Answer: 35.0%
Step-by-step explanation:
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A new fence is constructed on three sides of a housing block with area 240 m2. the fourth side facing the road is left open. if 52 m of fencing is used, what are the dimensions of the block?
To find the housing block dimensions, we set up a system of equations based on the total fencing and area given, and then solve for the length and width.
Explanation:The student has asked about finding the dimensions of a housing block where a new fence is constructed on three sides and the total area of the block is 240 m2. Given that 52 m of fencing is used, to determine the dimensions, we need to solve a system of equations derived from the perimeter and area provided.
Let's assume the length of the block is L meters, and the width is W meters. The area of the block (A) can thus be defined as A = L × W. Given that A = 240 m2, we have L × W = 240. Since the fence covers three sides, the total length of fencing used would be L + 2W, which is equal to 52 meters. Therefore, we have L + 2W = 52 meters.
To solve for L and W, we set up the system of equations:
L × W = 240L + 2W = 52From the second equation, we can express L as L = 52 - 2W and then substitute into the first equation to find W. Finally, we can determine the value for L using the found value of W.
Let 40 x 55 = n. Which of the choices shown is also equal to n?
A) (550 x 40)
B) (4 x 50) + (40 x 5)
C) (50 x 40) + (50 x 40)
D) (10 x 55) + (10 x 55) + (10 x 55) + (10 x 55)
Please Help!!!
Let x2−12x=61 . What values make an equivalent number sentence after completing the square?
The given equation is [tex] x^2-12x=61 [/tex]. Add 36 to both the sides of the equation, then
[tex] x^2-12x+36=61+36 [/tex].
The equation becomes,
[tex] x^2-12x+6^2=97\\
(x-6)^2=97 [/tex]
WILL MAKE BRAINLIEST!!!!!!!The arc length of a sector is equal to twice the radius. Express the arc length s as a function of the area a of the sector.
s=
The arc length as a function of the area of the sector is l=2√A.
What is the area of a sector?Area of a sector = 1/2 * arc length(l) * radius(r)
[tex]A=[/tex] [tex]\frac{1}{2} l*r[/tex]......(1)
It is given that the arc length of a sector is equal to twice the radius.
This means [tex]l=2r\\[/tex]
So, [tex]r=\frac{l}{2}[/tex]
Putting the value of r in (1)
[tex]A = \frac{l^{2} }{4}[/tex]
[tex]l^{2} =4A[/tex]
[tex]l=2\sqrt{A} \\[/tex]
So, the required function is l=2√A
Hence, the arc length as a function of the area of the sector is l=2√A.
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Simplify 72x6 y7 z .
True or False? A triangle with two congruent angles can never be scalene. A. True B. False
Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+20x-12=0
Answer:
D= 1,2,or 6
Step-by-step explanation:
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Consider the function f(x)=(x-9)/(x^3-81x)
Find the vertical asymptote(s) of f(x)
Answer:
Its A
x=0, -9
Step-by-step explanation:
just got it correct
The function f(x)=(x-9)/(x^3-81x) has three vertical asymptotes at x = 0, x = 9, and x = -9.
Explanation:To find the vertical asymptote(s) of the function f(x) = (x-9)/(x^3-81x), we need to determine the values of x for which the denominator equals zero. Setting the denominator equal to zero and solving for x, we get:
x^3 - 81x = 0x(x^2 - 81) = 0x(x - 9)(x + 9) = 0Therefore, the function has three vertical asymptotes at x = 0, x = 9, and x = -9.
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Complete the equation of the line through (-6,5) and (-3,-3) Use exact numbers. y=
The equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are given below.
(-6,5) and (-3,-3)
Then the equation of the line passing through the points (-6,5) and (-3,-3) will be
[tex]\rm (y + 3) = \left (\dfrac{-3-5}{-3+6} \right ) (x + 3)[/tex]
Simplify the equation, then the equation of the line will be
y + 3 = -(8/3)(x + 3)
y = -(8/3)x - 8 - 3
y = -(8/3)x - 11
Then the equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.
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Selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red pens
What are the trigonometric ratios of a right triangle ABC that has its right angle at C? AC=12 and BC=5
A class has 24 boys and 16 girls. on a test the class mean was 75. the mean of the girls' score was 72. what was the mean of the boys' scores?
The mean of the boys' scores was 77.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.
We have been given that the class has 24 boys and 16 girls.
And the class mean was 75
The total number of students in the class was:
24 + 16 = 40
Total scored by 40 students = 40 × 75 = 3000
Number of girls = 16 and their mean = 72
Total scored by girls = 16 × 72 = 1152
The difference between the scores will give the total score of boys:
⇒ 3000 - 1152 = 1848
Number of boys = 24
Their mean will be 1848 / 24
So the mean of the boys' scores = 77
Therefore, the mean of the boys' scores was 77.
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The depth of a lake, d, varies directly with r, the amount of rainfall last month. if k is the constant of variation, write an equation to represent the situation.
Please help asap, 70 points, THREE questions (:
Answer:
the answer for number 1 is 1.82
Step-by-step explanation:
In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b
The [tex]a^5b^3[/tex], [tex]ab^8[/tex], [tex]b^8[/tex], [tex]a^4b^4[/tex], [tex]a^8[/tex], and [tex]ab^7[/tex] are the possible variable terms and this can be determined by using the arithmetic operations.
Given :
Expression --- [tex]\rm (3a + 4b)^8[/tex]
The following calculation can be used in order to determine the possible variables from the given expression.
The given expression can be written as:
[tex]\rm (3a + 4b)^8=(3a+4b)^2(3a+4b)^2(3a+4b)^2(3a+4b)^2[/tex]
[tex]\rm (3a + 4b)^8=(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)[/tex]
Now, further simplify the above expression.
[tex]\rm (3a + 4b)^8=(81a^4+144a^2b^2+108a^3b+144a^2b^2+256b^4+192a^3b+108a^3b+192ab^3+144a^2b^2)(81a^4+144a^2b^2+108a^3b+144a^2b^2+256b^4+192a^3b+108a^3b+192ab^3+144a^2b^2)[/tex]
So, from the above calculation, it can be concluded that [tex]a^5b^3[/tex], [tex]ab^8[/tex], [tex]b^8[/tex], [tex]a^4b^4[/tex], [tex]a^8[/tex], and [tex]ab^7[/tex] are the possible variable terms.
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How to find two numbers that sum equal 15 and product are maximized?
A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428?
To find the percentage of observations between two values in a normal distribution, we can convert the values to z-scores and use a z-table to find the corresponding areas. In this case, the percentage of observations between 0.372 and 0.428 is 68.26%.
Explanation:To find the percentage of observations that will lie between 0.372 and 0.428 in a normal distribution with a mean of 0.40 and standard deviation of 0.028, we need to find the area under the curve between these two values.
Using a standard normal distribution table or z-table, we can convert the values to z-scores by subtracting the mean and dividing by the standard deviation. The z-score for 0.372 is (0.372 - 0.40) / 0.028 = -1, and the z-score for 0.428 is (0.428 - 0.40) / 0.028 = 1.
By looking up the corresponding area for these z-scores in the z-table, we find that the area to the left of -1 is 0.1587 and the area to the left of 1 is 0.8413. To find the percentage between -1 and 1, we subtract the smaller area from the larger area: 0.8413 - 0.1587 = 0.6826 or 68.26%.
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A city has a population of 260,000 people. Suppose that each year the population grows by 6.75% . What will the population be after 7 years? Use the calculator provided and round your answer to the nearest whole number.
The population of the city after 7 years will be approximately 393,574.
Explanation:To find the population after 7 years, we'll use the formula for exponential growth:
P = P0(1 + r)t
Where P is the future population, P0 is the initial population, r is the growth rate as a decimal, and t is the number of years.
In this case, P0 = 260,000, r = 6.75% = 0.0675 (decimal form), and t = 7.
Plugging in these values, we have:
P = 260,000(1 + 0.0675)7
Using a calculator, the population after 7 years is approximately 393,574.
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Frazier has $1,200 in savings. He works because he is saving money for college, and he earns $9 an hour. If Frazier saves 25 percent of his net pay, after 20 percent is taken out for tax, identify the expression which represents Frazier's savings.
A) 1.8x + 1,200
B) 3.6x + 1,200
C) 7.2x + 1,200
D) 9x + 1,200
the correct answer is A..!! I think...:(
Answer: The correct option is (A) [tex]1.8x+1200.[/tex]
Step-by-step explanation: Given that Frazier is saving money for college and has $1200 in savings. He earns $9 per hour. He saves 25% of his net pay after 20% taken out for tax.
We are to identify the expression that represents Frazier's savings.
Let, x represents the number of hours for which Frazier works.
So, the net pay of Frazier = $ 9x.
Since 20% of the net pay is taken out for tax, so total pay of Frazier after taking out tax is given by
[tex]I_t=9x-20\%\times 9x=9x-\dfrac{20}{100}\times 9x=9x-\dfrac{9x}{5}=\dfrac{36x}{5}.[/tex]
Now, Frazier's savings from his net pay is given by
[tex]I_s=25\%\times \dfrac{36x}{5}=\dfrac{25}{100}\times \dfrac{36x}{5}=\dfrac{9x}{5}=1.8x.[/tex]
Since Frazier has $1200 already in savings, so the equation representing Frazier's savings will be
[tex]1.8x+1200.[/tex]
Thus, the required equation is [tex]1.8x+1200.[/tex]
Option (A) is CORRECT.
Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept form)
The equation of the line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3) is y = (-1/2)x + 4.
What is the general equation of straight line? What is a mathematical function, equation and expression?straight line : The general equation of a straight line is -[y] = mx + c
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is to find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3).
The given equation is -
y - 12 = 2x - 8
y = 2x - 8 + 12
y = 2x + 4
Assume the equation of the line to be -
y = mx + c
Now -
m = -1/2 {m (1) x m (2) = - 1 → for perpendicular lines}
So, the equation can be written as -
3 = - 1/2 x 2 + c
c = 3 + 1
c = 4
Therefore, the equation of the line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3) is y = (-1/2)x + 4.
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If each person takes up 2.5 square feet of space, how many people can fit in an elevator that is 8 feet by 6 feet? Round to the nearest person.
2.5
19
38
48
Choose as many answers as apply.
An employee can legitimately claim the following as exemptions:
A. family pet
B. self
C. dependents
D. neighbor's cousin Al
Answer:
An employee can legitimately claim the following as exemptions:
B. Self
C. Dependents
Step-by-step explanation:
We know that an employee can claim the health and medical insurance ( which is also known as Medicare and Social security deductions) for himself or for himself, his/ her spouse and his family members or dependents.
Hence,
An employee can legitimately claim the following as exemptions:
B. Self
C. dependents.
Hence, option B and C are the correct options.
Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80 degrees. Approximately how tall is the tree? Enter the value rounded to the nearest tenth. Do not include the units of measure.
A bag contains 6 red, 7 blue, and 5 green coins. If 3 coins are randomly selected in succession, what is the probability of selecting a red coin, then a blue coin, and then a green coin, if replacement occurs each time?
If you answer 110 questions and get a 94% how many did you get wrong
EASY 14 POINTS, PLEASE HELP ASAP.
Go into a dark room with a flashlight and face the beam toward a wall. Change the flashlight's distance from the wall as well as the way you hold the flashlight. Which conic sections can you form? Explain.
Describe how you formed different conic sections with your flashlight. Take and upload digital pictures as needed. Look at other students' descriptions and pictures and tell whether you agree with them.
What other simple tasks can you do in your home to form any of the conic sections? Again, describe these and/or take pictures to share with other students.
Well really it would have to depend on the flashlight. Is it an led bulb or a regular bulb?
if it takes 18 gallons of gas to go 400 miles how many gallons would it take to go 300 miles
A. 5.5 gallons
B. 13.5 gallons
C. 16.6 gallons
D. 22.2 gallons
E. 24 gallons
We will use the ratio and proportion method ( an equation formed with two ratios that are equal) to solve the question “if it takes 18 gallons of gas to go 400 miles, how many gallons would it take to go 300 miles?”
Let x= the number of gallons for the gas to go 300 miles
18:400=X:300
400x=300*18
400x=5400
X=5400/400
X=13.5 so the answer is B.
Answer:
B
Step-by-step explanation:
its 13.5 gallons
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