Step-by-step explanation:
x = total area of land
x - 1/6 × x - 5/9 × x = 48.5 | multiply both sides by 6
6x - x - 30/9 × x = 291
5x - 30/9 × x = 291 | multitude both sides by 9
45x - 30x = 2,619
15x = 2,619
x = 174.6 acres
pineapples were planted on 174.6 × 1/6 = 29.1 acres.
durians were planted on 174.6 × 5/9 = 97 acres.
a) Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable
Answer:
175
Step-by-step explanation:
Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)
For the given problem, the average queue length is:
Average queue length = (50 * 35) / (1 - 50 * 35)
= 175
given the following pyramid identify the L, P, and B then find the surface area
Answer:
slant length (l) = 7.5 m
perimeter of base P = 40 m
area of base B = 100 m^2
Surface Area = 250 m^2
Step-by-step explanation:
Surface area of a pyramid formula
1/2Pl + B
1/2 (40)(7.5) + 100
150 + 100 = 250 square meters
Find f(x) and g(x) so that the
function given can be described
as y = f(g(x)).
Answer:
[tex]g(x) = x^3+1\\f(x) = x^2[/tex]
Step-by-step explanation:
Answer:
f(x)=x^2 and g(x)=x^3+1
Step-by-step explanation:
to find y=f(g(x))
substitute g(x) into f(x)
y= (x^3+1)^2.
50 people sponsor Paula and she raises a total of $180.65 for charity. 28 people sponsor Kate and she raises a total of $135.60 for charity. 45 people sponsor Sam and he raises a total of $169.25 for charity.
How much money is raised altogether by three of them?
$_____________
Answer:
485.5
Step-by-step explanation:
180.65+135.60+169.25
400g is what percent of 80kg?
Please answer all of the questions and if u are correct I will give u brainliest ;) xoxo <3
Answer:
the answer for the 2nd question is 1/4
Step-by-step explanation:
i took the test
Of the three functions in the tables, which represent linear relationships?
Answer:
D. f and h
Step-by-step explanation:
The function f is a liner function because for every increase in x, there is a proportional increase in f(x). This can be seen when the x value goes from 2 to 4, so a 2 unit increase, the f(x) value increases by 3. Since this is true for every interval of 2 in f(x) -- increase x by 2 results in an increase in 3 of f(x) -- then f(x) is a linear function.
The same principle can be applied to h(x), with each 4 unit increase in x, the h(x) value increase by 36.
The function g(x) is not a linear function because for each unit increase of x, there is not a proportional increase (or decrease) in g(x). As seen in the table, g(2)-g(1)= 8-4= 4. For g(x) to be a linear function, every other one unit increase in x should result in a 4 unit increase in g(x0. But this does not occur. g(3)-g(2)= 16-8= 8 , g(4)-g(3)= 32-16= 16, 8 and 16 are not equal to four so g(x) cannot be a linear function.
Two buses leave a station at the same time and travel in opposite directions. One bus travels12m/hrslower than the other. If the two buses are 765 miles apart after 6 hours, what is the rate of each bus?
distance = speed * time
the first bus speed = x
second bus = x - 12
the sum of distance = 765 miles
first distance = 6x
second distance = 6 (x -12)
6x + 6(x-12) = 765
x + x -12 = 127.5
2x = 139.5
x = 69.75 mi/h which is the faster bus
the second bus speed = 57.75 mi/h
what is the answer please?
Answer:
34.562
Step-by-step explanation:
To find the perimeter of a circle, it's 2 * the radius * pi. In this case, we have a semicircle, so it would be the circle's perimeter divided by 2, or just the radius * pi.
The radius, 11, times pi (3.142), is 34.562.
Brainliest, please :)
how to find the side length of x
A local dry cleaner interviewed 17 candidates for the positions of the cashier, washer, salesperson, and delivery driver. How many ways can they fill the 4 positions?
HELP PLSPLSPLS
Using the permutation formula, it is found that there are 57,120 ways to fill the 4 positions.
There are different roles, hence the order is important, which means that the permutation formula is used.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 4 roles are chosen from a set of 17, hence the number of ways is given by:
[tex]P_{17,4} = \frac{17!}{13!} = 57120[/tex].
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In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6965 subjects randomly selected from an online group involved with ears. There were 1302 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than 20%. Use the P-value method and use the normal distribution as an approximation to the binomial distribution
The hypothesis test shows that we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%
What is the claim that the return rate is less than 20% by using a statistical hypothesis method?The claim that the return rate is less than 20% is p < 0.2. From the given information, we can compute our null hypothesis and alternative hypothesis as:
[tex]\mathbf{H_o :p =0.2}[/tex]
[tex]\mathbf{H_i:p < 0.2}[/tex]
Given that:
Sample size (n) = 6965
Sample proportion [tex]\mathbf{\hat p = \dfrac{x}{n} = \dfrac{1302}{6965} \sim0.1869}[/tex]
The test statistics for this data can be computed as:
[tex]\mathbf{z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}}[/tex]
[tex]\mathbf{z = \dfrac{0.1869 -0.2}{\sqrt{\dfrac{0.2(1-0.2)}{6965}}}}[/tex]
[tex]\mathbf{z = \dfrac{-0.0131}{0.0047929}}[/tex]
z = -2.73
From the hypothesis testing, since the p < alternative hypothesis, then our test is a left-tailed test(one-tailed.
Hence, the p-value for the test statistics can be computed as:
P-value = P(Z ≤ z)
P-value = P(Z ≤ - 2.73)
By using the Excel function =NORMDIST (-2.73)
P-value = 0.00317
P-value ≅ 0.003
Therefore, we can conclude that since P-value is less than the significance level at ∝ = 0.01, we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%
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Step 2 of 2 : Suppose a sample of 782 suspected criminals is drawn. Of these people, 548 were not captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
What is confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
Given sample, n= 782
As, 548 were not captured.
x= 548
So, p= 548/ 782
p = 0.7007
q= 1- 0.7007 = 0.2993
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
Now,
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
For confidence level of 98% , z is 2.33
Now,
(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782
= (0.6625, 0.7388)
Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
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3(x-5)² +14(x-5)-24
Answer:
3x^{2} -16x-19
Step-by-step explanation:
If we are going to be simplying this problem, then we need to take it step by step.
Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.
Answer:
(3x - 19) • (x + 1)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((3•((x-5)2))+14•(x-5))-24
STEP
2
:
Equation at the end of step 2
(3 • (x - 5)2 + 14 • (x - 5)) - 24
STEP
3
:
Trying to factor by splitting the middle term
Factoring 3x2-16x-19
The first term is, 3x2 its coefficient is 3 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is -19
Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57
Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .
-57 + 1 = -56
-19 + 3 = -16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3
3x2 - 19x + 3x - 19
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x-19)
Add up the last 2 terms, pulling out common factors :
1 • (3x-19)
Step-5 : Add up the four terms of step 4 :
(x+1) • (3x-19)
Which is the desired factorization
A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many committees can be formed if no person can serve on more than one committee?
Answer:
1,260
Step-by-step explanation:
[tex]\implies C(9,4)*C(5,3)*C(2,2)[/tex]
[tex]\implies 9!/4!(9-4)!*5!/3!(5-3)!*2!/2!(2-2)![/tex]
[tex]\implies 9!/4!5!*5/3!2! *2!0![/tex]
[tex]\implies (9 * 8 * 7 * 6 / 4 * 3 * 2 * 1) * (5 * 4 / 2 * 1) * 1[/tex]
[tex]\implies 1260[/tex]
Therefore, 1,260 committees can be formed.
a.- Representa el cálculo del porcentaje de cada par de artículos y marca el que es más conveniente comprar.
1 el par de zapatos cuesta $90.Por la compra de dos pares , tienes el 25% del descuento total
2 el par de zapatos cuesta $90.El segundo par de zapatos esta con el 40% de descuento
El costo en la opción uno es menor que el de la opción dos, asi que la primera es la más conveniente.
¿Cual opción es más conveniente?
En la primera opción, el par de zapatos cuesta $90, y el segundo par tiene un descuento del 25%.
Entonces el costo por 2 pares es:
C = ($90 + $90)*(1 - 25%/100%)
Donde le aplicamos un descuento del 25% al total del costo de los dos zapatos, resolviendo esto obtenemos:
C = ($180)*(0.75) = $135.
En la segunda opcion tenemos que los pares cuestan $90, pero esta vez le aplicamos un descuento del 40% al segundo par.
C = $90 + $90*(1 - 40%/100%) =
C = $90 + $90*(0.6) = $144
Así, vemos que en la primera opción el costo es menor, entonces esa es la mejor opción.
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Based on the graph of g (x), on which intervals
are the function's values positive? Select all that
apply.
Answer:
[tex]\text{A}) \text{ } -\infty < x < 3\\\\\text{C}) \text{ } -1 < x < 2\\\\[/tex]
Step-by-step explanation:
The graph lies above the x-axis for these intervals.
In ΔABC, m < C = 50* , a = 14 and b = 15. Find the length of side c, to the nearest integer.
The length of the side c, to the nearest integer is 12.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
u² = s² + t² - 2(s)(t)·cos U
In ΔABC, m < C = 50* , a = 14 and b = 15.
We can solve for the length of side a to the nearest whole number using the Laws of Cosines
c² = b² + a²- 2ba CosC
Solving for the value of a, we have:
c² = 15² + 14²- 2(15)(14)cos50°
c² = 225 + 196 - 269.97
c² = 151.029
c = 12.28
Hence, The length of the side c, to the nearest integer is 12.
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Algebra 2 point slope form help
The slope of the line is
[tex]\frac{-1-4}{-1-0}=5[/tex]
So, the equation of the line in point-slope form is [tex]\boxed{y+1=5(x+1)}[/tex]
Find the truth set of each predicate.
The truth set for each predicate are:
a) d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}
b) d ∈ { 1, 2, 3, 6}
c) x ∈ { [-2, -1] U [1, 2]}
d) x ∈ {-2, -1, 1, 2}
How to find the truth set of each predicate?
We only need to find the sets of values such that the statements are true.
a)
We want to find vales of d, such that d is an integer, and 6/d is an integer.
Here the possible values of d will be:
d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}
Which are all the factors of 6, so all these integers divide 6.
b) Same as before, but this time the domain is a positive integer, so now the truth set will be:
d ∈ { 1, 2, 3, 6}
c) We want to find real values of x such that:
1 ≤ x² ≤ 4
If we apply the square root to the 3 sides, we get two inequalities:
-√1 ≥ x ≥ -√4
√1 ≤ x ≤ √4
Simplifying:
-1 ≥ x ≥ -2
1 ≤ x ≤ 2
So the truth set is:
x ∈ { [-2, -1] U [1, 2]}
c) Same as before, but now we only have integer solutions, so the truth set is:
x ∈ {-2, -1, 1, 2}
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Mountain Climbing Gym has a gym registration fee of $30 and then charges $55 per month for all access climbing.
Susie wanted to model what she has spent in total on the climbing gym at any given month in the future.
Fill in the blanks for the equation if C = total Cost and m = number of months.
Answer:
C=55m + 30
Step-by-step explanation:
You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.
The perimeter of a rectangle is 286 meters. Find the length and width if the length is an integer and the width is 5 times the next consecutive integer.
Answer:
See below
Step-by-step explanation:
Calculate the area of this triangle.
11 cm,
cn
18 cm
14 cm
Answer:
1/2*b*h
1/2*18*14
1*9*14
126
Can anyone help me solve this? Please and thank you!
It's the sum of a geometric sequence.
Let's rewrite it a bit:
[tex]\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]
And now let's calculate this sum [tex]\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}[/tex]
Now let's calculate the initial sum:
[tex]\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67[/tex]
What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer:
all real number {x | x is a real number}
Plss helppppppppppppppp
Answer: [tex]-\frac{3}{2} \leq x < 5[/tex]
Step-by-step explanation:
We can split this into two inequalities, namely [tex]2x-3 < x+2[/tex] and [tex]x+2 \leq 3x+5[/tex].
Solving the first inequality,
[tex]2x-3 < x+2\\\\x-3 < 2\\\\x < 5[/tex]
Solving the second inequality,
[tex]x+2 \leq 3x+5\\\\2 \leq 2x+5\\\\-3 \leq 2x\\\\-\frac{3}{2} \leq x[/tex]
So, the solution is [tex]-\frac{3}{2} \leq x < 5[/tex]
A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area of 135 square units.
Part A Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B What is the perimeter of the expanded rectangle?
The equation to model the above scenario is [tex]x^{2}[/tex] +22x - 23 = 0
The perimeter of the expanded rectangle is 48 units
What is a rectangle?A rectangle is a quadrilateral with its 4 angles 90°
Analysis:
First rectangle:
length = 10 + x
width = x
Second rectangle:
length = x + 14
width = x + 8
Area of expanded rectangle = 135 square unit
(x+8)(x+14) = 135
[tex]x^{2}[/tex] + 8x + 14x + 112 = 135
[tex]x^{2}[/tex] + 8x + 14x -23 = 0
[tex]x^{2}[/tex] + 22x -23 = 0
[tex]x^{2}[/tex] + 23x - x - 23 = 0
(x-1)(x+23) = 0
Therefore x = 1
Expanded length = 1+14 = 15
Expanded width = 1+8 = 9
Perimeter = 2(9+15) = 48 units
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114
4. Line p contains point (6,-5) and is perpendicular to line q. The equation for line gis y = 3x + 5.
Write an equation for line p.
Part I: Find the slope of line q. (1 point)
Part II: Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.) (1 point)
that
Part III: Use the point given for line p and the slope you found in Part II to write an equation for line pin
point-slope form: y - y₁ = m(x-x₁). (1 point)
Line q has slope 3, as you've found.
Any line perpendicular to q will then have slope -1/3, as you've found.
Line p thus has slope -1/3 and we know it passes through (6, -5), so from the point-slope formula we get the equation
[tex]y - (-5) = -\dfrac13 (x - 6) \implies \boxed{y + 5 = -\dfrac13 (x - 6)}[/tex]
Math Problem...can you help? (Functions)
Step-by-step explanation:
[tex]h(x) = \frac{3}{x}\\h(h(x)) = \frac{3}{\frac{3}{x}}\\\\h(h(x)) = \frac{3}{1} * \frac{x}{3}\\h(h(x)) = \frac{3x}{3}\\h(h(x)) = x\\\\\\f(f(x)) = (x^2-3)^2-3\\f(f(x)) = x^4+2(x^2)(-3)+(-3)^2-3\\f(f(x)) =x^4-6x^2+9-3\\f(f(x)) = x^4-6x^2+6\\[/tex]
Nick volunteers at the library shelving books.
The graph shows how many books Nick shelves one Saturday.
Graph of a diagonal line on a coordinate plane with ALTDCTime in hoursALTDC on x-axis and ALTDCNumber of BooksALTDC on y-axis. The diagonal line is going up and to the right. Line passes through points (0, 0), (2, 60) and (4, 120).
Part A
How many books does Nick shelve in 2 hours? Enter your answer in the box.
The book does nick shelve in 2 hours is 60.
What is graph?
Given coordinates:
(0, 0), (2, 60) and (4, 120).
If we look at the coordinates (2, 60)
The value corresponds to 2 hours is 60.
Hence, the book nick shelves in 2 hours is 60.
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