As per the given system of linear equation, the number of solution is infinite.
Linear equations:
An algebraic equation of the form
y = mx + b
Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept is known as linear equation.
Given,
A system of three linear equations in three variables is consistent and dependent.
Here we need to find the number of solution for this system.
Here we know that the given system of three linear equations in three variables which is consistent and dependent.
We know that, the system is said to be consistent if it has at least one solution. Which means that the system which has no solution is said to be inconsistent.
Similarly, the system is has consistent solution is said to be independent if it has only one solution whereas it is said to be dependent if it has an infinitely many solutions.
Therefore, here the given system of three linear equations in three variables which is consistent and dependent, the system has an infinitely many solutions.
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123.05 to the nearest cent
Answer:
123.00
Step-by-step explanation:
after calculating the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (e) must be reduced to just 0.025. if the original calculation led to a sample size of 1000, the sample size will now have to be . place your answer, as a whole number in the blank. for example, 2345 would be a legitimate entry.
The sample size will now have to be is 3200.
Given:
the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (e) must be reduced to just 0.025. if the original calculation led to a sample size of 1000.
n = p(1-p)(z/E)^2
800 = 0.5(1-0.5)(z/0.05)^2
800 = 0.5*0.5* z^2/0.0025
800 = 0.25 * z^2/0.0025
800 = 25/100*10000*z^2/25
800 = 1*100*z^2
800/100 = z^2
8 = z^2
z = [tex]\sqrt{8}[/tex]
z = 2.8284
n = p(1-p)(z/E)^2
= 0.25(2.8284/0.025)^2
= 0.25*(113.136)^2
= 0.25*12799.754496
= 3199.938 ≈ 3200
Therefore the sample size will now have to be is 3200.
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PLEASE ANSWER THIS WITH AN EXPLANATION TO THE ANSWERS!!
Answer:
It is A. C. and D.
Step-by-step explanation.
The question is asking for the three different points to be moved, answer choice A is the answer for one point, answer C is for the second point, and answer D is for the third point.
everyday a person uses about 90 liters of water at home 6 gallons is about 23 liters about how many liters of water does a person use at home daily?
Answer:
90 liters
Step-by-step explanation:
It's given in the question!
Nina has some nickels and 9 pennies in her pocket. Her friend, Maurice, has twice as many nickels as Nina. Together, these coins are worth 84¢. How many nickels does Nina have? Show all of your work and label your answers
Answer:
x = 5
Step-by-step explanation:
Let's say
x = #s of nickels Nina has (we are going to try to get X)
y = # of nickels Maurice has
5x + 9 < The amount Nina has
y = 2x < Amount that Maurice has
Add them both to the total, 84
5x + 9 + 5y = 84
Transfer the 9 to the other side
5x + 5y = 75
Substitute y with it's value
5x + 5(2x) = 75
5x + 10x = 75
15x = 75
Divide
x = 5
help please and thankyou
The length of the side x on the right triangle is 41.06
What is a right triangle?A right triangle is a triangle that has one interior angle of 90°
The parameters in the right triangle are;
Acute angle = 47°
Leg length of side adjacent to 47° = 28
Length of the hypotenuse = x
From trigonometric ratios, we have;
[tex]cos(\theta) =\mathbf{ \dfrac{Length \, of \, adjacent \, side}{Length \, of \, Hypotenuse}}[/tex]
The cosine of the 47° angle is therefore;
[tex]cos(47^{\circ}) = \dfrac{28}{x}[/tex]
From which we have;
[tex]x= \dfrac{28}{cos(47^{\circ}) } \approx 41.06[/tex]
The length of the side, x ≈ 41.06
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w+5r use w=4 and r=6
What is the slope of a line perpendicular to the line whose equation is x-2y=-8 Fully simplify your answer.
Answer:
[tex]-2[/tex]
Step-by-step explanation:
The perpendicular slope is the opposite of the reciprocal of the original slope. So, let's find the slope of this line! I will put it in slope-intercept form (y = )
[tex]x-2y=-8\\-2y=-8-x\\y=4+\frac{1}{2} x\\y=\frac{1}{2} x+4[/tex]
Here, I see that the slope of the line is [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2. The opposite of 2 is [tex]-2[/tex]. The slope of the perpendicular line is [tex]-2[/tex]!
Solve for g.
l= gT2
47²
What is g equal to?
g=1²2
g=4771
g=47²lT2
g=47
The value of g = 4π²l/T²
Operations:Operators are Mathematical operations that emphasize particular actions like summing up, dividing, and adding multiple times, etc.
In Mathematics, the basic arithmetic operations are Addition, Subtraction Division, and Multiplication.
The symbols which are used for each operation are
Addition - (+)
Subtraction - (-)
Division - (÷)
Multiplication - (x)
Given [tex]l = \frac{gT^{2} }{4 \pi ^{2} }[/tex]
To get the 'g' value we will use Multiplication and Division
Multiply both sides with 4π²
=> [tex]4 \pi ^{2} (l )= \frac{gT^{2} }{4 \pi ^{2} }(4 \pi ^{2} )[/tex]
=> [tex]4 \pi ^{2} (l )= gT^{2}[/tex]
Divide by T² on both sides
=> [tex]4 \pi ^{2} (l )\frac{1}{T^{2}} = g\frac{T^{2}}{T^{2}}[/tex]
=> [tex]\frac{ 4 \pi ^{2} l }{T^{2}} = g[/tex]
=> [tex]g = \frac{ 4 \pi ^{2} l }{T^{2}}[/tex]
Therefore,
The value of g = 4π²l/T²
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Which equation illustrates the identity property of multiplication? (x yi) × z = (xz yzi) (x yi) × 0 = 0 (x yi) × (z wi) = (z wi) × (x yi) (x yi) × 1 = (x yi)
The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .
In the question ,
Four equations are given , we need to find the equation that represents the identity property of multiplication .
we know that the identity property of multiplication states that the product of any number and 1 is the same given number .
For Example : the product of a number 'a' and 1 is = a , that is a×1 = a .
So , by the applying the definition of Identity property of multiplication we get that the equation that models the identity property is
(a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi)
Therefore , The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .
The given question is incomplete , the complete question is
Which equation illustrates the identity property of multiplication?
(a) (a + bi) × c = (ac + bci)
(b) (a + bi) × 0 = 0
(c) (a + bi) × (c + di) = (c + di) × (a + bi)
(d) (a + bi) × 1 = (a + bi)
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Use the quadratic formula to solve for x.
8x²-8x-1=0
Answer:
in the picture
Step-by-step explanation:
Hope this helped! Solve your problem: Use the quadratic formula to solve for x.
8x²-8x-1=0
Which expression has the value of 7?
(3)+4
(3+4)
Answer:
both
Step-by-step explanation:
because the first one, since the number 4 isn’t next to the parentheses then we are not multiplying so it’s actually adding so it still equals 7
In the expansion (2+3x)^n .the coefficient of x^3 and x^4 are in the ratio if 8:15 find n
In the binomial expansion of (2 + 3x)ⁿ, the value of n = 22/5
What is binomial expansion?Binomial expansion is the expansion of the binomial (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ where ⁿCₓaˣbⁿ⁻ˣ is the general term and x = 0 to n
How to find the ratio of the coefficients of x³ and x⁴ in the expansion of (2 + 3x)ⁿ?Since we require the expansion of (2 + 3x)ⁿ, comparing it with the binomial expansion equation above (a + b)ⁿ.
So, a = 2 and b = 3x
So, the binomial expansion is (2 + 3x)ⁿ = ∑ⁿCₓ2ˣ(3x)ⁿ⁻ˣ
= ∑ⁿCₓ2ˣ(3ⁿ⁻ˣ)xⁿ⁻ˣ
So, the general term of (2 + 3x)ⁿ = ∑ⁿCₓ2ˣ(3ⁿ⁻ˣ)xⁿ⁻ˣ and the coefficient term is ⁿCₓ2ˣ(3ⁿ⁻ˣ)
Now since coefficient of x³ and x⁴ are in the ratio if 8:15. Then
For the x³ term, xⁿ⁻ˣ = x³
⇒ n - x = 3
⇒ x =n - 3
So, substituting this into the coefficient term, we have
ⁿCₓ2ˣ(3ⁿ⁻ˣ) = ⁿCₙ₋₃2ⁿ⁻ˣ(3³) =
Also, for the x⁴ term, xⁿ⁻ˣ = x³
⇒ n - x = 4
⇒ x =n - 4
So, substituting this into the coefficient term, we have
ⁿCₓ2ˣ(3ⁿ⁻ˣ) = ⁿCₙ₋₄2ⁿ⁻ˣ(3⁴)
Now since coefficient of x³ and x⁴ are in the ratio if 8:15, we have that
ⁿCₙ₋₃2ⁿ⁻ˣ(3³)/ⁿCₙ₋₄2ⁿ⁻ˣ(3⁴) = 8/15
ⁿCₙ₋₃/(ⁿCₙ₋₄ × 3)= 8/15
ⁿCₙ₋₃/ⁿCₙ₋₄= 8/15 × 3
ⁿCₙ₋₃/ⁿCₙ₋₄= 8/5
n!/(n - 3)![n - (n - 3)]! ÷ n!/(n - 4)![n - (n - 4)]! = 8/5
n!/(n - 3)![n - n + 3)]! ÷ n!/(n - 4)![n - n + 4)]! = 8/5
n!/(n - 3)!3! ÷ n!/(n - 4)!4! = 8/5
n!/3!(n - 3)! ÷ n!/4!(n - 4)(n - 3)! = 8/5
n!/3!(n - 3)! × 4!(n - 4)(n - 3)!/n! = 8/5
4!/3! × (n - 4) = 8/5
4 × 3!/3! × (n - 4) = 8/5
4(n - 4) = 8/5
Dividing through by 4, we have
(n - 4) = 8/(5 × 4)
(n - 4) = 2/5
Cross-multiplying, we have
5(n - 4) = 2
Expanding the brackets, we have
5n - 20 = 2
5n = 20 + 2
5n = 22
n = 22/5
So, the value of n = 22/5
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Grace is going to invest $650 and leave it in an account for 15 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Grace to end up with $1,490?
Answer:
5.5%
Step-by-step explanation:
You want the interest rate that can be compounded continuously to give $1490 from an investment of $650 after 15 years.
ValueThe formula for account value with continuously compounded interest is ...
A = Pe^(rt) . . . . P=principal, r=interest rate, t=years
Interest rateSolving for r, we find ...
ln(A/P)/t = r
ln(1490/650)/15 = 0.0553...
The interest rate is about 5.5%.
<95141404393>
find the sum. [1 4 [0 0
0 3] 0 0]
Answer:
1st
Step-by-step explanation:
Explanation in the picture.
a random sample of 362 california residents responded to a municipal water district poll about how often they water the garden or lawn. the response choices were: daily, every other day, 2-3 times per week, once per week, less than once. the municipal water district wants to know if there is a difference between watering habits in northern california and southern california. a municipal water district employee conducted a chi-square test of independence. in this results table, the observed count appears above the expected count in each cell. daily every other day 2-3 times per week once per week less than once per week totals northern 17 19.2 24 33.1 62 160.0 48 37.6 11 12.1 162 southern 26 23.8 50 40.9 72 74.0 36 46.4 16 14.9 200 totals 43 55 153 84 27 362 which hypothesis is appropriate for a test of independence? check all that apply. group of answer choices : living in northern or southern california is not associated with watering habits. : living in northern or southern california is associated with watering habits. : the proportion of northern california residents watering daily is equal to the proportion of southern california residents watering daily. : the proportion of northern california residents watering daily is less than the proportion of southern california residents watering daily.
The correct answer is H0 : Living in Northern or southern California is not associated with watering habits and Ha : Living Northern or southern California is associated with watering habits.
Given that,
H0 : Living in Northern or southern California is not associated with watering habits.
Ha : Living Northern or southern California is associated with watering habits.
In independent test in that test we Check the two variables are independent or not. The chi square can be used for any variable. Both the group (independent) and test variable(dependent) can be nominal, ordinal, or grouped interval.
Therefore, The difference between living in Northern or Southern California and the difference between living in Northern or Southern California is that the former is related to watering practices.
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74 - 21 x 6 + 329 / 2
74-126+329/2
-52+329/2
277/2
138.5
Becky ha 5 candy bar. She want to hare with 3 friend. How much will each friend get
Answer:
The number of candy bars each friend will receive is 1.66.
Step-by-step explanation:
Given that Becky has 5 candy bars
She wants to share them with 3 friends.
To determine the number of candy bars each friend will receive
We need to determine the number of candy bars each friend will receive
So, the number of candy bars would be
5/3 which would = to 1.66
and that's how much she will give each friend
the bacteria count in a certain culture was 200 after 10 days and 1200 after 20 days. assume the bacteria are growing exponentially
The initial size of the bacteria culture is 33
The count of the bacteria after 10 days = 200
The count of bacteria after 20 days = 1200
The difference in time = 20 - 10
= 10 days
Then the exponential growth equation will be
1200 = 200×[tex]e^{10k}[/tex]
[tex]e^{10k}[/tex] = 1200 / 200
Divide the terms
[tex]e^{10k}[/tex] = 6
10k = ln(6)
10k = 1.79
k = 1.79 / 10
Divide the terms
k = 0.179
Use the same equation to find the initial size of the bacteria culture
200 = x × [tex]e^{10(0.179)}[/tex]
x = 200 / [tex]e^{10(0.179)}[/tex]
x = 200 / 5.99
Divide the terms
x = 33.38
x ≈ 33
Hence, the initial size of the bacteria culture is 33
The complete question is:
The bacteria count in a certain culture was 200 after 10 days and 1200 after 20 days. assume the bacteria are growing exponentially. Find the initial size of the bacteria culture
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what is 100x100x200x1x2000x10000,000x40000x1000002x0000003xxxxxxxxxxxx000000
Answer:16.e+6.18
Step-by-step explanation:
Review for Features of Functions Assessment
Suppose that the function f(x) = 20 + 5.5x represents the cost of making x t-shirts.
a. What is f(12)?
b. What does your answer to part a mean in context?
During the past five months, Elle
spent $3.25 on candy, $12.09 on
cupcakes, and $9.88 on chips. ABOUT
how much did Elle spend?
solve each linear inequality for y
1. 2x+3y>12
2. 3x-2y<6
3. 4y-2x≥4x+3(y-2)
Thus, solving the linear inequalities for y we have
y > 4 - (2/3)x,
y > (3/2)x - 3, and
y ≥ 6x - 6
We have to solve each of the linear inequality for y.
1. The given linear inequality is -
2x + 3y > 12
=> 3y > 12 - 2x
=> y > 4 - (2/3)x
2. The given linear inequality is -
3x - 2y < 6
=> -2y < 6 - 3x
=> 2y > 3x - 6
=> y > (3/2)x - 3
3. The given linear inequality is -
4y - 2x ≥ 4x + 3(y-2)
=> 4y - 2x ≥ 4x + 3y - 6
=> 4y - 3y ≥ 4x + 2x - 6
=> y ≥ 6x - 6
Thus, solving the linear inequalities for y we have
y > 4 - (2/3)x,
y > (3/2)x - 3, and
y ≥ 6x - 6
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You jog 2 kilometers in 12 minutes. Your friend jogs
3 kilometers in 16.5 minutes. Who jogs faster? How much sooner will the faster
jogger finish a five-kilometer race?
Answer:
Person 2 jogs faster as compared to person 1.
The time taken by the faster jogger finish a five-kilometer race will be, 27.5 minutes.
Step-by-step explanation:
speed = distance/time
i need help with this
Answer:
[tex](f+g)(x)=7x^2-3x-5[/tex]
Step-by-step explanation:
Step 1: What you are given & need to find
[tex]f(x)=\sqrt{16x^4}[/tex][tex]g(x)=3x^2-3x-5[/tex][tex](f+g)(x) = ?[/tex]Step 2: Set up the problem
[tex](f+g)(x) = f(x)+g(x)[/tex][tex](f+g)(x)=(\sqrt{16x^4} )+(3x^2-3x-5)[/tex]Step 3: Simplify
[tex](f+g)(x)=\sqrt{16x^4} +3x^2-3x-5[/tex][tex](f+g)(x)=4x^2+3x^2-3x-5[/tex][tex](f+g)(x)=7x^2-3x-5[/tex]PLEASE HELP ASAP pics below!!
Answer:
l = 1
Step-by-step explanation:
v = lwh
8 = l(2)(4)
8 = l8 Divide both sides by 8
1 = l
what is the range of the function f(x)=|x-5|-3
Answer:
[3, ∞]
Step-by-step explanation:
Calculate Average Speed
A train leaves London at 11:30 and arrives in Brighton at 12:30.
The distance between the two stations is 80 km.
Find the average speed in km/h.
Answer:
The average speed is 80km/h.
Step-by-step explanation:
In order to calculate the average speed you have to divide the total distance by the total elapsed time:
Let t represent time (in hours)
t=12:30-11:30=1
Let D represent distance (in kilometers)
D=80
Therefore, since t=/=0:
D/t=80/1=80km/h
And there you have it! Your answer is 80 km per hour.
A bike path is 12.5 miles. Dominic is 70% of the way to the end. How far is Dominic on the path? HELPPP PLEASE :
Answer:
The percentage of the distance Dominic is on the path is his distance
travelled as a fraction of the total distance when equivalent to 100.
The distance he has travelled on the path is 8.75 miles.
Reasons:
The given parameter are;
Length of Dominic's path = 12.5 miles
The length of the way Dominic is to
Step-by-step explanation:
Solve the following equations. Will give brainliest.
Answer:
[tex]x=10^{\frac{4}{3}}=\sqrt[3]{10000}[/tex]
Step-by-step explanation:
Given equation:
[tex]9^{\log_3 (\log x)}= \log x-2\log^2x+4[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^{\log_3 (\log x)}= \log x-2\log^2x+4[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2\log_3 (\log x)}= \log x-2\log^2x+4[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies 3^{\log_3 (\log x)^2}= \log x-2\log^2x+4[/tex]
[tex]\textsf{Apply log law}: \quad a^{\log_ab}=b[/tex]
[tex]\implies (\log x)^2= \log x-2\log^2x+4[/tex]
Simplify:
[tex]\implies\log ^2 x= \log x-2\log^2x+4[/tex]
[tex]\implies 3\log ^2 x- \log x-4=0[/tex]
Let log(x) = u:
[tex]\implies 3u^2-u-4=0[/tex]
Factor:
[tex]\implies 3u^2+3u-4u-4=0[/tex]
[tex]\implies 3u(u+1)-4(u+1)=0[/tex]
[tex]\implies (3u-4)(u+1)=0[/tex]
Apply the zero-product property:
[tex]\implies 3u-4=0 \implies u=\dfrac{4}{3}[/tex]
[tex]\implies u+1=0 \implies u=-1[/tex]
Substitute u=log(x) back in:
[tex]\implies \log x = -1[/tex]
[tex]\implies \log x= \dfrac{4}{3}[/tex]
On the left side of the original equation, we have log₃ (log x).
As logs of negative numbers cannot be taken, log(x)=-1 is not a valid solution since this would give log₃(-1) which is undefined.
Therefore, the only valid solution is:
[tex]\implies \log x= \dfrac{4}{3}[/tex]
[tex]\implies x=10^{\frac{4}{3}}[/tex]
[tex]\implies x=\left(10^4\right)^{\frac{1}{3}}[/tex]
[tex]\implies x=10000^{\frac{1}{3}}[/tex]
[tex]\implies x=\sqrt[3]{10000}[/tex]
Note: If a log has no base, assume that the base is 10.