What’s the difference between solving a whole number and a fraction?
There’s these two methods I saw but not sure when I should use them when I do stumble on a problem.
1 method: start by multiply the numerator towards the whole number and once u do then divide the numerator and denominator separately.
2 method: start by giving the whole number a 1 of the denominator and find the lCD of the fraction and start finishing the problem from either adding or subtracting.
Both the methods can be used to solve a mixed fraction including a whole number and a fraction or solving the difference of a whole number and a fraction.
What is Mixed Fraction?Mixed fractions are type of fractions which involve a whole number and a fraction. This is of the form a [tex]\frac{b}{c}[/tex]. This is actually a + [tex]\frac{b}{c}[/tex].
You can use either methods when solving a whole number and a fraction.
Let us take a whole number 3 and a fraction [tex]\frac{2}{10}[/tex] for instance.
First Method :
Solve it by cross multiplication.
Let the denominator of the whole number 3 be 1.
[tex]\frac{3}{1}[/tex] ± [tex]\frac{2}{10}[/tex] = [(3 × 10) ± (2 × 1)] / (1 × 10) = [30 ± 2] / 10
If the question is for adding, we get, [tex]\frac{3}{1}[/tex] + [tex]\frac{2}{10}[/tex] = (30 + 2) / 10 = 32/10
If the question is finding difference, we get, [tex]\frac{3}{1}[/tex] - [tex]\frac{2}{10}[/tex] = (30 - 2) / 10 = 28/10
Second Method :
Again let the denominator of the whole number be 1.
Find the LCD (Least Common Denominator) of 1 and 10.
This is 10.
So we have to make the denominator of [tex]\frac{3}{1}[/tex] to 10.
Multiply both numerator and denominator with 10, we get 30/10.
A normal multiplication of fractions, if the denominator is same add or subtract the numerators let the denominator be as such.
Now add or subtract [tex]\frac{30}{10}[/tex] ± [tex]\frac{2}{10}[/tex] = (30 ± 2) / 10.
Hence both the methods can be used.
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You are part of the rescue team in a ship at sea. One of your divers is 250 feet below sea level, and she injured herself. She has only a 7 minute supply of air in her tank, and can only rise towards the surface at a rate of 10 feet per minute. You are sending down a rescue sub. The sub can descend at a rate of 30 feet per minute. At what depth, to the nearest foot, will the two meet?
Answer:
To determine at what depth the rescue sub will meet the injured diver, we need to first calculate how long it will take the diver to reach the surface. Because the diver is rising at a rate of 10 feet per minute, and she has a 7 minute supply of air, it will take her 7 minutes to reach the surface.
Next, we need to calculate how long it will take the rescue sub to reach the diver. Because the diver is 250 feet below the surface, and the sub is descending at a rate of 30 feet per minute, it will take the sub 250 feet / 30 feet/minute = <<250/30=8.33>>8.33 minutes to reach the diver.
Finally, to determine at what depth the two will meet, we need to subtract the time it takes the diver to reach the surface (7 minutes) from the time it takes the sub to reach the diver (8.33 minutes). This gives us a total time of 8.33 minutes - 7 minutes = 1.33 minutes.
Since the diver is rising at a rate of 10 feet per minute, and the total time is 1.33 minutes, the depth at which the two will meet is 1.33 minutes * 10 feet/minute = 13.3 feet. Rounding to the nearest foot, we get a depth of 13 feet. Therefore, the rescue sub and the diver will meet at a depth of approximately 13 feet.
Write an equation to solve. Be sure to identify your variable.
Mrs. Kenney's class is
holding a canned food drive for Thanksgiving. Tara collected 10 more cans than Phil.
Laurie collected twice as many cans as Tara, If they collected 130 cans altogether, how
many cans did Tara collect?
The number of cans Tara collected is 35.
How to represent and solve equation?Mrs. Kenney's class is holding a canned food drive for Thanksgiving. Tara collected 10 more cans than Phil. Laurie collected twice as many cans as Tara. They collected 130 cans altogether.
Therefore, let's find the number of cans Tara collected.
Hence, using equation,
let
x = number of cans Phil collected
Number of cans Tara collected = x + 10
Number of cans Laurie collected = 2(x + 10) = 2x + 20
Therefore,
x + x + 10 + 2x + 20 = 130
4x + 30 = 130
4x = 130 - 30
4x = 100
x = 100 / 4
x = 25
Hence, Tara collected 25 + 10 = 35 cans.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
The equations represent circles that have a diameter of 12 units and a center that lies on the y-axis is x2 + (y – 3)2 = 36,x2 + (y – 3)2 = 36
How to Find diameter of the circle?
The standard form for finding the equation of a circle is expressed as;
(x-a)^2 + (y-b)^2 = b=r^2
where;
(a, b) is the center of the circle
r is the radius of the circle
Given the following:
diameter = 12 units
radius = 12/2 = 6 units
By substituting the values we these two equations.
A line dividing a circle into even halves is the definition of the diameter of a circle. This line begins at one location on the circle, travels through the middle, and then terminates on the other side. The diameter is the circle's longest chord, according to definition (or line segment that can be formed using two points along it). The distance to the other side is greatest for the line formed by these endpoints since it travels through the centre.There are an endless number of points on one half of a circle, and each of these points has a corresponding one on the opposite side, hence this circle can have an infinite number of diameters.To learn more about Diameter of the circle refer to:
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what is 5,000,374 * 2,000
let be a random variable with the following probability distribution. value of 1 0.10 2 0.75 3 0.05 4 0.05 5 0.05 complete the following. (a) find the expectation of . (b) find the variance var of
On solving the provided question we can say that - probability distribution, E(X)= 47.5, V(X)= 128.75, [tex]E(X^{2})[/tex] = 2605
What is probability distribution?A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that different possible experiment results will occur. The sample space and event probabilities are used to build a mathematical description of random occurrences.
E(X)= (20 * 0.05) + (30 *0.05)+ (40 * 0.35) + (50 * 0.20) + (60 *0.35)
= 1+ 1.5 + 14 + 10 + 21
= 47.5
V(X)= ((20-38)2 * 0.05) + ((30-38)2 *0.05)+ ((40-38)2 * 0.35) + (50-38)2 * 0.20) + ((60-38)2 *0.35)
= 16.2 + 3.2 + 1.4 + 28.8 +169.4
= 128.75
[tex]E(X^{2})[/tex]=
=(202 * 0.05) + (302 *0.05)+ (402 * 0.35) + (502 * 0.20) + (602 *0.35)
= 20 + 45 + 560 + 500 +1260
=2605
[tex]V(X^2)[/tex] = 2605 - ( 47.5)2
= 2385 - 2256.25
=128.75
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Graph AABC with vertices A(0, 2), B(3, 2), and C(2, 1) and its image after a reflection in the x-axis.
To graph the triangle AABC, we can plot the coordinates of the three vertices and then connect them to form the triangle. The coordinates of the vertices are (0, 2), (3, 2), and (2, 1), so we can plot these points on a coordinate grid and connect them with line segments to form the triangle:
|
|
| (2,1)
| /
| /
| /
|/
(0,2) __________ (3,2)
To reflect the triangle in the x-axis, we can multiply the y-coordinate of each vertex by -1. This will cause the triangle to be flipped over the x-axis. The coordinates of the reflected triangle are (0, -2), (3, -2), and (2, -1), so we can plot these points on the same coordinate grid and connect them with line segments to form the reflected triangle:
|
|
|
| /\
| / \
| / \
|/ \
(0,2) __________ (3,2)
|
|
| (2,-1)
|
The resulting graph shows the original triangle AABC and its image after reflection in the x-axis.
Answer:
A' = (0, -2)
B' = (3, -2)
C' = (2, -1)
Step-by-step explanation:
Given vertices of triangle ABC:
A = (0, 2)B = (3, 2)C = (2, 1)The mapping rule for a reflection in the x-axis is:
(x, y) → (x, -y)Therefore, the vertices of ΔA'B'C' are:
A' = (0, -2)B' = (3, -2)C' = (2, -1)
Yesterday the temperature at noon was 26.4°F. By midnight, it had decreased by
32.4°F. What was the temperature at midnight?
Answer:
-6°
Step-by-step explanation:
26.4 - 32.4 = -6
Subtract the absolute values of the both number and give the sign of the larger absolute value.
32.4 - 26.4 = 6
The sign will be negative because -32.4 has a larger absolute value (farther from zero) than 26.4
Answer:
- 6°F.
Step-by-step explanation:
26.4
- 32.4
= -6.0
The temperature at midnight:
-6°F.
Q23: Problem-solving
Work out the area of this triangle.
The area of the triangle is 11.1 square cm
How to determine the area of the triangle?From the question, we have the following parameters that can be used in our computation:
Legs = 3cm and h cm
Hypotenuse = 8 cm
The area of the triangle is calculated using
Area = 0.5 * b * h
Where
h = √(8² - 3²) --- this is gotten from the Pythagorean theorem
So, we have
h = 7.4
The area is then calculated as
Area = 0.5 * b * h
So, we have
Area = 0.5 * 3 * 7.4
Evaluate
Area = 11.1
Hence, the area is 11.1 square cm
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tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar how much flour and sugar coral will be use to make the cookies
The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.
The flour and sugar coral that will be use to make the cookies will be:
= 1 3/4 + 1/2
= 2 1/4
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Use the Law of Sines to solve the triangle. Round your answers to two decimal places. (Let B = 8° and c = 43.)
A =
a =
b=
A
O
b
C
135°
C
B
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles. In other words, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the angles opposite those sides, then we have:
a/sin(A) = b/sin(B) = c/sin(C)
In the given triangle, we are given the values of B and c, so we can use the Law of Sines to find the other side lengths and angles. We have:
a/sin(A) = c/sin(C)
Since c = 43 and C = 135°, we can plug these values into the equation to find a:
a/sin(A) = 43/sin(135°)
To find the value of a, we just need to solve for a by multiplying both sides of the equation by sin(A). We have:
a = 43 * sin(A) / sin(135°)
We know the value of B, so we can use the Law of Sines again to find the value of A:
sin(A) / a = sin(B) / b
Since B = 8° and b is unknown, we can plug these values into the equation to find a:
sin(A) / a = sin(8°) / b
To find the value of A, we just need to solve for A by dividing both sides of the equation by sin(A)/a. We have:
A = asin(8°) / b
Now that we know the values of A and c, we can use the Law of Sines one more time to find the value of b:
sin(A) / a = sin(B) / b
Since A and a are unknown, we can plug the known values into the equation to find b:
sin(A) / a = sin(B) / b
To find the value of b, we just need to solve for b by multiplying both sides of the equation by sin(B)/b. We have:
b = sin(B) / (sin(A) / a)
At this point, we have all the necessary values to compute the values of a, A, and b. We can plug the known values into the equations we derived above to find the unknown values.
First, let's find the value of a:
a = 43 * sin(A) / sin(135°)
We know the values of A and B, so we can plug these values into the equation to find a:
a = 43 * sin(A) / sin(135°)
= 43 * sin(180° - C - B) / sin(135°)
= 43 * sin(180° - 135° - 8°) / sin(135°)
= 43 * sin(37°) / sin(135°)
To compute the value of sin(37°), we can use a calculator or look up the value in a table of sines.
A circular kiddie pool has an area of about 28 square feet. An inflatable full-size circular pool has an area of about 113 square feet. How much greater
The radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.
By using the expression to approximate the radius of a circle, we want to compare the radius of the two pools.
The expression for the radius of a circle is:
R = √(A/3)
Where A is the area of said circle.
The circular kiddie swimming pool has an area of 28ft^2, we just replace that in the above expression to get:
R = √(28 ft^2/3) = 3 ft
The full-sized pool has an area of 113 ft^2, then its radius is:
R' = √(113 ft^2/3) = 6 ft
To see how much greater is the radius of the full-sized pool than the radius of the kiddie pool, we just take the quotient:
R'/R = 6ft/3ft
= 2
Hence, the radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.
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the p-value for the hypothesis test about factor b is . multiple choice less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 greater than 0.05
The p-value for the hypothesis test about factor b is greater than 0.05.
What is Hypothesis?
In effect, a theory is a hypothesis or group of hypotheses that refers to a particular issue or problem.
Thus, a hypothesis is a set of possible explanations or resolutions applicable to a situation. In other words, the hypotheses pose different scenarios in which the aim is to explain the origin and eventual resolution of the problem.
The p-value for the hypothesis test about factor b is greater than 0.05.
The p-value is a measure of statistical significance used in hypothesis testing. It represents the probability of obtaining a result at least as extreme as the one observed in the sample, given that the null hypothesis is true.
In general, a p-value less than 0.05 is considered statistically significant and indicates that the observed result is unlikely to have occurred by chance. A p-value between 0.01 and 0.025 is considered moderately significant, while a p-value between 0.025 and 0.05 is considered borderline significant. A p-value greater than 0.05 is not considered statistically significant and indicates that the observed result is likely due to chance.
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Describe hypothesis.
A theory is, in essence, a hypothesis or set of hypotheses pertaining to a certain subject or issue(s).
Consequently, a hypothesis is a group of potential explanations or solutions that could be applied to a situation. In other words, the hypotheses present many possibilities with the intent of illuminating the problem's origin and potential solutions.
The p-value for the factor b hypothesis test is higher than 0.05.
A statistical significance indicator used in hypothesis testing is the p-value. Given that the null hypothesis is true, it represents the likelihood of obtaining a result that is at least as extreme as the one seen in the sample.
A p-value of less than 0.05 is typically regarded as statistically significant and denotes the likelihood that the observed result did not arise by chance. While a p-value between 0.025 and 0.05 is regarded as borderline significant, one between 0.01 and 0.025 is regarded as moderately significant. The observed result is most likely the result of chance if the p-value is greater than 0.05, which is the threshold for statistical significance.
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Write the fraction 18/48 in simplest form.
Answer:
3/8
Step-by-step explanation:
Simplify the following:
18/48
The gcd of 18 and 48 is 6, so 18/48 = (6×3)/(6×8) = 6/6×3/8 = 3/8:
Answer: 3/8
I will give BRAINLIEST if correct the question is in the photo attached please answer Part A
Answer:
0-2 sec
Step-by-step explanation:
From the graph you can see the height is going UP from 0-2 sec...from then on it is going downward....
Classify the four angles of the quadrilateral.
Answer:
angle A is obtuse
angle B is acute
angle C obtuse
angle D is right
Answer:
Step-by-step explanation:
A is Obtuse Angle
B is Acute Angle
C is Obtuse Angle
D is Right Angle
How much do you have to invest today at 2% compounded monthly to obtain $1,000 in return in 4 years?
Answer:6 dollars
Step-by-step explanation:
Cuz u going to need to buy 3 mc flurries :D
Can somebody help me with this pls pls need it asap
Don’t just give me the answer add the steps to it too pls and Thank-You
1/6 because $160 as a fraction is 1/6
The first digit after the decimal point in a number is 5. What is the value of 5 in the number?
Answer:
1/2
Step-by-step explanation:
Let's say the number is 1.5
1.5 = 1 + 0.5
(1.5 = 1 + 0.5)*10 ==> multiply by 10 to remove decimals
15 = 10 + 5
5 is half of 10
Hence, 0.5 is half of 1 ==> 0.5 = 1/2
Question #2
0 of 3 points
Cynthia has a watch that counts the number of steps she takes every
day. When she goes for a casual walk, she can get 50 steps every
minute. She has already walked for 236 steps today and she wants to
get to 950 steps before she goes to school.
Which inequality represents the number of minutes (m) Cynthia would
need to walk to reach her goal before she gets to school?
X
0/3
The inequality that represents the number of minutes Cynthia would need to walk to reach her goal before she gets to school is;
50m + 236 ≥ 950
How to solve inequality word problems?We are told that;
Cynthia has a watch that counts the number of steps she takes every
day.
She can get 50 steps every minute for a casual walk.
Number of steps she has walked today = 236 steps
Number of steps she wants to get to before going to school = 950 steps
Now, if m represents the number of minutes Cynthia would need to walk to reach her goal before she gets to school, then the inequality equation her is;
50m + 236 ≥ 950
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. A sheet of card is 20 centimetres by 30 centimetres. What is
the maximum number of circular name badges, of diameter
60 millimetres, that can be cut from this piece of card?
The number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.
What is the area?
A region's size on a plane or curved surface is expressed by a measurement known as an area. Unlike the area of a plane region or plane area, which refers to the area of a shape or planar lamina, surface area describes the area of an open surface or the boundary of a three-dimensional object.
Given:
A sheet of the card is 20 centimeters by 30 centimeters,
The diameter of a badge, d = 60 mm or 6 cm,
Calculate the area of the sheet as shown below,
[tex]Area = length \times width[/tex]
Area = 20 × 30 = 600 cm²
Calculate the area of the badge as shown below,
[tex]Area = \pi d^2 / 4[/tex]
Area = 3.14 × 6² / 4
Area = 28.26 cm²
To calculate the number of badges[tex]No\ of\ badges = Area\ of \ sheet / Area \ of badge[/tex], use the formula given below,
Number of badges = 600 cm² / 28.26 cm²
Number of badges = 21.23 or 21
Therefore, the number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.
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At Fromazing, Frozen yogurt costs $0.50 per ounce. The cost of frozen yogurt per ounce at Frotastic is shown below:
Amount(oz) Cost
5 $2.40
8 $3.84
11 $5.28
14 $6.72 Silas says Frotastic is a better deal.
Sterling says Fromazing is a better deal.
Silas or Sterling. Justify your answer.
As Silas says Frotastic is a better deal. Because at Frotastic we get 1 ounce at $0.48
Define OunceThe ounce is derived from the Ancient Roman uncia, which was equal to one-twelfth (1/12) of a Roman pound and weighed around 27.35 grams, or 0.967 of an Avoirdupois ounce (libra). This originally meant "unit" because it originates from the Latin uno ('one'). The word "uncia" was borrowed twice: once into Old English as "ynsan" or "yndsan" from an unrecorded Vulgar Latin version that palatalized the "c" before the I to become the present English word "inch."
Here at Fromazing, 1 ounce of Frozen Yougurt costs $0.50 per ounce
whereas at Frotastic 5oz = $2.40
1oz = 2.40/5
= 0.48$
8oz = $3.84
1oz = 3.84/8
= $0.48
11 oz = $5.28
10z = 5.28/11
=$0.48
similar case for 14 oz = $6.72
1oz = 6.72/11
=$0.48
Therefore Frotastic is a better deal as Silas said
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A survey of 25 randomly sampled judges employed by the state of Florida found that they earned an average wage (including benefits) of $65.00 per hour. The sample standard deviation was $6.25 per hour.
The 99% confidence interval for the mean wage of all judges is given as follows:
($61.5, $68.5).
How to obtain the confidence interval?We have the standard deviation only for the sample, hence the t-distribution is used to obtain the confidence interval.
The equation that defines the bounds of the confidence interval is given as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 25 - 1 = 24 df, is t = 2.797
The remaining parameters are given as follows:
[tex]\overline{x} = 65, s = 6.25, n = 25[/tex]
Hence the lower bound of the interval is calculated as follows:
65 - 2.797 x 6.25/5 = $61.5.
The upper bound of the interval is of:
65 - 2.797 x 6.25/5 = $68.5.
Missing InformationThe problem asks for the 99% confidence interval for the mean wage of all judges.
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Inside a cooling tower, the temperature fell 5each hour for a total change of -35Find the number of hours it took for the change in temperature
Answer:
7 hours
Step-by-step explanation-35/-5=7
Find the slope of each of the following functions at the given points. f(x)=x²; (-3,9)
Answer:
the eqn given by the function is y=9---(1)
given point is(-3,9)=(X,y)
we know,
y=mx
mx=9 [from 1]
or,m(-3)=9 [from point]
or,m=9/-3
:.m=-3
hence, slope=-3
Margo solves several equations and then states that all of them have a solution of x = 7. However, Kenneth disagrees. Determine which of the following equations have a solution of x = 7 and then justify your response.
A. 6x + 11 = 55
B. -3x -18 = 39
C. 2x - 14 = - 28
D. 7x + 9 = 58
SHOW YOUR WORK!!!
a. [tex]6x+11=55[/tex]
Subtract 11 from both sides:
[tex]6x+11-11=55-11[/tex]
[tex]6x=44[/tex]
Divide both sides by 6:
[tex]\dfrac{6x}{6} =\dfrac{44}{6}[/tex]
[tex]x=7.333333[/tex]
___________________________
b. [tex]-3x-18=39[/tex]
Add 18 to both sides:
[tex]-3x-18+18=39+18[/tex]
[tex]-3x=57[/tex]
Divide both sides by -3:
[tex]\dfrac{-3x}{-3} =\dfrac{57}{-3}[/tex]
[tex]x=-19[/tex]
___________________________
c. [tex]2x-14=-28[/tex]
Add 14 to both sides:
[tex]2x-14+14=-28+14[/tex]
[tex]2x=-14[/tex]
Divide both sides by 2:
[tex]\dfrac{2x}{2} =\dfrac{-14}{2}[/tex]
[tex]x=-7[/tex]
___________________________
d. [tex]7x+9=58[/tex]
Subtract 9 from both sides:
[tex]7x+9-9=58-9[/tex]
[tex]7x=49[/tex]
Divide both sides by 7:
[tex]\dfrac{7x}{7} =\dfrac{49}{7}[/tex]
[tex]x=7[/tex]
___________________________
Only option d had a solution of x = 7.
The following graph shows a system of linear inequalities. Select the correct system:
The linear inequalities that represent the graph are y ≤ (1/2)x - 1 and y > 2x - 4. Then the correct option is C
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The intercepts are 2 and -1. Then the equation of the line is given as,
x / 2 + y / (-1) ≤ 1
y ≤ (1/2)x - 1
The intercepts are 2 and -4. Then the equation of the line is given as,
x / 2 + y / (-4) > 1
y > 2x - 4
The straight disparities that address the diagram are y ≤ (1/2)x - 1 and y > 2x - 4. Then, at that point, the right choice is C
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In college, we study large volumes of information - information that, unfortunately, we do not often retain for very long. The functionf(x)=80e^{-0.5x}+20describes the percentage of information, f(x), that a particular person remembers x weeks after learning the information. Find the percentage of information that is remembered after one year (52 weeks).
The percentage of information that is remembered by a particular person after one year (52 weeks) is 20%
The function f(x)=80e-0.5x+20 describes the percentage of information that a particular person remembers after x weeks.
To find the percentage of information that is remembered by a particular person after one year (52 weeks), we need to substitute x=52 in the given f(x).
f(x)=80[tex]e^{-0.5x}[/tex]+20
x=52, f(52)= 80[tex]e^{(-o.5\times 52)}[/tex]+20
=80[tex]e^{-26}[/tex]+20
=80(5.109 [tex]E^{-12[/tex])+20
= 4.087[tex]E^{-20}[/tex]+20
f(52)= 20
The percentage of information that is remembered by a particular person after one year (52 weeks) is 20%
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Charles needs to determine whether x+2 is a factor of f(x)=2x^4 -3x^3 +5x -16 .
How can Charles use the factor theorem to determine whether x+2 is a factor of f(x)?
Fill in the blanks using the word bank below:
f(-2) f(2) f(4) 30 2 320 is is not
Charles evaluates ________________ and determines its value to be______________Charles concludes that ______________ factor of .
Charles evaluates f(-2) and determines its value to be 30 Charles concludes that is not factor of f(x).
What is Factor theorem?
The factor theorem in algebra establishes a connection between a polynomial's factors and zeros. The polynomial remainder theorem has this particular special instance. A polynomial f(x) has a factor if and only if f=0, according to the factor theorem.
Given : f(x)=2x^4 -3x^3 +5x -16
By Factor theorem, If x+2 is a factor of f(x), then f(-2) should be equal to 0.
So, Charles can use factor theorem to determine whether x + 2 is a factor of f(x) by putting x=-2 in f(x),
f(x) = 2x^4 -3x^3 +5x -16
= 2×(-2)^4 - 3×(-2)^3 + 5(-2) - 16
= 2×16 + 3×8 - 10 - 16
= 32 + 24 -10 -16
= 56 -26
= 30.
Since, f(-2) ≠ 0, (x +2) is not a factor of f(x).
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It's for my calculus class, I'm terrible in his class, please help.
The value of the integral [tex]\int\limits^2_0 {f(x)} \, dx[/tex] is 5. The value of the integral [tex]\int\limits^5_2 {f(x)} \, dx[/tex] is 0. The value of the integral [tex]\int\limits^8_0 {f(x)} \, dx[/tex] is 25.
What is definite integral mean?The definite integral of a function over a limit represents the area under the curve bounded by the limit as given in integration.
The integral represents the area under the curve.
(a) [tex]\int\limits^2_0 {f(x)} \, dx[/tex] = area of the triangle with base 2 and height 5.
Area = (1/2)2 x 5 = 5 units square
(b) [tex]\int\limits^5_2 {f(x)} \, dx[/tex] = area under the triangle with base 1 and height 5 - area above the triangle with base 1 and height 5 = 0
(c) [tex]\int\limits^8_0 {f(x)} \, dx=\int\limits^2_0 {f(x)} \, dx+\int\limits^4_2 {f(x)} \, dx+\int\limits^8_4 {f(x)} \, dx[/tex]
⇒ 5 + 0 + 4 x 5 = 25 units sqaure.
Hence "integral [tex]\int\limits^2_0 {f(x)} \, dx[/tex] is 5. Integral [tex]\int\limits^5_2 {f(x)} \, dx[/tex] is 0. The value of the integral [tex]\int\limits^8_0 {f(x)} \, dx[/tex] is 25".
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