Answers
From the given graph, we have 2 points with coordinates:
[tex]\begin{gathered} (x_1,y_1)=(1,2) \\ \text{and} \\ (x_2,y_2)=(4,1) \end{gathered}[/tex]The equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]With the given points, we can find the slope m as follows:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{then} \\ m=\frac{1-2}{4-1} \end{gathered}[/tex]which gives
[tex]m=\frac{-1}{3}=-\frac{1}{3}[/tex]Then, our line equation has the form
[tex]y=-\frac{1}{3}x+b[/tex]Now, we can find the y-intercept b by substituting one of the two given points. For instance, if we substitute point (1,2) into the last result, we get
[tex]2=-\frac{1}{3}(1)+b[/tex]which gives
[tex]\begin{gathered} 2=-\frac{1}{3}+b \\ \text{then} \\ 2+\frac{1}{3}=b \\ \frac{7}{3}=b \end{gathered}[/tex]then, the line equations is
[tex]y=-\frac{1}{3}x+\frac{7}{3}[/tex]a) The linear function is
[tex]f(x)=-\frac{1}{3}x+\frac{7}{3}[/tex]b) What is f(6)?
In this case, we have that x=6. Then, by replacing this value into our function, we get
[tex]f(6)=-\frac{1}{3}(6)+\frac{7}{3}[/tex]which gives
[tex]\begin{gathered} f(6)=-\frac{6}{3}+\frac{7}{3} \\ f(6)=\frac{-6+7}{3} \\ f(6)=\frac{1}{3} \end{gathered}[/tex]therefore, the answer for part b is
[tex]\frac{1}{3}[/tex]Related Questions
The students in Cassie's class got to choose between pizza and burgers for the celebration on the last day of school. 8 students picked the pizza. If there are 10 students in all in Cassie's class, what percentage of the students picked the pizza? Write your answer using a percent sign (%).
Answers
0.80 x 100= 80
Answers is 80%
Suppose a triangle has sides a, b, and c, and that a² + b² < c². Let 9 be the
measure of the angle opposite the side of length c. Which of the following
must be true? Check all that apply.
A. The triangle is not a right triangle.
B. cose < 0
C. cose > 0
□ D. a² + b²-c² = 2abcose
SUBMIT
Answers
Using trigonometry we know that option (B) "cosθ < 0" is correct.
What is Trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.For a right-angle triangle, the sum of the square of the legs is equal to the hypotenuse side(longest side).
Therefore, for a right triangle
a² + b² = c²For the triangle that has a² + b² > c², it shows it is not a right triangle.
Let θ be the measure of the angle opposite the side of length c.We have to find the statements which are must be true.Cosine law:
c² = a² + b² - 2abcosθSubstitute the value then we get:
c² < c² - 2abcosθSubtracting c² on both sides of the inequality:
c² - c² < c²- c² - 2abcosθ0 < -2abcosθAdding 2abcosθ on both sides then we get:
2abcosθ < -2abcosθ + 2abcosθ = 02abcosθ < 0cosθ < 0cosθ is negative in the second quadrant and third quadrants.
Therefore, using trigonometry we know that option (B) "cosθ < 0" is correct.
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For each graph below, state whether it represents a function.
Answers
Graph 1: No, because it fails the vertical line test.
Graph 2: No, because it fails the vertical line test.
Graph 3: Yes, because it passes the vertical line test.
Graph 4: Yes, because it passes the vertical line test.
Graph 5: No, because it fails the vertical line test.
Graph 6: Yes, because it passes the vertical line test.
a bond issue outstanding that matures in 19 years. The bonds pay interest semiannually. The bonds have a face value of $1,000 and are currently priced at $995.28. The bonds carry a coupon rate of 3.5 percent. What is the aftertax cost of debt if the total tax rate is 22 percent? Multiple Choice
Answers
The after tax cost of debt for the bond is 2.73%
Given,
The face value of the bond, FV = $1000
Present value of the bond, PV = $995.28
Maturity period = 19 years
Coupon rate = 3.5%
Total tax rate = 22%
We have to find the after tax cost of debt for the bond.
The bond pays interest semiannually ;
so coupon rate = 3.5/2 = 1.75
Coupon payment , pmt= 0.0175 x 1000 = $17.5
Maturity, nper = 19 years x 2 = 38
Compute yield rate using spreadsheet = Rate(nper,pmt,-PV, FV)
Then,
= RATE(38, 17.5, -995.28, 1000)
Rate or yield is computed as 3.5%
The present value is negative as it is a cash outflow.
The cost of debt is 3.5%
The tax rate is 22%
After tax cost of debt = 3.5 (1 - 0.22) = 2.73%
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Transforming the graph of a quadratic, cubic, square root, or absolute value function
Answers
Explanation:
If we have a function g(x) = -f(x), then g(x) will be f(x) reflected across the x-axis.
If g(x) = f(x) - c, g(x) will be f(x) shifted c units down
If g(x) = f(x + c), g(x) will be f(x) shifted c units to the left.
In this case, the initial function is f(x) = |x| and g(x) = -|x + 3| - 2, then
g(x) = -f(x + 3) - 2
Therefore, g(x) will be the initial function reflected across the x-axis, shifted 3 units to the left and 2 units down.
Answer:
So, the graph for y = -|x + 3| - 2 will be:
What are the X and Y intercepts for the graph shown in the picture?
Answers
Based on the given figure, you can conclude:
x-intercepts:
x = 0
x = number in between 100 and 125, approximately 105
x = number greater than 175, approximately 180
y-intercepts:
y = 0
For the second and third x-intercepts there is no possible to specifiy the exact numbers due to the scale units of the graph.
Which words describe the polynomial? (Select all that apply) * (1 Point)
f (x) = x^4 - 2
quartic
trinomial
cubic
quadratic
binomial
Answers
A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.
What is meant by Quartic polynomial?A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.
Quartic in mathematics refers to something that is of the "fourth order," such as a function. One of the following is possible: Quartic function, a fourth-degree polynomial function. Quartic polynomial, a polynomial equation of degree 4, where an is a nonzero polynomial that defines the quartic equation.
A quartic equation, also known as an equation of the fourth degree, is an equation of the form that reduces a quartic polynomial to zero. A quartic function's derivative is a cubic function.
Therefore, the correct answer is option a) quartic.
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The length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.Which function defines the area of the rectangle?Hint: A=l⋅w
Answers
The area of a rectangle is calculated using the formula:
[tex]A=l\times w[/tex]where l is the length and w is the width.
The functions for the length and width are given to be:
[tex]\begin{gathered} l(x)=2x+1 \\ w(x)=x+4 \end{gathered}[/tex]Therefore, the area of the rectangle will be:
[tex]A=(2x+1)(x+4)[/tex]We can apply the FOIL Method:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Therefore, we have:
[tex]\begin{gathered} \left(2x+1\right)\left(x+4\right)=2x\cdot x+2x\cdot\:4+1\cdot\:x+1\cdot\:4 \\ =2x^2+8x+x+4 \end{gathered}[/tex]Simplifying, the area is:
[tex]a(x)=2x^2+9x+4[/tex]The SECOND OPTION is correct.
Using synthetic division what is the first row for the dividend (divided) and the divisor value using synthetic division process:
2x3−10x+2/x−4
Answers
Using synthetic division, the solution to the polynomial fraction expression is; 2x² - 10 + 12/(x - 4)
How to use Synthetic Division?We are given the polynomial fraction as;
(2x³ - 10x + 2)/(x- 4)
This means that we want to divide the polynomial (2x³ - 10x + 2) by (x - 4) using synthetic division.
For the divisor, we have x - 4, and that means x - 4 = 0, x = 4
So, we'll be using 4 for the synthetic division and we have;
-1 | 2 0 -10 2
× 0 0 10
-------------------------
2 0 -10 12
Now we will form the expression in the form of fraction again;
2x² - 10 + (12/(x - 4))
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name a number that is not a whole number
Answers
Whole numbers are the numbers 0, 1, 2, 3, 4, etc. (the natural numbers and zero). Negative numbers are not considered whole numbers. All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
For example.
- 2, - 10
Use the above data to calculate the correlation coefficient Answer Choices.0.890.94-0.89-0.94
Answers
Using the table, we have the following points:
(x1, y1) ==> (2.5, 3), (3.5, 4.5), (5, 4.8), (5.5, 5.2), (6, 5.5)
Let's find the correlation coefficient.
To find the correlation coefficient, apply the formula:
[tex]r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-\Sigma(x)^2)(n}\Sigma y^2-\Sigma(y)^2)}[/tex]Where:
n = 5
Σx = 2.5 + 3.5 + 5 + 5.5 + 6 = 22.5
Σy = 3 + 4.5 + 4.8 + 5.2 + 5.5 = 23
Σxy = 2.5⋅3 + 3.5⋅4.5 + 5⋅4.8 + 5.5⋅5.2 + 6⋅5.5 = 108.85
Σx² = 2.5² + 3.5² + 5² + 5.5² + 6² = 109.75
Σy² = 109.6
Plug in values in the formula and solve for r.
We have:
[tex]\begin{gathered} r=\frac{5(108.85)-(22.5)(23)}{\sqrt{(5(109.75)-22.5^2)(5(109.6)-(23)^2}} \\ \\ r=0.94 \end{gathered}[/tex]Therefore, the coefficient is 0.94
ANSWER:
0.94
Serum albumin levels in adults are distributed approximately Normally with a mean of 35 g/l and a standard deviation of 5 g/l. What is the probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l? (Enter your answer rounded to two decimal places.)
Answers
There is a 0.6915 = 69.15% probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented below:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.The mean and the standard deviation of the albumin levels are given as follows:
[tex]\mu = 35, \sigma = 5[/tex]
The probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l is one subtracted by the p-value of Z when X = 32.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (32.5 - 35)/5
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
1 - 0.3085 = 0.6915 = 69.15% probability.
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A rectangular driveway is 9 feet wide, and it has an area of 135 square feet. How lo g is the driveway
Answers
Area of a Rectangle
Given a rectangle of length L and width W, the area is calculated as follows:
A = L.W
We are given the area of A=135 square feet and the width is W= 9 ft. Solving for L:
[tex]L=\frac{A}{W}=\frac{135ft^2}{9ft}=15ft[/tex]The driveway is 15 feet long
I’m trying to do my homework help
Answers
The average rate of change f(x) on the interval -6 ≤ x ≥ 2 is; 5
What is the Average Rate of Change of the function?
Average rate of change is a measure of how much the function changed per unit, on average, over that interval. This is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Now, the formula for the average rate of change over the interval (a, b) is;
f'(x) = [f(b) - f(a)]/(b - a)
Now, we are given the interval as -6 ≤ x ≥ 2.
From the given polynomial graph, we see that;
f(2) = 0 and f(-6) = 40
Thus;
f'(x) = [f(-6) - f(0)]/(2 - (-6))
f'(x) = (40 - 0)/8
f'(x) = 5
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ng waffles for breakfast. The recipe calls for 1/2 cups of water for every 2Jemina pancake mix. How many cups water would he need for only oneake mix? Show your work
Answers
Ratio:
cups of water / pancake mix = (1/2) / 2
For 1 pancake mix, x cups of water:
x / 1 = (1/2) / 2
Solve for x, cross multiply:
2x = ( 1/2) 1
2x = 1/2
Divide both sides by 2
2x/2 = (1/2) / 2
x = 1/4
Answer:
She would need 1/4 cups of water
Help step by step pleaseeee
Answers
The graphic below includes the graph of the provided question.
The horizontal axis is x-axis
The vertical axis is y-axis.
How do collinear points work?Points that are situated along the same straight line but within a single line are known as collinear points. Two or more points in Euclidean geometry are said to be collinear if they are situated on a line that is either close to or far from one another.
In light of the information provided:All the points necessary to solve the equation will be positive and negative in turn, and that point will form a straight line through the origin, indicating that all the points are collinear.
You can change the value to fit your graph in the diagram that corresponds to the graph for the question that is attached below.
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What subset of real numbers does 1/2 belongs to?
Answers
Answer:
It belongs to the sets of natural numbers, {1, 2, 3, 4, 5, …}.
It is a whole number because the set of whole numbers includes the natural numbers plus zero. It is an integer since it is both a natural and whole number.
Answer: rational numbers if thats an answer
Step-by-step explanation:
I need help with homework I got the picture with the questions
Answers
We have the following:
[tex]\begin{gathered} \text{CAE}=135-45=90\degree \\ \text{EAF}=45-15=30\degree \\ \text{CAF}=\text{CAE}+\text{EAF}=90+30=120\degree \end{gathered}[/tex]help it’ll be greatly appreciated :(
Answers
In population 1:
Pattern is changing by 13.5 to 11.5 to 8.3
Which is 2 then 3.2.
In population 2:
Population is decreasing by 2.
Describe pattern.A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Given.
Pattern in which population is changing are:
In population 1:
It is changing by 13.5 to 11.5 to 8.3
Which is 2 then 3.2.
In population 2:
Population is decreasing by 2.
Completing the table:
Population 1 Population 2
42.8 29
38.6 27
33.4 25
27.2 23
Graph is mentioned below.
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Which expression can be used to determine the number of downloads on the meh day after the game was available
Answers
we have the sequence
1,790 2,555 3,320 4,085 4,850
so
a1=1,790 ----> first term
a2=2,555
a3=3,320
a4=4,085
a5=4,850
Find out the difference between consecutive terms
a2-a1=2,555-1,790=765
a3-a2=3,320-2,555=765
a4-a3=4,085-3,320=765
a5-a4=4,850-4,085=765
This is an arithmetic sequence
The common difference is d=765
so
[tex]a_n=a_1+d\left(n-1\right)[/tex]we have
d=765
a1=1,790
substitute
[tex]\begin{gathered} a_n=1,790+765(n-1) \\ a_n=1,790+765n-765 \\ a_n=1,025+765n \end{gathered}[/tex]The answer is option Bin the equation 8x - 1 = 3x + 4 the variable x represents the same value. Which value of x is the solution of the equation; x = 0, 1, 2, or 3? Explain.
Answers
Given the following expression:
a.) 8x - 1 = 3x + 4
Let's determine the value of x,
8x - 1 = 3x + 4
8x - 1 + 1 - 3x = 3x + 4 + 1 - 3x
8x - 3x = 4 + 1
5x = 5
5x/5 = 5/5
x = 1
Therefore, x = 1.
And then move the consistent to the right side and change the sign and you should get 8x-3=4+1
now you should have 8x-3x=4+1 now collect like terms and you should get 5x=4+1
Add the numbers And you should get 5x=5 divide both sides by 5 and you should get x1
What do the 2 points on the graph mean in terms of the situation
Answers
Coordinates - A pair of integers that show the location of a point on a graph. The first number represents the x-axis, while the second represents the y-axis.
Other names for this type of pair are ordered pair and numbered pair. A proportionate connection is one in which the values are all connected by the same constant value. A proportionate connection is also known as a linear relationship in mathematics.
Assume f(x) and g(x) are two functions that accept a real number as input and return a real number as output.
The intersection points of f(x) and g(x) are then those x values for which f(x)=g(x).
The precise numbers can sometimes be discovered by algebraically solving the equation f(x)=g(x).
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what is a root of a parabola?
Answers
The roots of a prabola is where the function intersects the x-axis.
So what's in the photo is what I need help with.
Answers
Answer:
1 == B No Solutions
2 == A One Solution
3 == C Infinitely Many Solutions
Explanation:
We first find go through each system and see which has one solution, no solutions, and infinitely many solutions.
1.
x
Noah operates an orange juice stand. On Monday he used 3 3/10 bags of oranges. On Tuesday he used 1/6 as many oranges as on Monday. How many bags of oranges did Noah use on Tuesday?
Write your answer as a fraction or as a whole or mixed number.
Answers
The number of bags of oranges Noah used on Tuesday as required to be determined in the task content is; 11/20 bags of oranges.
What is the number of bags of oranges used by Noah on Tuesday?It follows from the task content that Noah used 3 3/10 bags of oranges on Monday.
Hence, by expressing the mixed number, 3 3/10 as a fraction; we have; 33/10.
Therefore, since he uses 1/6 as many oranges as on Monday on Tuesday;
The number of bags of oranges used on Tuesday is; (1/6) × 33/10
= 33/60
= 11/20.
Therefore, the number of bags of oranges Noah uses on Tuesday is; 11/20.
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If y = 2x2 – 4, what is its inverse?
Answers
The inverse of the function y = 2 · x² - 4 is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4. (Correct choice: B)
How to find the inverse of a function
In this problem we have a quadratic function, whose inverse has to be found. First, we make the following substitution on the function:
y = x
x = y⁻¹
Now we proceed to clear y⁻¹ by using algebra properties:
x = 2 · (y⁻¹)² - 4
x + 4 = 2 · (y⁻¹)²
(x + 4) / 2 = (y⁻¹)²
√[(x + 4) / 2] = y⁻¹
y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4
The inverse of the function is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4.
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A survey showed that of college students read internet news on a regular basis and that of college students regularly watch the news on TV. The survey also showed that of college students both follow TV news regularly and read internet news regularly.
(a)What is the probability that a student watches TV news regularly, given that he or she regularly reads internet news? Round your answer to the nearest hundredth.
(b)What is the probability that a randomly selected college student reads internet news regularly, given that he or she watches TV news regularly? Round your answer to the nearest hundredth.
Answers
For the given values, the probability that a student watches TV news regularly is 0.833, the probability that a randomly selected college student reads internet news regularly is 0.240.
According to a survey, 83% of college students routinely watch the news on television, while 24% of college students read newspapers on a regular basis.
Additionally, the survey revealed that 20% of college students routinely read newspapers and watch TV news.
(A) Given that a student reads newspapers frequently,
The answer is [P(TV and newspapers)/P] where P(watches TV|reads newspapers) (newspapers)
= 0.20/0.24 = 0.833
(b) Given that a randomly chosen college student watches TV news frequently
The answer is that P(newspapers | watches TV) = [P(newspapers and TV)] / P. (TV)
= 0.20/0.83 = 0.240
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I need help solving an answering this practice problems from my pre-calculus prep guide
Answers
The general formula of a geometric sequence is:
[tex]a_n=a_1(r)^{n-1}[/tex]where,
n = 6
a₁ = -8100
r = -0.1
Replacing on the formula:
[tex]\begin{gathered} a_6\text{ = -8100}\times(-0.1)^{6-1} \\ a_6\text{ = 0.081} \end{gathered}[/tex]In december 2004 35% of student in the high school were satisfied with the lunches supplies through the school of the 856 survey, 265 inducted they were satisfied does this suggests the proportion of student satisfied with the quality of lunches has decreased
What does it means to make a type 2 error for the test
Answers
When one fails to reject a null hypothesis that is actually wrong, this error is known statistically as a type II error. This term is used in the context of hypothesis testing.
A type II error, often called an error of omission, results in a false negative. When the patient is infected, a disease test, for instance, can return a negative result. This is a type II error because, despite being wrong, we accept the test's negative conclusion.
The difference between a type I and type II error is that a type I error refers to the failure to reject a valid null hypothesis, whereas a type II error refers to the failure to do so. Despite the fact that the error does not happen by accident, it rejects the alternative theory.
The likelihood of mistakenly failing to reject the null hypothesis when it does not apply to the entire population is known as a type II error.
In essence, a type II error is a false negative.
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Can somebody please help me right now??? i’m stuck and i need help with this bad
Answers
Answer:
Is wolfgang Mozart's
Step-by-step explanation:
The central traits of the Classical style are all present in Mozart's music. Clarity, balance, and transparency are the hallmarks of his work, but simplistic notions of its delicacy mask the exceptional power of his finest masterpieces, such as the Piano Concerto No. 24 in C minor, K.