The mistake she had done is she should have reversed the inequality as per the division property of inequality.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
The inequality is:
500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10
Given:
Jamie had $500 in her savings account.
She wants to have at least $200 left in the account at the end of the school year.
The inequality she had done is
500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10
But when she was dividing she should have reversed the inequality as per the division property of inequality.
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another equation for y = 8x + 7
Select the correct answer.
What is √x^9y^4
in simplest form?
Answer:
x^3y^2
Step-by-step explanation:
[tex]\sqrt{x^9y^4}\\ =\sqrt{x^9}\sqrt{y^4}\\ = x^3y^2[/tex]
Can someone help with this pls
Answer:
This is C
Step-by-step explanation:
The slope is 4, meaning the integers are 4, 8, 12, 16, 20 etc. But then the last point is seen to be 40, meaning the answer is C because it is from 0-40 with a slope of 4.
Find the value
of each variable.
Answer:
y=37 degrees(vertical angles)
x=180-37(linear pair)=143 degrees
z=143 degrees(vertical angles)
Hope it helps!
Answer:
x = 180° - 37° = 143°
y = 37°
z = 180° - 37° = 143°
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 0.69(1.03)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the price f(t), in dollars, of product B after t years:
t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04
Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)
Answer:
A) 3%
B) Product A
Step-by-step explanation:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Part A
Product A
Assuming the function for Product A is exponential:
[tex]f(x) = 0.69(1.03)^x[/tex]
The base (b) is 1.03. As b > 1 then it is an increasing function.
To calculate the percentage increase/decrease, subtract 1 from the base:
⇒ 1.03 - 1 = 0.03 = 3%
Therefore, product A is increasing by 3% each year.
Part B
[tex]\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100[/tex]
To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:
[tex]\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%[/tex]
Check using different two consecutive values of f(t):
[tex]\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%[/tex]
Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.
Although the question has not asked, we can use the given information to easily create an exponential function for Product B.
Given:
a = 10,100b = 1.01n = t - 1 (as the initial value is for t = 1 not t = 0)[tex]\implies f(t) = 10100(1.01)^{t-1}[/tex]
To check this, substitute the values of t for 1 through 4 into the found function:
[tex]\implies f(1) = 10100(1.01)^{1-1}=10100[/tex]
[tex]\implies f(2) = 10100(1.01)^{2-1}=10201[/tex]
[tex]\implies f(3) = 10100(1.01)^{3-1}=10303.01[/tex]
[tex]\implies f(4) = 10100(1.01)^{4-1}=10406.04[/tex]
As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.
A projector was sold after allowing 10% discount on the marked price and levying 13% VAT .If the selling price of the projector after discount is Rs 5,850 , less than its selling price with VAT, find the marked price of the projector.
The marked price of the projector is $50,000.
What is the marked price?The price of the projector after the discount can be represented with:
(100 - 10%)x - 90%x = 0.90x
Where x is the marked price
The price of the projector after the VAT is : (1.13) x 0.90x = 1.02x
Difference in price = 1.02x - 0.90x = 5850
0.12x = 5850
x = 5850 / 0.12
x = $50,000
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Which pyramid has a greater volume, and how much greater is its volume? A rectangular pyramid on the left with a base of 7 inches by 6 inches and height of 3 inches. A rectangular pyramid on the right with a base of 4 inches by 3 inches and a height of 10 inches. The volume of the pyramid on the left is greater by 2 inches cubed. The volume of the pyramid on the left is greater by 6 inches cubed. The volume of the pyramid on the right is greater by 2 inches cubed. The volume of the pyramid on the right is greater by 6 inches cubed
The volume of the pyramid on the left is greater by 8 inches cubed
We have given that,
A rectangular pyramid on the left with a base of 7 inches by 6 inches and a height of 3 inches.
A rectangular pyramid on the right with a base of 4 inches by 3 inches and a height of 10 inches.
The volume of the pyramid on the left is greater by 2 inches cubed. The volume of the pyramid on the left is greater by 6 inches cubed.
The equation for finding the volume of a pyramid is,
What is the volume of a pyramid?lwh/3
when you input the values of the two pyramids into this equation you get the left pyramid having a volume of 128 inches cubed and the right pyramid having a volume of 120 inches cubed.
Therefore, 128 - 120 = 8
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Estimate the value of
0.581 -0.246
The value of expression is,
⇒ 0.335
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ 0.581 - 0.246
Now,
Since, The expression is,
⇒ 0.581 - 0.246
After subtraction we get;
⇒ 0.581 - 0.246
⇒ 0.335
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The graph shows the prices of different numbers of bushels of corn at a store in the current year. The table shows the prices of different numbers of bushels of corn at the same store for the previous year.
Part A: Describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. (5 points)
Part B: How many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? Show your work. (5 points)
#1
Take any two points
(3,24)(6,48)Slope
m=48-24/6-3m=24/3m=8#2
(3,21)(6,42)Slope:-
m=42-21/6-3m=21/3m=7Difference
1$Answer:
Part a you find the rate of change by finding the slope of the line the value is 8 it is (y2-y1)/(x2-x1) 48-24/6-3=24/3=8
Part b current year is 8 dollars a bushel and previous year is 7 dollars
Step-by-step explanation:
I need help asp. Identifying Geometric Figures.
Answer:
The angle created by OX and OZ is angle XOZ
The two rays that create YOX are ray OX and ray OY
The center of the circle is point O
Step-by-step explanation:
The image attached below shows a circle with a center at point O at which several rays meet to form the following angles, namely:
ray OX and ray OZ meet at center O to form angle XOZ.
ray OX and ray OY meet at the center O to form angel YOX.
Therefore:
The angle created by rays OX and OZ is <XOZ
The two rays that created <YOX are: OX and OY
The center of the circle is point O.
I hope this is helpful.
The proportional relationship between two variables, y and z, is represented by y = 11/2z. What is the constant of proportionality from z to y?
Answer:
Step-by-step explanation:
Comment
The constant you want is just the reciprocal of the constant you have been given. You can show it this way
y = 11/2 z Multiply both sides by 2
2y = 11z Divide both sides by 11
Answer
2/11 y = z
What is the vertex of the function f(x)=|x-9|+2
Answer:
vertex = (9, 2 )
Step-by-step explanation:
given the absolute value function
f(x) = a |x - h | + k
with vertex = (h, k )
then
f(x) = | x - 9 | + 2
has vertex = (9, 2 )
6.11.4 Test(TST): Circles Without Coordinates). The questions are in the document.
The value of AOB and BOC based in the information given in the circle will be 53°.
How to calculate the values in the circle?From the information given, the central angle is the angle that the vertex is at the center of the circle.
It was stated that OB bisects AOC. Therefore, since AOB is 53°, BOC is also 53°.
The value of AOC will now be:
= AOB + BOC
= 53° + 53°
= 106°
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rne subtracted 6x3 2x
find the difference.
from -3.x3 +
4x - 7. Use the drop-down menus
to identify the steps Lorne used
(-3x' + 5x7,+ 4x - 7) + (-6x3 + 2x -3)
(-3x°) + 5x2 + 4x + (-7) + (-6x3) + 2x + (-3)
[(-3x*) + (-6x°)] + [4x + 2x] + [(-7) + (-3)] + [5x2)
-9x° + 6x + (-10) + 5x2
-9x' + 5x2 + 6x - 10
If the price of an apple is Rs. 40, find the number of apples that can be brought for Rs. 200.
Answer:
5
Step-by-step explanation:
Divide 200 by 40 to get 5.
Answer:
ig 5 Apples can be Brought with Rs. 200
Step-by-step explanation:
Rs. 40 = 1 apple
Rs. 200 = ? Apple
therefore 5 apples can be brought...
Hope it Helps!!!
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form
Answer:
y = 3/4x + 2
Step-by-step explanation:
let me know if you want an explanation :))
1.Simplify using suitable properties
(i) 13−51+2
Answer:
This is my answer:
Step-by-step explanation:
The graph of which function has a minimum located at (4, –3)?
f(x) = one-halfx2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = one-halfx2 – 4x + 5
f(x) = 2x2 – 16x + 35
The parabola with the minimum at (4, -3) is the third option:
[tex]y = 0.5*x^2 - 4x + 5[/tex]
Which of the given parabolas has a minimum at (4, -3)?
Remember that for a parabola of the form:
[tex]y = a*x^2 + b*x + c[/tex]
If a > 0, the minimum is at the x-value of the vertex:
[tex]x = \frac{-b}{2a}[/tex]
If a < 0, there is no minimum (so we discard option 2).
Taking the third option:
[tex]y = 0.5*x^2 - 4x + 5[/tex]
The x-value of the vertex is:
[tex]x = \frac{-(-4)}{2*0.5} = 4[/tex]
As expected.
To get the y-value of the vertex (and minimum) we just evaluate the parabola equation in x = 4.
[tex]y = 0.5*(4)^2 - 4*4 + 5 = -3[/tex]
So the minimum is at (4, -3), as expected, so that is the correct option.
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what are the true statements
The largest number of Oscars received by a film in year X was 4. This was different in previous years. Below is a probability distribution for the number of Oscars per Oscar winning film. What is the standard deviation of this distribution
The standard deviation of the given discrete distribution, considering it's formula, is of 1.195.
How to find the mean and the standard deviation of a discrete distribution?The mean is given by the sum of the multiplications of each outcome by it's probability.The standard deviation is given by the square root of the sum of the squares of each outcome subtracted by the mean, multiplied by it's probability.Researching this problem on the internet, the distribution is given by:
P(X = 1) = 0.56.P(X = 2) = 0.23.P(X = 3) = 0.11.P(X = 4) = 0.05.P(X = 5) = 0.03.P(X = 6) = 0.02.Hence the mean is given by:
E(X) = 0.56(1) + 0.23(2) + 0.11(3) + 0.05(4) + 0.03(5) + 0.02(6) = 1.82.
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{0.56(1-1.82)^2+0.23(2-1.82)^2+0.11(3-1.82)^2 + \cdots + 0.02(6-1.82)^2} = 1.195[/tex].
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Angle QRS is bisected by ray RP. If angle QRP is 60 degrees, what would be the measure of angle QRS?
Answer:
6779
Step-by-step explanation:
69
The table shows the probabilities of certain prizes in a restaurant’s contest where the first 100 customers are winners.
A 2-column table with 6 rows. The first column is labeled prize with entries 1 dollar drink, 5 dollar meal, 5 dollar gift card, 10 dollar gift card, 20 dollar gift card, 100 dollar gift card. The second column is labeled number of prizes with entries 44, 25, 16, 10, 5, 1.
How does the $100 gift card affect the measure of center of the data?
A mean is an arithmetic average of a set of observations.
The correct option is (A).
What is Mean?
A mean is an arithmetic average of a set of observations.
Mean = (Sum of observations)/Number of observations
As, the median is the middle value.
Thus, the median will not be changed.
As, the mean is the arithmetic average.
So, the $100 gift will increase the mean value of the prizes.
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Answer:
A
Step-by-step explanation:
9(x - 11) = 9 what is x
Answer:
x=12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
12-1 is 11 and than 9 times 1 is 9
the gomez family drove 476 miles in 7 hours. what was their average speed, in miles per hour?
The average speed is 68 miles per hour
How to determine the average speed?The given parameters are:
Distance = 476 miles
Time = 7 hours
The average speed is calculated as:
Speed = Distance/Time
So, we have:
Speed = 476 miles/7 hours
Evaluate
Speed = 68 miles per hour
Hence, the average speed is 68 miles per hour
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How many solutions for x does the following equation have?
3(x + 8) − 1 = 3x + 4
A.
4
B.
1
C.
0
D.
infinite
Answer:
c. 0
Step-by-step explanation:
3(x+8) - 1 = 3x+4
3x+24-1 = 3x+4
3x+23 = 3x+4
There are no solutions since both equations have the same slope meaning they are parallel and they will never intersect since they have different y-intercepts.
light a flashes every 5 seconds Light b flashes every 6 seconds light c flashes every 7 seconds work out how long it will take for all of them to flash
Answer:
210 seconds
Step-by-step explanation:
LCM of 5,6 and 7
Can someone help me with question 3? I like to see the working and answer on paper, that would be more helpful, I’m in a hurry
The steps to draw all the three angles have been explained.
What is an Angle ?An angle is made by two rays that have one common end point known as vertex.
To make an angle congruent to the one given , the angle has to be copied
For making both ∠XYZ and∠ UVW , following steps will be followed.
Draw two rays separately and name it YZ and VW .Take a compass and draw a free hand arc from the point B and E and with the same measure draw a free hand arc from the point Y and V respectively.Take the compass to the angle ABC and DEF again , from the point where the arc intersects BC and EF , cut an arc on the ray AB and DE .With the same measure , keep the compass on the point the free hand arc intersected on the ray YZ and VW , cut the arc by the new arc .The point where both the arc intersects will be joined form the end points , Y and V , to form an angle.The angle formed will be copy of ∠ABC and∠ DEFNow to draw RST = ABC + DEF
Draw the angle ABC and repeat the steps to draw DEF taking , AB ray as the base of the angle.The angle obtained will be RST.
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3 - what = 11
please help with this one
Simplify 8 − (14). plsss help
Answer:
(-6)
Step-by-step explanation:
Integer subtraction:
If two numbers have different sign, subtract and the result will have the sign of the bigger number.
8 - 14 = (-6)
Subtract 8 from 14 and the bigger number is 14 and sign of 14 is (-).
So, the answer is (-6)
A biologist watches and records the number of hippos that visit a particular
watering hole over a 30-day period. What method is the scientist using to
collect data?
OA. Observational study
OB. Survey
C. Control
D. Experiment
The correct answer is option A which is Observational study.
What is an observational study?This is an example of an observational study because the biologist is not interfering or interacting with the subjects of the study but just watching and registering data (recording with cameras).
The biologist is not conducting an experiment because (he is not setting up special conditions to register different responses to drive conclusions), and the biologist is not making any survey (questionnaires for example).
Therefore the correct answer is option A which is Observational study.
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