By using a linear equation, we can see that after the 19 day the population will be less than 1000 mold spores.
How many days will it take for the population to be less than 1000 mold spores?We know that the population decays at a rate of 30 spores per day, and we have an initial population of 1560 mold spores.
Then, the population of spores after x days is given by the linear equation:
P(x) = 1560 - 30*x
The population will be exactly 1000 spores when:
P(x) = 1000 = 1560 - 30*x
We need to solve that for x.
30x = 1560 - 1000 = 560
x = 560/30 = 18.67
So after 18.67 days the population is 1000, this means that after the 19 day the population will be less than 1000 mold spores.
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I need help with this rational expression
Answer:
Step-by-step explanation:
[tex]\frac{x}{y} 6x+58\\(x+3)(x+8)\\[/tex]
The amount of money earned varies directly as the number of hours worked. After working 14 hours, Joe earned $119. How
much would Joe earn for working 20 hours?
Joe earned $140 for working 20 hours
To determine the value of a single unit from a specified multiple, use the unitary technique. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.
Joe worked 14 hours and earned = $119
Joe worked for 1 hour and earned = $ 119/ 14
Joe worked for 20 hours and earned = $ 119/ 14 x 20
= 4140
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Points A and B are plotted on a number line at -4 and 3. respectively. Find the coordinate of the point that represents the weighted averag
of A and B if point A has a weight of 2 and point B has a weight of 5.
The coordinate of the pointed that represented the weighted average of A and B is: 1
What is the explanation for the above?Note that X = [x1w1 + x2w2 +.......xnwn]/w1+w2 +....wn
Where x is the numbers and w is the weight.
Given,
A = - 4 : Weight = 2
B= 3 : Weight = 5
Hence, average is given as;
([-4 x 2] + [3 x 5])/2+5
= (-8 + 15)/7
= 7/7
= 1
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Percent change from 10,000 to 10,200
Calculator is showing a result of 78.987625. What is this to 2 decimal places
Answer:
78.99
Step-by-step explanation:
Rounding to the 2nd decimal place the number 78.987625
Write down everything upto and including the 2nd decimal: 78.98
Check out the next digit. If >= 5, then increase the 2nd decimal digit above by 1, if not leave it as is.
For 78.987625 the digit next to the 2 decimal digit is 7 so we increase 78.98 to 78.99
the volume of water is usually distributed with a mean of 62ml and standard deviation of 40ml. What is the probability that the volume will be greater than 90ml?
The probability of the volume of water being over 90 ml is 24.10%.
What exactly is the standard normal distribution?A symmetric probability distribution only with equal mean, mean, as well as mode values is known as a standard normal distribution.A statistical table as well as computer software is used to estimate the likelihood of a standard normal distribution.For the given question;
The mean of the sample is; μ = 62 ml.
The standard distribution is; σ = 40 ml.
The probability of the values must lie more than 90 ml.
Thus,
P(x > 90) = P[ (x - μ)/ σ ]
Substitute the values;
P(x > 90) = 1 - P[ (90 - 62)/ 40]
P(x > 90) = 1 - P[0.7]
P(x > 90) = 1 - 0.758
P(x > 90) = 0.2410
P(x > 90) = 24.10%
Therefore, the probability that the the volume of water will be greater than 90 ml is 24.10%.
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Given below are descriptions of two lines.
Line 1: Goes through (1,1) and (-2,7)
Line 2: Goes through (-1,4) and (1,0)
The slope of Line 1 is m =
|
The slope of Line 2 is m =
The slope of Line 1 is m = -2
The slope of Line 2 is m = -2
For Line 1;
(x₁, y₁) = (1, 1);
(x₂, y₂) = (-2, 7);
m₁ = (7-1)/(-2-1) = -2;
For Line 2;
(x₃, y₃) = (-1, 4);
(x₄, y₄) = (1, 0);
m₂ = (4-0)/(-1-1) = -2;
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Point B is on line segment
AC
. Given AB=3x, BC=4x+8, and AC=5x+10, determine the numerical length of
AC
.
Answer:
The length of AC is 15 units
Step-by-step explanation:
A jet plane traveling at 400 mph overtakes a propeller plane traveling at 250 mph that had a 2-hour head start. How far from the starting point are the planes?
Answer:
I think they're 800miles from starting point
Step-by-step explanation:
Use the distributive property to multiply (3w + 5)(–2w – 7).
-6w^2+31w+35
6w^2-21w-35
-6w^2-31w-35
6w^2-21w+30
Answer:
[tex]=-6w^2-31w-35[/tex]
Step-by-step explanation:
Apply Foil.
[tex]\left(3w+5\right)\left(-2w-7\right)=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)[/tex]
[tex]=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)[/tex]
[tex]=-6w^2-31w-35[/tex]
Use braces to write the members of the set, or state that the set has no members.
The integers between 2 and 6 (not inclusive)
A.
{3, 4, 5}
{3, 4, 5}
B.
{3, 4, 5, 6}
C.
{2, 3, 4, 5}
D.
{2, 3, 4, 5, 6}
Answer: A. {3, 4, 5}
Explanation:
Write out the whole numbers from 2 to 6 to get 2,3,4,5,6
But we erase the first and last values since we aren't including those endpoints. So we end up with 3,4,5
only number 13 solve for x plspls
In the given diagram, the value of x is 16
Calculating anglesFrom the question, we are to determine the value of x
In the given diagram, we can observe that (6x + 20)° and 4x° form a linear pair,
Thus, we can write that
(6x + 20)° + 4x° = 180°
Now, we will solve for x
(6x + 20)° + 4x° = 180°
6x + 20 + 4x = 180
10x = 180 - 20
10x = 160
x = 160/10
x = 16
Hence, the value of x is 16
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a certain ceiling is made up of tiles.every square mater of ceiling requries 10.75 tiles.fill in table with the missing values
Table is attached below-
1) 1 m² = 10.75 tiles
2) 10 m² = 107.5 tiles
3) 9.3 m² of tiles = 100 tiles
4) a m² = 10.5a tiles
We have been given that
Every square meter of ceiling requires 10.75 tiles.
we have find missing values in the table.
We know,
1 square meter of ceiling = 10.75 tiles. ...(i)
1. Therefore, the number of tiles corresponding to 1 square meter of ceiling is 10.75.
Multiply both sides by 10.
10×1 square meter of ceiling = 10×10.75 tiles.
10 square meter of ceiling = 107.5 tiles.
2. Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.
Divide both sides by 10.75 in (i).
(1/10.75) square meter of ceiling = 1 tile.
Multiply both sides by 100.
(100/10.75) square meter of ceiling = 100 tiles.
On approximating the value, we get
9.3 square meter of ceiling = 100 tiles.
3. Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.
Multiply both sides by a in (i).
a×1 square meter of ceiling = a×10.75 tiles.
a square meter of ceiling = 10.75a tiles.
4. Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.
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please help asap !!!!
Austin buys cookies and oranges at the store.
He pays a total of $34.18.
He pays a total of $6.86 for the cookies.
He buys 4 bags of oranges that each cost the same amount.
How much does each bag of oranges cost?
Answer: 6.83
Step-by-step explanation: 34.18 - 6.86 = 27.32 /4 = 6.83
A square that is 7 yd on a side is placed inside a rectangle that has a width of 9 yd and a length of 14 yd. What is the area of the region inside the rectangle that surrounds the square?
Answer: 77 yd^2
Step-by-step explanation:
S=Area of Square. s=side length of square. w=width of rectangle
l=length of rectangle. R=Area of Rectangle
S=s^2
S=7^2
S=49 yd^2
R=l*w
R=9*14
R=126 yd^2
R-S=
126-49=77 yd^2
consider the line y=9x-8 find the equation that is perpendicular to this line and passes through the point -8,3
The equation of line is y=-9x-69.
To solve this problem we need to know the concept of slope of line and equation of straight line.
Writing the standard form of line is in the form of y= mx+ c where m is the slope of line.
And we also know that the product of slope of a line perpendicular to the line is equal to -1.
Let us assume that the slope of required line is m'
So, m' × 9 = -1
⇒ m'= -9
Now, the equation of line will be;
[tex](y-3)=-9(x+8)[/tex]
⇒ y-3=-9x-72
⇒ y=-9x-69 is the standard equation of line perpendicular to the given line y=9x-8.
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Robert spends $30.45, before tax, at the bookstore. If the sales Tax rate in his city is 7.25%, and Robert started with $40, how much does Robert have left?
The amount of money Robert has left given the amount he started with and after deducting tax is approximately $7.34
How much does Robert have left after deducting tax?Tax can be defined as the compulsory levy paid by citizens of a particular country on their income, goods and be services.
Amount Robert started with = $40Amount Robert spent before tax = $30.45Tax rate = 7.25%Amount of tax = Tax rate × Amount Robert spent before tax
= 7.25% × $30.45
= 7.25/100 × 30.45
= 0.0725 × 30.45
= $2.207625
Total amount Robert spent = Amount Robert spent before tax + Amount of tax
= $30.45 + $2.207625
= $32.657625
Amount Robert has left = Amount Robert started with - Total amount Robert spent
= $40 - $32.657625
= $7.342375
Approximately,
$7.34
Therefore, the amount Robert has left after deducting tax is $7.34
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I sent an attachment
You have 10 quarters that you can use for a parking meter.
a. Copy and complete: Each time you put 1 quarter in the meter, you have 1 less quarter, so ? is a function of ?
b. Write a rule for the number y of quarters that you have left as a function of the number x of quarters you have used so far. Identify the domain of the function.
c. Make a table and identify the range of the function.
a) "how many quarters you have is a function of how many times you paid for the parking meter."
b) y = 10 - x
domain: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
range: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
c) table:
x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
y: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
How to complete the blanks?Here we know that you have a total of 10 quarters, and the parking meter costs 1 quarter.
Then, each time if we define two variables:
y = how many quarters you have.
x = how many times you paid for the parking meter.
We can write:
"y is a function of x"
Or:
"how many quarters you have is a function of how many times you paid for the parking meter."
b) The rule is really simple, it would be a linear relation:
y = 10 - x
The domain (the set of possible values of x) is:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
You can't use less than 0 quarters and you can't use more than 10.
c) The range is also:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Which represents the possible numbers of quarters that you can have.
And the table will be:
x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
y: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
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Interns,
Mr. Howell, the prestigious founder and owner of our company Coal is Gold Electricity would like you to perform an
analysis on the company’s emission control. The government is providing subsidies to encourage reducing emissions.
Mr. Howell would like to know is it worth reducing emissions with the subsidy. The pertinent information can be found
in Mr. Howell’s email below.
“Mr. Kleppin,
As you know, my company has supplied the energy needs of the entire state since 1968! I can’t believe they are
demanding that we reduce our emissions! This will force us to pass on the increase in the cost to our customers!
Thankfully, the government will be providing a subsidy to offset these costs! The current subsidy is $500 per pound of
pollution reduction each day with a minimum reduction of 15 pounds per day. I have spoken to the engineering
department regarding the cost to reduce emissions. They informed me that the average daily cost to us is a fixed daily
cost of $100 in addition to $30 times the square of the quantity of pounds of pollution reduced each day. Currently, I
would like to reduce emissions by 15 pounds of pollutant per day. At this level, what is the marginal average daily cost of
reducing emissions to 16 pounds of pollutant per day? What is the average daily cost at this reduction level? Is the
average daily cost increasing or decreasing at this reduction level? With the government subsidy, what would be our
average daily cost for reducing emissions by 15 pounds of pollutant per day? The government would like us to reduce
emissions by 20 pounds of pollutants per day. Could we accomplish this with no cost to us? If not, at what reduction level
would we have no cost to us? What do you recommend? I would like you, Mr. Kleppin, to give the interns a chance to
earn one of the 10 available positions at the end of their internship by giving them the opportunity to do the analysis.”
As per the given information about that Mr. Howell the prestigious founder and owner of our company Coal is Gold Electricity:-
POUNDS FC SQ. OF POUNDS TVC TC AC SUBSIDY
1 100 1 30 130 130.0 500
2 100 4 120 220 110.0 1000
3 100 9 270 370 123.3 1500
4 100 16 480 580 145.0 2000
5 100 25 750 850 170.0 2500
6 100 36 1080 1180 196.7 3000
7 100 49 1470 1570 224.3 3500
8 100 64 1920 2020 252.5 4000
9 100 81 2430 2530 281.1 4500
10 100 100 3000 3100 310.0 5000
11 100 121 3630 3730 339.1 5500
12 100 144 4320 4420 368.3 6000
13 100 169 5070 5170 397.7 6500
14 100 196 5880 5980 427.1 7000
15 100 225 6750 6850 456.7 7500
16 100 256 7680 7780 486.3 8000
17 100 289 8670 8770 515.9 8500
18 100 324 9720 9820 545.6 9000
19 100 361 10830 10930 575.3 9500
20 100 400 12000 12100 605.0 10000
Here, FC = Fixed Cost
TVC = Total Variable Cost
TC = Total Cost
AC = Average Cost
(i) Marginal Cost of a 16-pound reduction in emissions = 7680 - 6750
= $930
(ii) Average Price at a decline of 15-pound = 6850 / 15 = $456.67
( Every additional unit results in an increase in Variable Cost per unit. The Average Cost will thus rise as the amount increases. )
(iii) Since our expenses are less than the subsidies in pounds (15), there will be no net cost.
(iv) It will cost us $12,000 to maintain the decrease level at 20 pounds, of which the corporation may recoup $10,000. Thus, the final price will be $2100.
(v) Break Even can be calculated between 16-17 pounds (You can refer to the table for the clarifications)
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find the midpoint of a line segment with endpoints A(-5,5) and B(2,-5)
Answer:
(-1.5,0)
Step-by-step explanation:
Find the average for the x and y values.
x = [tex]\frac{(-5+ 2)}{2}[/tex] = [tex]\frac{-3}{2}[/tex] or -1.5
y = [tex]\frac{(5- 5)}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
A plastic page designed to hold trading cards will hold up to 8 cards. How many pages will be needed to store 583 cards? Give an appropriate counting number answer to the question. (Find the least counting number that will work.)
The number of pages that would be needed to store 583 cards is (blank).
Answer:
73 pages
Step-by-step explanation:
You want the number of pages required to hold 583 cards when each page will hold 8.
Least integerThe number of pages required is ...
(583 cards)/(8 cards/page) = 72 7/8 pages
The least integer greater than this number is 73
The number of pages needed to store 583 cards is 73.
Determine if the following relations represent a function
1. {(-1, -2), (0, -2), (1, -2), (2, -2)}
2. {(1, 0), (1,1), (1, 2), (1, -2)}
1) Yes, because each value of x maps onto only one value of y.
2) No, because the x-value of 1 maps onto 4 different y values.
Answer:
yes, a function.no, not a function.Step-by-step explanation:
You want to know if the given sets of ordered pairs represent a function.
FunctionA function is a relation that maps an input value to a single output value. On a graph, this means no two points are vertically aligned. For a table or set of ordered pairs, it means no input (x) value is repeated.
1.The input (x) values are {-1, 0, 1, 2} with no repeats. This relation is a function.
2.The input values are {1, 1, 1, 1} with repeats. This relation is not a function.
3. This diagram is a straightedge and compass construction
of the bisector of angle BAC. Only angle BAC is given.
Explain the steps of the construction in order. Include a
step for each new circle, line, and point.
A straight line that divides a given angle between two equal angles is referred to as an angle bisector. The following are the steps to constructing a bisector of angle BAC:
What is a compass construction?Construction with a straightedge and a set of compasses is a method for constructing lengths, angles, and other geometrical figures. It is also known as ruler-and-compass construction or classical construction.
These are the steps:Draw an internal arc using any radius and point A as the center to join lines BA and AC at points E and F, respectively.Draw an arc with point E as the center and a radius that is the same or different from the radius of the circle.Draw a second arc with the same radius and center point F, intersecting the first arc at point G. A thru G,Construct a straight line. This is an angle bisector of BAC.To know more about compass construction visit:
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Find an equation of the tangent line to the curve at the given point.
y = x³ - 3x + 1, (3, 19)
Answer:
y=24x-53.
Step-by-step explanation:
1) the slope-interception view of the required tangent line is
y=slope*x+interception;
2) y'=3x²-3;
3) slope=y'(3), then slope=3*3²-3=24;
4) the required equation of tangent line has the form
y=24x+interception;
5) to calculate the interception it is needed to substitute the given coordinates (3;19) into this equation:
19=24*3+interception; ⇒ interception=-53;
6) finally, the required equation is y=24x-53.
how many tablespoons are there in fluid ounces
Answer:
6
Step-by-step explanation:
There are six teaspoons in one fluid ounce - lots of conversion sites out there to get more info if needed.
Dave took an exam with 40 questions. He answered 32 correctly. What
was his grade for the exam? Write the grade as a percent.
www
% (Round to the nearest percent as needed.)
Step-by-step explanation:
40 = 100%
1% = 100%/100 = 40/100 = 0.4
how many % are 32 ?
as many % as 1% (0.4) can fit into 32 :
32 / 0.4 = 80%
his grade was 80%.
When the admission price for a baseball game was $5 per ticket, 35,000 tickets were sold. When the price was raised to $6, only 30,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively.
(a)
Find the profit P as a function of x, the number of tickets sold
The profit function is P(x) = ( - x² / 5000 ) + 11.9x - 95000.
35,000 baseball game tickets were sold at $5 per ticket.
When the price is raised to $6, then 30,000 tickets were sold.
The variable and fixed costs for the ballpark owners are $0.10 and $95,000 respectively.
Let's say x is the number of tickets sold, and P is the profit.
Then,
P = ax + b
At P = 5,
5 = (35000)a + b ---------(1)
At P = 6,
6 = (30000)a + b --------(2)
Subtracting (2) from (1),
5 - 6 = (35000)a + b - (30000)a - b
- 1 = 5000(a)
a = ( - 1/5000)
So if a = ( - 1/5000),
Then,
5 = (35000)a + b
5 = (35000)( - 1 / 5000 ) + b
5 = - 7 + b
b = 12
Therefore,
P(x) = ( - x /5000) + 12
Now, the profit function is:
Profit = Revenue - Costs
P(x) = R(x) - C(x)
Now, R(x) = xp(x)
R(x) = x[ ( - x/5000) + 12]
R(x) = ( - x² / 5000 ) + 12x
The fixed cost is F(x) = $95000
Hence, the costs will be:
C(x) = 95000 + (0.10)x
Therefore the profit function is:
P(x) = R(x) - C(x)
P(x) = ( - x² / 5000 ) + 12x - 95000 - (0.10)x
P(x) = ( - x² / 5000 ) + 11.9x - 95000
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4 is subtracted from the square of a number.
Answer: x^2-4
Step-by-step explanation: I can only assume that is the answer given the limited prompt. Please comment and let me know if that is the desired answer or if you need more help. (X = a number ^2 = squared -4 = 4 is subtracted)