Answer:
x = 3, -5
Step-by-step explanation:
I just know
Answer:
x= -5
x=3
Step-by-step explanation:
You are factoring here. The standard form of an equation is Ax² + Bx + C.
The 2 factors must multiple together to be C, but add together to be B. The easiest way to do this is to factor C.
C is -15. Factoring this, we find the only factors of 15 that will add together to be 2 are 5 & -3.
Therefore, the factors are (x+5) and (x-3). If you set each of these factor pairs to 0 and solve, the answers are:
x+5=0
x = -5
x-3 = 0
x=3
Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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In a survey of 320 college graduates, 36% reported that they stayed on their first full-time job less than 1 year. If 15 of those subjects are randomly selected without replacement for a follow-up survey, find the probability that exactly 5 of them stayed on their job for less than one-year.
Name the variables in the context of the problem.
State the requirements for binomial distribution for this problem.
Use the long formula above to find P(x)
Using the binomial distribution, there is a 0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, there is a fixed number of independent trials, each with only two possible outcomes, hence the binomial distribution is used. The values of the parameters are:
n = 15, p = 0.36.
The probability is P(X = 5), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.36)^{5}.(0.64)^{10} = 0.2094[/tex]
0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.
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solve the equation: z^ +4z+20+iz(a+1)=0 Where A is constant, has complex conjuget root. if one of roots this quadratic is z=B+2i?
The complex conjugate roots exists A = -1 - 4i or A = -1 + 12i.
How to estimate complex conjugate roots?
If one of the roots exists w = B + 2i, then the other root exists its conjugate w = B - 2i. So we can factorize the quadratic to
[tex]z^2+4z+20+iz(A+1) = (z-(B+2i))(z-(B-2i))[/tex]
Expand the right side and collect all the coefficients.
[tex]z^2+(4+(A+1)i)z+20 = z^2-2Bz+B^2+4[/tex]
From the z and constant terms, we have
[tex]$\left \{ {{4+(A+1)i = -2B} \atop {20 = B^2+4}} \right.[/tex]
From the second equation, we get
[tex]B^2 = 16[/tex]
B = ± 4
Then 4+(A+1)i = ± 8
(A + 1)i = 4 or (A + 1)i = -12
Since [tex]$\frac{1}{i} = -i[/tex], we have
[tex]$\frac{-A+1}{i} =4[/tex] or [tex]$\frac{-A+1}{i} =-12[/tex]
A+1 = -4i or A+1 = 12i
A = -1-4i or A = -1+12i
Therefore, the complex conjugate roots exists A = -1-4i or A = -1+12i.
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In the following triangle, point O is the midpoint of LM, and point P is the midpoint if LN.
Below is the proof that OP||MN. The proof is divided into four parts, where the title of each part indicates its main purpose.
Complete part D of the proof.
Part A: Prove LM/LO=2
Part B: Prove LN/LP=2
Part C: Prove LMN ~ LOP
Part D: Prove OP||MN
The complete proof for part D is given in the attached text. Hence, by the nature of the converse corresponding angle,
OP is parallel to MN. (OP ║ MN).
What is a mathematical proof?A mathematical proof is an argument that is inferential with respect to a mathematical assertion that demonstrates that the provided assumptions logically ensure the conclusion.
The complete proof for part D is given as follow:
If a transversal line "t" divides through OP and MN as given in the attached image, and SE and "T.F" are the divider of ∠QSD and ∠STM, then:
∠QSE = 1/2 ∠QSO; and
∠"STF" = 1/2 ∠STM
If the corresponding angle is ∠QST = "STF", then
QSD = "STF"
Hence, by the nature of the converse corresponding angle,
OP is parallel to MN
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a study of nickels showed that the standard deviation of the weight of nickels is 300 milligrams. A coin counter manufacture wishes to find the 90% confidence interval for the average weight of a nickel. What is the minimum number of nickels he needs to weigh to obtain an average accurate to within 20 milligrams?
Using the z-distribution, a sample of 609 nickels has to be weighed.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.For this problem, the parameters are:
[tex]M = 20, \sigma = 300, z = 1.645[/tex]
We solve for n to find the sample size, then:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]20 = 1.645\frac{300}{\sqrt{n}}[/tex]
[tex]20\sqrt{n} = 1.645 \times 300[/tex]
[tex]\sqrt{n} = 1.645 \times 15[/tex]
[tex](\sqrt{n})^2 = (1.645 \times 15)^2[/tex]
n = 608.9
Rounding up, a sample of 609 nickels has to be weighed.
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The volume of a prism with side lengths measured in millimeters is 20. How could this measurement be written? Check all that apply.
The unit measurement of the a volume in mm is mm³(millimetres cube.)
How to find volume ?Volume is is defined as the space occupied within the boundaries. The objects are usually solid objects.
The volume of a 3 dimensional figure is the product of the base area and the height.
Therefore, the units of volume is measured in cubic units.
The volume of a prism with side lengths measured in millimetres is 20.
Therefore, the measurement can be represented as follows:
20 mm³
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1. Which of the following results in the difference of two squares?
O (3r-5y) (3x - 5y)
O (5x+3y) (5x-3y)
O 4r²(3r-9)
O (2r-3y)2
The difference of two squares is (5x+3y) (5x-3y)
How to determine the difference of two squares?The difference of two squares of variables a and b is represented as:
(a + b)(a - b) = a^2 - b^2
By comparing the list of options, we have:
(5x+3y) (5x-3y)
This means that
a = 5x and b = 3y
Hence, the difference of two squares is (5x+3y) (5x-3y)
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An exponential function f ( x ) = a b x f ( x ) = a b x passes through the points (0, 10000) and (3, 2160). What are the values of a and b ?
The values of a and b of the exponential function are 10000 and 0.6 respectively
How to solve exponential functions?We are given that the exponential function is expressed in general form as; f(x) = abˣ
where;
a is a non-zero real number called the initial value
b is any positive real number such that
b ≠ 1.
The domain of f is all real numbers.
The range of f is all positive real numbers if a > 0.
The range of f is all negative real numbers if a < 0.
The y-intercept is (0, a)
The horizontal asymptote is; y = 0.
We are told that this exponential function passes through the coordinate points (0, 10000) and (3, 2160).
At coordinate point (0, 10000), we have;
10000 = ab⁰
a = 10000
Now, at the coordinate point (3, 2160), we have;
2160 = 10000(b)³
2160/10000 = b³
0.216 = b³
b = ∛0.216
b = 0.6
Thus, we can conclude that the values of a and b of the given exponential function are respectively 10000 and 0.6.
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What is the value of a?
O 5 units
05/
units
6 units
O 7 units
From the Δ YWZ we get c = 5 then the value of [tex]$a= 5 \frac{1}{3}[/tex].
How to estimate the value of a?In the given Δ YWZ
WZ² = YW² + YZ²
c² = 4² + 3² = 16 + 9 = 25
c = 5
In the Δ XYW
b² = 4² + a²-----(1)
In the right-angle Δ WXZ
(a + 3)² = b² + c²
a² + 9 + 6a = b²+ c²
By putting the value of b² from (1)
a² + 9 + 6a = 16 + a² + 25
Simplifying the above equation, we get
6a + 9 = 41
6a = 41 - 9
6a = 32
[tex]$a = \frac{32}{6} = \frac{16}{3}[/tex]
[tex]$a= 5 \frac{1}{3}[/tex]
Therefore, the value of [tex]$a= 5 \frac{1}{3}[/tex].
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Find the integrals:
∫30x^2/√(x-4) dx
u=x-4 and u=√(x-4)
I assume you're asked to compute
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx[/tex]
using both of the substitutions provided.
With [tex]u=x-4[/tex], we have [tex]x=u+4[/tex] and [tex]dx=du[/tex]. Then
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{30(u+4)^2}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \frac{u^2 + 8u + 16}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \left(u^{3/2} + 8u^{1/2} + 16u^{-1/2}\right) \, du \\\\ ~~~~~~~~ = 30 \left(\frac25 u^{5/2} + \frac{16}3 u^{3/2} + 32 u^{1/2}\right) + C \\\\ ~~~~~~~~ = 12 u^{5/2} + 160 u^{3/2} + 960 u^{1/2} + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4 \sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]
With [tex]u=\sqrt{x-4}[/tex], we have
[tex]u^2 = x-4 \implies x^2 = (u^2+4)^2[/tex]
and [tex]2u\,du=dx[/tex]. Then
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{60u \left(u^2+4\right)^2}u \, du \\\\ ~~~~~~~~ = 60 \int \left(u^4 + 8u^2 + 16\right) \, du \\\\ ~~~~~~~~ = 60 \left(\frac15 u^5 + \frac83 u^3 + 16u\right) + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4\sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]
Find the period of the function y = 2∕3 cos(4∕7x) + 2. Question 11 options: A) 7∕2π B) 4∕7π C) 3π D) 7∕4π
The period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π
How to determine the period of the function?The function is given as:
y = 2∕3 cos(4∕7x) + 2.
The above function is a cosine function
A cosine function is represented as:
y = A cos(B(x + C)) + D
Where the period is
Period = 2π/B
By comparing the equations, we have
B = 4/7
Substitute B = 4/7 in Period = 2π/B
Period = 2π/(4/7)
Express as product
Period = 2π * 7/4
Divide 4 by 2
Period = π * 7/2
Evaluate the product
Period = 7/2π
Hence, the period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π
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What is the domain of y = 4 log5 (x - 3)?
A. all real numbers
B. all real numbers greater than 4
C. all real numbers greater than 5
D. all real numbers greater than 3.
The domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.
How to determine the domain?The function is given as:
[tex]y=4\log_5(x-3)[/tex]
Set the expression in bracket greater than 0
x -3 > 0
Add 3 to both sides
x > 3
Hence, the domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.
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PLEASE someone help me with this question, I’ve been stuck on it for so long :(
Help is greatly appreciated! I know what the answer is ( back of my textbook) but i dont know how to figure it out
Oh also if it’s possible could you please take a picture of your handwritten answer instead of typing it since its easier for me to understand , but either way is fine :)
Answer:
13.5 litres
Step-by-step explanation:
the ratios are 2 : 3 : 4 = 2x : 3x : 4x ( x is a multiplier )
given Henrietta produced 1.5 litres more than Gladys , then
4x = 3x + 1.5 ( subtract 3x from both sides )
x = 1.5
then total milk produced by the 3 cows is
total = 2x + 3x + 4x = 9x = 9 × 1.5 = 13.5 litres
A ball is thrown downward from the top of a 120-foot building with an initial velocity of 20 feet per second. The
height of the ball h in feet after t seconds is given by the equation h= - 16t²-20t+120. How long after the
ball is thrown will it strike the ground?
Answer:
[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]
Step-by-step explanation:
The ball strikes the ground when h = 0.
[tex]-16t^2 - 20t + 120 = 0 \\ \\ 4t^2 + 5t - 30=0 \\ \\ t=\frac{-5 \pm \sqrt{5^{2}-4(4)(-30)}}{4(2)} \\ \\ t=\frac{-5 \pm \sqrt{505}}{8}[/tex]
However, as time most be positive, we only consider the positive case.
So,
[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]
Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.
Using simple interest, it is found that the APR is of 4.472%.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.The parameters are given as follows:
A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.
Hence the APR is found as follows:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]3067.08 = 3000(1 + 0.5r)[/tex]
[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]
1 + 0.5r = 1.02236
r = (1.02236 - 1)/0.5
r = 0.04472.
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Factor
(a-2b) (3x-5y) + (2b-a)(x-y)
Answer:
8by + 2ax - 4bx - 4ay
Step-by-step explanation:
I assume you mean expand so:
(a - 2b)(3x - 5y) + (2b - a)(x - y)
3ax - 5ay - 6bx + 10by + 2bx - 2by - ax + ay
Now collect like terms:
2ax - 4ay - 4bx + 8by
This is your answer but in a better order:
8by + 2ax - 4bx - 4ay
Maths-4
What is the smallest number that is divisible by each of the numbers given below
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
5040
3780
1260
2520
None of the above
Answer:
5040 is the right answer
Step-by-step explanation:
5040/1=5040
5040/2=2520
5040/3=1680
5040/4=1260
5040/5=1008
5040/6=840
5040/7=720
5040/8=630
5040/9=560
5040/10=504
when the subtracts 4 from both sides 1/2x=-1/2
Subtracting 4 from both sides of the equation ¹/₂x = -¹/₂ gives us; ¹/₂x - 4 = -¹/₂ - 4
How to use subtraction property of equality?We want to simply the expression which is;
¹/₂x = -¹/₂
Now, when we subtract 4 from both sides, it means we are using subtraction property of equality which states that subtracting the same value from both sides of an equation makes the equation still to be equal. Thus, we have;
¹/₂x - 4 = -¹/₂ - 4
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Rational expressions are often used in combining rates of work.
Rational expressions are often used in combining rates of work. Therefore, it's true.
What is rational expression?It should be noted that a rational expression is simply defined by a rational fraction.
They're are used in combining rates of work. Fir example, if Mr John performs 1/2 of his work and does 1/3 on another day. This can be expressed as:
= 1/2 + 1/3
= 5/6
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One month Kevin rented 2 movies and 5 video games for a total of $30. The next month he rented 8 movies and 3 video games for a total of $35. Find the rental cost for each movie and each video game. Rental cost for each movie: s Rental cost for each video game
Answer:
M = $2.5; V = $5
Step-by-step explanation:
We need to set up a system of equations to find the price for both movies (M) and video games (V).
We can use 2M + 5V = 30 and 8M + 3V = 35
We can use elimination:
[tex]-4(2m+5v=30)\\8m+3v=35\\\\-8m - 20v = -120\\8m+3v=35\\-17v=-85\\v=5\\\\2m+5(5)=30\\2m+25=30\\2m=5\\m=5/2 ;m=2.5[/tex]
The equation of line / is y=3x/a +5, where a is a positive constant. If the value of a in this equation is doubled, then the resulting equation will represent a line whose slope is how many times the slope of line / ?
The resulting equation will represent a line whose slope is 1/2 times the slope of the line
How to determine the slope of the new line?The equation of the line is given as:
y = 3x/a + 5
The constant a is a positive constant.
So, when the value of a in the equation is doubled, we have:
y = 3x/2a + 5
A linear equation is represented as
y = mx + b
Where m represents the slope.
So, we have:
m1 = 3/a
m2 = 3/2a
Substitute m1 = 3/a in m2 = 3/2a
m2 = 1/2 * m1
Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line
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he graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units
We conclude that the graph of f(x) is the graph of g(x) translated 3 units upwards.
How do relate the graphs of f(x) and g(x)?Here we have the functions:
[tex]f(x) = log(x) + 3\\\\g(x) = log(x)[/tex]
And we want to find a relation between them.
Remember that a vertical translation of N units (the sign of N defines the direction of the translation) is written as:
[tex]f(x) = g(x) + N[/tex]
In this case, we can see that N = 3, it is positive, so the translation is upwards. (This means that the whole graph of the function f(x) is translated upwards 3 units in the coordinate axis)
Then we conclude that the relation between the graphs of the given functions is that the graph of f(x) is the graph of g(x) translated 3 units upwards.
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How do you find the value of 5,016 with as few steps as possible?
The estimated value of 5,016 exists 1 / 264 ≈ 0.00379.
What is a fraction?Fractions describe the regions of a complete or group of objects. A fraction contains two regions. The number on the top of the line exists named the numerator. It describes how many equivalent regions of the real or group stand accepted. The number below the line exists named the denominator. It exhibits the total number of equivalent regions the whole exists divided into or the total number of the exact objects in a group.
How to estimate the value of 5,016 with as few steps?The value of 5,016 can be simplified by using a fraction
Consider a denominator 19, then
19 divided by 5,016, then we get
19 and 5016 have a common divisor of 19.
then, we get
19 / 5016 = 1 / 264
Now, you need to divide.
1 / 264 ≈ 0.00379
Therefore, the estimated value of 5,016 exists 1 / 264 ≈ 0.00379.
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f(x) = |2x +1| +3
g(x) = −2
Find (ƒ + g)(x).
Hello!
We are going to solve the question with our given functions.
We were given:
f(x) = |2x +1| + 3g(x) = -2Those are our two given functions, we will use those to solve for (f + g)(x).
Keep in mind that (f + g)(x) could also be written as f(x) + g(x)
With this knowledge, we can solve our question.
Solve:
(ƒ + g)(x) = f(x) + g(x)
Plug in our f(x) and g(x) functions and solve.
f(x) + g(x) = |2x +1| + 3 - 2
Simplify.
|2x +1| + 3 - 2
|2x +1| + 1
Since we can't simplify this any further, the above will be our answer.
(f + g)(x) = |2x +1| + 1
Answer:
|2x +1| + 1
i dont know answer please im in summer school
The centre and the radius of the circle is (-7, -1) and 6 units
Equation of a circleThe equation of the circle in standard from is expressed as:
x^2+y^2+2gx+2fy+C = 0
where;
(-g, -f) is the centre
r= √g²+f²-C
Given the equation below
x^2+y^2+14x+2y+14 = 0
2g = 14
g = 7
2f = 2
f =1
Hence the centre of the circle is (-7, -1)
Radius = √49+1-14
Radius = √36 = 6 units
Hence the centre and the radius of the circle is (-7, -1) and 6 units
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You want to put in a new concrete patio behind your house. You want it to be 12 ft wide by 14 ft long and it needs to be eight inches thick. You know that an 80 lb. bag of concrete yields 0.60 cubic feet. How many 80 lb. bags of concrete will you need for your patio?
Answer:
You will need 187 80 pounds bags of concrete.
Step-by-step explanation:
12x14x(2/3) x 0.6 = 186.666 or 187
Zendaya runs a farm stand that sells blueberries and grapes. Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25. Zendaya made $55 from selling a total of 33 pounds of blueberries and grapes. Write a system of equations that could be used to determine the number of pounds of blueberries sold and the number of pounds of grapes sold. Define the variables that you use to write the system.
The number of pounds of blueberries and grapes sold are 11 and 22.
According to the statement
we have given that the:
Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25.
And total money collected by selling pounds is $55
And total number of pounds sells = 33
And we have to find the Number of pounds of blueberries and grapes.
Let the number of pounds of blueberries is X
And Let the number of pounds of grapes is Y
So,
The equation becomes is:
X + Y = 33 -(1)
2.50X + 1.25Y = 55 -(2)
Now, From substitution method
From (1) equation
Y = 33 - X
put these in equation (2) then
2.50X + 1.25(33 - X ) = 55
2.50X + 41.25 - 1.25X = 55
1.25X = 13.75
X = 11
and the the value of Y becomes
Y = 33 - X
Y = 33 - 11
Y = 22.
So, The number of pounds of blueberries and grapes sold are 11 and 22.
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According to the American Community Survey, 27% of residents of the United States 25 years old or older had earned a bachelor degree. Suppose you select 12 residents of the United States 25 years old or older and recorded the number who had earned a bachelor degree. Round probabilities to 4 decimal places.
Explain why this is a binomial experiment.
Find and interpret the probability that exactly 5 of them had a bachelor degree.
Find and interpret the probability that fewer than 5 of them had a bachelor degree.
Find and interpret the probability that at least 5 of them had a bachelor degree.
Compute the mean and standard deviation of the binomial random variable.
a. The reason why this question is a binomial experiment is based on the fact that it is made up of an independent sample, it has a number that is fixed and a probability.
Each event is made up of two outcomes and they are random with the same success rate.
b. How to solve probability that exactly 5 had a bachelorwe have the following data n = 12, p = 0.27 and k = 5
We have to use the function to solve electronically
binompdf(n,p,k)
input the values
= binompdf(12,0.27,5)
This gives us
= 0.1255
(C) Probability that fewer than 5 have bachelorWe use the formula below
= binompdf(12,0.27,5-1)
This is = 0.7984
D. Probability of at least 5
1 - probability of fewer than 5
= 1 - 0.7984
= 0.2016
How to solve for the Mean = n*p
n = 12 , p = 0.27
Mean = 12*0.27 = 3.24
and
standard deviation = √npq
n = 12, p = 0.27 , q = 1- 0.27
= 0.73
sd = √12*.27*.73
= 1.54
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The scatterplot to the left shows the cost, CCC, in thousands of dollars, and living space, xxx, in square feet (\text{ft}^2)(ft
2
)left parenthesis, start text, f, t, end text, squared, right parenthesis for several houses in a certain neighborhood. According to the data, which of the following best approximates the cost for an additional square foot of living space for homes in this neighborhood?
Choose 1 answer:
\$80$80dollar sign, 80
\$300$300dollar sign, 300
\$1{,}000$1,000dollar sign, 1, comma, 000
\$13{,}000$13,000dollar sign, 13, comma, 000
According to the data, the cost of this house would increase by 0.08 thousand dollars ($80) for each additional square foot of living space.
How to determine the cost for an additional square foot?By critically observing the scatter plot, we can logically deduce that it shows a linear trend. Thus, the slope of the line of best fit is given by a ratio of change in cost to the change in living space.
Next, we would approximate two points on the line of best fit and then find the slope as follows:
Slope, m = ΔC/Δx
Slope, m = (C₂ - C₁)/(x₂ - x₁)
Slope, m = (400 - 200)/(4000 - 1500)
Slope, m = 0.08.
Therefore, the cost of this house would increase by approximately 0.08 thousand dollars ($80) for each additional square foot of living space.
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Solve the following:
3 x 10³ - 7000
(8 × (−5)) + (4² +2²)
Give your answer in simplest form.
Enter can you help me solve this I was doing very good up to now
Answer:
3x(10x10x10): 3x(1000): 3000-7000: -4000. (8x(-5)): -40. (4x4) +(2x2): (16 +4): 20