At cathode reduction occurs so, here Ag(s) will form because it has high reduction potential.
However, at anode oxidation occurs and , here the substance with high oxidation potential can oxidises easily so bromine will form.
Electrolysis:
Electrolysis, the process of passing an electric current through a substance to cause a chemical change. A chemical transformation is when a substance loses or gains electrons (oxidation or reduction).
Small silver ions or bromide ions or both.
Electrolysis of the remaining solution is dependent on concentration, pH, electrodes, current density, etc. Some bromine may be present at the anode if there is a significant amount of bromide ions in solution. Otherwise O₂ will occur. Some silver deposition may occur at the cathode if a significant concentration of silver ion solution is present. If not, the electrochemical reaction will be either oxygen reduction or hydrogen evolution.
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which statement about allele frequencies is false? the sum of all allele frequencies is 0. the sum of all allele frequencies is 1. it is possible to have a negative allele frequency. allele frequencies can be greater than 1 in some populations. all alleles have the same frequency.
The correct option is B , the sum of all allele frequencies is 1.
What is allele frequencies?
Allele frequency, or gene frequency, is that the frequency of allele cistron at a selected locus in a very population, expressed as a fraction or proportion. Specifically, it's the fraction of all chromosomes within the population that carry that allele over the full population or sample size.
Main body:
Allele frequency is totally different from genotype frequency or makeup frequency. Genotype and makeup frequencies may also be calculated and square measure vital for understanding however populations evolve, however they're not identical issue as allele frequency.
Hence the correct option is B.
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The two triangles are similar, solve for x.
Answer:
x = 10
Step-by-step explanation:
[tex]\frac{x-4}{4}[/tex] = [tex]\frac{15}{x}[/tex] ( x > 0 )
x(x - 4) = 15(4)
x² - 4x - 60 = 0
( x + 6 )( x - 10 ) = 0
x = 10
What is the function of a parent?.
The parent of a function is the simplest form of a group of functions.
Parent functions are the simplest form of a given family of functions. A family of functions is a group of functions that share the same highest degree and the same shape for their graphs.
The graph shows four graphs that exhibit the parabola. Since they all share the same highest degree of two and the same shape, we can group them as one family of function.
These four are all quadratic functions, and their simplest form would be[tex]y = x^2[/tex].
Hence, the parent function for this family is [tex]y = x^2[/tex]
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What is a translated image?.
Concept and uses of image translation are explain below.
What is a translated image?In math, a change is an activity that moves, flips, or changes a shape (called the preimage) to make another shape (called the picture). An interpretation is a sort of change that moves each point in a figure a similar distance in a similar course.
Benefits os translation of image.An interpretation is a kind of change that takes each point in a figure and slides it a similar distance in a similar course. This interpretation maps △ X Y Z \triangle{XYZ} △XYZtriangle, X, Y, Z onto the blue triangle. The outcome is another figure, called the picture. The picture is consistent to the first figure.
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A researcher has created a Bose-Einstein condensate in which the index of refraction is
20,000,000
. The velocity of light in this gas is closest to which of these? A snail in full speed run A car on a local street. A ray of light in acrylic or glass
5.996×10 15
meters/second
The velocity v=15 m/s that is equal to the speed of a car on a local street. So the option 2 is correct.
In the given question we have to find the velocity of light in this gas is closest to which of these.
A researcher has created a Bose-Einstein condensate in which the index of refraction is 20,000,000.
The given options are;
A snail in full speed run A car on a local streetA ray of light in acrylic or glass5.996×10^{15} meters/seconRefractive index of B-E condensate(n) = 20,000,000 = 2×10^7
n = c/v
v=c/n
where v = speed of light in B-E condensate
As we know that c=3×10^8 m/s
So v=3×10^8/2×10^7
v=30×10^7/2×10^7
v=15 m/s
This is the velocity equal to the speed of a car on a local street.
So the option 2 is correct.
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Fireman Fred needs to stay fit for his job. He runs 3 kilometers, 4 mornings a week. If it takes him 8 minutes and 15 seconds on average to run kilometre, how much time does he spend running over 4 weeks?
The time Fireman Fred spends running in 4 weeks, found from the average time it takes him to run 1 kilometer is 6.6 hours.
What is an average in mathematics?An average is the ratio of the sum of a set of values to the number of values in the set.
The distance Fireman Fred runs 4 morning in a week = 3 kilometers
The time it takes to run a kilometer = 8 minutes and 15 seconds
15 seconds = 0.25 minutes, therefore;
The time it takes to run a kilometer = 8.25 minutes
The time Fireman Fred spends running in 4 weeks is found as follows;
The distance Fireman Fred runs in a week = 3 × 4 kilometers = 12 kilometers per week
The total distance he runs in 4 weeks, D, is obtained using the equation;
D = 4 weeks × 12 kilometers per week = 48 kilometers
The total time = Time per kilometer × Number of Kilometers
The total time = 8.25 minutes/kilometer × 48 kilometers = 396 minutes
There are 60 minutes in one hour, therefore;
396 minutes = 396 minutes × (1/60) hour/minutes = 6.6 hours
The time Fireman Fred spends running over 4 weeks is 6.6 hours
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a manager is interested in estimating the mean time (in minutes) required to complete a job. his assistant uses a sample of 100 observations to report the confidence interval as [14.355, 17.645]. the population standard deviation is known to be equal to 10 minutes. (you may find it useful to reference the z table.) a. find the sample mean time used to compute the confidence interval.
The sample mean is 16 times used to compute the confidence interval.
What is the z test?
If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.
The given sample value 100 observation,
Sample mean = (Lower limit + Upper limit) / 2 = (14.355 + 17.645) / 2 = 16
Hence, the sample mean is 16 time used to compute the confidence interval.
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Which of the following is a solution of x^2+5x=-2
Answer:
x = [tex]\frac{-5 + \sqrt{17} }{2}[/tex]
Step-by-step explanation:
HOW TO SOLVE YOUR PROBLEM
1. Move terms to the left side
x² + 5x = -2
x² + 5x - (-2) = 0
2. Use the quadratic formula
x = [tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x² + 5x + 2 = 0
a = 1
b = 5
c = 2
x = [tex]\frac{-5 + \sqrt{5^2 - 4 * 1 * 2} }{2 * 1}[/tex]
3. Simplify
Evaluate the exponent
Multiply the numbers
Subtract the numbers
Multiply the numbers
Solution:
x = [tex]\frac{-5 + \sqrt{17} }{2}[/tex]
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10-29 locate the centroid y of the channel's cross-sectional area, and then determine the moment of inertia with respect to the x' axis passing through the centroid
The correct value of the moment of inertia is 128.
Let us consider the shaded area as rectangle 1 of 16 x 16 in minus the rectangle 2 of 12 x 4
Area of rectangle 1 = A₁ = 16 x 16
A₁ = 96
Area of rectangle 2 = A₂ = 12 x 4
A₂ = 48
y- coordinate of the centroid
y = [A₁*(6/2) - A₂*(2+2)] / (A₁-A₂)
y = [(96*3)-(48*4)] / 48
y = 2 in
Moment of inertia of 1 about x-axis
Iₓ = [{16*(6)²} / 12] + [A₁(3-2)²]
Iₓ = 384
Moment of inertia of 2 about x-axis
Iₓ' = [12(4)²/12] + A₂[2+(4/2)-2]²
Iₓ' = 256
Moment of inertia of the entire shaded area
Iₐ = Iₓ - Iₓ'
Iₐ = 384 - 256
Iₐ = 128
Therefore the moment of inertia of the cross sectional area with respect to x-axis is 128.
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What is 18.92 divided by11 equals 18.92 at the top 11 at the bottom explain your answer PLEASE I HAVE TO SUMMIT THIS IN 19 MIN!
The value of 18.92/11 is 1.72.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given term is 18.92 divided by 11,
The mathematical expression for 18.92 divided by 11,
= 18.92/11
= 1.72
The value of 18.92 divided by 11 is 1.72.
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if a within-subjects experiment produces 50 scores in treatment 1 and 50 scores in treatment 2, then the experiment must have employed .
If a between-subjects experiment produces 50 scores in treatment 1 and 50 scores in treatment 2, then the experiment must have employed 100 participants.
Why do between-subjects experimental designs employ random assignment?
Because it ensures that there are no systematic differences between the participants in each group, random assignment improves the study's internal validity. You can draw the conclusion from this that the independent variable is to blame for the results.
What is the metric that denotes the degree to which all scores typically differ from the mean?
Because it is reported in the original units of measurement and takes into account all of the scores in the data set, the standard deviation is the most widely used measure of variability. It reveals the average (or standard) distance that separates each score from the distribution's mean.
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Full Question = If a between-subjects experiment produces 50 scores in treatment 1 and 50 scores in treatment 2, then the experiment must have employed ____.
a. 100 participants
b. 25 participants
c. 50 participants
d. 200 participants
What are the 4 types of linear functions?.
The four types of representation of linear functions are graphs, tables , equations or verbal descriptions.
A linear function is of the mathematical form y = ax + b. This function can be represented in various ways.
The four types of linear function representations are:
A table of values, mapping diagram, or group of ordered pairs can all be used to locate a list of input values and their corresponding output values.Given a graph, we may rapidly determine whether a relationship is a function and, if so, to which function family it belongs.The rule for employing equation representation to change our input, x, into our output, y, is given to us.Example: a linear function is of the form: y = mx+c
Using verbal description representation, we can create a use case for our relationship.The variable y is twice the value of variable x (y = 2x)
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what is the answer to 3 divided by 1/8
At the Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 26 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.
a. In words, define the Random Variable X.
b. List the values that X may take on.
c. Give the distribution of X.
d. How many fencers are expected to not use the foil as their main weapon? (Round your answer to the nearest whole number.)
e. Find the probability that fifteen do not use the foil as their main weapon.
f. Based on numerical values, would you be surprised if all 26 did not use foil as their main weapon?
The correct answers listed below :
A)The percentage of fencers that don't utilize the foil as their primary weapon in A.
B.) X : 0, 1, 2, 3,..., 21
C.) X ~ p(X) ; 10.4
D.) 21 ~ 0.4
E.) 0.0895
F.) Yes. There is a low (less than 1%) chance that all 21 fencers will not use the foil as their primary weapon.
A.) Considering that 60% of fencers reportedly utilize the foil as their primary weapon;
Number of fencers who do not utilize foil as their primary weapon is the random variable (x);
( 100% - 60%) = (1 - 0.6) = 0.4
B.) Possible values for X include:
The sample size is 26;
X : 0, 1, 2,..., 26
The breakdown of X
X ~ B ; X ~ p(X) ; 26 *0.4
=10.4
How many fencers are anticipated to not utilize the foil as their primary weapon in Part (d)?
X * p(x) (x)
=26 * 0.4
= 8.4
= 8 (nearest whole number) (nearest whole number)
Determine the likelihood that eleven will not utilize the foil as their primary weapon in part (e).
P(x = 11)
Using the link between binomial probabilities:
P(x =x) is equal to nCx * px * (1 - p) (n - x)
P(x = 11) = 26C11 * 0.4^11 * 0.6^10
P(x = 11) = 0.0895
Would you be shocked if none of the 21 used foil as their primary weapon based on the numbers?
P(x = 26) = 26C21 * 0.4^26 * 0.6^0
P(x = 26) = < 0.00001 ( about 0) ( approximately 0)
It will therefore be surprising if all 26 do not employ foil as their primary weapon given this extremely low value, which is virtually equal to 0.
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does the data suggest that true average total body bone mineral content during post weaning exceeds that during lactation by more than 25 g? state and test the appropriate hypotheses using a significance level of 0.05. (note: the appropriate normal probability plot shows some curvature but not enough to cast substantial doubt on a normality assumption.)
The appropriate hypotheses using a significance level of 0.05 reject H0.
The hypothesis :
H0 : μL - μP ≥ 25
H0 : μL - μP < 25
The sample mean difference; Xd
d = L - P
Xd = Σd/n
d = -198,-336,-70,-18,-122,-9,-50,-5,-163,-86
Xd = - 1057 / 10
Xd = - 105.7
Using calculator ;
Standard deviation of difference, Sd = 103.845
The test statistic :
T = Xd ÷ (Sd/√n)
T = -105.7 ÷ (103.845/√10)
T = - 3.219
Decision region :
Reject H0 ; If P-value < α
The P-value : df = n - 1 ; 10 - 1 = 9
P-value(-3.219, 9) ; two-tailed = 0.00525
Hence the answer is, the appropriate hypotheses using a significance level of 0.05 reject H0.
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According to the 2010 u. S. Census, there are approximately 8 million people living in virginia. This is 2. 8 million less than 4 times the population of nevada. What is the population of nevada? the first step is to on both sides. The second step is to on both sides. The population of nevada is million.
According to the 2010 u. S. Census, there are approximately 8 million people living in Virginia. Hence ,the population of Nevada is 2.7 million.
What is an equation ?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
What is a balance addition equation ?For example, we might have an equation like 4 + 1 = 2 + 3. This is an addition equation that has already been solved because both sides equal the same thing. 4 + 1 is equal to 5, and so is 2 + 3. This is called a balanced addition equation.
What is the multiplication property for equality states ?The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.
According to the question ,the first step is to add 2.8 on both sides , then second step is to divide by 4 on both sides. And thus The population of Nevada is 2.7 million.
Given:
The population of Virginia is 8 million.
Let x be the population of Nevada
It is also given that the population of Virginia is 2.8 million less than 4 times the population of Nevada.
So,
4x - 2.8 = 8
Add 2.8 on both sides ,
4x - 2.8 +2.8 = 8 + 2.8
⇒ 4x = 10.8
Divide both sides by 2.8
⇒ x = 10.8/4
⇒ x = 2.7
Hence ,the streps involved are :
Hence, The first step is to add 2.8 on both sides add 2.8The second step is to divide by 4 on both sides.
The population of Nevada is 2.7 million.
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Answer: A, D, B
Step-by-step explanation:
The first step is to
✔ add 2.8
on both sides.
The second step is to
✔ divide by 4
on both sides.
The population of Nevada is
✔ 2.7
million.
Have a nice day
Help!!!!!!!!!!!??????
PLS
Answer:
Slope of line e is 2/3
Step-by-step explanation:
you know that equation for line d is y= 2/3x+3. because that line e is parallel to line d, it means that line e and d will never intersect which can only happen if both lines have the same slope. so that means line e's slope is 2/3
Answer:
2/3
Step-by-step explanation:
when a line is parallel to another line we say that the slopes are equal hence the slope of line e is 2/3.
NOTE: if a line is perpendicular to another the slope of line B the line is the negative reciprocal of the slope of Line A
for instance: if the slope was 2/3 the slope of the perpendicular line is -3/2
hope this helps.
At a company meeting, there were 30 people in attendance. 60% of them were managers. How many managers were in the meeting?
The number of many managers were in the meeting is
How to find the number of managers in meetinginformation from the problem
At a company meeting, there were 30 people in attendance.
60% of them were managers
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
60%
= 60 percent
= 60 / 100
= 0.6
The factor 0.6 of the total number of people in attendance are managers
0.6 * 30 = 18
The number of managers is 18
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calculate the mass of camphor that contains a million carbon atoms. be sure your answer has a unit symbol if necessary, and round it to significant digits.
By using Unitary method, it can be calculated that
[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]2.53 \times 10^{-17}[/tex] g of camphor
What is Unitary Method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, Unitary method will be used
Formula for Camphor = [tex]C_{10}H_{16}O[/tex]
Gram Molecular mass = [tex]12 \times 10 + 16 \times 1 + 16[/tex] = 152g
[tex]10 \times 6 \times 10^{23}[/tex] atoms of carbon is contained in 152 g of camphor
1 atoms of carbon is contained in [tex]\frac{152}{6 .023 \times 10^{24}}[/tex] g of camphor
[tex]1 \times 10^{7}[/tex] atoms of carbon is contained in [tex]\frac{152 \times 1 \times 10^7}{6 .023 \times 10^{24}}[/tex] g of camphor
[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]\frac{152 \times 1 \times 10^7}{6 .023 \times 10^{24}}[/tex] g of camphor
[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]2.53 \times 10^{-17}[/tex] g of camphor
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Convert the credit card rate to the APR. (Round your answer to the nearest percent.) Nebraska, 0.04089% daily rate
Annual percentage rate is 14.925% of credit card rate 0.04089.
Define annual percentage rate.The phrase annual percentage rate of charge (APR), which can also be referred to as a nominal APR or an effective APR (EAPR), refers to the interest rate for the entire year (annualized), as opposed to only a monthly fee or rate, as applied on a loan, home loan, credit card, etc. An annual percentage rate, or APR, is a figure that expresses the entire cost of borrowing money as a proportion of the loan's principle. An accurate picture of how much it costs to borrow money is intended to be provided by the APR on a loan or credit card.
Given,
Daily rate = 0.04089
Rate = 365
Annual percentage rate = Daily Rate% ×Rate
Annual percentage rate = 0.04089 × 365
Annual percentage rate = 14.925%
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Part (c) In words, state what your random variable X represents X represents the number of hours a woman works in a week X represents the number of women who work over 80 hours a week. X represents the average number of women who work over 80 hours a week. X represents the average number of hours women work in one week. Correct! The investigation involves the average number of hours that women work in a given week.
There is sufficient evidence to conclude that the average number of hours women work each week is more than 80 hours
The hypothesIs are
Ha : μ>80
Given the sample size n=68 and sample mean X 83 , sample standard deviation s=10
The test statistic is
t = x~ - 80/s/√n
t= 83-80/10/√68
t- 2.4738634
The P-value of the test is
P-value P(T> 2.4738634)
P-value 0.0080
When α=0.05,
Reject the null hypothesis since P-value 0.0080 a 0.05
i) The -a) 10090 two-sided confidence interval for mean based on the sample data is
{x}\pm t_{1-\α /2,n-1}\frac{s}/{√n}
Here the 95% confidence interval is
= 83 ± t1-0.05/2,67 10/V68
= (80.58,85.42)
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How could you find the length of the legs of an isosceles right triangle if you are only given the length of the hypotenuse?.
Answer:So for an isosceles right triangle with side length a , the hypotenuse has a length of a√2 . Similarly, if the hypotenuse of an isosceles right triangle has length of a , the legs have a length of a√2ora√22 each
Step-by-step explanation:
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.
FOR EXAMPLE What is the length of the legs of an isosceles right triangle if the hypotenuse is 8 units?
2 Answers By Expert Tutors. For an isoceles right trangle, the legs each have length x and the hypotenuse has length x √2. Therefore, since the hypotenuse has length 8√2, the legs must each be of length 8.
Why is the treaty important?.
A Treaty is important because it settled downs the global issues with diplomatic approach.
A treaty is an agreement between two countries with the set of rules defining the responsibilities and obligations for the countries.
Some issues which are not only important for the country but also for the issues which need attention globally.
A Treaty can be made for any purpose. It is stabilizes the relationship between two countries in a diplomatic manner without the unnecessary loss of resources and valuable human life.
A Treaty is a long term solution for the problems.
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Which of the following correctly states the relationship between SST (total sum of squares), SSB (sum of squares between), and SSW (sum of squares within)?
SST = SSB + SSW
The relationship between SST, SSB and SSW is SST = SSB + SSW
The SSW is stands for sum of squares within and the SSW is defined as the sum of squared differences between a number and its sample mean for all numbers
The SSB stands for sum of squares between and the SSB is defined as the the sum of squared differences between a value and the grand mean.
The SST stands for the the total sum of squares and SST is defined as the the squared differences between the observed dependent value and the mean
The total sum of squares is the sum of the sum of squares between and the sum of square within
Therefore
SST = SSB + SSW
Hence, the relationship between SST, SSB and SSW is SST = SSB + SSW
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When the image is larger than the pre-image the scale factor would be larger than 1?.
If the scale factor is greater than 1, the image is larger than the preimage
What are dilations?A transformation called dilatation alters a figure's size without altering its shape. A figure might become bigger or smaller due to dilation. The initial figure in dilatation is referred to as the preimage. The image is an enlarged figure. The center of dilatation is a fixed location from which figures are distorted.
What are reductions and enlargements?The scale factor specifies how much smaller or larger the picture will be when you dilate a figure.
• The picture is smaller than the preimage when the scaling factor is between 0 and 1. Reductions are referred to as dilations with scale factors between 0 and 1.
• The picture is larger than the preimage if the scale factor is greater than 1. Enlargements are defined as a dilation with a scale factor greater than 1. The prime sign, ', can be used to identify each new point in a dilated figure. For instance, point ', which stands for "prime," would be the dilated image of point.
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y = (2x + 3)(x - 1)(x - 4)
Give the:
a. leading term
b. leading coefficient
c. degree of polynomial
d. end behavior
e. turning point
f. x-intercept
g. y-intercept
h. sketch the graph
Answer:
Step-by-step explanation:
y = (2x^2-2x+3x-3)(x-4)
y = (2x^2+x-3)(x-4)
y = 2x^3+x^2-3x-8x^2-4x+12
y = 2x^3-7x^2-7x+ 12
a : 2x^3
b : 2
c : 3
d
lim x-> +oo x^3(2-7/x-7/x^2 + 12/x^3)
lim x-> +oo +oo(2-7/oo - 7/oo + 12/oo)
lim x->+oo +oo(2-0-0+0)
lim x->+oo +oo
lim x-> -oo x^3(2-7/x-7/x^2 + 12/x^3)
lim x-> -oo -oo(2-7/-oo - 7/-oo + 12/-oo)
lim x-> -oo -oo(2-0-0+0)
lim x-> -oo -oo
e
y = 2x^3-7x^2-7x+ 12
y’ = [2(x+h)^3 - 7(x+h)^2 - 7(x+h) + 12 - 2x^3 +7x^2 + 7x - 12]/h
y’ = [2(x^3+h^3+3x^2h+3h^2x) -7(x^2+h^2+2xh)-7x-7h-2x^3+7x^2+7x]/h
y’ = [2x^3+2h^3+6x^2h+6h^2x-7x^2-7h^2-14xh-7h-2x^3+7x^2]/h
y’ = [2h^3+6x^2h+6h^2x-7h^2-14xh-7h]/h
y’ = h (2h^2 + 6x^2 + 6hx - 7h - 14x - 7)/h
y’ = 2h^2 + 6x^2 + 6hx - 7h - 14x - 7
lim h->0 (6x^2 - 14x - 7)
y’ = 6x^2 - 14x - 7
y’’ = [6(x+h)^2 - 14(x+h) - 7 - 6x^2 + 14x + 7]/h
y’’ = [6(x^2+h^2+2xh) -14x-14h -6x^2+14x]/h
y’’ = [6x^2+6h^2+12xh-14h-6x^2]/h
y” = h(6h+12x-14)/h
y” = 6h + 12x - 14
lim h->0 (12x-14)
y” = 12x -14
12x - 14 = 0
6x - 7 = 0
x = 7/6
(2 *7/6+3)(7/6-1)(7/6-4)
(7/3 + 3) ( 1/6) (-17/6)
(16/3)(-17/36)
4/3 * -17/9
-68/27
turning point (7/6 ; -68/27)
f
(2x + 3)(x - 1)(x - 4) = 0
x = -3/2
x = 1
x = 4
A( -3/2,0)
B (1,0)
C (4,0)
g
y= 12
D (0, 12)
Answer:
a. 2x³
b. 2
c. 3
d. As x → -∞, f(x) → -∞. As x → ∞, f(x) → ∞.
e. (-0.4, 13.6) and (2.8, -18.6).
f. (-1.5, 0), (1, 0), (4, 0)
g. (0, 12)
h. See attachment.
Step-by-step explanation:
Given polynomial:
[tex]y=(2x+3)(x-1)(x-4)[/tex]
Leading term and Leading coefficient
The given polynomial is in factored form.
To find the leading term and the leading coefficient, simply multiply the variable terms of the factors:
[tex]\implies 2x \cdot x \cdot x = 2x^3[/tex]
Therefore:
Leading term = 2x³Leading coefficient = 2Degree of the polynomial
The degree of the polynomial is the exponent of the leading term.
Therefore, the degree of the given polynomial is 3.
End behaviour
As the degree of the polynomial is odd and the leading coefficient is positive, the end behaviour of the function is:
As x → -∞, f(x) → -∞As x → ∞, f(x) → ∞Turning points
The x-values of the turning points are when the derivative of the function equals zero.
Expand the polynomial:
[tex]\implies y=(2x+3)(x-1)(x-4)[/tex]
[tex]\implies y=(2x+3)(x^2-5x+4)[/tex]
[tex]\implies y=2x^3-10x^2+8x+3x^2-15x+12[/tex]
[tex]\implies y=2x^3-7x^2-7x+12[/tex]
Differentiate:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=6x^2-14x-7[/tex]
Set it to zero and solve for x:
[tex]\implies 6x^2-14x-7=0[/tex]
Solve using the quadratic formula:
[tex]\implies x=\dfrac{-(-14) \pm \sqrt{(-14)^2-4(6)(-7)}}{2(6)}[/tex]
[tex]\implies x=\dfrac{14 \pm \sqrt{364}}{12}[/tex]
[tex]\implies x=\dfrac{14 \pm 2\sqrt{91}}{12}[/tex]
[tex]\implies x=\dfrac{7\pm \sqrt{91}}{6}[/tex]
[tex]\implies x \approx-0.4, \;2.8\; \; \sf (1\;d.p.)[/tex]
Substitute the found values of x into the original polynomial to find the y-values of the turning points:
[tex]x=\dfrac{7- \sqrt{91}}{6}\implies y=13.6\; \; \sf (1\;d.p.)[/tex]
[tex]x=\dfrac{7+ \sqrt{91}}{6}\implies y=-18.6\; \; \sf (1\;d.p.)[/tex]
Therefore, the turning points of the polynomial (to the nearest tenth) are:
(-0.4, 13.6) and (2.8, -18.6)x-intercepts
The x-intercepts are when the function equals zero.
As the function is already in factored form, simply equal each of the factors to zero and solve for x:
[tex]\implies (2x+3)=0 \implies x=-1.5[/tex]
[tex]\implies (x-1)=0 \implies x=1[/tex]
[tex]\implies (x-4)=0 \implies x=4[/tex]
Therefore, the x-intercepts are:
(-1,5, 0), (1, 0), (4, 0)y-intercept
The y-intercept when x = 0:
[tex]\implies y=(2(0)+3)(0-1)(0-4)[/tex]
[tex]\implies y=3 \cdot -1 \cdot -4[/tex]
[tex]\implies y=12[/tex]
Therefore, the y-intercept is:
(0, 12)Sketch the graph
To sketch the graph:
Plot the x-intercepts (-1.5, 0), (1, 0) and (4, 0).Plot the y-intercept (0, 12).Plot the turning points (-0.4, 13.6) and (2.8, -18.6).Begin the curve in quadrant III, pass through the first x-intercept to the first turning point.Change direction, pass through the y-intercept, the second x-intercept and to the second turning point.Change direction, pass through the third x-intercept and continuing towards ∞ in quadrant I.In 2012, there were approximately 980 thouand
retaurant in the United State. In 2016, there
were 1046 thouand retaurant. A. Write an equation decribing the relationhip
between time and the number of retaurant. Ue
ordered pair of the form (year pat 2012, number
of retaurant in thouand). B. Ue thi equation to predict the number of eating
etablihment in 2018
In 2018 there are 1079 restaurants using the equation y=980+16.5x .
What is equation?
In algebra, in its simplest form, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x 5 = 14 is an equation where 3x 5 and 14 are two terms separated by an equal sign. There are two types of equations: identities and conditionals. Equality applies to all values of the variable. A conditional expression applies only to specific values of a variable. Equations are written as two expressions joined by an equal sign ("=").
Here restaurants in the United States is ,
=> 2012 = 980
=> 2016 = 1,046
Here in 4 years difference (2016 - 2012),
=> 1046-980 = 66 more restaurants .
Then in 4 years = 66 restaurants, Then
In 1 year = 66/4 = 16.5 .
Now slope m = 16.5
The order pair of the relationship between years and restaurants ,
(0, 980) and (4, 1,046)
Now the equation ,
=> y = 980+16.5 x
where Y = number of restaurants in one year
x = number of years in the past.
Number of restaurants in 2018,
=> Y = 980 + 16.5x
Years 2018-2012 = 6 years
Forecast number of restaurants,
=> Y = 980 + 16.5(6)
=> 1,079
Therefore the equation is y=980+16.5x and In 2018 there are 1079 restaurants.
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Diego then says if we take half of the first number and double the second the sum is 14.
The equation for the given phrase is 1/2(x)+2y=14.
Given that, Diego then says if we take half of the first number and double the second the sum is 14.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the first number be x and the second number be y.
Now, half of the first number and double the second the sum is 14
So, 1/2(x)+2y=14
Hence, the equation for the given phrase is 1/2(x)+2y=14.
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You win the Publishers Clearing House Sweepstakes. You can choose between getting a lump sum of $7,275,806 now or getting $900,0000 every year for 10 years, starting one year from now. If you take the money now and invest it, you'll expect to earn an annual return of 4% BAttempt 1/10 for 10 pts Part 1 Which option should you take? To compare the two options, first find out what is the 10 yearly payments worth to you as of today? No decimals Submit
The 10 yearly payments worth is $ 7299806.
The current value of a future sum of money or stream of cash flows at a certain rate of return is known as present value (PV). A discount rate or the interest rate that could be earned if invested is added to the future value for present value.
it is given that
PMT =$ 900000
Rate = 4%
years = 10
using the formula
PV = [tex]A * \frac{1 - \frac{1}{(1+R)^{N} } }{R}[/tex]
PV = (900000/0.04) × (1 - (1/ (1+0.04)^10))
PV = $ 7299806
the payment you receive today is $7299806
so, it is better to accept 10 annual payments as it has a higher value.
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I am having trouble finding 2 square roots to estimate the square root of 10. Can someone please help me?
Answer:
sqrt9 and sqrt16
Step-by-step explanation:
Since you're trying to find the sqrt10, find a perfect square less than 10 and another perfect square greater than 10.
sqrt9 is 3. And sqrt16 is 4. So the estimate of sqrt10 is much closer to sqrt9.
sqrt10 ~= 3.2
