[tex](-8x) + x + (-2x) = -8x + x - 2x = -9x[/tex]
Answer:
-9x
Step-by-step explanation:
-8x + x +(-2x)
*A negative multiplied by a positive makes a negative
-8x + x -2x
-7x-2x
-9x
Hope this helps!
PLEASE SOLVE IT
DONT STEAL POINYS!!
Answer:
A) 3
Step-by-step explanation:
Method 1)Ques: 30/(4√3 + 3√2) = 4√3 - a√2
Rationalise the denominator.
→ 30/(4√3 + 3√2) × (4√3 - 3√2)/(4√3 - 3√2) = 4√3 - a√2
→ (120√3 - 90√2)/(48 - 18) = 4√3 - a√2
→ (120√3 - 90√2)/30 = 4√3 - a√2
→ 120√3 - 90√2 = 120√3 - 30a√2
→ 90√2 = 30a√2
On solving we get,
→ a = 3
Method 2)Ques: 30/(4√3 + 3√2) = 4√3 - a√2
→ 30 = 4√3(4√3) + 4√3(-a√2) + 3√2(4√3) + 3√2(-a√2)
Solve the brackets,
→ 30 = 48 - 4a√6 + 12√6 - 6a
→ - 18 = - 4a√6 - 12√6 - 6a
Put like terms on one side,
→ - 18 + 6a = - 4√6 (a + 3)
Take the common,
→ 3(a - 3) = - 2√6 (a + 3)
→ 3 (a - 3) = 2√6 (-a - 3)
→ [3(a - 3)]/2√6 = - a - 3
Rationalise the denominator,
→ 2√6(3a - 9)/24 = - a - 3
→ (3a√6 - 9√6)/12 = - a - 3
→ √6(a - 3) = - 4a - 12
Do squaring on both sides,
→ [√6(a - 3)]² = - (4a + 12)²
→ 6(a² + 9 - 6a) = - (16a² + 144 + 96a)
Solve the brackets,
→ 6a² + 54 - 36a = - 16a² - 144 - 96a
→ 22a² - 132a + 198 = 0
→ 11a² - 66a + 99 = 0
→ a² - 6a + 9 = 0
Split the middle term,
→ a² - 3a - 3a + 9 = 0
→ a(a - 3) -3(a - 3) = 0
→ (a - 3)(a - 3) = 0
On comparing we get,
→ a = 3 (key to solve this and similar questions is rationalisation of the denominator)
Hence, the correct option is option A) 3.
Joyce paid $143.00 for an item at the store that was 35 percent off the original price. What was the original price?
Answer:
220
Step-by-step explanation:
GIven:
Joyce paid $143.00 for an item at the store that was 35 percent off the original price.
To Find:
What was the original price?
Solution:
Since that was 35 percent off the original price
Thus, 100 - 35 = 65
Equation:
143 = 0.65x
DIvide both sides by 0.65
143/0.65 = 0.65x/0.65
x = 220
Check Answer:
220 x 65% = 143
~Lenvy~
What is the prime factorization of 32?
OA) 232
OB) 23
OD) 28
I
Answer:
2 × 2 x 2 x 2 x 2 or 25
Answer:
2*2*2*2*2, which can be also written as [tex]2^5[/tex].
A water bottle has 16.9 fluid ounces of water. What is the total amount of water in a pack of 6 bottles?
Answer:
101.4 floz
Step-by-step explanation:
If I'm correct, you should multiply 16.9 by 6 because there are 6 bottles and each has 16.9 fluid ounces of water.
A water bottle has 16.9 fluid ounces of water, there would be a total of 101.4 fluid ounces of water.
We are given that each water bottle contains 16.9 fluid ounces of water. This is the capacity or volume of a single bottle.
To find the total amount of water in a pack of 6 bottles, we can multiply the amount of water in one bottle by the number of bottles in the pack.
Amount of water in one bottle: 16.9 fluid ounces
Number of bottles in the pack: 6
Total amount of water in the pack: 16.9 fluid ounces/bottle * 6 bottles = 101.4 fluid ounces
Therefore, there would be a total of 101.4 fluid ounces of water in a pack of 6 bottles.
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1) A class of 449 students went on a field trip.
They took 11 velvicles, some cars and some
buses. Find the number of cars and the
number of buses they took if each car holds
3 students and each bus hold 55 students.
Answer: A class of 449 students went on a field trip. They took 11 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 3 students and each bus holds 55 students.
Step-by-step explanation: they took 8 buses.
55 x 8 = 440
3 x 3 = 9
440 + 9 = 449
The differential equation dy dx equals the quotient of the quantity x plus 1 and y minus 3
produces a slope field with vertical tangents at y = 3
produces a slope field with vertical tangents at x = −1
produces a slope field with rows of parallel segments
I only
II only
III only
I and III
Answer:
I only
Step-by-step explanation:
dy/dx = x + 1 / y -3
(y - 3)dy = (x + 1) dx
integrate
1/2y^2 - 3x = 1/2x^2 + x
1/2y^2 = 1/2x^2 + 4x
y^2 = x^2 + 8x
y = (x^2 + 8x)^1/2
Researchers from the Educational Testing Service (ETS) found that providing immediate feedback to students answering openended questions can dramatically improve students’ future performance on exams ( Educational and Psychological Measurement, Feb. 2010). The ETS researchers used questions from the Graduate Record Examination (GRE) in the experiment. After obtaining feedback, students could revise their answers. Consider one of these questions. Initially, 50% of the students answered the question correctly. After providing immediate feedback to students who answered incorrectly, 70% answered correctly. Consider a bank of 100 open-ended questions similar to those on the GRE. (b) After providing immediate feedback, what is the probability that more than 10 of the students answer the question correctly? Group of answer choices 58.8% 41.2% 95.2% 4.8%
Complete question is;
Researchers from the Educational Testing Service (ETS) found that providing immediate feedback to students answering openended questions can dramatically improve students’ future performance on exams (Educational and Psychological Measurement, Feb. 2010). The ETS researchers used questions from the Graduate Record Examination (GRE) in the experiment. After obtaining feedback, students could revise their answers. Consider one of these questions. Initially, 50% of the students answered the question correctly. After providing immediate feedback to students who answered incorrectly, 70% answered correctly. Consider a bank of 100 open-ended questions similar to those on the GRE. a. In a random sample of 20 students, what is the probability that more than half initially answer the question correctly? b. Refer to part a . After providing immediate feedback, what is the probability that more than half of the students answer the question correctly?
Answer:
A) 41.2%
B) 95.2%
Step-by-step explanation:
This is a binomial probability distribution problem, so we will use the formula;
P(k) = (n!/(k!(n - k)!) × p^(k) × (1 - p)^(n-k)
A) Initially, 50% of the students answered the question correctly.
Thus, p = 0.5
Also,n = 20
Now, the probability that more than half initially answer the question correctly would be:
P(k > 10)
This can be expressed as;
P(k > 10) = P(11) + P(12) + P(13) + P(14) + P(15) + P(16) + P(17) + P(18) + P(19) + P(20)
P(11) = (20!/(11!(20 - 11)!) × 0.5^(11) × (1 - 0.5)^(20-11) = 0.1602
Similarly,
P(12) = (20!/(12!(20 - 12)!) × 0.5^(12) × (1 - 0.5)^(20-12) = 0.1201
P(13) = (20!/(13!(20 - 13)!) × 0.5^(13) × (1 - 0.5)^(20-13) = 0.0739
Using online binomial probability calculator we can get the remaining values which are;
P(14) = 0.037
P(15) = 0.0148
P(16) = 0.0046
P(17) = 0.0011
P(18) = 0.0002
P(19) = 0.00002
P(20) = 0
Thus;
P(k > 10) = 0.1602 + 0.1201 + 0.0739 + 0.037 + 0.0148 + 0.0046 + 0.0011 + 0.0002 + 0.00002 + 0 ≈ 0.41192 = 41.2%
B) After providing immediate feedback, we are told that 70% answered correctly.
Thus; p = 70% = 0.7
Similar to A above and using online binomial probability calculator, we have;
P(11) = 0.0654
P(12) = 0.1144
P(13) = 0.1643
P(14) = 0.1916
P(15) = 0.1789
P(16) = 0.1304
P(17) = 0.0716
P(18) = 0.0278
P(19) = 0.0068
P(20) = 0.0008
Thus;
P(k > 10) = 0.0654 + 0.1144 + 0.1643 + 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.952 = 95.2%
2. Multiply and simplify
(x^13-x^3+x^2+x-1)/(x*(x+1)*(x-1))
James bought the computer which was discounted from $350 to $273. What is the discount rate?
Explanation:
amount saved = 350-273 = 77 dollars.
Divide this amount over the original price
77/350 = 0.22 = 22% is the discount rate
can someone answer real quick
Answer:− -19s
Step-by-step explanation:
Move
helppppppppppppppppp
Answer:
31-32
Hyposis: SHe is the mother.
Conclusion: She's not.
Step-by-step explanation:
How do I get the y-coordinates?
Answer:
Plug the x values into the equation and the answers are the y values
EASY POINTS. all irregular/wrong answers will be reported and removed, this is not easy points if you don't know how to factor.
I need these to be in the greatest common factor form, i am in a business calc class and understand everything but the algebra :) i hate algebra.
1) 36x^2-24x
2)12x^2-24x
3)45x^3-30x
Step-by-step explanation:
1)
Take 12x as a common factor
12x(3x-2)
12 since both 36 and 24 are divisible by 12
2)
Take 12x as a common factor again
12x(x-2)
3)
Take 15x as a common factor
15x(3x²-2)
3x²-2 can be written as the difference of 2 squares
15x(√3 x+√2)(√3 x-√2)
Answer:
[tex]12x(3x-2); 12x(x-2); 15x(3x^2-2)[/tex]
Step-by-step explanation:
Look at the coefficients of the first espression. 36 and 24 are both multiples of 12. We can collect 12x from both and we get
[tex]36x^2-24x=12x(3x-2)[/tex]
Second, 12 and 24 are obviously one twice the other, the common factor is again 12x:
[tex]12x^2-24x = 12x(x^2-2)[/tex]
Third polynomial: this time the greatest common divisor of 45 and 30 is 15. Let's collect 15x from either
[tex]45x^3-30x=15x(3x^2-2)[/tex]
Instructions: Name the type of angle relationship. Set up the
equation and solve for x.
X + 89
850
»
Angle Relationship: These are
angles.
Equation:
Solve: 2
Check
Answer:
interior alternative angles
x=--4°
Step-by-step explanation:
please mark me as brainlest
Where is my buddy? Helllo buddy nice to see you
Answer:
[tex]\sf\fbox\red{Answer:-}[/tex]
gud noon!
dopamine is responsible for how we feel pleasure
[tex]\small\fbox{\blue{\underline{mαrk \; mє \; вrαínlíєѕt \; plєαѕє ♥}}}[/tex]
I need to know this hard wuestion!
The value '0' is between the points above sea level and points below sea level. '0' being neither negative nor positive means it cannot be below or above sea level, rather '0' meters represents sea level.
Hope that helps!
What is the value of x in the triangle?
A: 10/2
B: 10
C: 20
D 20/2
E: 10/3
Answer:
[tex]A. 10\sqrt{2}[/tex]
Step-by-step explanation:
The triangle is a 45-45-90 triangle, which has the property that the side across from the 90°, in this case, x, is equal to one of the other sides multiplied by [tex]\sqrt{2}[/tex].
So:
10 x [tex]\sqrt{2}[/tex] = [tex]10\sqrt{2}[/tex]
The value of x in the given triangle is 10√2. So, correct option is A.
In triangle ABC, since angle B is a right angle, we can use the Pythagorean theorem to find the length of side AC (denoted by x).
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, AB and BC are the two sides adjacent to the right angle:
AB² + BC² = AC²
Substitute the given values:
10² + 10² = x²
100 + 100 = x²
200 = x²
Now, to find the value of x, take the square root of both sides:
x = √200
Simplify the square root:
x = √(100 * 2)
x = 10√2
So, the value of x in the triangle is 10√2.
The correct answer is A: 10√2.
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A person wants to order ferns for his garden He checked the price at a nursery and found that the nursery charges 89 for delivery and $5 for each plant ordered He also noted that there are no debvery charges lors
of $70 or more. Based on his findings, he wrote the following functions
f(n) = 9+ Sn to represent the cost of n plants when a delivery charge is included
• g(n) = 5n to represent tt» cost of n plants with no delivery charge
Match the domain to the function
All positive integers All integers greater than or equal to 70 All positive integers less than 70 All integers greater than or equal to 14
All non-negative integers less than 14 All non-negative integers less than 70 All positive integers less than 14
Domain
Function
g(n)
Answer:All non-negative integers less than 70 for f(n) and All integers greater than or equal to 70
Step-by-step explanation:
It asks about the price before and after the free delivery.I’m not the best at explaining but I hope my answer helped.
The domain of the given functions are required.
The domain of [tex]f(n)[/tex] is All non-negative integers less than 14.
The domain of [tex]g(n)[/tex] is All integers greater than or equal to 14.
When the order is less than $70 a delivery charge of $89 is added and each plant costs $5.
The function representing the situation is
[tex]f(n)=89+5n[/tex]
If the order is or more than $70 then the function will be
[tex]g(n)=5n[/tex]
The domain of a function is the permissible values of [tex]n[/tex] for which the function is valid.
In the first function the number of plants that need to be bought so that the order will be 70 dollars would be
[tex]\dfrac{70}{5}=14[/tex]
So, only if less than 14 plants are bought then the first function can be used.
Also, the number of plants cannot be negative or zero hence it will be positive.
So, the domain of [tex]f(n)[/tex] is All non-negative integers less than 14.
In the second function the number of plants has to be 14 or more as it costs 70 dollars or more.
So, the domain of [tex]g(n)[/tex] is All integers greater than or equal to 14.
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In order for Tiger Woods to get the ball in the hole, he must get it within an area of 14.18 square inches. What is the approximate diameter of a golf hole?
30 points pls show work thank you so much!!!
It can be noted that the diameter will be 4.26 inches.
How to calculate the diameter?From the information given, the area has been given as 14.18 square inches.
Therefore, the diameter will be calculated thus:
πr²= 14.18
3.14 × r² = 14.8
r² = 14.18/3.14
r² = 4.5
r = 2.13
Therefore, the diameter will be;
= 2r
= 2 × 2.13
= 4.26 inches.
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The measure of angle B is 68 degrees. What is the measure of its supplementary angle?
112
suplementry angle add to 180 so 180_68=112
Patricia deposits 24% of her weekly paycheck into her savings account. This week, she deposits $120. How much was Patricia's total paycheck this week?
Answer:
$500
Step-by-step explanation:
To start, convert 24% to a decimal, or .24. Then, divide $120 by .24 to get the original amount, and you get $500. To check your work, you can multiply $500 by the 24% to make sure you get $120.
Hopefully this helps - let me know if you have any questions!
Exercises
1.
Create a real-world situation that relates to the points shown in the number line model. Be sure to describe the
relationship between the values of the two points and how it relates to their order on the number line.
0
A real-world situation to model the number line is: It was colder on Friday night than Saturday morning because 0 is greater than -1
How to interpret the number line?See attachment for the number line
From the figure, we have the following points
0 and -1
The number line can be modelled by temperature where a colder temperature is represented by 0, while the other temperature is -1 degrees Celsius
Hence, a complete scenario is:
On a Friday night, the measure of the temperature is 0 degrees Celsius. On Saturday morning, the temperature is -1 degree Celsius. It was colder on Friday night than Saturday morning because 0 is greater than -1
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What is the inverse of the function f(x) = 2x + 1?
Answer: X minus 1 over 2
Step-by-step explanation:
Use an inverse function calculator
Round to the nearest hundredth 13.711309201
Answer: 13.71
Step-by-step explanation:
Hundredths is the second place
Answer:
13.71
Step-by-step explanation:
The hundredths place is the second decimal, and, since the decimal after that is a 1, you round down and get 13.71
Which expression is equivalent to Measure of angle 4?
Which expression is equivalent to Measure of angle 4?
A triangle has angles 1, 2, 3. The exterior angle to angle 1 is 4, to angle 2 is 5, to angle 3 is 6.
Measure of angle 2 + measure of angle 3
Measure of angle 1 + measure of angle 2
Measure of angle 1 + measure of angle 3
Measure of angle 5 + measure of angle 6
Answer: A
Step-by-step explanation:
Answer:
The answer is A;
✔ m∠2 + m∠3
5) Justin went cliff diving. He started out on a cliff that
was 8 feet above the water, and ended up 15 feet
below the surface of the water. How far away from his
starting point was he when he finished?
Number
Answer:
23
Step-by-step explanation:
8+15=23
in all, he moved 8 feet to the water, then another 15 feet below the water. this means that he ended up (8+15) feet from where he started.
Answer:
23
Step-by-step explanation:
(a) A square has a perimeter of 68 cm. What is the length of each side?
Answer:
17cm
Step-by-step explanation:
The perimeter of a square is the 4 sides added up, so we can just divide 4 by 68 to find out what one length is.
68/4= 17
We can prove this by adding it again.
17+17+17+17=68
A ball is thrown straight up from the top of a building that is 400 ft high with an initial velocity of 64 ft/s. The height of the object can be modeled by the equation s ( t ) = -16 t2 + 64 t + 400.
In two or more complete sentences explain how to determine the time(s) the ball is higher than the building in interval notation.
Check the picture below.
the ball is higher than the building when y = 0, or namely when s(t) = 0, any other time is above it, and hmmm when it's that?
[tex]\stackrel{s(t)}{0}~~ = ~~-16t^2+64t+400\implies 0=-16(t^2-4t-25) \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{1}t^2\stackrel{\stackrel{b}{\downarrow }}{-4}t\stackrel{\stackrel{c}{\downarrow }}{-25} \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t= \cfrac{ - (-4) \pm \sqrt { (-4)^2 -4(1)(-25)}}{2(1)}\implies t=\cfrac{4\pm\sqrt{116}}{2}[/tex]
[tex]t=\cfrac{4\pm 2\sqrt{29}}{2}\implies t= \begin{cases} 2+\sqrt{29}~~\textit{\Large \checkmark}\\ 2-\sqrt{29} \end{cases}~\hfill \boxed{(0~~,~~2\sqrt{29})}[/tex]
notice, we can't use the 2-√29 because is a negative value and "t" is never negati ve, also notice the interval notation, we have parentheses on both sides.
Maya used a recipe in which 2 tablespoons of vinegar were mixed with 3 tablespoons of olive oil. Which statement about the amount of vinegar mixed with olive oil is true?
2 over 3 tablespoon of vinegar is mixed with every tablespoon of olive oil because the ratio of vinegar to olive oil is 2:3.
2 over 3 tablespoons of vinegar is mixed with every 5 tablespoons of olive oil because the ratio of vinegar to olive oil is 2:5.
2 over 5 tablespoons of vinegar is mixed with every 5 tablespoons of olive oil because the ratio of vinegar to olive oil is 2:5.
2 over 5 tablespoon of vinegar is mixed with every tablespoon of olive oil because the ratio of vinegar to olive oil is 2:3.
Answer:
Step-by-step explanation: becuase if the ratio is 2:3 then the ratio reduced to 1 would be 2/3:1
Answer:
(First Option): 2 over 3 tablespoon of vinegar is mixed with every tablespoon of olive oil
Step-by-step explanation
For every 2 tablespoons of vinegar, it was mixed with 3 tablespoons of olive oil. This leads to a ratio of 2:3, and that rules out option 2 and 3. To get the unit rate we divide 2 tablespoons of vinegar by 3 tablespoons of olive oil. This means that there is 2/3 tablespoons of vinegar for every tablespoon of olive oil and leads it to be answer choice 1.
Critical Thinking: Data Transformation In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 5, 9, 10, 11, 15.
(a) Use the defining formula, the computation formula, or a calculator to compute s.
(b) Multiply each data value by 5 to obtain the new data set 25, 45, 50, 55, 75. Compute s.
(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?
(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s 3.1 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calcula- tions? Given 1 mile 1.6 kilometers, what is the standard deviation in kilometers?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data : 5, 9, 10, 11, 15
s = √[(ΣX - m)² / (n - 1)]
n = number of sample = 5
m = mean
m = ΣX/n
m = (5 + 9 + 10+ 11 + 15) / 5
m = 50/5 = 10
s =√((5-10)^2 + (9-10)^2 + (10-10)^2 + (11-10)^2 + (15-10)^2) / 5-1
= 3.601
(B) Multiply each data value by 5 to obtain the new data set 25, 45, 50, 55, 75. Compute s.
m = ΣX/n
m = (25 + 45 + 50 + 55 + 75) / 5
m = 250/5 = 50
s =√((25-50)^2 + (45-50)^2 + (50-50)^2 + (55-50)^2 + (75-50)^2) / 5-1
= 18. 028
(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?
The standard deviation changes by almost c times multiplied by the initial value.
3.601 * 5 = 18.005 which is almost equivalent to 18.028
(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s 3.1 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calcula- tions?
No
Given 1 mile 1.6 kilometers, what is the standard deviation in kilometers?
If 1 mile = 1.6km
s = 3.1 miles
s in kilometers = (1.6 * 3.1) = 4.96km