Answer:
3 hours for miss patrick 5 hours for mr shah
Step-by-step explanation:
Answer: they have to work for 11.25 hours.
Step-by-step explanation:
Let x represent the number of months for which they have to work to make the same amount.
Each month, Miss Patrick spends $60 on transportation to work, and earns $24.50 per hour. This means that if she works for x hours in a month, the total amount that she would have is
24.5x - 60
Each month, Mr. Shah spends $150 on lab equipment and earns $32.50 per month. This means that if he works for x hours in a month, the total amount that he would have is
32.5x - 150
For them to have the same amount, the number of months would be
32.5x - 150 = 24.5x - 60
32.5x - 24.5x = - 60 + 150
8x = 90
x = 90/8
x = 11.25 hours
The sample consisted of 50 night students, with a sample mean GPA of 3.02 and a standard deviation of 0.08, and 25 day students, with a sample mean GPA of 3.04 and a standard deviation of 0.06. The test statistic is:
Answer: The test statistic is t= -0.90.
Step-by-step explanation:
Since we have given that
n₁ = 50
n₂ = 25
[tex]\bar{x_1}=3.02\\\\\bar{x_2}=3.04\\\\\sigma_1=0.08\\\\\sigma_2=0.06[/tex]
So, s would be
[tex]s=\sqrt{\dfrac{n_1\sigma_1^2+n_2\sigma_2^2}{n_1+n_2-2}}\\\\s=\sqrt{\dfrac{50\times 0.08^2+25\times 0.06^2}{50+25-2}}\\\\s=0.075[/tex]
So, the value of test statistic would be
[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{s(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\t=\dfrac{3.02-3.04}{0.074(\dfrac{1}{50}+\dfrac{1}{25})}\\\\t=\dfrac{-0.04}{0.074(0.02+0.04)}\\\\t=\dfrac{-0.04}{0.044}\\\\t=-0.90[/tex]
Hence, the test statistic is t= -0.90.
PLEASE HELP ME, IF CORRECTLY ANSWERED I’LL GIVE BRAINLIEST
Answer:
c=f(x)−ax^2−bx
Step-by-step explanation:
Answer:
C=1
Step-by-step explanation:
Put the first point in the equation y=ax^2+bx+c where x=0 and y=1 you get
1=a*0+b*0+c
1=c
Death Valley CA is 282 feet below sea level. Black Mountain, KY is 750 feet above sea level . How many more feet above sea level is Black Mountain than Death Valley?
From the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
Death Valley CA is 282 feet below sea level.
Black Mountain, KY is 750 feet above sea level.
Death Valley (282ft) + 282ft = sea level (0).
0 + 750ft = Black Mountain (750ft).
282ft + 750ft = 1032ft.
From Death Valley to Black Mountain, it rises 1032 feet. Death Valley is 1032 ft lower than Black Mountain in elevation.
Thus, from the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.
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Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t2. How long will the ball take to hit the ground?
Answer:
8.899s
Solve: -5t^+40t+40
4-2√2 is the time taken by the ball to hit the ground.
What is Distance?Distance is the total movement of an object without any regard to direction
Given that Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t². then we need to find the time for ball to hit the ground.
The given function is
h(t)=40t-5t²
Let h(t)=40
We get,
40t-5t²=40
5t²-40t+40=0
t²-8t+8=0
(t-4)²=8
t-4=±√8
t=±√8+4
t=√8+4; t=4-√8
By considering the reality we know t>0
t=4-2√2
Hence t=4-2√2 is the time taken by the ball to hit the ground.
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Joan is building a sandbox in the shape of a regular pentagon. The perimeter of the pentagon is 35y4 – 65x3 inches. What is the length of one side of the sandbox? 5y – 9 inches 5y4 – 9x3 inches 7y – 13 inches 7y4 – 13x3 inches
Answer:
Step-by-step explanation:
given that Joan is building a sandbox in the shape of a regular pentagon.
The perimeter of the pentagon is
[tex]35y^4 - 65x^3[/tex]inches.
Since regular pentagon we know that all sides are equal and there are totally five sides.
Perimeter of regular pentagon = 5*side
= 5a where a = length of side
Equate 5a to given perimeter to get
[tex]5a=35y^4 - 65x^3\\[/tex]
divide by 5
[tex]a=\frac{35y^4 - 65x^3}{5} \\=7y^4-13x^3[/tex]
Answer:
D. 7y^4 - 13x^3 inches
A family has a rectangular back yard that measures 5x+4 by 3x-2 they are building a square patio with side lengths that measure x+3. write an expression for the area of grass that will be left in the back yard after the patio is built. show your work.
Answer: 14x² - 4x - 17
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
The rectangular back yard measures 5x + 4 by 3x - 2. This means that the area of the rectangular back yard would be
Area = (5x + 4)(3x - 2)
Area = 15x² - 10x + 12x - 8
= 15x² + 2x - 8
The formula for determining the area of a square is expressed as
Area = length²
Length of square patio = x + 3
Area of square patio = (x + 3)(x + 3)
= x² + 3x + 3x + 9
= x² + 6x + 9
The expression for the area of grass that will be left in the back yard after the patio is built is
15x² + 2x - 8 - (x² + 6x + 9)
= 15x² + 2x - 8 - x² - 6x - 9
= 15x² - x² + 2x - 6x - 8 - 9
= 14x² - 4x - 17
Combined with the equation −9x + 3y = 12 creates a system of linear equations with no solution? Select one: A. 18x - 6y = 20 B. 3x - y = -4 C. -16x + 9y = 30 D. 5x + 8y = -1
Answer:
The correct option is A. 18x - 6y = 20
Step-by-step explanation:
A system of two equations has no solution if the lines having these equations are parallel to each other.
Also, two lines [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex] are parallel,
If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
While,
They coincide ( infinitely many solution ) if [tex]\frac{a_1}{a_2}=\frac{ b_1}{b_2}=\frac{c_1}{c_2}[/tex],
They are non parallel ( a unique solution ) if [tex]\frac{a_1}{a_2}\neq \frac{ b_1}{b_2}\neq \frac{c_1}{c_2}[/tex],
Here, the given equation,
-9x + 3y = 12
Since in lines -9x + 3y = 12 and 18x - 6y = 20,
[tex]\frac{-9}{18}=\frac{3}{-6}\neq \frac{12}{20}[/tex]
Hence, system −9x + 3y = 12, 18x - 6y = 20 has no solution.
In lines -9x + 3y = 12 and 3x - y = -4,
[tex]\frac{-9}{3}=\frac{3}{-1}= \frac{12}{-4}[/tex]
Hence, system −9x + 3y = 12, 3x - y = -4 has infinitely many solutions.
In lines -9x + 3y = 12 and -16x + 9y = 30 ,
[tex]\frac{-9}{-16}\neq \frac{3}{9}\neq \frac{12}{30}[/tex]
Hence, system −9x + 3y = 12, -16x + 9y = 30 has a solution.
In lines -9x + 3y = 12 and 5x + 8y = -1,
[tex]\frac{-9}{5}\neq \frac{3}{8}\neq \frac{12}{-1}[/tex]
Hence, system −9x + 3y = 12, 5x + 8y = -1 has a solution.
A company has 8 cars and 11 trucks.The state inspector will select 3 cars and 4 trucks to be tested for safety inspections in how many ways can this be done
Answer:
Number of ways to select 3 cars and 4 trucks = 18,480
Step-by-step explanation:
Let x be the number of ways to select 3 cars and 4 truck.
Given:
Total number of cars = 8
Total number of Trucks = 11
We need to find out how many ways can the inspector select 3 cars and 4 truck.
Solution:
Using combination formula.
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
Where, n = Total number of object.
m = Number of selected object.
We need to find out how many ways can the inspector select 3 cars and 4 truck from 8 cars and 11 trucks.
So, we write the the combination as given below.
[tex]8C_{3}\times 11C_{4} = Number\ of\ ways\ to\ selection[/tex]
[tex]\frac{8!}{3!(8-3)!} \times \frac{11!}{4!(11-4)!}= x[/tex]
[tex]x = \frac{8\times 7\times 6\times 5!}{3!\times 5!} \times \frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]
Factorial 5 and 7 is cancelled.
[tex]x = \frac{8\times 7\times 6}{6} \times \frac{11\times 10\times 9\times 8}{24}[/tex] ([tex]3! = 6\ and\ 4! = 24[/tex])
[tex]x = (8\times 7) \times (11\times 10\times 3)[/tex] ([tex]\frac{9\times 8}{24}=\frac{72}{24}=3[/tex])
[tex]x=56\times 330[/tex]
x = 18480
Therefore, the Inspector can select 3 cars and 4 trucks in 18,480 ways,
To determine how many ways the state inspector can select 3 cars from 8 and 4 trucks from 11, we need to calculate the combinations separately for each type of vehicle and then multiply them together to find the total number of ways to make both selections simultaneously.
### Selection of Cars:
The number of ways to choose 3 cars from 8 is a combination problem, because the order in which we select the cars does not matter. The formula for combinations, denoted as C(n, k), where n is the total number of items to choose from, and k is the number of items to be chosen, is given by:
C(n, k) = n! / (k! * (n - k)!)
Let's apply this formula to select 3 cars from 8:
C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8 × 7 × 6) / (3 × 2 × 1)
Simplify the factorials by canceling out common terms:
C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = (8/2) × (7/1) × (6/3) = 4 × 7 × 2 = 56
So, there are 56 ways to choose 3 cars out of 8.
### Selection of Trucks:
Similarly, to choose 4 trucks out of 11 we use the combination formula again:
C(11, 4) = 11! / (4! * (11 - 4)!) = 11! / (4! * 7!) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1)
Simplify the factorials:
C(11, 4) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = (11/1) × (10/2) × (9/3) × (8/4) = 11 × 5 × 3 × 2 = 330
So, there are 330 ways to choose 4 trucks out of 11.
### Total Ways:
To find the total number of ways to select both the cars and trucks for inspection, we multiply the number of ways to choose the cars by the number of ways to choose the trucks:
Total number of ways = number of ways to choose cars × number of ways to choose trucks
Total number of ways = 56 (from choosing cars) × 330 (from choosing trucks)
Total number of ways = 56 × 330 = 18480
Therefore, the state inspector can select 3 cars out of 8 and 4 trucks out of 11 in 18,480 different ways.
Here are summary statistics for randomly selected weights of newborn girls: nequals177, x overbarequals28.9 hg, sequals6.7 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 28.1 hgless thanmuless than30.7 hg with only 20 sample values, x overbarequals29.4 hg, and sequals2.3 hg? What is the confidence interval for the population mean mu?
Answer:
(32.2,34.7)
Step-by-step explanation:
Solution :
Given that,
\bar x = 33.4 hg
s = 6.4 hg
n = 177
Degrees of freedom = df = n - 1 = 177 - 1 = 176
At 99% confidence level the t is ,
α = 1 - 99% = 1 - 0.99 = 0.01
α / 2 = 0.01 / 2 = 0.005
tα /2,df = t0.005,176 = 2.604
Margin of error = E = tα/2,df * (s /√n)
= 2.604* ( 6.4/ √177)
= 1.25
The 95% confidence interval estimate of the population mean is,
\bar x - E < \mu < \bar x + E = 33.4 - 1.25 < \mu < 33.4 + 1.25
32.15 < \mu < 34.65
32.2 < \mu < 34.7
(32.2,34.7)
Question:
Here are summary statistics for randomly selected weights of newborn girls: n = 177, x = 28.9 hg, s = 6.7 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 28.1 hg < μ < 30.7 hg with only 20 sample values, x' =29.4 hg, and s = 2.3 hg? What is the confidence interval for the population mean μ?
Answer:
The confidence interval for the population mean μ is 27.73 ≤ μ ≤ 30.0714
Step-by-step explanation:
The equation to identify the confidence interval for the mean is given by
[tex]x'-z_{\frac{\alpha }{2}} \frac{s}{\sqrt{n} } \leq \mu\leq x'+z_{\frac{\alpha }{2}} \frac{s}{\sqrt{n} }[/tex]
Where
x' = Sample mean = 28.9
s = Standard deviation = 6.7
n = Sample size = 177
[tex]z_{\frac{\alpha }{2}}[/tex] = Critical value = 2.326
Therefore we have
[tex]28.9-2.326\frac{6.7}{\sqrt{177} } \leq \mu\leq 28.9+2.326 \frac{6.7}{\sqrt{177} }[/tex]
27.73 ≤ μ ≤ 30.0714
T test we have
t = [tex]\frac{x'-\mu}{\frac{s}{\sqrt{n} } }[/tex]
=[tex]\frac{29.4-28.9}{\frac{2.3}{\sqrt{16} } }[/tex] = 0.8696 which is < 1
df = 15 as sample size = 15
Upper tail statistics lies between 0.3 and 0.1
The solution set for -18 < 5x - 3 is _____.
-3 < x
3 < x
-3 > x
3 > x
Solution set for given inequality [tex]-18 < 5x - 3[/tex] is [tex]-3 < x[/tex].
What is solution set?" Solution set is defined as the such set of values which satisfies the given equation or any inequality."
According to the question,
Given inequality,
[tex]-18 < 5x - 3[/tex]
Add 3 both the side of inequality we get,
[tex]-18 +3 < 5x - 3 +3[/tex]
[tex]= -15 < 5x[/tex]
Divide both the side by 5 to get the solution set ,
[tex]-3 < x[/tex]
Hence, solution set for given inequality [tex]-18 < 5x - 3[/tex] is [tex]-3 < x[/tex].
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Final answer:
The solution set for the inequality -18 < 5x - 3 is -3 < x, after adding 3 to both sides and then dividing by 5.
Explanation:
The student has asked to find the solution set for the inequality -18 < 5x - 3. To solve this, we first isolate the variable x by adding 3 to both sides of the inequality:
-18 + 3 < 5x - 3 + 3
-15 < 5x
Then, we divide both sides by 5 to solve for x:
-15 / 5 < 5x / 5
-3 < x
This simplifies to the inequality x > -3, which means that the correct answer is: -3 < x.
For married couples living in a certain suburb, the probability that the husband willvote on a bond referendum is 0.21, the probability that his wife will vote in thereferendum is 0.28, and the probability that both the husband and wife will vote is0.15. What is the probability that:
Answer:
niglgapopfart
Step-by-step explanation:
12(5)6$78$???98
A circle in the xyxyx, y-plane has its center at the point (-6,1)(−6,1)(, minus, 6, comma, 1, ). If the point (7,12)(7,12)(, 7, comma, 12, )lies on the circle, what is the radius of the circle? Round the answer to the nearest tenth.
Answer:
r=17.0
Step-by-step explanation:
In a circle with center (h,k) and any point (x,y) on the circle, the radius of the circle is given as:
[tex](x -h)^2 + (y - k)^2 =r^2[/tex]
Center (h,k)=(-6,1)
(x,y)=(7,12)
[tex]r^2=(x -h)^2 + (y - k)^2 \\r^2=(7 -(-6))^2 + (12 - 1)^2\\r^2=(7 +6)^2 + 11^2\\r^2=13^2 + 11^2=169+121=290\\r=\sqrt{290}=17.03[/tex]
radius, r=17.0 (to the nearest tenth)
The radius of the circle with center (-6,1) and passing through the point (7,12) can be found using the distance formula. The radius, or distance between these two points, calculates to approximately 17.0 units when rounded to the nearest tenth.
Explanation:In Mathematics, you can determine the radius of a circle if you have the coordinates of the center and a point on the circle. Here, we have the center of the circle at (-6,1) and a point (7,12) lying on the circle. We will use the distance formula to find the radius, r, which is essentially the distance between these two points.
Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
By substituting the given points into the distance formula, we get
Radius (r) = sqrt((7 - (-6))^2 + (12 - 1)^2)
Sample calculation: r = sqrt((7 - (-6))^2 + (12 - 1)^2) = sqrt(169 + 121) = sqrt(290). Therefore, the radius of the circle, rounded to the nearest tenth, is approximately 17.0 units.
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Multiply.
−3y(5y3+11y2−y+8)
Express the answer in standard form.
Final answer:
The result of multiplying −3y by the polynomial (5y³+11y²−y+8) is −15y⁴ − 33y³ + 3y² − 24y when expressed in standard form.
Explanation:
To multiply the expression −3y(5y³+11y²−y+8), we will distribute the −3y across each term inside the parentheses. The process involves the use of the distributive property, often also known as the multiplication of polynomials. Here are the steps:
Multiply −3y by 5y³ to get −15y⁴.
Multiply −3y by 11y² to get −33y³.
Multiply −3y by −y to get 3y².
Multiply −3y by 8 to get −24y.
Combining all these products gives us the expression in standard form:
−15y⁴ − 33y³ + 3y² − 24y
HELP !
10 POINTS & BRANLIEST
Answer:
Name the congruent triangles:
triangle RWS, triangle SWT, and triangle TSR
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. He made a total of $220.00 in interest. How much was invested at 3.25%?
A $4000
B $3000
C $5000
D $3500
Answer: A $4000
Step-by-step explanation:
Let x represent the amount which he invested at 3% interest.
Let y represent the amount which he invested at 3.25% interest.
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. This means that
x + y = 7000
The formula for determining simple interest is expressed as
I = PRT/100
Considering the account paying 3% interest,
P = $x
T = 1 year
R = 3℅
I = (x × 3 × 1)/100 = 0.03x
Considering the account paying 3.25% interest,
P = $y
T = 1 year
R = 3.25℅
I = (y × 3.25 × 1)/100 = 0.0325y
He made a total of $220.00 in interest., it means that
0.03x + 0.0325y = 220 - - - - - - - -- -1
Substituting x = 7000 - y into equation 1, it becomes
0.03(7000- y) + 0.0325y = 220
210 - 0.03y + 0.0325y = 220
- 0.03y + 0.0325y = 220 - 210
0.0025y = 10
y = 10/0.0025
y = 4000
Polygon ABCDE is an irregular pentagon. Find the perimeter of the polygon. Round to the nearest tenth. Round to give final answer only.
Answer:
12.9
Step-by-step explanation:
AB = [tex]\sqrt{2^{2}+3^{2} }[/tex] = [tex]\sqrt{13}[/tex]
BC = [tex]\sqrt{2^{2}+2^{2} }[/tex] = [tex]2\sqrt{2}[/tex]
CD = [tex]\sqrt{1^{2}+2^{2} }[/tex] = [tex]\sqrt{5}[/tex]
DE = 3
EA = [tex]\sqrt{1^{2} + 2^{2} }[/tex] = [tex]\sqrt{5}[/tex]
The sum of all of these (in decimal form) is (approx.) 12.9
Answer:
13.9 units
Step-by-step explanation:
AB = sqrt(2² + 3²) = sqrt(13)
BC = sqrt(2² + 2² = sqrt(8)
CD = sqrt(1² + 2²) = sqrt(5)
DE = 3
EA = sqrt(1² + 2²) = sqrt(5)
Add all these:
13.9 units
A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probability that eight or fewer alarms are triggered.
Answer:
0.0865
Step-by-step explanation:
Binomial Problem with n = 9 and p(triggered) = 0.99
And the photo below is the full answer,
I could not insert the fomula and hope it will find you well.
45 percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions.
The solution is in the attachment
At a banquet, the ratio of the number of boys to the number of girls is 5 : 3. 20 boys leave and the ratio becomes 5 : 4. How many girls are at the banquet?
Answer:
There are 48 girls at the banquet
Step-by-step explanation:
Let the number of boys =x
Let the number of girls=y
Ratio Of boys to girls=5:3
Therefore, x:y=5:3......(1)
If 20 boys leave, the ratio becomes 5:4
Sine number of boys=x
If 20 boys leave, new number = x-20
Therefore, x-20:y=5:4......(2)
From (1),
3x=5y
From Equation (2),
4(x-20)=5y
Therefore: 3x=4x-80
x=80
From (1),
3x=5y
5y=3X80
y=240/5=48
Therefore, there are 48 girls at the banquet
A fire engine starts pumping water at 9:20 am at the rate of 800 gallons per minute. Another fire engine, pumping at the rate of 1000 gallons per minute, starts at 9:30 am. At what time will the two engines have pumped the same number of gallon
Answer:
10:10 AM
Step-by-step explanation:
The first thing is to use an identical time variable for both cases, we will do it as follows:
Let t = number of minutes of pumping time of the first fire engine
Therefore, for the second fire truck it would be:
(t-10) = pumping time of the second fire engine, since it started 10 min after the first engine.
To find the value of t, we equalize the equations of the first engine and the second engine:
We know that the first one would be: 800 * t
And the second: 1000 * (t-10)
Thus
1000 * (t-10) = 800 * t
1000 * t - 10000 = 800t
1000 * t - 800 * t = 10000
200 * t = 10000
t = 10000/200
t = 50 minutes
In other words, 50 minutes after the first engine starts pumping, it equaled the second
To know the time they were matched it would be like this:
9:20 AM +: 50 = 10:10 AM
Therefore, at 10:10 AM both engines were matched.
To check the above we have to:
50 * 800 = 40000
40 * 1000 = 40000
Therefore, in that time, they were equalized.
Answer:
At 10:10 am
Step-by-step explanation:
Hi to answer this question we have to write a system of equations:
Fire engine 1: 800 mWhere m: pumping time of the engine
Fire engine 2: 1000 (m-10)Because it starts 10 minute later
So, putting together both equations:
800m = 1000(m-10)
800m = 1000m - 10000
10000 = 1000m-800m
10000= 200m
10000/200=m
50 =m (50 minutes after the first engine starts)
So, 9:20 am + 50 minutes : 10:10 am .
Am I correct for the following questions? because I'm not sure if I am.
If not what are the correct choices?
Which of the lines are parallel?
(1) a and b
(2) a and c
(3) a and D
(4) b and c
(5) b and D
(6) c and D
Which of the lines are perpendicular?
(1) a and b
(2) a and c
(3) a and D
(4) b and c
(5) b and D
(6) c and D
Please show all the work on how you got your answers
Answer:
The answer to your question is C and D are parallel
B and C and B and D are perpendiculars.
Step-by-step explanation:
Data
Line A (-2, 3) (2, 2)
Line B (-3, 0) (3, -2)
Line C (2, 4) (0, -2)
Line D (0, 6) (-2, 0)
Process
1.- Calculate the slope of each line
m = (y2 - y1)/(x2 - x1)
Line A m = (2 - 3) / (2 + 2)
m = -1/4
Line B = (-2 - 0) / (3 + 3)
= -2/6
= -1/3
Line C = (-2 -4)/(0 - 2)
= -6/-2
= 3
Line D = (0 - 6) / (-2 - 0)
= -6/-2
= 3
2.- Conclusion
If the slopes are the same, the lines are parallel if are reciprocal, the lines are perpendicular
Line C ║ Line D
Line B ⊥ Line C and Line B ⊥ Line D
A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of a material that costs 11 cents per square centimeter, while the sides are made of a material that costs 8 cents per square centimeter. Express the total cost C of the material as a function of the radius r of the cylinder.
Answer:
The answer to the question is
The total cost C of the material as a function of the radius r of the cylinder is
0.6912·r² + 800/r Dollars.
Step-by-step explanation:
To solve the question, we note that
The area of the top and bottom combined = 2·π·r²
The area of the sides = 2·π·r·h
and the volume = πr²h = 500 cm²
Therefore height = 500/(πr²)
Substituting the value of h into the area of the side we have
Area of the side = 2πr·500/(πr²) = 1000/r
Therefore total area of can = Area of top + Area of bottom + Area of side
Whereby the cost of the can = 0.11×Area of top +0.11×Area of bottom +0.8×Area of side
Which is equal to
0.11×2×π×r²+ 0.8×1000/r = 0.6912·r² + 800/r
The cost of the can is $(0.6912·r² + 800/r)
To express the cost of the cylinder's material as a function of its radius, we first find the expression for the cylinder's height using the volume formula. The total cost C is computed by calculating the expenses for the top, bottom, and sides of the cylinder using their respective costs and surface areas. These give the final expression for the cost C(r)= 22πr^2 + 8000/r.
Explanation:Given that the volume of the right circular cylinder is 500 cubic centimeters, we can first use the formula for the volume of a cylinder, which is V=πr2h, where r is the radius of the base and h is the height of the cylinder. This can be rearranged to solve for h, giving us h=V/(πr2).
Next, the total cost C is given by the cost of the materials for the top, bottom, and sides of the cylinder: C= 2(11πr2)+ (8 * 2π*r*h). Plugging the expression h= 500/(πr2) into the cost function gives us: C = 22πr2 + (16πr * 500/r2), which simplifies to: C = 22πr2 + 8000/r. So, the total cost of the material as a function of the radius r of the cylinder is C(r)= 22πr2 + 8000/r.
Learn more about Cost Function of Cylinder here:https://brainly.com/question/33632992
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Jane invested $2500 into an RRSP that earned interest at 6% compounded semi annually for ten years a) find the balance of account at end of peroid b)how much interest is earned c) what is effective rate of interest
Answer:
Step-by-step explanation:
PV = $2500
r = 6%
Compounded semi annually for ten years => number of periods: 10*2 = 20
a. the balance of account at end of peroid (FV)
FV = PV [tex](1+r)^{n}[/tex] = 2500[tex](1+0.06)^{20}[/tex] = 8017.8386
b. How much interest is earned; FV - PV = 8017.8386 - 2500 = 5517.8686
c. what is effective rate of interest :
Answer:
The answers to the question are
a) The balance of account at end of period $4515.278
b) The interest earned $2515.278
c) The effective rate of interest is 0.0609 or 6.09 %
Step-by-step explanation:
To solve the question
a) Here we have the compound interest formula given by
[tex]A = P(1+\frac{r}{n})^{nt}[/tex] Where,
P = Initial investment = $2500
r = Annual interest rate = 6% =0.06
n = Number of compounding periods per year = 2
t = Number of years 10
From which we have
[tex]A = 2500*(1+\frac{0.06}{2})^{2*10}= 2500(1.03)^{20}[/tex] = $4515.278
The balance of account at end of period $4515.278
b) Interest earned = Balance - initial investment = $4515.278 - $2500 = $2515.278
c)
The effective interest rate is the interest rate that accrues to an investment or loan as a result of the compounding the interest for a given time period of time. It is also known as the effective annual interest rate
The effective rate of interest is given by
Effective rate = [tex](1+\frac{r}{n} )^n -1[/tex]Where
r = Annual interest rate
n = Number of annual compounding periods
this gives [tex](1+\frac{0.06}{2} )^{2} -1[/tex] = 0.0609 = 6.09 %
Which of the following equations represents the line with a slope of 5/2 and a y-intercept of 1?
y = 5/2x + 1
y = 2/5x - 1
y = 2/5x + 1
y = 5/2x - 1
Answer:
[tex]y = \frac{5}{2} x + 1[/tex]HOPE U UNDERSTOOD
MARK AS BRAINLIEST ONE
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A pair of children shoes comes in a box that measures 10.2 cm x 15 cm x 8 cm what is the volume of a shoebox A pair of children shoes comes in a box that measures 10.2 cm x 15 cm x 8 cm what is the volume of a shoebox
Answer:
1224 cm^3
Step-by-step explanation:
The shape of the box is a rectangular prism.
The volume of a rectangular prism is given by the formula below.
volume = length * width * height
volume = 10.2 cm * 15 cm * 8 cm
volume = 1224 cm^3
Final answer:
The volume of a shoebox with dimensions 10.2 cm x 15 cm x 8 cm is calculated by multiplying these three dimensions together, resulting in a volume of 1224 cm³.
Explanation:
To calculate the volume of a shoebox, you multiply its length by its width by its height. For a shoebox with dimensions of 10.2 cm, 15 cm, and 8 cm, the calculation would look like this:
Volume = Length × Width × Height
Volume = 10.2 cm × 15 cm × 8 cm
Volume = 1224 cm³
Therefore, the volume of the shoebox is 1224 cubic centimeters.
an equilateral triangle has an area of 25 √3 cm squared. what is the height
5 √ 3 c m
A t = √ 34 * s 2 = 25 √ 3
this makes the sides 10cm
At= 1/2 b * h
25 √ 3 = 12 ⋅ 10 ⋅ h = 5 √ 3 c m
Answer:
Height = 8.66 cm
Step-by-step explanation:
The formula for the area of an equilateral triangle is expressed as
A = S²√3/4,
where s represents the length of each side. The area of the given equilateral triangle is 25 √3 cm squared. Therefore
25 √3 = S²√3/4
Dividing both sides of the equation by √3, it becomes
25 √3/√3 = S²√3/4√3
25 = S²/4
Cross multiplying, it becomes
S² = 25 × 4 = 100
Taking square root of both sides of the equation, it becomes
√S² = √ 100
S = 10 cm
In an equilateral triangle, all the sides are equal. The height of the equilateral triangle divides it into two equal right angles triangle. The angles in each right angle triangle are 90, 60 and 30 degrees. To determine the height, h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
10² = h² + 5²
100 = h² + 25
h² = 100 - 25 = 75
h = √75
h = 8.66 cm
Tom is in dire need of a new washing machine. He knows what model he would like to get, but doesn't have the cash to pay for it. He plans to get a line of credit (credit card) at the store when he purchases his new washer. He found four different stores that carry the same washing machine for different prices. The lines of credit they offer also come with different APRs. Tom's primary goal is to minimize his monthly payment as he pays the washing machine off over the next 18 months. From which of the four stores should Tom purchase his washing machine? a. Bob's Nuts and Bolts b. Steve's Scratch and Dent c. Wally's Washing Machines d. Al's Appliances Please select the best answer from the choices provided A B C D
Answer:
b. Steve's Scratch and Dent.
Step-by-step explanation:
Tom should purchase his washing machine from Steve's Scratch and Dent.
Kristen bought a Home Theater for $750 and rented movies every month. The cost of each rental is $4.49 and the membership charges are $12/month. Which equation gives the total amount, A, she spent during the first six months on the number of rented movies, r, including the cost of the Home Theater?
Answer:
A = $822 + $4.49r
Step-by-step explanation:
The question asks to know the equation that describes how much spent in the first six months and also the cost of the home theater.
Firstly, the equation asks to represent the total amount spent by A. She spent $4.49 per rental and made a total of r rentals in the first six months, thus, the total amount of money she spent on rentals is thus 4.49 * r = $4.49r. Now, she also spends $12/month as membership charges. The total membership charges in the first 6 months is thus 6 * 12 = $72
Lastly, she bought the home theater itself $750. Thus, the total amount of money spent A is $750 + $72 + $4.49r
This translates to $822 + $4.49r
In equation form, A = $822 + $4.49r
Eli made fancy blue costume decorations for each of the dancers in his year-end dance performance.He used 1/10 of a meter of ribbon for each decoration,which he got by cutting 1/5 of a meter of ribbon into equal pieces. How many decorations did Eli make?
Answer: There are 2 decorations that Eli makes.
Step-by-step explanation:
Since we have given that
Length of a meter of ribbon used = [tex]\dfrac{1}{10}=\dfrac{1}{10}\times 100=10[/tex]
Length of a meter cut into equal pieces = [tex]\dfrac{1}{5}=\dfrac{1}{5}\times 100=20[/tex]
So, Number of decorations that Eli make is given by
[tex]\dfrac{\text{Length of total ribbon}}{\text{Length of ribbon used}}\\\\=\dfrac{20}{10}\\\\=2[/tex]
Hence, there are 2 decorations that Eli makes.
Final answer:
Eli made 2 decorations from 1/5 meter of ribbon by using 1/10 meter of ribbon for each decoration.
Explanation:
Eli made fancy blue costume decorations for each dancer in his year-end dance performance.
Eli used 1/10 of a meter of ribbon for each decoration and initially cut a 1/5 meter ribbon into equal pieces.
To calculate the number of decorations Eli made, we need to divide the length of ribbon he cut (1/5 meter) by the length of ribbon used for each decoration (1/10 meter).
To solve this, we simply perform the division:
= 1/5 meter / 1/10 meter
= 2.
Therefore, Eli made 2 decorations from 1/5 meter of ribbon.
The vector r = xˆi + y ˆj + zkˆ, called the position vector points from the origin (0, 0, 0) to an arbitrary point in space with coordinates (x, y, z). Use what you know about vectors to prove the following: All points (x, y, z) that satisfy the equation Ax + By + Cz = 0, where A, B, and C are constants, lie in a plane that passes through the origin and that is perpendicular to the vector Aˆi + Bˆj + Ckˆ. Sketch this vector and the plane.
Answer:
The vectors r and p = Aˆi + Bˆj + Ckˆ are perpendicular between them. Thus, the plane equation come from the fact that the dot product is equal to zero.
Step-by-step explanation:
The dot product of r and p
r*p = (xˆi + y ˆj + zk)*(Aˆi + Bˆj + Ckˆ) = Ax + By + Cz = 0