Answer:
1.7%
Step-by-step explanation:
We have to calculate the probability that the salesperson will make four or more sales if six sales calls are made on a given day, that is:
P (x => 4)
Therefore, we must calculate when x = 4, when x = 5, and when x = 6 and add. p = 0.2, n = 6
P (x = r) = nCr * p ^ r * (1 - p) ^ (n-r)
Also, nCr = n! / (r! * (n-r) !, now replacing:
P (x = 4) = 6! / (4! * (6-4)! * 0.20 ^ 4 * 0.80 ^ (6-4)
P (x = 4) = 15 * 0.001024 = 0.01536
P (x = 5) = 6! / (5! * (6-5)! * 0.20 ^ 5 * 0.80 ^ (6-5)
P (x = 5) = 6 * 0.000256 = 0.001536
P (x = 6) = 6! / (6! * (6-6)! * 0.20 ^ 6 * 0.80 ^ (6-6)
P (x = 6) = 1 * 0.000064 = 0.000064
now,
P (x => 4) = P (x = 4) + P (x = 5) + P (x = 6)
P (x => 4) = 0.01536) + 0.001536 + 0.000064
P (x => 4) = 0.01696 = 0.017
It means that the probability is 1.7%
Un prestigioso empresario decide repartir su herencia de S/ 176 000 entre sus tres hermanos Roberto, Luis y Armando, de manera DP al número de sus hijos e IP al monto de sus deudas. ¿Cuánto le corresponde a cada hermano?
Roberto :N° hijos 4,Monto de deudas (S/) : 2 000
Luis: N° hijos 3, Monto de deudas (S/): 6 000
Armando:N° hijos 5, Monto de deudas (S/): 8 000
Answer:
Amount received per brother based on number of children plus debt is given as
Roberto, S/ 55,333.33
Luis, S/ 46,000
Armando, S/ 74,666.67
Step-by-step explanation:
English Translation
A prestigious businessman decides to distribute his inheritance of S / 176,000 among his three brothers Roberto, Luis and Armando, DP to the number of his children and IP to the amount of his debts. How much corresponds to each brother?
Roberto: No of children 4, Amount of debts (S /): 2 000
Luis: No. of children 3, Amount of debts (S /): 6,000
Armando: No of children 5, Amount of debts (S /): 8,000
Solution
The man shares the inheritance according to the number of children per person and according to each brother's debts.
Assuming the debts are first settled,
The total debts = 2000 + 6000 + 8000 = S/ 16,000
We assume that each brother receives the respective debt amounts first, then the remaining cash is divided amongst the 3 brothers according to the number of their children.
Total amount available = S/ 176,000
total debt = S/ 16,000
Amount available less debts = 176,000 - 16,000 = S/ 160,000
There are 4, 3 and 5 children respectively for the 3 brothers.
Total number of children = 4+3+5 = 12.
Amount corresponding based on a per child basis =( S/ 160,000/12) = S/ 13,333.33
Meaning that each brother receives the following amount based on their children's sake
Roberto, 4 × S/ 13,333 = S/ 53,333.33
Luis, 3 × S/ 13,333.33 = S/ 40,000
Armando, 5 × S/ 13,333 = S/ 66,666.67
Total amount each brother then receives when the amount received due to debts are added
Roberto, 53,333.33 + 2,000 = S/ 55,333.33
Luis, 40,000 + 6,000 = S/ 46,000
Armando, 66,666.67 + 8,000 = S/ 74,666.67
To check, 55,333.33 + 46,000 + 74,666.67 = 176,000 (total inheritance!)
Hope this Helps!!!
Queremos ver como se reparte una dada suma entre 3 hermanos, siendo que tenemos unas dadas restricciones, donde debemos trabajar con relaciones directamente proporcionales e inversamente proporcionales.
Veremos que:
Roberto recibe: $112,640
Luis recibe: $28,160
Armando recibe: $35,200
Sabemos que lo que se reparte es directamente proporcional al número de hijos de cada hermano, e inversamente proporcional a las deudas de cada hijo.
Entonces, definamos las variables:
R = lo que recibe Roberto.
L = Lo que recibe Luis
A = lo que recibe Armando.
Tendremos que:
R + L + A = $176,000
directamente proporcional significa: y = k*xInversamente proporcional significa: y = k/zEntonces como lo que recibe cada hermano es directamente proporcional al número de hijos (x) e inversamente proporcional a la deuda (z) lo que cada hermano recibe será:
R = k*4/2,000L = k*3/6,000A = k*5/8,000Entonces podemos escribir:
R + L + A = $176,000
k*4/2,000 + k*3/6,000 + k*5/8,000 = $176,000
k*(4/2,000 + 3/6,000 + 5/8,000) = $176,000
k*(0.003125) = $176,000
k = $176,000/(0.003125) = $56,320,000
Ahora que conocemos el valor de k, podemos calcular lo que cada hermano recibe:
R = $56,320,000*(4/2,000) = $112,640
L = $56,320,000*(3/6,000) = $28,160
A = $56,320,000*(5/8,000) = $35,200
Si quieres aprender más, puedes leer:
https://brainly.com/question/18365407
Here It Is !!
More Otw
Answer:
3
Step-by-step explanation:
0 pairs mean when two "boxes" add together to make 0. For the x's we only have one because x + (-x) = x - x = 0. For the other ones we have two (the + means 1 and the - means -1) because 1 + (-1) = 1 - 1 = 0. Therefore the answer is 1 + 2 = 3.
Help me solve the equivalent expression (4x+2)-3x+5
Answer:
X+7
Step-by-step explanation:
Remove the parentheses:
4x+2-3x+5
Collect like terms:
4x-3x=x
2+5=7
Solution:
X+7
Hey there!
(4x + 2) - 3x + 5
= 4x + 2 - 3x + 5
COMBINE the LIKE TERMS
= (4x - 3x) + (2 + 5)
= 4x - 3x + 2 + 5
= 1x + 7
= x + 7
Therefore, your answer is: x + 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Let f(x)=−9x+1. Match the function with the description.
The graph of g is a reflection in the y-axis of the graph of f.
The graph of g is a reflection in the x-axis of the graph of f.
The graph of g is a horizontal translation 16 units right of the graph of f.
The graph of g is a vertical translation 16 units down of the graph of f.
Answer:
I guess that we want to find the function g(x) for the 4 cases.
first, f(x) = -9*x + 1.
a) The graph of g is a reflection in the y-axis of the graph of f.
First remember: if we have the point (x,y) and we reflect it over the y-axis, we get (-x,y)
then g(x) = f(-x) = -9*-x + 1 = 9*x + 1.
b) The graph of g is a reflection in the x-axis of the graph of f.
if we have a point (x, y) and we reflect it over the x-axis, the point transforms into (x, -y)
then we have: g(x) = -f(x) = 9*x - 1
c) The graph of g is a horizontal translation 16 units right of the graph of f.
When we want to have a translation in the x-axis, we must change x by x - A.
If A is positive, this transformation moves the graph by A units to the right, in this case, A = 16.
g(x) = f(x - 16) = -9*(x - 16) + 1
d) The graph of g is a vertical translation 16 units down of the graph of f.
For vertical translations, if we want to move the graph by A units down (A positive) we should do y = f(x) - A
In this case, A = 16.
then: g(x) = f(x) - 16 = -9*x + 1 - 16 = -9*x - 15.
2. CTfastrak bus waiting times are uniformly distributed from zero to 20 minutes. Find the probability that a randomly selected passenger will wait the following times for a CTfastrak bus. b. Between 5 and 10 minutes. c. Exactly 7.5922 minutes. d. Exactly 5 minutes. e. Between 15 and 25 minutes.
Answer:
b. 0.25
c. 0.05
d. 0.05
e. 0.25
Step-by-step explanation:
if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:
[tex]P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05[/tex]
Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:
[tex]P(X<x)=\frac{x-a}{b-a}=\frac{x-0}{20-0}=\frac{x}{20}[/tex]
Then, the probability that a randomly selected passenger will wait:
b. Between 5 and 10 minutes.
[tex]P(5<x<10) = P(x<10) - P(x<5)\\P(5<x<10) = \frac{10}{20} -\frac{5}{20}=0.25[/tex]
c. Exactly 7.5922 minutes
[tex]P(7.5922)=0.05[/tex]
d. Exactly 5 minutes
[tex]P(5)=0.05[/tex]
e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:
[tex]P(15<x<25)=P(15<x<20) \\P(15<x<20)=P(x<20) - P(x<15)\\P(15<x<20) = \frac{20}{20} -\frac{15}{20}=0.25[/tex]
This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line? (full problem attached)
Answer:
(0,34)
Step-by-step explanation:
For each rise of 14 in the x direction, this graph rises by -8 in the y direction. This means that, when x is 0, and the graph intersects the y axis, the y value will be 50-8-8=34. Therefore, the y intercept of this line is (0,34). Hope this helps!
Answer:
The answer is (0,34)
solve sqrt 3-5x= sqrt x+2 what is the value of x
Answer:
[tex]x=\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{3-5x}=\sqrt{x+2}\\Square\:both\:sides\\\left(\sqrt{3-5x}\right)^2=\left(\sqrt{x+2}\right)^2\\\mathrm{Expand\:}\left(\sqrt{3-5x}\right)^2:\quad 3-5x\\\mathrm{Expand\:}\left(\sqrt{x+2}\right)^2:\quad x+2\\3-5x=x+2\\\mathrm{Solve\:}\:3-5x=x+2:\quad x=\frac{1}{6}\\x=\frac{1}{6}\\\mathrm{Verify\:Solutions}:\quad x=\frac{1}{6}\space\mathrm{True}\\\mathrm{The\:solution\:is}\\x=\frac{1}{6}[/tex]
Answer:
A- 1/6
Step-by-step explanation:
GOT IT RIGHT ON EDGE
Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is a linear combination of the two independent solutions of this differential equation that you found first. You are not being asked for just one of these. You will need to determine the values of the two constant parameters c1 and c2. Similarly for finding y2 below. Find the function y2 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y2(0)=0,y′2(0)=1. y2= Find the Wronskian W(t)=W(y1,y2). W(t)= Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y1 and y2 form a fundamental set of solutions of 121y′′+110y′−24y=0.
Answer:
Step-by-step explanation:
The original equation is [tex]121y''+110y'-24y=0[/tex]. We propose that the solution of this equations is of the form [tex] y = Ae^{rt}[/tex]. Then, by replacing the derivatives we get the following
[tex]121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)[/tex]
Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that
[tex]121r^2+110r-24=0[/tex]
Recall that the roots of a polynomial of the form [tex]ax^2+bx+c[/tex] are given by the formula
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions
[tex]r_1 = -\frac{12}{11}[/tex]
[tex]r_2 = \frac{2}{11}[/tex]
So, in this case, the general solution is [tex]y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}[/tex]
a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations
[tex]c_1 + c_2 = 1[/tex]
[tex]c_1\frac{-12}{11} + c_2\frac{2}{11} = 0[/tex](or equivalently [tex]c_2 = 6c_1[/tex]
By replacing the second equation in the first one, we get [tex]7c_1 = 1 [/tex] which implies that [tex] c_1 = \frac{1}{7}, c_2 = \frac{6}{7}[/tex].
So [tex]y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}[/tex]
b) By using y(0) =0 and y'(0)=1 we get the equations
[tex] c_1+c_2 =0[/tex]
[tex]c_1\frac{-12}{11} + c_2\frac{2}{11} = 1[/tex](or equivalently [tex]-12c_1+2c_2 = 11[/tex]
By solving this system, the solution is [tex]c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}[/tex]
Then [tex]y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}[/tex]
c)
The Wronskian of the solutions is calculated as the determinant of the following matrix
[tex]\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2[/tex]
By plugging the values of [tex]y_1[/tex] and
We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by
[tex]e^{\int -p(x) dx}[/tex]
In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is
[tex]e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}[/tex]
Note that this function is always positive, and thus, never zero. So [tex]y_1, y_2[/tex] is a fundamental set of solutions.
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t2 + 72t + 100. what is the height of the bridge
Answer:
100
Step-by-step explanation:
When t=0 (no time has passed), the coin is at height 100. This means the bridge must be 100 units high for this to be possible.
Answer:
100
Step-by-step explanation:
:3
Which of the following is a radical equation?
X3 - 13
X+ 15 - 13
√x+3-13
x+3 - 13
Answer:
√x+3-13
Step-by-step explanation:
This answer is a radical equation because a square root is used in the equation. This makes the equation radical. The other choices have no square roots so they can't be the answers.
Round0.00359 to nearest ten thousand
Answer: 0.0036
Step-by-step explanation:
0.00359 — 0.0036
The nine rounds up
Find the area of a circle with radius, r = 9cm.
Give your answer in terms of π .
Answer:
[tex]81\pi[/tex]
Step-by-step explanation:
[tex]Area = \pi * r^{2} \\\pi *9^{2} =81\pi[/tex]
Answer:
81 π
Step-by-step explanation:
formula is radius squared times pi or π so the answer would be 9x9=81 and you said to leave in terms of π so the answer is 81 π.
A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. Ft. How much were the dimensions increased?
Answer:
4 ft
Step-by-step explanation:
288=16 * 18
12+4=16
14+4=18
The dimensions increased by 4 feet.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given;
Dimensions of rectangle = 12 + x and 14 + x
The area of the rectangle= (12 + x) (14 + x) = 288
x² + 26x + 168 = 288
x² + 26x - 120 = 0
(x + 30) (x - 4) = 0
x=-30, x =4
Hence, The dimensions increased by 4 feet.
Learn more about the area;
https://brainly.com/question/1658516
#SPJ2
It is believed that approximately 12% of the population of the United States is lefthanded. Suppose researchers suspect that the proportion of left-handed people is higher in certain states than the national average. The researchers conduct a sample of 200 randomly selected people in the state of Maine and find that 29 people in the sample are left-handed.
a. Write the null hypothesis and alternative hypothesis and define your parameter.
b. Show that the necessary conditions (Randomization Condition, 10% Condition, Sample Size Condition) are satisfied to perform a hypothesis test. Briefly explain how each condition is satisfied.
c. Perform the hypothesis test and find the P-value. (To show your work: Write down what values you are entering into the hypothesis testing calculator.)
d. Is there strong evidence that the left-handed rate in the state of Maine is higher than the national average? Briefly explain how you know.
Answer:
Step-by-step explanation:
a. Null hypothesis: P = p
Alternatives hypothesis: P =/ p
Where P is the hypothesized population proportion and p is the sample proportion
b. Performing a test of proportions
Randomization: the sample was randomly selected in the study
The population size is at least 20 times as big as the sample size.
The sample includes both successes and failures with 29 success and 171 failures.
c. To perform the hypothesis test: we have to find the standard deviation first
Sd = sqrt[ P * ( 1 - P ) / n ]
where P is the hypothesized value of population proportion, n is the sample size.
Sd = √[0.12*(1-0.12)/200]
Sd = √[0.12*(0.88/200]
Sd = √[0.12*(0.0044)]
Sd = √0.000528
Sd = 0.023
Then we can find the z score
z = (p - P) / σ where p = 29/200 = 0.145
z = (0.145-0.12)/ 0.023
z = 0.025/0.023
z = 1.09
Calculation the p value using 0.05 level of significance and a two waited test (p value calculator),
A p-value of 0.2757 which is greater than 0.05, thus we will fail to reject the null stating that there is not enough strong evidence that the left-handed rate in the state of Maine is higher than the national average.
If the figures below are similar, find the scale factor of Figure B to Figure A.
48
27
60
А
16
B
20
9
Answer:
The scale factor is 3.
Step-by-step explanation
Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.
Solve the following absolute value equation:
|2x-5|=7
x= -6 or x = 1
x = 6 or x = 1
x= -6 or x= -1
x = 6 or x= -1
Answer:
x = 6 x = -1
Step-by-step explanation:
When we have absolute value equations, we get two solutions, one positive and one negative
2x - 5 =7 2x -5= -7
Add 5 to each side
2x-5+5 = 7+5 2x -5+5 = -7+5
2x =12 2x = -2
Divide each side by 2
2x/2 =12/2 2x/2 = -2/2
x = 6 x = -1
Can someone help me with this worksheet? Will give all my points.
Answer:
Here are the formulas
Cube/Rectangular Prism:
Volume = Length*width*height
Surface area = 2(wl+hl+hw)
Lateral area= Area of vertical faces
Base area = length*width
Regular hexagonal prism:
Volume : (3sqrt3/2)*a^2*h
Surface Area = 6ah+3sqrt(3)a^2
lateral area: 6ah
base area = 3sqrt(3)s^2/2
Triangular prism
Volume: The volume of a triangular prism can be found by multiplying the base times the height.
Surface area: A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.
Etc.
x/x-2+x-1/x+1=-1
I'm having trouble figuring this out, an explanation on how to solve would suffice.
Answer:
x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Step-by-step explanation:
Solve for x over the real numbers:
x - 2 + x/x + 1 - 1/x = -1
x - 2 + x/x + 1 - 1/x = x - 1/x:
x - 1/x = -1
Bring x - 1/x together using the common denominator x:
(x^2 - 1)/x = -1
Multiply both sides by x:
x^2 - 1 = -x
Add x to both sides:
x^2 + x - 1 = 0
Add 1 to both sides:
x^2 + x = 1
Add 1/4 to both sides:
x^2 + x + 1/4 = 5/4
Write the left hand side as a square:
(x + 1/2)^2 = 5/4
Take the square root of both sides:
x + 1/2 = sqrt(5)/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
x = sqrt(5)/2 - 1/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
Answer: x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Suppose f(x) is continuous on [3,6] and −3≤f′(x)≤5 for all x in (3,6). Use the Mean Value Theorem to estimate f(6)−f(3).
Answer: -9 ≤ f(6) - f(3) ≤ 15
Step-by-step explanation:
In order to use the Mean Value Theorem, it must be continuous and differentiable. Both of these conditions are satisfied so we can continue.
Find f(6) - f(3) using the following formula:
[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]
Consider: a = 3, b = 6
[tex]\text{Then}\ f'(c)=\dfrac{f(6)-f(3)}{6-3}\\\\\\\rightarrow \quad 3f'(c)=f(6) - f(3)[/tex]
Given: -3 ≤ f'(x) ≤ 5
-9 ≤ 3f'(c) ≤ 15 Multiplied each side by 3
→ -9 ≤ f(6) - f(3) ≤ 15 Substituted 3f'(c) with f(6) - f(3)
The Sunshine Droogs are unhappy as they have not yet been paid for their concert. It was agreed they would be paid eleven thousand, four hundred and fifty three pounds for the concert. What is this amount in numbers?
Answer:
11453
Step-by-step explanation:
A researcher recruited 55 adults and tested their ability to remember a list of words. For each participant, the researcher counted the number of words correctly recalled and recorded their age (in years).
HYPOTHESIS
The research hypothesis is that age is related to memory performance.
This hypothesis is:__________.
a. directional
b. non-directional
Answer:
b. non-directional
Step-by-step explanation:
A directional hypothesis can be described as a hypothesis which predicts the direction of impact, either positive or negative, of one variable, especially independent variable, on the other variable which is known as an independent variable. For example, the hypothesis "age reduces memory performance" is a directional hypothesis. The reason is that "reduces" show the direction that age has a negative effect on memory performance.
On the other hand, non-directional hypothesis can be described as a hypothesis that does not predict the direction of impact but only states the relationship between two variables. For example, the research hypothesis is in the question that "age is related to memory performance" is non-directional hypothesis. This because the word "related" in the hypothesis only indicate that there is a relationship between the two variables, not the direction of effect of one variable on the other.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. -6 ≤ y ≤ 9
Step-by-step explanation:
→Looking at the graphed function, you can see that the line starts at when y = -6. Then the function slowly increases, until it finally stops when y = 9.
→This means that the range (y-values) of the function can be from -6 through 9.
The correct answer should be "A. -6 ≤ y ≤ 9."
what’s the sum of x+x^2+2 and x^2-2-x ?
Answer: The correct answer is: " 2x² " .
________________________________
Step-by-step explanation:
________________________________
We are asked: "What is the sum of: "x + x² + 2" and "x² − 2 − x" ?
Since we are to find the "sum" ;
→ We are to "add" these 2 (two) expressions together:
→ (x + x² + 2) + (x² − 2 − x) ;
Note: Let us rewrite the above, by adding the number "1" as a coefficient to: the values "x" ; and "x² " ; since there is an "implied coefficient of "1" ;
→ {since: "any value" ; multiplied by "1"; results in that exact same value.}.
→ (1x + 1x² + 2) + (1x² − 2 − 1x) ;
Rewrite as:
→ 1x + 1x² + 2) + (1x² − 2 − 1x) ;
Now, let us add the "coefficient" , "1" ; just before the expression:
"(1x² − 2 − 1x)" ;
{since "any value", multiplied by "1" , equals that same value.}.
And rewrite the expression; as follows:
→ (1x + 1x² + 2) + 1(1x² − 2 − 1x) ;
Now, let us consider the following part of the expression:
→ " +1(1x² − 2 − 1x) " ;
________________________________
Note the distributive property of multiplication:
→ " a(b+c) = ab + ac " ;
and likewise:
→ " a(b+c+d) = ab + ac + ad " .
________________________________
So; we have:
→ " +1(1x² − 2 − 1x) " ;
= (+1 * 1x²) + (+1 *-2) + (+1*-1x) ;
= + 1x² + (-2) + (-1x) ;
= +1x² − 2 − 1x ;
↔ ( + 1x² − 1x − 2)
Now, bring down the "left-hand side of the expression:
1x + 1x² + 2 ;
and add the rest of the expression:
→ 1x + 1x² + 2 + 1x² − 1x − 2 ;
________________________________
Now, simplify by combining the "like terms" ; as follows:
+1x² + 1x² = 2x² ;
+1x − 1x = 0 ;
+ 2 − 2 = 0 ;
________________________________
The answer is: " 2x² " .
________________________________
Hope this is helpful to you!
Best wishes!
________________________________
Answer:
The correct answer is: " 2x² " .
________________________________
Step-by-step explanation:
________________________________
We are asked: "What is the sum of: "x + x² + 2" and "x² − 2 − x" ?
Since we are to find the "sum" ;
→ We are to "add" these 2 (two) expressions together:
→ (x + x² + 2) + (x² − 2 − x) ;
Note: Let us rewrite the above, by adding the number "1" as a coefficient to: the values "x" ; and "x² " ; since there is an "implied coefficient of "1" ;
→ {since: "any value" ; multiplied by "1"; results in that exact same value.}.
→ (1x + 1x² + 2) + (1x² − 2 − 1x) ;
Rewrite as:
→ 1x + 1x² + 2) + (1x² − 2 − 1x) ;
Now, let us add the "coefficient" , "1" ; just before the expression:
"(1x² − 2 − 1x)" ;
{since "any value", multiplied by "1" , equals that same value.}.
And rewrite the expression; as follows:
→ (1x + 1x² + 2) + 1(1x² − 2 − 1x) ;
Now, let us consider the following part of the expression:
→ " +1(1x² − 2 − 1x) " ;
________________________________
Note the distributive property of multiplication:
→ " a(b+c) = ab + ac " ;
and likewise:
→ " a(b+c+d) = ab + ac + ad " .
________________________________
So; we have:
→ " +1(1x² − 2 − 1x) " ;
= (+1 * 1x²) + (+1 *-2) + (+1*-1x) ;
= + 1x² + (-2) + (-1x) ;
= +1x² − 2 − 1x ;
↔ ( + 1x² − 1x − 2)
Now, bring down the "left-hand side of the expression:
1x + 1x² + 2 ;
and add the rest of the expression:
→ 1x + 1x² + 2 + 1x² − 1x − 2 ;
________________________________
Now, simplify by combining the "like terms" ; as follows:
+1x² + 1x² = 2x² ;
+1x − 1x = 0 ;
+ 2 − 2 = 0 ;
________________________________
The answer is: " 2x² " .
Step-by-step explanation:
What is the equation of the line that is parallel to the given
line and passes through the point (-4,-6 )?
x= -6
x=-4
y=-6
y=-4
Answer:
The line on the graph is y = 4, where no matter what the value of x is, the value of y will always be 4. Therefore, any line parallel to this one will be y = ?. If it passes through (-4, -6), that means that the equation is y = -6.
Answer:
С)))) Y= -6
Step-by-step explanation:
just did on edg. :D
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $18.5 for a random sample of 2253 people. Assume the population standard deviation is known to be $6.1. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Answer:
= ( $18.2, $18.8)
Therefore, the 98% confidence interval (a,b) = ( $18.2, $18.8)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $18.50
Standard deviation r = $6.10
Number of samples n = 2253
Confidence interval = 98%
z(at 98% confidence) = 2.33
Substituting the values we have;
$18.5+/-2.33($6.1/√2253 )
$18.5+/-2.33($0.128513644290)
$18.5+/-$0.299436791196
$18.5+/-$0.3
= ( $18.2, $18.8)
Therefore at 98% confidence interval (a,b) = ( $18.2, $18.8)
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions. CHECK ALL THAT APPLY
Answer:
A. it would be shifted up
Step-by-step explanation:
Y=MX+B
B is the Y-intercept.
Answer:
a. it would be shifted up
Step-by-step explanation:
the difference between the original and the new function is that the b value is changed from -6 to +8, meaning the y-intercept value has increased. this would shift the graph up by 14.
At the neighborhood block party, John noticed that every 5 minutes, the
shadow of a nearby pine tree got six inches longer. The shadow was 12
feet long at 4:15pm. How long was the shadow at 5:00pm?
Answer:
7
Step-by-step explanation:
I think because at if you divide 45 by 6 because its 45 minutes from 4:15 to 5:00 and it grows 6 inches longer every five min
A car is discounted 10% and sells for $15,673. What was the discount amount?
Answer:
$1741.44
Step-by-step explanation:
The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:
10% = 90% × 1/9
The discount was ...
$15,673/9 = 1,741.44
_____
Check
The original is the sum of the discounted amount and the discount:
original price = $15,673.00 +1,741.44 = $17, 414.44
10% of that value is 1,741.44, as shown above.
Let D= {(x,y) | x^2+y^2 ≤ 4x} Using polar coordinates, What is the integral: ∬y^2/ (x^2+y^2)dxdy?
In polar coordinates, the inequality changes to
[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]
which is a circle of radius 2 and centered at (2, 0). The set D is then
[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]
The integral is then
[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]
[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]
There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,
[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]
so that the integral is
[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]
Then invoke another double-angle formula,
[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]
to change the integral to
[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]
[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]
A toy car is placed on the floor He moves in a straight line starting from rest and travels with a constant acceleration for three seconds reaching a velocity of 4 meters per second it then slows down with constant deceleration of 0.5 meters per second squared For four seconds before hitting the wall and stopping draw a velocity time graph for the toy car what is the total distance travelled by the toy car
Answer:
18 meters.
Step-by-step explanation:
There is a constant acceleration for 3 seconds, reaching 4 m/s. This, when drawn on a velocity/time graph, creates a diagonal line. The area underneath this line, which is the distance it travels, is found by the following: 0.5(l*h), the formula used to find the area of a triangle.
0.5(3*4)=6m
There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.
0.5(2*4)=4m
Now, all that remains is a rectangle of height 2 and a length of 4, so we find the area of it.
2*4=8m
Finally, we add each of these up.
6m+4m+8m=18m
Sorry if the step by step process was poorly explained, I'm not the best at explaining. Hope this helped, though. :^)
The total distance traveled by the toy car is 18 meters.
What is acceleration?Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.
For three seconds, there is a steady acceleration that reaches 4 m/s. This yields a diagonal line when drawn on a velocity/time graph. The following formula can be used to determine the region beneath this line, or the distance it travels:
The triangle area is calculated using the formula:-
A = 0.5(l x h).
A = 0.5(3 x 4)=6m
There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.
0.5(2 x 4)=4m
Now, all that remains is a rectangle of height 2 and a length of 4, so we find its area of it.
2 x 4 = 8m
Finally, we add each of these up.
6m+4m+8m=18m
Therefore, the total distance traveled by the toy car is 18 meters.
To know more about acceleration follow
https://brainly.com/question/23516420
#SPJ2