Answer:
The linear function that models the charge for hiring the technician for x hours is y=45*x + 55
Step-by-step explanation:
The linear function is defined by the equation
f(x) = mx + b or y = mx + b
where m is the slope of the line and b is the y-intercept.
In this case you want to represent a linear function that models the charge for hiring the technician for x hours, that is, y represents the charge for hiring the technician and x the number of hours.
Given the coordinates of two points (x1, y1) and (x2, y2), you can determine the equation of the line first knowing the slope m by:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
In this case, the points are:
(x1,y1)= (3,190)(x2,y2)= (7,370)So:
[tex]m=\frac{370-190}{7-3}[/tex]
Solving:
m=45
To obtain the value of b, once you have replaced the value of m in the equation, you must substitute the values of x and y for the values of the coordinates of one of the points, and solve for b to obtain its value. In this case you replace the value of point 1:
[tex]y=45*x+b[/tex]
[tex]190=45*3+b[/tex]
And you get:
190= 135 + b
190 - 135= b
55= b
So, the linear function that models the charge for hiring the technician for x hours is y=45*x + 55
We want to find a linear equation that models the charge for hiring the technician for x hours.
The correct option is D, the equation is:
y = ($45/h)*x + $55
We know that a general linear equation is written as:
y = a*x + b
where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have two points, one given by:
(3 hours, $190)
The other given by:
(7 hours, $370)
Then the slope is given by:
[tex]a = \frac{\$ 370 - \$ 190}{7h - 3h} = \$ 45/h[/tex]
This means that he charges $45 per hour.
Replacing that in the general equation we get:
y = ($45/h)*x + b
To find the value of b, we use the fact that he charges $190 for 3 hours, then we can solve:
$190 = ($45/h)*3h + b
$190 = $135 + b
$190 - $135 = b = $55
Then the equation is:
y = ($45/h)*x + $55
So the correct option is D.
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Can someone solve this? also, show work please. We need to find out what x is.
-6x + 13 = -5(7 +6x)
Answer:[tex] \huge{ \boxed{ \bold{ \tt{ x = - 2}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - 6x + 13 = - 5(7 + 6x) }[/tex]
Distribute -5 through the parentheses
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 5 \times 7 + ( - 5 )\times 6x}}[/tex]
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 35 + ( - 30x)}}[/tex]
[tex] \text{Remember} : \sf{( + ) \times ( - ) = ( - )}[/tex]
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 35 - 30x}}[/tex]
Move 30x to left hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 6x + 30x + 13 = - 35}}[/tex]
Move 13 to R.H.S ( Right Hand Side ) and change it's sign[tex] \longrightarrow{ \sf{ - 6x + 30x= - 35 - 13}}[/tex]
Combine like terms
[tex] \longrightarrow{ \sf{24x = - 35 - 13}}[/tex]
The negative integers are always added but posses the negative ( - ) sign.[tex] \longrightarrow{ \sf{24x = - 48 }}[/tex]
Divide both sides by 24
[tex] \longrightarrow{ \sf{ \frac{24x}{24} = \frac{ - 48}{24}}} [/tex]
Dividing a negative integer by a positive integers gives a negative integer.
[tex]\longrightarrow{\sf{x = -2 }}[/tex]
-----------------------------------------------------
Verification:L.H.S = -6x + 13
Plug the value of x and simplify
[tex] \longrightarrow{ \sf{ - 6 \times ( - 2) + 13}}[/tex]
Multiplying negative integers by a negative integer gives a positive integer.
[tex] \longrightarrow{ \sf{ 12 + 13}}[/tex]
Add the numbers : 12 and 13
[tex] \longrightarrow{ \sf{25}}[/tex]
R.H.S = -5 ( 7 + 6x )
plug the value of x and simplify
[tex] \longrightarrow{ \sf{ - 5(7 + 6 \times ( - 2)}})[/tex]
Multiplying a positive integer by any negative integer gives a negative integer.
[tex] \longrightarrow{ \sf - 5(7 + ( - 12)}[/tex]
[tex]\longrightarrow{\sf{-5(7 - 12)}}[/tex]
Subtract 12 from 7
[tex] \longrightarrow{ \sf{ - 5 \times ( - 5)}}[/tex]
[tex]\longrightarrow{\sf{25}}[/tex]
L.H.S = R.H.S
The value of x is -2 .
Hope I helped!
Best regards!
~TheAnimeGirl
A deck of 52 cards is shuffled. The first five cards of the deck are red. What is the probability that the last card in the deck is the ace of spades
Answer:
The answer is "[tex]\frac{1}{47}[/tex]".
Step-by-step explanation:
Although the five first players are red, the very first five cards are not spaded as the spad is a black card.
Its chance of the final card mostly on deck being the ace of spades is therefore determined as:
[tex]= \frac{1}{\text{Number of remaining cards with the initial 5 cards}} \\\\= \frac{1}{47}[/tex]
Thus, [tex]\frac{1}{47}[/tex] here is the necessary chance.
Answer:
1/47
Step-by-step explanation:
52 cards
5 red
probability= last card ace of spades
First do, 52-5, which gives you 47, and last card ace of spades, is 1, so 1/47 is the answer
1/47!
Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.Area: 49 square feet ft (smaller value) ft (larger value)
Answer:
Length = 7 ft
Breadth = 7 ft
Step-by-step explanation:
Let lenght of rectangle be x
and breadth be y
Area = [tex]49\ \text{ft}^2[/tex]
[tex]xy=49\\\Rightarrow x=\dfrac{49}{y}[/tex]
Permiter of a rectangle is given by
[tex]P=2(x+y)\\\Rightarrow P=2x+2y\\\Rightarrow P=2\times\dfrac{49}{y}+2y\\\Rightarrow P=\dfrac{98}{y}+2y[/tex]
Differentiating with respect to y we get
[tex]\dfrac{dP}{dy}=-\dfrac{98}{y^2}+2[/tex]
Equating with zero
[tex]0=-\dfrac{98}{y^2}+2\\\Rightarrow -2=-\dfrac{98}{y^2}\\\Rightarrow y^2=\dfrac{98}{2}\\\Rightarrow y^2=49\\\Rightarrow y=7[/tex]
Double derivative of the equation
[tex]\dfrac{d^2P}{dy^2}=2\dfrac{98}{y^3}\\\Rightarrow \dfrac{d^2P}{dy^2}=\dfrac{196}{y^3}>0[/tex]
So the value of y is minimum at 7.
[tex]x=\dfrac{49}{y}=\dfrac{49}{7}\\\Rightarrow x=7[/tex]
Hence, [tex]x=7,y=7[/tex]
The mimimum length and breadth of the rectangle is both 7 ft.
Multiplying and Dividing Radicals
Simplify the following expressions.
Last year, the cost of a family-sized dinner at a picnic was $8.50. This year, the cost is $11.56. What is the percent of increase of the price? (i need a step-by-step explanation not just the answer) will give out brainly if u tell me how to
Answer:
[tex]\%Increase = 36\%[/tex]
Step-by-step explanation:
Given
[tex]Initial = 8.50[/tex]
[tex]Final = 11.56[/tex]
Required
Determine the percentage increase
Percentage increase is calculated using:
[tex]\%Increase = \frac{Final - Initial}{Initial} * 100\%[/tex]
Substitute values for Final and Initial
[tex]\%Increase = \frac{11.56 - 8.50}{8.50} * 100\%[/tex]
[tex]\%Increase = \frac{3.06}{8.50} * 100\%[/tex]
[tex]\%Increase = \frac{3.06 * 100\%}{8.50}[/tex]
[tex]\%Increase = \frac{306\%}{8.50}[/tex]
[tex]\%Increase = 36\%[/tex]
Hence, the percentage increase in price is 36%
PLEASE HELP MATH HW DUE SOON
Answer:
One number is 43 and the other is -29
Step-by-step explanation:
If you add and subtract 36 it shows both possible answers, this is because it doesn't tell us if it is more or less than 7 so it could only be those 2 numbers
A slow pitch softball diamond is actually a square 61 ft on a side. How far is it from home to second base?
Answer:
This would be the same as an isosceles right triangle. It would be 61ft x (square root of 2) = ~86.3ft
This is rounded of course...
The distance from from home to second base is 86.26 ft.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, a slow pitch softball diamond is actually a square 61 ft on a side.
A slow-pitch softball diamond is actually a square shape.
The side length of the square is 61 ft
Here ABCD is square. The length of the side is AB=BC=CD=DA=60 feet.
Consider the distance between home base to second base is the hypotenuse if we draw a right triangle using the diagonal across the square and two sides of the square.
Let us assume the diagonal distance from home to second base BD=x.
Let us find the distance from home base to second base by using Pythagorean Theorem:
Now, x²=61²+61²
x²=3721+3721
x²=7442
x=√7442
x=86.26 ft
Therefore, the distance from from home to second base is 86.26 ft.
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Help me out plz. Struggling :( 5 and 4
Answer:
#5 = $676.40
#6 = $522.50
Step-by-step explanation:
Lets start with number 5.
Marla earns $17.80 per hour. If she works 38 hours a week she will earn $(17.80*38) per week which is $676.40 per week
Now for number 6
He earns $11.00 an hour for a 40 hour work week. If he gets paid 1.5 that (1.5 his normal rate) for overtime and he has 45 hours vs his 40 hours, heres how we solve:
Solve for his pay on a normal week:
11 * 40 = 440 a week on a normal week
Find out how much overtime
45-40 = 5 hours
Calculate the pay for the overtime
(11*1.5) x 5 =
16.50 x 5 = 82.5
Add the two pays together
440 + 82.50 = $522.50
also #4 is not provided to me to solve so if you want it solved update this question to include it
Hope this helps :)
The Cardiovascular Risk in Young Finns Study showed average baseline triglyceride levels among 920 people of 0.926 mmol/L associated with a total sum of squared deviations of approximately 160 mmol/L. If a linear regression analysis of baseline triglyceride levels on physical activity levels had an R-squared of 0.30, what are the sum of squared deviations explained by the regression model?
a. 112 mmol/L
b. Not enough information
c. 48 mmol/L
Answer:
The sum of the squared deviations explained by the regression model is:
c. 48 mmol/L
Step-by-step explanation:
Average baseline triglyceride levels among 920 people = 0.926 mmol/L
Total sum of squared deviations, approximately = 160 mmol/L
Linear regression analysis of baseline triglyceride levels on physical activity levels had an R-squared = 0.30
Therefore, the sum of the squared deviations explained by the regression model = 160 * 0.30 = 48 mmol/L
272 is the partial product of 34 and ?
Answer:
8
Step-by-step explanation:
cuz 272/34= 8
Answer:
Required Answer:-[tex]{:}\longmapsto [/tex][tex]\sf {\dfrac {272}{34}}[/tex]
[tex]{:}\longmapsto [/tex][tex]\sf 8[/tex]
Which equation represents a line that is parallel to the line y=3-2x
Answer:
any equation that include y = -2x
Step-by-step explanation:
if the equation has something like y = -2x + 4 or y = -5 - 2x is parallel
parallel lines have the same slope, the y intercept is not really important
What is 8.15 rounded to the nearest whole number
Answer:
the answer is 8.
Step-by-step explanation:
Brainliest? uwu
Answer:
8 :)
You round down. If it was 8.5 then you'd round up, anything below would be rounded down, for example, 8.4, 8.3, 8.2, 8.1.
Write an expression: 5 less than a product of 6 and 3
Answer:
(6)(3)-5
Step-by-step explanation:
92% of what number is 351.
Thanks
Answer:
x = 381.52
Step-by-step explanation:
We start by writing 92% in decimal form: 92% = 0.92
Now we want to find 92% of what number "x" equals 351, and write the equation in math form that represents such statement:
0.92 * x = 351
solve for "x" by dividing both sides by 0.92:
x = 351/0.92
which gives approximately:
x = 381.52
A concession stand sell hot dogs and hamburgers. At a football game, 84 hot dogs and 36 hamburgers were sold for $276. At another football game, 60 hotdogs and 18 hamburgers were sold for $174. Wrote a system of equations to represent this situation. Then solve the system of equations.
Answer:
The concession stand sold 46 hot dogs and 32 hamburgers.
Step-by-step explanation:
The first thing to do in algebraic problems is assign variables to things we don't know, so let's start there:
We don't know how many hot dogs the concession stand sold, so we will call that number d.
We don't know how many hamburgers the concession stand sold, so we will call that number h.
Now we translate the statements into algebraic equations:
The number of hot dogs and hamburgers that were sold is 78, so d+h=78.
If each hot dog is sold for 1.25, then the total revenue from hot dogs is given by 1.25d. In the same way, the total revenue from hamburgers is 1.50h. The total revenue from both hot dogs and hamburgers should be the sum of these, and since we are told the total revenue is 105.50, we can say 1.25d+1.5h=105.5.
We now have a system of two linear equations:
d+h=78
1.25d+1.5h=105.5
We can solve it using several methods, though I'm going to go with substitution. Use the first equation to solve for d:
d+h=78
→d=78−h
Now plug this in for d in the second equation:
1.25d+1.5h=105.5
→1.25(78−h)+1.5h=105.5
Solving for h, we have:
97.5−1.25h+1.5h=105.5
0.25h=8
h=8.25→h=32
Since h+d=78,
32+d=78→d=46
The concession stand therefore sold 46 hot dogs and 32 hamburgers.
From the given situation the cost of each hot dogs is $2 and the cost of each hamburgers is $3.
For the given situation we need to find a system of equations.
What are the system of equations?In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."
Let the cost of hot dogs be x and the cost of hamburgers be y.
At a football game, 84 hot dogs and 36 hamburgers were sold for $276 =
84x+36y=276
⇒ 21x+9y=69 ..........(1)
At another football game, 60 hotdogs and 18 hamburgers were sold for $174 = 60x+18y=174
⇒ 10x+3y=29 ..........(2)
Multiply equation (2) by 3, that is 30x+9y=87 ..........(3)
Subtract equation (3) and (1)
That is, 30x+9y-(21x+9y)=87-69
9x=18
⇒ x=2
Put x=2 in equation (1), we get 21(2)+9y=69
⇒ 42+9y=69
⇒ 9y=27
⇒ y=3
Therefore, from the given situation the cost of each hot dogs is $2 and the cost of each hamburgers is $3.
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List the solvent and solute(s) in the scenarios below.
A solution of 32% ethanol and 68% water
Answer:
no
Step-by-step explanation:
George set up a display of oval and round pots at his garden store.
He had 16 oval pots.
He had 3 times as many round pots as oval pots.
He found cracks in 4 of the pots, so he set them aside.
George put the rest of the pots in 6 rows, with the same number of pots in each row.
How many pots did George put in each row?
A. 7 pots
B. 8 pots
C. 10 pots
D. 12 pots
A box of 11 transistors has 4 defective ones.
A) If 2 transistors are drawn from the box together, what is the probability that both transistors are defective?
B) If 2 transistors are drawn from the box together, what is the probability that neither transistor is defective?
C) If 2 transistors are drawn from the box together, what is the probability that one transistor is defective?
Answer:
(a) 0.1325
(b) 0.4045
(c) 0.463
Step-by-step explanation:
Let X denote the number of defective transistors.
The proportion of defective transistors is, p = 4/11 = 0.364.
All the transistors are independent of the others.
The random variable X follows a binomial distribution.
(a)
Compute the probability that both transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=2)={2\choose 2}(0.364)^{2}(1-0.364)^{2-2}\\\\=1\times 0.132496\times 1\\\\=0.132496\\\\\approx 0.1325[/tex]
(b)
Compute the probability that neither transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=0)={2\choose 0}(0.364)^{0}(1-0.364)^{2-0}\\\\=1\times 1\times 0.404496\\\\=0.404496\\\\\approx 0.4045[/tex]
(c)
Compute the probability that one transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=1)={2\choose 1}(0.364)^{1}(1-0.364)^{2-1}\\\\=2\times 0.364\times 0.636\\\\=0.463008\\\\\approx 0.463[/tex]
Twice a number x minus 18
Step-by-step explanation:
Here is the answer...
Hope this helps you
Find the missing value.
Hint: Use the number line to find the missing value.
Helppp
Answer:
-2
Step-by-step explanation:
the multiplication of -×- will be + so if-×-will be plus then -7 after multiplying will be + so
_2+7=5
Answer is 12! Gl on what ur doing!
My first letter is in place and also in circus
My second's in rose but not in rise
My third's in command and also in plumber
My fourth's in point and also in spear
My fifth's in lane but not in lonely
My sixth's in Sunday and also in ring
My seventh's in cyclone and also in pastry
What am I?
Step-by-step explanation:
company
answer is company hope it helps
Answer: company
Step-by-step explanation:
In a class with 25 students, 17 have brown eyes. What is the ratio of students without brown eyes to students with brown eyes.
Answer:
8:17
Step-by-step explanation:
You have 4 quarts of brown stock.
You need 1 cups to make one serving of braised short ribs.
How many servings can you make?
F+G=K+7, K=7 prove: G=7
Step-by-step explanation:
K=7,
F+G=K+7
F+G=7+7
F=7, G=7 proved
PEOPLE SHOW ANSWERS PLEASE AND WILL GIVE BRAINLIEST 8. The ratio of cats to dogs at a pet show
is 1:3.
a) What percent of the pets at the
show are cats?
Find the values of x and y that satisfy the equation.
- 12x + yi = 60 - 13i
which is a characteristic of any function created by the product of two linear factors?
A. has an axis of symmetry
B. has a maximum
C. has two y intercepts
D. has two x intercepts
Answer:
the answer is d
Step-by-step explanation:
The characteristic of any function created by the product of two linear factors is; Choice D: has two x-intercepts.
According to the question;
We are required to determine which is a characteristic of any function created by the product of two linear factors.The product of two linear factors results in a quadratic function.
Since a quadratic function is a polynomial of degree two, 2.
In essence, the resulting function created by the product of two linear factors has two x-intercepts.
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Which is the better buy?
7-pound bag of barley for $6.72
312-ounce bag of barley for $28.08
Answer:
7-pound bag of barley for $6.72 is a better buy.
Step-by-step explanation:
7-pound bag of barley for $6.72
6.72 : 7 = 0.96
check your work: 0.96 x 7 = 6.72
so for the first offer you will be paying $0.96 per pound
312-ounce bag of barley for $28.08
1 pound = 16 ounces
312 ounces = 19.5 pounds
28.08 : 19.5 = 1.44
for the second offer you will be paying $1.44 per pound of barley. 7-pound bag of barley for $6.72 is a better buy because you will be less for each pound.
hope this helps!
Answer:
7-pound bag of barley for $6.72
Step-by-step explanation:
Evaulate and solve for the variable !
-2x + 3x - 5 = 6 - 21
Answer:
x = - 10
Step-by-step explanation:
Step 1:
- 2x + 3x - 5 = 6 - 21 Equation
Step 2:
x - 5 = - 15 Combine Like Term
Step 3:
x = - 15 + 5 Add
Answer:
x = - 10
Hope This Helps :)
Given the cost function
C
(
x
)
=
0.85
x
+
51
,
230
and the revenue function
R
(
x
)
=
1.94
x
, find the break-even point.
Answer:
2.r=1.94
1. c=0.85x+51/x
Step-by-step explanation: