The radius of the base of the vase in cm is 8.26 cm
How to determine the area Force (F) = 15 NPressure (P) = 700 N/m²Area (A) =?P = F / A
700 = 15 / A
Cross multiply
700 × A = 15
Divide both sides by 700
A = 15 / 700
Multiply by 10000 to express in cm²
A = (15 / 700) × 10000
A = 214.29 cm²
How to determine the radiusArea (A) = 214.29 cm²Pi (π) = 3.14Radius (r) = ?A = πr²
Divide both side by π
r² = A / π
Take the square root of both sides
r = √(A / π)
r = √(214.29 / 3.14)
r = 8.26 cm
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Dwight Donovan, the president of Finch Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of five years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $103,000 and for Project B are $41,000. The annual expected cash inflows are $34,441 for Project A and $12,522 for Project B. Both investments are expected to provide cash flow benefits for the next five years. Finch Enterprises’ desired rate of return is 8 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.)
1. The computation of the net present value of each project is as follows:
Project A Project B
NPV $36,523 $9,000
2. Based on the net present value approach, Project A should be adopted, instead of Project B.
What is the net present value?The net present value is the difference between the costs and the annual cash inflows discounted to their present values.
Data and Calculations:Project A Project B
Initial costs $103,000 $41,000
Annual cash inflows $34,441 $12,522
Project live 5 years 5 years
Rate of return 8% 8%
Annuity factor 3.993 3.993
PV of cash inflows $139,523 $50,000
NPV $36,523 $9,000
Question Completion:1. Compute the net present value of each project.
2. Which project should be adopted based on the net present value approach?
Thus, based on the net present value approach, Project A should be adopted.
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enter your answer in scientific notation
It takes 1.7 x 10 ^4 for light from the sun to reach the comet.
How do scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
Scientific notations have some of the profits as:
Better readability due to compact representation
Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.
A comet is about [tex]5.1 \times 10 ^9[/tex] km from the sun.
Light travels at about [tex]3.0 \times 10 ^5[/tex] km per second.
[tex]\dfrac{5.1 \times 10 ^9}{3.0 \times 10 ^5}[/tex]
= [tex]1.7 \times 10 ^4[/tex]
Hence, It takes 1.7 x 10 ^4 for light from the sun to reach the comet.
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The common _____ of two rays that make an angle is called the vertex.
your answer goes here
A summer camp cookout is planned for the campers and their families. there is room for 450 people. each adult costs $7, and each camper costs $4. there is a maximum budget of $1,150. write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers. x y ≤ 1,150 7x 4y ≤ 450 x y ≤ 450 7x 4y ≤ 1,150 x y ≤ 1,150 4x 7y ≤ 450 x y ≤ 450 4x 7y ≤ 1,150
Hence, the required inequality is x+y≤4, 7x+4y≤1150
What is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
How to solve?Let x be the number of adults and y be the number of campers.
There are rooms for 450 people, so
x+y≤450.
Each adult costs $7, then x adults cost $7x.
Each camper costs $4, then y campers cost $4y.
There is a maximum budget of $1,150, so
7x+4y≤1,150
Hence, you get the system of two inequalities:
x+y≤4
7x+4y≤1150
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Answer:
x + y [tex]\leq[/tex] 450
7x + 4y [tex]\leq[/tex] 1,150
Step-by-step explanation:
X and Y is the amount of people it can fit.
7 and 4 is the amount of money for each person.
7x is the amount per adult, 4y is the amount per camper.
Hope this helps.
A ride-sharing company charges $6 per mile plus a $10 surcharge during peak hours. Suppose Manish’s ride during peak hours costs $22. To determine how many miles he traveled during this ride, solve for x in the following equation: 6x + 10 = 22
Answer:
2 miles
Step-by-step explanation:
6X + 10 = 22
X = (22-10)/6 = 12/6 = 2 miles
Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f.
The function that is a tangent to the graph of f is [tex]f(x) = (5/4)x^4+60[/tex]
What is the concept of integral?The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.
Knowing that :
40x + y = 0 is tangent of f(x)slope of the line = -40therefore, f'(x)|x=a = -40, so only look for a we have:
[tex]5a^3 = -40\\a^3 = -8\\a = -2[/tex]
if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:
[tex]f'(x) = 5x^3\\f(x) = (5/4)x^4 + c\\80 = (5/4)(-2)^4 + c\\c = 60[/tex]
Therefore,
[tex]f(x) = (5/4)x^4+60[/tex]
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Write
2660
1000
as a decimal.
Which sentence from the source best supports the reason "recreational sports are valuable because youth need to exercise daily"? 1 2 3 4
The sentence that best supports the reason for youth recreational sports is (3) The US Department of Agriculture recommends that young people ages 6–17 should engage in 60 minutes of physical activity each day.
What are recreational sports?Recreational sports are competitive physical games played for fun and physical exercise with friends or as part of extra-curricular activities.
They do not involve professional sports persons.
Question Completion:Read this source of information. (1) American youth have school commitments and extracurricular activities. (2) Many also enjoy leisure activities, such as reading and playing video games. (3) The US Department of Agriculture recommends that young people ages 6–17 should engage in 60 minutes of physical activity each day. (4) The specific amount of activity needed for a healthy lifestyle depends on daily caloric intake.
Thus, the sentence that best supports the reason for youth recreational sports is Sentence 3.
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Answer:
ez 3
Step-by-step explanation:
Solve this system using the substitution method. -3x + 4y = 1 -4x + 5y = -2
Answer:
the x value is 13 and the y value is 10. x=13 and y=10
What is the number of Power set of A show step by step? A = {a,b, {a}, 3, {3}}.
By "number of Power set of A" I wonder if you mean the cardinality of the power set.
For any finite set with [tex]n[/tex] elements, its power set contains [tex]2^n[/tex] elements.
Here [tex]|A| = 5[/tex], so the power set will contain [tex]|\mathcal P(A)| = 2^5 = \boxed{32}[/tex] elements.
Recall that the power set is the set of all subsets of a given set
• subsets of [tex]A[/tex] of size 0 (1):
[tex]\emptyset[/tex]
• subsets of size 1 (5):
[tex]\{a\}\\ \{b\}\\ \{\{a\}\}\\ \{3\}\\ \{\{3\}\}[/tex]
• subsets of size 2 (10):
[tex]\{a,b\}\\ \{a,\{a\}\}\\ \{a, 3\}\\ \{a, \{3\}\}\\ \{b,\{a\}\}\\ \{b,3\}\\ \{b,\{3\}\}\\ \{\{a\},3\}\\ \{\{a\}, \{3\}\}\\ \{3,\{3\}\}[/tex]
• subsets of size 3 (10):
[tex]\{a,b,\{a\}\}\\ \{a,b,3\}\\ \{a,b,\{3\}\}\\ \{a,\{a\},3\}\\ \{a,\{a\},\{3\}\} \\ \{a,3,\{3\}\}\\ \{b,\{a\},3\}\\ \{b,\{a\},\{3\}\}\\ \{\{a\},3,\{3\}\}[/tex]
• subsets of size 4 (5):
[tex]\{a,b,\{a\},3\}\\ \{a,b\{a\},\{3\}\}\\ \{a,b,3,\{3\}\}\\ \{a,\{a\},3,\{3\}\}\\ \{b,\{a\},3,\{3\}\}[/tex]
• subsets of size 5 (1):
[tex]\{a,b,\{a\},3,\{3\}\}[/tex]
Here's my work, is it right?
SA=2πr^2+2πrh
r=3.6cm
h=21.9cm
2π(3.6)^2+2π(3.6)(21.9)
=576.7964cm^2
Answer:
no
Step-by-step explanation:
there are somethings you need to know. The given height is the combined height of the cylinder and hemisphere. but we need to use the height of cylinder in the formula so we subtract the original height by radius.
Next thing is that the formula 2πrh is for C.S.A of the cylinder but we need the base area as well for surface area of this combined solid. So we add base area (i.e πr²) to 2πrh.
Mila plants 820 hectares of potatoes and corn. To maximise his profit he plants 140 hectares more of potatoes than of corn. How many hectares of each does he plant?
Answer:
480 Hectares potatoes, 340 Hectares corn
Step-by-step explanation:
Let x be the land used to plant potatoes in hectares.
Let y be the land used to plant corn in hectares.
Given the information from the question, we know that:
x + y = 820 - Equation 1
and
x - y = 140 - Equation 2
as you can see here we have 2 equations, means we can solve them simulteanously to solve for both. We will use elimination method.
We will use Equation 1 - Equation 2.
x-x+y-(-y)=820-140
2y = 680
y = 680 ÷ 2 = 340 hectares
We substiture y into equation 1 to find x
x + 340 = 820
x = 820 - 340
= 480 hectares
Therefore, 480 hectares of potatoes and 340 hectares of corn were planted.
Answer:
p=x+140whilec=x x+140+x=820ans=340 Answer=corn 340. while potatoes 480if there are 24 sushi pieces in 6 packages of sushi how many pieces of sushi are in 2 packages of sushi HURRY!!!!
Answer: 8 pieces
Step-by-step explanation:
- if there are 24 pieces of sushi in 6 packages then 24/6 = 4 so there’s 4 pieces of sushi in each package
- since there’s 4 pieces of sushi in each pack just do 4 x 2 = 8
- so there’s 8 pieces of sushi in 2 packages
hope this helps :)
In a biology class, the final grade is based on several things; a lab score, scores on two major tests, ad score on the final exam. There are 100 points availablefor each score. However, the lab score is worth 25% of the total grade, each major test is worth 22.5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exam.
Given a normally distributed data set with the mean = 88 and the standard deviation = 6, according to the empirical rule, what percent of the data points are above 76?
According to the empirical rule, the percent of the data points that are above 76 is; 2.28%
How to use Empirical Rule in Statistics?We are given;
Mean; μ = 88
Standard deviation; σ = 6
Sample mean; x' = 76
Formula for z-score is;
z = (x' - μ)/σ
z = (76 - 88)/6
z = -2
Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%
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1 pts
The Dingles have some friends drop in. They wish to serve sherry but do nor have enough to serve
all the same kind. So they mix some which is 20% alcohol with some which is 14% alcohol and have
5 quarts which is 16% alcohol. How much of each kind of sherry did they have to mix?
Which expressions are equivalent to √1,120y? Select three options.
√√2-2-2-2-5-7-y-y
√2² √2² √2² √5² √7²√√
√2² √2² √2. √5.17.√7.SY
02.2.y√2-5-7-y
4y√70y
The expression that is equivalent to √1,120y is: 4√70y.
What are Equivalent Expressions?Expressions are said to be equivalent when the value of one is the same as the value of the other when evaluated or simplified.
Given the expression, √1,120y, we can simplify as shown below:
√(16 × 70 × y)
= 4√70y
Thus, 4√70y is equivalent to √1,120y .
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Find the first three terms of the sequence, Classify the sequence as arithmetic ( give d value ), geometric ( give r value ), both, or neither..... Sn = 10n
The first three terms of the sequence are 10, 20, and 30.
How to depict the sequence?The function given is 10n. In this case, the terms will be:
First term = 10n = 10 × 1 = 10
Second term = 10 × 2 = 40
Third term = 10 × 3 = 30
In this case, the first three terms of the sequence are 10, 20, and 30.
It an arithmetic sequence as there is a common difference of 10.
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what is the range of f(x)=3^x
Answer: [tex]f(x) > 0[/tex]
Step-by-step explanation:
The range of all exponential functions without a vertical shift is the set of positive real numbers.
The graph of the exponential function with base, e, has a_______ at _______ Its domain is _______ Its range is _____
The graph of the exponential function in discuss whose base is; e would have a y-intercept t at point (0, 1), with a domain as the set of all real numbers and its range as the set of all positive numbers.
What is the description of the graph of an exponential functions whose base is e?It follows from the task content that the function in discuss can be written as;
y = e^x.
Consequently, the y-intercept of the graph which corresponds to x= 0 is; (0, 1).
The domain and range of the graph as with other exponential functions are therefore given as the set of all real numbers and all real positive numbers respectively.
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QUICK PLEASE. George invested $1000 for 4 years. If the investments earned 5.5% compounded weekly, how many compounding period would occur and what is the interest rate?
The number of compounding period is 52.
The interest rate is 0.11%.
What is the compounding period and interest rate?The compounding period is the number of times the investment would earn a compound interest in a year. Because interest is compounded weekly, the compounding period would be equivalent to the number of weeks in a year. This is 52.
Interest rate = yearly interest / compounding period
5.5 / 52 = 0.11%
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How to get T. I have gotten this question wrong multiple times already. It is not simplified it wants it in the complete decimal form.
Answer:
t = 4.0
Step-by-step explanation:
1.) P(t) = 1578
2.) Divide both sides by 1400
3.) Take the natural log of both sides (to remove the "e")
4.) Divide both sides by 0.03
5.) Properly round to the 1st decimal place
What is the value of f(4) in the function below? f(x) = -1/1·2x A. 16 OB. 8 C. 2 OD. 4
Answer: 4
Step-by-step explanation:
[tex]f(4)=\frac{1}{4} \cdot 2^{4}=\frac{1}{4} \cdot 16=4[/tex]
Find the mean of the list of data 43,69, 48,37,85,57,95,102
WHAT IS THE VALUE OF THE EXPRESSION 8 MORE THEN 3 TIMES THE DIFFRENCE OF 4 AND A NUMBER WHEN N=3
The value of the expression as described in the task content is; 11.
What is the value of the expression?The expression as described in the task content is; 3(4 - N) +8.
However, the value of N in this scenario is; 3.
Therefore, the value of.the expression is;
3(4 - 3) +8
= 3(1) + 8
= 3+8
= 11.
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I need help with this question I got 1 as an answer but it’s saying it’s wrong
log 4 (x³ +255) = 4
Answer:
see image
Step-by-step explanation:
I did two different problems depending on whether the 4 beside the log is a base or not.
If the log IS the base, I got x = 1 as you did. But if the 4 is not the base then there is no base written and that means the base is 10.
For log problems that have log on one side of the equation only, then a good strategy is to change the equation from logarithmic form to exponential form. See image for work. Hope this helps.
The blue truck from old time is part to the right truck from hit road a green truck from super suppliers is part to the right of all time the white truck from Joe's hardware is part to the left of hit road how many trucks are between the Joe's hardware truck in a super supplier's truck
There are 2 trucks are between Joe's hardware truck in a super supplier's truck.
What is the reasoning?The reasoning is the capacity to make logical judgments based on newly available or previously known information.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
The blue truck from the old time is part to the right truck from hit road the green truck from super suppliers is part to the right of all time.
According to the information provided, there are only two trucks between the Super Suppliers truck and the Joe's Hardware truck.
Joe's Hardware is essentially on the left and Super Suppliers is on the right, with 2 trucks in between.
Thus, there are 2 trucks are between Joe's hardware truck in a super supplier's truck.
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What is the base of the expression ? 3 11 12 21
Answer:
[tex]11[/tex]
[tex]a {}^{b} [/tex]
a is the base and b is the exponent.
Step-by-step explanation:
HOPE THIS HELPS.
Solve for x. Round to the nearest tenth, if necessary.
K
Answer:
0.5
Step-by-step explanation:
The sides opposite and adjacent to the given angle are shown in this right triangle. The relation between them is given by the tangent trig function:
Tan = Opposite/Adjacent
tan(63°) = 1/x
Solve for xWe can multiply this equation by x/tan(63°) to find the value of x:
x = 1/tan(63°) ≈ 1/1.96261 ≈ 0.509525
The length x is about 0.5 units.
A cyclist rides her bike at a rate of 9 kilometers per hour. What is this rate in kilometers per minute? How many kilometers will the cyclist travel in 15 minutes? Do not round your answers.
The rate of 9 kilometers per hour in kilometers per minute is 0.15 km/min. The cyclist would travel 2.25 km in 15 minutes.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
60 km/h = 1 km/min
Hence:
9 km/h = 9 km/h * (1 km/min) / ( 60 km/h) = 0.15 km/min
In 15 minutes, distance = 0.15 km/min * 15 min = 2.25 km
The rate of 9 kilometers per hour in kilometers per minute is 0.15 km/min. The cyclist would travel 2.25 km in 15 minutes.
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