²
V ≈ 64.88
Therefore, the volume of the regular pyramid KO is approximately 64.88 cubic units.
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simplify the expression x + 8 and = 3: x by the power of 2 - xy
The given expression can be simplified to x2 - xy = 3.
What is expression?Expression is a way to communicate ideas, feelings, and thoughts. It can be verbal, physical, and/or written. Expression is the outward manifestation of your inner emotions, which can take many forms. Expression can be used to express joy, sadness, anger, and other emotion. It can also be used to articulate a point of view or opinion. Expression is an important part of communication and is a powerful tool to express oneself and one’s feelings.
This is happening because the addition of 8 to x can be rewritten as x2, and the equal sign can be used to indicate that the two sides of the equation must be equal. Therefore, both sides can be simplified to their original terms. Thus, the expression can be written as x2 - xy = 3.
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The given expression can be simplified to 25 + 5y + 4.
What is expression?Expression is a way to communicate ideas, feelings, and thoughts. It can be verbal, physical, and/or written. Expression is the outward manifestation of your inner emotions, which can take many forms. Expression can be used to express joy, sadness, anger, and other emotion. It can also be used to articulate a point of view or opinion. Expression is an important part of communication and is a powerful tool to express oneself and one’s feelings.
To simplify the expression x + 8 and = 3, we must first subtract 8 from both sides of the equation to get x = -5. We can then substitute -5 for x in the expression x2 - xy + 4, resulting in (-5)2 - (-5)y + 4.
Simplifying further, we get 25 - (-5)y + 4, or 25 + 5y + 4. Therefore, the simplified expression is 25 + 5y + 4.
This is happening because the addition of 8 to x can be rewritten as x2, and the equal sign can be used to indicate that the two sides of the equation must be equal. Therefore, both sides can be simplified to their original terms. Thus, the expression can be written as 25 + 5y + 4.
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What was the original price if after an increase of 25% the price was $225. 00?
As per the given percentage, the original price to be $180.00.
Let's begin by defining what percentage means. A percentage is a fraction that represents a portion of a whole expressed as a fraction of 100. For example, 25% can be written as 25/100 or 0.25 as a decimal.
Now, let's apply this concept to the problem. We know that the original price increased by 25%, which means the new price is 125% of the original price. We can represent this mathematically as:
New price = Original price + 25% of the original price
125% of the original price = Original price + 25% of the original price
1.25 x Original price = Original price + 0.25 x Original price
1.25 x Original price = 1.25 x Original price
Original price = (225.00 / 1.25)
Therefore, the original price was $180.00.
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Ajay is going to invest his money into 222 different stocks. Both stocks are independent, and each stock has a 50\%50%50, percent chance of being successful and a 50\%50%50, percent chance of failing. Each stock will make Ajay \$500$500dollar sign, 500 if it succeeds or lose him \$500$500dollar sign, 500 if it fails
The actual outcome of his investment could still be positive or negative, depending on the actual performance of the individual stock.
Since each stock has a 50% chance of being successful and a 50% chance of failing, the expected value of each stock is:
(0.5 * 500) + (0.5 * (-500)) = 0
That is, the expected value of each stock is zero, because the potential gain of $500 is balanced by the potential loss of $500.
Now, since the stocks are independent, the expected value of Ajay's entire investment is simply the sum of the expected values of each individual stock:
Expected value of Ajay's investment = 222 * 0 = 0
So the expected value of Ajay's investment is also zero dollars. This means that, on average, Ajay should not expect to make a profit or a loss from his investment in these 222 stocks. However, the actual outcome of his investment could still be positive or negative, depending on the actual performance of the individual stocks.
Ajay is going to invest his money into 222 different stocks. Both stocks are independent, and each stock has a 50\%50%50, percent chance of being successful and a 50\%50%50, percent chance of failing. Each stock will make Ajay \$500$500dollar sign, 500 if it succeeds or lose him \$500$500dollar sign, 500 if it fails
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Which list shows these numbers in order from least to greatest?
0. 009854 1. 98 V9 30%
The list that shows these numbers in order from least to greatest is:
0.009854, 30%, 1.98, V9
The reason for this order is as follows:
0.009854 is the smallest number, since it is a decimal between 0 and 1 with four digits after the decimal point.30% is the next smallest number. It is larger than 0.009854 but smaller than the other two numbers in the list. Note that "30%" is equivalent to the decimal 0.3.1.98 is the next largest number. It is larger than both 0.009854 and 30%, but smaller than "V9"."V9" is the largest number in the list, but we cannot directly compare it to the other three numbers since it is not a numerical value. Without additional context, we cannot determine its relative magnitude.For more such questions on Mathematical comparison: brainly.com/question/29006160
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What whole number is nearest to each square root? √22
Step-by-step explanation:
The square root of 22 is an irrational number, which means it cannot be expressed exactly as a finite decimal or a fraction. However, we can approximate it by finding the whole number that is closest to it.
To do this, we can use a calculator or estimation. For example, we can guess that the square root of 22 is between 4 and 5, since 4 squared is 16 and 5 squared is 25. Then we can try averaging these two numbers:
(4 + 5) / 2 = 4.5
This means that 4.5 is an approximate value of the square root of 22. The nearest whole number to 4.5 is 5, so we can say that the whole number nearest to the square root of 22 is 5.
The hands on a clock show it is 9:00. What angle measurement do the hands form?
The angle measurement between the hands of the clock is 270 degrees. At 9:00, the hour hand points directly to the 9 and the minute hand points directly to the 12.
We know that the hour hand moves 360 degrees in 12 hours (or 30 degrees per hour), and the minute hand moves 360 degrees in 60 minutes (or 6 degrees per minute).
To calculate the angle between the hands, we can use the formula:
angle = |30h - 11m/2|
where h is the hour (9 in this case) and m is the minute (0 in this case). Substituting these values into the formula, we get:
angle = |30(9) - 11(0)/2|
= |270|
= 270
Therefore, the angle between the hands of the clock is 270 degrees.
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Graph the function. Make sure to find the axis if symmetry, vertex, and 5 total points in order to graph. f(x)=x^2−8x+13
The axis of rotation is a perpendicular line that passes through the vertex, meaning the lowest point in the graph [tex](4, -3)[/tex].
Describe the vertex.A vertices is a place on a polygons where two ray or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the lines A, B, C, E, etc E in the aforementioned figures are vertices.
A vertex in a mathematical graph is what?A node of a graph, or one of the vertices from which a graph is formed and that can be connected by graph, is referred to as a "vertex" in computing. Moreover, the words "point," "junction," and "0-simplex" are employed.
To graph the function [tex]f(x) = x^2 - 8x + 13[/tex], we need to find its axis of symmetry, vertex, and a few other points.
Find the axis of symmetry
[tex]x = -b/2a[/tex]
In this case, [tex]a = 1[/tex] and [tex]b = -8[/tex], so the axis of symmetry is [tex]x = -(-8)/(2*1) = 4[/tex].
Find the vertex
[tex]f(4) = 4^2 - 8(4) + 13 = -3[/tex]
So the vertex is [tex](4, -3)[/tex].
To find other points,
When [tex]x = 0, y = 13[/tex]
When [tex]x = 1, y = 6[/tex]
When [tex]x = 2, y = 1[/tex]
When [tex]x = 3, y = -2[/tex]
When [tex]x = 5, y = 2[/tex]
These points cannot be connected on a graph to form a basic picture of the function.
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What is the measure of DEF
Answer:
72
Step-by-step explanation:
The measure of the inscribed angle(DEF) is half the measure of its intercepted arc (Arc FD)
The measure of are FD is 144 and half of that is 72.
So the measure of angle DEF is 72 degrees.
Answer:
72°
Step-by-step explanation:
∠DEF is an inscribed angle equal to half the arc on which it rests
∠DEF = 0,5 × 144 = 72°
Two joggers, one averaging 8 mph and one averaging 4 mph, start from a designated initial point. The slower jogger arrives at the end of the run 35 minutes after the other jogger. Find the distance of the run
The distance of the run is about 7.33 miles.
Let's anticipate that the distance of the run is "d" miles.
We realize that time = distance ÷ velocity.
For the first jogger who averages 8 mph, the time taken to finish the run may be represented as:
t = d ÷ 8
For the second jogger who averages 4 mph, the time taken to complete the same run may be represented as:
t + 35/60 = d ÷ 4
We can simplify this equation by substituting the value of "t" from the first equation:
d ÷ 8 + 35/60 = d ÷ 4
.
Multiplying each aspects through 24 (LCM of 8 and 4), we get:
3D + 7 = 6d
Simplifying this, we get:
d = 7.33 miles (rounded to two decimal locations)
Therefore, the distance of the run is about 7.33 miles.
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The distance between two points on a map is 20 cm. The actual distance is 980 m. What is the unitless scale of the map in simplest form?
In Linear equation, 196000 cm is the unitless scale of the map in simplest form.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
h = 1/2 t²
here
g = 980 m/sec²
t = 20 sec
Therefore, the distance h is: 196000 cm
h = 1/2 * 980 * 20² = 196000 cm
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1 point) Solve the equation x²−4x−21=0 byfactoring.The solutions are x1=and x2=with x1
The solutions of x1 = 7 and x2 = -3 with x1 through solving the quadratic equation x²−4x−21=0 by factoring
The equation :x² - 4x - 21 = 0, solve it by factoring it.The first step is to find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3.So, we rewrite the equation using -7 and 3 instead of -4x:x² - 7x + 3x - 21 = 0.
Group the first two terms and the last two terms: x(x - 7) + 3(x - 7) = 0.
Factor out the common factor of (x - 7): (x - 7)(x + 3) = 0.
Now, we have two factors that when multiplied, give us zero. This means that either (x - 7) = 0 or (x + 3) = 0.
Solving for x, we get: x = 7 or x = -3.
The solutions are x1 = 7 and x2 = -3.The equation x² - 4x - 21 = 0 can be solved by factoring it. To factor this equation, we first find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3. Then we rewrite the equation using -7 and 3 instead of -4x.
The resulting equation is x² - 7x + 3x - 21 = 0.
Next, we group the first two terms and the last two terms to get x(x - 7) + 3(x - 7) = 0.
We factor out the common factor of (x - 7) to get (x - 7)(x + 3) = 0.
We then solve for x to get x = 7 or x = -3. Therefore, the solutions are x1 = 7 and x2 = -3.
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1.1 Beth, Carolyn and George love reading their favourite bedtime stories together.
They take it in turns to read a page, always in the order Beth, then Carolyn, then George.
All twenty pages of the story are read on each occasion.
One evening, Beth is staying at Grandma's house but Carolyn and George still read the
same bedtime story and take it in turns to read a page with Carolyn reading the first
page.
In total, how many pages that Carolyn and George read are the same as the pages that
they would read if Beth was there?
Thus on the sixth, ninth, twelfth, fifteenth, and eighteenth pages, he reads the same pages.
what is unitary method ?To tackle proportionality-related mathematical problems, one can apply the unitary method. Finding the value of one unit and then utilising that value to calculate the value of another quantity with a different number of units is what this method entails. Consider the scenario where you are told that an automobile goes 300 miles in 5 hours. The unitary technique can be used as follows to determine how far the car drives in 8 hours: Calculate what an hour is worth: 1 hour is equal to 300/5, or 60 miles. 5 hours equals 1 unit. Use this number to calculate the value of eight hours: 8 hours equals 8/1 units, hence 8 x 60 = 480 miles are covered during that time.
given
Each of them reads roughly one-third of the story's pages when the three of them are reading it together.
As a result, Beth reads the first, fourth, seventh, and cdots pages, Carolyn reads the second, fifth, and eighth, and cdots pages, and George reads the third, sixth, and ninth.
When just Carolyn and George are reading the narrative, Carolyn reads the first page and George reads the second, and so on through the remaining pages.
Thus on the sixth, ninth, twelfth, fifteenth, and eighteenth pages, he reads the same pages.
So, $3+5=8 ($boxed) is the amount of pages that Carolyn and George read that are equal to the amount of pages they would have read if Beth had been present.
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Boubacar has a loyalty card good for a 11% discount at his local grocery store. If the total cost, before tax and discount, of all the items he wants to buy is c, which expression represents the cost after the discount?
The expression that represents the cost after the 11% discount is 0.89c. This means that Boubacar will pay 89% of the original cost after the discount has been applied.
How to calculate discount?To calculate the discount, you need to determine the discount rate, which is usually a percentage of the original price. Multiply the discount rate by the original price to find the amount of the discount.
Finally, subtract the discount amount from the original price to get the discounted price.
The discount that Boubacar gets on his purchase is 11% of the total cost before tax and discount. To calculate the discount, we multiply the total cost (c) by 11% or 0.11, which gives us:
Discount = 0.11c
To find the cost after the discount, we subtract the discount from the total cost. This gives us:
Cost after discount = c - Discount
Cost after discount = c - 0.11c
Cost after discount = 0.89c
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Anyone know this question?
The expression for the amount of change Zina should receive would then be 20 - (0.30 x 10) = 17.00. This means that Zina should receive 17.00 in change from the clerk.
What is amount?
Amount is the quantity or amount of something that is available, measurable, or given. It is a numerical value. Amount can refer to a quantity of money, goods, or services that is owed, requested, or given. It can also refer to the total cost of items or services. Amounts can be measured in both the physical and digital world. Amount is used in accounting, finance, and other fields to measure and keep track of assets and liabilities.
The expression that represents the amount of change Zina should receive is 20 - (0.30p). This expression takes the original amount of money given to the clerk, twenty dollars, and subtracts out the total cost of the bananas, which is 0.30p. The 'p' in this expression represents the number of pounds of bananas Zina purchased.
To determine the amount of change Zina should receive, the clerk must first calculate the total cost of the bananas. This is done by multiplying the number of pounds of bananas purchased by the cost per pound. Once the total cost of the bananas is calculated, it is then subtracted from the twenty dollars given. The resulting number is the amount of change Zina should receive.
For example, if Zina purchased 10 pounds of bananas at 30 cents per pound, the total cost of the bananas would be 10 x 0.30 = 3.00. The expression for the amount of change Zina should receive would then be 20 - (0.30 x 10) = 17.00. This means that Zina should receive 17.00 in change from the clerk.
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what’s the zeros of the function of f(x)=x^2+49
Answer:
This function has no zeroes
Step-by-step explanation:
To understand this problem we need to first understand what the zeroes of a function is; the zeroes of a function is the point at which the y value of a solution is equal to zero. So in this scenario all we need to do is plug 0 in for y:
[tex]0 = x^2 +49[/tex]
Subtract 49 from both sides:
[tex]-49 = x^2[/tex]
Now we can notice that [tex]x^2[/tex] is equal to -49; to our surprise there is no possible value for [tex]x^2[/tex] to be equal to a negative number. Therefore this function has no roots.
Step-by-step explanation:
a zero of a function means what value of x causes a functional value of 0 ?
so,
0 = x² + 49
-49 = x²
x = ±sqrt(-49)
this tells us that there is no solution in real numbers, because no square of any real number can be negative.
but the function still has 2 zeroes. they are numbers of the set of imaginary or complex numbers.
that means they base on the square root of -1, called i.
x = ±sqrt(49×-1) = ±7×sqrt(-1) = ±7i
A trapezoid has a base of 5 millimeters,
another base of 7 millimeters, and a height
of 6 millimeters. Explain how the area of the
trapezoid will change if the height and both
bases are doubled.
The area will rise by a factor of four if we double the base and height of a trapezoid.
Explain about the trapezoid?A quadrilateral with a single set of parallel sides is referred to as a trapezoid. The parallel and non-parallel sides are referred to as bases and legs, respectively. The distance between the bases of a trapezoid measured perpendicularly is its height.
The formula for a trapezoid's area is:
Area is equal to (base1+base2)*height / 2.
Considering that the height is 6 millimeters, the first base is 5 millimeters, and the secondary base is 7 millimeters, we may determine the trapezoid's initial area as follows:
Area = 1/2 *(5 + 7)* 6 = 36 sq. mm
Doubling the height and both bases:
New base 1 = 2 * 5 = 10 mm
New base 2 = 2 * 7 = 14 mm
New height = 2 * 6 = 12 mm
The new area of such trapezoid can be calculated using the same formula:
New Area = 1/2* (10 + 14) * 12 = 144 sq. mm
When we compare the new area to the old area, we are able to see that the new area has been four times bigger.
So, if the base and height of just a trapezoid are both doubled, the area will grow by a factor four.
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What single percentage change is equivalent to a 11% increase followed by a 21% decrease?
Answer:
Step-by-step explanation:
-10 perecent
because 21-11=10
true/false. using higher order functions, complete the mul by num function. this function should take an argument and return a one argument function that multiplies any value passed to it by the original number.
The statement "using higher order functions, complete the mul by num function. this function should take an argument and return a one argument function that multiplies any value passed to it by the original number" is True. It is possible to complete the `mul_by_num` function using higher order functions. A higher order function is a function that either takes one or more functions as arguments, or returns a function as its result.
In this case, the `mul_by_num` function should take an argument and return a one argument function that multiplies any value passed to it by the original number. Here's how you can do it:
```python
def mul_by_num(num):
def num_function(val):
return val * num
return num_function
```
The `mul_by_num` function takes an argument `num` and returns a one argument function `num_function` that multiplies any value passed to it by the original number `num`. The `num_function` is a higher order function because it is returned by the `mul_by_num` function.
You can use the `mul_by_num` function like this:
```python
mul_by_5 = mul_by_num(5)
print(mul_by_5(10)) # 50
```
The `mul_by_num` function is called with the argument `5` and returns a one argument function `mul_by_5` that multiplies any value passed to it by 5. When the `mul_by_5` function is called with the argument `10`, it returns the result `50`.
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21. *
21
Andy made a servings of tacos and
15 servings of nachos, and wants to set
up identical tables for the tacos and
nachos. He also doesn't want any left
over tacos or nachos. What is the most
number of tables Andy can set up?
10 poi
Andy can set up a maximum of 12 tables, each with 3 servings of tacos and 3 servings of nachos.
Let's assume that there are a limit of n servings per table. We need to get the greatest number of n that divides both 21 and 15 without leaving a remnant because Andy doesn't want any leftover tacos or nachos. In comparison to the factors of 15, which are 1, 3, 5, and 15, the factors of 21 are 1, 3, 7, and 21. Three is the highest number that divides both 21 and 15.
Thus, a maximum of three dishes can be placed on each table. We divide the total servings by the maximum servings per table to get how many tables Andy can set up:
Servings total: 21 + 15 = 36
3 serves maximum per table.
Amount of tables = Total Servings / Maximum Servings Per Table = 36 / 3 = 12
Hence, Andy can only put up a maximum of 12 tables, each with 3 tacos and 3 nachos.
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Zach has to cut wooden molding into 9 pieces that are each half a yard long. What is the total length of the molding in yards written as a mixed number?
Zach has to cut the wooden molding into 9 sections, resulting in a total length of 4 1/2 yards in various numbers.
what is length ?A measurement of length is the distance between two points on an item. It is one of the essential physical quantities used in physics and a fundamental idea in geometry. Typically, length is expressed in terms of meters, centimeters, feet, inches, or kilometers. Rulers, measuring instruments, and laser rangefinders are just a few of the tools that can be used to determine an object's length. When describing the size of geometric objects like lines, segments, or curves, length is frequently used in mathematics.
given
The overall length of the molding can be calculated by multiplying the length of each piece by the number of pieces, for example, if Zach needs to cut wooden molding into 9 pieces that are each half a yard long:
Total length equals each piece's length times the number of parts.
Overall length is 9 + (1/2 yard)
length overall: 9 2 yards
We can divide 9 by 2 and write the outcome as a mixed number to represent this:
with a residue of 1, 9 2 = 4
Zach has to cut the wooden molding into 9 sections, resulting in a total length of 4 1/2 yards in various numbers.
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a. In 2000, the population of a country was approximately \( 6.19 \) million and by 2050 it is projected to grow to 10 mallion. Use the exponentiat growth model \( \mathrm{A}=\mathrm{A}_{0} e^{k t} \)
The given data shows that in 2000, the population of a country was approximately 6.19 million, and by 2050, it is projected to grow to 10 million. The exponential growth model can be represented as:
A = A0e^{kt}
Where A0 = 6.19 (initial population in 2000), A = 10 (projected population in 2050), T = 50 - 00 = 50 years (time period between 2000 and 2050).
Substituting the values in the formula, we get:
10 = 6.19 e^{k × 50}
Solving for k:
e^{k × 50} = 10/6.19
k × 50 = ln(10/6.19)
k = ln(10/6.19) / 50
k = 0.0169
Therefore, the population of the country will be given by A = 6.19 e^{0.0169t} where t represents the time in years after 2000.
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