Answer:
width 14 perimeter 160 (l=66 cm)
A group of 10 friends decides to head up to a cabin in the woods (where nothing could possibly go wrong). Unfortunately, a number of these friends have dated each other in the past, and things are still a little awkward. To get the cabin, they need to divide up into some number of cars, and no two people who dated should be in the same car.
a. What is the smallest number of cars you need if all the relationships were strictly heterosexual? Represent an example of such a situation with a graph. What kind of graph do you get?
b. Because a number of these friends dated there are also conflicts between friends of the same gender, listed below. Now what is the smallest number of conflict-free cars they could take to the cabin?
Friend A B C D E F G H I J
Conflicts with BEJ ADG HJ BF Al DJ B CI EHJ ACFI
c. What do these questions have to do with coloring?
Answer:
a) 3
b) 3
c) because of the permutations and combinations involved
Step-by-step explanation:
a) Determine the smallest number of cars needed
The number of cars are the same as conflict free cars
hence we can group the friends without conflict into the same car
1st car we will have : ACFI in it
2nd car we will have : GD in it
third care we will have : BEJH in it
∴ number of car needed = 3
b) number of conflict free cars = 3
c) Coloring is important in the question because of the permutations and combinations involved
Work out the equation of the line that
is parallel to the line y= 5x - 3
passes through (-2, -4)
Answer:
y = 5x +6
Step-by-step explanation:
the slope of the given equation is 5. a slope of a line parallel has the same slope. so 5
y- -4 = 5(x - -2)
y+4 = 5x +10
y = 5x +6
What is 12 divided by 7?
Answer:
1.71428571429..........
Divide. Round to the nearest tenth. .48÷9.23
[tex].48 \div 9.23[/tex]
Element X decays radioactively with a half life of 6 minutes. If there are 970 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 139 grams?
y = a(.5) *
Answer: 16.81 min
Step-by-step explanation:
Given
Initial concentration [tex]A_o=970\ gm[/tex]
Half-time [tex]T_{\frac{1}{2}}=6\ min[/tex]
Decay at any time t is given by
[tex]A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}[/tex]
put values
[tex]\Rightarrow 139=970\cdot 2^{\dfrac{-t}{6}}\\\\\Rightarrow 2^{\dfrac{t}{6}}=6.978\\[/tex]
Taking log both sides
[tex]\Rightarrow \dfrac{t}{6}\times \ln (2)=\ln (6.978)\\\\\Rightarrow t=6\times 2.802\\\Rightarrow t=16.81\ \text{min}[/tex]
Can you help me with this problem please?????
Answer:
The answer is the first option I hope it helps
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Answer:
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April and Cody invest $5,000 each at their local bank. April invests at a 4% simple interest rate for three years. Cody invests at a 4% compound interest rate, and earns $624.32 in interest. What is the difference in their account balances at the end of 3 years?
Answer:
106.43
Step-by-step explanation:
The difference in their account balances at the end of 3 years is $24.32
Calculations and ParametersTo solve the compound interest for Cody
First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 5,000.00(1 + 0.04/1)(1)(3)
A = 5,000.00(1 + 0.04)(3)
A = $5,624.32
To solve for the simple interest for April
P * T * R/100
5000 * 4 * 3/100
= 60,000/100
= 600.
We add the S. I of April's investment
= 5,000 + 600
= $5600.
Therefore, the difference between their account balances is $5,624.32 - $5600 = $24.32
Read more about compound interest here:
https://brainly.com/question/24924853
#SPJ6
Alternate exterior angles congruent.
Which angle forms a pair of alternate
exterior angles with angle 1?
Answer:
<1 = <8
Step-by-step explanation:
Pair of alternate exterior angles are formed when two parallel lines are cut across by abl transversal line. The two angles are found on the other side of the parallel lines but located on opposite sides along the transversal line.
Thus, <1 and <8 are exterior angles of the parallel lines that are crossed by the transversal and they are on the alternate sides along the transversal.
Therefore, <1 and <8 form a pair of alternate exterior angles.
<1 = <8
Based on the picture what is the Minimum, Maximum, Median, Q1, Q3, And the IQR?
Answer:
lol I hope I'm right ...
Step-by-step explanation:
minimum=2, maximum=10, Q1=3, median=6, Q3=8, IQR= 5
A sample of 9 adult elephants had an average weight of 11,773 pounds. The standard deviation for the sample was 24 pounds. Find the 99% confidence interval of the population mean for the weights of adult elephants. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.
Answer:
99% C.I of the population mean is ( 11746, 11800 )
Step-by-step explanation:
Given the data in the question;
Sample size n = 9
mean x" = 11773
standard deviation s = 24
for 99% confidence interval
∝ = 1 - 99% = 1 - 0.99 = 0.01
∝/2 = 0.01/2 = 0.005
degree of freedom df = n - 1 = 9 - 1 = 8
now, Critical t-value : [tex]t_{\alpha /2, df[/tex] = [tex]t_{0.005, 8[/tex] = 3.355
Now, at 99% Confidence interval of the mean population is;
x" ± [ [tex]t_{\alpha /2, df[/tex] × s/√n ]
we substitute
11773 ± [ 3.355 × 24/√9 ]
11773 ± [ 3.355 × 8 ]
11773 ± 26.84
so
⇒ {11773 - 26.84}, {11773 + 26.84}
⇒ ( 11746, 11800 )
Therefore, 99% C.I of the population mean is ( 11746, 11800 )
area of it plssssssssssssSSssssssSSSsSSSSs
Answer:
40units²
Step-by-step explanation:
find the shapes you know the formula of. There's two shapes a rectangle and a trapezoid.
do the formula for rectangle
A = bh
A = 8×2
A = 16
Now the formula for Trapezoid
A = 1/2h(b+b)
A = 1/2×4(4+8)
A = 1/2×4(12)
A = 1/2(48)
A = 24
16+24 = 40
a watch company is developing packaging for its new watch. The designer uses octagons with a base of 30 in. squared and rectangles with a length of 10 in. to create a prototype for the new package. What is the volume of the new prototype?
Answer:
300in3
Step-by-step explanation:
Answer:
300in3
Step-by-step explanation:
find the least common multiple of 40a3bc and 28a2b4cd
Answer:
The least common multiple is [tex]280a^6b^4cd[/tex]
Step-by-step explanation:
We find the least common multiple of the constant, and of each term.
Least common multiple of 40 and 28:
40 - 28|2
20 - 14|2
10 - 7|2
5 - 7|5
1 - 7|7
1 - 1
2*2*2*5*7 = 280
LCM of a^3 and a².
Exponents are 3 and 2.
LCM of 3 and 2 is 6. So
[tex]a^6[/tex]
b and b^4
LCM of 1 and 4, which are the exponents, is 4. So
[tex]b^4[/tex]
c and c
LCM of 1 and 1 is 1. So c
d
In the first term, no d means that it is [tex]d^0 = 1[/tex]
In the second, [tex]d^1 = d[/tex]
LCM of 0 and 1 is 1. So
d
Least common multiple:
Multiplication of all the LCM's. So
[tex]280a^6b^4cd[/tex]
Mike works for his father sanding wooden rocking chairs. He earns $6 per chair. How many chairs does he need to sand in order to buy a portable CD player for $49.99
How to Evaluate 5/9 x 8
Answer:
4 4/9
Step-by-step explanation:
First, you have to set it up: 5/9 times 8/1
We made it 8/1 since it has to be a fraction in the multipying ocess and the one does not change the value.
Next, Multiply.
5/9x8/1=40/9 as an inproper fraction
As a proper fraction, it is written as 4 4/9
A 20 ft ladder leans against a building and reaches a point 13 ft above the ground. Find, to the nearest degree, the angle that the ladder makes with the ground
8b + 4 - 4b + 2 = what
8b+4-4b+2= 4b+6
collect the like terms and add
Melanie and Tracy are each finding the equation of the trend line that fits the data in the table below.
Participation in the School Band
Year
Number of students
2010
48
2011
52
2012
55
2013
59
Melanie uses the ordered pairs (2010, 48) and (2013, 59) to find her equation. Tracy defines x as the number of years since 2010 and uses the ordered pairs (0, 48) and (3, 59) to find her equation. How will the two girls’ equations compare?
They will have the same slopes and the same y-intercepts.
They will have the same slopes but different y-intercepts.
They will have different slopes but the same y-intercepts.
They will have different slopes and different y-intercepts.
Answer:
B. They will have the same slopes but different y-intercepts.Step-by-step explanation:
MelanieThe slope:
m = (59 - 48)/(2013 - 2010) = 11/3The y -intercept:
the starting point, 2010The equation off the line:
y = 11/3x + 2010TracyThe slope:
m = (59 - 48)/(3 - 0) = 11/3The y -intercept:
the starting point, 0The equation off the line:
y = 11/3xAs we see they get same slopes but different y-intercepts.
Correct choice is B
Answer:
B) They will have the same slopes but different y-intercepts.
Step-by-step explanation:
I got 100% :>
Wite the ratio for sin A.
Answer:
the ratio is 182
Step-by-step explanation:
sana po makatulong
Answer:
sine = opposite leg / hypotenusesin A = BC / ABsin A = 13/85sin A ≈ 0.15I NEED THIS ASAP. What is m
Answer:
The measure of ∠DFE is 67°.
Step-by-step explanation:
Angle GFE is a straight angle, meaning that its measure is 180°, per se.
180 - 113 = m of ∠DFE
180 - 113 = 67
what is 9,030×29,234?
Answer:
263,93802
Step-by-step explanation:
xd
Mikayla earns $ 100 every 8 hours at her new job. At
this rate, how much will she earn in 14 hours?
Answer:
$175
Step-by-step explanation:
$100/8 hours = $12.5 hourly
$12.5 * 14 hours = $175
5. Find the probability that a randomly chosen point in the figure lies in
the shaded region.
Answer:
D
Step-by-step explanation:
area of shaded region=1/2×8×8=32 sq. units
area of larger triangle=1/2×14×16=112 sq units
reqd. probability=32/112=2/7
25 points!! Pls help!! If not I will probably get a D pls I will mark brainliest but will report if answer is unrelated
Answer:
18 cm!
Step-by-step explanation:
i need help with my grade 10 math work
a) x2+ 7x − 8
Product =
Sum =
Numbers =
Answer:
(x-1) and (x+8).
Step-by-step explanation:
The given expression is :
[tex]x^2+7x-8[/tex]
We need to find the factors of this expression.
Product of two numbers = 8 and -1 = -8
Sum of two numbers = 8 and -1 = 7
So,
[tex]x^2+7x-8=x^2+8x-x-8\\\\=x(x+8)-1(x+8)\\\\=(x-1)(x+8)[/tex]
So, the factors of this expression are (x-1) and (x+8).
two parallel lines are cut by a transversal what is the measure of 2
Answer:
b 80
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
A P EE X
A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with A random sample of 12 sample specimens has a mean compressive strength of psi. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete.
Complete Question
A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with[tex]\sigma^2=1000[/tex]. A random sample of 12 sample specimens has a mean compressive strength of [tex]\=x=3207psi[/tex]. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete.
Answer:
[tex]CI=(3189.1,3224.9)[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=12[/tex]
Standard deviation [tex]\sigma^2=1000psi^2\\\sigma=\sqrt{1000} \\\sigma=31.6[/tex]
Sample mean [tex]\=x=3207[/tex]
Confidence level =95%
[tex]\alpha=100-95\\\alpha=0.05[/tex] significance level
From table \alpha 0.05
Gives
[tex]Z_c=1.96[/tex]
Generally the equation for confidence interval is mathematically given by
[tex]CI=(\=x-\frac{z_c*\sigma}{\sqrt{n} } ),\=X+\frac{Z_C*\sigma}{\sqrt{12} })[/tex]
[tex]CI=(3207-\frac{1.96*31.6}{\sqrt{12} } ),3207+\frac{1.96*31.6}{\sqrt{12} })[/tex]
[tex]CI=(3189.1,3224.9)[/tex]
What is the common difference for this arithmetic sequence?
-5, -1, 3, 7, 11,...
A. 4
B. 2
C. 5
D. 3
Answer:
5
Step-by-step explanation:
Negative is always negative positive is always positive
Plz help me well mark brainliest if correct!!
Answer:
(1, 1)
Step-by-step explanation:
not 100% sure though, but hope it helps