We have to solve this inequality:
[tex]\begin{gathered} |4x+5|+2>10 \\ |4x+5|>10-2 \\ |4x+5|>8 \end{gathered}[/tex]We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.
When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:
[tex]\begin{gathered} -(4x+5)>8 \\ -4x-5>8 \\ -4x>8+5 \\ -4x>13 \\ x<\frac{13}{-4} \\ x<-3.25 \end{gathered}[/tex]The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:
[tex]\begin{gathered} 4x+5>8 \\ 4x>8-5 \\ 4x>3 \\ x>\frac{3}{4} \\ x>0.75 \end{gathered}[/tex]Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.
We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).
Answer: (-∞, -3.25) ∪ (0.75, ∞)
How can use theorem 7-4 to find missing segments? (7-4 is similarity) :)
Given
AD = 6.4
BD = 3.6
Find
AC,BC and DC
Explanation
Using Pythogoras theorem in triangle ADC
[tex]AC^2=DC^2+6.4^2------(1)[/tex]Using PT in triangle BDC
[tex]BC^2=DC^2+3.6^2-------(2)[/tex]Adding equation (1) and (2)
[tex]\begin{gathered} AC^2+BC^2=DC^2+3.6^2+DC^2+6.4^2 \\ AC^2+BC^2=2DC^2+53.92 \end{gathered}[/tex]Using PT in triangle ABC
[tex]10^2=AC^2+BC^2[/tex]Equating above 2 equations
[tex]\begin{gathered} 100=2DC^2+53.92 \\ DC^2=23.04 \\ DC=4.8 \end{gathered}[/tex]Putting this value of DC in equation (2)
[tex]\begin{gathered} BC^2=4.8^2+3.6^2 \\ BC^2=23.04+12.96 \\ BC=6 \end{gathered}[/tex][tex]\begin{gathered} 10^2=AC^2+BC^2 \\ 100=AC^2+36 \\ AC=8 \end{gathered}[/tex]Final Answer
AC = 8
BC = 6
DC = 4.8
In a class of 10 boys and 12 girls, a committee of 4 members is to be formed. What is the probability to form a committee consisting of 2 boys and 2 girls?0.30400.40600.50600.2060
Consider all the different possible combinations of 4 members of the committee (b,b,b,b), (b,b,b,g),...(g,g,g,g). We need to use the binomial distribution given below
[tex]P(k)=(nbinomialk)p^k(1-p)^{n-k}[/tex]In our case
[tex]k=2,n=4,p=\frac{10}{10+12}=\frac{10}{22}=\frac{5}{11}[/tex]Then,
[tex]\begin{gathered} P(2)=(\frac{4!}{2!(4-2)!})(\frac{5}{11})^2(\frac{6}{11})^2 \\ \Rightarrow P(2)=6\cdot\frac{900}{14641} \\ \Rightarrow P(2)=0. \end{gathered}[/tex]A brownie recipe asks for two and two thirds times as much sugar as chocolate chips. If four and one third cups of sugar is used, what quantity of chocolatechips would then be needed, according to the recipe?0308X5?
Let's call C to the cups of chocolate chips and S to the cups of sugar. We are told that the cups of sugar are 2 2/3 times the cups of chocolate, then we can formulate the following equation:
[tex]S=2\frac{2}{3}C[/tex]In the case 4 1/3 of sugar is added, we can replace 4 1/3 for S to get:
[tex]4\frac{1}{3}=2\frac{2}{3}C[/tex]By dividing both sides by 2 2/3 we get:
[tex]\begin{gathered} 4\frac{1}{3}\div2\frac{2}{3}=2\frac{2}{3}C\div2\frac{2}{3} \\ 4\frac{1}{3}\div2\frac{2}{3}=C \end{gathered}[/tex]We can rewrite the mixed fractions to get:
[tex]\begin{gathered} \frac{4\times3+1}{3}\div\frac{2\times3+2}{3}=C \\ \frac{12+1}{3}\div\frac{6+2}{3}=C \\ \frac{13}{3}\div\frac{8}{3}=C \end{gathered}[/tex]By changing the division symbol to a multiplication symbol and flipping the 8/3, we get:
[tex]\begin{gathered} \frac{13}{3}\times\frac{3}{8}=C \\ \frac{13}{8}=C \\ \frac{8+5}{8}=C \\ \frac{8}{8}+\frac{5}{8}=C \\ 1+\frac{5}{8}=C \\ 1\frac{5}{8}=C \\ C=1\frac{5}{8} \end{gathered}[/tex]Then, 1 5/8 cups of chocolate chips are needed
It takes 14 electricians 18 days to wire a new housing subdivision. How many days would it take 24 electricians to do the same job?
Answer: 31 electricians
Step-by-step explanation:
We could set up a ratio for this problem. It takes 14 electricians 18 days to wire a new housing subdivision, so it would take 24 electricians x days to do the same job. 14/18 = 24/x. We can then cross multiply to find x.
X = 30.8 or approximately 31.
Hello, may I please have some help with this question. Thank you.
The total distance that Kim walked in 3 days is 6 2/3 miles. We would convert this distance to mixed numbers. To do this, we would multiply 6 by 3 and add 2. The denominator would still be 3. It becomes
20/3 miles
If she walked 20/3 miles in 3 days, the number of miles that she walked per day would be
total distance/number of days
It becomes
(20/3) / 3
If we change the division sign to multiplication, it means that we would flip 3 such that it becomes 1/3. Thus, we have
20/3 * 1/3 = 20/9
= By converting to mixed numbers, we would find how many 9's are in 20. It is 2. The remainder is 20 - 18 = 2
Thus, the answer is
2 2/9 miles per day
help meeeeeeeeee pleaseee !!!!!
The values of the functions are:
a. (f + g)(x) = 9x + 1
b. (f - g)(x) = -7x - 17
c. (f * g)(x) = 8x² - 55x - 72
d. (f/g)(x) = (x - 8)/(8x + 9)
How to Evaluate Functions?To evaluate a function for a given value of input, substitute the value of the input, x, into the function equation, evaluate and simplify.
Given the following:
f(x) = x - 8
g(x) = 8x + 9
a. (f + g)(x) = (x - 8) + (8x + 9)
Combine like terms
(f + g)(x) = 9x + 1
b. (f - g)(x) = (x - 8) - (8x + 9)
(f - g)(x) = x - 8 - 8x - 9
Combine like terms
(f - g)(x) = -7x - 17
c. (f * g)(x) = (x - 8)(8x + 9)
Expand
(f * g)(x) = x(8x + 9) -8(8x + 9)
(f * g)(x) = 8x² - 55x - 72
d. (f/g)(x) = (x - 8)/(8x + 9)
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A small radio transmitter broadcasts in a 60 mile radius. If you drive along a straight line from a city 75 miles north of the transmitter to a second city 76 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Answer:
Explanation:
We start by having a diagrammatic representation as follows:
y = -2x + 5a. What is the slope? b. What is the vertical intercept? c. What is the horizontal intercept? d. Graph the equation
Given: The equation below
[tex]y=-2x+5[/tex]To Determine: The slope, the vertical and horizontal intercept, and the graph of the equation
Solution
The general slope-intercept form of a straight line is as shown below
[tex]\begin{gathered} y=mx+c \\ Where \\ m=slope \\ c=vertical-intercept \end{gathered}[/tex]Let us compare the general slope-intercept form of a straight line to the given
[tex]\begin{gathered} y=mx+c \\ y=-2x+5 \\ slope=m=-2 \end{gathered}[/tex]The vertical intercept is the point where the x values is zero
[tex]\begin{gathered} y=-2x+5 \\ x=0 \\ y=-2(0)+5 \\ y=0+5 \\ y=5 \end{gathered}[/tex]The vertical intercept is y = 5, with coordinate (0, 5)
The horizontal intercept is the point where the y value is zero
[tex]\begin{gathered} y=-2x+5 \\ y=0 \\ 0=-2x+5 \\ 2x=5 \\ x=\frac{5}{2} \end{gathered}[/tex]The horizontal intercept is x = 5/2, with coordinate (5/2, 0)
The graph of the equation is as shown below
Answer Summary
(a) slope = -2
(b) Vertical intercept, y = 5
(c) Horizontal intercept, x = 5/2
What is the radius of a hemispherewith a volume of 281,250 cm??
Given:
The volume of the hemisphere = 281,250
Find-:
Radius of hemisphere
Explanation-:
The volume of the hemisphere is:
[tex]V=\frac{2}{3}\pi r^3[/tex]Given volume is 281250
[tex]\begin{gathered} V=\frac{2}{3}\pi r^3 \\ \\ 281250=\frac{2}{3}\pi r^3 \\ \\ r^3=\frac{281250\times3}{2\times\pi} \\ \\ r^3=134286.9832 \\ \\ r=51.209 \end{gathered}[/tex]So, the radius is 51.209 cm
The picture shows a system of linear and quadratic equations.
Drag each label to show whether it is a solution of the system or is not a solution of the system, or if it cannot be determined.
By identifying the intercepts in the given image, we conclude that the solutions of the system of equations are points B and F.
Does the system have solutions?When we have a system of 2 equations:
y = f(x)
y = g(x)
To solve it graphically, we have to graph both functions in the same coordinate axis and see in which points the graphs intercept (if they do). Each of these interceptions in the form (x, y) will be a solution for the equation f(x) = g(x) = y
In this case, we can see a line and a parabola (each of these is a different equation from the system), and we can see that the graphs intercept at points F and B (i think, the image is really small). Then the two solutions of the system of equations graphed are the points F and B
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Answer:
solution: F and B
NOT solution: the rest of the letters
Step-by-step explanation:
I did the work on imagine math
one motorcycle travels 80 miles per hour and the second motor ctcle travels 60 miles per hour if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcylce what distace does each of the motorcyle travel
The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .
In the question ,
let the time travelled by the slower motorcycle be "t" .
given , the faster one travelled 1 hour longer ,
So , the time travelled by faster motorcycle = "t+1" hour .
the speed of slower motorcycle = 60 miles per hour .
the speed of faster motorcycle = 80 miles per hour .
So , the distance covered by slower motorcycle = speed * time
= 60*(t)
the distance covered by the faster motorcycle = 80*(t+1) .
given that faster motorcycle travels twice the distance of the slower motorcycle
So According to the question
80*(t+1) = 2*60*(t)
simplifying further , we get
80t + 80 = 120t
120t - 80t = 80
40t = 80
t = 2 hours
distance covered by slower motorcycle = 60(2) = 120 miles
distance covered by faster motorcycle = 80(2+1) = 80*3 = 240 miles .
Therefore , The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .
The given question is incomplete , the complete question is
One motorcycle travels 80 miles per hour and the second motorcycle travels 60 miles per hour, if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcycle . What distance does each of the motorcycle travel ?
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Is there one line that passes through the point (3, 5) that is parallel to the lines represented by y = 2x - 4 and y = x - 4Explain.
If two lines are parallel, it means that they have the same slope. The given lines are
y = 2x - 4 and y = x - 4
The slope intercept form of a straight line is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
By comparing both equations with the slope intercept form,
For y = 2x - 4
Slope, m = 2
For y = x - 4
Slope, m = 1
We can see that the slopes are not eaual. Thus, the lines are not parallel.
Also, we can conclude that there is no line that passes through the point (3,5) that is parallel to both lines
There is no line that passes through the point (3,5) that is parallel to both lines.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
If two lines are parallel, it means that they have the same slope. The given lines are
y = 2x - 4 and y = x - 4
By comparing both equations with the slope-intercept form,
For y = 2x - 4
Slope, m = 2
For y = x - 4
Slope, m = 1
We can see that the slopes are not equal. Thus, the lines are not parallel.
Also, we can conclude that there is no line that passes through the point (3,5) that is parallel to both lines.
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Bob wants to build an ice skating rink in his backyard, but his wife says he can only use the part beyond the wood chipped path running through their yard. What wouldbe the area of his rink if it is triangular-shaped with sides of length 18 feet, 20 feet, and 22 feet? Round to the nearest square foot.
In order to calculate the area of the triangle, given the length of its three sides, we can use Heron's formula:
[tex]A=\sqrt{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}[/tex]Where p is the semi-perimeter.
So, calculating the value of p and then the area of the triangle, we have:
[tex]\begin{gathered} p=\frac{a+b+c}{2}=\frac{18+20+22}{2}=\frac{60}{2}=30 \\ A=\sqrt{30\left(12\right)\left(10\right)\left(8\right)} \\ A=\sqrt{28800} \\ A=169.7\text{ ft^^b2} \end{gathered}[/tex]Rounding to the nearest square foot, the area is 170 ft².
Will you ever completely remove the drug from your system? Explain your reasoning.
Answer
The drug cannot be completely eliminated from one's system.
This is because the kidney removes 25% of the drug, leaving 75% at any time; the 75% of any number will give a smaller number, but never zero.
So, the amount of the drug in the body system can become extremely low, but it can never be 0.
The mathematical proof is shown under explanation.
Explanation
We are told that the kidney filters off 25% of the drug out of the system every 4 hours.
This means that 75% of the dosage of the drug remains in the person's system every 4 hours.
If one starts with A₀ of the drug and classify every 4 hour time period as n
At n = 1,
A₁ = 0.75 (A₀)
A₂ = 0.75 (A₁) = 0.75² (A₀)
Aₙ = 0.75ⁿ (A₀)
For this question, we start wit 1000 mg
A₀ = 1000 mg
We are then asked to calculate if Aₙ, the amount of drug in the system after n time periods, can ever be 0
Aₙ = 0.75ⁿ (A₀)
0 = 0.75ⁿ (1000)
To solve for n, if there's an n for when the value of Aₙ = 0, we first divide both sides by 1000
0 = 0.75ⁿ (1000)
0 = 0.75ⁿ
We then take the natural logarithms of both sides
In 0 = In (0.75ⁿ)
In (0.75ⁿ) = In 0
n (In 0.75) = In 0
But, since In 0 does not exist, it shows that there is no value of n that can make the value of Aₙ go to 0.
Hope this Helps!!!
From the given proportional relationship, which of the following points lie on the same line?
As per given by the question,
There are given that a graph of line.
Now,
h
Consider the following when d = 14 ft. Give both exact values and approximations to the nearest hundredth.(a) Find the circumference of the figure.ftftx(b) Find the area of the figure.ft?x7A²teh
(a)Recall that the circumference of a circle is given by the following formula:
[tex]C=\pi d.[/tex]Where d is the diameter of the circle.
Substituting d=14 ft in the above formula, we get:
[tex]C=\pi(14ft)\approx43.98ft\text{.}[/tex](b) Recall that the area of a circle is given by the following formula:
[tex]A=\frac{\pi d^2}{4}.[/tex]Substituting d=14 ft in the above formula, we get:
[tex]A=\frac{\pi(14ft)^2}{4}=49\pi ft^2\approx153.94ft^2.[/tex]Answer:
(a)
Exact solution:
[tex]14\pi ft.^{}[/tex]Approximation:
[tex]43.98\text{ ft.}[/tex](b) Exact solution:
[tex]49\pi ft^2\text{.}[/tex]Approximation:
[tex]153.94ft^2.[/tex]Suppose elephant poaching reduces an initial animal population of 25,000 animals by 15% each year. 1. Find the rate of change.2. How many animals will be left in 10 years?
Answer
Initial animal population, P₀ = 25,000
1. Rate of change = 15% = 0.15
2. Animal left in 10 years?
To calculate the animals left in 10 years, we use the formula:
P(t) = P₀ (1 - r)^t in t years
t = 10, P₀ = 25,000, r = 15% = 0.15)
P₍₁₀₎ = 25000 (1 - 0.15)¹⁰
P₍₁₀₎ = 25000 (0.85)¹⁰
P₍₁₀₎ = 25000 (0.1969)
P₍₁₀₎ = 4922.50
Therefore, 4922.50 animals will be left in 10 years.
answer this, please?
Sidney made root beer floats for her friends when they came over. The table shows the ratio of cups of ice cream to cups of soda used to make the floats.
Ice Cream (cups) Soda (cups)
3.5 10.5
8 24
12.5 37.5
19 ?
At this rate, how much soda will Sidney use for 19 cups of ice cream?
30 cups
38 cups
57 cups
72 cups
Sidney will use 57 cups of soda for 19 cups of ice cream.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
From the table,
The ratio of cups of ice cream to cups of soda.
3.5 cups ice cream = 10.5 cups of soda
Divide both sides by 3.5.
1 cup of ice cream = 3 cups of soda
Multiply 19 on both sides.
19 cup of ice cream = 57 cups of soda
Thus,
57 cups of soda.
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Determine whether the equation represents an exponential growth function, anexponential decay function, and give the percent growth or decay.17. y = 18(1.3)^t
A exponential growth or decay function has the next general form:
[tex]y=a(1\pm r)^t[/tex]If it is :
(1+r) , (>1) the function growth
(1-r) , (<1) the function decay
------
The given equation:
[tex]y=18(1.3)^t[/tex]As the (1+r) is equal to 1.3 (> 1) then it is a exponential growth function.In (1+r) the r is the percent of growth, then for the given equation you have:
[tex]\begin{gathered} 1+r=1.3 \\ r=1.3-1 \\ \\ r=0.3 \end{gathered}[/tex]The percent of decay is 0.3 or 30%two parallel lines are intersected by a transversal one angle is 100 degrees, more info on the picture
Obtuse angles (90°–180°) are those that fall within this range. Right angles are those that have a 90 degree angle ( = 90°). Straight angles are those that have a 180 degree ( = 180°) angle.
Explain about the obtuse angle?Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement. A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.
We now understand that an obtuse angle is one that is greater than 90 degrees but less than 180 degrees. Obtuse angle examples include 110°, 135°, 150°, 179°, 91°, and more. As a result, all angles between 90° and 180° are obtuse angles.
Hence obtuse angle is one of the angle which is not correct 100 degree angle
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The following are the distances (in miles) to the nearest airport for 13 families.10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39Notice that the numbers are ordered from least to greatest.Give the five-number summary and the interquartile range for the data set.
We have the next given set for distances (in miles) to the nearest for 13airport families:
10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39
The minimum is the least number value. Then:
Minimum =10
In this case, we have 13 data, so :
- The middle number is the median:
10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39
Now, the lower quartile is given by the next equation:
[tex]=(n+1)\ast\frac{1}{4}[/tex]Replacing:
[tex]\begin{gathered} =(13+1)\ast\frac{1}{4} \\ =14\ast\frac{1}{4} \\ =3.5=4 \end{gathered}[/tex]The lower quartile is in the fourth position:
Lower quartile = 15
The upper quartile is given by the next equation:
[tex]\begin{gathered} =(n+1)\ast\frac{3}{4} \\ =(13+1)\ast\frac{3}{4} \\ =10.5=11 \end{gathered}[/tex]The upper quartile is located in the 11th position:
Upper quartile = 34
The interquartile range is given by:
IQR=upper quartile - lower quartile
IQR=34-15
The interquartile range =19
What is the slope of the line passing through the points (−1, 7) and (4, −1)? −5/62−8/5−2
Given the points:
(−1, 7) and (4, −1)
The slope of the line passing through the points is given by:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-7}{4-(-1)}=\frac{-8}{5}[/tex]So, the answer will be Slope = -8/5
Which of the following shows a graph of a tangent function in the form y = atan(bx − c) + d, such that b equals one fourth question mark
ANSWER :
EXPLANATION :
Cost of a CD: $14.50Markup: 30%
Given:
Cost of a CD = $14.50
Markup =30%
If markup 30% then:
[tex]\begin{gathered} =\frac{130}{100} \\ =1.3 \end{gathered}[/tex]So the cost is:
[tex]\begin{gathered} =1.3\times14.50 \\ =18.85 \end{gathered}[/tex]markup cost is 18.85
A teacher gets snacks for the class for $50 and also purchases 6 boxes of pencils. The teacher spent a total of $62. Write an equation that models the situation with x, the cost of one box of pencils.
Answer:
50 + 6x = 62
Explanation:
If x represents the cost of one box of pencils and the teacher got snacks for $50, purchased 6 boxes of pencils, and spent a total of $62, we can write the equation that models the above situation as shown below;
[tex]50+6x=62[/tex]The amounts of money three students earn at their jobs over time are given in the tablesStudent ETime (hr) Amount Earned2$15.005$37.508$60.00Student FTime (hr) Amount Earned3$27.006$54.0010$90.00Student GTime (hr) Amount Earned1$8.504$34.007S59.50According to the tables, which statement is true?Student E cams the most amount of money per hourStudent E cars more money per hour than studentStudent Goarns the least amount of money per hourStudent G earns less money per hour than student F
the answer is:
Student G earns less money per hour than student F
please give a VERY SHORT EXPLANATION NOT LONG! i inserted a picture of the question
If the amount of time spent is lesser than or equal to 250, so the price is $29, so we have the first part of the piecewise equation:
[tex]f(x)=29,\text{ x <= 250}[/tex]Then, for an amount of time greater than 250, the extra minutes are charged by 0.35 per minute, and this extra cost will add the fixed cost of $29, so the second part of the equation is:
[tex]f(x)=29+(x-250)0.35,\text{ x>250}[/tex]The option that shows the correct piecewise equation is option A.
Write the equation of the line through the given point. Use slope-intercept form. (-5,2); perpendicular to y = - 2/3x +5
Explanation
Step 1
we have a perpendicular line, its slope is
[tex]\begin{gathered} y=\frac{-2}{3}x+5 \\ \text{slope}=\frac{-2}{3} \end{gathered}[/tex]two lines are perpendicular if
[tex]\begin{gathered} \text{slope}1\cdot\text{ slope2 =-1} \\ \text{then} \\ \text{slope}1=\frac{-1}{\text{slope 2}} \end{gathered}[/tex]replace
[tex]\text{slope1}=\frac{\frac{-1}{1}}{\frac{-2}{3}}=\frac{-3}{-2}=\frac{3}{2}[/tex]so, our slope is 3/2
Step 2
using slope=3/2 and P(-5,2) find the equation of the line
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-2=\frac{3}{2}(x-(-5)) \\ y-2=\frac{3}{2}(x+5) \\ y-2=\frac{3}{2}x+\frac{15}{2} \\ y=\frac{3}{2}x+\frac{15}{2}+2 \\ y=\frac{3}{2}x+\frac{19}{2} \end{gathered}[/tex]Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 6. A(-3, 8), B(3, 2), C(7,1), D(5,-1)m(AB) m(CD) Types of Lines
There are 16 appetizers available at a restaurant. From these, Pablo is to choose 12 for his party. How many groups of 12 appetizers are possible?
EXPLANATION
This is a combinatory, as there are 12 groups, the combinatory will be as follows:
16C12 = 16!/[12!*(16-12)!] = 1820
In conclusion, there will be 1820 possible groups of 12 appetizers.