Two expressions that represent the perimeter of the pool are given as follows:
P = 8w + 4.P = 2.67l - 1.33.How to obtain the perimeter of a rectangle?The perimeter of a rectangle of length l and width w is given by the equation presented as follows:
P = 2(l + w).
The length is 2 more than 3 times the width, hence:
l = 3w + 2.
Thus one expression is:
P = 2(3w + 2 + w)
P = 8w + 4.
Writing the width as a function of the length, we have that:
3w = l - 2
w = (l - 2)/3.
Hence the second expression is of:
P = 2.67(l - 2) + 4.
P = 2.67l - 1.33.
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Samuel made 31 out of 40 field goals during football practice. What percent of the field goals did Samuel make?
The percent of the field goals did Samuel make will be 77.5%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Samuel made 31 out of 40 field goals during football practice. The percent of the field goals did Samuel make will be:
= 31 / 40 × 100
= 77.5%
The percentage is 77.5%.
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a is 60 miles from b. a starts for b at 20 mph, and b starts for a at 25 mph. when will a and b meet?
The problem describes a scenario in which two objects, A and B, start moving towards each other from different locations and speeds. Object A starts from point A, which is 60 miles away from object B, at a speed of 20 mph, while object B starts from point B at a speed of 25 mph.
To solve this problem, we can use the formula Distance = Speed x Time. We know that the total distance between A and B is 60 miles and we want to find the time at which they meet. Let's call that time "t". Let's also assume that they meet at some point "x" miles away from A. Then, the distance that A travels is 60 - x and the distance that B travels is x. Using the formula, we can set up an equation:
Distance A + Distance B = Total Distance
(60 - x) + x = 60
Simplifying this equation, we get:
60 - x + x = 60
60 = 60
This equation is always true, so it doesn't give us any information about when A and B will meet. However, we can use the formula Distance = Speed x Time to set up another equation that relates the distance and speeds of A and B to the time they travel before meeting:
Distance A = Speed A x Time
Distance B = Speed B x Time
Substituting the distances and speeds we know, we get:
(60 - x) = 20t
x = 25t
We can use either equation to solve for t, but let's use the second equation. Substituting x = 25t, we get:
(60 - 25t) = 20t
Simplifying and solving for t, we get:
60 = 45t
t = 4/3
Therefore, A and B will meet after traveling for 4/3 hours, or 1 hour and 20 minutes.
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. You deposit $200 each month into an account earning 3% interest compounded monthly for 30 years. How much total interest will you earn in 30 years?
The total interest you will earn in 30 years is approximately $241.61.
To calculate the total interest earned in 30 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount is $200, the annual interest rate is 3% (or 0.03 as a decimal), the interest is compounded monthly (so n = 12), and the time period is 30 years (so t = 30).
Plugging in these values into the formula:
A = 200(1 + 0.03/12)^(12*30) - 200
Now we can simplify and calculate:
A = 200(1.0025)^(360) - 200
A = 200(2.208040033) - 200
A ≈ 441.6080066 - 200
A ≈ 241.6080066
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f(g(3))
How do I solve this ???
Answer:
fg . 3
Step-by-step explanation:
f(g(3)) = 3fg
steps:
Remove parentheses: (a) = a
= fg . 3
Suppose that v1, v2, v3, v4 is a basis for vector space V . Is
it true that v1 + 2v2, v2 + 2v3, v4 is also a basis for V ?
It is true that v1 + 2v2, v2 + 2v3, v4 is also a basis for V.
Suppose that v1, v2, v3, v4 is a basis for vector space V. A basis for a vector space is a set of vectors that are linearly independent and span the entire vector space. In other words, any vector in the vector space can be written as a linear combination of the basis vectors.
In this case, the vectors v1 + 2v2, v2 + 2v3, and v4 are linear combinations of the original basis vectors v1, v2, v3, and v4. Therefore, they are also linearly independent and span the entire vector space V. As a result, the set {v1 + 2v2, v2 + 2v3, v4} is also a basis for V.
In general, any set of vectors that are linearly independent and span the entire vector space can be considered a basis for that vector space. Therefore, it is true that v1 + 2v2, v2 + 2v3, v4 is also a basis for V.
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A lilly pond starts with 1 lilly pad and every day the amount doubles. how many lilly pads are in the pond after d days
After d days, the number of lily pads in the pond can be calculated using the formula 2^d. So, if d is the number of days, then the number of lily pads after d days would be 2^d.
Each day, the number of lily pads doubles. So, on the first day, there is 1 lily pad. On the second day, the number doubles to 2. On the third day, it doubles again to 4, and so on. This doubling pattern continues for d days.
To calculate the number of lily pads after d days, we raise 2 to the power of d (2^d). This is because each day, the number of lily pads doubles, which can be represented as 2^1, 2^2, 2^3, and so on. By substituting the value of d into the equation, we can find the number of lily pads after d days.
For example, if d = 5, then the number of lily pads after 5 days would be 2^5 = 32. This means that there would be 32 lily pads in the pond after 5 days.
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Losing 50 dollars may affect one’s level of happiness more than winning 50 dollars. This illustrates the concept of __________ aversion. A. Loss B. Preference C. Risk D. Decision Please select the best answer from the choices provided A B C D.
Answer:
loss
it affects you more to lose something than to gain
Answer:
Loss
Step-by-step explanation:
Solve for b in the literal equation a+ b+ c= 180
Answer:
b = 180 - a - c
Step-by-step explanation:
To solve for b given the literal equation, a + b + c = 180:
Subtract a and c from both sides:
a + b + c = 180
a - a + b + c - c = 180 - a - c
b = 180 - a - c
Which of the following numbers can be expressed as repeating decimals? (5 points) 3 over 7 , 2 over 5 , 3 over 4 , 2 over 9
Answer:
3/7 and 2/9 are repeating decimals.
Step-by-step explanation:
A movie lasts 2 1/3 hours james watches 3/4 of the movie then pauses it while he eat dinner how long did he spend watching the movie. And how did you solve it.
Rewrite the length of the movie as an improper fraction.
2 1/3 = 7/3
Now multiply the length of the movie by 3/4
7/3 x 3/4 = (7 x3) / (3 x 4) = 21/12 = 1 3/4 hours
Please help!!!! I need an answer asap
Answer:
I think its
(-5,5)
Step-by-step explanation:
(-5,5) is da answer
Step-by-step explanation:
(-5,5)
12.
ΥΥΥΥΥ
help please
Answer:
لطفا دانش مغز بزرگ من تست من قاشق تخم مرغ لاک پشت راه من را از طریق شما
Step-by-step explanation:
Answer:
I believe th e andwer to that is y5
given triangle ABC find the values of x and y. In your final answer, include all of your calculations.
Answer:
Step-by-step explanation:
X = ?
y = ?
The big triangle ABC is a right triangle, we can use Pythagoras theorem to find side y, then use SOH CAH TOA to find angles :)
also, there is a special rule for a triangle set up like this one
2CD = BD
for this triangle then,
2CD = 9
CD = 4.5
X = 13.5
now use Pythagoras to find y
\(13.5^{2}\) = \(6^{2}\) + \(y^{2}\)
182.25 -36 = \(y^{2}\)
\(\sqrt{146.25}\) = y
12.093386 = y
now that you have all 3 sides of the big triangle, use which ever trig function you are most comfy with to find angle B or C, i'll find C
CAH = Cos(C) = Adj / Hyp
Cos(C) = 6 / 13.5
arcCos(Cos(C)) = arcCos(6/13.5)
C = 63.6122°
now find B
180 = 90 + 63.6122 + B
26.3877° = B
got it?
4. write the following in standard form
four hundred, thirty - two thousand, six hundred eight
How to do this?? URGENT PLS HELP WILL GIVE BRAINLIEST
Answer:
Point T is at (4,3)
Step-by-step explanation:
uh, I did math
Answer:
(4,3)
Step-by-step explanation:
goodluck
what does 7/12 + 5/6 equal
\(\dfrac 7{12} + \dfrac 56\\\\\\=\dfrac 7{12} + \dfrac{10}{12}\\\\\\=\dfrac{7+10}{12}\\\\\\=\dfrac{17}{12}\)
what does \( \frac{7}{12} + \frac{5}{6} \) equal
▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
Solution:-= \(\frac{7}{12} + \frac{5}{6}\)LCM of 12 and 6 = 12
= \( \frac{7 + 10}{12} \)= \( \frac{17}{12} \)= \(1 \frac{5}{12} \)The length of a rectangle measures 5/8 of a foot. The width of the rectangle measures 2 1/2 feet. What is the area of the rectangle?
Answer:
1 9/16 square feet or 1.5625 square feet
Step-by-step explanation:
Area of a rectangle is Length x Width
First convert 2 1/2 into a number that is just a fraction.
2 = 4/2 so 4/2 + 1/2 = 5/2
Now you can multiply the two fractions to find the area.
area = 5 5 25
-- x -- = -----
8 2 16
To simplify this, you know 16/16 = 1 so subtract 16 from the numerator which leaves 9/16
Your answer will be 1 and 9/16
Jack ran 2/8 mile and Roy ran 2/3 mile. What benchmark fractions can be used to estimate how much farther Roy ran than Jack?
Answer:
Jack ran 1/4 of a mile.
Step-by-step explanation:
Step-by-step explanation:
jack ran 1/4 of a mile more than jack did
The dimensions of the inner square pyramid have a ratio 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid
a. The surface area of the outer square pyramid is 11.25 square centimeters. b. The side length of the inner square pyramid is 2.25 centimeters.
a. To find the surface area of the outer square pyramid, we need to calculate the area of each of its faces and add them together. The outer square pyramid has four triangular faces and a square base.
Area of a triangular face = (1/2) x base x height
Area of a triangular face = (1/2) x 1.5 cm x 3 cm = 2.25 cm²
The area of the square base can be found using the formula for the area of a square:
Area of square base = side length²
Area of square base = 1.5 cm x 1.5 cm = 2.25 cm²
Therefore, the total surface area of the outer square pyramid is:
Surface area = 4 x area of triangular face + area of square base
Surface area = 4 x 2.25 cm² + 2.25 cm²
Surface area = 11.25 cm²
Therefore, the surface area of the outer square pyramid is 11.25 square centimeters.
b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. Let's call the side length of the inner square pyramid "x". Since the ratio of the dimensions is 2:3, we know that the side length of the outer square pyramid is (3/2)x.
The volume of a square pyramid can be calculated using the formula:
Volume = (1/3) x base area x height
Since the two pyramids are similar, the ratio of their volumes is the cube of the ratio of their corresponding side lengths:
Volume of inner pyramid / Volume of outer pyramid = (x / (3/2)x)³ = (2/3)³
We also know that the volume of the outer pyramid is:
Volume of outer pyramid = (1/3) x base area x height
The height of the two pyramids is the same, since they are stacked on top of each other, so we can write:
Volume of inner pyramid / Volume of outer pyramid = (1/3) x base area of inner pyramid / (1/3) x base area of outer pyramid
Simplifying this expression, we get:
(x / (3/2)x)³ = (1/3) x² / (1/3) (3/2x)²
Solving for x, we get:
x = (3/2)²
x = 2.25
Therefore, the side length of the inner square pyramid is 2.25 centimeters.
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The complete question is :
a. For the outer square pyramid, the side length of the base is 1.5 centimeters and the height of one of the triangular faces is 3 centimeters. What is the surface area of the outer square pyramid?
b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid?
What is the length of BC in the right triangle below?
Hey there! :)
Answer:
C. BC = 39 units.
Step-by-step explanation:
Use the Pythagorean theorem to solve for BC. Let BC = c, AB = a, and AC = b.
c² = a² + b²
c² = 15² + 36²
Square and simplify:
c² = 225 + 1296
c² = 1521
c = √1521
c = 39 units.
Therefore:
BC = 39 units.
Answer:
C. 39
Step-by-step explanation:
Use Pythagorean Theorem to find the missing length
15² + 36² = C² Simplify
225 + 1296 = C² Add
1521 = C² Take the square root of both sides
39 = C
The value of the test statistic for the test H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9 is
The value of the test statistic for the test is 1.52
How to determine the value of the test statistic for the test?From the question, we have the following parameters that can be used in our computation:
H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9
The above parameters mean that
Sample mean = 3.8Number of samples = 52x = 4.2Standard deviation = 1.9The value of the test statistic for the test is calculated as
\(t = \frac{x - \mu_0}{s/\sqrt n}\)
Substitute the known values in the above equation
\(t = \frac{4.2 - 3.8}{1.9/\sqrt {52}}\)
Evaluate the equation
t = 1.52
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Matt had 6 books to read. Each book has 11 pages. He has already read 60 pages. How many pages does he have left to read? The answer
11 c. What is a limited liability partnership? For what kind of company or owners could this be a good option?
Answer:
Limited Liability partnership allows for a partnership structure where each partner's liabilities are limited to the amount they put into the business.
The kinds of businesses that limited liability partnerships would be a good option for jobs like:
-Law firms
-Accounting firms
-Doctor offices
Step-by-step explanation:
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Identify the graph and describe the solution set of this system of inequalities y<-3x-2 y>-3x+8 A. The solution set is shown by region C.B. There is no solution.C. The solution set is shown by region B.D. The solution set is shown by region A
The inequalities have no solution since their graph does not intersect or overlap.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The inequality given is y<-3x-2 and y>-3x+8, if we plot the graph of the two inequalities, the graph of the inequalities will never meet at any point.
Hence, The inequalities have no solution since their graph does not intersect or overlap.
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Answer:
B. There is no solution.
Step-by-step explanation:
And katie stop deleting my answers
For p=0 and q=0, find the truth values of the conjunction, disjunction, exclusive or, conditional statement, and biconditional of these propositions. b) For p=0 and q=1, find the truth values of the conjunction, disjunction, exclusive or, conditional statement, and biconditional of these propositions.
For the given values of p and q, we have determined the truth values of the conjunction, disjunction, exclusive or, conditional statement, and biconditional
For p=0 and q=0:
- Conjunction (p AND q): 0
- Disjunction (p OR q): 0
- Exclusive or (p XOR q): 0
- Conditional statement (p -> q): 1
- Biconditional (p <-> q): 1
When p=0 and q=0, the conjunction (p AND q) evaluates to 0 because both p and q are false.
The disjunction (p OR q) also evaluates to 0 because neither p nor q is true.
The exclusive or (p XOR q) evaluates to 0 since p and q have the same truth value (both false).
The conditional statement (p -> q) evaluates to 1 because the implication "if p then q" is true when p is false.
The biconditional (p <-> q) evaluates to 1 because both p and q have the same truth value (both false).
For p=0 and q=1:
- Conjunction (p AND q): 0
- Disjunction (p OR q): 1
- Exclusive or (p XOR q): 1
- Conditional statement (p -> q): 1
- Biconditional (p <-> q): 0
Explanation and Calculations:
When p=0 and q=1, the conjunction (p AND q) evaluates to 0 because one of the propositions (p) is false.
The disjunction (p OR q) evaluates to 1 because at least one of the propositions (q) is true.
The exclusive or (p XOR q) evaluates to 1 because the propositions have different truth values (one true, one false).
The conditional statement (p -> q) evaluates to 1 because the implication "if p then q" is true when p is false.
The biconditional (p <-> q) evaluates to 0 because p and q have different truth values.
For the given values of p and q, we have determined the truth values of the conjunction, disjunction, exclusive or, conditional statement, and biconditional. These truth values are based on the definitions of logical operators in classical logic
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Answer the following questions for the function
f(x) = x sqrt(x^2 + 36) defined on the interval - 5 ≤ r ≤ 6. F(x) is concave down on the interval x = to x =
f(x) is concave up on the interval x = to x = The inflection point for this function is at x = The minimum for this function occurs at x = The maximum for this function occurs at x =
f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6.
f(x) is concave up on the interval -6 ≤ x ≤ 0.
To determine where f(x) is concave up or concave down, we need to calculate the second derivative of f(x):
f(x) = x √(\(x^2\) + 36)
f'(x) = √\(x^2\) + 36) + \(x^2\) √(\(x^2\) + 36)
f''(x) = (x (\(x^2\) +72) )/((\(x^2\)+36)\(^(3\)/2))
To find where f(x) is concave up or concave down, we need to find where f''(x) > 0 (concave up) or f''(x) < 0 (concave down).
f''(x) = 0 when x = 0 or x = +/-6.
Thus, f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6, and concave up on the interval -6 ≤ x ≤ 0.
The inflection point for this function is at x = 0.
To find the minimum and maximum for this function, we need to look at the endpoints and critical points of the interval -5 ≤ x ≤ 6.
f(-5) = -5√61 and f(6) = 6√72, so the minimum occurs at x = -5 and the maximum occurs at x = 6.
Therefore:
f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6.
f(x) is concave up on the interval -6 ≤ x ≤ 0.
The inflection point for this function is at x = 0.
The minimum for this function occurs at x = -5.
The maximum for this function occurs at x = 6.
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What is the coefficient in the expression 4n + 1? *
a. 4
b. n
c. 1
Answer:
A. 4
Step-by-step explanation:
B is the variable. C is not apart of the function. I Hope this helps. Im trying to level up so I'd appreiciate it if you marked me as brainliest. Thank you!
Please help me with this geometry question
Answer:
2) 40
Step-by-step explanation:
the perimeter of Rhombus =
4 × (√(12/2)²+(16/2)² )
= 4× (√6²+8²)
= 4× (√100)
= 4×10
= 40
Q) 4 × (√(12/2)²+(16/2)² )
→ 4 × (√6²+8²)
→ 4 × (√100)
→ 4 × 10
→ 40 is the perimeter of rhombus.
how many soulitons?? 4x-6=2(2x-3)
ASAP PLEASE HELP
5 of 10
Solve for
52 - 2 > 6
Give your answer as an improper fraction in its simplest form,
Answer:
True, 52-2 equals 50, 50 is greater than 6.
Step-by-step explanation: