Let's begin by identifying key information given to us:
\(y=-x+7\)In order to graph this equation, we will assume values for the x-variable to obtain the output. This is shown below:
\(\begin{gathered} y=-x+7 \\ x=-5 \\ y=-(-5)+7=5+7=12 \\ \Rightarrow(-5,12) \\ \\ x=-1 \\ y=-(-1)+7=1+7=8 \\ \Rightarrow(-1,8) \\ \\ x=2 \\ y=-2+7=5 \\ (2,5) \\ \\ x=4 \\ y=-4+7=3 \\ \Rightarrow(4,3) \\ \\ x=7 \\ y=-7+7=0 \\ \Rightarrow(7,0) \end{gathered}\)We will proceed to plot this on a graph as shown below:
what is a power of a power
Answer:
The power of a power rule states that if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same.
Step-by-step explanation:
Diane, Sam, and Boris served a total of 54 orders Monday at the school cafeteria. Diane served 6 fewer orders than Sam. Boris served 2 times as
many orders as Sam. How many orders did they each serve?
Number of orders Diane served:
Number of orders Sam served:
Number of orders Boris served:
Answer:
Let's denote:
- The number of orders Diane served as `D`
- The number of orders Sam served as `S`
- The number of orders Boris served as `B`
From the problem, we know:
1. `D + S + B = 54` (the total number of orders they served)
2. `D = S - 6` (Diane served 6 fewer orders than Sam)
3. `B = 2S` (Boris served 2 times as many orders as Sam)
We can substitute equations 2 and 3 into equation 1 to solve for the variables:
Substitute `D` and `B` in equation 1:
`(S - 6) + S + 2S = 54`
Combine like terms:
`4S - 6 = 54`
Add 6 to both sides:
`4S = 60`
Divide by 4:
`S = 15`
Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:
`D = S - 6 = 15 - 6 = 9`
`B = 2S = 2 * 15 = 30`
So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.
joey goes to the carnival. he spends $26. he buys himself a supersize shake for $5.00. He also buys six regular-size sundaes. Write an equation that you could solve to find out how much each sundae costs.
HELP PLS, IT'S A TEST-
A computer software company has submitted bids on two separate government contracts, A and B. The company estimates that it has a 36 percent chance of winning contract A and a 53 percent chance of winning contract B. The company believes that winning contract A is independent of winning contract B. Answer the following questions, rounding your answers to two decimal places where appropriate.
a) What is the probability that the company will win both contracts?
b)What is the probability that the company will win at least one of the two contracts?
Now suppose that the company believes that, given that it wins contract B, it has a 40 percent chance of winning contract A.
c)What is the probability that the company will win both contracts?
d) What is the probability that the company will win at least one of the two contracts?
e) If the company wins contract B, what is the probability that it will not win contract A?
Using probability concepts, it is found that there is a:
a) 0.1908 = 19.08% probability that the company will win both contracts.
b) 0.6992 = 69.92% probability that the company will win at least one of the two contracts.
c) 0.212 = 21.2% probability that the company will win both contracts.
d) 0.6992 = 69.92% probability that the company will win at least one of the two contracts.
e) 60% probability that it will not win contract A.
Conditional probability:
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which
P(B|A) is the probability of event B happening, given that A happened. \(P(A \cap B)\) is the probability of both A and B happening. P(A) is the probability of A happening.Item a:
0.36 probability of winning contract A.0.53 probability of winning contract B.The probability of both is the multiplication of each probability, thus:
\(p = 0.36(0.53) = 0.1908\)
0.1908 = 19.08% probability that the company will win both contracts.
Item b:
1 - 0.36 = 0.64 probability of not winning contract A.1 - 0.53 = 0.47 probability of not winning contract B.The probability of winning none is:
\(p_N = 0.64(0.47) = 0.3008\)
The probability of winning at least one is:
\(p = 1 - p_N = 1 - 0.3008 = 0.6992\)
0.6992 = 69.92% probability that the company will win at least one of the two contracts.
Item c:
Now, conditional probability is used, considering \(P(B) = 0.53, P(A|B) = 0.4\). Hence:
\(P(A \cap B) = P(B)P(A|B) = 0.53(0.4) = 0.212\)
0.212 = 21.2% probability that the company will win both contracts.
Item d:
If it doesn't wins contract A, the probability of not winning B is the same as in item B, so the probability of winning none is the same, which means that the probability of winning at least one is the same, that is:
0.6992 = 69.92% probability that the company will win at least one of the two contracts.
Item e:
If it wins contract B, it has a 40% percent change of winning contract A, thus 100% - 40% = 60% probability that it will not win contract A.A similar problem is given at https://brainly.com/question/25229135
As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than 10 hours per week, but wants to make at least $200 per week. The inequalities 20x + 25y ≥ 200 and
x + y < 10 represent the situation. Which is true of the graph of the solution set? Check all that apply.
Answer:the line x+y<10 has a negative slope and a positive y intercept
The line representing 20x+25y>200 is solid and the graph is shaded above line
The overlapping region contains the point (4,5)
Step-by-step explanation:
;)
Answer:
The answers are B, C, and E.
Step-by-step explanation:
I got it right on edge
Help is for now please
**PLEASE HELP!!*
George is comparing the graphs of two functions f(x)=3^x and g(x)=3x^2+x-1 for different values of x. Which statement best compares the values of the functions as the value of x increases?
A. F(x) will eventually exceed g(x) for all real numbers greater than a certain x-value
B.g(x) will eventually exceed f(x) for all real numbers greater than a certain x-value
C. F(x) is greater than g(x) for all values of x.
D. G(x) is greater than f(x) for all values of x.
Divide 3/5÷4 please help ASAP please
Answer: The answer is 2.4
Step-by-step explanation:Hope this helps
I Need helppp! Please helpp!!
9514 1404 393
Answer:
x = 1/2
Step-by-step explanation:
There are some different ways to find the area of a donut shape. One is to multiply its centerline length by its width. We'll use that here to find the shaded area of the sector.
The centerline radius of shaded area A is ...
(6x -2) cm + (1/2)(4x cm) = 8x -2 cm
The length of the centerline is ...
s = rθ = (8x -2)(π/4) . . . . . . for a central angle of 45° = π/4 radians
Then the area A is ...
area A = (π/4)(8x -2)(4x) = 2πx(4x -1) . . . cm^2
__
The radius of circle B is ((4 -4x) cm)/2 = (2 -2x) cm. The area of circle B is ...
A = πr^2 = π(2 -2x)^2 cm^2
We're told the two areas are equal, so we have ...
2πx(4x -1) = π(2 -2x)^2 . . . . . . . expressions for the areas are equal
8x^2 -2x = 4x^2 -8x +4 . . . . . . divide by π, eliminate parentheses
4x^2 +6x -4 = 0 . . . . . . . . . . . . subtract the right-side expression
2(2x -1)(x +2) = 0 . . . . . . . . . . . factor
x = 1/2 or -2 . . . . . . . only the positive solution is useful here
The value of x is 1/2.
I have a screenshot attached.
( 4, 6) -> right 4, up 6
( -4,6)-> left 4 , up 6
(6,-4)-> right 6, down 4
Answer:
(4,6) = right 4 up 6...(-4,6)= left 4 up 6 and the last one is up 6 left 4
Find the missing angle according to the Triangle Exterior Angle Theorem
Answer:
x = 105 degrees
Step-by-step explanation:
First, figure out the interior angle, we can do this ading the two angles and then subtracting the sum from 180 (since the interior angle of a triangle adds up to 180 degrees)
180 - (55 + 50) = 75
next, we can figure out x by taking the sum (75) and subtracting that from 180 since it is a supplementary angle:
180 - 75 = 105
x = 105
Answer:
105 degrees!
Step-by-step explanation:
all the angles in a triangle must add to 180.
50+55= 105
therefore, the missing angle would be 75
x+75 must also add to 180 so the answer would be: 105 because 75+105= 180
Hope this helps!!
Rewrite as a simplified fraction.
_
0.23 = ?
Answer:
23/100
Step-by-step explanation:
If I had 60 units needed and units per case was 14 how many full cases and additional items are needed to fufill the order
Q. Select the correct graph for each inequality.
A
B
C
D
Answer:
b is answer xd un s sisjxdxdxdxd
Using the slope formula, find the slope of the line through the given points. (4. - 2) and ( - 2, - 2)
Hi! I'm happy to help!
To solve this problem, we have to find the slope, which is rise over run, or how much the line rises and how far forward the line goes.
We find the slope using this formula (slope formula)
m(slope)=\(\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)
This refers to the second y point minus the first y point, divided by the second x point minus the first x point. Y refers to the y axis, so that is the rise, because it is the difference of height in the line. X refers to the x axis, so that is the run, because it is the difference in how far it travels forward.
Our second y point is -2, our first y point is also -2. Our second x point is -2, and our first y point is 4. Let's plug in our values.
\(\frac{-2-(-2)}{-2-4}\)
Let's simplify this so there isn't a double negative.
\(\frac{-2+2}{-2-4}\)
Now, let's solve
\(\frac{0}{-6}\)
0 divided by -6, is still 0, so there is no slope or the slope is 0. This means that the line is horizontal and the y coordinate doesn't change.
I hope this was helpful, keep learning! :D
Kylee's car was broken into, and her stereo and GPS system worth $425 total
were stolen. If Kylee's insurance policy summary is given below, how much
will Kylee receive from her insurance company when she files her claim?
answer
= amount to be paid by kylee to repair her car = $ 400
And this loss is claimed under comprehensive deductible worth $375
So the extra amount which is to be paid to insurance company is =$ 25
= $ 25
Kylee receive from her insurance company when she files her claim for $25.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Kylee's car was broken into, and her stereo and GPS system worth $425 total were stolen.
The amount to be paid by Kylee to repair her car is $400
And this loss is claimed under a comprehensive deductible worth $375.
So the extra amount which is to be paid to an insurance company will be
⇒ $400 - $375
⇒ $25
Kylee receive from her insurance company when she files her claim for $25.
The complete question is...
Kylee's car was broken into, and her stereo and GPS system worth $425 total were stolen. If Kylee's insurance policy summary is given below.
The amount to be paid by Kylee to repair her car is $400
And this loss is claimed under a comprehensive deductible worth $375.
How much will Kylee receive from her insurance company when she files her claim?
More about the Algebra link is given below.
https://brainly.com/question/953809
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Make y the subject of formula A = \(\pi x^{2} - \pi y{2}\)
BRAINLIESTT PLSS !!!
\(\pi \times {y}^{2} = \pi \times {x}^{2} - A\)
y² = x² - A/pi
y = sqrt(x² - A/pi)
What answer is this I can’t find it
In problems 6 and 7, write an inequality that describes each
statement.
6. Each item in the store costs a dollar or less. Use the variable c.
7. The population of China is at least 1,000,000,000 people.
Answer:
6. c <= 1
7. p >= 1 000 000 000
Step-by-step explanation:
6. a dollar or less = $1 dollar or less than $1; therefore, <= sign is used
7. at least = the minimum of the number given; therefore, >= sign is used.
(if you are struggling with which sign is the "greater than" or "less than," remember that the bigger ones are what they are most likely to eat, for example, 100 > 1; imagine signs like Pacman eating those balls)
2) There are 40 boys and 16 girls in a class of students. What is the ratio of girls to students?
Add boys and girls together for total students:
40 + 16 = 56 total students
Girls to total students is 16/56
Divide both numbers by 8 to get 2/7
The ratio is 2/7
\(\sf{\bold{\blue{\underline{\underline{Given}}}}}\)
There are 40 boys and 16 girls in a class of students. ⠀⠀⠀⠀\(\sf{\bold{\red{\underline{\underline{To\:Find}}}}}\)
⠀What is the ratio of girls to students?⠀⠀⠀\(\sf{\bold{\purple{\underline{\underline{Solution}}}}}\)
In a class,
boys=40
girls =16
So,
The students of the class =
boys+girls 40+1656According to the question,
we have to find the ratio of girls to the total students
ratio=\(\sf{\dfrac{girls}{students} }\) ratio=\(\sf{\dfrac{16}{56} }\) ratio=\(\sf{\dfrac{\cancel{16}}{\cancel{56}} }\)ratio=\(\sf{\dfrac{2}{7} }\) ratio=\(\sf{2:7 }\)⠀⠀⠀⠀
\(\sf{\bold{\green{\underline{\underline{Answer}}}}}\)
⠀⠀⠀⠀
Hence,the ratio of girls to students is 2:7
⠀⠀⠀⠀
please help me solve
The equation for the line of best fit is: C. y = 0.894x + 0.535.
How to determine the equation for the line of best fit?In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;
x y x² y² xy__
5 4 25 16 20
6 6 36 36 36
9 9 81 81 81
10 11 100 121 110
14 12 196 144 168
Sum 438 398 415
Next, we would calculate the mean of the x and y variables as follows;
Mean = [∑(x)]/n
Mean = 44/5
Mean, \(\bar{x}\) = 8.8
Mean = [∑(y)]/n
Mean = 42/5
Mean, \(\bar{y}\) = 8.4
∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)
∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4
∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²
∑(x - \(\bar{x}\))² = 50.8
Now, we can determine the slope coefficient for the line of best fit:
Slope (b) = 45.4/50.8
Slope (b) = 0.894.
Lastly, we would determine the intercept (a) as follows;
\(a = \bar{y} - b\bar{x}\)
a = 8.4 - (0.894)8.8
a = 0.535
Therefore, the required equation is y = 0.894x + 0.535.
Read more on linear regression here: brainly.com/question/16793283
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Luis includes sit ups and push ups as part of his training for the race. This graph shows his plan for increasing the number of sit ups and push ups he does each week. Write an equation that can be used to find the number of sit ups, y, luis will do during week x.
Answer:
y = 10x
Step-by-step explanation:
y = number of sit-ups
x = number of weeks
Equation of that can be used to find the number of sit-ups can be generated using the graph in the slope-intercept form, y = mx + b. Where, slope = m, and y-intercept is b.
Let's find slope using two points on the blue line, (0, 0) and (3, 30):
Slope (m) = change in y/change in x
m = (30 - 0)/(3 - 0)
m = 30/3
m = 10
b = 0 (the point where the line intercepts the y-axis)
✔️To write the equation, substitute m = 10 and b = 0, into y = mx + b
y = 10x + 0
y = 10x
What’s the correct answer for this question?
Answer:
\( 6\)
Step-by-step explanation:
In the given figure, secants PA and PC are intersecting outside of the circle at point P.
PA = PB + AB = 7 + 5 = 12
PC = 14, PD =?
By the property of intersecting secants outside of a circle:
\( PB \times PA = PD\times PC\\
\therefore 7\times 12 = PD \times 14\\
\therefore 84 =PD \times 14\\\\
\therefore PD = \frac{84}{14}\\\\
\therefore PD = 6\\\\
\)
Answer: PD = 6
Step-by-step explanation:
PD = PB + AB = 12
When two secant lines intersect each other outside a circle, the products of their segments are equal. This is:
PB x PA = PD x PC
7 x 12 = PD x 14
PD = 7 x 12 / 14
PD = 6
Cold Beans wants to make a blend of their two best coffees, Guatemalan and Jamaican coffee. The pound of Guatemalan Coffee costs $11/lb and the other one costs $5/lb. If they want the cost of a 6 pound bag of blend to be $8/lb, how much Guatemalan coffee should they use per pound of the blend?
For each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.
This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.
Let's assume that x pounds of Guatemalan coffee are used per pound of the blend.
Given information:
Cost of Guatemalan coffee = $11/lb
Cost of the other coffee = $5/lb
Desired cost of the blend = $8/lb
Total weight of the blend = 6 pounds
To find the ratio of Guatemalan coffee to the total blend, we can set up the equation:
\((x \times 11 + (6 - x) \times 5) / 6 = 8\)
In this equation, \((x \times 11)\) represents the cost of the Guatemalan coffee in the blend, and\(((6 - x) \times 5)\) represents the cost of the other coffee in the blend.
The numerator is the total cost of the blend, and we divide it by 6 (the total weight of the blend) to find the cost per pound.
Now, let's solve the equation for x:
(11x + 30 - 5x) / 6 = 8
6x + 30 = 48
6x = 48 - 30
6x = 18
x = 18/6
x = 3
Therefore, for each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.
This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.
To summarize, to achieve a cost of $8 per pound for a 6-pound bag of blend, Cold Beans should use 3 pounds of Guatemalan coffee per pound of the blend.
For similar question on cost.
https://brainly.com/question/2292799
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6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives: y = x – 5
Answer:
x =6y =13Step-by-step explanation:
This is the method I am familiar with.
I Hope It helps :)
\(METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\\)
\(Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6\)
Answer:
Correct answers is
Step-by-step explanation:
1. 3
2. B
3. 6
4. (6,13)
last year, Nicole biked n miles. This year, she biked 524 miles. Using n, write an expression for the total number of miles she biked.
Answer:
n+524
Step-by-step explanation:
you add both years worth of biking together!
To borrow money, you pawn your guitar Based on the value of the guitar, the pawnbroker loans you 5840 One month later, you get the guitar back by paying the pawnbroker $1272 What annual interest rate did you pay?You will pay a simple interest rate of %(Round to the nearest whole number as needed)
1272 = 5840 x r x 1
r = 1272 / 5840
r = 0.22
r = 22%
Interest rate = 22 %
x-2y+3z=-1
-3x+6y-9z=3
2x-4y+6z=-2
Step-by-step explanation:
out of the first equation we get
x = 2y - 3z - 1
this we use in the second equation
-3(2y - 3z - 1) + 6y - 9z = 3
-6y + 9z + 3 + 6y - 9z = 3
0 = 0
this is the same equation as the first one, just multiplied by -3.
and we see the third equation is again the same one as the first just multiplied by 2.
so, there are infinite solutions.
this has not a single solution, as in the end this is just one equation with 3 variables.
The water level is a number that indicates whether the level is above or below normal using positive or negative values. After a heavy storm, the water level of a river is −3.7 feet. This level is 1/2 times 2.5 feet more than the previous water level.
What was the previous water level?
A. -18.5
B. -9.9
C. -4.9
D. -4.3
Note: I think it is -4.9. If you have the actual right answer please leave it down below. Thanks.
Answer:
I also believe it is -4.9 but I may be mistaken
Step-by-step explanation:
standard form. (x+8)(x−6)
Answer:
x^2-2x-48
Step-by-step explanation:
FOIL
Firsts = x*x = x^2
outside = x*-6 = -6x
inside = 8*x = 8x
lasts = 8*-6 = -48
add all together x^2-6x+8x-48 = x^2-2x-48
Answer:
x² + 2x - 48
Step-by-step explanation:
( x + 8 ) ( x - 6 )
= x ( x - 6 ) + 8 ( x - 6 )
= x*x - 6*x + 8*x + 8*( - 6 )
= x² - 6x + 8x - 48
= x² + 2x - 48