If function 'f' is defined by f(x)=2-x and 2f(p)=8 then the value of f(2p) is 6.
Given, f(x) = 2-x
Solve this problem by making a series of substitutions.
First, find the value of p.
Then use the definition of the function f to find the value of f(2p).
We are given
f(x) = 2 - x
Multiply both sides by 2, and simplify.
2f(x) = 2(-x +2)
2f(x) = -2x + 4
Let x = p.
2f(p) = -2(p) + 4
We are given that 2f(p) = 8.
Substitute 20 for 2f(p).
8 = -2p + 4
2p = -4
p = -2
Now we know that p = -2, so we can find f(2p).
f(x) = -x + 2
f(2p) = -2p + 2
Substitute -2 for p.
f(2p) = -2(-2) + 2
f(2p) = 4 +2
f(2p) = 6
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The triangles are similar. Find the value of the variable.
PLEASE HELP MEEEEe
jhchnthnht
The equation of the perpendicular bisector of BC with B(-2, 1), and C(4, 2) is y = 7.6 - 6•x
Which method can be used to find the equation of the perpendicular bisector?The slope, m, of the line BC is calculated as follows;
m = (2 - 1)/(4 - (-2)) = 1/6The slope of the perpendicular line to BC is -1/(1/6) = -6
The midpoint of the line BC is found as follows;
[tex] \left( - 2 + \frac{4 - ( - 2)}{2}, \: 1 + \frac{2 - 1}{2} \right) = (1,\: 1.5)[/tex]
The perpendicular bisector is the perpendicular line constructed from the midpoint of BC.
The equation of the perpendicular bisector in point and slope form is therefore;
(y - 1.5) = -6•(x - 1)
y - 1.6 = -6•x + 6
y = -6•x + 6 + 1.6 = 7.6 - 6•x
Which gives;
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1. Find the pattern in this sequence. Then write
the next three terms in the sequence.
5,2,1,...
Answer:
-1,-3,-4 it is just subtracting the same amount.
Step-by-step explanation:
Of the 17 students in a programming class, 6 own 1 computer, 3 own 2 computers, 3 own 3 computers, 2 own 4 computers, and 3 own 5 computers
The median number of computers owned by the 17 students is 2.
What is median in statistics?A dataset's median represents the midpoint; half of the data points are smaller and half are greater than the median.
Identifying the median: The data points should be arranged from smallest to largest. The median is the middle data point in the list if the number of data points is odd.
The total number of students are 17.
The data can be arranged in the following table
number of students number of computers
6 1
3 2
3 3
2 4
3 5
Arrange the given frequencies in the increasing order-
1 1 1 1 1 1 2 2 2 3 3 3 4 4 5 5 5
The middle term of the arrange frequencies is 17/2 = 8.5
Median = (8 term + 9 term)/2
= (2 + 2)/2
= 2
Therefore, the median number of computers owned by the 17 students is 2.
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The correct question is -
Of the 17 students in a programming class, 6 own 1 computer, 3 own 2 computers, 3 own 3 computers, 2 own 4
computers, and 3 own 5 computers. What is the median number of computers owned by the 17 students?
Segment AB has point A located at (4, 2). If the distance from A to B is 3 units, which of the following could be used to calculate the coordinates for point B? (5 points) 3 = square root of the quantity of x minus 2 all squared plus y minus 4 all squared 3 = square root of the quantity of x minus 4 all squared plus y minus 2 all squared 3 = square root of the quantity of x plus 2 all squared plus y plus 4 all squared 3 = square root of the quantity of x plus 4 all squared plus y plus 2 all squared
Applying the distance formula, to calculate the coordinates of B, use: 3 =√[(x-4)² + (y-2)²]
What is the Distance Formula?The distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], is used to find the distance between two points on a coordinate plane.
We are given one point A(4, 2), let:
B (x, y) = (x2, y2)
A(4, 2) = (x1, y1)
d = 3 units
Plug in the values into the distance formula to find how to calculate the coordinates of B:
3 =√[(x-4)² + (y-2)²]
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can someone help me with answer C? its the last one i need
Using the monthly payment formula, it is found that her down payment should be of $1,419.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are:
A = 250, r = 0.072, n = 72.
Hence:
r/12 = 0.072/12 = 0.006.
We solve for P to find the total amount of the monthly payments, hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]P\frac{0.006(1.006)^{72}}{(1.006)^{72}-1} = 250[/tex]
0.0171452057P = 250
P = 250/0.0171452057
P = $14,581.
The total payment is of $16,000, hence her down payment should be of:
16000 - 14581 = $1,419.
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In the diagram AB/BC = AD/DE
Substitute the known values into the proportion and solve for DE
Answer:
[tex]\huge\boxed{\sf DE = 9}[/tex]
Step-by-step explanation:
From the figure,
AB = 2
BC = 3
AD = 6
Substitute in the given formula
[tex]\displaystyle \frac{AB}{BC} =\frac{AD}{DE} \\\\\frac{2}{3} = \frac{6}{DE} \\\\Cross \ Multiply \\\\2 \times DE = 6 \times 3\\\\2DE = 18\\\\Divide \ 2 \ to \ both \ sides\\\\DE = 18/2\\\\DE = 9\\\\\rule[225]{225}{2}[/tex]
Margie is practicing for an upcoming tennis tournament. Her first serve is good 20 out of 30 times on average. Margie wants to know the estimated probability that her first serve will be good at least four of the next six times she serves. How could she design a simulation for this scenario
Probability that Margie's first serve will be good at least four of the next six times she serves is 0.68
What is Binomial Distribution in Probability?
Assume that n independent replications of a random experiment with exactly two outcomes are performed. Success has a probability of [tex]p[/tex], while failure has a probability of [tex]q[/tex]. Assume that out of these n times, we will experience success [tex]x[/tex] times and failure [tex]n-x[/tex] times. There are [tex]^nC_x[/tex] different ways in which we can succeed. If, [tex]X[/tex] has a binomial distribution, then,
[tex]P(X=x)=p(x)[/tex]
[tex]=[/tex] [tex]^nC_xp^xq^{n-x}[/tex]
for [tex]x[/tex] = 0, 1,..., n. Here, [tex]q=1-p[/tex]. A binomial variate is any such random variable [tex]X[/tex]. A group of n separate Bernoullian trials is known as a binomial trial. Binomial distribution requirements:
There are just two outcomes, success and failure, for each trial.The quantity "[tex]n[/tex]" of trials is finite.The trials run separately from one another.For each trial, the odds of success [tex]p[/tex], or failure [tex]q[/tex], remain constant.
Given,
Probability of good serves = Success
⇒ [tex]p=\frac{20}{30}[/tex]
⇒[tex]p=\frac{2}{3}[/tex]
Failure = [tex]q[/tex]
⇒ [tex]q=1-p[/tex]
⇒ [tex]q=1-\frac{2}{3}[/tex]
⇒ [tex]q=\frac{1}{3}[/tex]
Number of trials [tex]= n[/tex]
[tex]n=6[/tex]
Probability of at least four good serve = [tex]P(4 < X < 6)[/tex]
According to the binomial distribution,
Therefore,
[tex]P(4 \leq X \leq 6)=P(X=4)+P(X=5)+P(X=6)[/tex]
[tex]=[/tex] [tex]^6C_4(\frac{2}{3}) ^4(\frac{1}{3})^2+ ^6C_5(\frac{2}{3}) ^5(\frac{1}{3})^1+^6C_6(\frac{2}{3}) ^6(\frac{1}{3})^0[/tex]
[tex]=[/tex] [tex]15\times\frac{16}{729} +6\times\frac{32}{729} +1\times\frac{64}{729}[/tex]
[tex]=[/tex] [tex]\frac{496}{729}[/tex]
[tex]= 0.68[/tex]
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A saleslady is paid a commission of 3% on goods worth 100,000.she is also paid a salary of 11000.in a certain month she sold 360 shoes at460 each.the following month she had a salary increase of 20%.her total earnings were 22,200 calculate total amount of money received from sales of shoes that month
The total amount of money received from sales of shoes that month = $4968
Calculating sales commissionSalary = $11000
Number of shoes sold = 360
Cost of 1 shoe = $460
Total cost of shoes sold = 360 x 460
Total cost of shoes sold = $165600
Since $165600 is greater than $100000, she will earn a commission of 3%
Commission = (3/100) x $165600
Commission = $4968
The commission is the amount of money received from sales of shoes. Other earnings are salary or increment
Therefore, the total amount of money received from sales of shoes that month = $4968
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Geometry: Write a formal proof, ASAP!!!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex] \sf \: \angle1 \cong \angle3[/tex][tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \: \angle1 \cong \angle2[/tex]
( by corresponding angle pair )
[tex]\qquad❖ \: \sf \: \angle2 \cong \angle3[/tex]
( given in the question )
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \angle1 \cong \angle3[/tex]
witch is a value of a perfect square
Answer:
it depends.
Step-by-step explanation:
A perfect square is a number that can be expressed as the product of an interger by itself or as the second exponent of an interger. For example, 25 is a perfect square because it is the product of interger 5 by itself, 5 × 5 =25.
If point E is the midpoint of and point D is the midpoint of , which expression represents the value of s
The length of ED is half the length of AB.
What is the length?Distance is measured by length. Length is a quantity with the dimension distance in the International System of Quantities. Most measurement systems use a base unit for length from which all other units are derived. The meter is the foundation unit of length in the International System of Units.Reasons:
The given parameters are;
In ΔABC, point E is the midpoint of AC
The midpoint of BC is the point D
Segment ED = s
Segment CE = p
Segment EA = r
Segment CD = q
Segment DB = t
Segment ED = s
Segment AB = u
Required:
The expression that represents the value of [tex]s[/tex].
Solution:
CE = 0.5 × AC Definition of midpoint
CD = 0.5 × CB Definition of midpoint
Therefore, we have;
[tex]\frac{CE}{AC} =\frac{CD}{CB} =0.5[/tex]
Therefore, given that ∠C ≅ ∠C, by the reflexive property, we have;
ΔABC is similar to ΔCDE by Side-Angle-Side similarity
Which gives;
[tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} =0.5=\frac{1}{2}[/tex]
ED = s and AB = u which gives;
[tex]\frac{ED}{AB}=\frac{s}{u} =0.5=\frac{1}{2}[/tex]
[tex]\frac{s}{u} =\frac{1}{2}[/tex]
Which gives:
[tex]s=\frac{1}{2} *u[/tex]
The expression that represents the value of s is; s = one-half u
Therefore, the length of ED is half the length of AB.
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The question you are looking for is here:
If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of s? triangle CAB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED, CE equals p, EA equals r, CD equals q, DB equals t, ED equals s, and AB equals u s equals p over q s = one half s equals q over p s = 2u
Convenience sampling Multiple Choice is the same as simple random sampling. ensures that samples are representative of the population. is an unbiased sampling method. collects sample information from groups that are easy to obtain.
Option (d) is correct. Convenience sampling collects sample information from easy-to-collect groups.
Given convenient sampling.
Convenience sampling is defined as a method adopted by researchers in which they collect market research data from a pre-existing group of respondents. This is the most commonly used sampling technique because it is extremely fast, simple and economical. In many cases, members are easily accessible to be part of the template. It is non-probability sampling and therefore different from random sampling. Since the samples are taken for convenience, the samples are not always representative of the population and therefore have bias. In this case, people were sampled simply because they were convenient.
Thus, convenience sampling collects sample information from easy-to-collect groups.
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A cylinder with a base diameter of x units has a volume of πx3 cubic units. a cylinder with a base diameter of x units has a volume of pi x cubed cubic units. which statements about the cylinder are true? select two options.
The height of the cylinder is 4 x units.
The area of the cylinder’s base is One-fourthπx2 square units .
What is the volume of cylinder?
We know the volume of a cylinder is given by the formula π r2 h, where r is the radius of the cylinder and h is the height.
Formula for volume of the cylinder
V = r² π h
Volume of the cylinder= πx³
Diameter=x
Radius (r)=diameter/2
r = x/2
V = r² π h
πx³=(x/2)² πh
πx³= (x²/4)πh
Divide both sides by π
x³ =(x²/4)h
Make h the subject of the formula
h = x³ ÷ x²/4
=x³ ×4 / x²
=4x³ / x²
=4 * x * x * x / x * x
h=4x
Area of the base:
B = r² π
r=x/2
B=(x/2)² * π
=(x²/4)π
=πx²/4
=1/4(πx²)
Therefore, The area of the cylinder’s base is One-fourthπx2 square units.
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The complete question is -
A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.
Write the equation of the line which passes through (5, −2) and (3, 4) in standard form.
The equation of the line is 3x + y = 1
How to determine the equation of the line?The points are given as:
(5, −2) and (3, 4)
Start by calculating the slope (m)
m =(y2 - y1)/(x2 - x1)
This gives
m = (4 + 2)/(3 - 5)
Evaluate
m = -3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = -3(x + 2) +5
So, we have:
y = -3x - 6 + 5
Evaluate the like terms
y = -3x - 1
Rewrite as:
3x + y = 1
Hence, the equation of the line is 3x + y = 1
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Determine the missing digit (denoted with*) for the American Express Traveler's Check identification number 783920*814 a) 3
b) 2
c) 6
d) 9
The missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.
In this question,
A Check Digit is a decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.
A check digit is a digit added to a string of numbers for error detection purposes. Normally, the check digit is computed from the other digits in the string. A check digit helps digital systems detect changes when data is transferred from transmitter to receiver.
The last digit of a bar code number is a calculated check digit. The check digit is calculated from all the other numbers in the bar code and helps to confirm the integrity of your bar code number.
The American Express Traveler's Check identification number is 783920*814.
In Airline tickets, there are several digits plus a check digit.
Divide the ID number by 7. The check digit is the remainder.
Sum of digits = 7+8+3+9+2+0+8+1+4
⇒ 42
Now divide the sum by 7, the remainder is
⇒ 42 mod 7 = 42 - (5×7)
⇒ 42 mod 7 = 6
Hence we can conclude that the missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.
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The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.
Using the z-distribution, it is found that the 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).
If we had increased the confidence level, the margin of error also would have increased.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96. Increasing the confidence level, z also increases, hence the margin of error also would have increased.
The sample size and the estimate are given as follows:
[tex]n = 450, \pi = 0.47[/tex].
The lower and the upper bound of the interval are given, respectively, by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.4239[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.5161[/tex]
The 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).
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Find the equation of a circle with center at (5, 6) and radius 8.
Answer:
(x - 5)^2 + (y - 6)^2 = 64
Step-by-step explanation:
Every circumference is in the form:
(x - xc)^2 + (y - yc)^2 = r^2
Where xc is the x of the center. Yc is the y of the center. r is the radius. We just plug in the values and we're done.
Answer:
[tex](x-5)^2+(y-6)^2=64[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
center = (a, b)radius = rGiven:
center = (5, 6)radius = 8 unitsSubstitute the given values into the formula:
[tex]\implies (x-5)^2+(y-6)^2=8^2[/tex]
[tex]\implies (x-5)^2+(y-6)^2=64[/tex]
Therefore, the equation of a circle with the given values is:
[tex](x-5)^2+(y-6)^2=64[/tex]
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What is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result?.
Distributive property is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result.
What is distributive property?Firstly, to distribute means to divide something or give a share or part of something.
Distributive property explains that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Therefore, distributive property is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result.
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1.an examination in three subjects algebra,biology ,chemistry was taken by 41 students. the following table shows how many students failed in each single subject and their various combinations: subject a b c ab ac bc abc failed 12 5 8 2 6 3 1 how many students failed at least in one subject?
(d) Percentage of viewers given they are 18 to 34 who prefer videos on a mobile or laptop device. (Round your answer to 2 decimal places.)\
52.94% of the viewers prefer videos on a mobile or laptop device
How to determine the percentage?The given parameters are
Viewers that prefer videos on a mobile or laptop device = 18
Total number of viewers = 34
The percentage of voters in this category is then calculated as
Percentage = 18/34 * 100%
Evaluate the expression
Percentage = 52.94%
Hence, 52.94% of the viewers prefer videos on a mobile or laptop device
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Suppose the risk-free rate is 3.2 percent and the market portfolio has an expected return of 9.9 percent. the market portfolio has a variance of .0282. portfolio z has a correlation coefficient with the market of .18 and a variance of .3185. according to the capital asset pricing model, what is the expected return on portfolio z?
Beta = Correlation x (Variance of Z)^0.5 / (Variance of Market)^0.5
Beta = 0.18 x (0.3185)^0.5 / (0.0282)^0.5
Beta = 0.604927
CAPM equation:
Expected return = Risk free rate + Beta x (Market return - Risk free rate)
Expected return = 3.2% + 0.604927 x (9.9% - 3.2%)
Expected return = 7.25% is the answer.
Portfolio return refers to the return or loss realized on an investment portfolio that includes multiple types of investments. The portfolio is intended to provide returns based on the defined objectives of the investment strategy and the risk tolerance of the type of investor covered by the portfolio.
The basic formula for expected return is to multiply the weight of each asset in the portfolio by the expected return and then add up all these numbers. In other words, the expected return of a portfolio is a weighted average of the returns of the individual components.
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PLEASE HELP ME THIS IS MY LAST DAY TO GET THIS DONE!!!!! ILL MARK BRAINLY
The expression that is not a rational expression is:
[tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex]
What is a rational expression?A rational expression is an expression that has a variable in the denominator.
For expression [tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex], x + 3 is a common term to the numerator and denominator, hence it is simplified to 2x - 1 and is not a rational expression.
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The option that is not a rational expression is [tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]
How to find rational expression?Rational expression are fraction whose numerator and denominator are polynomials.
In other words, rational expression is the ratio of two polynomials.
Therefore, an example of a ration expression is as follows:
[tex]\frac{x^{2}+9 }{x + 1}[/tex]
Therefore, the option that is not a rational expression is as follows;
[tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]
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how much would 500 invested at 4% interest compounded continuously be worth after 7 years? round your answer to the nearest cent
Answer: the answer is 661.55
Step-by-step explanation:
interest formula: F = Pe^(rt)
Compare the theoretical probability to the experimental probability of landing on H.
The correct statement comparing the theoretical and experimental probabilities is given as follows:
[tex]\frac{1}{4} < \frac{7}{25}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:
T(H) = 1/4.
The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:
E(H) = 28/100 = 7/25.
Hence the correct statement is:
[tex]\frac{1}{4} < \frac{7}{25}[/tex].
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what is the mode of 250 100 75 200 150 100?
[tex]\textbf{Heya !}[/tex]
the mode is the number that occurs the most
All numbers here occur once, except [tex]\sf{100}[/tex].
so 100 is the mode.
`hope it was helpful to u ~
If BE−→− bisects ∠ABD and m∠ABD = 66°, find m∠ABE.
Answer:
∠ABE = 33°
Step-by-step explanation:
Angle bisector:Angle bisector is a straight line that divides the angle into two congruent (equal) angles.
So, BE bisects the ∠ABD into two equal angles.
⇒∠ABE will be half of ∠ABD
∠ABD = ∠ABE + ∠BED
66° = ∠ABE + ∠ABE
66 = 2∠ABE
∠ABE = 66/2
∠ABE = 33°
A rectangular pen has a length 4 feet greater than its width. Find the area
A. x+4
b. x^2+4x
c. 4x
d. x^2+8x+16
Answer:
b. x^2+4x
Step-by-step explanation:
So since you don't know the width, you can just represent it as a variable, and in this case that variable will be "x". Now using this variable we can use it to represent the length since there is a relationship between the width and length which is given. Since the length is 4 feet greater than the width, we can represent the length as (x+4). Now to find the area, we simply multiply the length * width, which is x * (x+4) = x^2 + 4x
Help me please help me fast
The value of [tex]f^{-1}(49)[/tex] is 4
Inverse of a function
The given function is:
[tex]f(x)=(x+3)^2[/tex]
Let f(x) be represented by y
[tex]y=(x+3)^2[/tex]
Make x the subject of the formula
[tex]\sqrt{y} =x+3[/tex]
Subtract 3 from both sides
[tex]x=\sqrt{y} -3[/tex]
Replace x by [tex]f^{-1}(x)[/tex] and let y be replaced by x
[tex]f^{-1}(x)=\sqrt{x} -3[/tex]
Substitute x = 49 into the inverse function
[tex]f^{-1}(x)=\sqrt{49} -3\\\\f^{-1}(x)=7-3\\\\f^{-1}(x)=4[/tex]
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What is the slope of the line shown below?
(-1,-4)
(2, 2)
Answer:
2
Step-by-step explanation:
(-1,-4) (2,2)
To find the slope, use the equation y2-y1/x2-x1
2-(-4)/2-(-1) = 6/3
6/3=2
2 is the slope.