Answer:
-(x + 3)^2 = -15
Step-by-step explanation:
:) got it right
In politics, marketing, etc. We often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Describe the conclusion about p using an absolute value inequality.
Answer: |p-72% |≤ 4%
Step-by-step explanation:
Let p be the population proportion.
The absolute inequality about p using an absolute value inequality.:
[tex]|p-\hat{p}| \leq E[/tex] , where E = margin of error, [tex]\hat{p}[/tex] = sample proportion
Given: A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .
|p-72% |≤ 4%
⇒ 72% - 4% ≤ p ≤ 72% +4%
⇒ 68% ≤ p ≤ 76%.
i.e. p is most likely to be between 68% and 76% (.
The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
What is absolute value inequality?An expression using absolute functions and inequality signs is known as an absolute value inequality.
We know that the absolute value inequality about p using an absolute value inequality is written as,
[tex]|p-\hat p| \leq E[/tex]
where E is the margin of error and [tex]\hat p[/tex] is the sample proportion.
Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,
[tex]|p-0.72|\leq 0.04\\\\(0.72-0.04)\leq p \leq (0.72+0.04)\\\\0.68 \leq p\leq 0.76[/tex]
Thus, the p is most likely to be between the range of 68% to 76%.
Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,
[tex]|p-\hat p|\leq E\\\\|p-0.32|\leq 0.022\\\\(0.32-0.022)\leq p \leq (0.32+0.022)\\\\0.298\leq p\leq 0.342[/tex]
Thus, the p is most likely to be between the range of 29.8% to 34.2%.
Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
Learn more about Absolute Value Inequality:
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6 points are place on the line a, 4 points are placed on the line b. How many triangles is it possible to form such that their verticies will be the given points, if a ∥b?
Answer: 96
Step-by-step explanation:
Ok, lines a and b are parallel.
We can separate this problem in two cases:
Case 1: 2 vertex in line a, and one vertex in line b.
Here we use the relation:
"In a group of N elements, the total combinations of sets of K elements is given by"
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.
Then if we have two vertices in line a, we have:
N = 6, K = 2
[tex]C = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15[/tex]
And the other vertex can be on any of the four points on the line b, so the total number of triangles is:
C = 15*4 = 60.
But we still have the case 2, where we have 2 vertices on line b, and one on line a.
First, the combination for the two vertices in line b is:
We use N = 4 and K = 2.
[tex]C = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6[/tex]
And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:
C = 6*6 = 36
Then, putting together the two cases, we have a total of:
60 + 36 = 96 different triangles
A mother who is 35 years old has two sons, one of whom is twice as old as the other. In 3 years the sum of all their ages will be 59 years. How old are the boys at present ?
Answer:
son2: 5
son1: 10
Step-by-step explanation:
2x (son1) + x (son2) + 35 (mother) + 3 (years)*3 (people) = 59
3x = 15
x = 5
The age of each boy at present will be 2 years and 3 years.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Let the age of the sons will be x and y.
A mother who is 35 years old has two sons, one of whom is twice as old as the other. Then the equation will be
x = 2y
In 3 years, the sum of all their ages will be 59 years. Then the equation will be
x + y + x + 1 + y + 1 + x + 2 + y + 2 + 35 = 59
Simplify the equation, we have
3x + 3y + 41 = 59
6y + 3y = 59 – 41
9y = 18
y = 2
Then the value of x will be
x = 2y
x = 2(2)
x = 4
Thus, the age of each boy at present will be 2 years and 3 years.
More about the linear system link is given below.
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Can anyone tell me the answer of the question attached below??
Answer: AE = 5
Step-by-step explanation:
I sketched the triangle based on the information provided.
since ∠A = 90° and is divided into three equal angles, then ∠BAD, ∠DAE, and ∠CAE = 30°
Since AB = 5 and BC = 10, then ΔCAB is a 30°-60°-90° triangle which implies that ∠B = 60° and ∠C = 30°
Using the Triangle Sum Theorem, we can conclude that ∠ADB = 90°, ∠ADE = 90°, ∠ AED = 60°, AND ∠ AEC = 120°
We can see that ΔAEC is an isosceles triangle. Draw a perpendicular to divide it into two congruent right triangles. Label the intersection as Z. ΔAEZ and ΔCEZ are 30°-60°-90° triangles.
Using the 30°-60°-90° rules for ΔABC we can calculate that AC = 5√3.
Since we divided ΔAEC into two congruent triangles, then AZ = [tex]\dfrac{5\sqrt 3}{2}[/tex]
Now use the 30°-60°-90° rules to calculate AE = 5
A timeline. 27 B C E to 180 C E PAX ROMANA. 44 B C E The Roman Empire was founded. 80 C E The Colosseum was built. 121 C E Hadrian's Wall was built in England to keep out enemies. 306 C E Constantine became emperor.
How many years passed between the building of the Colosseum and the building of Hadrian’s Wall?
201
121
41
36
Answer:
the answer is 41
Step-by-step explanation:
C. 41
Step-by-step explanation:
Al’s Produce Stand sells 6 ears of corn for $1.50. Barbara’s Produce Stand sells 13 ears of corn for $3.12. Write two equations, one for each produce stand, that model the relationship between the number of ears of corn sold and the cost.
Answer:
6n = 1.50
and
13n = 3.12
Step-by-step explanation:
Here in this question, we are interested in writing equations that relate the number of ears of corn sold and the cost.
For Al’s produce stand, let the price per corn sold be n
Thus;
6 * n = 1.50
6n = $1.50 •••••••(i)
For the second;
let the price per corn sold be n;
13 * n = $3.12
-> 13n = 3.12 •••••••••(ii)
Solve using quadratic formula.
1.)5x^2+13x=6
2.)3x^2+1=-5x
PLEASE HELP!!! WILL MARK BRAINLIEST!!!
Answer:
1. 2/5,-3 2. [tex]x=\frac{-5+-\sqrt{13} }{6}[/tex]
Step-by-step explanation:
i used the quadratic formula to find x also please note that 2 has 2 answers bc of the +- beofre the sqrt of 13
Step-by-step explanation:
1).5x² + 13x - 6 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a = 5 , b = 13 c = - 6
We have
[tex]x = \frac{ - 13± \sqrt{ {13}^{2} - 4(5)( - 6) } }{2(5)} [/tex]
[tex]x = \frac{ - 13± \sqrt{169 + 120} }{10} [/tex]
[tex]x = \frac{ - 13± \sqrt{289} }{10} [/tex]
[tex]x = \frac{ - 13±17}{10} [/tex]
[tex]x = \frac{ - 13 + 17}{10} \: \: \: \: \: or \: \: \: \: x = \frac{ - 13 - 17}{10} [/tex]
x = 2/5 or x = - 32).3x² + 5x + 1 = 0
a = 3 , b = 5 , c = 1
[tex]x = \frac{ -5 ± \sqrt{ {5}^{2} - 4(3)(1)} }{2(3)} [/tex]
[tex]x = \frac{ - 5± \sqrt{25 - 12} }{6} [/tex]
[tex]x = \frac{ - 5± \sqrt{13} }{6} [/tex]
[tex]x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} [/tex]
Hope this helps you
Find the coefficient of third term of (2x−1)^6.
240
using pascals trianle
for the power 6 it is
1, 6,15,20, 15,6, 1
and for the third term (2x)^4 and (-1)^2
[tex]15 \times {(2x)}^{4} \times {( - 1)}^{2} [/tex]
[tex]240 {x}^{4} [/tex]
Since only the coefficient is needed
the answer is 240.
The required coefficient of third term is 480.
Coefficient of the third term of (2x−1)^6 to be determine.
Coefficient is defined as the integer present adjacent to the variable.
Here, (2x−1)^6
Using binomial expansion,
Third term = P(6,2)(2x)^6-2(-1)^2
= 6*5*16x^4
= 480x^4
Thus, the required coefficient of third term is 480.
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jim buys a calculator that is marked 30% off. If he paid $35, what was the original price?
Answer:
x = 50
Step-by-step explanation:
Let x be the original price.
He got 30% off
The discount is .30x
Subtract this from the original price to get the price he paid
x - .30x = price he paid
.70x = price he paid
.70x = 35
Divide each side by .7
.70x/.7 = 35/.7
x=50
Angles L and M are supplementary. What is the sum of
their measures?
The sum of the measures of angles L and M is
180 degree
Step-by-step explanation:
supplementary means anhke havinv sum of 180 degree
so sum to two supplemrntary angles is 180 drgree
Supplementary angles always add to 180.
One way I think of it is "supplementary angles form a straight angle", and both the words "supplementary" and "straight" start with the letter "S".
In contrast, complementary angles form a corner. Both "complementary" and "corner" start with "co". By "corner", I mean a 90 degree corner.
Multiply. (2x - 3)(x + 4) a 2x² + 11x - 12 b 2x² + 5x - 12 c 2x² + 11x - 7 d 2x² + 3x - 7
Answer:
2x^2 +5x-12
Step-by-step explanation:
(2x - 3)(x + 4)
FOIL
first 2x*x = 2x^2
outer 2x*4 = 8x
inner -3x
last -3*4 = -12
Add these together
2x^2 +8x-3x-12
Combine like terms
2x^2 +5x-12
if your ans is correct i will choose you as a brainlist when the number of student of a school was increased by 30% it became 455. Find the previous number student.
Step-by-step explanation:
find 30% of 455
which is = 136.5
then subtract 136.5 from the original number(455)
455 - 136.5
=318.5 student
If we did not write the equation 5x=21, instead we wrote it 21=5x,
we would get a different solution.
O True
O False
Answer:
Step-by-step explanation:
5x = 21 and 21 = 5x are identical relationships, and so the solution would be the same in both cases. (Commutative Property: order of addition/subtraction is immaterial)
Is △FHK similar to △GHJ? If so, which postulate or theorem proves these two triangles are similar? △FHK is similar to △GHJ by the SSS Similarity Theorem. △FHK is similar to △GHJ by the SSA Similarity Theorem. △FHK is similar to △GHJ by the SAS Similarity Theorem. △FHK is not similar to △GHJ.
Answer:
ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Step-by-step explanation:
Picture for the given question is missing; find the picture attached.
If [tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex] and ∠H ≅ ∠H
Then ΔFHK ~ ΔGHJ
[tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex]
[tex]\frac{(12+10)}{10}=\frac{(15+18)}{15}[/tex]
[tex]\frac{22}{10}=\frac{33}{15}[/tex]
[tex]\frac{11}{5}=\frac{11}{5}[/tex]
Since, [tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex] and ∠H ≅ ∠H [By reflexive property]
Therefore, ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Option (3) will be the answer.
Answer:
ΔFHK and ΔGHJ are similar triangles by the SAS similarity theorem.
Step-by-step explanation:
Verified correct with test results.
Loreto quería decorar un viejo tambor metálico para usarlo de paragüero. Para ello, contaba con un grueso cordón que pretendía pegar en el contorno del borde superior del tambor. Sabiendo que el diámetro de este era 58,5 cm, cortó el cordón, dejando el trozo más largo de 175,5 cm de longitud de modo que le alcanzara justo, pero le faltaron 7 cm. ¿Cuál fue el error de Loreto?
Answer:
u should put the question in English to so English people can also help
3. One rule of thumb for estimating crowds is that each person Occupies 2.5 square feet.
Use this rule to estimate the size of the crowd watching a parade along the 1-mile
section of the route in Question 2.
mile
Answer:
5.83142789
Step-by-step explanation:
did it on a graphing calculator, hope this helps
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
The third option: x= [tex]\frac{8}{3} \pi[/tex]
Step-by-step explanation:
Arc length formula=[tex]\frac{Central Angle}{360} * 2\pi r[/tex]
Arc length = [tex]\frac{120}{360} *2\pi (4)[/tex]
=[tex]\frac{8}{3}\pi[/tex]
whats the squareroot of 72 needs to be simplified
Answer: 6√2
Step-by-step explanation: The easiest way to do this problem is to factor 72 as 2 · 36, then recognize 36 as a perfect square, 6 · 6.
There's no need to factor further because the 6's pair up
so a 6 comes out of the radical leaving a 2 inside.
So our answer is 6√2.
Always be on the lookout for perfect squares!
Work is attached below.
Set A={XIX is an even whole number between 0 and 2) = 0
True? or false?
false
Step-by-step explanation:
false
How to do this question plz answer me step by
Answer:
481.92
Step-by-step explanation:
First find the increase
466.98 * 3.2%
466.98 * .032
14.94336
Add this to the original amount
466.98+14.94336
481.92336
Round to 2 decimal places
481.92
Find the length of the base and the height and calculate the area
Answer:
44
Step-by-step explanation:
base = 3- -5 = 8
height = 8 - -3 = 11
1/2 bh
1/2(8)(11) = 44
A cube whose edge is 20 cm 1 point
long, has circles on each of its
faces painted black. What is the
total area of the unpainted
surface of the cube if the
circles are of the largest
possible areas?(a) 90.72 cm2 (b)
256.72 cm² (c) 330.3 cm² (d)
514.28 cm?
Answer:
Unpainted surface area = 514.28 cm²
Step-by-step explanation:
Given:
Side of cube = 20 Cm
Radius of circle = 20 / 2 = 10 Cm
Find:
Unpainted surface area
Computation:
Unpainted surface area = Surface area of cube - 6(Area of circle)
Unpainted surface area = 6a² - 6[πr²]
Unpainted surface area = 6[a² - πr²]
Unpainted surface area = 6[20² - π10²]
Unpainted surface area = 6[400 - 314.285714]
Unpainted surface area = 514.28 cm²
Can someone plz help me ASAP!!!!!!!!
Answer:
A) The number halfway between -2 and 6 is 2.
B) -10 is halfway between -18 and 8
20 PTS PLEASE HELP!!!!
Select the correct answer from each drop-down menu.
The function below describes the number of students who enrolled at a university, where f(t) represents the number of students and t represents the time in years.
Initially, (1.03, 3, 19,055, 18,500) students enroll at the university. Every,(1years, t years, 2years, 3years) the number of students who enroll at the university increases by a factor of (1.03, 3, 19,055, 18,500).
Answer:
Initially 18,500 students
Every 1 year
increase by a factor 1.03
Step-by-step explanation:
The missing information is selected from the given options from the drop down menu. The correct answers are : Initially 18,500 students enroll at the university. Every 1 years the number of students who enroll at the university increases by a factor 1.03.
F(t) = 18,500 * (1.03)^t
SIMPLIFY.
(5c^2 + c) - (3c^2 + 11c)
Answer:2 c^2 - 10c
Step-by-step explanation:
Manuel made at least one error as he found the value of this expression. Identify the step in which Manuel made his first error. After identifying the step with the first error, explain the corrected steps and find the final answer.
Answer:
Manuel made his first mistake in step 2 leading to the continuous mistakes
Final answer=185
Step-by-step explanation:
Manuel made at least one error as she found the value of this expression. 2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50) Step 1: 2(-20) + 3(-25) + 5(20) + 4(50) Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50) Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405 Identify the step in which Chris made her first error. After identifying the step with the first error, write the corrected steps and find the final answer.
2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50)
Step 1: 2(-20) + 3(-25) + 5(20) + 4(50)
Step 2: -40 - 75 + 100 +
200
Step 3: -115 + 300
Step 4: 185
Manuel made his first error in step 2 by combining two different terms into one as he has done
(3 + 2)(-20 + -25) and also (5 + 4)(20 + 50)
Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50)
Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405
He should have evaluated the terms separately as I have done above, giving us 185 as the final answer in contrast to his 405 final answer.
Can someone please help! Thx
Answer:
Hey there!
The angle is 24 degrees.
The angle complementary to the 66 degrees is 24 degrees, and the unknown angle is also 24 degrees because these are alternate interior angles.
Let me know if this helps :)
Solve this problem... Really urgent
Answer:
[tex] \boxed{\sf Time \ taken = 15 \ minutes} [/tex]
Given:
Initial speed (u) = 65 km/h
Final speed (v) = 85 km/h
Acceleration (a) = 80 km/h²
To Find:
Time taken for car to achieve a speed of 85 km/h in minutes
Step-by-step explanation:
[tex]\sf From \ equation \ of \ motion:[/tex]
[tex] \boxed{ \bold{v = u + at}}[/tex]
By substituting value of v, u & a we get:
[tex] \sf \implies 85 = 65 + 80t[/tex]
Substract 65 from both sides:
[tex] \sf \implies 85 - 65 = 65 - 65 + 80t[/tex]
[tex] \sf \implies 20 = 80t[/tex]
[tex] \sf \implies 80t = 20[/tex]
Dividing both sides by 80:
[tex] \sf \implies \frac{ \cancel{80}t}{ \cancel{80}} = \frac{20}{80} [/tex]
[tex] \sf \implies t = \frac{2 \cancel{0}}{8 \cancel{0}} [/tex]
[tex] \sf \implies t = \frac{ \cancel{2}}{ \cancel{2} \times 4} [/tex]
[tex] \sf \implies t = \frac{1}{4} \: h[/tex]
[tex] \sf \implies t = \frac{1}{4} \times 60 \: minutes[/tex]
[tex] \sf \implies t = 15 \: minutes[/tex]
So,
Time taken for car to achieve a speed of 85 km/h in minutes = 15 minutes
A cyclist travels at $20$ kilometers per hour when cycling uphill, $24$ kilometers per hour when cycling on flat ground, and $30$ kilometers per hour when cycling downhill. On a sunny day, they cycle the hilly road from Aopslandia to Beast Island before turning around and cycling back to Aopslandia. What was their average speed during the entire round trip?
Answer:
Average speed during the trip = 24 km/h
Step-by-step explanation:
Given:
Speed of cyclist uphill, [tex]v_1[/tex] = 20 km/hr
Speed of cyclist on flat ground = 24 km/h
Speed of cyclist downhill, [tex]v_2[/tex] = 30 km/h
Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.
That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h
To find:
Average speed during the entire trip = ?
Solution:
Let the distance between Beast Island and Aopslandia = D km
Let the time taken to reach Beast Island from Aopslandia = [tex]T_1\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_1 = 20 = \dfrac{D}{T_1}[/tex]
[tex]\Rightarrow T_1 = \dfrac{D}{20} ..... (1)[/tex]
Let the time taken to reach Aopslandia back from Beast Island = [tex]T_2\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_2 = 30 = \dfrac{D}{T_2}[/tex]
[tex]\Rightarrow T_2 = \dfrac{D}{30} ..... (2)[/tex]
Formula for average speed is given as:
[tex]\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}[/tex]
Here total distance = D + D = 2D km
Total Time is [tex]T_1+T_2[/tex] hours.
Putting the values in the formula and using equations (1) and (2):
[tex]\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}[/tex]
So, Average speed during the trip = 24 km/h
The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.
Answer:
83 adult tickets and 217 student tickets.
Step-by-step explanation:
Let number of adult tickets sold = [tex]x[/tex]
Given that total number of tickets = 300
So, number of student tickets = 300 - [tex]x[/tex]
Cost of adult ticket = $15
Cost of student ticket = $11
Total collection from adult tickets = $[tex]15x[/tex]
Total collection from student tickets = [tex](300-x)\times 11 = 3300-11x[/tex]
Given that overall collection = $3630
[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]
So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.
Now , collection = $3632
