Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.The inequality that describes the situation is:250 - 179.85 ≤ x
where x represents the amount of money Mr. Donovan still needs to spend in order to meet the Angler's Club requirement.
To solve for x, we first subtract 179.85 from 250 to get:
70.15 ≤ x
Therefore, Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.
In summary, Mr. Donovan's spending so far this month is less than the minimum required by the Angler's Club, and he needs to spend at least $70.15 more to meet the requirement.
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The area of a rectangle is 60 square inches. The length and the width can vary. Enter an equation to find the length (l) for any possible width (w).
Answer:
l=(60÷w)
Step-by-step explanation:
since area =l×w
thats 60=l×w
l=60÷w
in preparation for the upcoming school year, a teacher looks at raw test scores on the statewide standardized test for the students in her class. instead of looking at the scores relative to the norms in the state, the teacher wants to understand the scores relative to the students who will be in the class. to do so, she decides to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class. the mean test score in her upcoming class is 130, and the standard deviation is 26.2.
The student's test score is 0.76 standard deviations above the mean of the class.
A z-score is a measure of how many standard deviations a data point is from the mean of the data set. It is calculated by subtracting the mean from the data point and dividing by the standard deviation. In this case, the teacher wants to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class.
The formula for calculating a z-score is:
z-score = (data point - mean) / standard deviation
Using the mean and standard deviation provided in the question, the teacher can calculate the z-score for each student's test score by plugging in the values into the formula. For example, if a student scored 150 on the test, their z-score would be:
z-score = (150 - 130) / 26.2
z-score = 0.76
This means that the student's test score is 0.76 standard deviations above the mean of the class. The teacher can use this information to understand how each student's test score compares to the rest of the class.
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Which function is increasing at the highest rate? A. x 1 2 3 4 5 g(x) -5 -4 -3 -2 -1 B. A linear function, f, with an x-intercept of 8 and a y-intercept of -4. C. A linear function on a coordinate plane passes through (minus 1, 3), and (2, minus 3) which intercepts axis at (0.5, 0), and (0, 1) D. Reset Next
The linear function with the greatest slope is at option A.
What is slope of a line?The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
Find the slope for all the function to determine the highest rate:
A. The slope of g(x) is 1, since the change in y is 1 for every 1 unit increase in x.
B. The slope of f is -4/8 or -1/2.
C. The slope of the line passing through (-1, 3) and (2, -3) is (-3 - 3)/(2 - (-1)) = -2/3.
We observe that the slope of linear equation in A is greater.
Hence, the linear function with the greatest slope is at option A.
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A parallel combination of a R1 = 5 ohms and R2 = 15 ohms, the IT
= 10 amps. What is the current drawn by R2? Express your answer in
milli amps?
The current drawn by R2 is 3.333A or 3333mA in parallel combination in ohms.
In a parallel combination, the voltage across both resistors is the same. However, the current is divided between the two resistors based on their individual resistances. Using Ohms law (V = IR), we can find the voltage across the resistors:
According to the specific resistances of the resistors in a parallel circuit, the current is distributed among them. More current will flow through the resistor with the lower resistance than the one with the greater resistance. This is due to the fact that the lower resistance provides less resistance to the current flow. In this instance, R1 will draw more current than R2 since it has a lower resistance than R2.
V = IR1 = (10A)(5Ω) = 50V
V = IR2 = (I)(15Ω)
We can find current I by solving this particular equation:
I = V/R2 = (50V)/(15Ω) = 3.33A
Convert this ampere value to milliamps, in which we have to multiply by 1000:
I = 3.33A * 1000 = 3333mA or 3.333A
Current drawn by R2 is 3.333A or 3333mA.
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12.
Find x and y in trapezoid TRAP below.
Answer:
x = 115 , y = 40
Step-by-step explanation:
in a trapezoid
• each lower base angle is supplementary to the upper base angle on the same side.
∠ ART = 40° + 25° = 65°
then
∠ PAR = 180° - ∠ ART = 180° - 65° = 115° , so
∠ PAR = x = 115
the sum of the 3 angles in Δ PAR = 180° , that is
x + y + 25 = 180
115 + y + 25 = 180
140 + y = 180 ( subtract 140 from both sides )
y = 40
4x + 1 over 3 y2
What is the value of the expression above when x = 2 and y = 3? You must show all work and calculations to receive full credit.
The value of the expression 4x+1/3y² when x = 2 and y = 3 is 1/3
What is substitution of variable?In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
Finding the value of the expression, we substitute the given values for the variables
(4x+1)/(3y²
when x = 2 and y = 3
4( 2) +1/3(3)²
= 8 + 1/( 3 × 9)
= 9/27
= 1/3
therefore the value of the expression is 1/3
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Match each division problem on the left to its quotient on the right.
When the denominator is zero, the divisor is undefined.
Define the term division?In mathematics, division is the process of dividing a quantity into equal pieces or groups. Division reverses the effects of multiplication because it is the inverse operation of multiplication. The amount being divided is referred to as the dividend in division, and the number by which it is being divided is referred to as the divisor. The quotient is the outcome of a division operation.
Explanation:
Left side Right side
0 ÷ 70 = 0 ⇒ Zero
862 / 0 ⇒ Undefined
97 ÷ 0 ⇒ Undefined
[tex]\frac{0}{764}[/tex] = 0 ⇒ Zero
When the denominator is zero, the divisor is undefined.
When the molecule is zero, the divisor is zeros.
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Find the area of each side and total them for the surface area of the composite shape
The sοlutiοn οf the given prοblem οf area cοmes οut tο be the cοmpοsite shape in the picture has a surface area οf 96 square centimetres.
What is area, exactly?Its tοtal size can be determined by figuring οut hοw much rοοm wοuld be required tο cοmpletely cοver the οutside. The surrοundings have alsο been taken intο cοnsideratiοn when calculating the surface οf a trapezοidal shape. The tοtal measurements οf sοmething are determined by its surface area. Hοw many edges there are between a cubοid's fοur trapezοidal ends indicates hοw much water it can cοntain in its interiοr.
Here,
Let's start by listing each separate surface that cοntributes tο the cοmpοsite shape. There are twο triangles and fοur squares.
We can use the fοllοwing methοd tο determine the area οf each rectangle:
=> Length = 5 centimetre, width = 4 cm, sο area = 5 cm x 4 cm = 20 cm² fοr rectangle 1.
=> Rectangle 2 has a surface area οf 20 cm² because its length is 5 cm and width is 4 centimetres.
=> Rectangle 3 has a 6 centimetre length and a 4 cm width,
=> area = 6 cm x 4 cm, οr 24 cm².
=> Rectangle 4 has a 6 centimetre length and a 4 cm width, sο
=> area = 6 cm x 4 cm, οr 24 cm².
The fοllοwing algοrithm can be used tο determine each triangle's area:
=> area = (Base × Height) / 2
Area οf Triangle 1 : (2 cm x 4 cm) / 2 = 4 cm²
Area οf Triangle 2: (2 centimetre x 4 cm) / 2 = 4 cm²
Tοtal Surface Space equals 96 cm² (20 cm², 20 cm², 24 cm², 24 cm², 4 cm², 4 cm²)
Cοnsequently, the cοmpοsite shape in the picture has a surface area οf 96 square centimetres.
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Pls help Algebra1 pls pls
Answer:
1,4,5
Step-by-step explanation:
Jist Multiply these
Help with pre calc question
Therefore , the solution of the given problem of angles comes out to be k can be any number, so θ = 0 + k180 or θ = 180 + k180
An angle meaning is what?A tilt is a form in Euclidean geometry made up of two lines, or conical faces, that divide at the structure's centre and apex. At their junctions, two rays may combine to form an angle. Angle is another outcome of two entities interacting. Dihedral shapes best describe them. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends. The term "angle" was first used in the Latin term "angulus," which is translated as "horn" in English.
Here,
The solution can be factored to begin with:
=> tanθ(tanθ + 3) = 0
Either
=> tanθ = 0 or tanθ + 3 = 0
will result in the satisfaction of this equation.
When sin = 0, can be any integer multiple of 180 degrees, including zero.
We can find tan by solving for 3 when tan + 3 = 0.
=> tanθ = -3
There are no answers to this problem because there isn't any angle whose tangent is -3.
As a result, the following are the answers to the equation
tan²θ + 3tanθ = 0 :
k can be any number, so θ = 0 + k180 or θ = 180 + k180
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Rectangle MPAT has vertices M(1, 2), P(1, 3), A(3, 3), and T(3, 2). Rectangle MPAT was translated 1 unit right and 2 units up to produce rectangle M'P'A'T Which coordinates describe the vertices of the image? O M'(1, 4), P'(1, 5), A'(3, 5), and T"(3, 4) O M'(2, 2), P'(2, 3), A'(4, 3), and T'(4, 2) O M'(2, 4), P' (2, 5), A'(4, 5), and T'(4,4) O M'(3, 3), P'(3, 4), A'(5, 4), and T'(5, 5)
The coordinate set that describes the image of rectangle MPAT after the translation of 1 unit right and 2 units up is:
M'(2, 4), P'(2, 5), A'(4, 5), and T'(4, 4).
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for the ordered pairs of the vertices of a figure are defined as follows:
Translation left a units: (x, y) -> (x - a, y).Translation right a units: (x, y) -> (x + a, y).Translation up a units: (x,y) -> (x, y + a).Translation down a units: (x,y) -> (x, y - a).The vertices of the original rectangle are given as follows:
M(1, 2), P(1, 3), A(3, 3), and T(3, 2).
The translation is given as follows:
1 unit right.2 units up.Hence the equation is:
(x, y) -> (x + 1, y + 2).
Then the coordinates of the vertices are given as follows:
M'(2, 4), P'(2, 5), A'(4, 5), and T'(4, 4).
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A bag has 7 blue cubes, 4 red cubes, and 14 green cubes. If you draw a cube and replace it in the bag 100 times, which of the following amounts would you expect to pull? Select all that apply.
-
Video
A) Pull two times as many green cubes as blue cubes
B) Pull a blue cube 28 times
C) Pull 60 red cubes
D) Pull more blue cubes than green cubes
E) Pull a red cube 16 times
The correct options are A) Pull two times as many green cubes as blue cubes , B) Pull a blue cube 28 times, and E) Pull a red cube 16 times.
To determine which of the following amounts you would expect to pull, we need to calculate the probabilities of drawing each color cube and then apply that probability to 100 draws.
1. Calculate the total number of cubes in the bag:
Total cubes = 7 blue + 4 red + 14 green = 25 cubes
2. Calculate the probability of drawing each color:
P(blue) = 7/25
P(red) = 4/25
P(green) = 14/25
3. Apply the probabilities to 100 draws:
Blue: 100 × (7/25) = 28
Red: 100 × (4/25) = 16
Green: 100 × (14/25) = 56
Now we can evaluate the given statements:
A) Pull two times as many green cubes as blue cubes
56 green cubes is exactly 2 times 28 blue cubes, so A is correct.
B) Pull a blue cube 28 times
As calculated earlier, you would expect to pull a blue cube 28 times. B is correct.
C) Pull 60 red cubes
The expected number of red cubes is 16, not 60. C is incorrect.
D) Pull more blue cubes than green cubes
You would expect to pull 28 blue cubes and 56 green cubes, so D is incorrect.
E) Pull a red cube 16 times
As calculated earlier, you would expect to pull a red cube 16 times. E is correct.
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We say that a point estimator is unbiased if (choose one):its sampling distribution is centered exactly at the parameter it estimates. The standard deviation of its sampling distribution decreases as the sample size increases. Its sampling distribution is normal. Its value is always equal to the parameter it estimates. Choices (A), (B), and (C) are all true. The next four questions refer to the following information:A study was conducted in order to estimate ?, the mean number of weekly hours that U. S. Adults use computers at home. Suppose a random sample of 81 U. S. Adults gives a mean weekly computer usage time of 8. 5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3. 6 hours
The correct answer is (A): "its sampling distribution is centered exactly at the parameter it estimates."
An estimator is a statistic that is used to estimate an unknown parameter in a population. A point estimator is a single value that is used to estimate the population parameter. The goal of a point estimator is to provide an estimate that is as close to the true value of the parameter as possible.
One way to evaluate the quality of a point estimator is to look at its bias, which is the difference between the expected value of the estimator and the true value of the parameter it is estimating. An estimator is unbiased if its expected value is equal to the true value of the parameter it estimates. In other words, an unbiased estimator is centered exactly at the parameter it estimates.
In the context of the given problem, the sample mean of weekly computer usage time (8.5 hours) is a point estimator for the population mean weekly computer usage time. To evaluate whether this estimator is unbiased, we would need to look at its sampling distribution and check whether its expected value (i.e., the mean of the sampling distribution) is equal to the true population mean.
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Which reason completes the proof for step 6?
A. Definition of midsegment
B. Definition of median
C. Definition of midpoint
D. Definition of slope
The correct answer is A. Definition of midsegment. In this step, the proof is demonstrating that the midsegment of a triangle is parallel to the median of the triangle.
What is a triangle?A triangle is a three-sided polygon. It is one of the basic shapes in geometry. It has three sides and three angles, with the sum of the angles of a triangle being always 180 degrees. Triangles come in various shapes and sizes, and are classified by their angles or sides. Examples of triangle shapes include equilateral, isosceles and scalene.
The midsegment is defined as the line segment that connects the midpoints of two sides of the triangle. The median is defined as the line segment that connects a vertex of the triangle with the midpoint of the opposite side. Therefore, in order to prove that the midsegment is parallel to the median, the definition of the midsegment must be used. The definition of the midsegment states that it is the line segment that connects the midpoints of two sides of the triangle, which is necessary in order to prove that it is parallel to the median. Therefore, A. Definition of midsegment is the correct answer for this step in the proof.
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3ab−1=2ab−3 what is the value of ab
Answer:
ab = -2
Step-by-step explanation:
3ab - 1 = 2ab - 3
(minus 2ab on both sides of the equation)
ab - 1 = -3
(plus one of both sides of the equation)
ab = -2
what point of the number line is 1/4 of the way from point 0 to -3
The point on the number line that is 1/4 of the way from point 0 to -3 is located at the point 3/4.
What is a number line?
A number line is a straight line that represents the real numbers as points or marks on the line. The numbers increase from left to right, and each point on the line corresponds to a specific number.
To find the point on the number line that is 1/4 of the way from point 0 to -3, we can use the following formula:
point = starting point + fraction of distance * total distance
The starting point is 0, and the total distance is the distance between 0 and -3, which is 3. So the total distance is 3.
Now, we need to find the fraction of the distance that is 1/4 of the total distance. This can be written as:
fraction of distance = 1/4
So the formula becomes:
point = 0 + 1/4 * 3
Simplifying the expression, we get:
point = 3/4
Therefore, the point on the number line that is 1/4 of the way from point 0 to -3 is located at the point 3/4.
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64,000÷10 to the fourth power
64,000÷10 to the fourth power is equal to 0.64 × 10⁴
What is Algebraic expression?In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.
To solve this, we need to remember the order of operations, which is parentheses, exponents, multiplication and division (performed left to right), and addition and subtraction (also performed left to right).
First, we need to calculate 10 to the fourth power:
10 to the fourth power means 10 multiplied by itself four times:
10⁴ = 10,000
Now we can substitute that value into the original expression:
64,000 ÷ 10,000 = 0.64 × 10⁴
Therefore, 64,000÷10 to the fourth power is equal to 0.64 × 10⁴
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find
the slope between (3,-3) and (12,-2) 50 POINTS SOLVE ASAP
Answer: slope is 1/9
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
i used a website math-way . its a very accurate response. it usually is at least but you should use it.
Greatest common factor
Answer:
10[tex]x^{5}[/tex]
Step-by-step explanation:
The list is: 30[tex]x^{7}[/tex], 60[tex]x^{5}[/tex], 110[tex]x^{8}[/tex]
Find the GCF
We see
30, 60, and 110 have the greatest common factor is 10.
[tex]x^{7}[/tex], [tex]x^{5}[/tex], [tex]x^{8}[/tex] have the greatest common factor is [tex]x^{5}[/tex]
So, the greatest common factor for the list of terms is 10 [tex]x^{5}[/tex]
Paige has some cards. Each card has a
colour on it.
If she chooses a card at random, then
P(blue) and P(white) = 1.
18'
=
Calculate P(neither blue nor white).
Give your answer as a fraction in its
simplest form.
The response will be P(neither blue nor white) = 0, in accordance with the information provided.
In math, what is a fraction?A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, in which the both the numerator and the denominator are divided. In a simple fraction, both are integers. The numerator or decrease of a complicated fraction contains a fraction. The numerator of an appropriate fraction is less than the denominator.
The total probability of all potential outcomes must equal 1. As P(blue) and P(white) are both 1, there cannot be any other card colors. P(neither blue nor white) is therefore equal to zero.
If there are additional cards of different colors and the information provided is insufficient or inaccurate, we can also apply the following formula:
P(neither blue nor white) = 1 - P(blue) - P(white)
Assuming that there are just three possible card colors (blue, white, and another color), the following equation can be constructed using the provided data:
P(blue) + P(white) + P(another color) = 1
P(white) and P(blue) are both 1, so we have:
1 + 1 + P(another color) = 1
When we simplify this equation, we obtain:
P(another color) = -1
The presented information does not support the notion that there are merely three possible card colors, hence this is not a legitimate probability. Hence, the only viable response is.
P(neither blue nor white) = 0
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The answer is 0/1, which can be simplified to 0.
what is probability?
Probability is a measure of the likelihood or chance of an event occurring.
If P(blue) and P(white) are both 1, it means that all the cards are either blue or white.
Let's assume there are a total of n cards. Then,
P(blue) + P(white) = 1
=> Number of blue cards + Number of white cards = n
Given that P(blue) = P(white) = 1, we can conclude that there are n/2 blue cards and n/2 white cards.
Therefore, the probability of choosing a card that is neither blue nor white is the probability of choosing a card of a different color. There are no other colors given, so we can assume that there are no cards of any other color.
Hence, the probability of choosing a card that is neither blue nor white is 0.
So, P(neither blue nor white) = 0.
Therefore, the answer is 0/1, which can be simplified to 0.
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A square frame has a side of 8 inches. What is its perimeter?
Answer:
Step-by-step explanation:
Mr. Smith's class has 7 boys and 10 girls. If two students are randomly selected, what is the probability they are both boys? After selecting the first student, he does not go back in the room before the second student is selected. Answer as a simplified fraction.
Answer:
21/136
Step-by-step explanation:
The probability of selecting a boy from the class on the first draw is 7 boys out of 17 students total, or 7/17.
After the first boy is selected, there will be 6 boys and 10 girls left in the class.
So the probability of selecting a boy on the second draw, given that a boy was already selected on the first draw, will be 6 boys out of 16 remaining students, or 6/16.
To find the probability that both students selected are boys, we can multiply the probabilities of selecting a boy on the first and second draws:
P(boy and then boy) = P(boy on first draw) x P(boy on second draw | boy on first draw)
P(boy and then boy) = (7/17) x (6/16)
P(boy and then boy) = 21/136
Therefore, the probability of selecting two boys from Mr. Smith's class is 21/136.
Answer:
[tex] \frac{21}{136} [/tex]
Step-by-step explanation:
[tex] \frac{7}{17} \times \frac{6}{16} = \frac{7}{17} \times \frac{3}{8} = \frac{21}{136} [/tex]
Let A(t) be the function t+1t−1. Find the following: A(8)=A(−5)= A(31)= A(−71)= In each box, enter your answer as an integer or reduced fraction. Enter DNE for Does Not Exist, or oo for Infinity.
A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36
Function: A(t) = (t+1)/(t-1)For the given function A(t), the following values are to be calculated: A(8), A(-5), A(3/1), and A(-71/1)A(8):We need to substitute t=8 in the function. A(8) = (8+1)/(8-1) = 9/7Therefore, A(8) = 9/7A(-5):We need to substitute t=-5 in the function. A(-5) = (-5+1)/(-5-1) = -1/3Therefore, A(-5) = -1/3A(3/1):We need to substitute t=3/1 in the function. A(3/1) = (3/1+1)/(3/1-1) = (4)/(2/1) = 4*1/2 = 2Therefore, A(3/1) = 2A(-71/1):We need to substitute t=-71/1 in the function. A(-71/1) = (-71/1+1)/(-71/1-1) = (-70/1)/(-72/1) = (-5/36)Therefore, A(-71/1) = -5/36Therefore, the respective answers for the given values of the function A(t) are as follows: A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36
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6. These polygons are similar but not drawn to scale.
30
What is the value of x?
Ox=7.2
Ox 8.6
Ox=215
Ox-258
3
(1 point)
Answer:
look on the yt theres alot of helpful things on there and ive had to do this simliar things and stuff so thats why yt viedo of this should help you
Step-by-step explanation: try a yt viedo to help on this math i wish you luck
What is the area of this figure?
Answer:
223.67
Step-by-step explanation:
Given that u is indirectly proportional to t^(3)-3, if u=24 when t=2, what is u when t=3 ?
If u is indirectly proportional to t³ - 3, the value of u when t = 3 is 5.
If u is indirectly proportional to t³ - 3, what is the value of u when t = 3?Proportional relationships are relationships between two variables where their ratios are equivalent.
Given that;
u is indirectly proportional to t³ - 3;
u ∝ 1/( t³ - 3)
u = k/( t³ - 3)
Where k is the proportionality constant.
First, we determine the proportionality constant.
To find k, we can use the initial condition that;
u = 24t = 224 = k / (2³- 3)
24 = k / (8 - 3)
24 = k / 5
k = 24 × 5
k = 120
Hence, the equation relating u and t is:
u = k/( t³ - 3)
Plug in k = 120
u = 120/( t³ - 3)
To find u when t = 3, we can substitute t = 3 into the equation:
u = 120/( t³ - 3)
u = 120/( 3³ - 3)
u = 120/( 27 - 3)
u = 120/24
u = 5
Therefore, the value of u is 5.
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the area of the rectangle is 24x^3y^5 square inches its width is 12xy^2 what is the length of the rectangle
As a result, the rectangle is 2x^2y^3 inches long.
Why is it known as a rectangle?The Latin word rectus, which meaning "right" or "straight," is where the "recto" in "rectangle" comes from. A rectangle possesses straight sides due to its right angles. Rectitude, a different term derived from the same root and denoting moral uprightness.
We may employ the following formula to determine the rectangular area:
area = length x width
Since we are aware of the surface and the breadth in this instance, we can determine the length:
area = 24x^3y^5
width = 12xy^2
area = length x width
24x^3y^5 = length x 12xy^2
When we multiply both sides by 12xy^2, we get:
2x^2y^3 = length
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True or false: If you are comparing two or more data sets and the distribution of at least one data set is symmetrical, you can use the mean and the standard deviation to compare them.
Answer:
True:)
Step-by-step explanation:
would appreciate if someone could help
Answer:
X AXIS WILL BE ON 4,2 AND Y AXIS WILL BE 4,2 ON BEHALF OF BOTH ANGLES HAVING QUADILATERAL AND THEN APPLY THEOREMS FOR THE EASY SOLUTIONS..
Score on last try: 0 of 1 pts. See Details for more. Find \( \frac{d y}{d x} \), if \( y=u^{3}-2 u \) and \( u=2 x^{2}-1 \). \[ \frac{d y}{d x}= \] Question Help: B Video B eBook D Post to forum
The answer is [tex]\(\frac{dy}{dx} = 24x\left( 2x^{2}-1 \right)^{2}-8x\)[/tex]To find [tex]( \frac{d y}{d x} \)[/tex]), let's apply the Chain Rule.
It is the most popular technique for differentiating composite functions, and it involves applying the derivative to the outer function and then to the inner function, multiplied by the derivative of the inner function.
Expression [tex]\(y = u^3 - 2u\) and \(u = 2x^2 - 1\),[/tex] Let us apply the chain rule; [tex]\( \frac{d y}{d x}= \frac{dy}{du}\frac{du}{dx}\)[/tex] , So [tex]\( \frac{d y}{d x}= \left( 3u^{2}-2 \right)\left( 4x \right) \).[/tex]
Put the value of u in the above equation, we have\[tex]( \frac{d y}{d x}= \left( 3\left( 2x^{2}-1 \right)^{2}-2 \right)\left( 4x \right) \)[/tex] , Thus [tex]\(\frac{dy}{dx} = 24x\left( 2x^{2}-1 \right)^{2}-8x\)[/tex] is the answer.
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