Answer:
W = 10
L = 20
Step-by-step explanation:
2L + 2W = 60
L = 2W
Substitute for L in the first equation
2(2W) + 2W = 60
4W + 2W = 60
6W = 60
W = 10
Plug in W in the first equation
2L + 2(10) = 60
2L + 20 = 60
2L = 40
L = 20
Plug both answers in both equations to check
2(20) + 2(10) = 60
20 = 2 * 10
Hope that helps!
Find the quadratic root of 3 x² - 4x + 2
Answer:
it has no real roots.
and the 2nd answer is correct.
Step-by-step explanation:
Answer:
this quadratic equation has two roots:
x = (2+i√(2))/3 , (2-i√(2))/3
Steps:
3x²-4x+2=0
x = (4±√((-4)²-4×3×2))/2×3
x = (4±√(16-24))/6
x = (4±√(-8))/6
x = (4±√(-2×4))/6
x = (4±√(-2)×√(4))/6
x = (4±i√(2)×2)/6
x = (2±i√(2))/3
x = (2+i√(2))/3 , (2-i√(2))/3
Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term
is two times the fifth term. Find the common difference and the first term.
Answer:
The first term is -6 and common difference is 3
Step-by-step explanation:
The nth term of an arithmetic progression is expressed as;
Tn = a + (n-1)d
T3 = a+2d
T4 = a + 3d
If the third term of an arithmetic sequence less than the fourth term by three
T3 = T4 - 3
a+2d = a+3d - 3
2d - 3d = -3
-d = -3
d = 3
Similarly;
T7 = a+6d
T5 = a+4d
If the seventh term is two times the fifth term, the;
T7 = 2T5
a+6d = 2(a+4d)
a+6d = 2a+8d
Since d = 3
a + 6(3) = 2a + 8(3)
a+18 = 2a + 24
a-2a = 24 - 18
-a = 6
a = -6
Hence the first term is -6 and common difference is 3
Dylan is creating clay at home for an art project. The recipe calls for 6 cups of water and 5.5 cups of flour. Dylan would like to make more clay than the recipe calls for and so he puts 44 cups of flour in the bowl instead. How many cups of water should he use?
Answer:
48 cups of water
Step-by-step explanation:
Using the provided ratio of 6:5.5...
if 6:5.5
then
48:44
GIVING BRAINLEST TO WHOEVER ANSWERS CORRECT
This list gives information about a video collection.
Study the list carefully. Then, use the drop-down menu to complete the statement below about the list.
Answer:
everything is black :/
Step-by-step explanations:
Find the area of a parallelogram with vertices (-7, 2), (6, 2), (6, -5), and (-7, -5). Use the coordinate grid below to help you find your answer.
Answer:91
Step-by-step explanation:
(05.05 MC) The area of a triangle is 24 square Inches. What is the height of the triangle if the base length is 6 inches? (10 points)
1) 4 inches
2) 8 inches
3) 18 inches
4) 20 inches
Answer:
It’s 8 inches
Step-by-step explanation:
Answer:
8 inches
Step-by-step explanation:
I got it right on my FLVS test :D
what is the mean of 6,5,4,5,8,2
Answer: 5
Step-by-step explanation:
Answer:
Step-by-step explanation:
5
Plot points on the number line to represent all whole numbers that round to 200 to the nearest hundred and 250 when rounded to the nearest ten.
Answer:
To round a number to the nearest hundred, you make it into the hundred that is closest. Take the number 246, for example, which is between 200 and 300. It is closer to 200. So 246 rounded to the nearest hundred is 200.
If a cube has a volume of 1/8 cubic units, what is the area of one or its faces?
Answer:
The area of one of the faces of the cube is equal to 1/4 cubic units.
Step-by-step explanation:
Given that a cube has a volume of 1/8 cubic units, to determine what is the area of one of its faces, the following calculations must be performed, knowing that the volume of a cube is equal to the value of one of its sides cubed , and the area of one of its faces is equal to the multiplication between its base and its height:
1/8 = 0.125
3√0.125 = 0.5
0.5 x 0.5 = 0.25
0.25 = 1/4
Therefore, the area of one of the faces of the cube is equal to 1/4 cubic units.
PLS HELP
Pilar is playing with a motorized toy boat. She puts the boat in a lake and it travels 400m at a constant speed. On the way back to Pilar, the boat travels the same route at the same speed for 2 minutes, and then Pilar uses the remote control to increase the boat's speed by 10 m/min. So the return trip is 60 seconds faster. How long does the return trip take?
Answer:
7 minutes
Step-by-step explanation:
the trip takes 7 mins
Pilar puts the boat in a lake that travels 400 meters at a constant speed. The time. On the return, the speed was the same for 2 minutes and then increase by 10m/min. The time boat takes in return back = 8 minutes
Solution for the time taken by speed changeThe given information states that the away distance the boat traveled = 400 m
The time traveled at the same initial speed, v₁, by the boat on the way back = 2 minutes.
The increase in speed of the boat by Pilar = 10 m/min
The new speed, v₂ = v₁ + 10
The time for the return trip, t₂ = 60 seconds (1 minute) faster than the time for the trip, t₁
[tex]t_2 = t_i - 1[/tex]
Therefore we have;
[tex]v_i\times t_i = v_i \times 2 + v_2 \times (t_2-2) \\= 400\\v_i \times 2 + (v_i + 10) \times (t_2-2) = 400\\(v_i + 10) \times t_2 - 20 = 400\\[/tex]
but
[tex]v_i = \frac {400}{t} = \frac{400)}{t_2+ 1}[/tex]
Which gives;
[tex]\frac{(400) }{(t₂ + 1} + 10) \times t_2 - 20 = 400\\10\times ( t_2²+ 36·t_2-2)/(t_2+1) = 40010 \times t_2^²+ 10 \times t_2-420 = 0[/tex]
[tex]t_2^2+ t_2-42 = 0[/tex]
[tex](t_2 - 7)(t_2 + 6) = 0[/tex]
[tex]t_2 = 7[/tex] minutes or [tex]-6[/tex] minutes
Given that t₂ is a natural number, we have,
t₂ = 7 minutes
Whereby, [tex]t_2 = t_i - 1[/tex], we have;
[tex]7 = t_i - 1[/tex]
[tex]t_{i} = 1 + 7 = 8[/tex] Minutes
The trip normally takes 8 minutes
Learn more about speed and distance:
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A)32 ft
B) 60 Ft
C) 72ft
D) 96ft
Answer:
96
Step-by-step explanation:
16 * 6 = 96
an employee at the metropolitan museum of art surveyed a random sample of 150 visitors to the museum. of those visitors, 45 people bought food at the cafeteria.based on those results, how many people out of 1750 visitors to the museum would be expected to buy food for the cafeteria?
Answer:
525 people would be expected
Step-by-step explanation:
45 out of 150 or 45/150 is simplified to 3/10
1750 people * 3/10 = 525
Answer:
525 is the answer
Step-by-step explanation:
I need help solving this problem.
(f+g-k)(x) means to add the equations f(x) and g(x) then subtract k(x)
2x^2 + 3x + 4x - 9 = 2x^2 +7x -9
2x^2 + 7x - 9 - x^2 -7x = x^2 -9
The answer is : x^2 - 9
The answer I got is x^3 + 14x - 9x
if you actually know plz give an explanation to the answer so i know you aren't just answering for points, please help this is due before 12:00
Answer:
B
Step-by-step explanation:
Probability of getting 9 or 11 = 2 /6 =1/3
Probability of getting tails in coin = 1/ 2
Probability of getting 9 or 11 AND tails in coin toss = 1/2 * 1/3
= 1/6
please help me I will give a brainlist
Answer:
prett sure it's b
Step-by-step explanation:
Answer to this please
Answer:
2, -2
Step-by-step explanation:
You start at -1, 2
-1 ,2
3, -4
add the Transformations to the starting coordinates and end up getting
2,-2
A random sample of 41 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $19.55 per car. The population standard deviation is $6.33. Estimate the mean bill for all cars from the drive-thru with 97% confidence.
Answer:
[tex]19.55\pm2.145[/tex]
Step-by-step explanation:
We use the equation [tex]\bar x\pm z^*\sigma/\sqrt n[/tex], where [tex]\bar x=19.55[/tex], [tex]\sigma=6.33[/tex], [tex]n=41[/tex], and [tex]z^*=2.17[/tex]. We obtain [tex]z^*[/tex] from the z-score of a 0.97 confidence level.
The 97% confidence interval estimate for the mean bill for all cars from the drive-thru is approximately $17.23 to $21.87.
To estimate the mean bill for all cars from the drive-thru with 97% confidence, we can use a confidence interval.
Sample size (n) = 41
Sample mean (x(bar)) = $19.55
Population standard deviation (σ) = $6.33
To calculate the confidence interval, we'll use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
First, we need to calculate the standard error, which is the standard deviation of the sample mean.
Standard Error (SE) = Population Standard Deviation / √(Sample Size)
SE = $6.33 / √(41)
Next, we determine the critical value based on the desired confidence level. Since we want a 97% confidence interval, we need to find the critical value corresponding to a 97% confidence level.
The critical value can be obtained from a standard normal distribution table or by using a calculator. For a 97% confidence level, the critical value is approximately 2.17.
Now, we can calculate the confidence interval:
Confidence Interval = $19.55 ± (2.17 * SE)
Substituting the values:
Confidence Interval = $19.55 ± (2.17 * ($6.33 / √41))
Calculating this, we find:
Confidence Interval ≈ $19.55 ± $2.32
Therefore, the 97% confidence interval estimate for the mean bill for all cars from the drive-thru is approximately $17.23 to $21.87.
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#SPJ2
the co-terminal angle of -120°
Answer:
-480°, 240° (among others)
Step-by-step explanation:
± 360
Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800; SSTR = 4560.
Required:
a. Set up the ANOVA table for this problem.
b. Use α= .05 to test for any significant difference in the means for the three assembly methods.
Answer:
H0 is rejected.There difference in the means for the three assembly methods.
Step-by-step explanation:
Calculating gives the following results.
ANOVA Table
Source DF Sum Mean F Statistic
of Square Square
Treatments 2 4560 2280 9.865
(between groups)
Error 27 6240 231.111
Total 29 10,800
Error SS= SST -SSTR = -10,800-4560=6240
d.f for SSTr = r-1= 3-1
D.f for SST= n-r= 30-3= 27
Total D.f= d.f for SSTr+D.f for SST= 27+29
MSTR= SSTR/d.f= 4560/2= 2280
MSError= Error SS/ d.f= 6240/27=231.111
F test= MSTR/ MsError= 2280/231.11= 9.865
The P- value < 0.01 which is less than 0.05 therefore H0 is rejected.
There is sufficient evidence to reject H0.
In ARST, the measure of ZT=90°, the measure of ZR=39°, and TR = 55 feet. Find the
length of ST to the nearest tenth of a foot.
Answer:
44.5 ft
Step-by-step explanation:
Reference angle = 39°
Opposite = x
Adjacent = 55
Apply trigonometric function TOA:
Tan 39 = Opp/Adj
Tan 39 = x/55
55 × Tan 39 = x
44.5381218 = x
x ≈ 44.5 ft
please help! which angles are congruent?
Answer:
All of the angles
Step-by-step explanation:
All of the angles
Answer: Opposite angles
Step-by-step explanation: As you can see, angles B and D are opposite from each other and they have matching angles. Angles A and C are opposite from each other and they have matching angles. So the opposite angles are congruent. Congruent = identical
Answer with steps please i have 1 mark on this with steps
Ahamd wants to cover a box that is 6 cm long 4 cm high and 4 cm wide with material on all the sides how much material does he need
Answer:
56cm²
Explanation:
the amount of material he needs would be the total surface area of the box. surface area can be calculated by finding the sum of surface area of all the sides of the box. since the opposite sides are equal, we can find the surface area of 3 different sides and then multiply it by 2.
(4 + 4) + (4 + 6) + (6 + 4) × 2
= 8 + 10 + 10 × 2
= 28 × 2
= 56cm²
i hope this helps! :D
Please need help on this
Step-by-step explanation:
Standard form is
[tex] {x}^{2} + {y}^{2} + ax + by + c = 0 \\ [/tex]
[tex] {x}^{2} + {y}^{2} - 18y + 5 = 0[/tex]
explain C = 15 + 0.6Yd
Help with these questions
In a particular year, a total of 50,127 students studied in two of the most popular host countries when traveling abroad. If 8383 more students studied in the most
popular host country than in the second most popular host country, find how many students studied abroad in each country.
There were students who studied abroad in the most popular host country.
Answer:
In the most popular abroad country: 29,255 students
In the second-most one: 20,872 students
Step-by-step explanation:
Let's write the situation in an equation to help us solve this. X represents the amount of students in the second most popular country. So we know that in total, there's 50,127 students so let's make an equation that equals this. ???????=50,127. As we know, the most popular country has 8383 more students than the second one so we can write it as x+8383 and for the second most popular country, we can write it as x. We know that both of the countries students combined equal 50,127 students so we have our equation. (x)+(x+8383)=50,127 students. After solving the equation, you get x=20, 872. As we know x=the amount of students in the second most popular country which means there's 20,872 students in the second one. Additionally, for the first most popular one, the equation for the amount of students in it is x+8383 so..... 20,872+8383=Total number of students in the most popular one which is 29,255 students.
3. Use computer drawing software to construct a quadrilateral with
two pairs of parallel sides and two angles measuring 125°. What
geometric shape describes this quadrilateral?
9514 1404 393
Answer:
parallelogram
Step-by-step explanation:
A shape with two pairs of parallel sides is a parallelogram. If an angle is something other than 90°, then the figure is not a rectangle.
In your backpack there are three math books, two science books, and five notebooks. If you reach into your backpack and select a math book, and then reach in and select a notebook, are these independent events? Explain.
A. No. You did not replace the first book, so that changed the probability that you would draw a notebook second.
B. Yes. The probability of drawing a notebook was the same regardless of replacing the math book.
C. No. These are dependent events and you can calculate the probability of this outcome using the formula
D. Yes. You can use this formula to calculate the probability of this outcome
Branliest to correct answer
What is the length of side 'y'?
Answer:
B
Step-by-step explanation:
John needs to divide the sample in half once the number of bacteria has reached 1000. How many hours after the initial time must be divide the sample?
Answer:
Option A
Step-by-step explanation:
The complete question is attached here
The rate of increase of bacterial population be K
As we know
[tex]Y = Y_0 * e^{kT}[/tex]
where Y is the final population. In this case it is 1000
K is the rate of increase of population i.e 3 times per hour
T is the time in hours
Y0 is the initial population = 5
Substituting the given values, we get -
[tex]1000 = 5 *e^{3*T}\\200 = e^{3*T}[/tex]
Taking log on both sides, we get -
ln [tex]200[/tex] = ln [tex]e^{3T}[/tex]
[tex]2.718 * 2.301 = 3T[/tex]
T = 2.084 hours
hence, option A is correct
The number of hours required after the initial time must be divide the sample by John is 2.084 hours.
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=ba^x+c[/tex]
Here, a, b, and c are the real number
John needs to divide the sample in half once the number of bacteria has reached 1000.
The table of this bacterial growth is,
Time(hours) Number of bacteria
0 5
1 15
2 45
The rate of increasing the bacteria each hour is,
[tex]x=\dfrac{15}{5}=3\\x=\dfrac{45}{15}=3[/tex]
Thus, the exponential rate is 3.
Now the number of reached is 1000, and the initial population was 5. Therefore, for the time t, the exponential function can be given as,
[tex]1000=5e^{3t}\\\dfrac{1000}{5}=e^{3y}\\200=e^{3y}[/tex]
Taking log both the sides as,
[tex]\ln (200)=\ln e^{3t}\\2.301=0.434({3t})\\t=2.084[/tex]
Hence, the number of hours required after the initial time must be divide the sample by John is 2.084 hours.
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