Answer:
87 people in the restaurant, 45 people eat in the car and 57 people eat at home.
Step-by-step explanation:
Let x be 'restaurant-purchased meals eaten in a restaurant', y be the 'restaurant-purchased meals eaten in a car' and z be the 'restaurant-purchased meals eaten at home'.
We can use the given information "the total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 189" to write an equation [tex]x+y+z=189[/tex].
We can use the information "the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 15" to write another equation [tex]y+z=x+15[/tex].
We can use the information "thirty more restaurant-purchased meals will be eaten in a restaurant than at home" to write the third equation as x=z+30
Now we need to solve this system of three equations to get the values of x, y and z.
We can solve for x directly from the first two equations.
[tex]x+x+15=189\\2x=174\\x=87[/tex]
Substituting this value of x in the third equation we can get the value of z.
[tex]87=z+30\\z=57[/tex]
Finally, we can substitute the values of x and z in the first (or second) equation to get the value of y.
[tex]87+y+57=189\\y+144=189\\y=45[/tex]
Therefore, 87 people in the restaurant, 45 people eat in the car and 57 people eat at home.
Eric estimated 28x48 by finding 30x50. His estimate was 1,500,but he says the actual product will be greater than that amount.Is he correct? Explain how you know
Answer:
Eric is not correct.
Step-by-step explanation:
We have been given that Eric estimated [tex]28\times 48[/tex] by finding [tex]30\times 50[/tex]. His estimate was 1500, but he says the actual product will be greater than that amount.
To find if Eric is correct or not, let us see how to estimate an answer.
While estimating our given numbers we will round to nearest tenth and change the digit to the right of the rounding place to 0.
As 8 is greater than 5, so we will round 28 to 30 and 48 to 50.
Since we are rounding up, so our estimated answer will be greater than actual answer, therefore, Eric is not correct.
The ordered pairs model an exponential growth function. {(−1,34), (0,51), (1,76.5), (2,114.75)} What is the function equation? f(x)=__________
Answer:
[tex]y= 51(1.5)^x[/tex]
Step-by-step explanation:
The ordered pairs model an exponential growth function. {(−1,34), (0,51), (1,76.5), (2,114.75)}
Exponential function equation is y=ab^x
Lets plug in the ordered pairs and find our 'a' and 'b'
(0,51)
[tex]51= ab^0[/tex]
a= 51
(−1,34)
[tex]34= 51b^{-1}[/tex]
Divide both sides by 51
[tex]\frac{34}{51} = b^{-1}[/tex]
So b = 51/34
b= 1.5
Plug in the values of 'a' and 'b'
Equation becomes [tex]y= 51(1.5)^x[/tex]
find the polynomial function
Answer:
y = 2x³ +x² -3x +6
Step-by-step explanation:
The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)
_____
If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.
___
Writing the equations
... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing
For x = -1:
... -a +b -c +6 = 8
For x = 1
... a + b + c + 6 = 6
For x = 2
... 8a +4b +2c +6 = 20
In augmented matrix terms, this set of linear equations looks like ...
[tex]\left[\begin{array}{ccc|c}-1&1&-1&2\\1&1&1&0\\8&4&2&14\end{array}\right][/tex]
___
Solving the equations
There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.
If you add the first two equations, you get ...
... 2b = 2 ⇒ b = 1
Substituting that into the first equation allows you to simplify it to ...
... -a -c = 1
Dividing the third equation by 2 (and substituting for b) makes it ...
... 4a +c = 5
Adding these equations gives ...
... 3a = 6 ⇒ a = 2
Then ...
... c = -a -1 = -2 -1 = -3
And our polynomial function is ...
... y = 2x³ +x² -3x +6
Two events E1 and E2 are called independent if p(E1 â© E2) = p(E1)p(E2). For each of the following pairs of events, which are subsets of the set of all possible outcomes when a coin is tossed three times, determine whether or not they are independent. a) E1: tails comes up with the coin is tossed the first time; E2: heads comes up when the coin is tossed the second time. b) E1: the first coin comes up tails; E2: two, and not three, heads come up in a row. c) E1: the second coin comes up tails; E2: two, and not three, heads come up in a row.
Answer: a) Independent
b) Independent
c) Dependent
Step-by-step explanation:
Since, If a coin is tossed three times,
Then, total number of outcomes, n(S) = 8
a) [tex]E_1[/tex] : tails comes up with the coin is tossed the first time;
[tex]E_1[/tex] = { TTT, THH, THT, TTH }
[tex]E_2[/tex] : heads comes up when the coin is tossed the second time.
[tex]E_2[/tex] = { THT, HHH, THH, HHT }
Thus, [tex]n(E_1)=4[/tex]
⇒ [tex]P(E_1)=\frac{n(E_1)}{n(S)}=\frac{4}{8}=\frac{1}{2} [/tex]
Similarly, [tex]P(E_2)=\frac{1}{2}[/tex]
⇒ [tex]P(E_1)\times P(E_2)=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4} [/tex]
Since, [tex]E_1\cap E_2 [/tex] = { THH, THT }
[tex]n(E_1\cap E_2) = 2 [/tex]
⇒ [tex]P(E_1\cap E_2) = \frac{n(E_1\cap E_2)}{n(S)}= \frac{2}{8}=\frac{1}{4}[/tex]
Thus, [tex]P(E_1\cap E_2)=P(E_1)\timesP(E_2)[/tex]
Therefore, [tex]E_1[/tex] and [tex]E_2[/tex] are independent events.
B) [tex]E_1[/tex] : the first coin comes up tails
[tex]E_1[/tex] = { TTT, THH, THT, TTH }
[tex]E_2[/tex] : two, and not three, heads come up in a row
[tex]E_2[/tex] = { HHT, THH }
Thus, [tex]n(E_1)=4[/tex]
⇒ [tex]P(E_1)=\frac{n(E_1)}{n(S)}=\frac{4}{8}=\frac{1}{2} [/tex]
Similarly, [tex]P(E_2)=\frac{1}{4}[/tex]
⇒ [tex]P(E_1)\times P(E_2)=\frac{1}{2}\times \frac{1}{4}=\frac{1}{8} [/tex]
Since, [tex]E_1\cap E_2 [/tex] = { THH }
[tex]n(E_1\cap E_2) = 1 [/tex]
⇒ [tex]P(E_1\cap E_2) = \frac{n(E_1\cap E_2)}{n(S)}= \frac{1}{8}[/tex]
Thus, [tex]P(E_1\cap E_2)=P(E_1)\timesP(E_2)[/tex]
Therefore, [tex]E_1[/tex] and [tex]E_2[/tex] are independent events.
C) [tex]E_1[/tex] : the second coin comes up tails;
[tex]E_1[/tex] = { HTH, HTT, TTT, TTH }
[tex]E_2[/tex] : two, and not three, heads come up in a row
[tex]E_2[/tex] = { HHT, THH }
Thus, [tex]n(E_1)=4[/tex]
⇒ [tex]P(E_1)=\frac{n(E_1)}{n(S)}=\frac{4}{8}=\frac{1}{2} [/tex]
Similarly, [tex]P(E_2)=\frac{1}{4}[/tex]
⇒ [tex]P(E_1)\times P(E_2)=\frac{1}{2}\times \frac{1}{4}=\frac{1}{8} [/tex]
Since, [tex]E_1\cap E_2 [/tex] = [tex]\phi[/tex]
[tex]n(E_1\cap E_2) = 0 [/tex]
⇒ [tex]P(E_1\cap E_2) = 0[/tex]
Thus, [tex]P(E_1\cap E_2)\neq P(E_1)\timesP(E_2)[/tex]
Therefore, [tex]E_1[/tex] and [tex]E_2[/tex] are dependent events.
Answer:
P (E1) = 18 / 38
P (E2) = 18 / 38
P (E1 and E2) = 10 / 38
Step-by-step explanation:
Can you please put the answer to 60000000x1500 because I have a really important test cin=ming up and
Find the Value of x
(a)8\3
(b)8
(c)4\3
(d)16
Answer:
(a) 8√3
Step-by-step explanation:
All of the triangles are similar, so the ratio of hypotenuse to long side is the same for all. Comparing the middle-size triangle to the largest, we have ...
... x/12 = 16/x
... x² = 192 . . . . . . . . . . . . . multiply by 12x; next take the square root
... x = √192 = 8√3 . . . . . . seems to match answer choice (a)
What is the correct classification of the power function?
Answer:
Cubic
Step-by-step explanation:
A cubic function is a function whose degree is 3 (the highest exponent or power on the variable). It has a distinctive sideways S shape that can either start down and end up or start up and end down. It also crosses through the x-axis an odd number of times. It will have up to three x-intercepts or roots.
What is the slope of the line? – –Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of ? y + 2 =(x + 3) y – 2 = (x – 3) y + 3 = (x + 2) y – 3 = (x – 2)
Answer:
The correct answer is B) y – 2 = (x – 3)
Step-by-step explanation:
In order to find this, look at the base form of point-slope form.
y - y1 = m(x - x1)
Seeing as there is subtraction symbols after x and y, we know that we would be subtracting the x and y values. Since 2 is the y value, it would go in for y1 and 3 being the x value puts it in for x1. Once you do that, you'll get the equation above.
Answer:
-1/2
Step-by-step explanation:
Lisa spent 8 minutes on the phone while routing 2 phone calls. In all, how many phone calls does Lisa have to route to spend a total of 12 minutes on the phone? Solve using unit rates.
Lisa spends 4 minutes per call, so to spend a total of 12 minutes on the phone, she needs to route 3 calls.
Lisa spent 8 minutes on the phone routing 2 phone calls, which means she spends 4 minutes per call. This is calculated using the unit rate which is the time spent per phone call. To find out how many phone calls Lisa would have to route to spend a total of 12 minutes, we can set up a proportion where 4 minutes corresponds to 1 phone call (the unit rate), and 12 minutes corresponds to the number of phone calls we want to find (let's call it x calls).
The proportion is as follows:
4 minutes/1 call = 12 minutes/x calls
Cross-multiplying to solve for x gives us:
4 * x = 12 * 1
4x = 12
x = 12 / 4
x = 3 calls
Therefore, Lisa needs to route a total of 3 calls to spend 12 minutes on the phone.
Two boxes are stacked together.
What is the combined volume of the two boxes?
A. 105 cm
B. 280 cm
C. 385 cm
D. 4,200 cm
The formula of a volume of a rectangle prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
The larger rectangle prism:
[tex]l = 10cm,\ w=7cm,\ h=4cm[/tex]
Substitute:
[tex]V_1=(10)(7)(4)=280\ cm^3[/tex]
The smaller rectangle prism:
[tex]l=3cm,\ w=7cm,\ h=5cm[/tex]
Substitute:
[tex]V_2=(3)(7)(5)=105\ cm^3[/tex]
Total volume:
[tex]V=V_1+V_2\to V=280\ cm^3+105\ cm^3=385\ cm^3[/tex]
Answer: C. 385 cm³.The combined volume is 385 cm³
What is a rectangular parallelepiped?A rectangular parallelepiped is a polyhedron with six faces, which is also known as a hexahedron, each of which is a parallelogram.Volume of a rectangular parallelepiped can be calculated by multiplying its length , breadth and height.How to calculate the combined volume?The two boxes can be said to have a shape of rectangular parallelepiped.For the lower box, the volume will be = (7 x 10 x 4) cm³ = 280 cm³
For the upper box, the volume will be = (7 x 5 x 3) cm³ = 105 cm³
Now, for the combined volume, we need to add the individual volumes of the two boxes.∴ Combined volume will be equal to = ( 280 + 105) cm³ = 385 cm³
Option C is correct.
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A box of Munchkins contains chocolate and glazed donut holes. If Jacob ate 2 chocolate
Munchkins, then 1/11 of the remaining Munchkins would be chocolate. If he instead added 4
glazed Munchkins to the original box, 1/7 of the Munchkins would be chocolate. How many total
Munchkins are in the original box?
Answer:
24 munchkins.
Step-by-step explanation:
Let C be the number of chocolate and D be number of glazed donut holes in the original box.
We are told if Jacob ate 2 chocolate munchkins, then 1/11 of the remaining Munchkins would be chocolate. We can represent this information as:
[tex]C-2=\frac{1}{11}*(C+D-2)...(1)[/tex]
We are also told if he instead added 4 glazed Munchkins to the original box, 1/7 of the Munchkins would be chocolate. We can represent this information as:
[tex]C=\frac{1}{7}*(C+D+4)...(2)[/tex]
Upon substituting C's value from equation (2) in equation (1) we will get,
[tex]\frac{1}{7}*(C+D+4)-2=\frac{1}{11}*(C+D-2)[/tex]
Let us have a common denominator on right side of equation.
[tex]\frac{1}{7}*(C+D+4)-\frac{7*2}{7}=\frac{1}{11}*(C+D-2)[/tex]
[tex]\frac{C+D+4-14}{7}=\frac{1}{11}*(C+D-2)[/tex]
Multiplying both sides of our equation by 7, we will get,
[tex]7*\frac{C+D-10}{7}=7*\frac{1}{11}*(C+D-2)[/tex]
[tex]C+D-10=\frac{7}{11}*(C+D-2)[/tex]
Multiplying both sides of our equation by 11, we will get,
[tex]11*(C+D-10)=11*\frac{7}{11}*(C+D-2)[/tex]
[tex]11*(C+D-10)=7*(C+D-2)[/tex]
[tex]11C+11D-110=7C+7D-14[/tex]
[tex]11C-7C+11D-7D=-14+110[/tex]
[tex]4C+4D=96[/tex]
[tex]4(C+D)=96[/tex]
[tex](C+D)=\frac{96}{4}[/tex]
[tex](C+D)=24[/tex]
Therefore, the total number of Munchkins in original box is 24.
Robbie Morse has a $47,500 insurance policy. The annual premium is $987.53. Robbie pays $90.00 monthly.
How much does Robbie pay in twelve months?
$
How much more does Robbie pay?
$
What percentage does Robbie pay (to the nearest percent)?
%
Answer:
Robbie pay in twelve months $1080 .
$92.47 more Robbie pay and 9.36 %(Approx) Robbie pay.
Step-by-step explanation:
As given
Robbie Morse has a $47,500 insurance policy.
The annual premium is $987.53.
Robbie pays $90.00 monthly.
First find out the Robbie pay in twelve months .
Robbie pay in twelve months = 12 × 90
= $ 1080
Second find out how much more does Robbie pay .
Robbie pay extra = Robbie pay in twelve months - annual premium
= $ 1080 - $987.53
= $92.47
Therefore the $92.47 more Robbie pay .
Third find out the what percentage does Robbie pay .
Formula
[tex]Percentage = \frac{Robbies\ pay\ more\times 100}{annual\ premium}[/tex]
Robbies pay more = $92.47
Annual premium = $987.53
Put in the above
[tex]Percentage = \frac{92.47\times 100}{987.53}[/tex]
[tex]Percentage = \frac{9247}{987.53}[/tex]
Percentage = 9.36 % (Approx)
9.36 %(Approx) Robbie pay.
Robbie pays a total of $1,080.00 over twelve months, which is $92.47 more than the annual premium. This amount is approximately 9% more than the original annual premium.
To determine how much Robbie pays for his monthly premium over twelve months, we need to perform the following calculations:
First, calculate the total amount Robbie pays monthly. He pays $90.00 monthly, so over twelve months:
$90.00 times 12 = $1,080.00
Next, we need to find out how much more Robbie pays compared to the annual premium of $987.53:
$1,080.00 - $987.53 = $92.47
Percentage Calculation:
To find the percentage Robbie pays compared to the original annual premium, use the formula:
(difference / original amount) times 100
($92.47 / $987.53) times 100 ≈ 9%
Thus, Robbie pays approximately 9% more than the annual premium.
Please help! Urgent!
Examine triangle ABC. (look at picture)
What is the value of x?
A) 37
B) 48
C) 127
D) 138
Answer:
x = 127 degrees
Step-by-step explanation:
By the external angle of a triangle theorem:-
x + 5 = 79 + m < ACB
m < ACB = 180 - x, so:-
x + 5 = 79 + 180 - x
2x = 79 + 180 - 5 = 254
x = 127 ( answer)
Answer:
If you look at my screenshot it will show you the correct answer.
Step-by-step explanation:
What is the value of the discriminant of the quadratic equation -2x^2=-8x+8, and what does its value mean about the number of real number solutions the equation has?
Answer:
B on edg
Step-by-step explanation:
You got this chief.
Can anyone please tell me what I’m doing wrong. It’s not giving me the full marks.
Answer:
Area shaded part = 116 to three sig digs.
Step-by-step explanation:
I don't know if your answer is correct or not, but the number of sig digs is not. The way the question has been posed is not to 3 sig digs either.
The answer should be 116 if they want it to three sig digs.
Let's see if the answer is correct
Area of the whole circle.
Area of a circle = pi*r^2r = 6.5 cm Note: this is 2 sig digs.pi= 3.14Area = 3.14 * 6.5^2Area = 3.14 * 42.25Area= 132.665Area of unshaded smaller circle
pi = 3.14r = 2.3Area = 3.14 * 2.3^2Area = 3.14 * 5.29Area = 16.61Area of the shaded part
Area of shaded part = area of the whole circle - Area of smaller circleArea of the shaded part = 132.66 - 16.61Area of the shaded part = 116.01To 3 sig digs is 116Answer:
116 cm^2 to 3 significant figures.
Step-by-step explanation:
Your calculations are correct. You just haven't corrected the answer to 3 significant figures.
Help me with this question! Anybody. {will receive 15 pts.}
Answer:
The answer is 5.
Step-by-step explanation:
5+(-9) or
5-9=-4
could someone help me?
Answer:
See below
Step-by-step explanation:
m < 1 = 180 - m<4 (supplementary angles)
= 180 - 143
= 37 degrees
m <2 = m< 4 ( opposite angles)
= 143 degrees
M< 3 = m < 1 = 37 degrees (opposite angle)
Angle 1 measures 143 degrees, while angles 2 and 3 both measure 37 degrees.
To find the measure of angle 2, we can use the fact that adjacent angles on a straight line are supplementary. This means that angle 2 and angle 4 add up to 180 degrees. Since angle 4 is 143 degrees, angle 2 is 180 - 143 = 37 degrees.
To find the measure of angle 3, we can use the fact that corresponding angles of parallel lines cut by a transversal are congruent. This means that angle 3 and angle 2 have the same measure. Since angle 2 is 37 degrees, angle 3 is also 37 degrees.
Therefore, the measures of angle 1, 2, and 3 are 143 degrees, 37 degrees, and 37 degrees, respectively.
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contractors insurance has a $75 sign-up fee. Once singed up the insurace cost $61 each month. Which of the following equations represents the relationship between the number of months a contractor is insured,m, and the total cost of contractors insurance,c?
Answer:
The equation should read c = 61m + 75
Step-by-step explanation:
We can find this because we know that the 61 dollars is a dependent cost on the number of months. Therefore they have to be multiplied together.
The 75 is a constant, which means it gets added to the end.
You are required to take five? courses, one each in? humanities, sociology,? science, math, and music. You have a choice of 4 humanities? courses, 6 sociology? courses, 6 science? courses, 2 math? courses, and 8 music courses. How many different sets of five courses are? possible?
By applying the combinatorics principle in mathematics, the student has a total of 2304 possible sets of courses to choose from across the five disciplines.
Explanation:The subject of this question is a mathematical problem related to combinatorics, specifically the counting principle. When you're choosing one item from a set, like how many courses you can choose, you're often dealing with combinations or permutations. In this case, since the order of taking the courses does not matter, we're dealing with a type of combination.
To find the total number of course sets, simply multiply the number of possible courses in each discipline: 4 options in humanities, 6 in sociology, 6 in science, 2 in math, and 8 in music. So, the total number of different course sets you could take is 4 * 6 * 6 * 2 * 8 = 2304 different sets of five courses.
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Which function represents a line with a slope of ?4 and a y-intercept of ?2? A) y = 4x ? 2 B) y = ?4x + 2 Eliminate C) y = ?4x ? 2 D) y = ?2x ? 4
Answer:
A function describes this way is y = 4x + 2
Step-by-step explanation:
In order to find this, we have to start with slope-intercept form.
y = mx + b
Knowing this, we can then input the slope in for m and the intercept in for b. This will give us the equation.
y = 4x + 2
How do i translate (x,y) ?
One of my questions is asking me to translate , (x,y) i know the formula for translating, (a,b) x+a,y+b But a=x and b=y. How do i solve this?
Answer: (x, y - 8)
Step-by-step explanation:
Start with the innermost parentheses (reflection over the y-axis), which changes the sign of the y-coordinate:
(x, y) → (-x, y)Now perform the next inner parenthesis (rotation 180°), which changes the signs of both the x- and y-coordinates:
(-x, y) → (x, -y)Now perform the last set of parenthesis (reflection over y=4), which has the rule of (x, y) → (x, y + 2(4 - y)) = (x, y + 8 - 2y) = (x, 8 - y):
(x, -y) → (x, -8 + y)Ben is 20 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 33 times as old as Daniel.
how old is Ben now?
Answer: 33
Step-by-step explanation:
Today 3 years ago
Ben: x + 20 (x + 20) - 3
Dan: x x - 3
3 years ago, Ben was 3 times as old as Daniel
⇒ (x + 20) - 3 = 3(x - 3)
x + 17 = 3x - 9
17 = 2x - 9
26 = 2x
13 = x
Today, Ben = x + 20
= 13 + 20
= 33
Answer:
Ben is 33 years old
Step-by-step explanation:
Let Ben’s age = B
Let Daniel’s age = x
B = x + 20 (20 years older than Daniel)
Their ages 3 years ago:
B = 3x (also given in problem)
B = x + 20 (given in problem)
x + 20 = 3x (Since both equations are equal to B, set them equal to each other)
20 = 2x (simplify)
x = 10
B = 10 + 20 = 30
Their ages now:
Add 3 to their "ages three years ago"
New x = Daniel’s age = old age + 3 = 10 + 3 = 13 years old
B = Ben’s age = old age + 3 = 30 + 3 = 33 years old
kiran and clare live 24 mile away from each other along a rail trail. One Saturday the two friends started walking toward each other along a trail at 8:00 am with a plan to have a picnic when they meet if kiran walks 3 miles per hour while clare walks 3.4 miles per hour. At what time will the two friends meet and have their picnic
Answer:
[tex]11:45\ am[/tex]
Step-by-step explanation:
Total distance between Kiran and Clare is 24 miles. They started walking at 8.00 am.
Speed of Kiran is 3 miles/hr and speed of Clare is 3.4 miles/hr.
So the relative speed of them is,
[tex]=3+3.4=6.4[/tex] miles/hr
Both the speed are added as they moving in opposite direction.
We know that,
[tex]\text{Relative speed}=\dfrac{\text{Relative distance}}{\text{Time}}[/tex]
i.e [tex]\text{Time}=\dfrac{\text{Relative distance}}{\text{Relative speed}}[/tex]
Putting the values,
[tex]t=\dfrac{24}{6.4}=3.75\ hr=3\ hr\ 45\ min[/tex]
As they started at 8.00 am, so the time at which will meet will be,
[tex]=8+3\ hr\ 45\ min=11:45[/tex]
Answer:
11:45PM
Step-by-step explanation:
What is the solution of the equation?
Answer:
The answer is x = 7
Step-by-step explanation:
√2x − 5 + 4 = x
= √2x − 5 + 4 + − 4 = x + −4 (add -4 to both sides)
=√2x − 5 = x − 4
=√2x−5=x−4
2x−5=(x−4)2 (Square both sides)
2x−5=x2−8x+16
2x−5−(x2−8x+16)=x2−8x+16−(x2−8x+16)(Subtract x^2-8x+16 from both sides)
−x2+10x−21=0
(−x+3)(x−7)=0 (Factor left side of equation)
−x+3=0 or x−7=0 (Set factors equal to 0)
x=3 or x=7
Answer: 7
Step-by-step explanation:
[tex]\sqrt{2x-5}+4 = x[/tex]
Restriction: x ≥ 4 why? because [tex]\sqrt{2x-5}\geq0[/tex]
[tex]\sqrt{2x-5}+4 = x[/tex]
-4 -4
[tex]\sqrt{2x-5} = x - 4[/tex]
[tex](\sqrt{2x-5})^2 = (x - 4)^2[/tex]
2x - 5 = x² - 8x + 16
-2x +5 -2x +5
0 = x² - 10x + 21
0 = (x - 3) (x - 7)
0 = x - 3 0 = x - 7
3 = x [tex]\big{\boxed{7=x}}[/tex]
↓
not valid
The graphic shows the schedule network diagram (in minutes) for assembling a toy train set. What is the duration of the critical path?
A) 38 minutes
B) 41 minutes
C) 49 minutes
D) 51 minutes
The critical path in a project schedule is the longest sequence of tasks from start to finish and determines the minimum total duration for the project. Without the diagram, the correct duration from your multiple-choice options cannot be determined accurately. The correct answer represents the duration of the longest path from the given options.
Explanation:Without the graphic showing the schedule network diagram for assembling a toy train set, providing an accurate answer would be difficult. Normally, in project management, a Critical Path represents the longest sequence of tasks (or activities) in a project schedule from start to finish. It determines the minimum total duration required to complete the project. You identify the critical path by adding the times for the activities in each sequence and determining the longest path in the project.
In this case, assuming that you have the diagram in front of you and you've calculated the total duration for all paths, one of the multiple choice options (A) 38 minutes, (B) 41 minutes, (C) 49 minutes, or (D) 51 minutes would represent the duration of the critical path in the network diagram.
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A construction company plans to invest in a building project. There is a 30% chance that the company will lose $30,000, a 40% chance of a break even, and a 30% chance of a $60,000 profit. Based ONLY on this information, what should the company do?
The expected value is $9,000.00, so the company should proceed with the project.
B) The expected value is $18,000.00, so the company should proceed with the project.
C) The expected value is −$9,000.00, so the company should not proceed with the project.
D) The expected value is −$18,000.00, so the company should not proceed with the project.
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given that
30% chance that the company will lose $30000.
40% chance of a break even that there is no loss and no profit.
30% chance that the company will profit $ 60000.
As we know the formula for "Expectation":
So, Expected value will be
[tex]\frac{30}{100}\times (-30000)+\frac{40}{100}\times 0+\frac{30}{100}\times 60000\\\\=03\times (-30000)+0.4\times 0+0.3\times 60000\\\\=-9000+18000\\\\=\$9000[/tex]
Expected value is $9000. So, the company should proceed with the project.
Hence, Option 'A' is correct.
Noah is thinking of two fractions that have the same sum of 3/5. Each fraction has a numerator of 1. What are the denimonitors of the fractions? Enter your answers in the box
Answer:
The denominators of fractions are : 2 and 10
Step-by-step explanation:
[tex]\text{Let the two fractions be : }\frac{1}{x}\thinspace and\thinspace \frac{1}{y}\\\\\implies \frac{1}{x}+\frac{1}{y}=\frac{3}{5}\\\\\implies 5\cdot x +5\cdot y-3\cdot x\cdot y=0[/tex]
By hit and trial method, if we put x = 2 and y = 10 then the resulting equation (1) is satisfied and all the conditions hold.
So, the denominators are 2 and 10
Through the hit and trial method, the value of the denominator 'a' is 2 and the value of denominator 'b' is 10 and there is also the use of arithmetic operations.
Given :
Noah is thinking of two fractions that have the same sum of 3/5.Each fraction has a numerator of 1.To determine the denominator of the two fractions whose sum is 3/5, first, let that numbers be 1/a and 1/b.
[tex]\dfrac{1}{a}+\dfrac{1}{b}= \dfrac{3}{5}[/tex]
[tex]5a + 5b = 3ab[/tex]
Now, put a = 2 then b becomes:
[tex]10 + 5b = 6b[/tex]
b = 10
So, through the hit and trial method, the value of a is 2 and the value of b is 10.
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D is the midpoint of CE. E has coordinates (−8, −3), and D has coordinates (2, 3). Find the coordinates of C.
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad E(\stackrel{x_2}{-8}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-8+x}{2}~~,~~\cfrac{-3+y}{2} \right)=\stackrel{\stackrel{midpoint}{D}}{(2,3)}\implies \begin{cases} \cfrac{-8+x}{2}=2\\[1em] -8+x=4\\ \boxed{x=12}\\[-0.5em] \hrulefill\\ \cfrac{-3+y}{2}=3\\[1em] -3+y=6\\ \boxed{y=9} \end{cases}[/tex]
Paul is 2 years younger than patricia. Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia. How old is paul currently.
Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia.
That gives us the equations 1.25d=p and 1.5(d−10)=(p−10). Solving gives us 25 for Daniel and 20 for Patricia.
Paul is two years younger than Patricia.
20−2=18
To solve the problem, we set up an equation based on the given relationships and information. After solving it, we find that Patricia is 40 years old and Paul (who is 2 years younger) is 38 years old.
Explanation:Let's denote Patricia's current age as 'P', Paul's age as 'P-2' (since Paul is 2 years younger than Patricia), and Daniel's age as 'P+0.25P' (since Daniel is 25% older than Patricia).
According to the problem, ten years ago, Daniel was 50% older than Patricia. So, we create the equation '0.5(P-10) = P+0.25P-10' to represent this situation.
Solving the equation, we find P (Patricia's current age) equals 40 years. Hence, Paul's current age would be 'P-2', which is 38 years.
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PLEASE HELP! :( what is the sum of the geometric series
15
E 2(1/3)^3
x = 0
rounded to the nearest whole number???
A) 1
B) 2
C) 3
D) 4
the picture is attached! i don’t get it please help!