The number of cars at a car dealership is reduced by 10% in the first sales quarter of the year. If the number of cars decreased an additional 20% over the second sales quarter of the year, then by what percent did the number of cars decrease over the two sales quarters? A) 25% B) 28% C) 30% D) 45%
Answer:
B) 28%=================
Let the initial price be x.
After the first sales quarter the price is reduced by 10% and became:
x - 10% = x - 0.1x = 0.9xAfter the second sales quarter the price is reduced by 20% and became:
0.9x - 20% = 0.9x - 0.2*0.9x = 0.9x - 0.18x = 0.72xThe decrease over the two quarters is:
x - 0.72x = 0.28xThis is equivalent of 28%, hence the correct answer choice is B.
The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm. Their present sum after cutting 2cm from each is 30cm. What is the length of the shorter pole? The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm . Their present sum after cutting 2cm from each is 30cm . What is the length of the shorter pole ?
Answer:
15 cm
Step-by-step explanation:
The length of the shorter pole can be found by forming and subsequently solving 2 equations.
Start by defining the variables that are going to be used in the working.
Let the original length of the shorter pole be a cm and that of the longer pole be b cm.
'Product' refers to the multiplication operation.
ab= 285 -----(1)
On the other hand, 'sum' refers to the addition operation.
Length of shorter pole after cutting= a -2
Length of longer pole after cutting= b -2
(a -2) +(b-2)= 30
a +b -4= 30
Adding 4 to both sides:
a +b= 30 +4
a +b= 34 -----(2)
From (2):
a= 34 -b -----(3)
Let's solve by substitution:
Substitute (3) into (1):
b(34 -b)= 285
Expand:
34b -b²= 285
b² -34b +285= 0
Factorise:
(b -15)(b -19)= 0
b -15= 0 or b -19= 0
b= 15 or b= 19
Substitute into (1):
a(15)= 285 or a(19)= 285
a= 285 ÷15 or a= 285 ÷19
a= 19 or a= 15
Since a <b, a= 15 and b= 19.
Thus, the length of the shorter pole is 15 cm.
solve for x for this problem
Answer:
x = 5 and 6
Step-by-step explanation:
1. Square both sides
x - 5 = (x - 5)(x - 5)
2. Simplify the right side
x - 5 = x^2 - 10x + 25
3. Add 5 to both sides
x = x^2 - 10x + 30
4. Subtract x from both sides
0 = x^2 - 11x + 30
5. Factor
0 = (x-5)(x-6)
x = 5,6
Answer:
x = 5 , x = 6
Step-by-step explanation:
[tex]\sqrt{x-5}[/tex] = x - 5 ( square both sides )
x - 5 = (x - 5)² ← expand using FOIL
x - 5 = x² - 10x + 25 ← subtract x - 5 from both sides
0 = x² - 11x + 30 ← in standard form
0 = (x - 5)(x - 6) ← in factored form
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x - 6 = 0 ⇒ x = 6
As a check
substitute these values into the equation and if both sides are equal then these values are the solutions.
x = 5
left side = [tex]\sqrt{5-5}[/tex] = [tex]\sqrt{0}[/tex] = 0
right side = 5 - 5 = 0
then x = 5 is a solution
----------------------------------
x = 6
left side = [tex]\sqrt{6-5}[/tex] = [tex]\sqrt{1}[/tex] = 1
right side = 6 - 5 = 1
then x = 6 is a solution
simplify (8x^2y^3)/(2x^4y)
Answer:
[tex]=\frac{4y^2}{x^2}[/tex]
Step-by-step explanation:
[tex]\frac{(8x^2y^3)}{(2x^4y)}[/tex]
[tex]=\frac{(8x^2y^3)}{(2x^4y)}\\[/tex]
[tex]=\frac{8y^2}{2x^2}[/tex]
[tex]=\frac{4y^2}{x^2}[/tex]
I Hope This helps :)
Find the solution to the system
of equations.
432G
K
3
-4-3-2-1 1 2 3 4
-1
==x+2
21
4234
([?], [ ])
Enter
Answer:
(-2, 0)
Step-by-step explanation:
The solution to the system is the point where the graphs intersect.
Simplify 1-4 can you show how you got the answer on a sheet of paper. Really need help
Answer:
first 1*3+1-3*4+1
then it is in fraction
the answer is -5
Which is the rate of change for the interval between 3
and 6 on the x-axis?
O -3
O -2
0 2
O 3
Answer: 2
Step-by-step explanation:
When x = 3, y = -2.
When x = 6, y = 4.
The average rate of change over the interval is:
[tex]\frac{-2-4}{3-6}=\frac{-6}{-3}=\boxed{2}[/tex]
graph the equation y+3=2(x+3)?
Answer:
see attached
Step-by-step explanation:
You recognize the equation of the line as being given in point-slope form:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
y +3 = 2(x +3) . . . . . . given equation
This tells you the point is (h, k) = (-3, -3), and the slope is m = 2.
__
You can graph the equation by plotting the point (-3, -3) and drawing a line with a slope of 2. It will rise 2 units for each unit to the right.
Determine which of the following statements about the given triangles is true.
Answer:
The answer be the 2 one
Step-by-step explanation:
I do it and it come right
Jack and Susan bought together 28 books. Susan bought 11 books. Which one of the
following equations represents the number of books bought by Jack? Let x be the
number of books bought by Jack.
Answer:
11 + x = 28
Step-by-step explanation:
The number of books they bought must add to 28.
13. Find the values of x and y in the diagram below.
א
9
13
7
y
3
10
17
Answer:
x = 2
y = 4
Step-by-step explanation:
Let's start with the 7 in the middle. Subtract the 1 on its upper left to get 6.
Add the 3 on its lower left to get 10.
so, 3 - x = 1. x = 2
17 - y = 13. y = 4
Question is attached………
Answer:
d. 11:15
Step-by-step explanation:
1) officer1: distance 75 miles, velocity 60mil/h; officer2: distance 25 miles, velocity 55mil/h;
2) time, which is spent officer1 is: 75/60=1.25[h]=75 [min]. If the officer1 leaves his office at 10:00, the arrival time is 11:15;
3) time which is spent officer2 is: 25/55=5/11[h]≈27[min]. The arrival time is 10:27.
4) finally, the both officers are in the required location at 11:15.
Question 2 of 11
What system of equations would you use to solve the problem below?
A test is worth 100 points. Multiple-choice questions are worth 3 points and
short-answer questions are worth 5 points. If the test has 28 questions, how
many multiple-choice questions are there?
If the number of multiple-choice questions is x and the number of short answer questions is y, then:
[tex]x+y=28\\\\3x+5y=100[/tex]
Jack has a rectangular piece of land, the area of which is represented by a1 = 9.5l. His brother has a different rectangular piece of land, the area of which is represented by a2 = l(14 − l). Let a represent the area in square meters and l represent the length in meters of the pieces of land. The two equations plotted on a graph meet at a point as shown in the image.
The area of the brothers’ pieces of land will be the same when the length is ______ meters.
Answer:2
Step-by-step explanation:
Answer: 13
Step-by-step explanation:
Given that G=ab find the percentage increase in G when both a and b
increase by 10%
The percentage change in G is 21 %
What is Percentage change ?Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.
It is given that
G = ab
when a is increased by 10% the new a will be = 1.1 a
When b is increased by 10% the new b will be 1.1 b
So,
G' = 1.1a *1.1 b
G' = 1.21 ab
G' = 1.21
(G' - G)*100/G = (1.21-1)*100/1
The percentage change is 21 %
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Find the critical point for f(x)=x^2-2x+4 and determine their nature.
Select one:
O a. (3, 1) minimum point
O b. (1, 3) minimum point
O c. (1, 3) maximum point
O d. (3, 1) maximum point
translate algebra 2 to standard form
Adding 2x to both sides, we get [tex]\boxed{2x+y=5}[/tex]
3 Three children share this chocolate equally.
What fraction does each child get?
Each child gets
CHALLENGE?
Answer: Each child gets 1/3
Step-by-step explanation: x/3
The surface area of a cone is 250 square centimeters. The height of the cone is double the length of its radius.
What is the height of the cone to the nearest centimeter?
A.
10 centimeters
B.
20 centimeters
C.
15 centimeters
D.
5 centimeters
Answer: C
Step-by-step explanation:
just took it
The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.
Given that, the surface area of a cone is 250 square centimetres. The height of the cone is double the length of its radius.
We need to find what is the height of the cone to the nearest centimetre.
What is the surface area of a cone?The area occupied by the surface/boundary of a cone is known as the surface area of a cone. It is always measured in square units. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as a curved surface area.
If the radius of the base of the cone is "r" and the slant height of the cone is "l", the surface area of a cone is given as total surface area, T = πr(r + l) square units
Now, let the radius of a cone be x.
Then the height of the cone is 2x.
Slant height=√x²+4x²
=√5x
So, the surface area of cone=πx(x+2.24x)
⇒250=3.14 × 3.24x²
⇒x²=24.57
⇒x=4.95≈5 centimetre
So, height=2x=10 centimetre
The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.
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The diagram shows a line joining O to P.
The gradient of the line is 2
The length of the line is √2645
Work out the coordinates of P.
Answer: (23, 46)
Step-by-step explanation:
The equation of the line is y = 2x, and we can thus represent point P as (x, 2x)
Substituting into the distance formula,
[tex]\sqrt{2645}=\sqrt{(x)^{2}+(2x)^{2}}\\\\2645=x^2 + (2x)^2\\\\2645=x^2 + 4x^2\\\\2645=5x^2\\\\529=x^2\\\\x=23[/tex]
Thus, the coordinates of P are (23, 46)
A line passes through the point (5,-11) and has slope of -2.
Find an equation of this line.
y = -2x – 1
y = 5x – 11
y = 5x – 2
y = -2x – 11
Answer:
y=-2x -1
Step-by-step explanation:
(y-y1) = m(x-x1)
y-(-11) = -2(x-5)
y+11 = -2x + 10
subtract 11 on both sides thus
y = -2x -1
Find the average of the numbers 6 4/7, 1 5/56, 9 1/7, 3 5/8. Write the solution as a mixed number or a fraction in lowest terms.
Answer:
[tex]\frac{187}{112}[/tex]
Step-by-step explanation:
Just add them all up in the calculator and divide by the number of numbers, which in this case is 4
Step-by-step explanation:
follow the steps in the attached
Graph the function f(x) = x+4 -1.
This can be simplified to [tex]f(x)=x+3[/tex], and is thus a line with a slope of 1 and a y-intercept of 3.
Suppose two sets of scores have the same mean, but different
standard deviations, o, and o₂, with 0₂ > 0₁ Which statement
1
2
best describes the variability of these data sets?
02
(1) Data set one has the greater variability.
(2) Data set two has the greater variability.
(3) The variability will be the same for each data set.
(4) No conclusion can be made regarding the variability of
either set.
Data set two has the greater variability option (2) Data set two has the greater variability is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
Two sets of scores have the same mean, but different standard deviations.
σ₁ and σ₂ (σ₂ > σ₁)
Coefficient of variation = [SD/(mean)]×100
[tex]\rm CV = \dfrac{\sigma }{|x|}\times100[/tex]
σ₂ > σ₁
Divide by |x| on both sides
σ₂/|x| > σ₁/|x|
[tex]\rm \dfrac{\sigma }{|x_1|}\times100 > \dfrac{\sigma }{|x_2|}\times100[/tex]
(CV)₂ > (CV)₁
Thus, data set two has the greater variability option (2) Data set two has the greater variability is correct.
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Camp pine cone has 20 campers for every 6 counselors if there are 60 campers how many counselors are needed
Answer:
18
Step-by-step explanation:
20*3=60 so do 6*3 to get your answer
Write 1 3/4 as a decimal and as a percent
Answer:
Decimal: 1.75
Percentage: 175%
Hey there!
1 3/4
= 1 * 4 + 3 / 4
= 4 + 3 / 4
= 7 / 4
= 7 ÷ 4
= 1.75
= 1.75 * 100
= 175%
Therefore, your answer should be:
• 1.75 (as your decimal form)
• 175% (as your percentage form)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A horse was galloping at average speed of 50km/hr for the first 12 minutes. For the next x minutes, the horse slowed down and it’s average speed decreases to 30km/hr. The average speed of the horse for the whole journey is 45km/h. Find its total distance travelled in kilometres
The total distance travelled is 1075.91 km.
What is average speed?The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.
45 * (x +12)= 50* 1/5 + 1/2 *x
45x + 540= 10+ 0.5 x
44.5 x = 530
x= 11.91 (neglect the negative sign cause time can't be negative)
So, distance= 45* 23.91 = 1075.91 Km
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What is the solution to the following equation?
-3+x= -8
A. x = -5
B. x=5
C. x = 11
D. x=-11
Answer:
[tex]\mathsf {A. x = -5}[/tex]
Step-by-step explanation:
[tex]\implies \mathsf {-3 + x = -8}[/tex]
[tex]\implies \mathsf {x = -8 + 3}[/tex]
[tex]\implies \mathsf {x = -5}[/tex]
Find the nth term of this quadratic sequence
4, 16, 36, 64, 100, ...
Answer:
144, 196, 256
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A retired woman has 70,000toinvestbutneedstomake
9,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. Set up and solve the equation for how much the woman should invest in each option to sustain exactly a $9,000 annual return.
Answer:
$51,250 at 15%$18,750 at 7%Step-by-step explanation:
The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.
__
setupLet x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...
0.15x +0.07(70000-x) = 9000
__
solutionSimplifying the equation gives a 2-step linear equation.
0.08x +4900 = 9000 . . . . simplified
0.08x = 4100 . . . . . . . . . . subtract 4900
x = 51,250 . . . . . . . . . . . .divide by 0.08
70000 -x = 18,750
The woman should invest $51,250 at 15% and $18,750 at 7%.
