Using concept of Linear equation in two variables, we got 23 is denomination count of 5$ bills and 21 is denomination count of 20$ bills.
Linear equations are used to solve equation in which two variables are connected with each other via some specific methods.
The linear equations in two variables are the equations in which each one of the two variables are of the highest exponent order of the 1 and have one, none, or may be infinitely many solutions. The standard form of a two-variable linear equation is given by ax + by + c = 0 where x and y are the two variables. The solutions can also be written in form of ordered pairs like (x, y).
It is given that 5$ bills are 2 more than 20$ bills,
so let suppose 20$ bills denomination count is x,
then 5$ bills denomination count=x+2;
It is also given that 535$ worth is summation of 5$ bills and 20$ bills
Therefore,[5×(x+2)+(20×x)]=535
On solving for x, we get x=21
Therfore,20$ bills denomination count is 21,and 5$ bills denomination count is 23.
Hence,5$ bills denomination count is 23 and 20$ bills denomination count is 21
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a recipe uses 1 aubergine for every 3 people. how many aubergines should you buy for 10 people
Answer:
3 1/3 I am assuming that you cannot by 1/3 of an aubergines, so you would need to buy 4. if you can buy a partial one then it would be 3 1/3
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] = [tex]\frac{a}{10}[/tex] Set up a proportion and then cross multiply and solve for a
3a = 10 Divide both sides by 3
a = [tex]\frac{10}{3}[/tex] = 3 1/3
For a set of five numbers,
the mode is 8
the median is 12
Work out one possible set of five numbers.
Step-by-step explanation:
mode = the number appearing the most often in the list of data.
median = the middle number. half of the other numbers are smaller, and the other half is larger.
so, we know one number already : 12 in the middle.
that gives us
_ _ 12 _ _
a good mode is when it has a real majority (e.g. every other number appears only once, but the mode number appears twice).
so, 8 should appear twice.
as 8 is smaller than 12, it can only be on the left side of 12.
that gives us
8 8 12 _ _
note we need 2 numbers larger than 12, but each appearing only once.
so, e.g.
8 8 12 13 14
Select all the equations that have the same solution as 2x-5=15
Answer:
B, D, E
Step-by-step explanation:
2x - 5 = 15
2x = 20
x = 10
B) 2x = 20
x = 10
D) 2x - 20 = 0
2x = 20
x = 10
E)4x - 10 = 30
4x = 40
x = 10
Please help, i really need help please
Answer:
m∠1 = 151°
m∠2 = 29°
m∠3 = 151°
Step-by-step explanation:
We can use knowledge of vertical angles and supplementary angles.
➜ Vertical angles are congruent
➜ Supplementary angles are equal to 180° when added together
Answer:
m∠1 = 151, m∠2 = 29, m∠3 = 151.
Step-by-step explanation:
We know m∠4 is equal to 29. We know m∠4 and m∠2 are equal because they are vertical angles. That means m∠2 is 29. Now, m∠4 and m∠3 equal 180, and m∠2 and m∠1 also equal 180. Since we know m∠4 is 29, you can do 29 + m∠3 = 180. You get m∠3 = 151. Now, m∠1 and m∠3 are also equal because they are vertical angles. That means m∠1 is equal to 151 as well. So your final answers are m∠1 = 151, m∠2 = 29, and m∠3 = 151.
How far up a wall will an 11-meter ladder reach, if the foot of the ladder is 4 meters away from the base of the wall?
A. 11 m
B. 4 m
C.
D.
Answer:
√105 meters, or about 10.25 meters
Step-by-step explanation:
[tex] {x}^{2} + {4}^{2} = {11}^{2} [/tex]
[tex] {x}^{2} + 16 = 121[/tex]
[tex] {x}^{2} = 105[/tex]
[tex]x = \sqrt{105} = 10.25[/tex]
Answer:
10.246 or sqrt(105)
Step-by-step explanation:
Given,
length of the ladder = 11 m
distance of the foot of the ladder from the base of the wall = 4 m
According to Pythagoras' theorem,
(hypotenuse)^2 = (side1)^2 + (side2)^2
As per the problem,
hypotenuse = 11m
side1 = distance from wall = 4 m
side2 = height reached by the ladder on the wall
that is, (11)^2 = (4)^2 + (side2)^2
121 = 16 + (side2)^2
121 - 16 = (side2)^2
(side2)^2 = 105
(side2) = sqrt(105) = 10.246 m
Hence, the ladder can reach up to 10.246 m height on the wall.
7 ft
9 ft
26 ft
What is the area?
The total area of the figure is 298.17 ft².
What is termed as the area of the figure?The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.Sketch a square on a paper piece with a pencil. It is a two-dimensional figure. The area of the shape just on paper is referred to as its Area.For the given question;
Let divide the given the figure in three parts;
RectangleTrianglesemi circleThe dimensions of the rectangle is;
Length = 26 - 9 = 15 ft
Breadth = 9 ft
Area = length x breadth
Area = 15 x 9
Area = 135 ft²
The dimension of the triangle is-
Base = 9 ft
Height = 15 - 7 = 8 cm
Area = (1/2) base x height
Area = (1/2) x 9 x 8
Area = 36 ft²
The dimension of semi circle is -
Radius = 9 ft
Area = πr²/2
Area = 3.14 x 9² / 2
Area = 127.17 ft²
Total area = rectangle +triangle + semicircle
Total area = 135 + 36 + 127.17
Total area = 298.17 ft²
Thus, the total area of the figure is 298.17 ft².
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An empty 16 gallon tank is being filled with gasoline at a rate of 2 gallons per minute. State the Domain and Range using interval notation or set notation
The volume of gasoline in the tank as a function of time can be determined as,
[tex]V=2t[/tex]The time taken to fill the tank can be determined as,
[tex]\begin{gathered} 16=2t \\ t=8 \end{gathered}[/tex]Thus, the requried domain is,
[tex]t\in\lbrack0,8\rbrack[/tex]The range of the function can be determined as,
[tex]V\in\lbrack0,16\rbrack[/tex]Thus, the above expressions gives the required domain and range of the function.
A square has approximately 300 square feet . The length of each side of the square is between which two whole numbers?
Area = 300 ft^2
Formula
Area = length of a side x length of a side
Substitution
300 = length of a side ^2
[tex]\sqrt{300}[/tex][tex]\sqrt{300}\text{ = 17.32}[/tex]The length of a side is between 17 and 18
Answer:
The length of the side of the square is approximately [tex]17.32[/tex] feet, which lies between the whole numbers [tex]17[/tex] and [tex]18[/tex].
Step-by-step explanation:
Step 1: Assume your variable
Since all the sides of a square are the same, let's consider the side to be the variable: [tex]x[/tex].
Step 2: Create an equation
The formula for the area of a square is:
[tex]\text{Area}=\text{Side}^{2}[/tex]
We have assumed the side to be [tex]x[/tex], and the area is said to be [tex]300[/tex], so substitute these values into the formula:
[tex]\text{Area}=\text{Side}^{2}\\300=x^{2}[/tex]
Step 3: Solve the equation
Using the formula for the area of a square, we came to find an equation:
[tex]x^{2}=300[/tex]
Now, let's find the value of [tex]x[/tex]:
[tex]x^{2}=300\\\\\text{Square root both sides of the equation:}\\\sqrt{x^{2}}=\sqrt{300}\\\\\text{Simplify:}\\x=\sqrt{300}\\\\\text{Calculate:}\\x\approx 17.32[/tex]
The length of the side of the square is approximately [tex]17.32[/tex] feet.
As we know, this number lies between [tex]17[/tex] and [tex]18[/tex].
You type 41 words per minute. How many minutes does it take you to type 615 words?
Given:
Type 41 words per min.
Find-:
How many min. take you to type 615 words
Explanation-:
1 min words type = 41
For 615 words,
41 words typed in 1 min.
For 1 words type it take min is:
[tex]1\text{ Words take time=}\frac{1}{41}\text{ min.}[/tex]For 615 words:
[tex]\begin{gathered} \text{ Time}=\frac{1}{41}\times615 \\ \\ =\frac{615}{41} \\ \\ =15 \end{gathered}[/tex]For type 615 words take time is 15 min.
Answer:
15 minutes.
Step-by-step explanation:
615 / 41
= 15
WHATS THE ANSWER PLSZ HELP
Answer:
a. 0.8 = 0.5 + 0.3
b. 30.9 = 2.7 + 28.2
c. 15.4 = 3.1 + 2.4 + 9.9
d. 17.4 = 15.2 + 1.4 + 0.8
e. 42.5 = 39.2 + 2.5 + 0.8
f. 8 = 4 + 4
g. 35 = 23 + 8 + 4
h. 84 = 53 + 3 + 28
i. 121 = 11 + 17 + 93
j. 35 = 24 + 8 + 3
3) A car can travel 442 miles on 26 gallons of gasoline. How much gasoline will it need to go 102 miles?
The car will need 6 gallons of gasoline to travel 102 miles
Explanation:Given that the car travels 442 miles on 26 gallons of gasoline.
Because the more the distance, the more the volume of gasoline used, this is a direct proportion.
So, we have:
[tex]\begin{gathered} V=\frac{102\times26}{442} \\ \\ =6 \end{gathered}[/tex]It will need 6 gallons.
Bob is planning to start an it business, servicing computers that are infected with viruses. to start his new enterprise, bob estimates that he will need to spend $5,000 on equipment $6,000 on premises, $4,000 on advertising. all of these costs are fixed. he is planning on charging his customers $250 each to fix an infected computer. for each computer that he fixes, he must spend $25 on parts and software. suppose we let x be the number of computers that bob fixes. if bob only fixes 50 computers, what is his total loss?
If Bob only fixes 50 computers, his total loss is $3,750.
What is the total loss?The total loss results from the negative difference between the total revenue and the total costs.
The total costs consist of variable and fixed costs.
The result is a loss when the total costs exceed the total revenue. This result becomes a profit or income when the total revenue exceeds the total costs.
Fixed Costs:Equipment = $5,000
Premises = $6,000
Advertising = $4,000
Total fixed costs = $15,000
Variable cost per unit = $25
Selling price per unit = $250
Total number of computers fixed = 50
The total variable cost for 50 units = $1,250 (50 x $25)
The total costs (fixed and variable) = $16,250
The sales revenue for 50 units = $12,500 (50 x $250)
Loss = $3,750 ($12,500 - $16,250)
Thus, Bob will incur a total loss of $3,750 if he fixes only 50 computers based on his fixed and variable costs.
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Jake has a 8 pounds of lunch meat to serve for a picnic lunch. He plans to serve each adult 2/3 of a pound. Part B: The price of lunch meat is $7.36 per pound. Which equation can be used to determine the total cost, c, for lunch meat that weighs a total p pounds? Then find the cost of the lunch meat. •p/7.36=c •p=7.36c, the cost is $1.09 •c=7.36p, the cost is $58.88 •p+7.36-c, the cost is $15.36
Part B
The most appropriate choice for linear equation will be given by -
Third option is correct
c = 7.36p is the required equation for total cost of p pounds of meat
The cost is $58.88
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Price of one pound of meat = $7.36
Cost of p pounds of meat = $7.36p
By the problem,
c = 7.36p
This is the required equation for total cost of p pounds of meat
Putting p = 8
c = [tex]7.36 \times 8\\[/tex]
c = $58.88
Third option is correct
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2The shape shown is made up of three similar right-angled triangles.22The smallest triangle has two sides of side-length 2, as shown.What is the area of the shape?1412 + 12V22824 + 20V56Erase
The triangles are similar. The smaller is isosceles, so the 3 of them are as well.
Let's Start by finding the hypotenuse of the smaller one:
a² = 2
Determine the relationship between lines a, b, and c line a y=5x -3 line b X + 5y=2 line c -10y - 2x =0
Among the given lines line a y = 5x - 3, line b x + 5y = 2, and line c -10y - 2x =0, lines a and line b are intersecting, lines a and c are intersecting whereas lines b and c are parallel to each other.
Write the given lines in standard form
Line a -5x + y = -3
Line b x + 5y = 2
Line c -2x - 10y = 0
a1 = -5, b1 = 1, c1 = -3
a2 = 1, b2 = 5, c2 = 2
a3 = -2, b3 = -10, c3 = 0
a1/a2 = -5/1
b1/b2 = 1/5
c1/c2 = -3/2
As we see that
a1/a2 ≠ b1/b2
Hence, lines a and b are intersecting.
a1/a3 = -5/-2
b1/b3 = 1/-10
As we see that
a1/a3 ≠ b1/b3
Hence, lines a and c are intersecting.
a2/a3 = 1/-2
b2/b3 = 5/-10 = 1/-2
c2/c3 = 2/0
As we see that
a2/a3 = b2/b3 ≠ c2/c3
Hence, lines b and c are parallel.
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D
E
F
The measure of angle D is 50°, the measure of angle E is 80°, and the
measure of angle F is 10 x. What is the value of x?
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Since angle D is 50, E is 80, we can add those two for now, 50+80=130, to make it 180, we can do 180-130 which gives us 50. So the value of x is 5. Sorry that its pretty confusing
a raised rectangular garden is two feet more than three times as long as it is wide. the depth of the pool is half the width. if the length is 11 feet, what is the volume?
Answer:
49.5ft³
Step-by-step explanation:
If it is 2 ft more than 3 times as long as it is wide then:
l = 3w + 2
which means:
w = (l-2)/3
and:
d = 1/2((l-2)/3)
Now just substitute in 11 for l
w = (11 - 2)/3
w = 9/3
w = 3
d = 1/2((11-2)/3)
d = 1/2(9/3)
d = 1/2(3)
d = 1.5
So the total volume is:
11 * 3 * 1.5
49.5
0.9(x+1.4)−2.3+0.1x=1.6
please help, I'm really not sure how to do this.
Answer:
x = 2.64
Step-by-step explanation:
Do the distributive property first.
0.9(x + 1.4)
0.9(x) + 0.9(1.4)
0.9x + 1.26 - 2.3 + 0.1x = 1.6
Simplify the left side by adding like terms. I'm going rewrite the equation and group the like terms together.
0.9x + 0.1x + 1.26 - 2.3 = 1.6
1x - 1.04 = 1.6
1x is the same as x, so I am going to remove the 1. Solve for x.
x - 1.04 + 1.04 = 1.6 +1.04
x = 2.64
Write the equation of the line that passes through the points (3,1)(3,1) and (-7,-1)(−7,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
[tex]\textsf{Point-slope form}: \quad y-1=\dfrac{1}{5}(x-3)[/tex]
Step-by-step explanation:
Define the given points:
(x₁, y₁) = (3, 1)(x₂, y₂) = (-7, -1)Substitute the defined points into the slope formula to find the slope of the line:
[tex]\implies \textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{-7-3}-\dfrac{-2}{-10}=\dfrac{1}{5}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=\dfrac{1}{5}(x-3)[/tex]
Simplify to slope-intercept form, if necessary:
[tex]\implies y-1=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]
[tex]\implies y=\dfrac{1}{5}x+\dfrac{2}{5}[/tex]
-6+ (-3) how to find answer?
Answer:
-9
Step-by-step explanation:
−6 − 3
= −6 + −3
= -9
Answer:
-9!
Step-by-step explanation:
When you add negatives, it becomes more negative. Think of -6 getting 3 smaller.
The ratios in an equivalent ratio and 3:12 , 4:16 and 5:20 if frost number is 10 what is the second number ?
Mr. Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long. If each DVD is 11⁄20 inches wide, how many DVDs can he put side-by-side on the shelf?
DVDs
The number of DVDs that he can put side-by-side on the shelf is 19.
How to calculate the value?From the information, Mr Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long and each DVD is 11⁄20 inches wide.
The number of DVDs that can be put will be the division of the numbers that are given. This will be:
= Length of shelf / Width of each DVD
= 10 2/3 ÷ 11/20
= 32/3 ÷ 11/20
= 32/3 × 20/11
= 640 / 33
= 19 13/33
= 19 approximately
He can put 19 DVD.
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Which of the following describes the graph of y 3 -3 in a coordinate plane?
ANSWER
The boundary line is a solid horizontal line that passes through (0, -3). The half-plane that does not contan the origin is shaded.
(the answer is the second option)
EXPLANATION
The graph is
the life of light bulbs is distributed normally. the variance of the lifetime is 225225 and the mean lifetime of a bulb is 520520 hours. find the probability of a bulb lasting for at most 533533 hours. round your answer to four decimal places.
The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225. The probability that a light bulb will survive at most 533 hours is 0.86.
Given that,
The lifespan of light bulbs is generally distributed. The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225.
We have to calculate the probability that a light bulb will survive at most 533 hours.
We would use the normal distribution formula, which is stated as, because the lifespan of light bulbs is distributed regularly,
z = (x - µ)/σ
Where
x = life of light bulbs.
µ = mean lifetime
σ = standard deviation
From the information given,
µ = 520 hours
Variance = 225
σ = √variance = √225
σ = 15
The probability that a light bulb will last for no more than 560 hours is given by
P(x ≤ 533)
For x = 533
z = (533 - 520)/15 = 0.86
According to the normal distribution table, 0.86 represents the probability for the z score.
Therefore, the probability that a light bulb will survive at most 533 hours is 0.86.
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Which of the following represents the dimensions of the room
Given:
The length of the rectangular room is 6 more than the width.
The area of the room, A = 27 square units.
Required:
We need to find the dimensions of the given rectangular room.
Explanation:
Let w be the width of the rectangle.
6 more than means add 6.
The length of the rectangle, l= w+6.
Consider the area of the rectangle formula.
[tex]A=lw[/tex]Substitute A = 27, and l=w+6 in the formula.
[tex]27=(w+6)w[/tex][tex]27=w^2+6w[/tex]Subtract 27 from both sides of the equation.
[tex]27-27=w^2+6w-27[/tex][tex]0=w^2+6w-27[/tex][tex]w^2+6w-27=0[/tex][tex]Use\text{ }6w=9w-3w.[/tex][tex]w^2+9w-3w-27=0[/tex]Take out the common multiple.
[tex]w(w+9)-3(w+9)=0[/tex][tex](w+9)(w-3)=0[/tex][tex](w+9)=0,(w-3)=0[/tex][tex]w=-9,3[/tex]The measure is always positive.
[tex]w=3\text{ units,}[/tex]Substitute w =3 in the equation l =w+6.
[tex]l=3+6=9\text{ units.}[/tex]We get l =9 units and w =3 units.
Final answer:
The dimensions of the room are 3 and 9.
Bethany is building a storage trunk. 5ft long, 4ft height and 2ft wide. how much wood is needed to make the trunk
Answer:
76 square feet of wood.
Explanation:
Bethany is building a storage trunk with the following dimensions:
• Length = 5 ft.
,• Height = 4 ft.
,• Width = 2 ft.
We are to determine how much wood is needed to make the trunk.
The amount of wood that will be needed to make the truck is the surface area of the trunk. The storage trunk is in the shape of a rectangular prism.
The surface area of a rectangular prism is found using the formula below:
[tex]\text{Surface Area=2(LW+LH+WH)}[/tex]Substitute the given dimensions:
[tex]\begin{gathered} \text{Surface Area}=2(5\times2+5\times4+2\times4) \\ =2(10+20+8) \\ =2\times38 \\ =76\; ft^2 \end{gathered}[/tex]Bethany needs 76 square feet of wood to make the trunk.
At a high school, students can choose between three art electives, four history electives, and five computer electives.
Fach student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
O
7C2
1202
С
.?
122
O (G) 4401)
12Cz
12P2
Mark this and return
Save and Exit
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Expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.
As given in the question,
Number of art electives students = 3
Number of history electives students = 4
Number of computer electives students = 5
Choosing an art electives students = ³C₁
Choosing an history electives students = ⁴C₁
Expression represents the probability that a student chooses an art elective and a history elective
= (³C₁⁴C₁) / ¹²C₂
Therefore, expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.
The complete question is:
At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
a. ⁷C₂ / ¹²C₂
b. ⁷P₂ / ¹²P₂
c. (³C₁⁴C₁) / ¹²C₂
d. (³P₁⁴P₁) / ¹²P₂
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
The answer is 75 degrees
Step-by-step explanation:
Remember that the sum of the three angles of any triangle is 180 degrees.
So, 180=58+47+x
180=105+x
75=x
A tree initially measured 18 feet tall. Over the next 3½ years, it grew to a final height of 35½ feet. During those 3½ years, what was the average yearly growth rate of the height of the tree?
Answer:
The average yearly growth o
Explanation:
Given that the tree grew from 18 ft 35 1/2 feet in 3 1/2 years.
The growth within these years is:
35 1/2 - 18
= 35.5 - 18
= 17.5
Now, this averages:
17.5/3.5 (3.5 is the number of years)
= 5
The average is 5 ft per year
Solve 2x + 32 + x = 17.
x = 5
x = 0.2
x = −0.2
x = −5
Please and thank you.
2x+32+x = 17
Combine 2x and X to get 3x.
3x+32 = 17
Subtract 32 on both sides.
3x = 17−32
Remains 32 of 17 to obtain −15.
3x = −15
Divide both sides by 3.
x = -15/3
Divide −15 by 3 to get −5.
x = −5
The last option is correct.The value of x after solving the given equation 2x + 32 + x = 17, is x = -5, which is the last option.
Given an equation:
2x + 32 + x = 17
It is required to find the value of x after solving or simplifying the equation.
In order to get the value of x, the equation has to be solved in such a way that the terms with the variable have to be placed on one side and the constant terms on the other side.
Consider:
2x + 32 + x = 17
Add x and 2x since they are like terms in variables.
3x + 32 = 17
Subtract 32 from both sides of the equation.
3x = 17 - 32
3x = -15
Divide both sides of the equation by 3.
x = -5
Hence, the value of x is -5.
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