The number of counters Rick has is equal to 12 counters.
The number of counters Tony has is equal to 1:1.5.
The value of p is 1.5.
In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let R represent the number of counters Rick has.
Let S represent the number of counters Selma has.
Let O represent the number of counters Tony has.
Let T represent total number of counters.
Translating the word problem into an algebraic equation, we have;
S = 2R .....equation 1.
O = 2R - 6 ......equation 2.
T = R + S + O ......equation 3.
Substituting equation 1 and equation 2 into equation 3, we have:
T = R + S + O
54 = R + 2R + 2R - 6
54 = 5R - 6
5R = 54 + 6
5R = 60
R = 60/5
R = 12 counters.
For Tony, the number of counters is given by:
O = 2R - 6
O = 2(12) - 6
O = 24 - 6
O = 18 counters.
In ratio form, we have:
O = 1:P
O = 1:(18/12)
O = 1:1.5
The number of counters Rick has is equal to 12 counters.
The number of counters Tony has is equal to 1:1.5.
The value of p is 1.5.
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Find an equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.
The equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16x - 8y + 8z = 32
We know that the equation of plane passing through point (x₁, y₁, z₁) is given by,
A(x - x₁) + B(y - y₁) + C(z - z₁) = 0
where, A, B, and C are direction ratios
In the question, the plane passes through point (0, -3,1)
Let (x₁, y₁, z₁) = (0, -3,1)
Using above formula the equation of the plane will be in the form,
A(x -0) + B(y - (-3))+C(z - 1) = 0
Ax + B(y + 3)+C(z - 1) = 0 ..........(1)
The required plane is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.
So, their normal to the required plane would be perpendicular to the normal of both the planes.
The normal to the required plane is a cross-product of the normals of planes.
A cross-product of the normals of planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16i - 8j + 8k
So, the direction ratios,
A = 16, B = -8, C = 8
So equation (1) becomes,
16x - 8(y + 3) + 8(z - 1) = 0
16x - 8y - 24 + 8z - 8 = 0
16x - 8y + 8z - 32 = 0 is the required equation of the plane
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Francesca had 32 cups of flour. She used 2/8 of the flour for a recipe. How much flour did Francesca use? Write an equation to model your work.
Answer:
8 cups of flour
Step-by-step explanation:
If you want an equation it will be:
[tex]\frac{2}{8} * \frac{32}{1} = \frac{64}{8} = 8[/tex]
So Francessa used 8 cups of flour
i need to verify that this is true. (1-sinx)(1+cscx)=cscx-sinx
We can conclude that (1-sinx)(1+cscx)=cscx-sinx is a true equation.
What is equation?An equation is a mathematical expression containing symbols, constants, and/or numbers that combine to create an equation that states the equality of two mathematical expressions. Equations are used to describe relationships between different quantities and can be used to model real-world phenomena. Equations can also be used to solve problems and make predictions about a system.
To verify that this equation is true, we can use algebraic manipulation. First, we need to expand the left side of the equation. We can do this by multiplying (1-sinx) by (1+cscx). This gives us the equation (1-sinx)(1+cscx) = 1+cscx-sinx-sinxcscx.
Next, we need to simplify the right side of the equation. We can do this by combining the two terms with a minus sign. This gives us cscx-sinx.
Finally, we can compare the two equations. We see that both equations are equal, so the original equation is true.
Therefore, we can conclude that (1-sinx)(1+cscx)=cscx-sinx is a true equation.
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a) The average of daily income of a plumber from Sunday to Friday is Rs 1,300 in the last week. If he earned Rs 2,000 on Saturday, find his average of daily income of the week.
Answer: To find the average of daily income of the week, we need to find the total income of the week and divide it by the number of days in the week.
We know that the average daily income of the week is Rs 1,300 and we know that he earned Rs 2,000 on Saturday. To find the total income for the week, we can add the Saturday income to the average daily income for the 6 days.
Therefore, the total income for the week = Rs 1,300 (average daily income) x 6 (days) + Rs 2,000 (Saturday income) = Rs 7,800 + Rs 2,000 = Rs 9,800
To find the average daily income for the week, we divide the total income by the number of days in the week (7)
Average daily income = Rs 9,800 / 7 = Rs 1,400
Therefore, the average daily income of the plumber for the week is Rs 1,400.
Step-by-step explanation:
The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas.
a. If the car has gone 140 miles, how much gas was used? Show your thinking.
b. Write an equation that represents the inverse function: the gallons of gas as a function of distance in miles
a)
g = m / 40
g = 140 /40
g = 3.5
b)
m = 40g
m / 40 = g
A wheel 2. 0 m in diameter lies in the vertical plane and rotates about its central axis with a constant angular acceleration of 4 rad^-2 The wheel starts from rest at t=0 and the radius vector of a point A on the wheel makes an angle of 60º with the horizontal at this instant. Calculate the angular speed of the wheel, the angular position of the point A and the total acceleration at t=2s
The angular speed is 8 rad/s and the angular position of point A will be 8m/s².
The angular speed of the wheel at t=2s can be calculated using the equation ω=αt, where ω is the angular speed, α is the angular acceleration and t is the time. Substituting the given values, we get ω = 4 (2) = 8 rad/s.
The angular position of point A at t=2s can be calculated using the equation
θ = ωt + (1/2)αt².
Substituting the given values, we get
θ = 8 (2) + (1/2) (4) (2²) = 24 rad.
The total acceleration of point A at t=2s can be calculated using the equation a = rα, where a is the total acceleration, r is the radius of the wheel and α is the angular acceleration. Substituting the given values, we get a = 2 (4) = 8 m/s²
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A transformation is applied to a figure to create a new figure. Which transformation does not preserve congruence?
The transformation that does not preserve congruence is translation
The term called transformation is defined as the process of changing the position of an object on an xy-plane.
Here we have know that the transformation is applied to a figure to create a new figure.
And here we also know that the only transformation that does not preserve congruence is a translation 7 units down
So the transformation of figure and the reflection preserve the congruence since it only create a mirror image of the figure.
And the term called dilation also preserve congruence since it only enlarges the given figure.
Here we want to know that concept of translation a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
Based on this definition we have conclude that the solution is translation.
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Which line is parallel to the line y=12x+5
What is square root 25x²y^2/square root xy in simplest form? Assume X>o and y>0.
Is figure B a scale factor of figure A What is x
Answer:
Step-by-step explanation:
Step 1:
Make a proportion:
10/5 = 22/x
Step 2:
Cross multiply:
10x=22*5
10x=110
Step 3:
Divide by 10 to isolate x:
x=11
you have invited 86 people to a meeting. of those people, 12 from the north cannot attend, 4 from the south cannot attend, 6 from the east cannot attend, and 12 from the west cannot attend. how many people should you expect to attend the meeting?
An initial investment is $9565. It grows at a rate of 4% a year. Interest is compounded yearly. What is the value after 10 years? Round your answer to the nearest penny.
The future value of the investment after 10 years is $14,158.54.
What is the future value?The future value refers to the value of an investment whose present value is compounded at an interest rate into the future.
We can compute the future value using an online finance calculator as below.
N (# of periods) = 10 years
I/Y (Interest per year) = 4%
PV (Present Value) = $9,565
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $14,158.54
Total Interest = $4,593.54
Thus, in 10 years, the initial investment of $9,565 at 4% a year will grow to $14,158.54.
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5
Ty earns $14 an hour working on weekdays and
$21 an hour working on weekends. If he wants to
make at least $600 by working a total of 36 hours
in a week, to the nearest hour, at least how many
hours does he need work on the weekends?
a
Ty works 22 hours in weekdays and 14 hours in weekends to earn at least $600 by working a total of 36 hours in a week.
In the question, we have to find how many hours he need work on the weekends.
Let he work x hours on weekdays.
Let he work y hours on weekends.
He works total 36 hours. So the required question is:
x + y = 36..................(1)
Ty earns $14 an hour working on weekdays. If he works x hours, then he earns total 14x.
Ty earns $21 an hour working on weekends. If he works y hours, then he earns total 21x.
He earns total $600.
So the required equation is:
14x + 21y = 600..................(2)
Multiply equation 1 by 21 and subtract by equation 2
21x + 21y - (14x + 21y) = 756 - 600
Simplify
7x = 156
Divide by 7 on both side, we get
x = 22.29
x = 22
Now put the value of x in equation 1, we get
22 + y = 36
Subtract 22 on both side, we get
y = 14
Hence, he works 22 hours in weekdays and 14 hours in weekends.
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Use benchmarks to estimate 11.47 + 9.02
Step-by-step explanation:
11.47 + 9.02
= 20.49 ...
[its takes so much time to solve and write here so plzzz =》]
MARK ME AS BRAINLIEST ...Given the graph below, which of the following statements is true?
○The graph represents a one-to-one function because every x-value is paired with only one y-value.
○The graph represents a one-to-one function because it is defined for all x-values.
○The graph does not represent a one-to-one function because it does not pass through the origin.
○The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
The answer is The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
What is the one-to-one function?
The one-to-one function is a special function that maps every element of the range to exactly one element of its domain i.e, the outputs never repeat. As an example, the function g(x) = x - 4 is a one-to-one function since it produces a different answer for every input.
To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.
To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.
Of course, it passes the vertical line test, so it's a function.
Does it pass the horizontal line test? NO! As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places.
We, therefore eliminate choices A and B.
We can eliminate choice C because nowhere is it requires a function to pass through the origin for it to be one-to-one.
Hence, the answer is The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
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Answer:
D for Edge
Step-by-step explanation:
y
PLEASEEEEEEEEEE HELPPPP
The expression for the cost of gasoline and oil will be C. 3.35c + 2.65g
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case, it should be noted that Joe bought g gallons of gasoline and c cans ofg oil. The prices were givn as well.
The expression for the cost of gasoline and oil will be:
= 3.35 × c + (2.65 × g)
= 3.35c + 2.65g
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hEEEELLLLLPPPPPP
Select all of the terms that apply to the shape.
hexagon
convex
irregular polygon
octagon
decagon
concave
heptagon
pentagon
regular polygon
nonagon
the shape is a arow pointing up and downn
Pentagon, irregular polygon and convex polygon are the names that apply to the given form.
What is a polygon?A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
A pentagon is a polygon with five sides, and if these sides are uneven, it is an irregular pentagon, also known as an irregular polygon.
A convex polygon is one with all of its internal angles smaller than 180°.
As a result, the terms for the given form are pentagon, irregular polygon, and convex polygon.
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The question seems incomplete, the missing figure has been attached below
If 8; 2x; 2y forms an arithmetic sequence and 2x ; 2y; 36 forms a geometric sequence determine the values of x and y. Arithmetic and Geometric Series
Answer:
36
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. A geometric sequence is a sequence of numbers in which any two consecutive terms have a constant ratio.
Given that 8, 2x, 2y is an arithmetic sequence, we know that:
2x - 8 = 2y - 2x
x = y
Given that 2x, 2y, 36 is a geometric sequence, we know that:
(2y)/(2x) = 36/2y
y^2 = 36x
Now, we can use the first equation to substitute for y in the second equation, and get:
x^2 = 36x
x^2 - 36x = 0
x(x-36) = 0
So x = 0 or x = 36
However, x cannot be equal to zero because in that case the second term of the arithmetic sequence will be zero, and it will not be a valid solution. Therefore, x = 36.
So, y = x = 36.
Therefore, the values of x and y are 36.
7. The cost of half a dozen candles is R30. What is the cost of one candle?
Answer: 5R
Step-by-step explanation:
Half a dozen =6 pieces
R30/6=5R
How much is one dozen?
One dozen is equal to 12, so one half of a dozen is 6.
If 6 candles are priced at R30, we can divide R30 by 6 to get the cost of 1 candle.
30 ÷ 6 = 5.
Therefore, each candle costs R5.
Need help for this question
Answer:
Step-by-step explanation: Hello! You know that there are 3 students who scored 55, 4 students who scored 60, 8 students who scored 65, 4 students who scored 70, 4 students who scored 75, 1 student who scored 80, 9 students who scored 85, and 5 students who scored 90. To find the mean of a set of values, here is the formula:
a + b + c + d + e . . .
--------------------------
2
Each variable should represent the score of a single student, so write each score for each individual student.
(55 + 55 + 55 + 60 + 60 + 60 + 60 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 70 + 70 + 70 + 70 + 75 + 75 + 75 + 75 + 80 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 90 + 90 + 90 + 90 + 90)/2
You could divide all of this by 2 or you could multiply the values and then add them:
((55 x 3) + (60 x 4) + (65 x 8) + (70 x 4) + (75 x 4) + 80 + (85 x 9) + (90 x 4))/2
Either way works, but the second way is probably faster.
--------------------------------------------------------------------------------------------------
How to find the answer:
55 x 3 = 165
60 x 4 = 240
65 x 8 = 520
70 x 4 = 280
80 = 80
85 x 9 = 765
90 x 4 = 360
Substitute this into the equation
(165 + 240 + 520 + 280 + 80 + 765 + 360)/2
(405 + 800 + 845 + 360)/2
(1205 + 1205)/2
2410/2
= 1205
The answer is 1205
1. Gerald works 18 hours each week. He earns $10 per hour. Write an expression to find how much Gerald earns in 1 week. Write an expression to find how much Gerald earns in 4 weeks. PLS HURRY!!!
The expression for the amount earned in one week per hour is 18 x $10
The expression for the amount earned in four weeks is 18 x $10 x 4
What are the expressions?An expression is when numbers or letters are connected together by a mathematical operation without an equal to sign. An example of an expression is a + 3b.
The amount earned in one week = total number of hours worked in a week x amount earned per hour
18 x $10
The amount earned in four weeks = total number of hours worked in a week x amount earned per hour x 4
18 x $10 x 4
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I WILL GIVE BRAINLIEST HELPPPPPPP
Answer:
sorry I want to help you but I can't sorry
Step-by-step explanation:
i don't know how to solve this
Can someone just help explain one of the problems and I’ll try the rest? Thank you!
A circle has a circumference of 36 cm. What is the length
of an arc that has a measure of 190°?
The length of an arc that has a measure of 190° is equal to 9 cm.
How to calculate the length of an arc?In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle is given by:
Length of an arc = 2πr × θ/360
Length of an arc = C × θ/360
Where:
r represents the radius of a circle.C represents the circumference of a circle.θ represents the angle subtended by the arc.Substituting the given points into the length of an arc formula, we have the following;
Length of an arc = 36 × 90/360
Length of an arc = 36 × 1/4
Length of an arc = 9 cm.
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the 140 employees in a factory are either right handed or left handed
The frequency table is given below.
The probability that a person chosen is a left-handed female is 31/140.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total number of employees = 140
Male:
Number of male = 65
Right-handed.
= Total number of right-handed - Female right handed
90 - 44 = 46
Left-handed.
= 65 - 46
= 19
Female:
Number of females.
= Total employees - Number of males
= 140 - 65
= 75
Right-handed.
= 75 - 31
= 44
Left-handed.
= 31
Now,
The frequency table.
RH = 46
LH = 19
Male = 65
140
Female = 75
RH = 44
LH = 31
Now,
The probability that a person is a left-handed female.
= Number of left-handed females / Total number of employees
31/140
Thus,
The frequency table is given above.
The probability that a person is a left-handed female is 31/140.
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Ms. Lambert took her family to Pimento Garden on Sunday for dinner. The total bill was $73.25, and she wanted to leave an 18% tip. How much
money should she leave for the tip? *Make sure your answer rounded to correct money form.
Answer: The answer is $13.19.
Step-by-step explanation:
1- Turn the percentage into a decimal by moving the percent sign twice to the left.
2- Multiply the bill by the decimal.
3-youll get 13.185 so you'll round up to 13.19.
hope this helps!!
Please answer this edpuzzle! PLEASE! Whoever answers it first, I will mark you brainliest.
The simplified algebraic expression for this problem is given as follows:
5x + 2y + 11.
How to simplify the algebraic expression?The algebraic expression for this problem is defined as follows:
9x + 2y + 3 - 4x + 8.
To simplify the expression, we combine the like terms, which are the terms that have the same unknown variable, hence:
9x - 4x = 5x.2y.3 + 8 = 11.Hence the simplified algebraic expression for this problem is given as follows:
5x + 2y + 11.
Meaning that the third option is the correct option.
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d.
What do you notice about the graph of the quadratic equation and where it crosses the
x-axis? How do these values compare to the solutions of x2 - 6x + 5 = 0? Explain.
This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.
The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation x2 - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.
The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.
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If 6x/x^2-3x is subtracted from the sum of 3/5x-15 and x+3/x-3 what is the result?
If 6x/(x²-3x) is subtracted from the sum of 3/(5x-15) and (x+3)/(x-3) , then the result is (12 - 5x)/(x - 3) .
The sum of the algebraic expressions 3/(5x-15) and (x+3)/(x-3) are written as ; ⇒ 3/(5x-15) + (x+3)/(x-3) ;
taking 5 common from the denominator of the first term ,
we get ;
⇒ 3/5(x-3) + (x+3)/(x-3) ;
taking LCM as 5(x-3) and simplifying further ,
we have ;
⇒ 3/5(x-3) + (x+3)/(x-3) ;
⇒ [3 + 5(x+3)]/5(x-3) ;
⇒ (5x + 18)/5(x-3) .......equation(1)
Now 6x/(x²-3x) is subtracted from the equation(1)
⇒ (5x + 18)/5(x-3) - 6x/(x²-3x) ;
⇒ (5x + 18)/5(x-3) - 6x/x(x-3) ;
⇒ (5x + 18)/5(x-3) - 6/(x-3) ;
taking LCM as as 5(x-3) and simplifying further ,
we have ;
⇒ (5x + 18 - 30)/5(x-3) ;
⇒ (5x -12)/5(x-3) ;
Therefore , the final result is (5x -12)/5(x-3) .
The given question is incomplete , the complete question is
If 6x/(x²-3x) is subtracted from the sum of 3/(5x-15) and (x+3)/(x-3) . What is the result ?
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A 4-pack of coffee mugs costs $2.20. What is the unit price?
Answer:
The unit price for a coffee mug is $0.55.
Step-by-step explanation:
The unit price is simply just the price per unit.
We have a 4-pack of coffee mugs that costs $2.20.
He have 4 units and the price per 4 units.
Lets evaluate the price per 1 unit.
[tex]\frac{2.20}{4} =\frac{x}{1}[/tex]
Lets solve for [tex]x[/tex].
Divide [tex]x[/tex] by 1.
[tex]x=\frac{2.20}{4}[/tex]
Divide 2.20 by 4.
[tex]x=0.55[/tex]