This approach ensures that each house is in range of at least one tower while minimizing the number of towers needed to cover all houses.
To determine the minimum number of towers needed to cover all houses, we can start by sorting the house locations in ascending order. Then, we can place the first tower at x1+r, which covers all houses to the left of x1+r. We can continue placing towers at the first house that is not covered by the previous tower, with its location being the maximum distance from the previous tower that can still cover all houses within its radius.
Specifically, for any house x[i], we can check if it is within the radius of the current tower. If it is not, we place a new tower at x[i-1]+r and repeat the process. Once all houses are covered, we can return the number of towers used and their locations. This algorithm has a time complexity of O(n log n) due to the initial sorting step but can be optimized to O(n) by using a linear search instead.
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Rewrite each equation in factored form and solve using zero product property. Find the solutions of each equation. Use the notes about r * k = c and r + k = b. In the first problem c is 6 and b is -7. So you need the same r and k that multiply to be 6 but also add to be -7. The numbers you find will be the solutions
The factored form of the equation are as follows;
(d - 6)(d - 1) = 0(x + 9)(x + 9) = 0(u + 12)(u - 5) = 0How to write equation in factored form?Converting a quadratic function to factored form is called factoring.
Therefore,
let's factor the equation,
a.
d² - 7d + 6 = 0
d² - d - 6d + 6 = 0
d(d - 1) - 6(d - 1) = 0
(d - 6)(d - 1) = 0
b.
x² + 18x + 81 = 0
x² + 9x + 9x + 81 = 0
x(x + 9) + 9(x + 9) = 0
(x + 9)(x + 9) = 0
c.
u² + 7u - 60 = 0
u² - 5u + 12u - 60 = 0
u(u - 5) 12(u - 5) = 0
(u + 12)(u - 5) = 0
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Ben has typed 180 and can type 30 words per minute. millie has typed 60 and can type 50 words per minute. how many minutes will it take for millie to catch up with ben.
The time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.
We assume the minutes taken by Millie to catch up with Ben to be x minutes.
The number of words Ben has already typed = 180.
The unit rate for Ben for the typing of words = 30 per minute.
Therefore, words typed by Ben in x minutes = 30x words.
Therefore, the total number of words typed by Ben = 180 + 30x words.
The number of words Millie has already typed = 60.
The unit rate for Millie for the typing of words = 50 per minute.
Therefore, words typed by Millie in x minutes = 50x words.
Therefore, the total number of words typed by Millie = 60 + 50x words.
As Millie needs to catch up with Ben after x minutes, the total number of words typed by them needs to be equal, that is, 60 + 50x = 180 + 30x, which is the required linear equation in one variable.
To find the minutes taken by Millie to catch up with Ben, we solve this linear equation in one variable as follows:
60 + 50x = 180 + 30x,
or, 60 + 50x - 30x = 180 + 30x - 30x {Subtracting 30x from both sides},
or, 60 + 20x = 180 {Simplifying},
or, 60 + 20x - 60 = 180 - 60 {Subtracting 60 from both sides},
or, 20x = 120 {Simplifying},
or, 20x/20 = 120/20 {Dividing both sides by 20},
or, x = 6 {Simplifying}.
Thus, the time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.
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Find the value of X. Round to the nearest tenth HELP ASAP!!!!
Answer: 22.5
Step-by-step explanation:
[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]
A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.
Which is a possible turning point for the continuous function f(x)?
(–2, 0)
(0, –2)
(2, –1)
(4, 0)
On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).
A possible critical point of the function f(x) is given by: (0,-2)
What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
At these points, the function can change from decreasing to increasing, or vice-versa.
For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).
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Find the area of each figure as described or shown. Write final answer on blank provided. Show work. Include units as part of your answer. If needed, round answer to 2 decimal places.
Answer:
482.84u², 42.5cm², 51.5ft²
Step-by-step explanation:
1) A = 2(1 + √2)a²
A = 2(1 + √2)(80 / 8)²
A = 482.84units²
2) Square = 5²
Square = 25
T1 = 3 x 5 / 2
T1 = 7.5
T2 = 4 x 5 / 2
T2 = 10
Total = 10 + 7.5 + 25
Total = 42.5cm²
3) Rect = 4(8 + 3)
Rect = 44
T1 = 2 x 3 / 2
T1 = 3
T2 = 3 x 3 / 2
T2 = 4.5
Total = 3 + 4.5 + 44
Total = 51.5ft²
Gerri purchases a coupon book with discounts for her favorite coffee shop. every coupon for the coffee shop offers the same discount. the table shows her total savings, y, based on the number of coupons, x, used from the book. a table showing coffee shop coupon savings with 2 columns and 6 rows. the first column, x, has the entries, 0, 5, 10, 15, 20. the second column, y, has the entries. negative 20, negative 10, 0, 10, 20.
Slope 2 and y intercept is 10
The question seems to be incomplete and complete and the complete question is shown in the image
The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases.
When x = 0, the corresponding y-value is the y-intercept. In the particular context of word problems, the y-intercept (that is, the point when x = 0) also refers to the starting value.
Y-intercept is the point at which the line intersects the y axis- meaning x = 0
From the table y = -20 when x= 0
y-intercept: -20
To find the slope
m = ΔY/ΔX
m = -20+10/0-5 = 2
Hence the slope is 2 and y intercept is 10
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What’s 1/6 to 3 dp does anyone know?
❄ Hi there,
[tex]\sf{\dfrac{1}{6}\approx0.167}[/tex], rounded to 3 DP (decimal places)
[tex]\left\vert\textsf{Decimal Places = Number of digits after the decimal point}\vert[/tex]
Why round? Because the entire number goes on for ever and ever.
So, we need to round. 1/6 rounded to 3 decimal places is 0.167. We have 3 numbers after the decimal point.
❄
What are the possible lengths of the third hallway? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
The possible length of the third hallway is between 30 yards and 150 yards.
How to find the third length of a triangle?The hallway forms a triangle .
Therefore, using triangle inequality theorem, It states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Hence,
90 + 60 > x
Where
x is the third side
x + 60 > 90
x + 90 > 60
Therefore, the possible length of the third hallway is between 30 yards and 150 yards.
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Answer:
D: between 30 yards and 150 yards
0.00000007 as a fraction
Answer:
7/100000000
Step-by-step explanation:
to find this out we can start by saying that 0.7 is 7/10
every 0 in front of 7 after that is adding another 0 to 10
so
0.07 is 7/100
0.00000007 is 7/100000000
Select the correct answer from each drop-down menu. a comic-strip writer churns out different numbers of comic strips each day. the writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set. 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8 the data in the distribution is . if the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is .
Mean = 3.5
Median = 3
Distribution is negatively skewed.
What is skew in the distribution?
The distribution has no skewness if the mean and median are equal.
The median exceeds the mean in a favorably skewed distribution.
The distribution is also negatively skewed if the median is lower than the mean.
Given,
Data set : 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8
Mean = [tex]\frac{1+1+2+2+2+3+3+3+3+4+4+4+5+5+6+8}{16}[/tex]
Mean = [tex]\frac{56}{16}[/tex]
Mean = [tex]3.5[/tex]
Median = mid value of the data set when the values are arranged in ascending order
Here,
the two mid values = [tex]3, 3[/tex]
Median = [tex]\frac{3+3}{2}[/tex]
Median = [tex]\frac{6}{2}[/tex]
Median = [tex]3[/tex]
Now, as the mean is larger than the median therefore the distribution will be skewed negatively.
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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.
ヾ(•ω•`)o
The angle measurements in the diagram are represented by the following expressions.
The angle measurements of angle B as represented in the diagram shown is 150°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the diagram:
∠A = ∠B (alternate interior angles)
Hence:
8x - 10 = 3x + 90
x = 20
∠B = 3(20) + 90 = 150°
The angle measurements of angle B as represented in the diagram shown is 150°
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iteration-Find the first 3 iterates of the function look at pic pls help!!!!!
The first 3 iterates of the function are D. 3, -3, 9.
How to calculate the value?The function given is:
f(x) = -2x + 3
= -2(0) + 3
= 3
When x = 3
f(x) = -2x + 3
= -2(3) + 3
= -6 + 3
= -3
When x = -3
f(x) = -2x + 3
= -2(-3) + 3
= 9
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11 points
please help me
Answer:
40%
8%
15%
37%
Step-by-step explanation:
The solutions are in the image
Clark works for Acme Bank and asks for your assistance. He wants you to look at a property that's about to go into foreclosure and provide him with a report on its current marketability and an approximate market value. What's Clark most likely asking you to provide
The information that Clark is asking me to provide for him regarding the property is called Brokers Price Opinion (BPO).
What is BPO?
The term BPO refers to Brokers Price Opinion. It is the opinion of a genuine real estate professional regarding the accurate pricing of a property.
The information that Clark is asking me to provide for him regarding the property is called Brokers Price Opinion (BPO).
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Solve the simultaneous equations x - 5y = 0 and 15x + 10y = 17
The solutions of the equations x - 5y = 0 and 15x + 10y = 17 at x and y is 1 and 1/5 respectively.
Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.
Given that:
The linear equations are:
x - 5y = 0
15x + 10y = 17
Solve the equations using elimination method:
Multiply equation 1 by 2
2(x - 5y) = 0
15x + 10y = 17
This can be solved as:
2x-10y = 0.....(1)
15x + 10y = 17....(2)
On subtracting equation 1 from 2
17x = 17
x = 1
The value of x is 1.
Substitute the value of x in equation (1)
2(1)-10y = 0
2=10y
y = 1/5
Thus, the value of x and y is 1 and 1/5 respectively.
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Revenue function: r(x) = 60x cost function: c(x) = 12 + 7x profit function: p(x) =
Profit function : p(x) = 53 x - 12
Cost is the total cost of producing the output.
The cost function consists of two different types of costs:
- Variable costs
- Fixed costs.
Variable costs vary with output (number of units produced). Total variable costs can be
expressed as the product of variable costs per unit and the number of units produced. If there are multiple items
manufactured costs are higher.
Fixed costs usually do not vary with performance.
Revenue is the total payment received from the sale of goods or the provision of a service.
The revenue function R() reflects the revenue from selling “” quantity of output items at price
"p" after item.
() =
Profit functions
The profit function P() is the difference between the revenue function R(x) and the total cost function C()
So P() = R() – C()
=−
Now, Profit = Revenue - Cost
= 60 x - ( 12 + 7 x)
= 60 x -12 -7 x
Profit = 53 x - 12
Hence, Profit function : p(x) = 53 x - 12
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Compared to the graph of f(x) = x², the graph of g(x) = (x − 2)² +3
is the result of translating f(x)
Answer:
Vertical shift up 3
Horizontal shift to the right 2
Brainliest, please :)
Answer:
Step-by-step explanation:
f(x) is moved 2 units to the right followed by 3 units up,
can someone help me i know nothing about graphs
Answer:
The answer is B.
Step-by-step explanation:
The function F(x) = x would be the “parent function”. Meaning the +4 we see in G(x) would be a translation, because the function is not multiplied.
if you have ever seen the formula y = mx + b then you should be able to see that +4 would be referencing b in the linear equation, and because m is the same in both lines, we can say that the two functions only change is b, because b represents the y-intercept, if b was 0 in f(x)=x and was 4 in g(x)=x+4, the graph would be shifted 4 units up.
if you want to learn how to understand functions and linear equations, I recommend using khan academy. It is really helpfull in explaining topics of math.
Call line that passes through the point x, y with a y intercept of b and a slope of m can be represented by the equation y=mx + b. a line is drawn on the coordinate plane that passes through the .3, -6 and has a slope of four the y-intercept of the line is
Answer: (0, -7.2)
Step-by-step explanation:
Substituting into point-slope form, the equation is
[tex]y+6=4(x-0.3)[/tex]
The y-intercept is when x=0, so substituting in x=0,
[tex]y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2[/tex]
So, the y-intercept is (0, -7.2).
Which expression can be used to find the volume of the sphere?
A sphere with diameter 10 inches.
V = four-thirds pi r squared = Four-thirds (3.14) (5) squared
V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed
V = four-thirds pi r cubed = Four-thirds (3.14) (10) cubed
V = four-thirds pi r squared = Four-thirds (3.14) (10) squared
I think its (B)
V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed
Help me with alg 2 please!
The probability that 5 boys would be selected would be 5/6720
How to determine the probabilityFrom the information given, the probability can be calculated using permutation
The formula for permutation is given as;
Permutation = [tex]\frac{n!}{n - r!}[/tex]
Where;
n is number of sets = 8r is the number of objects selected = 5Substitute the values into the formula
Permutation = [tex]\frac{8!}{8 - 5!}[/tex] = [tex]\frac{8!}{3!}[/tex] = [tex]\frac{40, 320}{6}[/tex] = 6720
The probability that 5 boys would be selected is 5/6720
Thus, the probability that 5 boys would be selected would be 5/6720
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Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)
1 2 5 8 10
Probability 0.35 0.2 0.1 0.2 0.15
Expected Value = [? ]
Round to the nearest hundredth.
Enter
Answer:
4.35
Step-by-step explanation:
The expected value can be defined as: [tex]\sum{x_i*p_i}[/tex] where x_i = the payout, and p_i = the probability of it occurring.
This gives us the expression: [tex](1 * 0.35) + (2 * 0.2) + (5 * 0.1) + (8 * 0.2) + (10 * 0.15) = 0.35 + 0.4 + 0.5 + 1.6 + 1.5 = 4.35[/tex]
So the expected payout is 4.35
3. A gardener uses 2 packages of lettuce seeds for 3 garden rows, each 5 feet long. How many packages of seeds does the gardener need to plant 45 feet of lettuce rows? Use the table to help.
Seeds (pkg) 2,4
Lettuce (rows) 3, 6
A 27
B 16
C 6
D 80
I need this with explanation please:(
Answer:
C) 6
Step-by-step explanation:
3 garden rows = 3*5 = 15 feet
we know we need 2 packages per each 15 feet
45/15=3 so 3 15 in 45, we just multiply 3 and 2 to get 6 packages
ASAP PLEASE I NEED YouR HELP
Subtract − 4 b 2 + 4 b − 4 from 3 b 2 + 2 b − 5 .
Step-by-step explanation:
I assume the question really looks like
-4b² + 4b - 4 is to be subtracted from 3b² + 2b - 5.
so,
3b² + 2b - 5 - (-4b² + 4b - 4) =
= 3b² + 2b - 5 + 4b² - 4b + 4 =
= 7b² - 2b - 1
(X+m)(c+n) if m=5 and n=-7
Answer: -7/5
Step-by-step explanation:
x = - 5cm^2 - 7m^2 + 35/ m (5c - 7), C = (cross out the equal sign) 7/5 and m = (cross out the equal sign) 0 and n = -7/5
Compare [tex]99![/tex] and [tex]50^{99}[/tex].
Hint: Identity [tex](a+b)(a-b)=a^2-b^2[/tex].
50^99 is greater than 99!
How to compare the numbers?The numbers are given as:
99! and 50^99
When the above numbers are estimated using a calculator, we have:
99! = 9.332622e+155
50^99 = 1.577722e+168
Next, we compare the exponents
168 and 155
168 is greater than 155
Hence, 50^99 is greater than 99!
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Cost of 4 tables and 3 chairs is $225 and 3 tables and 4
chairs cost $195. Find the cost of 2 chairs and 1 table.
The cost of 2 chairs is = $30
The cost of 1 table = $60
Step-by-step explanation:
Let a table represent x
A chair represents y
4x + 3y = 225.......eq 1
3x + 4y = 195........eq 2
Use elimination method
x - y = 30
x= 30 + y...... Eq 3
Substitute the value of x into equation 1
4(30+ y) + 3y= 225
120 + 4y + 3y= 225
7y + 120= 225
7y= 225-120
7y= 105
y= 15
Substitute the value of y in eq 2
3x + 15 = 195
3x= 195-15
3x= 180
x= 60
Therefore, the cost of 2 chairs is 15 * 2= $30
The cost of 1 table = $60
Answer:
65
Step-by-step explanation:
A badminton net is tethered to the ground with a strand of rope that forms a 50 angle with the ground. What is the length of the rope, x? Write an equation and show work below. Round to the nearest tenth.
Answer:
5.4 ft to nearest tenth.
Step-by-step explanation:
We know the adjacent side of the right triangle and we need the hypotenuse so we use the cosine:
cos 50 = 3.5/x
x = 3.5 / cos 50
= 5.445 ft.
If f(x) = x-2, what is f¹(x)?
f¹(x) = 9x + 18
ƒ²¹(x) = x + 2
f¹(x) = 9x+2
ƒ¹ (x) = -2x +
Interchange x and y
[tex]\\ \tt\leadsto x=\dfrac{1}{9}y-2[/tex]
Solve for y[tex]\\ \tt\leadsto \dfrac{1}{9}y=x+2[/tex]
[tex]\\ \tt\leadsto y=9(x+2)[/tex]
[tex]\\ \tt\leadsto y=9x+18[/tex]
That's the inverse[tex]\\ \tt\leadsto f^{-1}(x)=9x+18[/tex]
Answer:
[tex]f^{-1}(x)=9x+18[/tex]
Step-by-step explanation:
[tex]f^{-1}(x)[/tex] is the notation for the inverse of a function.
The inverse of a function is its reflection in the line y = x.
Given function:
[tex]f(x)=\dfrac{1}{9}x-2[/tex]
To find the inverse of the given function:
Replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=\dfrac{1}{9}x-2[/tex]
Rearrange the equation to make x the subject:
[tex]\implies y+2=\dfrac{1}{9}x[/tex]
[tex]\implies 9(y+2)=x[/tex]
[tex]\implies x=9y+18[/tex]
Replace x with [tex]f^{-1}(x)[/tex] and y with x:
[tex]\implies f^{-1}(x)=9x+18[/tex]
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pls help :,)
What is the area of this triangle?
units²
Answer:
6 [tex]units^{2}[/tex]
Step-by-step explanation:
The formula for the area of a triangle is A = [tex]\frac{1}{2} bh[/tex]. The base in this case is the length of DE, 4 - 1 = 3 units. The height of this triangle is 1 + 3 = 4 units.
A = [tex]\frac{1}{2} bh[/tex] = [tex]\frac{1}{2} *3*4[/tex] = 6