Answer:
The cost price of the article is Rs 1050
The marked price of the article Rs 1200
Step-by-step explanation:
The given discount on the article = 20%
The amount loss = Rs 90
With a discount of 5% the amount gained = Rs 90
Let the cost price of the article = X
Let the marked price of the article = Y
Therefore, we have;
(1 - 0.2) × Y = X - Rs 90
(1 - 0.5) × Y = X + Rs 90
Which gives;
0.8·Y = X - Rs 90 .......................(1)
0.95·Y = X + Rs 90.....................(2)
Subtracting equation (1) from equation (2), we have;
0.95·Y-0.8·Y = X + Rs 90 - (X - Rs 90) = X - X + Rs 90 + Rs 90 = Rs 180
0.15·Y = Rs 180
Y = Rs 180/0.15 = Rs 1200
Therefor, the marked price of the article = Rs 1200
From;
0.8·Y = X - Rs 90, we have;
0.8×Rs 1200 = X - Rs 90
X = 0.8× 1200 + 90 = Rs 1050
Therefore, the cost price of the article = Rs 1050.
Select the correct answer.
Which of the following represents a function?
Answer:
D.
Step-by-step explanation:
A function is when each x-value has only 1 y-value.
A: When x = 5, there are two values for y.
B: When x = -3, there are two values for y.
C: When x = -4, there are two y-values.
D: Each x-value has exactly one y-value.
So, your answer should be D.
Hope this helps!
Option (D) is accurate since the fourth option's x value has exactly one y value.
D. {(₋7,9), (₋4,₋9), (5,15), (7,19)}
What are functions?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that x's value determines what y's value will be. This reliance can be expressed as follows: y = f (x)
Given,
In the first case, y has two different values of 13 and 17, which is not permitted in a function, with the same value of x = 5. The first case is not a function as a result.
For the same value of x = 3 in the second case, y has two different values of 1 and 1, which is not permitted in a function. The second example is therefore not a function.
In the third case, for the same value of x = ₋4, y has two different values of 52 and 16 which is not allowed in a function. Therefore, third case is not a function.
Here, in the fourth situation, no x value is identical and there is only one possible y value.
Hence we get the answer as {(₋7,9), (₋4,₋9), (5,15), (7,19)} which represents the function.
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My state's lottery has 30 white balls numbered from 1 through 30 and 20 red balls numbered from 1 through 20. In each lottery drawing, 3 of the white balls and 2 of the red balls are drawn. To win, you must match all 3 white balls and both red balls, without regard to the order in which they were drawn. How many possible different combinations may be drawn?
Answer:
I dont give you the answer right away so you will read what i write and fully understand :D
Step-by-step explanation:
We are picking 3 balls from 30 balls, so its C(30,3) because the order of picking the balls doesnt matter. We also need to pick 2 balls from 20 balls, which is C(20,2). So the answer is C(30,3) * C(20,2).
Nine-banded armadillos always give birth to quadruplets—four identical babies (called pups). Jenny’s armadillo has produced four female pups. Jenny realizes that each of those pups could eventually have four more armadillos.
a. How many armadillos would Jenny have if the four pups grew up to have four more pups each?
b. What if every generation of Jenny’s armadillos was female? How many armadillos would there be if you only count the ones in the 5th generation? Can you write a formula for the number of armadillos in any given generation? Please explain what each variable and each number in your formula means.
c. According to this formula the world should be overrun with armadillos after 20 to 25 generations. Why isn’t this true in real life?
Answer:
a. 16; b. aₙ = 4ⁿ⁻¹; c. predation and carrying capacity will limit the population
Step-by-step explanation:
a. The first female had 4 pups.
If each of them had 4 pups, there would be 4 × 4 = 4² = 16 pups.
b. 1st generation = 1 pup
2nd generation = 4 × 1 pup = 4 pups
3rd generation = 4 × 4 pups = 16 pups
4th generation = 4 × 16 pups = 64 pups
5th generation = 4 × 64 pups = 256 pups
The sequence is 1, 4, 16, 64, 256, …
We can also write it as 4⁰, 4¹, 4², 4³, 4⁴, …
Note that the exponent is one less than the number of the generation.
Thus, the general formula for the nth term, aₙ, is
aₙ = 4ⁿ⁻¹, where
n = the number of the generation
a = the number of pups in that generation.
c. a₂₅ = 4²⁵⁻¹ = 4²⁴ ≈ 281 000 000 000 000 or 281 trillion
The population would not reach that number because there would not be enough food for all those pups. Pups would die of starvation until their numbers equalled the carrying capacity of the ecosystem and would level off at that point.
There would also be increased predation by coyotes, bobcats, etc. This would also keep the population growth in check,
Which is the graph of f(x) = (x - 1)(x + 4)?
4
2
2.
2
4
B
-6
2
X
-2
8
-6
Ty
6
2
Answer:
Its the last option. On the bottom.
Step-by-step explanation:
You need to Solve for x to find the zeroes of the equation.
x-1=0 So one x is at 1.
x+4=0 So the other x is at -4.
This graph is also not negative so it does not get flipped across the x-axis
The graph of the function [tex]f(x) = (x - 1)(x + 4)[/tex] is graph (d)
How to determine the graphThe equation of the function is given as:
[tex]f(x) = (x - 1)(x + 4)[/tex]
From the above function, we have the zeros of the function to be:
1 and -4
This means that:
The graph of the function passes through the x-axis at x =1 and x = -4The graph opens upwardHence, the graph is graph (d)
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The number of people contacted at each level of a phone tree can be represented by f(x) = 3^x where x represents the level.
What is x when f(x) = 27?
A. X = 2; At level 2, 27 people will be contacted.
B. x = 24; At level 24, 27 people will be contacted.
C. x = 3; At level 3, 27 people will be contacted.
D. x = 9; At level 9,27 people will be contacted.
Answer:
3
Step-by-step explanation:
Answer:
c is the correct answer
Step-by-step explanation:
WILL GIVE BRANLIEST AND 20 POINTS!!
List the coordinates of FOUR vertices that create the feasible region on the graph. Submit your answer in the form of FOUR ordered Pairs (x, y)
Step-by-step explanation:
The coordinates of the feasible region are:(In clockwise direction)
(200, 200)
(300, 200)
(500, 0)
(300, 0)
What is the value of x
Answer:
4
Step-by-step explanation:
For the first triangle which is triangle <KJL
Hypotenuse= 8✓2
Angle=30°
Opposite = ?
Therefore we will use Sine formula
Sin30° = Y/8✓2
Y=4✓2
For the second triangle which is triangle <JML
Hypotenuse= 4✓2
Opposite=X
Angle=45°
Therefore we will use Sine formula again
Sin45°=X/4✓2
X=4
Answer:
x = 4Step-by-step explanation:
ΔJKL is half of equilateral triangle and ΔJML is half of square.
We can use properties of these triangles (picture):
m∠KJL=90° and m∠JKL = 30° ⇒ JL = 0.5KL = 0.5•8√2 = 4√2
m∠JML=90° and m∠MJL = 45° ⇒ JL = ML√2
4√2 = x√2
x = 4
2.) Evaluate 6a² if a = 4
Answer:
96
Step-by-step explanation:
We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.
What is the slope of the line shown below? (-2,3) (-4,-9)
Answer:
6Step-by-step explanation:
Let the points be A and B
A ( - 2 , 3 ) -------> ( x1 , x2 )
B ( -4 , -9 ) -------> ( x2 , y2 )
Now, finding the slope:
[tex]slope \: (m) = \frac{y2 - y1}{x2 - x1} [/tex]
Plug the values
[tex] = \frac{ - 9 - 3}{ - 4 - ( - 2)} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 4 - ( - 2)} [/tex]
When there is a (-) in front of an expression in parentheses , change the sign of each term in expression
[tex] = \frac{ - 12}{ - 4 + 2} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 2} [/tex]
Reduce the fraction with -2
[tex] = 6[/tex]
Hope this helps..
Best regards!!
Drew likes to take the long way to school each morning. He walks 3 blocks west and then 3 blocks north to arrive at the school. Today he is running late and decides go directly to school to save time. (Assume there is nothing obstructing his path.) If one block is 310 feet, how many feet will he travel if he goes directly to school? Round to the nearest tenth of a foot.
Answer:
Distance travel by Drew = 1,315.21 feet (Approx)
Step-by-step explanation:
Given:
Total block in north = 3
Total block in west = 3
1 block = 310 feet
Find:
Distance travel by Drew
Computation:
Total distance in north = 3 × 310 = 930 feet
Total distance in west = 3 × 310 = 930 feet
Distance travel by Drew = √Total distance in north² + Total distance in west²
Distance travel by Drew = √930² + 930²
Distance travel by Drew = √864,900 + 864,900
Distance travel by Drew = √1,729,800
Distance travel by Drew = 1,315.21 feet (Approx)
The principal feature of the redesigned checks is a series of printed instructions that the company hopes will help merchants confirm a check’s authenticity, which includes reminders to watch the endorsement, compare signatures, and view the watermark while holding the check to the light.
(A) which includes reminders to watch the endorsement, compare signatures, and view
(B) which include reminders for watching the endorsement, to compare signatures and view
(C) by including reminders for watching the endorsement, comparing signatures, and viewing
(D) including reminders to watch the endorsement, comparing signatures and viewing
(E) including reminders to watch the endorsement, compare signatures, and view
Answer:
(E) including reminders to watch the endorsement, compare signatures, and view
Step-by-step explanation:
The principle features that will help the company to confirms checks authenticity. It include endorsements and compare the signatures with the designated signatories. If the signatures are matched correctly with the assigned signatories the check is hold in light to view the watermark on it.
In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture.
Answer:
18m square
Step-by-step explanation:
Formula for rectangular- based pyramid is L x W x H divided by 3
= 3 x 5 x 3.6 divided by 3 = 18
So you would need 18 m square for the sculpture
Please answer it now in two minutes
Answer:
y = 4
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
y × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 4
Answer:
y=4
Step-by-step explanation:
If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.
So, by the law of sines we can say that:
[tex]\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}[/tex]
Solving for y, we get:
[tex]sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4[/tex]
The net profit in dollars per day for a small business owner is given by the equation f(x) = -0.1x^2 + 6 x + 4, where x is the number of employees he hires. If he hires the number of employees that will maximize his profit, what will his profit be in dollars per day? (Enter an exact number.) dollars per day
Answer:
[tex]\large \boxed{\sf \ \ \text{The maximum profit is \$94 per day.} \ \ }[/tex]
Step-by-step explanation:
Hello,
The coefficient in [tex]x^2[/tex] is negative.
So, there is a maximum at the vertex point which is
[tex]x=-\dfrac{b}{2a}==\dfrac{-6}{-0.2}=\dfrac{6}{0.2}=30[/tex]
And then the maximum is f(30)=
[tex]-0.1\cdot 30^2+6\cdot 30 +4=-90 +180+4=94[/tex]
So the maximum profit is 94 $ per day.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Bob and Dan earned a total of $72
shoveling snow. If Bob earned 3 times as
much as Dan, how much did each boy
earn?
Answer:
see explanation
Step-by-step explanation:
If Dan earns $x then Bob earns $3x ( 3 times as much as Dan ), then
x + 3x = 72 , that is
4x = 72 ( divide both sides by 4 )
x = 18
Thus
Dan earns $18 and Bob earns 3 × $18 = $54
The earning of Bob will be 54 dollars and the earning of Dan will be 18 dollars.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Let the earning by Bob be x and the earning by Dan be y.
Bob and Dan earned a total of $72 shoveling snow. Then the equation will be
x + y = 72 ...1
If Bob earned 3 times as much as Dan. Then the equation will be
x = 3y ...2
Substitute the value of x in equation 1, then the equation will be
3y + y = 72
4y = 72
y = $18
Then the money earned by Bob will be
x = 3y
x = 3(18)
x = $54
Thus, the earning of Bob will be 54 dollars and the earning of Dan will be 18 dollars.
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How many real solutions In this problem
Answer:
D
Step-by-step explanation:
Given
y = x² + 1
y = x
Equating gives
x² + 1 = x ( subtract x from both sides )
x² - x + 1 = 0
Consider the discriminant Δ = b² - 4ac
with a = 1, b = - 1 and c = 1
b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3
Since b² - 4ac < 0 then there are no real solutions
please help ASAP. Which statement below is NOT true for the graph of a quadratic function? a) the axis of symmetry intersects the parabola at the vertex b) when the coefficient of x^2 is positive, the vertex of the parabola is a minimum point c)The vertex of a parabola is its highest or lowest level d) the parabola is symmetrical about the y-axis
Answer:
Step-by-step explanation:
All of these statements about a vertical parabola with known vertex are true.
The statement which is not always true about the graph of a quadratic function is option d) the parabola is symmetrical about the y-axis.
What is Parabola?A parabola is a open U shaped curve on a plane where all the points on the curve will be at an equal distance from a fixed point called focus and a fixed line called directrix.
Vertex of a parabola is the point where the parabola intersects with it's line of symmetry. So the vertex will always lie at the maximum point or the minimum point.
Axis of symmetry is the line that passes through the vertex of a parabola.
Graph of the quadratic equation will always be a parabola.
When the coefficient of x² is positive, then the vertex of the parabola will be at a minimum point and if the coefficient is negative, then the vertex will be at a maximum point.
The parabola is symmetrical to y axis only if the vertex of the parabola lies on the Y axis. So it will not be always true.
Hence the statement the parabola is symmetrical about the y-axis is not always true.
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how to do this question plz
Answer:
48.
Step-by-step explanation:
[tex]\frac{24\sqrt{72} }{3\sqrt{2} }[/tex]
= (24 / 3) * [tex]\frac{\sqrt{72}} {\sqrt{2} }[/tex]
= 8 * [tex]\frac{\sqrt{72} * \sqrt{2}} {\sqrt{2} * \sqrt{2} }[/tex]
= 8 * [tex]\frac{\sqrt{144}} {2}[/tex]
= 8 * (12 / 2)
= 8 * 6
= 48.
Hope this helps!
Andrew's bicycle has tires with a radius of 7 inches. What is the area of one of the bicycle tires, in terms of π?
Answer:
49π
Step-by-step explanation:
The formula for the area of a circle is,
[tex]\pi r^2[/tex]
If the radius is 7 inches we need to plug that in for r in the formula.
π(7)^2
7*7 = 49
Thus,
the area in terms of pi is 49π.
Hope this helps :)
Answer:
49πStep-by-step explanation:
[tex]r = 7\\A = ?\\A =\pi r^2\\A =\pi7^2\\A = 49\pi[/tex]
17. Mary bought 10 quarts of juice at the
grocery. How many gallons of juice did
she buy?
A 1.4 gal
C 3.5 gal
B 2.5 gal
D 4.5 gal
Pls help
Answer:
B 2.5 Gal
Step-by-step explanation:
Answer:
I think the correct answer may be B.
Step-by-step explanation:
Which line will have no solution with the parabola y - x + 2 = x2?
5
3+
N
-5 -4 -3 -4
2 3 4 5 X
th
-3
44+
-5
Answer:
yes
Step-by-step explanation: i agree its 3
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply. x = one-half y minus 3 2 x minus y = negative 6 2 x minus y = negative 3 x = one-half (y minus 3) y = 10 (x minus 1)
Answer: x=one-half y minus
Step-by-step explanation:
Answer:
x=1/2 y-3
Step-by-step explanation:
Two choises! Pick the right one!
Answer:
The function has a maximum value of 3 that occurs at x = 1.
Step-by-step explanation:
First, note that the leading coefficient is negative. This means that the parabola will curve downwards. Because of this, the function has a maximum. The maximum value will simply be the vertex.
The formula for the x-coordinate of the vertex is -b/2a.
a=-3, b=6, c=0
Plug in the numbers:
x=-(6)/2(-3)
=-6/-6=1
Now, plug 1 back into the original function:
-3x^2+6x
-3(1)^2+6(1)
=-3(1)+6
=-3+6
=3
Drag a statement or reason to each box to complete this proof.
If -5(x + 8) = -25, then x =
-3
Find the product. (5p + 2)2^
Answer:
25p^2 + 4 + 20p
Step-by-step explanation:
(5p + 2)^2 = (5p)^2 + (2)^2 + 2 × 5p × 2
= 25p^2 + 4 + 20p
8 7 12 7 11
10 7 12
Find:
a)the median
b) the range
c)the mode
Answer:
a) Median: 9
b) Range: 5
c) Mode: 7
Step-by-step explanation:
The median is the number in the middle.
First, you put the numbers in order: 7, 7, 7, 8, 10, 11, 12, 12
The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.
To find the range, you minus the highest number and the lowest number, 12-7=5.
Mode is the most occurring and repetitive number, in this case, 7, because it is written 3 times.
Hope this helps!!!
Answer:
[tex]\boxed{\mathrm {Median = 9}}[/tex]
[tex]\boxed{\mathrm{Range = 5}}[/tex]
[tex]\boxed{\mathrm{Mode = 7}}[/tex]
Step-by-step explanation:
The observations are:
8,7,12,7,11,10,7,12
In ascending order:
=> 7,7,7,8,10,11,12,12
A) Median => Middlemost no.
Median = 8,10
=> [tex]\frac{8+10}{2}[/tex]
=> [tex]\frac{18}{2}[/tex]
Median = 9
B) Range = Highest No. = Lowest No.
RANGE = 12-7
Range = 5
C) Mode => frequently occurring number
Mode = 7
Help me please
I’m having so much trouble
Answer:
Step-by-step explanation:
5 * 45 = 225
225+75=300
300/500=0.6
The tank will be 60% full.
If this helped, make sure to mark it as brainliest :D
Answer:
C.60%
Step-by-step explanation:
45 x 5 = 225 225 + 75 = 300
300 / 500 = 0.6 = 60%
how many unique planes can be determined by four noncoplanar points?
Answer:
Four unique planes
Step-by-step explanation:
Given that the points are non co-planar, triangular planes can be formed by the joining of three points
The points will therefore appear to be at the corners of a triangular pyramid or tetrahedron such that together the four points will form a three dimensional figure bounded by triangular planes
The number of triangular planes that can therefore be formed is given by the combination of four objects taking three at a time as follows;
₄C₃ = 4!/(3!×(4-3)! = 4
Which gives four possible unique planes.
Please help me!!!!!! I do not understand...
Answer:
the second one........the shape of the conic section os circle
An airline company advertises that 100% of their flights are on time after checking 5 flights from yesterday and finding that these 5 were on time.
a) What is population of interest?
b) What is the sample?
c) Was this a representative sample? Explain.
d) How should the company determine the percentage of their flights that are on time?
Answer with explanation:
Given: An airline company advertises that 100% of their flights are on time after checking 5 flights from yesterday and finding that these 5 were on time.
a) population: A large group of observations have characteristics related to the point of the study.
Here, population: "All flights operated by the company"
b) Sample: It is a subset of the population.
Here, Sample: "5 flights from yesterday"
(c)
Since the number of flights per day operated by an airline company is much larger than 5 ( generally in hundreds).
i.e. the sample is too small to be able to assure that the results are true.
Hence, this is not a representative sample.
(d) To determine the percentage of their flights that are on time we use the following formula:
(Number of flights are on time) ÷ (Total flights) x 100