. Your roommate, Sarah, offered to buy groceries for
you and your other roommate. The total bill was
$82. She forgot to save the individual receipts but
remembered that your groceries were $0.05 cheaper
than half of her groceries, and that your other
roommate’s groceries were $2.10 more than your
groceries. How much was each of your share of the
groceries?
According to the given information, your share of the groceries was $39.95, your other roommate's share was $42.05, and Sarah's share was $0.
What is equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
Let's call the amount of money Sarah spent on groceries "S".
Let's call the amount of money you spent on groceries "Y".
Let's call the amount of money your other roommate spent on groceries "O".
We know that:
S + Y + O = 82 (the total bill was $82)
Y = (S/2) - 0.05 (your groceries were $0.05 cheaper than half of Sarah's groceries)
O = Y + 2.10 (your other roommate's groceries were $2.10 more than your groceries)
We can use the second equation to substitute Y in the third equation:
O = Y + 2.10
O = (S/2) - 0.05 + 2.10
O = (S/2) + 2.05
We can now substitute both equations into the first equation:
S + Y + O = 82
S + ((S/2) - 0.05) + ((S/2) + 2.05) = 82
2S + 4 = 164
2S = 160
S = 80
Now that we know S, we can substitute it into the other equations to find Y and O:
Y = (S/2) - 0.05 = (80/2) - 0.05 = 39.95
O = Y + 2.10 = 39.95 + 2.10 = 42.05
So your share of the groceries was $39.95, your other roommate's share was $42.05, and Sarah's share was $80 - ($39.95 + $42.05) = $82 - $82 = $0.
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Prove the following,in a semigroup:
By induction, we can conclude that in a semigroup, all products of x1, x2, ...... xn (in that order) are equal.
What is semigroup?A semigroup is a mathematical structure consisting of a set of elements along with an associative binary operation. The operation must be associative, meaning that the result of the operation is independent of the order of the operands.
We can prove this by induction. Let S be a semigroup and x1, x2, x3, ..., xn be the elements of S.
Base Case: When n = 2, then the product of x1 and x2 is x1x2.
Inductive Step: Assume that the product of x1, x2, ..., xn (in that order) is equal. Then we can prove that the product of x1, x2, ..., xn+1 (in that order) is also equal.
Let a be the product of x1, x2, ..., xn (in that order). Then a = x1x2x3....xn.
Now the product of x1, x2, ..., xn+1 (in that order) is a x xn+1. Since S is a semigroup, a x xn+1 = x1x2x3....xn x xn+1.
Since the product of x1, x2, ..., xn (in that order) is equal, a = x1x2x3....xn. Therefore, the product of x1, x2, ..., xn+1 (in that order) is also equal.
By induction, we can conclude that in a semigroup, all products of x1, x2, ...... xn (in that order) are equal.
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I need help with question I’m stuck on trying to figure out what a b and C’s angles are if it’s obtuse reflex acute and etc
Answer:
[tex]\measuredangle \textsf{ BCA is Actue.}[/tex]
[tex]\measuredangle \textsf{ CAB is Actue.}[/tex]
[tex]\measuredangle \textsf{ ABC is Right}.[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked what type of angles are provided.}[/tex]
[tex]\textsf{First, the question is asking for the \underline{measure}, which \underline{affects} the types of angles.}[/tex]
[tex]\textsf{This Triangle is a \underline{Right Triangle}, according to the \underline{Angle Markings}.}[/tex]
[tex]\textsf{One angle must be \underline{Right}, and that angle is} \ \boxed{ \measuredangle \textsf{ABC.}}[/tex]
[tex]\textsf{Becuase a Triangle adds up to \underline{180}}^{\circ}\textsf{, the other \underline{2} angles are \underline{less than 90}}^{\circ}.[/tex]
[tex]\textsf{Meaning, that} \ \boxed{\measuredangle \textsf{BCA}} \ \textsf{and} \ \boxed{\measuredangle \ \textsf{CAB}} \ \textsf{are \underline{Acute}.}[/tex]
[tex]\fbox{\textsf{Notes:}}[/tex]
[tex]\textsf{An Acute Angle is \underline{less} than 90}^{\circ}.[/tex]
[tex]\textsf{A Right Angle is \underline{equal} to 90}^{\circ}.[/tex]
[tex]\textsf{An Obtuse Angle is \underline{greater} than 90}^{\circ} \textsf{, but \underline{less} than 180}^{\circ}.[/tex]
[tex]\textsf{A Straight Angle is \underline{equal} to 180}^{\circ}.[/tex]
[tex]\textsf{A Reflex Angle is \underline{greater} to 180}^{\circ} \textsf{, but \underline{less} than 360}^{\circ}.[/tex]
Compare the functions f(x) =2* and g (x) = 225x by completing parts (a) and (b).
The values that completes the given function table is as attached.
For x ≥ 13, the table suggests that f(x) is always greater that g(x)
How to solve Function Tables?We are given the functions;
f(x) = 2ˣ and g(x) = 225x
Thus, to fill the function table, we have;
f(6) = 2⁶ = 64
f(7) = 2⁷ = 128
f(12) = 2¹² = 4096
f(13) = 2¹³ = 8192
f(14) = 2¹⁴ = 16384
g(6) = 225 * 6 = 1350
g(7) = 225 * 7 = 1575
g(12) = 225 * 12 = 2700
g(13) = 225 * 13 = 2925
g(14) = 225 * 14 = 3150
For x ≥ 13, the table suggests that f(x) is always greater that g(x)
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he table to the right is based on the assumption that 1% of breast tumors are malignant. It also assumes that mammogram screening is 90% accurate. Complete parts (a) through (c) below
Using probability,
a. In positive mammogram, the chance of having cancer is= 7.217%
b. If patient has cancer, chance of positive mammogram is = 90%
c. A woman with negative mammogram has cancer is = 0.114%
What do you mean by probability?
The chances of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. We may be sure or not sure about the results of an event.
When this happens, we say that there is a chance that the event will happen or not happen. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
Now in the question,
1247 women had a positive mammogram. Out of which 90 actually had cancer. So, in positive mammogram, the chance of having cancer is:
=90/1247
= 7.217%.
100 women who received mammogram cancer or which 90 had a positive mammogram. So, if patient has cancer, chance of positive mammogram is = 90/100
= 90%.
Now 8753 women had a negative mammogram of which 10 actually had cancer. So, a woman with negative mammogram has cancer is
= 10/8753
= 0.114%
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The complete question is:
he table to the right is based on the assumption that 1% of breast tumors are malignant. It also assumes that mammogram screening is 90% accurate. Complete parts (a) through (c) below
Write an equation of the line that passes through a pair of points:
ú
T
-3 -2 -1
a.
y=x+3
b. y=x-3
5.
4+
3+
2+
1+
7
-1
-2+
-3
4
1 2,
3
5 X
c.
d.
y = -x + 2
y = -x-2
The equation of the given line is expressed as:
y = x - 3
What is the equation of the line?The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula for the equation of a line between two coordinates is:
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
The pair of coordinate points marked are:
(4, 1) and (5, 2)
Thus, the equation of the line is:
(y - 1)/(x - 4) = (2 - 1)/(5 - 4)
y - 1 = x - 4
y = x - 3
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Name the minor arc and find it’s measure. Then name the major arc and find it’s measure.
Consequently, 308 °is the main arc's length and minor arc is 52°
An angle whose apex is a circle's center is said to have a center angle.
what is a major and minor curve defined as?The minor arc connects two locations on a circle in the shortest distance possible. The main arc connecting them is the longest arc.
. For instance, two locations A and B on a circle are connected by two arcs:
the major arc, which travels clockwise around the circle, and the minor arc, which travels anticlockwise (the minor arc) .
The minor arc's length is equivalent to the center angle's length in degrees.
Consequently, the minor arc is 52 degrees in length.
The major arc's measure is equivalent to 360 ° minus the minor arc's measurement.
The main arc's length is therefore 360 – 52 = 308 °.
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Ronald made some chili with 1/2 of a can of black beans and 7/10 of a can of pinto beans.
How many cans of beans did Ronald use in all?
Write your answer as a fraction or as a whole or mixed nunver.
Submit
cans
Total of 3/5 can of black beans and pinto beans used in preparing the chili by Ronald.
Explain about the fraction of the number?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator either denominator of a complex fraction.
Fraction of beans used by Ronald to make chili.
black beans = 1/2 can
pinto beans = 7/10 can
Thus,
total beans = 1/2 can + 7/10 can
total beans = (1/2 + 7/10) can
Simplifying:
total beans = (5*1 + 7)/ 2*10 can
total beans = 12/20 can
total beans = 3/5 can
Thus, total of 3/5 can of black beans and pinto beans used in preparing the chili by Ronald.
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Solve for y.
9x-2y=6
Hello !
Answer:
[tex] \large \boxed{ \sf y = - 3 + \frac{9}{2} x}[/tex]
Step-by-step explanation:
We want to isolate y in the following equality :
[tex] \sf9x - 2y = 6[/tex]
First, let's substract 9x from both sides of the equality :
[tex] \sf9x - 2y - 9x= 6 - 9x[/tex]
[tex] \sf - 2y = 6 - 9x[/tex]
Now let's divide both sides by -2 :
[tex] \sf \frac{ - 2y}{ - 2} = \frac{6 - 9x}{ - 2} [/tex]
[tex] \boxed{ \sf y = - 3 + \frac{9}{2} x}[/tex]
Have a nice day ;)
What is -2, 3 reflected over the y- axis?????
I NEED THE ANSWER ASAP
Answer:
2, 3
Step-by-step explanation:
When a point is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, if you reflect the point (-2, 3) over the y-axis, it will become (2, 3).
(Sorry, I tried to provide a picture but I could not.)
The cost function for a certain company is C = 60x + 300 and the revenue is given by R = 100x − 0.5x2. Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $15000
The values of x that would give a profit of $300 is 20 and 60.
Revenue is the total amount of money that can be made from selling x items while cost is the amount of money used to produce x items.
Profit is the difference between revenue and cost. Profit is given by
Profit = Revenue - Cost
Since Cost C = 60x + 300, Revenue R = 100x − 0.5x², hence:
Profit = Revenue - Cost
Profit = 100x − 0.5x² - (60x + 300)
Profit = 40x - 0.5x² - 300
For a profit of $300:
300 = 40x - 0.5x² - 300
0.5x² - 40x + 600 = 0
x = 20 and x = 60
Hence the values of x that would give a profit of $300 is 20 and 60.
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Carla is using geometry software to design a stained-glass window. She begins by drawing the lines and angles shown. Carla adjusts the diagram so that ∠5 = 2 · ∠6. Later Carla's assistant, Joe, adjusts the diagram again so that ∠5 = 3 · ∠6. What is the change in ∠6 from Carla's adjustment to Joe's adjustment? Explain
The angle ∠5 and ∠6 are 135° and 45° respectively.
Define the term geometry?The study of points, lines, and shapes, as well as their characteristics and connections in two and three dimensions, is the subject of the mathematic branch known as geometry. It contains ideas like polygons, circles, triangles, angles, and solids.
For, Carla's adjustment,
angle ∠5 = 2 • angle ∠6
Then, ∠5 + ∠6 = 180° ( by linear pair)
2 × ∠6 + ∠6 = 180°
3 × ∠6 = 180°
∠6 = 60°
Then, ∠5 = 120°
For, Carla's assistant Joe adjustment
∠5 = 3 × ∠6
Again, ∠5 + ∠6 = 180° ( by linear pair)
3 ×∠6 + ∠6 = 180°
4 ×∠6 = 180°
∠6 = 45° Then, ∠5 = 135°
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The value of houses in a city is decreasing at a continuous growth rate of 3% per year. For a house that currently costs $450,000
a) Write the exponential growth function
b) What would be the value of this house 4 years from now?
c) How many years till the value of the house is $300,000
a) The exponential decay function that models the situation whereby the value of houses in a city is decreasing at a rate of 3% per year is f(x) = 450,000 x 0.97^x.
b) The value of this house that currently costs $450,000, based on the above exponential decay function, 4 years from now is $398,381.76.
c) It will take 13.3 years till the value of the house is $300,000.
What is an exponential decay function?An exponential decay function describes an exponential function whereby the value of an asset reduces consistently at a constant percentage rate over a period.
The formula for an exponential decay is given as y=a(1-b)^x.
In this exponential decay formula, y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has elapsed.
Finally, we can use an online finance calculator to determine the number of years till the value of the house reduces to $300,000.
The current cost of a house in the city = $450,000
The decreasing rate per year = 3%
Continuous annual decreasing factor = 0.97 (100% - 3%)
Let the value of the house in x years = f(x)
Exponential decay function:a) f(x) = 450,000 x 0.97^x
b) Value of the house 4 years from now = 450,000 x 0.97^4
= $398,381.76
c) The number of years till the value is $300,000:
300,000 = 450,000 x 0.97^x
I/Y (Interest per year) = -3%
PV (Present Value) = $450,000
PMT (Periodic Payment) = $-0
FV (Future Value) = $-300000
Results:
Number of period (#) = 13.312
Thus, the total Decay after 13.312 years is $150,000.00 ($450,000 - $300,000).
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Help me please please please
The probability that a biscuit is made by machine J and is not broken is given as follows:
0.245 = 24.5%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
In this problem, we are given a probability tree, hence to obtain the desired probability we must just choose the correct node.
The desired node is given as follows:
0.25 of the biscuits are made by machine J.Of these biscuits, 0.98 are not defective.Hence the probability that a biscuit is made by machine J and is not broken is given as follows:
0.25 x 0.98 = 0.245.
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A taxi driver had 22 fares to and from the airport last Monday. The price for a ride to the airport is $2.50, and the price for a ride from the airport is $13. The driver collected a total of $202 for the day. Let x represent the number of trips to the airport and y represent the number of trips from the airport. Write the ordered pair (x,y) that represents the solution in this situation.
Answer:dear
Step-by-step explanation:
257,540.765
Please I need assistance please help
The length of the diagonal of the television screen is equal to 56 cm to the nearest centimeter using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
we shall represent the length of the diagonal with the letter x so by Pythagoras rule we can write:
x² = 34² + 45²
x² = 1156 + 2025
x² = 3181
x = √3181 {take square root of both sides}
x = 56.4004
Therefore, the length of the diagonal of the television screen is equal to 56 cm to the nearest centimeter using the Pythagoras rule.
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Find the equation of a line that passes through the point (-2,-3) and has a gradient of -3.
Leave your answer in the form
y
=
m
x
+
c
Answer:
y=-3x+3
Step-by-step explanation:
y=mx+c
Substitute y = -3
x = -2
-3 = -3*-2+c
-3 = -6+c
-6+c = -3
c = -3+6
=3
y= -3x+3
1
A number x is multiplied by 4, and 2
is added to it; the result is less than 82.
Find the range of values of x.
Based on the given statement, the range of values of x is the values that do not exceed 82
How to determine the range of values of x.From the question, we have the following parameters that can be used in our computation:
A number x is multiplied by 4, and 2 is added to it; the result is less than 82.Using the above as a guide, we have the following:
The output of the operation cannot exceed 82
The range is teh set of the output values
This means that the range is all set of real values less than or equal to 82
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Answer:
Step-by-step explanation
Need help on Q1 , by using substitution and need checks
Answer:
x = -3 ; y = 5
Step-by-step explanation:
Hey there!
This question has given us information about both of the given variables, x, and y
It tells us the y is equal to x plus 8 and that x plus y is equal to 2
If y is equal to x plus 8, we can
substitute the y value into the second equation
This will give us the following equation:
x + (x + 8) = 2
Now we simplify to solve for x
2x + 8 = 2
2x = -6
x = -3
Now that we know the x value, we can substitute that value into any one of the two equations given to solve for y
I'm going to use the first equation
Since we know that x is -3, we can now input it into the first equation and then simplify;
y = -3 + 8
y = 5
Answer:
[tex]\bf (-3,5)[/tex]Step-by-step explanation:
[tex]\tt y=x+8\\x+y=2[/tex]
Substitute y= x+8, into x + y=2:-
[tex]\tt x+y=2[/tex]
Let y = x+8
[tex]\tt x+x+8=2[/tex]
[tex]\tt 2x+8=2[/tex]
Solve for x :-
[tex]\tt 2x+8=2[/tex]
Subtract both sides by 8:-
[tex]\tt 2x+8-8=2-8[/tex]
[tex]\tt 2x=-6[/tex]
Divide both sides by 2:-
[tex]\tt \cfrac{2x}{2} =\cfrac{-6}{2}[/tex]
[tex]\boxed{\bf x=-3}[/tex]
Now, to solve for y, Substitute x = -3 into y=x+8:-
[tex]\tt y=x+8[/tex]
Let x = -3
[tex]\tt y=-3+8[/tex]
Simplify:-
*-3 + 8 = 5*
[tex]\boxed{ \bf y=5}[/tex]
Therefore, the solutions to the given system are x= -3 & y =5.
______________________
Hope this helps!
which equation has an infinite number of solutions?
The equation 8(x-9)=6(2x-12)-4x (option C) has an infinite number of solutions.
How to check for infinite number of solutions?Let's simplify the given equation and solve for x:
8(x-9) = 6(2x-12) - 4x
8x - 72 = 12x - 72 - 4x // Distributing 6
8x - 72 = 8x - 72 // Simplifying
We can see that both sides of the equation are equal, and there is no variable 'x' present. This means that the equation is an identity and it will hold true for any value of x.
Therefore, this equation has an infinite number of solutions, since any value of x will satisfy the equation.
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Given: AM = MC, BN = NC Prove: ΔABC ~ ΔMNC.
The required prove to show that ΔABC is similar to ΔMNC is explained below.
What are similar triangles?A given set of triangles are said to be similar if on comparing their corresponding properties, there exist some common relations among them. The similarity of two or more triangles do not imply that they are congruent.
Considering the given diagram, we have;
AM = MC (Given)
BN = NC (Given)
BC = BN + NC (addition property of a line segment)
AC = AM + MC (addition property of a line segment)
NC/ BC = MC/ AC = constant
<ACB = <MCN (Reflexive property)
Therefore,
ΔABC ~ ΔMNC (Side-Angle-Side theorem)
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Graphs of Polynomial Functions
The polynomial which is as described in the task content is; P (x) = -0.2 (x - 1)² (x +4).
What is the formula for the polynomial P(x) as described?It follows from the task content that; P(x) has a root of multiplicity 2 at x = 1 and a root with multiplicity of 1 at (x - 4).
Therefore, the polynomial would take the form;
P(x) = a (x - 1)² (x + 4)
Therefore, since the y-intercept is; y = -0.8
Therefore, we have that!
-0.8 = a (0-1)² (0+4)
-0.8 = 4a
a = -0.8 / 4
a = -0.2
Ultimately, the formula for the polynomial P(x) as given in the task content is; P (x) = -0.2 (x - 1)² (x +4).
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Find the domain and range of the composition
Therefore , the solution of the given problem of domain comes out to be (a) Domain of fog: {1, 6} and (b) Range of fog: {1, 6} .
Describe domain.The range of potential values that a function can take is known as its domain. These numbers serve as a representation for the x-values of an equation like f. (x). The range of potential numbers on which a function can be used is known as its domain. The result that the function gives following the entry of the x value is this set.
Here,
To find the domain and range of the composition fog, we need to evaluate fog(x) for all x in the domain of g that maps to the domain of f.
Since g maps 1 to 5 and 6 to 4, we have:
fog(1) = f(g(1)) = f(5) = 6
fog(6) = f(g(6)) = f(4) = 1
Therefore, the domain of fog is {1, 6} and the range of fog is {1, 6}, written in set notation as:
(a) Domain of fog: {1, 6}
(b) Range of fog: {1, 6}
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How to write 0.03 + 8 + 0.2 + 50 in word form
Answer:
Fifty eight and twenty-three hundredths
Step-by-step explanation:
Cones A and B both have volume 48bold pi cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B. Explain how you know Cone B has the same volume as Cone A.
Cone B does not have volume 48bold pi cubic units with these dimensions, but it does have the same volume as Cone A because they both have volume 48bold pi cubic units.
what is a cone?A cone, also known as a vertex, is a three-dimensional polygonal object with a flat base and a soft tapering apex. In a plane with no vertices, a cone is formed by connecting a story arc of lines, half-lines, but rather routes those are common to all focuses on the outpost. A cone is a muti structure with just a peaceful transition from a flat, round or, base towards the vertex and apex, which represents as the base's axis. A three-dimensional polygonal shape with only an upwardly flat curved surface is known as a cone.
Because Cone A has a volume of 48bold pi cubic units, we can use the volume of a cone formula to calculate its height:
Cone volume = 1/3 * base area * height
1/3 * pi * 62 * 4 = 48bold pi
48pi = 48bold pi
As a result, Cone A's height is 4 units. The radius is also 6 units, as we can see.
Cone volume = 1/3 * base area * height
[tex]1/3 * pi * r2 * h = 48\\144 = r^2 * h\\144 = 8^2 * 3\\144 = 192[/tex]
Cone B does not have volume 48bold pi cubic units with these dimensions, but it does have the same volume as Cone A because they both have volume 48bold pi cubic units.
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A smart tablet manufacturer test 1 out of every 25screens for flaws out of 125 tablets tested 2 had defective screens how many defective screens should the manufacturer expect out of 45000 smart tablets
Answer:
720
Explanation:
[tex]2:125[/tex]
[tex]x:45000[/tex]
to go from 125 to 45000 we need to multiply by 360
that's why we will multiply 2 with 360 to balance both ratios
when we do that we get 720
2:125
[tex]\bold{720:45000}[/tex]
Answer:
720
Step-by-step explanation:
*THESE ARE 4 SIMPLE GEOMETRY QUESTIONS!!*
Hello please help! I dont know a single thing about geometry and i need your help!
Very appreciated!
1. B.
2. C.
3. A.
4. C.
Tina used 10 1/2 yards of yarn to make three yarn dolls. She used 3 1/2 yards of yarn for the first doll and 4 1/8yards for the second doll. How much yarn did Tina use for the third doll?
Answer:
To find how much yarn Tina used for the third doll, we can subtract the total amount of yarn used for the first two dolls from the total amount of yarn used.
Total amount of yarn used = 10 1/2 yards
Amount used for first doll = 3 1/2 yards
Amount used for second doll = 4 1/8 yards
To add 3 1/2 and 4 1/8, we need to find a common denominator:
3 1/2 = 7/2
4 1/8 = 33/8
Common denominator = 8
So, 3 1/2 = 28/8 and 4 1/8 = 33/8
Total amount used for first two dolls = 28/8 + 33/8 = 61/8
Subtracting the total amount used for the first two dolls from the total amount of yarn used:
10 1/2 - 61/8 = 84/8 - 61/8 = 23/8
Therefore, Tina used 23/8 yards of yarn for the third doll.
I need help with this question thank you
Step-by-step explanation:
that makes NOP and QRP similar triangles.
that means that there is one common scale factor for the lengths of all pairs of correlating sides.
that means
QR/NO = RP/OP
OP = OR + RP
20/32 = RP/(12 + RP)
20(12 + RP) = 32RP
240 + 20RP = 32RP
240 = 12RP
RP = 20
if 8 cookies are shared between 4 people how many cookies would each person get
2
you divide 8 with 4 and the answer is 2