Answer:
Tom paints the fence in 24 hours and Bill paints the fence in 12
Step-by-step explanation:
T = 1 fence / x hours
B = 1 fence / x - 12 hours
B + T = 1 fence / 8 hours
( 1 fence / x - 12 hours ) + ( 1 fence / x hours ) = 1 fence / 8 hours
( 1 / x - 12 ) + ( 1 / x ) = 1 / 8
multiply through all the denominators to get:
8x + 8 (x - 12 ) = x( x - 12 )
8x + 8x - 96 = x^2 - 12x
combine like terms to get:
x^2 - 28x + 96 = 0
factor to get:
( x - 4 ) ( x - 24 ) = 0
x = 4, 24
4 won't work, because that would mean Bill would take a negative amount of time to paint the fence by himself, so that means
Tom paints the fence in 24 hours and Bill paints the fence in 12
A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is given by the binomial distribution. Probability calculations are quicker when using the Normal approximation to the binomial distribution. Which of the following is false
a. The approximation requires np 10 and n(1 â p) 10.
b. The sample size here is too small to use the Normal approximation to the binomial.
c. The approximation requires np 30.
d. The Normal approximation works better if the success probability p is close to p = 0.5.
Complete options are;
a. The approximation requires np > 10 and n(1 - p) > 10.
b. The sample size here is too small to use the Normal approximation to the binomial.
c. The approximation requires np > 30.
d. The Normal approximation works better if the success probability p is close to p = 0.5.
Answer:
Option C is false
Step-by-step explanation:
Looking at the options,
In normal approximation to the binomial,
n is the sample size,
p is the given probability.
q = 1 - p
Now, one of the conditions for using normal approximation to the binomial is that; np and nq or n(1 - p) must be greater than 10.
This means that option A is true because we require np or n(1 - p) to be greater than 10.
From Central limit theorem, the sample size needs to be more than 30 for us to use normal approximation. Our sample is 10. Thus, option B is true.
The approximation doesn't require np > 30. Rather it's the sample size that needs to be more than 30. Thus, option C is false.
Generally, when the value of p in a binomial is close to 0.5, the normal approximations will work better than when the value of p is closer to either 0 or 1. The reason is that: for p = 0.5, the binomial distribution will be symmetrical. Thus, option D is correct.
Of the last 10 contestants on a game show, 8 won a prize. Considering this data, how many of the next 20 contestants would you expect to win a prize?
In 2017, it was estimated that the average amount spent on winter holiday gifts in the United States was $906. Based on the estimate from the Waldfogel study, how much of this would be deadweight loss
Based on the estimate from the Waldfogel study, 10[tex]\%[/tex] of this would be a deadweight loss, i.e., [tex]\[/tex]90.6 would be the deadweight loss.
Deadweight loss means the economic inefficiency that takes place when the allotment of resources in a market isn't at the optimal position.
The study suggested that the average recipient's valuation of the gift received was approximately 90[tex]\%[/tex] of the actual purchase price of the gift.
This means that 10[tex]\%[/tex] of the value of the gift gets lost in between.
This loss of 10[tex]\%[/tex] in value constitutes the deadweight loss.
The average amount spent on gifts = $906
Percentage loss in value = 10[tex]\%[/tex] or 0.10
Calculation of the deadweight loss,
DWL = Average amount spent on gifts × Percentage loss in value
DWL = [tex]\[/tex]906 × 0.10
Thus, the deadweight loss would be [tex]\[/tex]90.6.
Learn more about a deadweight loss here:
https://brainly.com/question/32082652
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Two numbers have a distance of four units from zero on a number line the numbers can be graphed on the number line as points a and B dragon drop the labels to the correct position on the number line (25 points!!!!!!)
A controlled operation that yields a set of results is called a
Answer:
is called a controlled operation
Step-by-step explanation:
that's what its called i just know
Which table of ordered pairs represents a proportional relationship?
Whoever answers correctly and first-will be marked brainiest :)
A rectangle with an area of 12 square units, what are the demensions?
Answer:
area= base(length)*height(width)
possible dimensions
4 *3, 3*4
6*2, 2*6
12*1, 1*12
The total distance an ant crawls varies directly with the time in seconds. The ant crawls a total distance of 160 centimeters in 20 seconds.
What is the time in seconds the ant crawls when the total distance is 216 centimeters?
8 s
11 s
25 s
27 s
Answer:
27sStep-by-step explanation:
Given data
total distance=160 cm
time taken =20seconds
We know that speed =distance/time
So let us solve for the speed of the ant
speed=160/20
speed= 8cm/s
Also when the distance is 216,and the ant uses the same speed,it will take the ant
time=distance/speed
time=216/8
time= 27seconds
[tex]\int{[sin(9x)cos(9x)]} \, dx[/tex]
Recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
Then we can write
sin(9x) cos(9x) = 1/2 sin(2 • 9x) = 1/2 sin(18x)
Then
∫ sin(9x) cos(9x) dx
= 1/2 ∫ sin(18x) dx
= -1/2 • 1/18 cos(18x) + C
= -1/36 cos(18x) + C
though you could continue with another double angle identity,
cos(2x) = cos²(x) - sin²(x)
to rewrite the antiderivative as
= -1/36 (cos²(9x) - sin²(9x)) + C
= 1/36 (sin²(9x) - cos²(9x)) + C
does anyone know the answer?
Answer:
£0.60
Step-by-step explanation:
If each pack costs £1.59 and Nadia orders 15 packs,
then the total order before discount = 1.59 x 15 = £23.85
From the table given, we can see that for an order of £23.85 a 2.5% discount will be applied.
Divide £23.85 by 100 to get 1%: £23.85 ÷ 100 = £0.2385
Now multiply by 2.5 to get 2.5%: £0.2385 × 2.5 = £0.59625 = £0.60
Alternatively, the calculation in one expression is:
(1.59 × 15) × 0.025 = 0.59625
What is the value of 17^0
Answer:
1
Step-by-step explanation:
Anything to the exponent of 0 is 1.
Arc length and sector area question
Answer:
<aob=1/2(can + ab)
<aob=1/2(25+46)
<aob=1/2(71)
<aob=35.5
Can someone PLS HELP
Answer: 72 square feet
Step-by-step explanation: just multiply 8* 7 = 56 then 8*2 = 16 and add = 72
Find the length of cable 1 in the diagram below
Answer:
cable 1 ≈ 54.63 ft
Step-by-step explanation:
using Pythagoras' identity in the right triangle having cable 1 as its hypotenuse.
let cable 1 be x , then
x² = 22² + 50² = 484 + 2500 = 2984 ( take square root of both sides )
x = [tex]\sqrt{2984}[/tex] ≈ 54.63 ft ( to 2 dec. places )
The standard unit of measurement for length is the:
mile
centimeter
meter
yard
Answer:
meter (m) is the standard unit measurement for length .
Answer:
it is meter just to let yall know
Step-by-step explanation:
2/5×6/7= in simplist or mixed form
Answer:
2/5x6/7 = 12/35
Step-by-step explanation:
when we multiply fractions we multiply the denominators together and the numerators as well, so 2 x 6 = 12. and 5 x 7 =35
12/35
What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final
answer to the nearest hundredth. 5, 20, x
Answer:
[tex]\sf x= 14.04^{\circ \:}[/tex]
using tan rule:
[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]
solve:
[tex]\rightarrow \sf tan(x)= \dfrac{5}{20}[/tex]
[tex]\rightarrow \sf x= tan^{-1}(\dfrac{5}{20})[/tex]
[tex]\rightarrow \sf x= 14.04^{\circ \:}[/tex]
Answer:
x = 14.04° (nearest hundredth)
Step-by-step explanation:
Use the tan trig ratio:
[tex]\mathsf{\tan(\theta)=\dfrac{O}{A}}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta=x[/tex]O = 5A = 20[tex]\implies \mathsf{\tan(x)=\dfrac{5}{20}}[/tex]
[tex]\implies \mathsf{x=\arctan\left(\dfrac{5}{20}\right)}[/tex]
[tex]\implies \mathsf{x=14.04\textdegree \ (nearest \ hundredth)}[/tex]
wo mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $75per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1800. How long did each mechanic work?
Answer:
he first one worked 15 hours, the second one worked 5 hours.
Step-by-step explanation:
First mechanic worked x hours, then second one worked 20 - x hours
First one charged $95*x, second one charged $75*(20-x)
Total charge = 95x + 75(20 - x) = 1800
95x + 1500 - 75x = 1800
20x = 300
x = 15, 20 - x = 5
So the first one worked 15 hours, the second one worked 5 hours.
The average time it takes a group of students to complete a certain statistics exam is 55.6 minutes. The standard deviation is 9 minutes. Assume the exam completion times are normally distributed. If 40 randomly selected students take the exam, what is the probability that the mean completion time for the group will be less than 45 minutes?
At Ariel's family reunion, Ariel hands out watermelon for the annual seed-spitting contest.
She gives a watermelon slice to each kid at the reunion. She also gives a slice to 40 adults.
Ariel hands out 90 watermelon slices in all.
Which equation can you use to find how many kids k are at the reunion?
k
90
K-40 = 90
k + 40 = 90
40k = 90
40
Solve this equation for k to find how many kids are at the reunion.
kids
1 Suppose that $61,000 is invested at 55% interest, compounded quarterly. a) Find the function for the amount to which the investment grows after t years b) Find the amount of money in the account at t=0.3.7, and 10 years. 12 %
a) The function for the amount to which the investment grows after t years is A(t) = (Simplify your answer. Type an expression using t as the variable )
Answer:
i think its a
Step-by-step explanation:
Please answer this question I don't have time please.
Answer:
The juice bar can sell 3 more cups of the passion juice than the berry juice (last one)
Step-by-step explanation:
Passion: 768/16=48
Berry: 810/18=45
passion can fill 48 cups while berry can fill 45 cups, so passion fills +3
:)
What measure would you use to compare the middle 50% wait times for cars in two different car wash locations?
Explain.
Answer:
what is the answer i dont know you tell him to ask another person because i m back bencheer
Find the equation of a line that passes through the point (0,4) and has a gradient of 2.
Leave your answer in the form
y
=
m
x
+
c
Answer:
[tex]y = \frac{x}{2} + 4[/tex]
write and solve and equation to find ABE
Answer:
77
Step-by-step explanation:
<DBE and <ABE are supplementary angles so their sum is equal to 180
<DBE is given as 103
103 + <ABE = 180 subtract 103 from both sides
<ABE = 77
Could you please help me on this
Answer:
-x^2 +10x + 7
[tex]-x^2 +10x + 7[/tex]
Step-by-step explanation:
its the gray shaded area [(x+1)*(x+7)] minus the white area [(x-1)*(2x)]
AKA: [(x+1)*(x+7)] - [(x-1)*(2x)]
so first you foil to get both areas
gray region: (x+1)*(x+7) = x^2 + 8x + 7
white region: (x-1)*(2x) = 2x^2 - 2x
and then you subtract the white from the gray
[tex](x^2 + 8x + 7) - (2x^2 - 2x)[/tex]
-x^2 +10x + 7
Anyone know the answer to this
Answer:
The answer is d
Step-by-step explanation:
To find out the asnwer, we need to find the value of X. First, we know that X is the same vaule in each equation so we have to find out a number can by multiplied to 9,6, and 5 and get the 3 numbers in either a,b,c, or d. 9x9=81,6x9=54, 5x9=45. These 3 answers matches the number in the choices.
⅚ times ¾ simplified
Answer:
[tex]\frac{5}{8}[/tex]
I hope this helps!
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
to multiply fractions, multiply the numerators together then the denominators.
5 * 3 = 15
6 * 4 = 24
15/24
now simplify that fraction.
15/24
divide both sides by 3
5/8
A triangle has vertices at R(1, 1), S(–2, –4), and T(–3, –3). The triangle is transformed according to the rule R0, 270°. What are the coordinates of S'?
(–4, 2)
(–2, 4)
(2, 4)
(4, –2)
Answer:
(-4,2)
Step-by-step explanation:
Knowing that/Given that:
The vertices of the triangle are rotated about the origin by 270° counter-clockwise.
In Addition, This transformation changes the co-ordinate (x,y) to (y,-x).
Before (x,y) After ( y, - x)
Vertices New vertices after 270° rotation
R= (1,1) R' = (1,-1)
S= (-2,-4) S' = (-4,2)
T= (-3,-3) T' = (-3,3)
Hence, the answer is (-4,2)
~Lenvy~
I need help with this math question
Answer:
-1/4x+3/4
or
-0.25x+0.75
Step-by-step explanation:
g(x) = mx + b
m = slope
b = initial value
m = -1/4
b = 3/4
g(x) = -1/4x+3/4
Hope this helped, let me know if you need more help!