The linear approximation found to estimate ln(0.97) is 9.1%.
What is linear approximation?The definition of a linear approximation of a function is simply utilising a line to approximate the value of the function at a point. We recall the idea of the tangent line as soon as we see a curve (of a function) and a point on it. The value of the function at any point that is very close to the provided point can be roughly determined using the equation of the tangent line if the equation of the tangent line is found at the supplied point.
The given function is f(x) = ln(x).
We start by finding the equation of the tangent line at x=1 to the graph of y=lnx.
f(1)=ln(1)=0
We know the derivative of f(x) will be f'(x)=1/x
f'(1)=1/1=1
Therefore, the equation of the tangent is:y−y1=m(x−x1)
y−0=1(x−1)
y=x−1
An approximation for ln(1.19) would be y=1.19−1=0.19
The actual value, obtained using a calculator, would be 0.174. This means the percent error is (0.19−0.174)/0.174 ×100
= 9.1%
Therefore, the linear approximation found to estimate ln(0.97) is 9.1%.
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In the data set shown below, what is the value of the quartiles?
{1.3, 1.5, 1.7 2.95, 2, 2.5, 2.7, 2.9, 3, 3.1}
A. Q1 = 1.6; Q2 = 2.5; Q3 = 2.92
B. Q1 = 1.7; Q2 = 2.5; Q3 = 3
C. Q1 = 1.7; Q2 = 2.5; Q3 = 2.9
D. Q1 = 1.6; Q2 = 2.5; Q3 = 2.95
Answer:
To find the value of the quartiles, we need to first find the median of the data set. The median is the middle value of the data set, or the value that separates the lower half of the data from the upper half. In this data set, the median is 2.5, as it is the middle value when the data is arranged in ascending order.
Once we have the median, we can find the first and third quartiles. The first quartile, also known as Q1, is the median of the lower half of the data set, and the third quartile, also known as Q3, is the median of the upper half of the data set. In this data set, the lower half of the data is {1.3, 1.5, 1.7, 2, 2.5}, and the upper half of the data is {2.7, 2.9, 3, 3.1}. The median of the lower half is 1.7, and the median of the upper half is 2.9.
Therefore, the value of the quartiles is Q1 = 1.7, Q2 = 2.5, and Q3 = 2.9.
Option C, Q1 = 1.7; Q2 = 2.5; Q3 = 2.9, is the correct answer.
Step-by-step explanation:
Answer:
2.95
Step-by-step explanation:
Please help I’m not sure how to do this
The proof that shows that ΔLMN ≅ ΔQPN by either SSS or SAS is explained below.
How to Prove that Two Triangles are Congruent by SAS or SSS?If we can show that two triangles have two pairs of congruent sides and a pair of corresponding congruent included angles, then we can state they are congruent triangles based on the SAS theorem.
On the other hand, if all three corresponding side lengths are congruent to each other, then the triangles are congruent by the SSS theorem.
The proof that can be used to show that the two triangles are congruent by SAS is shown below:
Statement Reasons
1. ∠L ≅ ∠Q, LM ≅ QP, 1. Given
MN ≅PN, NL ≅ NQ
2. ΔLMN ≅ ΔQPN 2. SSS
Based on the given information we are given, another way of writing this proof can be:
Statement Reasons
1. ∠L ≅ ∠Q, LM ≅ QP, 1. Given
MN ≅PN, NL ≅ NQ
2. ΔLMN ≅ ΔQPN 2. SAS
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Please help I don't understand hurry
Answer:
760
Step-by-step explanation:
You want to know the number of devices without defect if 3% of a day's production of 784 devices are defective.
Number defectiveThe number of defective devices produced in a day is expected to be ...
3% × 784 = 23.52 ≈ 24 . . . . devices
Number without defectThe number without defect will be the remaining number of devices:
784 -24 = 760
About 760 devices are without defect.
Points A(-6,10) and B(2,14) lie on circle O with its center at (2,4) what are the coordinates of point C, which is the midpoint of AB what is the relationship between chord AB and segment OC select the correct answer from drop down menu point C is located at chord Ab is segment OC
The coordinates of point C is (-2, 12)
The segment OC is perpendicular to the chord AB.
What is midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
Points A(-6,10) and B(2,14) lie on circle O with its center at (2,4).
C is the midpoint of the chord AB.
Now,
The coordinates of C = (x, y).
x = (-6 + 2) / 2 = -4/2 = -2
y = (10 + 14) / 2 = 24/2 = 12
(x, y ) = (-2, 12)
The relationship between chord AB and segment OC.
The segment OC is perpendicular to the chord AB.
Thus,
The coordinates of C is (-2, 12)
The relationship between segment OC and chord AB is that segment OC is perpendicular to chord AB.
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ASAP I NEED HELP ON THIS!!!!
FIRST PERSON TO ANSWER ALL THE QUESTIONS GETS BRAINILEST!!!
Answer the questions on the picture!!!
35. To find the number of gallons of gasoline used, we need to divide the number of miles traveled by the number of miles per gallon. In this case, we can let represent the number of gallons of gasoline used. We can then write the following equation to represent the situation:
27 miles/gallon * = 324 miles
To solve for , we need to divide both sides of the equation by 27 miles/gallon to get:
= 324 miles / 27 miles/gallon
This simplifies to:
= 12 gallons
36. To find the number of pounds of apples per hour, we need to divide the total number of pounds picked by the number of hours it took to pick them. In this case, we can divide 15,830 pounds by 8 hours to get:
15,830 pounds / 8 hours = 1,978.75 pounds/hour
Therefore, George Adrian picked about 1,978.75 pounds of apples per hour.
37. The equation m/5 = 50 can be used to describe how much money a quintet has to earn in order for each member to receive $50. In this equation, the variable m represents the total amount of money the quintet earns, and the number 5 represents the number of members in the quintet. The expression m/5 represents the amount of money that each member of the quintet receives, and the number 50 represents the target amount of money each member should receive.
The equation states that if the quintet earns a total of m dollars, then each member will receive m/5 dollars, which should be equal to 50 dollars. Therefore, this equation can be used to find the total amount of money the quintet needs to earn in order for each member to receive $50.
38. To estimate the solution of the equation 12x=-38, we can use the equation x=-38/12. This equation states that the solution of the given equation is equal to the negative of 38 divided by 12.
To estimate the solution, we can divide the negative of 38 by 12 to get:
x = -38/12 = -3.17
Therefore, the estimated solution is about -3.17. Note that this is just an estimate, and the exact solution may be slightly different.
Note: Please study hard in math.
Answer:The answer is 27x=324 miles
Step-by-step explanation:
17/6 divided 5/3 what’s the answer
Answer:
17/6 divided by 5/3 is equal to 17/6 * 3/5, which simplifies to 51/30.
The student made a mistake in solving the equation above. What did the student do wrong?
In solving the equation, the student did the division wrong, and 29.4/4.2 = 7 which is correct.
What is division?Multiplication is the opposite of division.
If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
So, the equation is:
4.2p = 29.4
Let's solve as follows:
4.2p = 29.4
p = 29.4/4.2
p = 7
So, the value of p comes to 7.
Where in the image, the value of p is 123.48 which is wrong as the division is not done properly.
Therefore, in solving the equation, the student did the division wrong, and 29.4/4.2 = 7 which is correct.
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If Triangle ABC has been translated 4 units to the right into Triangle DEF, what are the coordinates of Point E?
Answer:
D(6, -2)
Step-by-step explanation:
You want the coordinates of point E in ∆DEF congruent to ∆ABC after, it has been translated 4 units to the right.
Corresponding pointsThe triangle names tell us that point E is the image of point B after the translation.
TranslationMoving a point to the right 4 units adds 4 to its x-coordinate.
B(2, -2) ⇒ E(2+4, -2) = E(6, -2)
Which graph represents 12 = 3x + 4y line a, line b, line c
Answer:
green line or "b"
Step-by-step explanation:
we can set this up into the slope intercept form
y=mx+b
where m is the slope and b is y intercept
12=3x+4y
-3x -3x
-3x+12=4y
/4. /4. /4
-3/4x+3=y
we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"
hopes this helps please mark rainliest
Please help! I'm running out of time
Answer:
the first one
Step-by-step explanation:
The sum of two numbers is 58. If the larger number is ten less
Answer:
than twice the smaller number, what are the numbers?
Let's call the smaller number x and the larger number y. We know that x + y = 58 and y = 2x - 10. We can substitute the second equation into the first to get x + (2x - 10) = 58. Combining like terms, we get 3x - 10 = 58, which means that x = 24. Plugging this back into the equation y = 2x - 10, we get y = 48. So, the two numbers are 24 and 48.
What is the end behavior of the polynomial function?
Answer:
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree (which comes from the exponent on the leading term) and the leading coefficient (+ or –) of a polynomial function determines the end behavior of the graph.
Step-by-step explanation: hope this helps!
The function approaches negative infinity as x approaches positive infinity and the function approaches negative infinity as x approaches positive infinity. Option C is correct.
What is the end behavior of the functions?The end behavior of a polynomial function describes the behavior of the function as x becomes very large in either the positive or negative direction.
As x approaches negative infinity, the function becomes more and more positive. As x approaches positive infinity, the function becomes more and more negative.
As x → -∞, y → ∞
As x → +∞, y → -∞
In other words, the function approaches negative infinity as x approaches positive infinity and the function approaches negative infinity as x approaches positive infinity.
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Consider the functions f(x) = 223 + 922 + 3x + 12 and g(x) = 323 + 10x2 + × + 8.
The graph of their difference, f(x) - g(x), is shown on the coordinate grid.
What is/are the solution(s) to the equation f(x) - g(x) = 4?
List the solutions from least to greatest separated by a coma(s).
The solutions for the given equation is x=0, x=-4 and x=3.
The given functions are f(x)=2x³+9x²+13x+12 and g(x)=3x³+10x²+x+8.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Now, f(x)-g(x)
= 2x³+9x²+13x+12-(3x³+10x²+x+8)
= 2x³+9x²+13x+12-3x³-10x²-x-8
= -x³-x²+12x+4
Graph the cubic using its end behavior and a few selected points.
Rises to the left and falls to the right
Plot (-2, -16), (-1, -8), (0, 4), (1, 14) and (2, 16)
Given f(x)-g(x)=4
-x³-x²+12x+4=4
⇒ -x³-x²+12x=0
⇒ -x(x²+x-12)=0
⇒ x=0 and x²+x-12=0
⇒ x=0 and x²+4x-3x-12=0
⇒ (x+4)(x-3)=0
⇒ x=0, x=-4 and x=3
Therefore, the solutions for the given equation is x=0, x=-4 and x=3.
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identify the measure of angle x. i need answer asap
After solving the angles, the measure of angle x is 145°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.
The vertex of an angle is the location where two points come together.
The Latin word "angulus," which means "corner," is where the term "angle" originates.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
A geometrical shape called an angle is created by connecting two rays at their termini.
In most cases, an angle is expressed in degrees.
(Refer to the image attached below)
We can see that ∠ABC is a straight angle.
∠ABC = ∠ABD + ∠DBC where ∠ABD is x.
Now, solve for x as follows:
∠ABD + ∠DBC = ∠ABC
x + 35 = 180
x = 180 - 35
x = 145°
Therefore, after solving the angles, the measure of angle x is 145°.
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A self-serve frozen yogurt store made these graphs to study the data collected about its customers' purchases. Which statement is true?
A circle graph is divided into 5 unequal parts. From largest to smallest, the parts are: Chocolate, 38 percent. Strawberry, 30 percent. Vanilla, 22 percent. Other, 10 percent. A line graph is entitled Yogurt Sales in 2011. It shows Month and Units Sold. January, 1000. February, just below 1000. March, between 1000 and 2000. April, just above 3000. May, between 4000 and 5000. June, 5000. July, between 5000 and 6000. August, 6000. September, just below 6000. October, 5000. November, 3000. December, just above 1000. A stem and leaf plot is entitled Ounces Sold Last Friday. It shows two leaves labeled, Leaf (3 to 4 p.m.) and Leaf (7 to 8 p.m.). Leaf (3 to 4 p.m.): Stem, 0; leaf, 6, 6, 8, 8, 8, 9, 9. Stem, 1; leaf, 0, 0, 1, 2, 5. Stem, 2; leaf, 3. Stem, 3; leaf, blank. Leaf (7 to 8 p.m.): Stem, 0; leaf, 7, 8. Stem, 1; leaf, 2, 2, 4, 6, 6, 6, 8. Stem, 2; leaf, 0, 0, 0, 5. Stem, 3; leaf, 2.
The statement that is true about the self-serve frozen yogurt store is;
Option C: The yogurt sales had a decreasing trend in the last four months of 2011
How to Interpret graph data?
From the attached file, we see a pie chart, a graph and a table.
Now, let us access the given options;
a) The percentage that prefer chocolate = 38%
Percentage that prefer vanilla and strawberry combined = 22% + 30% = 52%.
Thus, the given statement is wrong
b) From the graph curve, we see that;
Number of units sold in November = 3000 units
Number of units sold in August = 6000 units
Difference is 3000 units and not 4000 units and so the statement is wrong.
c) We see that for the last four months the curve showed a decreasing slope which means a decreasing trend of units sold.
d) This is not correct because the median number of ounces sold from 3 to 4pm was not more than the median number of ounces sold from 7 to 8pm on the stem leaf plot.
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Create an equivalent expression for ( 1.4³ / 1.2⁴)⁻⁶
1.4³/1.2²
1.2²/1.4³
1.4¹⁶/1.2²⁴
1.2²⁴/1.4¹⁶
The correct answer is: [D]: " [tex]\frac{(1.2)^2^4}{(1.4)^1^8}[/tex] "
Step-by-step explanation:
Given: ( 1.4³ / 1.2⁴)⁻⁶ ;
Note the following properties of exponents:
1) [tex]a^-^b = \frac{1}{a^b}[/tex] ; { [tex]a\neq 0[/tex] } ; and:
2) the 'power of a fraction' rule:
[tex](\frac{a}{b})^c} =\frac{a^c}{b^c}[/tex] ; [tex]b\neq 0[/tex] '
As such:
[tex](\frac{1.4^3}{1.2^4})^{-6}[/tex] ;
= 1 ÷ ( [tex]\frac{1.4^3}{1.2^4})^{6}[/tex] ;
= [tex]\frac{1}{1}[/tex] ÷ ( [tex]\frac{1.4^3}{1.2^4})^{6}[/tex] ;;
= [tex]\frac{1}{1}[/tex] ÷ [tex]\frac{1.4^(^3^*^6^)}{1.2^(^4^*^6^)}[/tex] ;
Note the follow property of exponents:
" [tex](\frac{a}{b})^c = \frac{a^c}{b^c}[/tex] " ; {" b ≠ 0 "}.
⇒ = [tex]\frac{1}{1}[/tex] ÷ [tex]\frac{1.4^(^1^8^)}{1.2^(^2^4^)}[/tex]
Note: Dividing by a fraction or a number; is the same as multiplying by the reciprocal (invert) of that number.
= [tex]\frac{1}{1}[/tex] * [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] ;
= " [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] " ;
which corresponds to:
Answer choice: [D]: " [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] " .
____________
Hope this is helpful! Best of luck!
____________
Pls help me. I’m stuck on this
The value of t for the given triangle angle will be equal to 1.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given the three angles of the triangle are 111,34, and 35t. The value of t will be calculated as,
35t + 111 + 34 = 180
35t = 180 - 111 - 34
35t = 35
t = 1
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A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a short vertical support.
What is the length x of a diagonal support, to the nearest tenth of a foot?
x≈_____ feet
Oh where do I even start?
9(3a+8)
give the right answer please
Answer:
27a + 72
Step-by-step explanation:
Open the brackets
9(3a) + 9(8)
27a +72
Answer:
27a + 72
Step-by-step explanation:
9(3a + 8)
Using the distributive property, we can multiply 9 by everything in parentheses, which now gives us: 27a + 72
We cannot simplify this further, as we have an unknown value in the variable a, thus we cannot apply 72 to 27a, or inverse.
Meaning that, the answer is 27a + 72
prove that every subgroup of order $p^{n-1}$ with g order p n is a normal subgroup math.stackexchange
For every prime power pn that divides the order of a finite group G, the Sylow theorems ensure the existence of a subgroup of G of order pn.
What is subgroup?
Sn1 is transitive because normal subgroups of primitive groups are, and as a result, pn1! A transitive group of degree p's centralizer now has order. Given that p is a prime number and n is a positive integer, let G be a finite group of order pn. Assume that H is an index-containing subgroup of G. Note that you can prove it for any boolean interval of rank 4 if you also know the normal subgroups of G. A homomorphism is produced by the left multiplication that G naturally performs on G/H.
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please have the right answers nothing wrong
The total distance walked in each case is given below;
15 feet4.5 feet6.75 feet1.5 feet1.5x feetWhat is the total distance?Jada's pet turtle walked 10 feet, and then half that length again
Total distance = 10 + (1/2 of 10)
= 10 + (1/2 × 10)
= 10 + 5
= 15 feet
Jada's pet baby brother walked 3 feet, and then half that length again
Total distance = 3 + (1/2 of 3)
= 3 + (1/2 × 3)
= 3 + 1.5
= 4.5 feet
Jada's pet hamster walked 4.5 feet, and then half that length again
Total distance = 4.5 + (1/2 × 4.5)
= 4.5 + 2.25
= 6.75 feet
Jada's pet robot walked 1 foot, and then half that length again
Total distance = 1 foot + (1/2 × 1)
= 1 + 0.5
= 1.5 feet
A person walked x feet, and then half that length again
Total distance = x + (1/2 × x)
= x + 1/2x
= 1.5x feet
In conclusion, the total distance is calculated by adding the initial distance and additional distance
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Which of the following sentences includes a non-restrictive clause?
O Alan discovered that chickens are able to recognize the faces and voices they see and hear often.
O Giana, who collects anything relating chickens, found the perfect life-sized chicken hat to add to her collection.
O Roosters have an internal clock that causes them to crow at daybreak.
O The chicken gained quite the social media following after being featured in a video wearing a tutu while dancing
The sentence that includes a non-restrictive clause is given as follows:
Giana, who collects anything relating chickens, found the perfect life-sized chicken hat to add to her collection.
What are restrictive and non-restrictive clauses?Restrictive and non-restrictive clauses are defined as follows:
Restrictive clauses: Provides necessary information about a sentence.Non-restrictive clauses: Provides non-necessary information about a sentence.The sentence with the non-restrictive clause in this problem is given as follows:
Giana, who collects anything relating chickens, found the perfect life-sized chicken hat to add to her collection.
However, the following sentence could be understood just as easily:
Giana found the perfect life-sized chicken hat to add to her collection.
Meaning that the "who collects anything relating chickens" noum is unnecessary, and thus the second option is correct.
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In the equation 2x = 36 - 8, what is the next step in the equation solving sequence?
Answer:
The next step is to combine constants
Step-by-step explanation:
The cost of 2 kg of carrots is £7 Work out the cost of 5 kg of carrots.
Answer:
56
Step-by-step explanation:
Dana has two pieces of string. One is 1/7 foot long, and the other is 3/4 foot long. Write 1/7 and 3/4 using a common denominator.
1/7 and 3/4 can be written using a common denominator as [tex]\frac{4 + 21}{28}[/tex] or [tex]\frac{4}{28}[/tex] foot and [tex]\frac{21}{28}[/tex] foot.
The term Common denominator is used when the denominator of a number of fractions is a common multiple given fraction.
To calculate the common denominator: Find the LCM of the fractions given.Divide the LCM of the fractions by the denominator given.Multiply the answer by the numerator.Repeat the above step for all the given fractions.To calculate the common denominator of 1/7 :Step 1
find the LCM of 7 and 4 = 28
Steps 2 and 3
Divide the LCM of the fractions = 28, by the denominator given 7 and 4 and Multiply the answer by the numerator.
For 1/7
(28/7) * 1
=4* 1
=4
Thus For 1/7, we have :
4/28
To calculate the common denominator of 1/7 and 3/4 :Step 1
find the LCM of 7 and 4 = 28
Step 2 and 3
Divide the LCM of the fractions = 28, by the denominator given 7 and 4 and Multiply the answer by the numerator.
For 1/7
(28/7) * 1
=4* 1
=4
Thus For 1/7, we have :
= 4/28
To calculate the common denominator of 3/4 :Step 1
find the LCM of 7 and 4 = 28
Steps 2 and 3
Divide the LCM of the fractions = 28, by the denominator given 4 and 3 and Multiply the answer by the numerator.
For 3/4
(28/4) * 3
= 7* 3
=21
Thus For 3/4 , we have :
21/28
Hence,1/7 and 3/4 can be written using a common denominator as [tex]\frac{4 + 21}{28}[/tex] or [tex]\frac{4}{28}[/tex] and [tex]\frac{21}{28}[/tex].
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What is 30/31 as a percentage?
Answer:
Around 96.77%
Step-by-step explanation: Take 100 divided by 31 and then multiply the product of that by 30.
The following equation can be used to model the distance remaining on route to a destination while traveling at a constant rate of speed
d = 125 - 35t
How many miles will be left to drive after 3 hours?
The distance left after 3 hour's drive is 20 miles.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
We have.
d = 125 - 35t
d is the distance left after traveling t hours.
Now,
t = 3.
d = 125 - 35 x 3
d = 125 - 105
d = 20
Thus,
The number of miles left after 3 hour drive is 20 miles.
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HELP PLEASE!!!!!!!! APPLY THE DISTRIBUTIVE PROPERTY USING THE GCF TO WRITE EQUIVALENT EXPRESSION. 0.3x - 2.7 HELP PLEASE!!!!!
Answer:
To apply the distributive property using the greatest common factor (GCF) to write an equivalent expression for 0.3x - 2.7, we need to find the GCF of the coefficients of the terms in the expression. In this case, the GCF is 0.3, so we can write the expression as 0.3(x - 9). This is an equivalent expression to 0.3x - 2.7, because multiplying 0.3 by the difference of x and 9 produces the same result as subtracting 2.7 from 0.3x.
Step-by-step explanation:
A club swimming pool is 34 ft wide and 48 ft long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 344 ft2. How wide can the strip be?
Answer:
29
he area of the pool is 34 ft * 48 ft = <<34*48=1632>>1632 ft2.
Thus, the total area of the pool and the border strip is 1632 ft2 + 344 ft2 = <<1632+344=1976>>1976 ft2.
Hence, the border strip is 1976 ft2/34 ft = <<1976/34=58>>58 ft long.
Therefore, the border strip can be 58 ft/2 = <<58/2=29>>29 ft wide. Answer: {29}.