Answer:
Step-by-step explanation:
To solve the problem, we start by labeling 1/3 of 3/8 like this:
N1/D1 of N2/D2
Then we use this fraction of a fraction formula to solve the problem:
(N1 x N2) / (D1 x D2)
When we enter 1/3 of 3/8 into the formula, we get:
(1 x 3) / (3 x 8) = 3/24
Therefore, the answer to 1/3 of 3/8 in its lowest form is:
1/3 of 3/8 = 1/8
Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary. cos θ = ? A = 22 H = 38
Answer: To find the angle θ in a right triangle given the cosine value, we can use the inverse cosine function, also known as arccos.
cos θ = A/H = 22/38
θ = arccos (22/38)
Using a table of trigonometric values or a calculator, we can find the value of arccos (22/38) to be approximately 56.3 degrees.
So, θ = 56.3° (rounded to the nearest degree).
Step-by-step explanation:
Show that if f is a function from S to T, where S and T are finite sets with |S| > |T|, then there are elements s1 and s2 in S such that f(s1) = f(s2), or in other words, f is not one-to-one.
Hence proved f is not one-to-one.
What do you mean by function?A function is a mathematical concept that assigns a unique output value for each input value.
In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.
Functions play a central role in mathematics and are used to model real-world phenomena and to study the relationships between variables. They are also used in computer programming to perform specific tasks, such as converting temperatures from Celsius to Fahrenheit or calculating the square root of a number.
Suppose that f is a function from S to T, where |S| > |T|. This means that there are more elements in S than there are in T.
Since f maps elements of S to elements of T, we can think of f as pairing elements of S with elements of T. However, since |S| > |T|, there will be at least two elements of S that are paired with the same element of T, and these two elements are s1 and s2.
Therefore, f is not one-to-one, as f(s1) = f(s2), meaning that two different elements of S are mapped to the same element of T.
This shows that if f is a function from S to T, where |S| > |T|, then there must exist elements s1 and s2 in S such that f(s1) = f(s2), and hence f is not one-to-one.
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i need help with test statistic and p value
The p=value of this sample is p = 0.076
What is meant by p-value?You should understand that the p value is a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true.
P values are used in hypothesis testing to help decide whether to reject the null hypothesis. The smaller the p value, the more likely you are to reject the null hypothesis.
This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 73.8
For the alternative hypothesis,
µ ≠ 73.8
Since the number of samples is small and no population standard deviation is given, the distribution is a student's true
Since n = 59,
Degrees of freedom, df = n - 1 = 59 - 1 = 58
t = (x - µ)/(s/√n)
Where
x = sample mean = 76.6
µ = population mean = 73.8
s = samples standard deviation = 8.6
t = (76.6 - 73.8)/(8.6/√58) = 2.8/1.13= 2.4779
We would determine the p-value using the t-test calculator. It becomes
p = 2.4779
Since alpha, 0.01 < than the p-value, 2.4779, then we would fail to reject the null hypothesis. Therefore, At a 1 % level of significance, the sample data showed that there is no significant evidence that μ ≠ 73.8
Therefore, this p-value leads to a decision to accept the null hypothesis
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The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet in
second, how far will fall in 3 seconds? How long will it take an object to fall 400 feet?
Answer:
144 feet
5 seconds
Step-by-step explanation:
A directly proportional distance between s and t can be written as
s ∝ t²
or in equation form
s(t) = k · t²
k = constant of proportionality
Given s = 16 feet for t = 1 second we get
16 = k (1)²
or
k = 16
and the equation is s(t) = 16t²
In 3 seconds the object will fall
s(3) = 16 (3)²
= 16 x 9
= 144
s(3) = 144
To find time taken to fall 400 feet, substitute for s s(t) = 400
400 = 16t²
16t² = 400
t² = 400/16 = 25
t = ± √25 = ± 5 seconds
Since time is non-negatiive,
t = 5 seconds
find a formula for the probability distribution of random variable X representing the outcome when a single die is rolled once
When a singular die is rolled once, the results are represented by the probability distribution P(X = x) = 1/6, 1,2,3,4,5,6 for random variable X.
What are examples and probability?Probability is the potential outcome of any random occurrence. This expression relates to estimating the chance that any certain event will take place. How likely are we to get a head, for example, if we flip the coin into the air? The solution to this question is based on the potential number of occurrences.
When one die is rolled, there are only six possible outcomes: 1, 2, 3, 4, and 5. Due to the equal likelihood of each scenario, its sp risk is 1/6. The following is true for the required posterior distribution of the random variable x:
P(X = x) = 1/6, 1,2,3,4,5,6
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Match each expression on the left with an equivalent expression on the right
95 is 85% of what number?
Answer:
111.76
Step-by-step explanation:
My attempt:
To find the number that 95 is 85% of, we can set up an equation using the information given. Let's call this number "x".
According to the problem, 95 is 85% of x, so we can write this as an equation:
95 = 0.85x
Now we can solve for x by dividing both sides by 0.85:
x = 111.76
So 95 is 85% of 111.76.
Answer:
111.76
Step-by-step explanation:
1.We have, 85% × x = 95 or, 85 100 × x = 95
2. Multiplying both sides by 100 and dividing both sides by 85,
we have x = 95 × 100/85
x = 111.76
Find the center of the mass of a thin plate of constant density covering the region bounded by the x-axis and the curve y=3cosx, -pi/3 <= x <= pi/3
The y-coordinate of center of mass is 1.2819 kg.
Describe Center of mass?The center of mass, also known as the center of gravity, is a point in a system of objects where the total mass of the objects is concentrated. It represents the balance point of the system and is the point at which the system would balance if it were suspended from that point. The position of the center of mass is dependent on the distribution of mass in the objects making up the system.
The centre of mass of region R is given by
[tex]$\mathrm{\bar{y}=\frac{\int_{R}\rho y_{e}dA}{Mass_{regionR}} \ \ where \ y_{e} \ center \ of \ mass \ of \ element}[/tex]
For the vertical element,
[tex]\mathrm{y_{e}=\dfrac{y}{2}}[/tex]
Find the numerator of the y coordinate of Center of Mass
[tex]$\mathrm{\frac{1}{2}\int_{R}\rho yydx=\frac{\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (3cosx)^2dx=\frac{9\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} cos^2xdx=\frac{9\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (\frac{1+cos(2x)}{2})dx}[/tex]
[tex]$\mathrn{\frac{9\rho}{4} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (1+cos(2x))dx=\frac{9\rho}{4} [x+\frac{sin(2x)}{2}]_{\frac{-\pi}{3}}^{\frac{\pi}{3}}}[/tex]
[tex]$\mathrm{\frac{9\rho}{4} \left[\frac{\pi}{3}+\frac{sin(2(\frac{\pi}{3}))}{2}\right ]-\frac{9\rho}{4} \left[\frac{-\pi}{3}+\frac{sin(2(\frac{-\pi}{3}))}{2}\right ]}[/tex]
[tex]$\mathrn{\frac{9\rho}{4} \left[\frac{\pi}{3}+\frac{\sqrt{3}}{4}\right ]-\frac{9\rho}{4} \left[\frac{-\pi}{3}-\frac{\sqrt{3}}{4}\right ]=\frac{9\rho }{4} \left[\frac{2\pi}{3}+\frac{\sqrt{3}}{2}\right ]}[/tex]
Therefore, the y-coordinate of center of mass is
[tex]$\mathrm{\bar{y}=\frac{\dfrac{9\rho }{4}\left [\dfrac{2\pi}{3}+\dfrac{\sqrt{3}}{2}\right ]}{3\rho \sqrt{3}}=\frac{\sqrt{3}}{4}\left [\frac{2\pi}{3}+\frac{\sqrt{3}}{2}\right ]=\frac{3}{8}+\frac{\sqrt{3}\pi}{6}=1.2819}[/tex]
Thus, The y-coordinate of center of mass is 1.2819 kg
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The center of mass of a thin plate of constant density is determined by its area and the distribution of its mass.
How will you find the center of the mass?To find the center of mass of this plate, we first need to calculate its area. We can do this by using the formula for the area of a region bounded by the x-axis and a curve y=f(x):
A = ∫[tex]a^{b}[/tex] ydx = ∫-pi/3^pi/3 3cosx dx
A = 3∫-pi/3^pi/3cosx dx
A = 3(sin(pi/3) - sin(-pi/3))
A = 3(sin(pi/3) + sin(pi/3))
A = 6sin(pi/3)
A = 6*(1/2)
A = 3
Now that we know the area of the plate, we can calculate its center of mass. To do this, we need to use the formula for the center of mass of a region bounded by the x-axis and a curve y=f(x):
xcm = 1/A ∫[tex]a^{b}[/tex] xydx
xcm = 1/3 ∫-pi/3^pi/3 x(3cosx) dx
xcm = 1/3 ∫-pi/3^pi/3 3xcosx dx
xcm = 1/3(3(sin(pi/3) - sin(-pi/3)) - 3xsin(pi/3) + 3xsin(-pi/3))
xcm = 1/3(6sin(pi/3) - 3pi/3sin(pi/3) + 3(-pi/3)sin(-pi/3))
xcm = 1/3(6sin(pi/3) - 3pi/3sin(pi/3) + 3pi/3sin(pi/3))
xcm = 0
Therefore, the center of mass of the plate is located at (0, 0).
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if , then abc and def are congruent by the asa criterion
If C.)Angle B is congruent to angle E then ∆ABC and ∆DEF are congruent by the ASA criterion.
What is Congruence?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
According to the ASA congruence postulate, two triangles are congruent when two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.
Looking at our diagram, we can see that the angle C and side CB of ABC are, respectively, congruent with the angle F and side FE of DEF.
Since CB is a side of ABC between angles C and B and FE is a side of DEF between angles F and E, angle B must be equal to angle E for these two triangles to be congruent by ASA.
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1. If , _____ then ∆ABC and ∆DEF are congruent by the ASA criterion.
A.) AB=DE
B.)CA=FD
C.)Angle B is congruent to angle E
D.)Angle A is congruent to angle D
As shown above, a classic deck of cards is made up of 52 cards. Suppose ne card is selected at random and
calculate the following probabilities.
Round solutions to three decimal places, if necessary.
The probability that a 8 of Diamonds is selected is
The probability that a Heart or Spade is selected is
The probability that a number smaller than 7 (counting the ace as a 1) is selected is
Step-by-step explanation:
a probability is always the ratio of
desired cases / totally possible cases
in our case, where we pull one card out of 52, the totally possible cases are, of course, 52.
now, we need to find the number of desired cases.
8 of diamonds is pulled.
well, that is one specific card. no other card matches this criteria. so, the probability is
1/52 = 0.019230769... ≈ 0.019
heart or spade is selected.
we have 13 cards of heart.
we have 13 cards of spades.
there is no overlap, so, together they are 26.
the probably is then
26/52 = 1/2 = 0.5
number smaller than 7 is pulled.
"smaller than 7" means 1..6.
that means 6 cards of each of the 4 suits = 24 cards.
the probability is then
24/52 = 6/13 = 0.461538462... ≈ 0.462
What are the benefits and limitations of quadratic models in real-world applications such as bridge design?
The benefits and limitations of quadratic models in real-world applications such as bridge design are listed below.
What are the benefits and limitations of quadratic models in real-world applications such as bridge design?Quadratic models are often used in real-world applications, such as bridge design, because of their ability to describe complex relationships between variables.
Some benefits of using quadratic models in these applications include:
1. Flexibility: Quadratic models are more flexible than linear models and can better capture non-linear relationships between variables.
2. Accuracy: Quadratic models can provide a more accurate representation of the data compared to linear models, especially when the data exhibits a curved trend.
3. Prediction: Quadratic models can be used to make predictions about the future based on past data. For example, they can be used to predict the load-bearing capacity of a bridge over time.
However, there are also some limitations of using quadratic models in real-world applications such as bridge design:
1. Overfitting: Quadratic models have the potential to overfit the data, leading to poor generalization to new data. This can result in an overly complex model that does not accurately represent the underlying relationships in the data.
2. Computational complexity: Quadratic models can be computationally more complex than linear models and require more advanced optimization techniques to solve.
3. Interpretation: Quadratic models can be difficult to interpret, making it challenging to understand the underlying relationships between variables.
4. Unpredictable behavior: Quadratic models can exhibit unpredictable behavior for certain input values, which may not be suitable for certain applications such as bridge design where the model must be reliable and predictable.
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The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000.
c) Find the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less.
The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x < 53.68 ) = 0.8439
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P
Now , the equation will be
The observed value of x = 53.68 cm
The mean of the sample μ = 49.9 cm
The standard deviation of the sample σ = 3.74 cm
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 53.68 - 49.9 ) / 3.74
z = 1.0107
Now ,the p value from the z table is
P ( x < 53.68 ) = 0.84392
And , the probability is P ( x < 53.68 ) = 84.392 %
Hence , the probability is 84.392 %
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The midpoint of AB is at (-2,4). If A=(5,7), find B
B is: (?)
Using the midpoint formula, B is: (-9, 1).
How to Use the Midpoint Formula?The midpoint of a line segment is given by the average of the coordinates of the endpoints. So, the midpoint of AB is (-2,4), and A = (5, 7), we can find B by using the midpoint formula:
M(x, y) = [(x1 + x2)/2, (y1 + y2)/2]
Given:
A(5, 7) = (x1, y1)
B(?, ?) = (x2, y2)
M(x, y)
Plug in the values:
(-2, 4) = [(5 + x2)/2, (7 + y2)/2]
Solve for each coordinates of B:
-2 = (5 + x2)/2
-4 = 5 + x2
-4 - 5 = x2
x2 = -9
4 = (7 + y2)/2
8 = 7 + y2
8 - 7 = y2
y2 = 1
B is: (-9, 1)
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Mrs. Farley made 24 meat patties out of 72 ounces of hamburgers. How many ounces of hamburgers are in each meat patty?
Answer: Each meat patty would have 72 ounces of hamburger divided by 24 patties, which is equal to 3 ounces per patty.
Step-by-step explanation:
I need help with this problem
Using Trigonometric identities, On the interval 0 2, we wish to locate all solutions to the equation 2sin() = 3. The sole answer is = 1.05.
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
what is the solutions of 2sin(θ)=−√3 on the interval 0≤θ 2π?Determining the answer to the following equation is therefore important: 2sin(θ) = √3
To begin, split both sides by two to obtain:
sin(θ) = (√3)/2
Now consider the behavior of the inverse sine function:
Asin(x) = sin(x) and Asin(x) = x
We can therefore apply this to both sides to obtain:
Asin(sin(s)) = Asin(sin(s))/3)
θ = Asin((√3)/2) = 1.05
The single solution in the interval is: because we know that the sine function's period is 2 and that there is only one solution on the range between 0 and 2:
θ = 1.05
sin(3θ) = √3/2
θ = π/9 + 2kπ/3, 2π/9 + 2kπ/3
We obtain = /9, 2/9 if k = 0.
We obtain = 7/9 and 8/9 if k = 1.
We obtain = 13/9 and 14/9 if k = 2.
Other values of k produce values of beyond the range [0, 2].
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Can someone tell me how i find this problem?
Answer:
9.80
Step-by-step explanation:
x²=14²-10² = 196-100 = 96
x=√96 = √(16*6 ) = 4*√6 =4*2.45=9.80
Suppose that mean retail price per gallon of regular grade gasoline 83.55 with standard deviation of 80.10 and that the retail price per gallon has bell-shaped distribution. NOTE: Please use empirical rule approximations for this problem_ What percentage of regular grade gasoline sells for between 83.35 and 83.75 per gallon (to decimal)? 95 What percentage of regular grade gasoline sells for between $3.35 and 83.65 per gallon (to decimal)? c: What percentage of regular grade gasoline sells for ess than 83.75 per gallon (to decimal)?
The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Describe Standard Deviation?It is a statistical calculation that provides a way of summarizing how much a set of values deviates from the mean, or average, of those values.
The standard deviation is calculated by first finding the difference between each value in the set and the mean, squaring these differences, summing the squares, and dividing by the number of values in the set. The square root of this result gives the standard deviation.
A low standard deviation indicates that the values in a set are closely clustered around the mean, while a high standard deviation indicates that the values are more spread out. The standard deviation is useful in many applications, including quality control, finance, and social sciences, as it provides a way to quantify the variability of a set of values and to make meaningful comparisons between different sets of data.
We can estimate the answer by using the cumulative distribution function (CDF) of the normal distribution. The CDF gives us the probability that a random variable is less than or equal to a certain value. We would need to use a calculator or software to determine the exact value of the CDF, but we can estimate it using the empirical rule.
Since approximately 68% of regular grade gasoline falls within one standard deviation of the mean, we can estimate that roughly 68% of gasoline is less than 83.75.
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Fill The Blank !!Maya's math teacher said that each question answered correctly on a test would be worth 5 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test. The independent variable,x,represents the _____ ,and the dependent variable is the _____because the ______depends on the _____A function relating these variables isR(X)=___So R(14)= ____ , meaning 14 ________________________________
The independent variable, x, represents the number of questions Maya answered correctly, and the dependent variable is the score, because the score depends on the number of questions Maya answered correctly. A function relating these variables is R(x) = [5x].
So R(14) = [70], meaning 14 correct answers will give a score of 70.
What is a variable?
In mathematics, a variable is referred to as the alphanumeric symbol used to represent a number or numerical value. An unknown quantity is represented as a variable in algebraic equations.
The variables can be divided into two groups, including dependent variable and independent variable.
We are given that each question answered correctly on a test would be worth 5 points.
So, the dependent variable is the score as it depends on the number of questions Maya answered correctly.
The independent variable is the number of questions Maya answered correctly.
From this, we get the function as R(x) = [5x].
Substituting 14 in place of x, we get
R(14) = [70]
This means that 14 correct answers will give a score of 70.
Hence, the independent variable, x, represents the number of questions Maya answered correctly, and the dependent variable is the score, because the score depends on the number of questions Maya answered correctly.
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Write an equation that is perpendicular to
y
=
−
6
x
+
3
y=−6x+3 and goes through the point
(
12
,
10
)
(12,10).
The equation of the required perpendicular line is 6y = x - 48
With an example, define perpendicular line?
Lines at right angles to one another are referred to as perpendicular lines (90 degrees). A parallel line is shown as "||," which stands for the symbol. Perpendicular lines are denoted with the symbol "". Illustration of parallel lines The opposite sides of a rectangle.
equation = y =−6x+3
m₁ = -6
Let's consider the slope of the line perpendicular to the given line as m₂
m₁ * m₂ = -1
-6 * m₂ = -1
m₂ = 1/6
The equation of the line perpendicular to the given line and passing through the point (12,10)
y - y₁ = m (x - x₁ )
y - 10 = 1/6( x - 12 )
6( y - 10 ) = (x- 12 )
6y - 60 = x - 12
6y = x - 12 + 60
6y = x - 48
Thus, the equation of the required line is 6y = x - 48
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out of 200 bolts, 5 are defective. determine the probability that a randomly selected sample (without replacement) of size 10 will have no defective bolts. compare the results for hypergeometric distribution and its binomial approximation
The Hypergeometric distribution is 0.7717, and the binomial distribution is 0.7763. The probability from the binomial approximation is greater than the probability from hypergeometric distribution.
What is Hypergeometric distribution?In statistics, a hypergeometric distribution is a distribution function in which members of two groups are chosen from without being replaced. The absence of replacements in the hypergeometric distribution sets it apart from the binomial distribution. As a result, it is frequently used in random sampling to ensure statistical quality.
Given that,
The number of defective bolts are 5 out of 200.
Thus, the probability of 0 defective bolts is given as:
1. Hypergeometric distribution:
P (X= 0) = 5C 0 (195C 10) / (200C 10)
= 0.7717
2. Binomial approximation:
B(n, m/ N)
P (X= 0) = 10C 0 (0.025)^0 (1-0.025)^10
= 0.7763
Thus, probability from the binomial approximation is greater than the probability from hypergeometric distribution.
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Find the volume of the figure. Express answers in terms of pi, then round to the nearest whole number.
Answer: V=144π cm³
Step-by-step explanation:
A data set on SharkAttacks Worldwide posted on StatCranch rocords data on all shark attacks in recorded history including attacks before 1800 . Variables contained in the data indude time of attack, date, location, activily the victim was engaged in when attacked, whether or not the injury was fatal, and species of shark. Which of the following questions could not be answered using the data get? Solect al that apply A. Aracks by which species of thark are more likey ta cesult in a fatality? B. In what month do most shark attacks occur? C. Which count,itwas the most shark attacks per year? D. Are shark antacks more ikely to occur in warm temperature or cooler temperatures?
Find the zeros of the quadratic equation y=4(x+9)²-36
The zeros of the quadratic equation y=4(x+9)²-36 are -6 and -12.
What is a quadratic equation?
Any equation of the form ax² + bx + c = 0where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
Given:
y=4(x+9)²-36
on solving the bracket ,we get
y = 4x² + 324 + 72x - 36
or
y = 4x² + 72x + 288
or
y = 4(x² + 18x + 72)
or
y = 4(x² + 12x + 6x + 72)
or
y = 4(x(x+12)+6(x+12))
or
y = 4(x+6)(x+12)
Therefore , zeroes are -6 and -12.
Hence , the zeros of the quadratic equation y=4(x+9)²-36 are -6 and -12.
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Can someone help a brothra out
It would be A. y = -log x
I did it on desmos the graph website
A coin consists of brass and zinc and weighs 2.5 g if 1.75 g of brass are used to make the coin what percent of the coin is made of zinc
Answer:.
Step-by-step explanation:
.
Graph the equation −3x+5y=7 by plotting points using the line tool.
A graph of the linear equation -3x + 5y = 7 in slope-intercept form is shown in the image attached below.
What is a graph?In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate respectively.
Next, we would rearrange and simplify the given given linear equation in slope-intercept form in order to enable us plot it on a graph:
-3x + 5y = 7
5y = 3x + 7
y = 3x/5 + 7/5
Lastly, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
In conclusion, the slope of this linear equation is equal to 3/5 and it does not represent a proportional relationship.
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find the root of 4x²-12x+9=0 graphically taken values of x from -1 to + 4
Answer:
To find the roots of 4x² - 12x + 9 = 0 graphically, we need to plot the equation on a graph and find the x-intercepts, which are the roots.
Here are the steps to graph the equation:
Plot the x-axis and y-axis on the graph
Plot the points (x, 4x² - 12x + 9) for several values of x within the range of -1 to 4.
Connect the points to form a smooth curve.
Find the x-intercepts, where the curve intersects the x-axis. These points represent the roots of the equation.
After finding the x-intercepts, we can use the x-value of each intercept to substitute back into the original equation to find the corresponding y-value. This confirms that the x-intercepts are indeed the roots of the equation.
Note: The above steps can also be done using a graphing calculator or software.
A sine function has the following key features:
Period =12
Amplitude=4
Midline:y=1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the grapn closest to the first point.
Please show me on a graph how to do this.
Compared with the parent function y= sin(x), the graph of 4 sin[ (π/6)x ] + 1 will be stretched vertically by a scale factor of 4, translated 1 unit up, and with a shorter distance between the peaks.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varied quantities and other variables.
Here, we have
1) The parent function is sin(x)
2) sin(x) has:
Middle line: y = 0
Amplitude: 1 because the function goes from 1 unit up to 1 unit down the middle line.
Period: 2π because the sine function repeats every 2π unit.
y-intercept: (0,0) because sin(0) = 0.
Now look at how these changes in the function reflect on the parameters:
A sin (ωx + B) + C:
That function will have:
amplitude A, because the amplitude is scaled by that factor
Period: 2π / ω, because the function is compressed horizontally by that factor.
It will be translated B units to the left
It will be translated C units up.
And you need
Period = 12 => 2π / ω = 12 => ω = π/6
A = 4
Translate the midline from y = 0 to y = 1 => shift the function 1 unit up => C = 1.
Translate the y-intercept from y = 0 to y = 1, which is already accomplished when you translate the function 1 unit up.
So, this is the function searched
y = A sin (ωx + B) + C = 4 sin[ (π/6)x ] + 1
Now you can check the amplitude, the period, the middle line, and the y-intercept of that y = 4 sin[ (π/6)x ] + 1.
Hence, compared with the parent function y= sin(x), the graph of 4 sin[ (π/6)x ] + 1 will be stretched vertically by a scale factor of 4, translated 1 unit up, and with a shorter distance between the peaks.
To learn more about the function from the given link
https://brainly.com/question/10439235
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PLEASE HELP!!! I already graphed it but I need the solution. I'll give you brainlest:))))
The solution of the system of equations is equal to (3, 4).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (3, 4).
Read more on a graph here: brainly.com/question/4546414
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Surface area of 15 yd
Surface area is, [tex]225\pi (yd^{2})[/tex] or [tex]706.86(yd^{2})[/tex] .
Step-by-step explanation:1. Identify the shape of the surface area of which we need to calcuiate the area.As we may see in the image, the surface area has the shape of a circle.
2. Recall the area formula for circles.Formula: [tex]A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
3. Identify the given data.As we can see in the image, the radius of this circle is 15 yd (yards).
4. Use the data and calculate with the formula.[tex]A=\pi (15yd)^{2}\\ \\A=225\pi (yd^{2}) =706.86(yd^{2})[/tex]
5. Conclude.Surface area is, [tex]225\pi (yd^{2})[/tex] or [tex]706.86(yd^{2})[/tex] (706.86 square yards).