n(n+1)(n+5) can be a multiple of 3.
Utilizing the mathematical induction formula for any n > N, we are going to demonstrate it.
P(n) = n(n+1) n(n+5) = 3d, where d N
P(1)=1(2)(6)=12, that is cleavable by three, for n=1.
Suppose P(k) is true.
Where m N k three +6k a pair of +5k=3m k, P(k)=k(k+1)(k+5)=3m.
3\s =−6k \s2\s −5k+3m
We will currently demonstrate that P(k+1) is true.
P(k+1)=K+1, K+2, K+6, K 3 +9 K 2, K twenty K + twelve
When we plug the worth of k three into the equation on top of, we tend to get 3m6k a pair of 5k)+9k a pair of +20k+12 =3.
m+3k \s2\s +15k+12\s=3
(m+k \s2\s +5k+4)
in which r=m+k a pair of + 5k + four
P(k+1) is often true since P(k) is often true.
Therefore, in step with the induction principle, P(n) is cleavable by three for all n N.
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HELP ASP show your work please
Answer: 8 days
Step-by-step explanation:
1) Set up an equation. Let x be the day
3,500 >= 2(816) + x(100+95)
The 816 is just two times (Plane ticket back and forth) so it doesn't go into the x. 100 and 95 do as it is one day.
2) Solve the equation
3,500 >= 2(816) + x(100+95)
1868 >= 195x
9.57 >= x
3) Rounding
Since the x has to be less than 9.57, our next option is 8
Which of the following is NOT Linear/does not increase at a constant rate?
Answer: The one that starts with (-4,10)
Step-by-step explanation:
Linear means that the numbers are going up at a constant rate. It means, that the y will go up corrosponding x.
1) Linear
X goes up 2 per 4 y
2) Linear
X goes up 1 per 3y
3) Linear
X goes up 2 per 4y
4) Not Linear
X goes up 2 per Unequal growth y.
You can tell because it goes up by +5 until the last where it goes up +7
The table on the right gives the annual income for eight families, in thousands of dollars.Find the mean and standard deviation for family incomo.Family A B C D E F G HIncome 47 42 44 45 43 45 48 46The mean of the data set is thousand dollars. (Round to three decimal places as needed)
We can compute the mean by;
[tex]\operatorname{mean}=\frac{47+42+44+45+43+45+48+46}{8}=45[/tex]and the standard deviation by;
[tex]\frac{\sum ^{}_{}(x-\operatorname{mean})^2}{\sum ^{}_{}f}=\frac{28}{8}=3.5[/tex]So the mean of the data set is 45.
The standard deviation is 3.5
Arturo asked all of his classmates if they prefer soccer or football. He found that 16 students prefer football while 20 prefer soccer. Which ratio represents the number of students who prefer soccer to the total number of students in Arturo's class? 5 4 4 Mark this and return Save and Exit Next Submit J ContentViewers/AssessmentViewer/Activity#
The number of students who prefer soccer to the total number of students in Arturo's class is represented by:
16:20
Dividing by 4 on each side of the proportion we have
4:5
Final answer is: 4:5
Analyze the solution. If there is an error, circle the error and show the correct solution
Notice that on the second step, we have the following:
[tex]\begin{gathered} -2(x-7)=6 \\ +2\text{ +2} \end{gathered}[/tex]in this case, the -2 is multiplying x-7, then to eliminate it, we have to divide by 2 both sides of the equation.
if we divide by -2, we have the following:
[tex]\begin{gathered} -2(x-7)=6 \\ \Rightarrow x-7=\frac{6}{-2}=-3 \\ \Rightarrow x-7=-3 \end{gathered}[/tex]finally, if we add7 on both sides, we get:
[tex]\begin{gathered} x-7+7=-3+7 \\ \Rightarrow x=4 \end{gathered}[/tex]therefore, x = 4
Suppose ΔPQR is rotated 270° about the origin, (0,0). Find the coordinates of P′, Q′, and R′. Then sketch ΔP′Q′R′.
In case it is a 270º Counter-clockwise rotation:
P'(3,-3), Q'(5,-5), R'(6,-3)
In case it is a 270º Clockwise rotation:
P'(-3, 3), Q'(-5,5), R'(-6,3)
1) Since in this case, there is a 270º rotation about the origin then we can write out the following:
As there is no mention of the direction then we'll do it for both cases.
2) For a 270º Counter-Clockwise rotation
Pre-image rule Image
P(3,3) (x,y)=(y,-x) P'(3,-3)
Q(5,5) Q'(5,-5)
R(3,6) R'(6,-3)
3) For a Clockwise Direction
Pre-image rule Image
P(3,3) (x,y)=(-y,x) P'(-3, 3)
Q(5,5) Q'(-5,5)
R(3,6) R'(-6,3)
Question 4Scott is constructing a taste of values that satisfies the definition of function.InpertOutput20320O16Which number could be placed in the empty cell so that the table of values satisfies the definition of afunction?
Remember that
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
so
in this problem
the input value must be 3
answer is option CRachel and Nicole are training to run a half-marathon. Rachel begins by running 30 minutes on the first day of training. Each day she increases the time she runs by 3 minutes. Nicole’s training follows the function f(x)=5x+30, where x is the number of days since the training began, and f(x) is the time in minutes she runs each day. What is the rate of change in minutes per day for the training program that has the slowest rate of change?
............ minutes per day
The slowest rate of change that is the slowest for the training program is: 3 minutes per day.
What is the Rate of Change of a Function?In a given function that is expressed in slope-intercept form as .f(x) = mx + b, the rate of change of the function is represented as "m", while the starting or initial value is represented as "b" in the equation.
Given that Rachel increases the time she runs by 3 minutes for each day, then, the rate of change per day for the training program or Rachel is 3.
Given that the function .f(x) = 5x + 30 represents the minutes Nicole runs per day in the training program, then the rate of change is represented as "5" in the equation. This means that each day, Nicole increases her time of running by 5 minutes as compared to 3 minutes per day that Rachel increases her daily runs.
3 minutes per day is slower than 5 minutes per day, in order words, the slowest rate of change is therefore: 3 minutes per day.
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On a horizontal number lime, -6 is located to the left of -1. Enter an inequality that represents this statment.
the expression "-6 is located to the left of -1" can be written as follow:
-6 < - 1
where the < symbol means "lower than", that is, you have "-6 is lower than -1".
Which equation is equivalent to
5x - 2(7x + 1) = 14x?
A. -9x - 2 = 14x
B. -9x + 1 = 14x
C. -9x + 2 = 14x
D. 12x 1 = 14x
Option A, -9x - 2 = 14x is the required equivalent equation for the equation 5x - 2(7x + 1) = 14x.
What are equivalent equations?
Equations with the same answer or solution are said to be equivalent. Comparisons between linear equations are common. When graphed, linear equations result in straight lines with a slope and a y-intercept. The characteristics that make a linear equation linear are crucial in establishing if two linear equations are equivalent. Although it may not seem like it at first, there are mathematical procedures to determine whether the equivalent equations will have the same solution.
To get equivalent equation of the given equation, we need to simplify it.
So, given equation
5x - 2(7x + 1) = 14x
Lets multiply -2 with 7x+1, we get
5x-14x-2=14x
it can be written as:
-9x - 2 = 14x
This is required equivalent equation.
Therefore, option A is correct answer
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Marcus just got a summer job as acashier making $8.50 an hour andhas already saved $50. If he wantsto earn at least $475 for a newcomputer, how many hours musthe work? Write an inequality andsolve.
Marcus's hourly income = $8.50
Amount that has already been saved by Marcus = $50
If Marcus wants to earn at least $475 for a new computer:
Let the amount of hours he will work to earn $475 = t
Since he earns $8.50 hourly and he already saved $475, the inequality will be of the form:
50 + 8.50t ≥ 475
8.50t ≥ 475 - 50
8.50t ≥ 425
t ≥ 425 / 8.50
t ≥ 50
Marcus must work for at least 50 hours
What value does the 4 represent in the number 347, 490
A.40
Explanation
Step 1 (with number 347 and 490)
347
the digit 7 is at one's place
digit 4 is at ten's place
and digit 3 is at hundred's place
then
[tex]347=(3\cdot100)+(4\cdot10)+(7\cdot1)[/tex]the value 4 represents is
[tex]\begin{gathered} \text{value}=4\cdot10=40 \\ \\ \text{value =40} \end{gathered}[/tex]
Answer: 40,000
Step-by-step explanation:
347800:three hundered and forty-seven thousand. Big chunugess
s
ii) A plate holds 7 cup cakes, each with a different colour icing,
and 4 brownies, each of a different size. Find the number of different
ways these 11 cakes can be arranged in a row if no brownie is next to
another brownie.
iii) A plate of biscuits holds 4 identical chocolate biscuits, 6
identical shortbread biscuits and 2 identical gingerbread biscuits.
These biscuits are all placed in a row. Find how many different
arrangements are possible if the chocolate biscuits are all kept
together.
Using the arrangements formula, the number of ways to organize the plates in each case is given as follows:
ii) No brownie next to another brownie: 570,240
iii) Chocolate biscuits kept together: 8,709,120.
What is the arrangements formula?The number of possible arrangements of a set of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In item a, if the brownies cannot be together, we have that:
In 8 of the 11 positions(combination), the arrangements will be of 4! and 4!, due to the 4 brownies and the 4 cupcakes.In the remaining 3 positions, they will be organized in 3! ways.Hence the number of ways to organize the cupcakes is:
[tex]C_{11,8} \times 4! \times 4! \times 3! = \frac{11!}{8!3!} \times 4! \times 4! \times 3! = 570,240[/tex]
In item b, the chocolate biscuits have to be kept together, hence:
The 4 biscuits can be ordered in 9 positions, from 1-4 to 9-12.In these positions, they are arranged in 4! ways.The remaining biscuits are arranged in 8! ways.Hence the number of ways that the biscuits can be arranged is:
9 x 4! x 8! = 8,709,120.
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A doctor visits her patients during morning rounds. In how many ways can the doctor visit 5 patients during the morning rounds?
The following table shows the rental charge of a room in a lodge for different number of days. Find the rate of change.
Rate of change is $35.
Define rate of change.The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time. Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in measurable parameters like average speed or average velocity calls for the knowledge of the average rate of change. The rate of change is expressed by a line's slope. It is frequently used while discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.
Given,
Table shows the rental charge of a room in a lodge for different number of days.
y₂ = 245
y₁ = 105
x₂ = 7
x₁ = 3
Rate of change = [tex]\frac{y_{2}-y_{2} }{x_{2}-x_{1} }[/tex]
Rate of change = [tex]\frac{245-105}{7 -3}[/tex]
Rate of change = 35
Rate of change is $35.
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Solve for x:
X=
76⁰
9x+1
40°
7 is the value of x, and 64° is the measure of the unknown angle.
Triangle angles of 76°, (9x+1)°, and 40° are provided.
According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.
One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.
Now, the total of a triangle's three angles equals
76°+(9x+1)°+40°= 180°
⇒ 116+9x+1 = 180
⇒ 9x + 117 = 180
⇒ 9x = 63
⇒ x = 7
So, 9x+1=64°
As a result, x is equal to 7 and the unmeasured angle is 64°.
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Simplify √50 over √2
In order to simplify this expression, we need to use the following property:
[tex]\frac{\sqrt[]{a}}{\sqrt[]{b}}=\sqrt[]{\frac{a}{b}}[/tex]So we have that:
[tex]\frac{\sqrt[]{50}}{\sqrt[]{2}}=\sqrt[]{\frac{50}{2}}=\sqrt[]{25}=5[/tex]So the answer is 5.
Graph the line with slope 2/3
passing through the point (3,-1).
The graph of the line with slope 2/3 and passing through the point (3,-1) is given by
What is an equation of the line?
An equation of the line is a way of representing the set points which form a line in coordinates system. A basic equation of line is y=mx+c
We are given the slope of line as 2/3 and the line passes through the point (3,-1)
We substitute the values in slope intercept form we get
[tex]-1=\frac{2}{3}*3 +c\\c=-1-2\\c=-3[/tex]
Substituting the value of c in the original equation we get
y=2/3x-3
Hence the plot the graph of the above equation
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A recipe Carmen is
making calls for 4 cups of milk. She has 1 liter of milk.
Her sister says she has enough milk. Is her sister
correct? Explain.
Answer:
Step-by-step explanation:
Yes, Carmen's sister is correct because 1 liter equals 4.227 (rounded) so yes carmen would have enough milk!
2. Technology required.
X
2.3
2.8
3.1
3
3.5
3.8
y
6.2
5.7
4.7
3.2
3
2.8
a. What is the equation of the line of best fit? Round
numbers to 2 decimal places.
b. What does the equation estimate for y when x is 2.3?
Round to 3 decimal places.
c. How does the estimated value compare to the actual value
from the table when x is 2.3?
The line of best fit using Desmos has the equation y = approximately y=-2.45x+11.82.When x = 2.3 y = 6.18.The residual is thus 0.02.
What is the residual value ?The line of best fit using Desmos has the equation y = approximately -2.45 x + 11.82y=-2.45x+11.82.When x = 2.3, y = about 2.45 x 2.3 + 11.82 = 6.18.The calculated difference between the expected value and the actual value is nearly 6.2 - 6.18 = 0.02. Therefore, there is hardly any difference at all. The residual is thus 0.02When x = 3, y = roughly 2.45 x 3 + 11.82, or 4.47 y = 2.45 x 3 + 11.82, or 4.47 when x = 3. Since the actual value is 3.2, the discrepancy between it and the projected value is equal to 3.2 - 4.47, or -1.27. The residual is thus 1.27.so The line of best fit using Desmos has the equation y = approximately y=-2.45x+11.82.When x = 2.3 y = 6.18.The residual is thus 0.02.To learn more about residual refer to:
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HELP
PLEAE I NEED HELP EPKPELPELPEL
Answer:
[tex]\sqrt{89}[/tex] cm
Step-by-step explanation:
use the pythagorean theorem
[tex]5^{2} +8^{2} =x^{2}[/tex]
25+64=[tex]x^{2}[/tex]
89=[tex]x^{2}[/tex]
[tex]\sqrt{89} =x[/tex]
Under his cell phone plan, Logan pays a flat cost of $58 per month and $3 per gigabyte. He wants to keep his bill under $70 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes he can use while staying within his budget
6. The net profit margin ratio for two companies is modelled by
by
8x
3x - 1
for company B where x is the number of items sold in thousands. Sam is trying
5x
2x - 3
for company A and
to decide in which company he should buy stock so he is going to compare the ratios. He
has researched both companies and he knows that each produces over 25 000 items per
month.
(C: 25)
a) He wants to find out if theywould ever have the same ratio and if so when. How would
you tell him how to find this mathematically? What should he have found as his answer
to the question?
b) Which company has a higher ratio for 30 000 items sold? What is that ratio to the
nearest thousand for both companies?
We deduce that the ratios would be the same for 2111 sales.
Consequently, it is obvious that firm B has a better ratio for 30000 sales.
What is the concept of ratio and proportion?Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
if A = B then
5x/(3x-3) = 8x/(3x-1)
24x^2 - 24x = 15x^2 - 5x
9x^2 - 19x = 0
x(9x - 19) = 0
x = 0 , not possible because zero number of sales is not possible
or
x = 19/9 thousands = approximately 2111
Therefore, we conclude 2111 sales, the ratios would be the same.
For the second part :
we substitute the value of x as 30000 in the equations to see which ratio is bigger
8*30000/3*30000-1=2.666 or 2.7
5*30000/2*30000-3=2.5
Therefore we can clearly see that the company b has a higher ratio for 30000 sales.
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I NEED HELP PLEASE!
How many books must the publisher produce and sell so that the production cost will equal the money from sales
Step by step explanation:
Assuming x as the number of books, the function of production cost is:
[tex]C(x)=45240+9.25x[/tex]And the selling price function would be:
[tex]S(x)=25.5x[/tex]For rhe production cost to be equal to the money from sales we have:
[tex]\begin{gathered} 25.5x=45240+9.25x \\ 25.5x-9.25x=45240 \\ 16.25x=45240 \\ x=\frac{45240}{16.25} \\ x=2784 \end{gathered}[/tex]Answer:
The publisher must produce 2784 books
Liam bought 6 9/8 pounds of steak. He used 2 1/18 pound of steak for a cookoutfill in each blankRounded to the closest benchmark, Liam bought ??? pounds of steak.Rounded to the closest benchmark, Liam used about ??? pounds of steak for the cookout.Liam has about ??? pounds of steak remaining after the cookout.
Given:
[tex]\begin{gathered} \text{ Amount of steak Liam bought = 6}\frac{9}{8}\text{ pounds} \\ \\ \text{Amount of steak he used = 2}\frac{1}{18}\text{ pounds} \end{gathered}[/tex]Let's answer the following rounded to the closest benchmark.
WILL GIVE BRAINLIEST
please solve using order of elimination and show work pleasse
Answer:
c. no solution
d. x = 11, y = -5
Step-by-step explanation:
c.
3x - y = 7----->3x - (3x - 2) = 7
y = 3x - 2 3x - 3x + 2 = 7
2 = 7, so no solution
d.
x + 2y = 1 ----> 3x + 6y = 3
3x + 5y = 8----> 3x + 5y = 8
-----------------
y = -5
x + 2(-5) = 1
x - 10 = 1
x = 11
What whole number n makes 6/78<1/n<5/55 true?
the expression is,
[tex]\frac{6}{78}<\frac{1}{n}<\frac{5}{55}[/tex][tex]\begin{gathered} \frac{6}{78}<\frac{1}{n} \\ n<\frac{78}{6} \\ n<13 \end{gathered}[/tex]Now,
[tex]\begin{gathered} \frac{1}{n}<\frac{5}{55} \\ \frac{1}{n}<\frac{1}{11} \\ n>11 \end{gathered}[/tex]so the number n is between 11 and 13
that is n = 12
thus, the answer is n = 12
Find the distance between the two points rounding to the nearest tenth.
(1,-3) and (-7,2)
Answer:
Length between two points is given as √(x1-x2)²+(y1-y2)², where x and y are the coordinates of the points.
Distance = √(1-(-7))²+(-3-2)²
= √8²+(-5)²
= √64+25
= √89
= 9.43
= 9.4 (nearest tenth)
Please help me help help me please help help me
1. Subtract 5 in both sides of the equation:
[tex]\begin{gathered} 5-5+2\ln (x)=4-5 \\ 2\ln (x)=-1 \end{gathered}[/tex]2. Divide both sides of the euqation into 2:
[tex]\begin{gathered} \frac{2\ln (x)}{2}=-\frac{1}{2} \\ \\ \ln (x)=-\frac{1}{2} \end{gathered}[/tex]3. Wrie the lograrithm in exponential form:
[tex]\begin{gathered} \ln (x)=b \\ x=e^b \\ \\ \\ \ln (x)=-\frac{1}{2} \\ \\ x=e^{-\frac{1}{2}} \end{gathered}[/tex]4. Use properties of powers to rewrite:
[tex]\begin{gathered} x=\frac{1}{e^{\frac{1}{2}}} \\ \\ x=\frac{1}{\sqrt[]{e}} \end{gathered}[/tex]5. Evaluate:
[tex]x\approx0.607[/tex]Then, the solution for the given equation is approximately 0.607