Average growth rate = 4.2 cm/week.
So, common difference d = 4.2
The height of the tree a0 = 200 centimeters.
The height of the tree after end of the first week a₁ = 200 + 4.2 = 200 + 4.2(1)
The height of the tree after end of the second week a₂ = 200 + 4.2 + 4.2 = 200 + 4.2(2).
The height of the tree after end of the third week a3 = 200 + 4.2 + 4.2 + 4.2 = 200 + 4.2(3).
The height of the tree after the end of the nth week an = 200 + 4.2(n).
The equation is a_n = 200 + 4.2(n).
What is the domain of the function f(x) = x2 + 3x + 5?
A regular octagon has side length 10.9 in. The perimeter of the octagon is 87.2 in and the area is 392.4 in2. A second octagon has side lengths equal to 16.35 in. Find the area of the second octagon.
To solve this problem, let us first calculate for the Perimeter of the other octagon. The formula for Perimeter is:
Perimeter = n * l
Where n is the number of sides (8) and l is the length of one side. Let us say that first octagon is 1 and the second octagon is 2 so that:
Perimeter 2 = 8 * 16.35 in = 130.8 inch
We know that Area is directly proportional to the square of Perimeter for a regular polygon:
Area = k * Perimeter^2
Where k is the constant of proportionality. Therefore we can equate 1 and 2 since k is constant:
Area 1 / Perimeter 1^2 = Area 2 / Perimeter 2^2
Substituting the known values:
392.4 inches^2 / (87.2 inch)^2 = Area 2 / (130.8 inch)^2
Area 2 = 882.9 inches^2
Therefore the area of the larger octagon is about 882.9 square inches.
you need 2 3/4 wheelbarrows of sand to make 8 wheelbarrows of concrete. how much sand will you need to make 248 cubic feet of concrete
A. 84 cubic feet
B. 85 1/4 cubic feet
C. 682 cubic feet
D. Not enough info
Answer:
Option B.
Step-by-step explanation:
We need [tex]2\frac{3}{4}[/tex] wheelbarrows of sand for 8 wheelbarrows of concrete.
That means ratio between sand and concrete is [tex]2\frac{3}{4}:8[/tex]
Or [tex]\frac{11}{4}:8[/tex]
Now we have to calculate the amount of sand to make 248 cubic feet of concrete.
If the amount of sand required is x cubic feet then the ratio of sand and concrete will be x : 248.
Since both the ratios should be same therefore,
[tex]\frac{x}{248}=\frac{\frac{11}{4} }{8}[/tex]
[tex]\frac{x}{248}=\frac{11}{32}[/tex]
x = [tex]\frac{11\times 248}{32}[/tex]
x = [tex]\frac{2728}{32}[/tex]
x = [tex]\frac{341}{4}[/tex]
= [tex]85\frac{1}{4}[/tex] cubic feet
Option B will be the answer.
Suppose Sn is defined as 2 + 22 + 23 + . . . + 2n . What is the next step in your proof of Sn = 2(2n - 1), after you verify that Sn is valid for n = 1?
A. Show that Sn is valid for n = k + 2.
B. Assume that Sn is valid for n = k .
C. Verify that Sn is valid for n = 1.
D. Show that Sn is valid for n = k.
A cylinder has a diameter of 14 cm and a height of 20 cm.
a. Find the total surface area of the cylinder.
b. If gift wrap cost $3 per square centimeter, how much will it cost to cover the cylinder with gift wrap? Use 3.14 for π.
c. Find the volume of the cylinder.
The total surface area of the cylinder is approximately 1187.72 cm², the volume is approximately 3077.2 cm³, and the cost to cover it with gift wrap at $3 per square centimeter is $3,558.76.
Finding the Surface Area and Volume of a CylinderThe surface area of a cylinder is calculated using the formula: Surface Area = 2πr(height) + 2πr². With a diameter of 14 cm, the radius (r) is half of that, which is 7 cm. Plugging in the values, the surface area is 2π(7 cm)(20 cm) + 2π(7 cm)².
For part b, once we have calculated the surface area, we can determine the cost to cover the cylinder using the given price per square centimeter. If S represents the total surface area, the cost will be $3 times S.
The volume of the cylinder can be found with the formula V = πr²h, and using the radius of 7 cm and a height of 20 cm, we get the volume V = π(7 cm)²(20 cm).
Performing these calculations:
Surface Area = 2π(7 cm)(20 cm) + 2π(7 cm)² = 2π(7 cm)(20 cm) + 2π(49 cm²) = 2π(140 cm²) + 2π(49 cm²) = 280π cm² + 98π cm² = 378π cm².Volume = π(7 cm)²(20 cm) = π49 cm²20 cm = 980π cm³.Cost = $3 × 378π cm² = $1134π.Using 3.14 for π, we get:
Surface Area = 378π cm² = 1187.72 cm² (approximately).Volume = 980π cm³ = 3077.2 cm³ (approximately).Cost = $1134π = $3,558.76 (approximately).March 21, the 80th day of the year, is the spring equinox. find the number of hours of daylight in fairbanks on this day
the slope of a line is -2 and the line contains the points (7,4) and (x,12). what is the value of x?
Two similar regular hexagons have a common center. If each side of the big hexagon is twice the side of the small one and the area of the small hexagon is 3 sq. in, what is the area of the big hexagon?
The area of the larger square is 4 times larger than the area of the smaller square. The area of the big hexagon is 12 sq. in.
Explanation:The area of the larger square is 4 times larger than the area of the smaller square. This is because the area of a square is proportional to the square of its side length.
In this case, the side length of the larger square is twice the side length of the smaller square, so the area of the larger square is 2² times greater than the area of the smaller square.
Given that the area of the small hexagon is 3 sq. in, the area of the big hexagon can be found by multiplying the area of the small hexagon by the square of the scale factor:
Area of big hexagon = (scale factor)² * Area of small hexagon = 2² * 3 sq. in = 12 sq. in
Upper a 18a 18?-footfoot ladder is leaning against a building. if the bottom of the ladder is sliding along the pavement directly away from the building at 22 ?feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 44 feet from the? wall?
What are the intercepts of the graphed function?
x-intercept = (–1, 0)
y-intercept = (–3, 0)
x-intercept = (0, –1)
y-intercept = (0, –3)
x-intercept = (0, –1)
y-intercept = (–3, 0)
x-intercept = (–1, 0)
y-intercept = (0, –3
we know that
The x-intercept is the value of x when the the value of y is equal to zero
and
The y-intercept is the value of y when the the value of x is equal to zero
In the graphed function we have that
the value of x when the the value of y is equal to zero is [tex]-1[/tex]
therefore
the x-intercept is equal to the point [tex](-1,0)[/tex]
the value of y when the the value of x is equal to zero is [tex]-3[/tex]
therefore
the y-intercept is equal to the point [tex](0,-3)[/tex]
the answer is
x-intercept = (–1, 0)
y-intercept = (0, –3)
simplify 10a + 3b + 7a+ 6b
Let x denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. suppose that for banner-tailed kangaroo rats, x has an exponential distribution with parameter λ = 0.01357. what is the value of the median distance?
To solve this problem, all we have to do is to use the formula below, plug in the value of the parameter λ, then calculate for the median distance. The formula is:
Median = ln 2 / λ
Substituting:
Median = ln 2 / 0.01357
Median = 51.08 m
At the beginning of the year, a firm has current assets of $316 and current liabilities of $220. at the end of the year, the current assets are $469 and the current liabilities are $260. what is the change in net working capital?
The solution is $ 153
The change in the net working capital is $ 153
What is Net Working Capital?
The difference between a company's current assets and current or short-term liabilities is known as net working capital, or working capital.
Cash flow will have an operational origin, when there is a net decrease in working capital
Working Capital = Current Assets - Current Liabilities
Given data ,
Let the change in net working capital be A
Now , the equation will be
Working Capital at the beginning = Current Assets - Current Liabilities
Substituting the values in the equation , we get
Working Capital at the beginning = 316 - 220
Working Capital at the beginning = $ 96
And ,
Working Capital at the end = Current Assets - Current Liabilities
Substituting the values in the equation , we get
Working Capital at the end = 469 - 260
Working Capital at the end = $ 209
So ,
The change in net working capital A = Working Capital at the end - Working Capital at the beginning
Substituting the values in the equation , we get
The change in net working capital A = 209 - 96
The change in net working capital A = $ 153
Therefore , the value of A is $ 153
Hence , change in the net working capital is $ 153
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What is the axis of symmetry and vertex for the function f(x) = 3(x – 2)2 + 4?
x =
Answer:
x= 2 vertex: (2,4)
Step-by-step explanation:
just did the assignment
What is the value of x to the nearest tenth?
What is the least common multiple of 2, 10 and 6
The least common multiple of 2, 10 and 6 by using the definition of multiple is 30.
The lowest possible number that can be divisible by all the given numbers is called as least common multiple (LCM). It is the smallest multiple which is common in all the numbers.
The least common multiple of 2, 10 and 6 can be calculated as:
The multiples of 2 are: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34.........
The multiples of 10 are: 10,20,30,40,50,60,70.............
The multiples of 6 are: 6,12,18,24,39,36,42,48,54,60,66...........
The lowest common multiple among 2,10,6 is 30.
Thus, the least common multiple of 2, 10 and 6 is 30.
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Write a research problem that would be best studied using a probability sample.
A lawn sprinkler sprays water 8 feet at full pressure as it rotates 360 degrees. If the water pressure is reduced by 50%, what is the difference in the area covered?
Answer:
[tex]150.72 feet^2[/tex] is the difference in the area covered.
Step-by-step explanation:
A lawn sprinkler sprays water 8 feet at full pressure, P.
A lawn sprinkler rotates 360 degree which means area covered by sprinkler is of circular shape. Since the sprinkler is in center and sprays the the water 8 feet away in all the direction while rotating.
Radius of the circle = 8 feet
Maximum pressure = P
As we know that higher the pressure higher will the force by which water will move out of the sprinkler. And with more force, sprinkler will able to spray water farther.
So we this we can say that pressure of the sprinkler is directly proportional to the radius of the circle in which water sprayed
[tex]pressure\propto Radius[/tex]
[tex]P\propto r[/tex]
[tex]\frac{P_1}{r_1}=\frac{P_2}{r_2}=constant[/tex]
[tex]P_1=P.P_2=P-50\%\times P=0.5 P[/tex]
[tex]r_1=8 feet.r_2=?[/tex]
[tex]r_2=\frac{0.5 P\times 8 feet}{P}=4 feet[/tex]
Area when , [tex]r_1= 8 feet[/tex] (Area of circle=[tex]\pi (radius)^2[/tex])
[tex]A=\pi r_1^{2}=\pi (8 feet)^2[/tex]
Area when ,[tex]r_2= 4 feet[/tex]
[tex]A'=\pi r_1^{2}=\pi (4 feet)^2[/tex]
Difference in Area = A- A'
[tex]\pi (8 feet)^2-\pi(4 feet)^2=\pi(48 feet^2)=150.72 feet^2[/tex]
[tex]150.72 feet^2[/tex] is the difference in the area covered.
The sales tax for an item was $22.50 and it cost $450 before tax. Find the sales tax rate. Write your answer as a percentage.
Final answer:
The sales tax rate is found by dividing the amount of sales tax by the cost of the item before tax and then multiplying by 100. In this case, the sales tax rate is 5%.
Explanation:
To find the sales tax rate of an item, you need the amount of sales tax paid and the cost of the item before tax. The formula to calculate the sales tax rate is:
sales tax rate = (amount of sales tax \/ cost of the item before tax) \ 100
Applying the formula, we have:
sales tax rate = ($22.50 \/ $450) \ 100
sales tax rate = 0.05 \ 100
sales tax rate = 5%
Therefore, the sales tax rate for the item is 5%.
The volume of a box(V) varies directly with its length(l). If a box in the group has a length of 30 inches, and the girth of 20 inches (perimeter of the side formed by the width and height), what is its height? Use k = 24. (Hint: Volume = length • width • height. Solve for length, and substitute into the equation for constant of proportionality.)?
csc(-x)/1+tan^2x) = ?
in the problem 10-4=6, whats the correct term for the number 4
A total of
564
tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?
Shannon Perfumeries sells two fragrances. The table contains the price corresponding to the number of bottles of fragrance A. Bottles Price($) 3 78 6 156 9 234 The graph represents the relationship of the price with respect to the number of bottles of fragrance B. The unit rate of fragrance A is $ , and the unit rate of fragrance B is $ . Fragrance has the greater unit rate.
Answer:
since he missed b ill answer it for your b is 24 because when you look at the grragh it goes from 0 then to 24 so its unit rate would be 24
Step-by-step explanation:
The unit rate of fragrance A is; $ 26, and the unit rate of fragrance B is; $ 24. Hence Fragrance A has the greater unit rate.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
According to the condition the rate of the fragrance A will be;
78/3 = 156/6
= 234/9
= 26 $ per bottle
According to the graph the price of the fragrance B will be;
24/4 = 48/2
=24 $ per bottle
Therefore, the unit rate of fragrance A is; $ 26, and the unit rate of fragrance B is; $ 24.
Hence, Fragrance A has the greater unit rate.
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If each dimension of the rectangular prism is doubled, how will its total surface area change?
mc006-1.jpg
[Not drawn to scale]
The surface area doubles.
The surface area triples.
The surface area increases by a factor of four.
The surface area increases by a factor of eight.
Answer:
inceases by factor four
Step-by-step explanation:
If your monthly net (after-tax) income is $1,500, what should be your maximum amount spent on credit payments? A. $200 B. $300 C. $400 D. $500
According to budgeting guidelines often referred to as the 20/30/50 rule, no more than 20% of your net income should be spent on debt repayments. Therefore, the maximum amount spent on credit payments for a $1,500 monthly income should be $300.
Explanation:The best practice for budgeting recommends that no more than 20% of your net monthly income should be spent on debt repayments, including credit payments. This is commonly referred to as the 20/30/50 rule. Therefore, given a monthly net income of $1,500, the maximum amount spent on credit payments should be 20% of $1,500, which equals to $300.
Here's how you would calculate it:
Convert 20% to decimal form by dividing it by 100. 20/100 = 0.2.Multiply the decimal by your net income to get your maximum spend on credit payments. 0.2 x $1,500 = $300.So, the correct answer is B. $300.
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identify the real and imaginary parts of the complex number. -5 + 6i
A congested computer network has a 0.010 probability of losing a data packet and packet losses are independent events. a lost packet must be resent. round your answers to four decimal places (e.g. 98.7654). (a) what is the probability that an e-mail message with 100 packets will need any resent?
How many times greater is 700 than 70
Answer:
10 times greater
Step-by-step explanation:
700÷70=10
Jalil and Victoria are each asked to solve the equation ax – c = bx + d for x. Jalil says it is not possible to isolate x because each x has a different unknown coefficient. Victoria believes there is a solution, and shows Jalil her work: ax – c = bx + d ax – bx = d + c x (a – b) = d + c x = How can Victoria justify Step 3 of her work?
IT is A: Rewrite the expression on the left using the distributive property.