Solving a system of equations we can see:
Sutopa has $73.20Maneet has $97.60Kim has $115.60How much money each of them has?
First, let's define the variables:
S = money that Sutopa has.M = money that Maneet has.K = money that Kim has.We can write the system of equations:
S = (3/4)*M
M = K - $18
S + M + K = $286.40
First, we can rewrite the second equation to get:
K = M + $18
Now we can replace the first and second equations into the third one:
(3/4)*M + M + (M + $18) = $286.40
Now we can solve this for M:
M*(1 + 1 + 3/4) = $286.40 - $18
M = $268.40*(4/11) = $97.60
Now we can find the other two values:
K = M + $18 = $97.60 + $18 = $115.60
S = (3/4)*M = (3/4)*$97.60 = $73.20
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A triangle has vertices at coordinates $(11,1)$, $(2,3)$ and $(3,7)$. What is the number of units in the length of the longest side of the triangle
Answer:
10 units
Step-by-step explanation:
the longest length is from (11, 1) to (3, 7) and can be clearly shown when graphed
now to find the length you must use the pythagorean theorem
the distance between 11 and 3 is 8 and the distance between 1 and 7 is 6 so
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
c = 10
that is your answer
Please someone help me, I don't get it
Answer:
a) x = 1.5 and x = -0.3
b) x = -8 and x = 5
Step-by-step explanation:
a)
The given equation follows the general structure: ax² + bx + c = 0.
Therefore, if a = 5, b = -6, and c = -2, you can substitute the values into the quadratic formula and solve for "x".
b)
Another way of solving polynomials is through factorization. After rearranging the equation to fit the general structure of a quadratic (as seen above), you can factor by asking yourself the question, which 2 numbers multiply to "c" (-40) and add to "b" (3)? The answers will make up your factors.
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1. }[/tex]
[tex]\mathsf{5x^2 - 6x - 2 = 0}[/tex]
[tex]\huge\textbf{Use the quadratic formula to solve:}[/tex]
[tex]\mathsf{x = \dfrac{-(-6)\pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathsf{x = \dfrac{6 \pm \sqrt{76}}{10}}[/tex]
[tex]\huge\textbf{Simplify that as well:}[/tex]
[tex]\mathsf{x = \dfrac{3}{5} + \dfrac{1}{5}\sqrt{19}\ or\ x = \dfrac{3}{5} + (-\dfrac{1}{5})\sqrt{19}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x \approx 1.5 \ or\ x\approx -0.3{}\ }}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{x^2 + 3x = 40}[/tex]
[tex]\huge\textbf{Subtract 40 to both sides:}[/tex]
[tex]\mathsf{x^2 + 3x - 40 = 40 - 40}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x^2+ 3x - 40 = 0}[/tex]
[tex]\huge\textbf{Factor the left side of the equation:}[/tex]
[tex]\mathsf{(x - 5)\times (x + 8) = 0}[/tex]
[tex]\mathsf{(x - 5)(x + 8) = 0}[/tex]
[tex]\huge\textbf{Set the factors to equal to 0:}[/tex]
[tex]\mathsf{x - 5 = 0 \ or\ even\ x + 8 = 0}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = 5\ or\ x = -8}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 5\ or \ x = -8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when _____
As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution whenever the sample size is large.
What is the Central limit theorem?The Central limit theorem says that the normal probability distribution is used to approximate the sampling distribution of the sample proportions and sample means whenever the sample size is large.Approximation of the distribution occurs when the sample size is greater than or equal to 30 and n(1 - p) ≥ 5.Thus, as a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution when the sample size is large and each element is selected independently from the same population.
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18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit.
Andrew should make 6 bookcase and 12 tv stand to maximize his profut $1560.
Given that 18 pieces of furniture is made and the materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00 and he has $600.00 to spend on materials. He makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand.
Let x represent the number of book case and let y represent number of tv stand.
Total number of book case and total number of tv stand is x+y≤18 ......(1)
Total amount of book case and total amount of tv stand is 20x+40y≤600 ......(2)
minimum amount of book case is x≥0 and minimum amount of tv stand is y≥0.
Now, solve the inequality (1) by converting it into equality and substituting x=0 and y=0, we get
x+y=18
When x=0 then
0+y=18
y=18
When y=0 then
x+0=18
x=18
Now, solve the inequality (2) by converting it into equality and substituting x=0 and y=0, we get
20x+40y=600
When x=0 then
20(0)+40y=600
40y=600
y=15
when y=0 then
20x+40(0)=600
20x=600
x=30
Further, we will grph the inequalities and we get feasible region and taking boundary point from graph.
From the graph the vertices of the feasible region is (0,0),(6,12),(0,15) and (18,0)
Further, we will find the maximization profit for the equation Z=60x+100y
When (x,y)=(0,0) then
Z=60(0)+100(0)
Z=0
When (x,y)=(6,12) then
Z=60(6)+12(100)
Z=360+1200
Z=1560
When (x,y)=(0,15) then
Z=60(0)+12(15)
Z=0+1500
Z=1500
When (x,y)=(18,0) then
Z=60(18)+100(0)
Z=1080
Hence, maximum profit is $1560 when andrew should build 6 bookcase and 12 tv stand.
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URGENT!!
Given the following table with selected values of f (x) and g(x), evaluate f (g(4)).
x –6 –4 1 3 4
f (x) 4 –1 –6 1 3
g(x) 1 4 3 –4 –6
–4
–1
1
4
Answer:
f[g(4)] = 4
Step-by-step explanation:
Given table:
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} x & -6 & -4 & 1 & 3 & 4\\\cline{1-6} f(x) & 4 & -1 & -6 & 1 & 3 \\\cline{1-6} g(x) & 1 & 4 & 3 & -4 & -6 \\\cline{1-6}\end{array}[/tex]
f[g(4)] is a composite function.
When calculating composite functions, always work from inside the brackets out.
Begin with g(4): g(4) is the value of function g(x) when x = 4.
From inspection of the given table, g(4) = -6
Therefore, f[g(4)] = f(-6)
f(-6) is the value of function f(x) when x = -6.
From inspection of the given table, f(-6) = 4
Therefore, f[g(4)] = 4
As we can see
g(4)=-6So
f(g(4))f(-6)4A recipe for dessert calls for 1/3 cup of powdered sugar and 2/6 cup of brown
sugar. What is the total amount of sugar needed for the recipe
Answer:
2/3
Step-by-step explanation:
1/3 cup powdered sugar
2/6 cup brown sugar
Reduce 2/6 to 1/3.
1/3 + 1/3 = 2/3
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: No, they are not similar
Step-by-step explanation:
Similar triangles are triangles with congruent angles.
33° ≠ 32°
These triangles are not similar.
Divide 24x2y + 8xy2 + 8xy by -4xy.
What is the quotient?
The quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2
How to determine the quotient?The statement is given as:
Divide 24x2y + 8xy2 + 8xy by -4xy
The quotient is represented as:
Quotient = (24x^2y + 8xy^2 + 8xy)/(-4xy)
Factor out -4xy
Quotient = (-4xy)(-6x - 2y - 2)/(-4xy)
Evaluate the quotient
Quotient = -6x - 2y - 2
Hence, the quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2
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Triangle L N M is shown. Angle L N M is 90 degrees and angle N M L is 20 degrees. The length of L N is 21.
Use the diagram to complete the statements.
The measure of angle L is
°.
The trigonometric ratio that uses ∠M and LN to solve for NM is
.
The length of NM, to the nearest tenth, is approximately
.
The length of the triangle will be equal to 2.7.
How to calculate the length?It should be noted that that sin will be the opposite divided by the hypothenuse.
The measure of angle L is 20°.
This will be:
sin 20 = LN/8
NM = 8 sin 20
NM = 2.7
In conclusion, NM is 2.7.
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Answer: 2.7
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
Lines (1) and (2) are parallel. Find sides M
and N. Round your answer to the nearest
tenth.
P
A
M
(2)->
155⁰
N
Answer:
M = 4.5
N = 2.1
Step-by-step explanation:
angle p would be 25. 180 - 155 = 25
M = 5cos25 =4.5 rounded to the tenths place.
M = 5sin25 = 2.1 rounded.
2+8+32+128…..,n=9
Evaluate each geometric series described
The value of 2+8+32+128…..,n=9 is 174762
How to evaluate the series?The series is given as:
2+8+32+128…..,n=9
Start by calculating the common ratio (r)
r = 8/2
r = 4
The sum of the series is then calculated as:
[tex]S_n = \frac{a *(r^n - 1)}{r -1}[/tex]
This gives
[tex]S_9 = \frac{2 *(4^9 - 1)}{4 -1}[/tex]
Evaluate the difference
[tex]S_9 = \frac{2 *( 262143)}{3}[/tex]
Evaluate the quotient
[tex]S_9 = 174762[/tex]
Hence, the value of 2+8+32+128…..,n=9 is 174762
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1. What is the value of the 4th iterate of
f(x) = 3x-1/x2 if x0 = -2? Round to three decimal places.
The value of the 4th iterate of the given function f(x) is -2.096
2nd option is correct.
A function's iterate is a function that is expressed as repetition of another (already iterated) function; this latter function may be referred to as the iterand.
Any function taken on its own is regarded as the first iteration.
A function is said to have an identity function at iteration zero.
According to the question,
f(x) = (3x-1)/[tex]x^{2}[/tex]
[tex]x_{o}[/tex] = -2
The first iterate is calculated by finding f(-2).
f(-2) = (3(-2)-1)/4
f(-2) = -1.75
Similarly, the next iterates are calculated as follows:
f(-1.75) = -2.048
f(-2.048) = -1.71
f(-1.71) = -2.096
Thus, the fourth iterate for the given function is [tex]x_{4}[/tex]= -2.096
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Drag each tile to the correct box.
Graph the functions as transformations of f(x) = x^(2).
Arrange the parabolas with respect to the position of their vertices from left to right.
Answer:
Step-by-step explanation:
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Answer:
? = 120°
Step-by-step explanation:
the central angle is the same as the arc that subtends it , that is
? = 120°
Tatiana has a special puzzle in which all of the pieces fit together in any way. There is no goal picture. Instead, the goal of the puzzle is to make different patterns and pictures using the pieces. If Tatiana has 50 unique puzzle pieces and she plans to use all of them, how many possible pictures can she create
It is an example of Permutation without repetition.
To find the number of pictures can create.
what is permutation and combination?An arrangement of things in a certain sequence is what we refer to as a permutation. The constituents or components of sets are presented in this section in a sequential or chronological fashion. A coming together or merging of several parts or characteristics in which each of the constituent parts or traits retains its unique identity.
Given that:
50 unique pieces of puzzle
Use them all to solve puzzle
No repetition is allowed therefore
Since no repetition is allowed because all puzzle pieces are required to be used.
Therefore each of the 50 pieces can be used max one time
Therefore if we start with piece like this " 1 2 3 .. up to ... 50 " it is one combination
Another could be "2 1 3 .. up to .. 50" or "3 1 2 .. up to 50" and so on
So we see that we can see that we can select the first piece in 50 ways 49 left which could be selected for second piece then 48, 47 respectively
Therefore 50X49X48X47X46X....X1 = 50!
Hence, It is an example of Permutation without repetition.
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Option is missing
A. Combination with repetition
B. Permutation with repetition
C. Combination without repetition
D. Permutation without repetition
2 (3/4 - x/3) = 1 1/4
solve for x
The value of x is 17/12
How to solve for x?The equation is given as
2 (3/4 - x/3) = 1 1/4
Express as improper fractions
2 (3/4 - x/3) = 5/4
Divide through by 2
3/4 - x/3 = 5/9
Collect like terms
x/3 = 3/4 - 5/9
Multiply through by 3
x = 9/4 - 15/9
Evaluate
x = (81 - 30)/36
Evaluate
x = 51/36
Simplify
x = 17/12
Hence, the value of x is 17/12
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This table shows the ratio of drummers to flute players in the school band.
The missing value from the table is 4.
What is the missing value?Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained in another value.
In order to determine the missing number, we first have to determine the rate of change of the number of drummers.
Rate of change:
4 - 3 = 1
2 -1 = 1
3 - 2 = 1
So, the rate of change is 1. Thus, the missing number : 3 + 1 = 4
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Answer: missing value is 5
Step-by-step explanation:
The slant height and radius of a cone are 4 and 1, respectively. Unrolling the curved surface gives a circular sector with center angle $n^\circ.$ Find $n.$
The centre angle of circular sector is n = 90 degrees (approximately).
What is circular sector?A sector is referred to as a component of a circular made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radius of the circle at its ends.
A piece of pizzas can be used as an analogy for the form of a circle's sector.
The formula for finding the angle formed at the circular sector in radian is;
Let 'n' be the centre angle.
Let 'l' be the slant height of the cone which is equal to radius of circular sector.
Let 'r' be the radius of the cone.
First, calculate the total length of the circular sector say 'L' which is equal to the circumference of the circular base of the cone.
circumference = 2[tex]\pi[/tex]r
= 2×3.14×1
= 6.28
Now,
centre angle = length of circular sector/radius of circle
n = L/l
n = 6.28/4
n = 1.57 radian
Convert radian in degree as;
n = (1.57×180)/[tex]\pi[/tex]
n = 89.95
n = 90 degrees (approximately)
Therefore, the angle made by the circular sector is 90 dergees.
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The correct question is-
The slant height and radius of a cone are 4 and 1, respectively. Unrolling the curved surface gives a circular sector with center angle n degrees. Find n.
Compare the graphs of the functions listed below.
Function 1: y = 0.25x2
Function 2: y = 4x2
Function 3: y = -½x2
Function 4: y = -16x2
The graph of
✔ function 1
is the widest.
The graph of
is the narrowest.
Answer:
Function 1 is the widestFunction 4 is the narrowestStep-by-step explanation:
The graph is widest when the coefficient of [tex]x^2[/tex] has the smallest absolute value.
The graph is narrowest when the coefficient of [tex]x^2[/tex] has the largest absolute value.
By comparing the graphs of the functions, function 1: y = 0.25x2 is the widest and function 4: y = -16x2 is the narrowest.
The graph is widest when the coefficient of [tex]x^{2}[/tex] has the smallest absolute value.
The graph is narrowest when the coefficient of [tex]x^{2}[/tex] has the largest absolute value.
The answer lies in the coefficient for the [tex]x^{2}[/tex] term. When the absolute value of the coefficient gets bigger, the graph gets narrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).
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Meredith found the following partial containers of detergent in the basement: 12 quart, 114 gallons, and 34 gallon. how many quarts of detergent did meredith find in all?
Quarts of detergent 1208
First, we convert each unit to its pint equivalent.
1 gallon =eight US Pint
114 gallons =114 X eight =912 Pint
34 gallon =34 X 8 =272 Pint
further, 1 quart =2 Pint
12 quart = 12 X 2 Pint =24 Pint
including the three values
912+272+24=1208 Pint
therefore, Meredith will want 1,208 Pint boxes.
The unitary technique is a way of solving trouble by way of first finding the fee of a single unit, and then finding the essential value with the aid of multiplying the unmarried unit price.
The system of the unitary technique is to locate the fee of an unmarried unit after which multiply the fee of a single unit to a wide variety of devices to get the vital fee.
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The area of a rectangular cocktail table is x²-18x +32. If the width is x-16, what is it's length?
Answer:
x-2
Step-by-step explanation:
The formula for area of rectangle is length x width
And we know that width is x-16
And we know that the area is [tex]x^{2} -18x +32[/tex]
So we know that when x-2 is multiplied with x-16, it gives off [tex]x^{2} -18x +32[/tex]
Tiffany started a doggle daycare where she offered a variety of services, including grooming. She charges an hourly rate of
$9 and a fee for each service.
Fluffy's human paid $58 for her 3 hour stay. Complete the function for a visit of x hours which includes grooming.
Express the function in slope-intercept form.
The linear function in slope-intercept form for the cost of a visit of x hours is given as follows:
C(x) = 9x + 31.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the rate means that the slope is of m = 9. When x = 3, C(x) = 58, hence the y-intercept is found as follows:
C(x) = 9x + b
58 = 9(3) + b
b = 31.
Hence the equation is:
C(x) = 9x + 31.
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The gas co2 is diffusin at steady state through a tube 20 cm long having a diameter of 1 cm and containing n2 at 350 k . the total pressur is constant at 101.3kpa . the partial pressure of co2 at one end is 456 mmhg and 76 mmhg at the end . the diffusivity is 0.167 cm2 /s at 298 k . calculate the mass rate of co2 if the partial pressure remains constant.
The value is J = 1.71*10^-6 kmol/m^2.s
According to the given conditions we get,
The length the tube l= 0.20m
The diameter of the tube d= 0.01m
The total pressure inside the tube P= 101.32kPa
The partial pressure of CO2 at the first end is
P1= 456mm Hg = 60794.832 Pa
The partial pressure of CO2 at the other end is
P2= 76mm Hg = 10132.472 Pa
The temperature is T = 298 K
The diffusion coefficient D= 1.67* 10^-5 m^2/s
Generally the molar flux of CO2 is mathematically represented as
J= D{p1-p2} / R.T
Here R is the gas constant with value R= 8.314 j/kmol
So we get J= 1.71 * 10^-3 mol/m^2.sec
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Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. www represents the volume of water andrei uses (in liters) if he uses nnn marbles. w=32-0.05nw=32−0.05nw, equals, 32, minus, 0, point, 05, n what is the volume of each marble?
Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:
w = 32 - 0.05n
The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.
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Answer:
.05 liters
Step-by-step explanation:
can anyone solve this 100+3-4(4-5) divided by 6+5+5+5+300
Stronger evidence against the null hypothesis is indicated by: Group of answer choices lower levels of significance. smaller p-values. lower probabilities for the power of the test. smaller critical values.
Stronger evidence against the null hypothesis is indicated by: smaller p-values.
What is null hypothesis?A statistical conjecture known as a null hypothesis asserts that certain features of a population or data-generating process are not different from one another.
A mechanism to reject the null hypothesis with a predetermined level of confidence is provided by hypothesis testing.
The alternative hypothesis is supported if the null hypothesis can be rejected.
The foundation of the scientific falsification principle is null hypothesis testing. The null hypothesis presupposes that any variation in the selected characteristics you observe in a set of data is the result of chance.
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the sum of three numbers is 78. the third number is 3 times the first. the first number is 7 more than the second. what are the numbers?
Answer:
17
Step-by-step explanation:
x+3x+x-7=78
5x-7=78
5x=78+7
5x=85
x=85/5
x=17
Answer:
The three numbers are 17, 10 and 51.
Step-by-step explanation:
Let the first, second, and third numbers be [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex] respectively.
• From the question, we know:
sum of the numbers is 78.
∴ [tex]x + y + z = 78[/tex] ----------(1st equation)
Let's express both [tex]x[/tex] and [tex]z[/tex] in terms of [tex]\bf y[/tex] :
• We know that:
the third number is 3 times the first.
∴ [tex]z = 3x[/tex]
⇒ [tex]x = \frac{z}{3}[/tex] ----------(2nd equation)
• We also know that:
the first number is 7 more than the second.
∴ [tex]\boxed{x = 7 + y}[/tex]
Substituting [tex]x = \frac{z}{3}[/tex] (from 2nd equation)
⇒ [tex]\frac{z}{3} = 7 + y[/tex]
⇒ [tex]\boxed{z = 21 + 3y}[/tex]
• We can now substitute [tex]x = 7 + y[/tex] and [tex]z = 21 + 3y[/tex] into the first equation:
[tex]x + y + z = 78[/tex]
⇒ [tex](7 + y) + y + (21 + 3y) = 78[/tex]
⇒ [tex]5y + 28 = 78[/tex]
⇒ [tex]5y = 50[/tex]
⇒ [tex]y = \bf 10[/tex]
∴ [tex]x = 7 + 10\\[/tex]
⇒ [tex]x = \bf 17[/tex]
[tex]z = 21 + 3(10)[/tex]
⇒ [tex]z = \bf 51[/tex]
∴ The three numbers are 17, 10 and 51.
Instructions: Find the measure of the indicated angle to the nearest degree.
Answer:
15.78°
Step-by-step explanation:
Let the angle be x.
From the x, the known sides are the opposite side, O(13) and the adjacent side, A(46)
Therefore, The trigonometric ratio is the tangent ratio.
tan x = O/A
tan x =13/46
x = 15.78°
how many 'words' can be made from the name ESTABROK with no restrictions
The number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.
How to determine the number of waysGiven the word:
ESTABROK
Then n = 8
p = 6
The formula for permutation without restrictions
P = n! ( n - p + 1)!
P = 8! ( 8 - 6 + 1) !
P = 8! (8 - 7)!
P = 8! (1)!
P = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 × 1
P = 40, 320 ways
Thus, the number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.
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mean of four consecutive even numbers is 15. Enter each number separated by a comma
Answer:
12, 14, 16, 18
Step-by-step explanation:
(x + (x+2) + (x+4) + (x+6))/4 = 15
^ solve algebraically
you'll get (4x+12)/4 = 15
then: 4x + 12 = 60
then 4x = 60-12
then 4x = 48
then x = 12
x is 12 so then do substitution
so you get
12 + (12+2) + (12+4) + (12+6)
12, 14, 16, 18