Hello!
3a = 7b =>
=> 3 × a = 7 × b =>
=> a/b = 7/3
Good luck! :)
Tamir wants to buy a snowboard. The original price is $760. How much will Tamir pay if he buys it during the sale?
Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened?
Answer:
Lf(x) = Lg(x) = Lh(x) = 1 - 2x
value of the functions and their derivative are the same at x = 0
Step-by-step explanation:
Given :
f(x) = (x − 1)^2,
g(x) = e^−2x ,
h(x) = 1 + ln(1 − 2x).
a) Determine Linearization of f, g and h at a = 0
L(x) = f (a) + f'(a) (x-a) ( linearization of f at a )
for f(x) = (x − 1)^2
f'(x ) = 2( x - 1 )
at x = 0
f' = -2
hence the Linearization at a = 0
Lf (x) = f(0) + f'(0) ( x - 0 )
Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x
For g(x) = e^−2x
g'(x) = -2e^-2x
at x = 0
g(0) = 1
g'(0) = -2e^0 = -2
hence linearization at a = 0
Lg(x) = g ( 0 ) + g' (0) (x - 0 )
Lg(x) = 1 - 2x
For h(x) = 1 + ln(1 − 2x).
h'(x) = -2 / ( 1 - 2x )
at x = 0
h(0) = 1
h'(0) = -2
hence linearization at a = 0
Lh(x) = h(0) + h'(0) (x-0)
= 1 - 2x
Observation and reason
The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0
We roll a pair dice 10,000 times. Estimate the probability that the number of times we get snake eyes (two ones) is between 280 and 300.
Answer:
0.3573 = 35.7%
Step-by-step explanation:
We roll a pair of dice 10,000 times so the mean and standard deviation is,
μ = 10000/36 =277.7 σ = [tex]\sqrt{10000*\frac{35}{36^{2} } } =16.4[/tex]
[tex]z_{1}[/tex] = (280 - 277.7)/16.4 = .14
[tex]z_{2}[/tex] = (300 - 277.7)/16.4 = 1.35
Probablity (range)
0.3573
Z(low)=0.14 0.555766357
Z(upper)=1.36 0.91304644
What is the value of the expression [-7] + [-4]
Answer:
11
Step-by-step explanation:
I'm assuming that [.] fldenote absolute value even tho the absolute value function is represented by (|.|)
value of [-7] will be positive that us 7.
= 7 + 4
= 11
What is the value of x?
Answer:
22
Step-by-step explanation:
3x-14= 4(x-9)
3×-14= 4x-36
4x-36-3x+14=0
×-22÷0
x=22
Xavier is testing different types of planting soil to determine which type is most effective in growing blueberry bushes. He purchases two different brands of planting soil from a local store. Xavier applies Brand A to an area of the yard that receives full sunlight and Brand B to another area of the yard that is in partial sunlight. He waters the area with Brand B daily; he waters the area with Brand A every other day. At the end of the study, Xavier concludes Brand A is more effective in growing blueberry bushes. Why is his conclusion not valid?
Answer:
He did not control for lurking variables and their impacts on the results of his experiment. Amount of sunlight and water received are two outside variables(or confounding variables) that may impact the growth of his plants and influence the results. He needs to apply the same amount of sunlight and water to each plant within a different planting soil in order to rule out the influence of those two variables and test the sole effect of the soil brand on the plant growth. Otherwise, it would be hard to determine whether his plant growth was because of the soil brand or the different amounts of sunlight and water received
Answer:
Invalid
Step-by-step explanation:
Xavier did not control variables or the impacts of the results. Confounding variable being sunlight and water received are two outside variables that can impact growth influence results. Within a different planting soil, Xavier will apply the same amount of sunlight & water to each plant to rule out the influence of those two variables. The test for sole effect on the plant with growth otherwise be determine. Is the plant growth because of the soil brand or the different amounts of sunlight and water received? This could and will impaired the results of this experiment, therefore, making it invalid.
HELP AGAIN
235 ≤-8(1+5x)+3
i need the steps as well
Answer:
x ≤ -6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
235 ≤ -8(1 + 5x) + 3
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 3 on both sides: 232 ≤ -8(1 + 5x)[Division Property of Equality] Divide -8 on both sides: -29 ≥ 1 + 5x[Subtraction Property of Equality] Subtract 1 on both sides: -30 ≥ 5x[Division Property of Equality] Divide 5 on both sides: -6 ≥ xRewrite: x ≤ -6Step-by-step explanation:
To solve for x, make sure you move everything else to the other side of the ≤ sign.
So,
[tex]235\leq -8(1+5x)+3\\232\leq -8-40x\\240\leq -40x\\-6\geq x[/tex]
* Remember that the sign changes anytime you divide by a negative number!
So your answer is:
[tex]x\leq -6[/tex], x is less than or equal to -6.
Help asap!!!!!!
A.
B.
C.
D.
Answer:
Function has a minimum value
So, f(x)=0 and f(4)=-3
f(x)= - 1/2x^2+4x-11f(4)=-3 and f(x)=-x+4
f(4)=0
OAmalOHopeO
a student estimates the length of a room to be 20 feet. The actual length is 20.25 feet. What is the percent error?
Answer:
Percent error=1.23%
Step-by-step explanation:
We are given that
Estimate length of room=20 feet
Actual length of room=20.25 feet
We have to find the percent error.
To find the percent error we will find the difference between the estimate length and actual length of room.
Difference=Actual length of room-Estimate length of room
Difference=20.25-20
Difference=0.25 feet
Now,
Percent error=[tex]\frac{Difference}{actual\;length}\times 100[/tex]
Percent error=[tex]\frac{0.25}{20.25}\times 100[/tex]
Percent error=1.23%
Factorize : 4(x+y)^2 -9(x-y)^2
Answer:
Step-by-step explanation:
[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]
= -5x² + 25xy + xy - 5y²
= 5x(-x + 5y) - y(-x +5y)
= (-x + 5y)(5x - y)
Complete the following statement.
Answer:
Hello dude
[tex] - 1 \frac{21}{24} + 1 \frac{22}{24} = + \frac{1}{24} [/tex]
so it's positive
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
26.3 times 1.2 please do with explanation worth 15 points
Answer - It’s 31.56
Step-by-step explanation: You just do regular multiplication and then add the decimal point
If BcA, AnB=(1,4,5)and AuB= (1,2,3,4,5,6) find B?
Hello,
if B ⊂ A then A∩B=B
So B={1,4,5}
As per the given value of sets, B is (1,4,5).
What is a set?A set is a collection of one or multiple data.
Given,
B ⊂ A
[tex]A[/tex] ∩ [tex]B = (1,4,5)[/tex]
[tex]A[/tex] ∪ [tex]B = (1,2,3,4,5,6)[/tex]
As B ⊂ A, therefor, B is a subset of A.
Therefore, [tex]A[/tex] ∩ [tex]B = B[/tex] and [tex]A[/tex] ∪ [tex]B = A[/tex]
Hence, [tex]B = A[/tex] ∩ [tex]B = (1,4,5)[/tex].
Learn more about a set here:
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Nikola thinks that the model that reflects the growth of smartphones shipped from manufacturers to stores around the world may be logistic rather than exponential. Do you agree with Nikola
Answer:
When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.
Step-by-step explanation:
Exponential model:
The variable keeps growing consistently, at a fixed rate.
Logistic model:
The variable starts growing, but as it approaches a limit, for example, the carry capacity of an environment, the growth rate starts to decrease, until the variable stabilizes at a fixed value.
Growth of smartphones shipped from manufacturers to stores around the world.
When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.
Monique made several batches of soup.
Each batch required 3/4 of a pound of potatoes. She used a total of 6 1/2 pounds. How many batches did she make?
Answer:
8 batches
in workings show whats left over but not counted.
As a batch its a whole number as the multiplier will usually be the fraction
and fraction / fraction should always show fraction but the whole number given with a remainder can be shown if not a whole number.
Step-by-step explanation:
6 1/2 = 6.5
and ;
3/4 of a pound = 0.75 of 1 pound
6.5 / 0.75 = 8.7 or in full workings write = 8.6666.....7
8.7/ 1 = 8 batches with 0.7 or 0.66667 left over
Answer In fraction for exam question given in fraction 8.7 = 8 batches
with 7/10 left over.
Find, correct to the nearest degree, the three angles of the triangle with the given ven
A(1, 0, -1), B(4, -3,0), C(1, 2, 3)
o
CAB =
O
LABC =
O
LBCA =
9514 1404 393
Answer:
∠CAB = 86°
∠ABC = 43°
∠BCA = 51°
Step-by-step explanation:
This can be done a couple of different ways (as with most math problems). We can use the distance formula to find the side lengths, then the law of cosines to find the angles. Or, we could use the dot product. In the end, the math is about the same.
The lengths of the sides are given by the distance formula.
AB² = (4-1)² +(-3-0)² +(0-(-1)) = 16 +9 +1 = 26
BC² = (1-4)² +(2-(-3))³ +(3-0)² = 9 +25 +9 = 43
CA² = (1-1)² +(0-2)² +(-1-3)² = 4 +16 = 20
From the law of cosines, ...
∠A = arccos((AB² +CA² -BC²)/(2·AB·CA)) = arccos((26 +20 -43)/(2√(26·20)))
∠A = arccos(3/(4√130)) ≈ 86°
∠B = arccos((AB² +BC² -AC²)/(2·AB·BC)) = arccos((26 +43 -20)/(2√(26·43)))
∠B = arccos(49/(2√1118)) ≈ 43°
∠C = arccos((BC² +CA² -AB²)/(2·BC·CA)) = arccos((43 +20 -26)/(2√(43·20)))
∠C = arccos(37/(4√215)) ≈ 51°
The three angles are ...
∠CAB = 86°
∠ABC = 43°
∠BCA = 51°
_____
Additional comment
This sort of repetitive arithmetic is nicely done by a spreadsheet.
Find the third term of a geometric progression if the sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
Given:
The sum of the first three terms = 12
The sum of the first six terms = (−84).
To find:
The third term of a geometric progression.
Solution:
The sum of first n term of a geometric progression is:
[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]
Where, a is the first term and r is the common ratio.
The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex] ...(i)
[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex] ...(ii)
Divide (ii) by (i), we get
[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]
[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]
[tex]r^3+1=-7[/tex]
[tex]r^3=-7-1[/tex]
[tex]r^3=-8[/tex]
Taking cube root on both sides, we get
[tex]r=-2[/tex]
Putting [tex]r=-2[/tex] in (i), we get
[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]
[tex]\dfrac{a(-8-1)}{-3}=12[/tex]
[tex]\dfrac{-9a}{-3}=12[/tex]
[tex]3a=12[/tex]
Divide both sides by 3.
[tex]a=4[/tex]
The nth term of a geometric progression is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get
[tex]a_3=4(-2)^{3-1}[/tex]
[tex]a_3=4(-2)^{2}[/tex]
[tex]a_3=4(4)[/tex]
[tex]a_3=16[/tex]
Therefore, the third term of the geometric progression is 16.
How would I solve the question below? In what order would I solve it?
4 ⋅ 3 + 2 ⋅ 9 − 40
Step-by-step explanation:
You would multiply 4 and 3, and 2 and 9 separately, then add them, then subtract 40. Remember PEMDAS.
(4*3) + (2*9) - 40
12 + 18 - 40
-10
Hope that helps
)
Gos
1. Select all the relations that represent a
function.
(3,2), (2,1), (3,9) (4,7)
(1,7), (2,2), (3,5) (4,8)
(2,6), (6,5), (3,2) (5,3)
(4,3), (3,3), (2,3) (1,3)
(2,2), (2,5), (2,1) (2,3)
Answer:
(1,7), (2,2), (3,5) (4,8)
(2,6), (6,5), (3,2) (5,3)
(4,3), (3,3), (2,3) (1,3)
Step-by-step explanation:
those represent functions b/c the domain of the relation is not written twice
Hope that'll help!
PLEASE HELP ASAP! What is the value of x in the inequality start fraction seven plus two x over five end fraction minus three less than x ?
A. x greater than negative start fraction eight over three end fraction
B. x less than negative start fraction eight over three end fraction
C. x greater than start fraction eight over three end fraction
D. x less than negative start fraction three over eight end fraction
Answer:
A
Step-by-step explanation:
the first one in the picture
If Mr. David does a job in x hours and Mr. Ludwig in y hours. What part of the job they could do together if they worked for k hrs?
Answer:
(1/x + 1/y)k is the answer :)
3. Express the strength of a solution both as a ratio and as a percentage if
2 L of the solution contain 400 mg of solute.
Answer:
1 : 5000
0.02%
Step-by-step explanation:
A solution = solute + solvent
A 2 Litre solution = (2 * 1000) = 2000 mg
Having, 400 mg of solute ;
Recall ;
1 mg = 0.001 ml
400 mg = (0.001 * 400) = 0.4 ml
The strength of the solution :
Amount of solute / Amount of solution
0.4 / 2000
As a ratio :
0.4 / 2000 = (0.4 * 10) / (2000*10) = 4 / 20000 = 1 / 5000 = 1 : 5000 (as a ratio)
0.4 / 2000
= 0.0002
(0.0002 * 100%) = 0.02% (As a percentage)
simplify 3x⁵y³ ÷2y² step by step
Answer:
3/2 x^5 y
Step-by-step explanation:
3x^5y^3
----------------
2y^2
Simplify the y terms
y^3 / y^2 = y^(3-2) = y
3/2 x^5 y
Answer:
[tex] \frac{3}{2} x {}^{5} y {}^{} [/tex]
Step-by-step explanation:
it's all in the image
Suppose the figure KLMN is dilated using a scale factor of 1/3 with the center of dilation at the origin. Which are the ordered pairs for the image?
1. K’(-1,3), L’(-3,0), M’(⅔, -8/3), N’(2, 4/3)
2. K’(-9,27), L’(-27,0), M’(6, -24), N’(18, 12)
3. K’(0,6), L’(-6,-3), M’(-1, -5), N’(3, 1)
4. K’(3,-1), L’(0,-3), M’(-8/3, ⅔), N’(4/3,2)
Answer:
K’(-1,3), L’(-3,0), M’(⅔, -8/3), N’(2, 4/3)
Step-by-step explanation:
7/3a - 8/5 +4/15a
Simplified
Answer:
13/5a - 8/5
Step-by-step explanation:
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
The simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is,7/3a - 8/5 +4/15a.
We have to simplify the expression.
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
=7/3a - 8/5 +4/15a
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
Thus, the simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
Learn more about the expression here:
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In a random sample of students at a university, stated that they were nonsmokers. Based on this sample, compute a confidence interval for the proportion of all students at the university who are nonsmokers. Then find the lower limit and upper limit of the confidence interval.
Answer:
(0.8165 ; 0.8819)
Lower boundary = 0.8165
Upper boundary = 0.8819
Step-by-step explanation:
Given :
Sample proportion. Phat = x/ n = 276/ 325 = 0.8492
Confidence interval :
Phat ± margin of error
Margin of Error = Zα/2* [√Phat(1 - Phat) / n]
Phat ± Zα/2* [√Phat(1 - Phat) / n]
The 90% Z critical value is = 1.645
0.8492 ± 1.645*[√0.8492(1 - 0.8492) / 325)
0.8492 ± 1.645*[√0.8492(0.1508) / 325]
0.8492 ± 1.645*√0.0003940288
0.8492 ± 0.0326535
Lower boundary = 0.8492 - 0.0326535 = 0.8165
Upper boundary = 0.8492 + 0.0326535 = 0.8819
Confidence interval = (0.8165 ; 0.8819)
solve 5x^2-2=-12 by taking the square root
Answer:
[tex]x = \sqrt{-2} = 2i[/tex]
Step-by-step explanation:
[tex]5x^2-2=-12[/tex]
[tex]5x^2 =-10[/tex]
[tex]x^2 =-2[/tex]
[tex]x = \sqrt{-2} = 2i[/tex]
I only need the odd numbers answered
Answer:
1.a+4=11
a=7
2.6=g+8
g=2
3.
?
4.k+8=3
k=-5
5.j+0=9
j=9
6.12+y=15
y=3
7.h-4=0
h=4
8.m-7=1
m=8
9.w+5=4
w=-2
10.b-28=33
b=61
11.45+f=48
f=3
12.n+7.1=8.6
n=1.5
Hope This Helps!!!
write the following sets in the set builder form C={1,4,9,16,25}
C={ check example in book}
identify the system by type
Answer:
Inconsistent system
Step-by-step explanation:
Given
The attached graph
Required
The type of system
When two lines are parallel, it means they have the same slope and as such, the system has no solution.
Equations with the same slope are:
[tex]y = 2x + 6[/tex]
[tex]y = 2x- 8[/tex]
Both have a slope of 2
Such system are referred to inconsistent system.
Hence, (c) is correct.
