The profit as a percentage of the cost price is 20%
Finding the profit as a percentage of the cost priceFrom the question, we have the following parameters that can be used in our computation:
Car cost #450,000It;s being sold for #540,000.The profit is the difference beyween the selling price and the coste price
So, we have
Profit = 540000 - 450000
Evaluate
Profit = 90000
Next, we have
Percentage = Profit/Cost price * 100
This gives
Percentage = 90000/450000* 100
Evaluate
Percentage = 20%
Hence, teh percentage is 20%
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Answer:
Step-by-step explanation:
To find the profit as a percentage of the cost price, we need to calculate the profit first.
Profit = Selling price - Cost price
Profit = #540,000 - #450,000
Profit = #90,000
Now we can calculate the profit percentage as follows:
Profit percentage = (Profit / Cost price) x 100
Profit percentage = (#90,000 / #450,000) x 100
Profit percentage = 20%
Therefore, the profit as a percentage of the cost price is 20%.
The table shows the net revenue in millions of dollars of a company every three months for two years. An exponential function can be used to model the data.
Company
Time, x (months) Net Revenue, r(x) (millions of dollars)
3 274
6 389
9 467
12 560
15 960
18 1,100
21 1,320
24 1,584
Which function best models the data?
r(x)=223.06(1.09)^x
r(x)=1.09(223.06)^x
r(x)=2,232.91(0.92)^x
r(x)=0.92(2,232.91)^x
An exponential function that best models the data include the following: A. [tex]r(x) = 223.06(1.09)^x[/tex]
How to determine the equation of line of best fit?In this scenario, the Company Time, x (months) would be plotted on the x-axis (x-coordinate) of the scatter plot while the Net Revenue, r(x (millions of dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the Company Time, x (months) and the Net Revenue, r(x (millions of dollars), an exponential equation for the line of best fit is given by:
[tex]r(x) = 223.06(1.09)^x[/tex]
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The chemical element mercury has a melting point of -39. The melting point of bromine is -7. Which statement is an accurate comparison of these melting points?
From the given statements, the first statement which states, the melting point of mercury is 32 degrees cooler than the melting point of bromine is correct.
Given that, the melting point of mercury = -39
the melting point of bromine = -7
the difference between both melting points = -39 - (-7) = -32
In math, as we go to the negative values, the value of the number decreases. [-7 > -39]
From the above analysis, we can conclude that the melting point of mercury is 32 degrees cooler than the melting point of bromine. So, the option A which is the first statement is correct from the given image.
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NEED HELP ASAP!! WILL MARK BRAINLEST!!! PLS DONT GUESS IF YOU DONT KNOW!!
Answer:
it is A
Step-by-step explanation:
def correct! a+ student
Answer: D
Step-by-step explanation:
The answer has to be A or D because they're the only ones that look like real box-and-whisker plots. The mean is the line in the middle of the "box", so calculating the mean should be easy enough.
Add all the numbers together and then divided by the number of numbers.
56+72+75+98+73+86+48+95+69+88+75+92 = 972
There are 12 numbers.
972/12 = 77.25
Only option D represents the proper mean.
Round 473,615 to the nearest hundred
Rounding 473,615 to the nearest hundred gives us 473,600.
We have,
Rounding a number to the nearest hundred means that you are looking at the digit in the tens place of the number.
If that digit is 5 or greater, you round up the digit in the hundreds place, and if it is less than 5, you keep the digit in the hundreds place the same.
In the case of 473,615, the digit in the tens place is 1, which is less than 5. So we keep the digit in the hundreds place (3) the same and round the remaining digits to zero.
Thus,
Rounding 473,615 to the nearest hundred gives us 473,600.
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A popular Dilbert cartoon strip (popular among statisticians, anyway) shows an allegedly “random” number generator produces the sequence 999999 with the accompanying comment, “That’s the problem with randomness: you can never be sure.” Most people would agree that 999999 seems less “random” than, say, 703928, but in what sense is that true? Imagine we randomly generate a six-digit number, i.e., we make six draws with replacement from the digits 0 through 9. (a) What is the probability of generating 999999?
(b) What is the probability of generating 703928?
(c) What is the probability of generating a sequence of six identical digits?
(d) What is the probability of generating a sequence with no identical digits? (Comparing the answers to (c) and (d) gives some sense of why some sequences feel intuitively more random than others
.)
(e) Here's a real challenge: what is the probability of generating a sequence with exactly one repeated digit?
(a) the probability of generating 999999 is [tex](1/10)^6[/tex]
(b) the probability of generating 703928 is [tex](1/10)^6[/tex]
(c) the probability of generating a sequence of six identical digits is [tex](1/10)^6[/tex]
(d) the probability of generating a sequence with no identical digits is 15,120/1,000,000.
(e) the probability of generating a sequence with exactly one repeated digit is[tex]10 * 6 * (9^4).[/tex]
What is probability?Probability is described as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
The probability of generating a sequence with no identical digits is calculated as (10/10) * (9/10) * (8/10) * (7/10) * (6/10) * (5/10) = 15,120/1,000,000.
We start by choosing the digit to be repeated, which can be done in 10 ways and the next thing is to choose the position of the repeated digit, and can be done in 6 ways.
We then see that remaining four positions can be filled out with any of the other 9 digits and this can also be done in [tex]9^4[/tex] ways.
So we can conclude that the number of possibilities in this case is [tex]10 * 6 * 9^4.[/tex]
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Which of the following table represents a linear function?
The table that represents a linear function is the second table.
Which of the tables represents a linear function?A linear function is written as:
y = ax + b
We can see that for each increase of 1 unit in the value of x, the value of y increases by a units.
Then we need to identify the table where the increases in the y-value are constant.
With that in mind we can discard options 1, 3 and 4.
Wher particularly options 1 and 4 show that sometimes the y-value increases and sometimes decreases, that is why we discard these.
Then the remainign option must be the correct one, which is the second option.
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According to the NCAA 7.1% of high school women cross country runners will end up running cross country at the collegiate level. If 30 female high school cross country runners are selected at random, what is the probability that exactly 2 of them will run cross country in college. Express your answer as a probability between 0 and 1 and round your answer to three decimal places.
Answer:
Step-by-step explanation:
A population of 10 000 insects decreases by 9% every year. Write a formula to calculate the number of insects
left after a certain number of years. Use your formula to determine how many years it would take for the insect
population to reduce to less than half its present size.
Answer:
f(t) = 10000·0.91^5about 7.3 yearsStep-by-step explanation:
You want the formula that describes the decay of an insect population from 10000 by 9% per year, and the years it takes for the population to decline by half.
Exponential functionAn exponential function will have the form ...
f(t) = (initial value) · (growth factor)^t
where ...
growth factor = 1 + growth rate
ApplicationHere, the growth rate is -9% per year, so the growth factor is ...
1 -9% = 1 -0.09 = 0.91
The population is then ...
f(t) = 10000·0.91^t . . . . . formula for number of insects
Half lifeWe can solve for t when f(t) = 5000 (half the original population):
5000 = 10000·0.91^t
1/2 = 0.91^t . . . . . . . . . . . divide by 10,000
ln(1/2) = t·ln(0.91) . . . . . take logarithms
t = ln(0.5)/ln(0.91) ≈ 7.3496 ≈ 7.3 . . . . years
It would take about 7.3 years for the population to reduce to less than half its present size.
__
Additional comment
We have rounded the time period to the nearest tenth, 7.3 years. At the end of that period, the population is modeled to be about 5023, not quite "less than half." To get below half the original population would take almost 7.35 years.
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1) Use the figure to answer the
following question.
What is the volume of the following figure?
9 cubic units
10 cubic units
20 cubic units
1 cubic unit
Answer:
10
Step-by-step explanation:
If you multiply the width with the length and height , you will get nine, then add that lonely brick on top to get ten
What is the range of this data ?
60 65 70 75 80 85 90 95 100
Find the quotient and remainder using synthetic division for
x^5
-
x^4
+
1
x^3
-
1
x^2
+
1
x
-
10
/x
-
1
The quotient is
The remainder is
The solution to the given problem of equation comes out to be quotient : x² +x+6+2/(x+2) and remainder is 2.
We have to find the remainder and quotient
Given : synthetic division for
x³ + 3x² + 8x + 14
------------------------
x + 2
Write the problem in synthetic division format
-2 | 1 3 8 14
-2 -2
------------------------
1 1 6
Carry down the leading coefficient, unchanged, to below the division symbol
-2 | 1 3 8 14
-2 -2
---------------------------
1 1 6
Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:
1(-2)=-2
-2 | 1 3 8 14
-2 - 2
------------------
1 1 6
=> We get:
As x² +x+6+ 2/(x+2)
and remainder is 2
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Ms. Toney bought a rug for her classroom. The rug is 8 feet wide. The diagonal length of the rug is 14 feet. What would be the length of the rug she bought?
Answer:
11.49
Step-by-step explanation:
a^2+b^2=c^2
think of this as a triangle, we are going to use Pythagorean theorem.
the hypotenus is 14 ft and one of the legs is 8 ft. so the other leg is x
8^2 + x^2 = 14^2
64 + x^2 = 196
subtract the 64 on both sides
x^2 = 132
to counter the square we square root it
so x = the square root of 132 which comes out to a decimal
11.489....
rounded it would be 11.49
hope this helped
5. Find the volume of the pyramid below? 4. Find the volume of the cone below.
40m
30m
52m
The volume of the rectangular pyramid is 20800 m³.
How to find the volume of a pyramid?The volume of the pyramid can be found as follows:
The pyramid is a rectangular base pyramid. Therefore,
volume of the pyramid = 1 / 3 Bh
where
B = base areah = height of the pyramidTherefore,
B = 52 × 30
B = 1560 m²
volume of the pyramid = 1 / 3 × 1560 × 40
volume of the pyramid = 62400 / 3
volume of the pyramid = 20800 m³
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Tim brought $40.50 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1
4
as much as the souvenir, and the souvenir cost
2
3
the cost of the pass. Tim had $2.00 left over after buying these items.
What was the cost of each item?
Answer:
Let x be the cost of the pass.
Then the cost of the souvenir is (2/3)x.
The cost of the burger is (1/4) of the cost of the souvenir, which is (1/4)(2/3)x = (1/6)x.
The total cost of the items is x + (2/3)x + (1/6)x = (11/6)x.
Tim had $2.00 left over after buying these items, so we can set up the equation:
(11/6)x + 2 = 40.50
Solving for x, we get:
x = 18
Therefore, the cost of the pass is $18, the cost of the souvenir is (2/3)($18) = $12, and the cost of the burger is (1/6)($18) = $3.
Which two statements about angles on a transversal crossing parallel lines contradict each other?
I. ∠1 and ∠2 are same-side interior angles.
II. m∠1 = m∠2
III. m∠1 + m∠2 = 90
The solution is: I. ∠1 and ∠2 are same-side interior angles and,
III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.
Here, we have,
given that,
We have to find which two statements about angles on a transversal crossing parallel lines contradict each other.
we know that,
If a transversal intersects or crosses parallel lines, adjacent angles are supplementary.
Corresponding angles are those that are in the same relative position, between the crossing line and the parallel lines.
now, we have,
I. ∠1 and ∠2 are same-side interior angles it can be possible.
Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines.
Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary. If , then m ∠ 1 + m ∠ 2 = 180 ∘ .
so, if number-l is true, so, we get,
II. m∠1 = m∠2 may be true,
III. m∠1 + m∠2 = 90, never can be true.
so, we get,
if, l. holds then lll. contradicts that.
Hence, The solution is: I. ∠1 and ∠2 are same-side interior angles and,
III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.
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The area of the trapezium, pqrs is
Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!
To start, let's quickly review what a trapezium is. A trapezium, also known as a trapezoid, is a four-sided geometric shape with two parallel sides (called the bases) and two non-parallel sides (called the legs). The distance between the two parallel sides is known as the height.
In order to find the area of a trapezium, we use the formula:
Area = (sum of bases x height) / 2
So for trapezium PQRS, we need to identify the length of its two bases and its height in order to use this formula.
Without any specific measurements given in your question, I'll assume we don't have any numerical values to work with. Instead, let's use variables to represent the length of each base and the height.
We can call the shorter base PQ, and the longer base SR. Let's say PQ has a length of 'a' units, and SR has a length of 'b' units. For the height, let's call it h.
So, the formula for the area of trapezium PQRS becomes:
Area = ((a + b) x h) / 2
This means that to find the area of the trapezium, we simply need to know the lengths of the two bases (a and b) and the height (h).
Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!
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2 divided by blank equals 0.2
Answer:
10
Step-by-step explanation:
2 / 10 = 0.2
2 divided by ten is two-tenths.
Answer: 2 divided by 10 is 0.2
If the perimeter of the large square tile is 48 inches
and the perimeter of the smaller square is 16 inches,
what is the perimeter of one of the isosceles
trapezoids?
Answer: 27.3 inches
Step-by-step explanation:
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer: 29.9986-----30.0 degrees
Step-by-step explanation:
x = [tex]tan^-^1(5.6/9.7)\\\\toa[/tex]
[tex]\tan(x )=\cfrac{\stackrel{opposite}{5.6}}{\underset{adjacent}{9.7}} \implies \tan^{-1}(~~\tan( x )~~) \approx \tan^{-1}\left( 0.58 \right) \\\\\\ x \approx\tan^{-1}\left( 0.58 \right)\implies x \approx 30.0^o[/tex]
NO LINKS!! URGENT HELP PLEASE!!
What is the surface of this problem? Please show work!!
Answer:
720 m^2
Step-by-step explanation:
Solution:
The formula for the surface area of a triangular prism is:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
= (S1 +S2 + S3)L + bh
where,
b is the bottom edge of the base triangle,h is the height of the base triangle,L is the length of the prism andS1, S2, and S3 are the three edges (sides) of the base triangle(bh) is the combined area of the two triangular faces [2 × (1/2 × bh)] = bhGiven:
side 1 (S1) : 5 m
side 2(S2): x m
side 3(S3): 12 m
length (l)=22m
Here we need to find side 2, we can easily find it using Pythagoras' theorem.
a^2+b^2=c^2
5^2+12^2=x^2
x^2=169
x=[tex]\sqrt{169}=13 m[/tex]
therefore, side 2 is 13 m.
Substituting value in the formula
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
= (S1 +S2 + S3)L + bh
Surface Area=(5+13+12)*22+5*12= 720 m^2
Answer:
720 m²
Step-by-step explanation:
The given diagram shows a triangular prism.
A triangular prism consists of two congruent triangular bases and three rectangular faces connecting these bases.
To calculate the surface area of the triangular prism, we first need to calculate the length of the hypotenuse of the right triangular base. To do this, we can use Pythagoras Theorem:
[tex]\begin{aligned}\sf Hypotenuse\;of\;triangular\;base&=\sqrt{5^2+12^2}\\&=\sqrt{25+144}\\&=\sqrt{169}\\&=13\; \sf m\end{aligned}[/tex]
The surface area of a triangular prism is the sum of the areas of all its faces. Therefore:
[tex]\begin{aligned}\sf Total\;surface\;area&=2\left(\dfrac{1}{2} \cdot 5 \cdot 12\right)+12\cdot 22+5 \cdot 22+13 \cdot 22\\\\&=60+264+110+286\\\\&=720\; \sf m^2\end{aligned}[/tex]
Therefore, the total surface area of the given triangular prism is 720 m².
Solve the following system of equations a2+b2 ; 3a2 -2ab-b2
The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).
The given system of equations can be solved using the substitution method. We can begin by solving the first equation,[tex]a^2 + b^2[/tex], for either a or b. Let's solve for a:
[tex]a^2 + b^2 = 0[/tex]
[tex]a^2 + b^2 = 0[/tex]
[tex]a^2 = -b^2[/tex]
[tex]a = \pm\sqrt(-b^2)[/tex]
We can substitute this expression for a into the second equation, [tex]3a^2 - 2ab - b^2 = 0[/tex], and simplify:
[tex]3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0[/tex]
[tex]3b^2 - 2b^2 - b^2 = 0[/tex]
0 = 0
Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation [tex]a^2 + b^2 = 0[/tex] will also satisfy the equation [tex]3a^2 - 2ab - b^2 = 0[/tex]
However, the equation [tex]a^2 + b^2 = 0[/tex] only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).
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Given m ∥ n, find the value of x.
Answer:
x=20
Step-by-step explanation:
On line n, the two unknown angles are supplementary, so we need their sum to be 180° and we can find x that way:
(6x-4)°+(3x+4)°=180°
6x+3x-4+4=180
9x=180
x=20
A right triangle has a hypotenuse of 15 centimeters.
What are possible lengths for the two legs of the
triangle?
Answer:
Step-by-step explanation:
Since the given figure is a right triangle, we can use Pythagorean Theorem
where c² = a² + b²
c = 15
15² = a² + b²
Since 15 is the hypotenuse, we can then say that the possible legs of the triangle are less than 15.
225 - a² = b²
we will do trial and error
let a be 14
225 - 14² = b²
b = √29
a = 14cm, b = √29cm, c = 15cm
let a be 13
225 - 13² = b²
b = 2√14
a = 13cm, b = 2√14cm, c = 15cm
let a be 12
225 - 12² = b²
b = 9
a = 12cm, b = 9cm, c = 15cm
You can solve for other possible values using the same process as above. Since there are no conditions whether the lengths of the legs should be a whole number or not then the above dimensions can be considered. If you're looking for an answer that consists of whole numbers then the answer would be a = 12cm, b = 9cm and c = 15cm
Find the slope of each line.
Answer:
Step-by-step explanation:
slope is rise over run or y over x
Let m be the slope
On this case, simply count the units for both x and y from tip to tip of the line segment
m = y/x
direction of the line is up and right so the sign is both positive
m = 4/1
m = 4
m = y/x
direction of the line is down and right so y is negative and x is positive
m = -3/4
HELP! NEED ANSWERS FAST
Answer:
BF×BA= DF×CF
9×2=3x
x = 6
AB=9
CD=11
Gina puts $5500 into an account earning 5.25% interest compounded continuously how long will it take for the amount in the account to go to $7450
Using the formula of compound interest, the number of years is 7.6 years
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
The formula of compound interest is given as;
[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]
A = Compounded InterestP = Principalr = raten = number of times compoundedt = number of years.But in this case, the interest was compounded continuously
[tex]A = Pe^r^t[/tex]
Substituting the values into the formula;
[tex]7450 = 5500e^(^0^.^0^5^2^5 ^* ^t^)[/tex]
Solving for t;
t = 7.6 years
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Johnny uses a wheelbarrow to move planting soil to a delivery truck. The volume of planting soil that fits in the wheelbarrow measures
2
2 feet by
3
3 feet by
1.5
1.5 feet. The delivery truck measures
11
11 feet by
8
8 feet and is
6
6 feet tall. Johnny puts planting soil in the delivery truck until the truck is
70
70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is
70
70% full?
The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.
What is the volume of a solid?The volume of a solid is the three dimensional space the solid occupies.
The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;
Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³
Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³
70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³
The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0
The number of times Johnny needs to use the wheelbarrow is about 41 times
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Polygon PSRT is drawn with vertices at P(1, 5), S(1, 0), R(−2, −3), T(−4, 2). Determine the image vertices of P′ if the preimage is rotated 90° counterclockwise.
P′(1, 5)
P′(−1, −5)
P′(5, −1)
P′(−5, 1)
The image polygon P'S'R'T' has vertices P'(-5, 1), S'(0, -1), R'(3, -2), and T'(-2, -4).
To determine the image vertices of P' when the preimage is rotated 90° counterclockwise, we can use the following formula:
(x', y') = (-y, x)
where (x, y) are the coordinates of the preimage vertex, and (x', y') are the coordinates of the image vertex after rotation.
Using this formula for each vertex of the polygon PSRT, we get:
For P(1, 5), rotating 90° counterclockwise gives us P'(-5, 1).
For S(1, 0), rotating 90° counterclockwise gives us S'(0, -1).
For R(-2, -3), rotating 90° counterclockwise gives us R'(3, -2).
For T(-4, 2), rotating 90° counterclockwise gives us T'(-2, -4).
Therefore, the image polygon P'S'R'T' has vertices P'(-5, 1), S'(0, -1), R'(3, -2), and T'(-2, -4).
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polar point : (6,3π).
Find three additional polar representations of the point, using −2 < < 2. (Enter your answers in order from smallest to largest first by r-value, then by -value.)
Find three additional polar representations of the point, using −2π<θ<2π. (Enter your answers in order from smallest to largest first by r-value, then by θ-value.) (r,θ)= ( (r,θ)r= ( (r,θ)= ( Question: That's it! Find three additional polar representations of the point, using −2π<θ<2π.
in how many ways can first , second , and third prizes be awarded in a cont with 925 contestants? assume there is no ties
Answer:
Step-by-step explanation:
[tex]\frac{925!}{(925-3)!}= 923*924*925=788,888,100[/tex]
To determine the number of ways the first, second, and third prizes can be awarded in a contest with 925 contestants, we can use the concept of permutations.
For the first prize, there are 925 contestants eligible to win. After the first prize is awarded, there are 924 remaining contestants for the second prize. Finally, for the third prize, there are 923 remaining contestants.
The number of ways to award the prizes can be calculated as the product of the number of choices for each prize:
Number of ways = 925 * 924 * 923
Calculating this expression, we find:
Number of ways = 779,449,100
Therefore, there are 779,449,100 ways to award the first, second, and third prizes in the contest with 925 contestants.