A linear equation that represents the total cost in dollars of the oil change is Y = 25X + 40
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Linear Equations in Standard Form
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.
Given :
Cost of the oil (calculated once) = $40
Cost of labour (calculated per hour) = $25
Thus , a linear equation that represents the total cost in dollars of the oil change if it requires x hours of labor can be expressed as Y = 25X + 40 where X represents no . of working hours of labour and Y represents total cost .
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A recipe recommends cooking a roast between 35 and 45 minutes per pound. Which of the following cooking times for a 10-pound roast follows the recommendation?
Answer:
If one of the answers is 5 hours and 50 minutes, that. If its 7 hours and 30 minutes, that. In between is 6 hours and 40 minutes.
Step-by-step explanation:
You have a student who says the sum of 3/4 and 5/6 is 4/5. Do you agree with them? Explain and solve this problem. Draw a model and explain how to solve this problem. Explain why we need common denominators.
The sum of 3/4 and 4/5 is 31/20 and To divide the common denominators by the individual denominators without using fractions or decimals, we need common denominators or the LCM of the two denominators.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, are two fractions 3/4 and 4.5 and their sum is,
= 3/4 + 4/5.
= (15 + 16)/20.
= 31/20.
So, the answer of the student is wrong.
We need common denominators or LCM of the two denominators so that we can divide the common denominators by the individual denominators without having fractions or decimals.
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A list of brownies for chocolate brownies given at the right will make 16 brownies. Use the list to decide how much each ingredient needed to make 20 brownies, one cup butter, 6 ounces unsweetened chocolate, 2 cup sugar, 1/2 teaspoon vanilla, four eggs half cup flour.
The ingredients for 4 brownies would be: 1/2 cup butter, 15/4 ounces unsweetened chocolate, 9/8 cup sugar, 3 teaspoons vanilla, 3 eggs, and 3/4 cup flour.
What exactly is a proportion?A percentage is a component of a total amount, and the measures are related by the rule of three.
Keep in mind that in a particular ratio, such as: a/b=c/d a*d=b*c
Create the following ratio for each ingredient:1/8 cup butter, 5/8 ounces of unsweetened chocolate, 1/4 cup sugar, 1/8 teaspoon vanilla, 1/2 egg, and 3/16 cup flour.
Explanation:
Given that the original recipe calls for 16 brownies;
Butter:
(1/8)/16=b/12
(2/3)(12)=16b
8=16b
b=1/2
Chocolate:
5/16=c/12
60=16c
c=60/16
c=15/4
Sugar: (3/2)/16=s/12
(3/2)(12)=16s
18=16s
s=18/16
s=9/8
Vanilla: 2/16=v/12
24=16v
v=3/2
Eggs: 2/16=e/12
e=3/2
Flour:1/16=f/12
f=3/4
As a result, the following would be the components for four brownies,
3/4 cups flour, 1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, and 3/2 eggs.
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Use the given conditions to find the values of all six trigonometric functions. (If an answer is undefined, enter UNDEFINED.) sec(x) = − 9/5, tan(x) < 0sin(x)=cos(x)=tan(x)=csc(x)=sec(x)=ot(x)=
The given conditions to find the values of all six trigonometric functions is cos (x) =-5/9, sin (x) = 2 root(14)/9, tan(x)= - 2 root(14)/5 and cot(x)= - 5 (2 root 14), csc(x)= 9 /2root (14).
What is trigonometric functions ?
Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the angles and sides of a triangle.
[tex]$\sec (x)=-\frac{9}{5} < 0$[/tex]and [tex]$\tan (x) < 0$[/tex]
so, x is in the second quadrant.
So, [tex]$\cot (x), \cos (x)$[/tex]are negative and [tex]$\sin (x), \csc (x)$[/tex] are positive.
Hence,
[tex]$$\begin{aligned}\cos (x) & =\frac{1}{\sec (x)}=-\frac{5}{9} \\\sin (x) & =\sqrt{1-\cos ^2(x)}=\sqrt{1-\frac{25}{81}}=\frac{2 \sqrt{14}}{9} \\\tan (x) & =\frac{\sin (x)}{\cos (x)} \\& =-\frac{2 \sqrt{14}}{5} \\\cot (x) & =\frac{1}{\tan (x)}=-\frac{5}{2 \sqrt{14}} \\\csc (x) & =\frac{1}{\sin (x)}=\frac{9}{2 \sqrt{14}}\end{aligned}$$[/tex]
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Ethan and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.30. He bought a total of 14 apples and bananas altogether. Determine the number of apples, x,x, and the number of bananas, y,y, that Ethan bought.
The number of apples x will be 10 and the number of bananas y will be 4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Ethan and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.30. He bought a total of 14 apples and bananas altogether.
The number of apples and bananas will be calculated as,
0.75x +0.30y = 6
x + y = 14 or x = 14 - y
0.75(14-y) = 0.30y = 6
10.5-0.75y + 0.30y = 6
y = 10
x = 14 - y
x = 14 - 10 = 4
Therefore, the number of apples x will be 10 and the number of bananas y will be 4.
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A cone has a radius of 4 cm and a height of 12 cm. What is the volume of the cone, to the nearest whole centimeter?
Volume = 201 cm
Step-by-step explanation:How do I find the volume of a cone?Here is an equation to help you find the volume of a cone:
V=πr²[tex]\frac{h}{3}[/tex]=π·4²·[tex]\frac{12}{3}[/tex] ≈ 201.06193cm³
This equation is what I used to solve your question. The answer is 201.06193, but is says round to the nearest whole number, so the answer is actually 201 cm.
In the equation:
V means Volume
π means Pi (3.14)
r² means radius squared
[tex]\frac{h}{3}[/tex] means height divided by 3
4² means 4 · 4
[tex]\frac{12}3}[/tex] means 12 ÷ 3
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
5. Can a triangle be drawn with side lengths of 7.3 meters, 4.6 meters, and 11 meters? Explain.
Yes, a triangle can be drawn with side lengths of 7.3 meters, 4.6 meters, and 11 meters this is in the case whereby the lengths of any two sides combined is longer than the length of the 3rd side.
What is triangle inequality?Triangle inequality, in Euclidean geometry, theorem can be described as the theorem that states that the sum of any two sides of a triangle is greater than or equal to the third side.
This can be represented using the symbols, {a + b ≥ c.} and this can be explained that the the shortest distance between two points is a straight line.
Then cherck this illustration to confirm that we are right:
7.3 + 4.6 > 11
7.3 + 11 > 4.6
4.6 + 11 > 7.3
Hence from this we can see that triangle can be drawn
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trying to find the arc length of the arc for the polar curve r=8cosθ between 0 and π4
Answer:
Step-by-step explanation:
To find the arc length of the polar curve r = 8cosθ between 0 and π/4, we can use the formula for arc length:
L = ∫a^b √(r^2 + (dr/dθ)^2) dθ
Substituting in the values for r and dθ, we get:
L = ∫0^(π/4) √(8^2cos^2θ + (-8sinθ)^2) dθ
= ∫0^(π/4) √(64cos^2θ + 64sin^2θ) dθ
= ∫0^(π/4) √(64) dθ
= ∫0^(π/4) 8 dθ
= 8(π/4 - 0)
= 8π/4
= 2π
Therefore, the arc length of the polar curve r = 8cosθ between 0 and π/4 is 2π.
El perímetro de un jardín rectangular es 376 m.
Si la longitud del jardín es 99 m, ¿cuál es su anchura?
Answer:
89 m
Step-by-step explanation:
p/2 = 376/2 = 188 m
l + a = 188
a = 188 - l
a = 188 - 99
a = 89 m
Difference between 246 and 31 tripled
The difference between 246 and 31 tripled is
246 - 31³ = -29545How to calculate the difference between 246 and 31 tripledThe problem is solved using subtraction
the term difference is similar to subtraction in mathematics
Then tripling is raise to power 3 or exponents of 3, hence after subtraction then exponents is applied to the end result of subtraction to give the answer
The subtraction
= 246 - 31
= 215
The exponents
= 215³
= 215 * 215 * 215
= 9938375
'
On the second thought, we have a different answer in this case
= 246 - 31³
= 346 - 31 * 31 * 31
= -29545
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The difference between two same side interior angles of two paralell lines is 35 degrees. Find the measures of the two angles.
Weight of an empty carton is 8.350 kg. Apples weighing 21.475 kg are packed into it. Find the total weight of the carton
The total weight of the carton after packing the apples is 29.825 kg.
Step-by-step explanation:1. Write the individual weights.Empty carton: 8.350 kg
Apples: 21.475 kg
2. Do an addition.Since we are placing the apples inside the empty carton, now the carton will also contain the weight of the apples, additional to its own weight.
8.350 kg + 21.475 kg= 29.825 kg.
3. Express the result.The total weight of the carton after packing the apples is 29.825 kg.
A single card is drawn from a standard 52 card deck fund the conditional probability that the card is a spade given that it is a 10
When the card is a jack, there is a 0.25 probability that you will receive a spade.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability.
The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application. Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our question-
P(Spade) = 13/52 = 1/4 P(Jack) = 4/52
= 1/13 P(Spade and Jack)
= (1/4)(1/13) = 1/52 P(Spade/Jack)
= P(Spade and Jack)/P(Jack)
= (1/52)/(1/13) = (1/52)(13/1)
= 13/52 = 1/4 = 0.25
Hence, When the card is a jack, there is a 0.25 probability that you will receive a spade.
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Complete question-
A single card is drawn from a standard 52- card deck. Find the conditional probability that the card is a spade, given that it is a jack.?
Kennedy High School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent. Here are the positions and the people interested in each.
Based on this list, how many ways are there to fill the four committee positions?
There are 160 ways to fill the four committee positions.
What is Combination?
The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words means "Selection of things," where the order of the items is irrelevant.Faculty members can be selected in A = 2 ways
Male student can be selected in B= 4 ways
Female student can be selected in C = 4 ways
One parent can be selected in D = 5 ways.
Total number of ways to select committee of four = A*B*C*D
= 2* 4 * 4 * 5
= 160 Ways
Hence, there are 160 ways to fill the four committee positions.
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Alexa has $900 in a savings account that earns 2% annually. The interest is not compounded. How much will she have in total in 5 years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
Alex will have a total of $990 in 5 years.
Step-by-step explanation:
Using the formula [tex]i=prt[/tex] we get [tex]i=900[/tex] × [tex]0.2[/tex] × [tex]5[/tex] which equals 90
[tex]900 + 90 = 990[/tex]
Graph the line with the equation y = -x - 2.
The required graph is as follows.
What is graph of an equation in x and y?The graph of an equation in x and y is the value of y for the
corresponding value of x.
Given,
y = -x - 2
or x + y = -2
The line cuts x axis when y = 0 and cuts y axis when x = 0.
Therefore, the line cuts x axis at x = -2
the line cuts y axis at y = -2
Hence, required graph is:
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An animal shelter has 8 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the animal shelter?
Answer:
25
Step-by-step explanation:
32/100=8/x
cross multiply
32x=100(8)
32x=800
/32. /32
x=25
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What is the value of x?
Use the provided picture
Draw a model for 1.8 divided by 0.6
Answer: 1.8 divided by 0.6 is 3
The equation of the model for 1.8 is divided by 0.6 will be E = 1.8 / 0.6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the number 1.8 is divided by the number 0.6. The mathematical model for the division can be written as:-
E = 1.8 / 0.6
Hence, the equation of the model for 1.8 is divided by 0.6 will be E = 1.8 / 0.6.
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You decide to contribute to a mutual fund that averages 3.7% return per year. If you contribute $575 quarterly.
Round all answers to the nearest cent as needed.
a) How much will be in the account after 10 years? $
b) How much of this money did you deposit? $
c) How much of this money is interest earned? $
a) After 10 years, the amount (future value) in the mutual fund will be $27,679.22.
b) The total amount deposited in the mutual fund is $23,000.
c) The amount of interest earned on the quarterly deposits is $4,679.22.
What is the future value?The future value is the compounded present value of periodic deposits.
The future value is compounded at an interest rate per period.
We can compute the future value using an online finance calculator, which also shows the total deposits and interest earned.
N (# of periods) = 40 quarters (10 years x 4)
I/Y (Interest per year) = 3.7%
PV (Present Value) = $0
PMT (Periodic Payment) = $575
Results:
Future Value (FV) = $27,679.22
Sum of all periodic payments = $23,000 ($575 x 40 quarters)
Total Interest = $4,679.22
Thus, making a quarterly deposit of $575 for 10 years at 3.7% APR will yield a future value of $27,679.22.
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If an object is dropped from a height of 85 feet, the function h(t) = -16t2 +85 gives the height
of the object after t seconds. Approximately, when will the object hit the ground?
Answer:
Step-by-step explanation: h(t)=-16t2+85
Let h(t)=0 to find when the object will hit the ground
0=-16t2+85
Solve for t=?
We need to get t term on its own
Take 85 from both sides
0-85=-16t2+85-85
-85=-16t2
To get t term on its own
Divide both sides by -16
-85/-16=-16t2/-16
5.3=t2
We have to solve for t squared that means we must take the square root of both sides
the square root of 5.3=gives + or - 2.3 seconds we can't have negative time so discard -2.3 seconds
can someone help me quick? don’t just put the answer, explain it please
Step-by-step explanation:
Riders must be at least 48 inches. "At least" means greater than or equal to. Therefore, the inequality is:
h ≥ 48
To graph this, we draw a solid dot at the 48 mark (because it can equal 48) and an arrow to the right (because it can be greater than 48).
A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.
The quadratic function
h(t) = 16t+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown. What is the maximum height of the ball? (Write the answer to the nearest hundredth)
After solving, the maximum height of the ball is 90.25 feet.
In the given question,
A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.
The quadratic function
h(t) = -16t^2+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown.
We have to find the maximum height of the ball.
Height is given that;
h(t) = -16t^2+52t + 48
Now comparing the given equation by the standard equation ax^2+bx+c=0
Here b = 52, a = -16
For maximum height put t= -b/2a
t = -52/2(-16)
t = 52/32
t = 1.625
Maximum height
h(1.625) = -16(1.625)^2+52(1.625) + 48
h(1.625) = -42.25+ 84.5 + 48
h(1.625) = 90.25 feet
The maximum height of the ball is 90.25 feet.
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Drag and drop the range of each data set into the boxes.
Answer:
Data set 1: 20
Data set 2: 25
Step-by-step explanation:
Range is where you take the lowest value and subtract it from the highest value. So with data set 1, the highest number is 40 and the lowest is 20.cSo 40-20=20. Answer 20. Then with data set number 2, the highest number is 60 and the lowest is 35. So 60-35=25. Answer 25.
I hope this helps!!!
y = 3x +2
y = 3x - 3
These lines are...
Answer:
Step-by-step explanation:
Work out the area of this triangle.
8 cm
11 cm
13 cm
Answer:
44
Step-by-step explanation:
BxH/2=Area
8x11=88
88/2=44
area=44
Credit card disclosure: "Your due date is at least 25 days after the end of the billing cycle. We will not
charge you interest on new purchases provided that you have paid your previous balance in full by the due
date each month." Identify the true statement.
The 25 days after the end of the billing cycle is referred to as the grace period
If you pay your previous balance in full after the due date, the credit card company will not charge you
interest
days is an exceptionally long period without paying a credit card bill
If you make the minimum payment on your card within the 25 day period, the credit card company will
not charge you interest
If you make the minimum payment on your card within the 25-day period, the credit card company will not charge you interest. Option D is correct.
What is the investment?Investment is defined as when an individual spends money on something that returns him or her higher money than the money they or invest.
Here,
According to the statment, "Your due date is at least 25 days after the end of the billing cycle. We will not charge you interest on new purchases provided that you have paid your previous balance in full by the due date each month"
Since al the option are wrong except option D
Option D is true. because the statement mentioned the same statement as mentioned in the given statment.
Thus, Option D is correct.
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how do you say hi in spanish
Answer:
hola
Step-by-step explanation:
Answer: You say Hola
Step-by-step explanation:
Which sounds like (Ohw·laa) = This means Hi or Hello
Calculate the volume of water that runs off the Shoppes at Fremont parking lot after a 5 cm rainfall event. Assume that all water that falls on the parking lot runs off.[200m x 100m = 20,000m2[5cm x 1m/ 100cm = 0.05m]20,000m2 x 0.05m = 1000m3
The volume of water that runs off the Shoppes at Fremont parking lot after a 5 cm rainfall event is [tex]1000m^{3}[/tex].
Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.
Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.
Basically, the volume of a liquid is measured in liters, where 1 liter is equal to 1000 cubic centimeters.
1 liter = 1000 cubic centimeters = 0.001 cubic meters
Hence,
1 cubic meters = 1000 liters
Given,
[200m x 100m = [tex]20000m^{2}[/tex]]
[5cm x 1m/ 100cm = 0.05m]
20,000m2 x 0.05m = [tex]1000m^{3}[/tex]
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If cos(θ)=-1/4 and θ is in the 3rd quadrant, find the exact value for
sin(θ).