The zeros of the given equation are -5 and -7
Zeros of a quadratic equationQuadratic equations are equations that has a leading degree of 2. Given the factors of a quadratic equation as expressed below;
(-3x - 15)(x+7) = 0
The expressions -3x -15 and x + 7 are the factors of the equation. Equating both factors to zero
-3x - 15 = 0
Add 15 to both sides of the equation
-3x -15 + 15 = 0 + 15
-3x = 15
Divide both sides of the equation by -3
-3x/-3 = 15/-3
x = -5
Similarly;
x + 7 = 0
x = -7
Hence the zeros of the given equation are -5 and -7
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A 10-acre parcel was sold for $3.50 per square foot. What was the total selling price for the parcel
Answer:
The total selling price for the parcel is 1,524,600 dollars.
Step-by-step explanation:
We are given that 10 acre parcel was sold for $3.50.
First we need to figure out how many square foot is in 10 acres.
when we convert 10 acres we get 435600 square feet.
Since we know that parcel was sold for $3.50 per square foot we simply multiply 435600 by 3.5 = 1,524,600
A right rectangular prism has these dimensions:
Length: Fraction 1 and 1 over 3 units
Width: Fraction 5 over 6 unit
Height: Fraction 2 over 3 unit
How many cubes of side length 1 over 6 unit are required to completely pack the prism without any gap or overlap?
160 cubes required to completely pack the prism without any gap or overlap
How to determine the number of cubes?The dimensions of the rectangular prism are given as:
Length = 1 1/3
Width = 5/6
Height = 2/3
The volume is
Volume = Length * Width * Height
This gives
Volume = 1 1/3 * 5/6 * 2/3
Evaluate the product
Volume = 20/27
The side length of the cube is
L = 1/6
The volume of the cube is
V = (1/6)^3
Evaluate
V = 1/216
The number of cubes required to completely pack the prism without any gap or overlap is
n = (20/27) / (1/216)
Evaluate
n = 160
Hence, 160 cubes required to completely pack the prism without any gap or overlap
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find the length of MN
Answer:
The length of MN is 5 cm
Step-by-step explanation:
Add the segment LX, parallel to QP.
Recall the properties of midsegment:
Midsegment is parallel to side,Midsegment is half the length of the parallel side.We have:
Since QL = LR, the point L is midpoint of Q,Since PN = NL, the point N is midpoint of PL,Since LX is parallel to QP, LX is midsegment of ΔPRQ.Find the length of LX:
LX = QP/2 = 20/2 = 10 cmSince QP ║ LX ║ NM, the segment NM is the midsegment of ΔPLX.
Find the length of NM:
NM = LX/2 = 10/2 = 5 cmKiran was trying to solve the equation 3x 8 = 7x - 8. She said, "The equation has no
solutions because the constant is the same." Do you agree with Kiran? Explain your
reasoning
The statement that the equation has no solutions because the constant is the same is true
How to determine the true statement?The equation is given as:
3x - 8 = 7x- 8
Add 8 to both sides
3x - 8 + 8= 7x- 8 + 8
Evaluate the like terms
3x = 7x
Divide both sides by x
3 = 7
The above equation is false, because 3 and 7 are not equal
This means that the statement that the equation has no solutions because the constant is the same is true
Hence, I agree with Kiran
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Find smallest number which on adding to 19 it is exactly divisible by 28,36 and 45 (LCM).
Answer:
1241
Step-by-step explanation:
∴
L.C.M. of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260
∴
the required number is 1260 - 19 = 1241
Hence, if we add 19 to 1241 we will get 1260 which is exactly divisible by 28, 36 and 45.
cuanto da (9+4m)² cuadrado de binomio ayudaaaaa
Answer:
16m^2 + 72m + 81
Step-by-step explanation:
you expand it, by (9+4m)(9+4m), using distributive property you get
81 + 36m + 36m + 16m^2, simplifying you get the answer
alegbra 2: pls help!!
Kiara and Sean are setting off model rockets. Kiara's rocket's flight pattern can be modeled by the function f(t)= -16t² +80t. Sean's rocket's flight
pattern can be modeled by the function h(t) = -16t² + 120t+64. In each function, t is the time in seconds after the rockets launch and f(t) and h(t)
are the heights of the rockets in feet.
How many seconds after Kiara's rocket returns to the ground does
Sean's rocket return to the ground?
Enter your response as a numeric answer. Do not include spaces, units,
or commas in your response.
Answer:
Sean's rocket lands 3 seconds after Kiara's rocket.
Step-by-step explanation:
Kiara: f(t)= -16t² + 80t
Sean: h(t) = -16t² + 120t + 64
Assume that both rockets launch at the same time. We need to be suspicious of Sean's rocket launch. His equation for height has "+64" at the end, whereas Kiara's has no such term. The +64 is the starting height iof Sean's rocket. So Kiara has a 64 foot disadvantage from the start. But if it is a race to the ground, then the 64 feet may be a disadvantage. [Turn the rocket upside down, in that case. :) ]
We want the time, t, at which f(t) and h(t) are both equal to 0 (ground). So we can set both equation to 0 and calculate t:
Kiara: f(t)= -16t² + 80t
0 = -16t² + 80t
Use the quadratic equation or solve by factoring. I'll factor:
0 = -16t(t - 5)
T can either be 0 or 5
We'll choose 5. Kiara's rocket lands in 5 seconds.
Sean: h(t) = -16t² + 120t + 64
0= -16t² + 120t + 64
We can also factor this equation (or solve with the quadratic equation):
0 = -8(t-8)(2t+1)
T can be 8 or -(1/2) seconds. We'll use 8 seconds. Sean's rocket lands in 8 seconds.
Sean's rocket lands 3 seconds after Kiara's rocket.
A dealer marked the price of a digital watch as Rs 6,000. She then allowed 20% discount to make 20% profit. If she increased the discount to 25%, by how much was the profit percent decreased?
Profit decreased by 7.5%
Answer:
Solution Given:
Marked Price= Rs 6,000
discount =20%
Selling Price =M.P- discount% of M.P
=M.P(1-discount%)
=6000(1-20%)
= Rs 4,800
Again
Profit = 20%
Cost Price=(S.P*100)/(100+profit%)
= (4800*100)/(100+20%)
= Rs 4,000
For discount 25%
Marked Price =Rs 6,000
Selling Price =M.P - discount% of M.P
=M.P(1-discount%)
=6000(1-25%)
=Rs 4,500
Profit = S.P- C.P= Rs 4,500- Rs 4,000=Rs 500
Profit %=Profit/C.P* 100%= 500/4000*100 = 12.5%
Profit % decreased from 20% to 12.5%
Profit decreased by 7.5%
Answer:
7.5%
Step-by-step explanation:
Marked Price
Rs 6,000
Discounted Price
If the price is discounted by 20%, then the discounted price is 80% of the marked price:
[tex]\implies \sf Discounted\:Price =80\% \textsf{ of marked price}[/tex]
[tex]\implies \sf Discounted\:Price =0.8 \times 6000[/tex]
[tex]\implies \sf Discounted\:Price = 4800\:Rs[/tex]
Cost Price
If the dealer makes 20% when selling the watch at the discounted price, then the cost price is:
[tex]\implies \sf Cost\:Price=\dfrac{100\%}{120\%} \times 4800[/tex]
[tex]\implies \sf Cost\:Price=\dfrac{4800}{1.2}[/tex]
[tex]\implies \sf Cost\:Price=4000\:Rs[/tex]
Discount of 25%
If the price is discounted by 25%, then the discounted price is 75% of the marked price:
[tex]\implies \sf Discounted\:Price =75\% \textsf{ of marked price}[/tex]
[tex]\implies \sf Discounted\:Price =0.75\times 6000[/tex]
[tex]\implies \sf Discounted\:Price = 4500\:Rs[/tex]
Profit after 25% discount
[tex]\implies \sf Profit=\dfrac{discounted\:price}{cost\:price}-1 \times 100[/tex]
[tex]\implies \sf Profit=\dfrac{4500}{4000}-1 \times 100[/tex]
[tex]\implies \sf Profit=12.5\%[/tex]
Therefore, the profit decreased from 20% to 12.5% which means the profit percent decreased by 7.5%.
A private jet flies the same distance in 10 hours that a commercial jet flies in 7 hours. if the speed of the commercial jet was 144mph less than 2 times the speed of the private jet, find the speed of each jet.
The speed of private jet is = 252 mph
The speed of commercial jet is = 360 mph
What is speed ?
Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector.Let the speed of private jet be x mph.
Then the speed of commercial jet will be = 2x - 144
Equation forms:
10x = 7 ( 2x - 144 )
Solving for x
10x = 14x - 1008
⇒ 10x - 14x = - 1008
⇒ - 4x = - 1008
⇒ x = 252
So, x = 252
Hence, the speed of private jet is = 252 mph
The speed of commercial jet is = = 2(252) - 144 = 360 mph
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Please help !!! Need help !!!
Please help me on this one I wrote it out :(
Answer:
D) 3
Step-by-step explanation:
22 * 2 = 44
To have a remainder 3, the number should be 44 + 3 = 47
47 ÷ 22 , leaves a remainder 3.
47 +22 = 69
69 ÷ 3 leaves a remainder 3.
69 +22 = 91
91 ÷ 3 leaves a remainder 3.
Answer: 47 , 69 , 91
Answer:B:1
Step-by-step explanation:
Write each number out and divide by 22 until you get one that’s answer is 3
Find the midpoint of the line segment joining the points (-1,-3) and (-11,10).
Answer: Midpoint=(−6 ,3.5)
Step-by-step explanation:
=(1+22,1+22)M=(x1+x22,y1+y22)=(−1+−112,−3+102)M=(−1+−112,−3+102)=(−122,72)M=(−122,72)=(−6,312)
Answer:
(-6,3.5)
Step-by-step explanation:
x = [tex]\frac{-1-11}{2}[/tex] = [tex]\frac{-12}{2}[/tex] = -6
y = [tex]\frac{-3+10}{2}[/tex] = [tex]\frac{7}{2}[/tex] = 3.5
Please help me with alg 2 questions
6) The solution of the system of linear equations is (x, y, z) = (2, 5, 3).
11) The average depth of the water is 0.35 kilometers.
12) The dollar value of the deposit after 10 years is $ 1205.85.
13) Three horses need a consumption of 930 pounds of hay for the month of July.
14) The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.
15) Anna has a mean time of 7.39 minutes.
How to analyze algebraic equations
In this question we must analyze and resolve on algebraic equations such as linear equations or conic sections. 6) We must use algebra properties to solve on the system of linear equations. First, we clear x in the first equation:
x = y - z
Then, we apply it in the two remaining equations:
- 5 · (y - z) + 3 · y - 2 · z = - 1
2 · (y - z) - y + 4 · z = 11
- 2 · y + 3 · z = - 1
y + 2 · z = 11
Second, we clear y in the second expression and we substitute into the first expression:
y = 11 - 2 · z
- 2 · (11 - 2 · z) + 3 · z = -1
- 22 + 7 · z = - 1
z = 3
y = 5
x = 2
The solution of the system of linear equations is (x, y, z) = (2, 5, 3).
11) There is a function of the speed of a tsunami in terms of the average depth of the water. The former variable is known and we need to clear d in the formula to find the missing value:
145 = 356 · √d
d = (145 / 356)²
d = 0.345 km
The average depth of the water is 0.35 kilometers.
12) The compound interest model is shown below:
C' = C · (1 + r / 100)ˣ (1)
Where:
C' - Initial capitalC - Current capitalr - Interest ratex - Number of periodsIf we know that C = 500, r = 4.5 and x = 20, then the resulting capital after 10 years is:
C' = 500 · (1 + 4.5 / 100)²⁰
C' = 1205.85
The dollar value of the deposit after 10 years is $ 1205.85.
13) The situations indicates a direct variation as the amount of hay is directly proportional to the number of days. Hence, we have the following linear model for the hay consumption of one horse:
y = m · x (2)
y = 10 · x
Where:
m - Hay consumption rate, in pounds per day.x - Time, in days.y - Consumed hay, in pounds.The total consumption of three horses during July is equal to the product of the number of horses and consumed hay by one horse during one month:
y' = 3 · [10 · (31)]
y' = 930
Three horses need a consumption of 930 pounds of hay for the month of July.
14) There is the general equation of the circumference and we must transform it into its vertex form to find information about the radius. This can done by algebraic procedures:
x² + y² + 8 · y + 8 · y + 28 = 0
(x² + 8 · y) + (y² + 8 · y) = - 28
(x² + 8 · y + 16) + (y² + 8 · y + 16) = 4
(x + 4)² + (y + 4)² = 2²
The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.
15) We need to sum all the times described in the table and divide it by the number of data to find the mean time for a 1-kilometer race:
x = (7.25 + 7.40 + 7.20 + 7.10 + 8.00 + 8.10 + 6.75 + 7.35 + 7.25 + 7.45) / 10
x = 7.39
Anna has a mean time of 7.39 minutes.
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how do you calculate this
Answer:
y = - 2x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1-1}{0-(-1)}[/tex] = [tex]\frac{-2}{0+1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = - 2x - 1 ← equation of line
PLEASE HELP ASAP
Which sequence shows the numbers in order from least to
greatest?
OA) 62.85, 1-9, 6.28 x 10²
OB) 1-9, 6.28 x 10², 62.85
OC) 62.85, 6.28 x 10², 1-9
OD) -9,62.85, 6.28 x 10²
Answer:
Step-by-step explanation:
D, -9, 62.85, 6.28x100(628)
Answer:
Step-by-step explanation:
The answer would be C
Since of course negative 5 is a negative and any negative number plus a positive number would end up being a negative number and that means that that would be the least since no other number is a negative. The square root of 132.... Can it be bigger than 7 5/16? Yeah. Because the Square root of 132, if rounded, it would be 11 which 11 is greater than 7 which would mean the correct order would be -5 x 10^2, 7 5/16, and the square root of 132.
give me brainlyest
200 σ j=1 2j( j 3) describe the steps to evaluate the summation. what is the sum?
The sum of the equation is = 5494000.
What does summation mean in math?The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
Briefing:Distribute 2j to (j+3).
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used.
The sum is 5,494,000.
Calculation according to the statement:[tex]\sum_{j=1}^{200} 2 j(j+3)[/tex]
simplifying them we get:
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j[/tex]
Split the summation into smaller summations that fit the summation rules.
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j[/tex]
[tex]\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}[/tex]
The formula for the summation of a polynomial with degree 2
is:
[tex]\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}[/tex]
Substitute the values into the formula and make sure to multiply by the front term.
[tex](2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$[/tex]
we get: 5373400
Evaluating same as above : [tex]6 \sum_{j=1}^{200} j[/tex]
we get: 120600
Add the results of the summations.
5373400 + 120600
= 5494000
The sum of the equation is = 5494000.
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A certain amount of concentrate is mixed with water to create a juice. The table shows the amount of concentrate, in ounces remaining, in the original container after x ounces of juice are made. How many ounces of concentrate were in the original container before any juice was made? PLEASE HELP ME
TheThe number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.
Number of ouncesA. Let assume the two are linear relationship
Let y represent juice made
Let x represent the concentrate remaining
Hence:
Slope=600-200/200-280
Slope=400/-80
Slope=-5
y=-5x+b
Where:
x=200
y=-5(200)+b=600
y=-1000+b=600
b=1600
Thus,
y=-5x+1600
y=0. -5x+1600=0
-5x=-1600
divide both side by 5x
x=-1600/-5
x=320 ounces
B. x=0
y=1600 ounces
Therefore the number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.
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Find the missing probability.
The value of the missing probability is:
P(A) = 1/5
So the correct option is D.
How to find the missing probability?First, we know that:
P(A∩B) = probability that events A and B are true = 3/100
And we also know that:
P(B|A) = probability that event B is true given that event A is true = 3/20
Here we have the rule:
P(A∩B) = P(B|A)*P(A)
Replacing the first two:
3/100 = (3/20)*P(A)
Solving for P(A), we get:
(3/100)*(20/3) = 1/5 = P(A).
So we conclude that the correct option for the missing probability is the one in option D.
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Find all x-values in the interval for which the function is equal to its average value. (enter your answers as a comma-separated list. )
All the x-values in the interval for which the function is equal to its average value [tex]5-\sqrt{5}[/tex] .
An interval program language period accommodates the numbers mendacity between specific given numbers. for instance, the set of numbers x gratifying 0 ≤ x ≤ five is a c programming language that contains zero, five, and all numbers among 0 and five.
The interval program language period is the distinction between the higher class restriction and the lower magnificence restriction. As an example, the dimensions of the class c program language period for the first class is 30 – 21 = 9. further, the size of the class c programming language for the second magnificence is forty – 31 = nine.
In arithmetic, an interval language is fixed of actual numbers that carry all actual numbers mendacity among any numbers of the set. For example, the set of numbers x pleasurable zero ≤ x ≤ 1 is a language that includes zero, 1, and all numbers in between.
f(x)=(91-55 [0,1]
value of the function on the interval [0,1] is (9-0)
Let x-5=3
now, find the value of x, for which
f(x) =(2x-5) 2 =
5/X-5 =√5
24 X = 54√5 and 5. √5
Strs [ay] and 5- 5-√5 €0.4]
value of x is 5- sqrt15
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Can I get some help finding the x of the triangle please?
Answer:
61
Step-by-step explanation:
You can see that the sides are both 6. That means that this triangle is an isosceles triangle.
Therefore do this:
180-58=122
122/2= 61
So x= 61 Degrees
Hope This helps! :)
Answer:
x = 61
Step-by-step explanation:
This triangle is an isosceles triangle which means 2 sides are congruent. This also means the 2 angles across from the congruent sides are congruent. So, you would subtract 58 from 180 which equals 122. Then you would divide that in half, which gets you 61. (The angle 58 is the one across from the side that is not congruent to the others. That is why I used it)
Assume you took $5,000 out of the bank to purchase a car worth $5,000. How much did you net worth change?
Your net worth change by zero dollars.
What is net worth?Net worth is the difference between asset and liability.
In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.
Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.
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Type the correct answer in each box. Use numerals instead of words.
This system of equations has been placed in a matrix:
y = 650x + 175
y = 25,080 − 120x
The system of equations when been placed in a matrix yields
[tex]\left[\begin{array}{ccc}650&-1\\120&1\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}-175\\25080\end{array}\right][/tex]
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
y = 650x + 175 and;
y = 25080 - 120x
Rearranging the equations gives:
650x - y = -175 and;
120x + y = 25080
Placing the equations in a matrix gives:
[tex]\left[\begin{array}{ccc}650&-1\\120&1\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}-175\\25080\end{array}\right][/tex]
The system of equations when been placed in a matrix yields
[tex]\left[\begin{array}{ccc}650&-1\\120&1\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}-175\\25080\end{array}\right][/tex]
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LOTS OF POINTS!!!! look at pic
Answer:
2x+6-(x^2+6x+9)*pi
Step-by-step explanation:
2*(x+3) - (x+3)^2*pi
2x+6-(x^2+6x+9)*pi
um I think there are answer choices so I don't know if I have to keep going but that should be right
What error did zacharias make? the –5 should be 5. the 52 should be –52. the 2 in the numerator should be –2. the 2 in the denominator should be –2.
The error made by zacharias in solving the quadratic equation 0 = -2x² + 5x - 3 using quadratic formula is; the 2 in the numerator should be –2.
Quadratic equationThere are four methods of solving quadratic equation. Namely;
Factorization methodCompleting the square methodGraphical methodFormula method0 = -2x² + 5x - 3
Using quadratic formulax = -b ± √b² - 4ac / 2a
where,
a = -2b = 5c = -3x = -b ± √b² - 4ac / 2a
x = -5 ± √5² - 4(-2)(-3) / 2(-2)
= -5 ± √25 - (24) / -2
= -5 ± √1 / -2
= -5/2 ± 1/2
= -5/2 - 1/2 or x = -5/2 + 1/2
= -5-1 / 2 or -5+1/ 2
x = -6/2 or -4/2
x = -3 or -2
Therefore, the solution to the quadratic equation is x = -3 or -2
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Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point and its radius is
units.
The required answers are:
1) The center of the circle = (4, 8)
2) The radius of the circle = 2.5 units
3) The equation of the circle = (x - 4)² + (y - 8)² = 6.25
What is the equation of a circle?The equation of the circle which has a center at (h, k) and a radius of 'r' units is (x - h)² + (y - k)² = r²
To calculate radius 'r', we have r = sqrt( (x1 - h)² + (y1 - k)²)
Where (x1, y1) is the point that lies on the circle.
Calculation:Given that,
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)
We know that the longest chord on a circle is nothing but the diameter of the circle.
So, the center is the midpoint of the diameter. I.e.,
(h, k) = ([tex]\frac{4+4}{2}[/tex], [tex]\frac{5.5+10.5}{2}[/tex])
⇒ (h, k) = (4, 8)
Therefore, the center of the circle is (4, 8)
Then, the radius is calculated by
r = sqrt( (x1 - h)² + (y1 - k)²)
⇒ r = [tex]\sqrt{(4-4)^2+(5.5-8)^2}[/tex]
⇒ r = 2.5 units
Thus, the radius of the circle is 2.5 units.
So, the equation of the circle with center (4, 8) and radius of 2.5 units is,
(x - h)² + (y - k)² = r²
⇒ (x - 4)² + (y - 8)² = 2.5²
⇒ (x - 4)² + (y - 8)² = 6.25
Thus, the equation of the circle is x - 4)² + (y - 8)² = 6.25.
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The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.8 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( , ) b. What is the median recovery time? days c. What is the Z-score for a patient that took 4 days to recover? d. What is the probability of spending more than 3.8 days in recovery? e. What is the probability of spending between 3.2 and 4.2 days in recovery? f. The 90th percentile for recovery times is days.
Using the normal distribution, we have that the desired information is given as follows:
a) X ~ N(3,1.8).
b) 3 days.
c) Z = 0.5556.
d) 0.33 = 33%.
e) 0.2048 = 20.48%.
f) 5.3 days.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 3, \sigma = 1.8[/tex]
Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.
The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:
Z = (4 - 3)/1.8 = 0.5556.
The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:
Z = (3.8 - 3)/1.8 = 0.44.
Z = 0.44 has a p-value of 0.67.
1 - 0.67 = 0.33.
The probability is of 0.33 = 33%.
The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:
X = 4.2:
Z = (4.2 - 3)/1.8
Z = 0.67.
Z = 0.67 has a p-value of 0.7486.
X = 3.2:
Z = (3.2 - 3)/1.8
Z = 0.11.
Z = 0.11 has a p-value of 0.5438.
0.7486 - 0.5438 = 0.2048 = 20.48%.
The 90th percentile is X when Z = 1.28, hence:
1.28 = (X - 3)/1.8
X - 3 = 1.8 x 1.28
X = 5.3 days.
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I am thinking of a whole number greater than 0 whose square equals to its square root. How many such numbers are there?
(A) 0
(B) 1
(C) 2
(D) 4
Answer:
(B) 1
Step-by-step explanation:
The number of such integers will be the number of places where the functions f(x) = x² and g(x) = √x intersect.
Graphical solutionThe attachment shows the graphical solution to f(x) = g(x) for x > 0. There is exactly one point of intersection at x=1.
There is one such number.
Your friends and you notice a classmate who always has brand new clothes, shoes, and electronics. What would you need to know in order to tell if this classmate’s family is actually wealthy?
To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.
What is an asset?In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.
Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.
In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.
The asset should more than the debt.
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PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP
Answer:
We multiply by 2 and add 4
Step-by-step explanation:
To find the pattern, we find the slope
m = ( y2-y1)/(x2-x1)
m = ( 10-6)/(3-1)
m = 4/2
m =2
We are multiplying by 2
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Using the point (1,6)
6 = 2(1)+b
6 = 2+b
The y intercept is 4
y = 2x+4
We multiply by 2 and add 4
Jaquelyn wants to start getting to school on time more often. She is looking at some of her habits.
On Monday, she is late twenty percent of the time.
When she is late on Monday, she is late on Tuesday 60% of the time.
When she is not late on Monday, she is late on Tuesday 20% of the time.
What is the approximate probability that Jaquelyn will be late on Tuesday, given she was late to school on Monday?
Given that Jaquelyn was tardy on Monday, there is a 12 percent chance she will be late on Tuesday as well.
What is the Probability?
How likely it is that a stated event would occur is assessed using probability. The event would have a probability of 1 if it happened with certainty. The probability of an occurrence would be zero if it were absolutely guaranteed that it would not occur.
As getting late on Monday and Tuesday are independent events, their probabilities can be multiplied.
So the probability of getting late on Tuesday, given she was late to school on Monday = Probability of being late on Monday x Probability of she being late on Monday and she is late on Tuesday 60% of the time.
= 0.2 x 0.6
= 0.12
Thus the approximate probability that Jaquelyn will be late on Tuesday, given she was late to school on Monday will be 0.12
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